Basic

📁 Source: Mathlib/CategoryTheory/Category/Basic.lean

Statistics

Metric	Count
Definitions toCategoryStruct, CategoryStruct, comp, id, toQuiver, LargeCategory, SmallCategory, aesop_cat?, aesop_cat_nonterminal, cat_disch, categoryTheoryDischarger, evalSorryIfSorry, rfl_cat, sorryIfSorry, uliftCategory, «term_=≫_», «term_≫=_», «term_≫_», «term𝟙», category_theory_universes	20
Theorems assoc, assoc', comp_id, id_comp, left_cancellation, right_cancellation, cancel_epi, cancel_epi_assoc_iff, cancel_epi_id, cancel_mono, cancel_mono_assoc_iff, cancel_mono_id, comp_dite, comp_ite, dite_comp, epi_comp, epi_comp', epi_iff_forall_injective, epi_of_epi, epi_of_epi_fac, eq_of_comp_left_eq, eq_of_comp_left_eq', eq_of_comp_right_eq, eq_of_comp_right_eq', eq_whisker, id_of_comp_left_id, id_of_comp_right_id, instEpiId, instEpiOfIsThin, instMonoId, instMonoOfIsThin, ite_comp, mono_comp, mono_comp', mono_iff_forall_injective, mono_of_mono, mono_of_mono_fac, whisker_eq	38
Total	58

CategoryTheory

Definitions

Name	Category	Theorems
CategoryStruct 📖	CompData	—
LargeCategory 📖	CompOp	—
SmallCategory 📖	CompOp	—
aesop_cat? 📖	CompOp	—
aesop_cat_nonterminal 📖	CompOp	—
cat_disch 📖	CompOp	—
categoryTheoryDischarger 📖	CompOp	—
evalSorryIfSorry 📖	CompOp	—
rfl_cat 📖	CompOp	—
sorryIfSorry 📖	CompOp	—
uliftCategory 📖	CompOp	14 math math: ULift.upFunctor_obj_down, instIsCofilteredULift, ULift.equivalence_unitIso_inv, ULift.equivalence_counitIso_hom_app, ULift.downFunctor_map, ULift.equivalence_unitIso_hom, instIsConnectedULiftHomULift, ULift.equivalence_functor, instIsFilteredULift, ULift.equivalence_counitIso_inv_app, ULift.downFunctor_obj, ULift.upFunctor_map, ULift.equivalence_inverse, countableCategoryUlift
«term_=≫_» 📖	CompOp	—
«term_≫=_» 📖	CompOp	—
«term_≫_» 📖	CompOp	—
«term𝟙» 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
cancel_epi 📖	mathematical	—	CategoryStruct.comp Category.toCategoryStruct	—	Epi.left_cancellation
cancel_epi_assoc_iff 📖	mathematical	—	CategoryStruct.comp Category.toCategoryStruct	—	cancel_epi Category.assoc
cancel_epi_id 📖	mathematical	—	CategoryStruct.comp Category.toCategoryStruct CategoryStruct.id	—	Category.comp_id cancel_epi
cancel_mono 📖	mathematical	—	CategoryStruct.comp Category.toCategoryStruct	—	Mono.right_cancellation
cancel_mono_assoc_iff 📖	mathematical	—	CategoryStruct.comp Category.toCategoryStruct	—	cancel_mono Category.assoc'
cancel_mono_id 📖	mathematical	—	CategoryStruct.comp Category.toCategoryStruct CategoryStruct.id	—	Category.id_comp cancel_mono
comp_dite 📖	mathematical	—	CategoryStruct.comp Category.toCategoryStruct Quiver.Hom CategoryStruct.toQuiver	—	—
comp_ite 📖	mathematical	—	CategoryStruct.comp Category.toCategoryStruct Quiver.Hom CategoryStruct.toQuiver	—	—
dite_comp 📖	mathematical	—	CategoryStruct.comp Category.toCategoryStruct Quiver.Hom CategoryStruct.toQuiver	—	—
epi_comp 📖	mathematical	—	Epi CategoryStruct.comp Category.toCategoryStruct	—	cancel_epi cancel_epi_assoc_iff
epi_comp' 📖	mathematical	—	Epi CategoryStruct.comp Category.toCategoryStruct	—	epi_comp
epi_iff_forall_injective 📖	mathematical	—	Epi Quiver.Hom CategoryStruct.toQuiver Category.toCategoryStruct CategoryStruct.comp	—	cancel_epi
epi_of_epi 📖	mathematical	—	Epi	—	cancel_epi Category.assoc
epi_of_epi_fac 📖	mathematical	CategoryStruct.comp Category.toCategoryStruct	Epi	—	epi_of_epi
eq_of_comp_left_eq 📖	—	CategoryStruct.comp Category.toCategoryStruct	—	—	Category.comp_id
eq_of_comp_left_eq' 📖	—	CategoryStruct.comp Category.toCategoryStruct	—	—	eq_of_comp_left_eq
eq_of_comp_right_eq 📖	—	CategoryStruct.comp Category.toCategoryStruct	—	—	Category.id_comp
eq_of_comp_right_eq' 📖	—	CategoryStruct.comp Category.toCategoryStruct	—	—	eq_of_comp_right_eq
eq_whisker 📖	mathematical	—	CategoryStruct.comp Category.toCategoryStruct	—	—
id_of_comp_left_id 📖	mathematical	CategoryStruct.comp Category.toCategoryStruct	CategoryStruct.id	—	Category.comp_id
id_of_comp_right_id 📖	mathematical	CategoryStruct.comp Category.toCategoryStruct	CategoryStruct.id	—	Category.id_comp
instEpiId 📖	mathematical	—	Epi CategoryStruct.id Category.toCategoryStruct	—	Category.id_comp
instEpiOfIsThin 📖	mathematical	Quiver.IsThin CategoryStruct.toQuiver Category.toCategoryStruct	Epi	—	—
instMonoId 📖	mathematical	—	Mono CategoryStruct.id Category.toCategoryStruct	—	Category.comp_id
instMonoOfIsThin 📖	mathematical	Quiver.IsThin CategoryStruct.toQuiver Category.toCategoryStruct	Mono	—	—
ite_comp 📖	mathematical	—	CategoryStruct.comp Category.toCategoryStruct Quiver.Hom CategoryStruct.toQuiver	—	—
mono_comp 📖	mathematical	—	Mono CategoryStruct.comp Category.toCategoryStruct	—	cancel_mono cancel_mono_assoc_iff
mono_comp' 📖	mathematical	—	Mono CategoryStruct.comp Category.toCategoryStruct	—	mono_comp
mono_iff_forall_injective 📖	mathematical	—	Mono Quiver.Hom CategoryStruct.toQuiver Category.toCategoryStruct CategoryStruct.comp	—	cancel_mono
mono_of_mono 📖	mathematical	—	Mono	—	cancel_mono Category.assoc'
mono_of_mono_fac 📖	mathematical	CategoryStruct.comp Category.toCategoryStruct	Mono	—	mono_of_mono
whisker_eq 📖	mathematical	—	CategoryStruct.comp Category.toCategoryStruct	—	—

CategoryTheory.Category

Definitions

Name	Category	Theorems
toCategoryStruct 📖	CompOp	16291 math math: CategoryTheory.Equivalence.adjointify_η_ε_assoc, CategoryTheory.biconeCategoryStruct_comp, TopologicalSpace.OpenNhds.coe_id, CategoryTheory.Limits.MonoFactorisation.fac, CategoryTheory.Functor.inr_biprodComparison', CategoryTheory.Limits.Trident.condition_assoc, CategoryTheory.Limits.limMap_π, CategoryTheory.Localization.Monoidal.leftUnitor_hom_app, CategoryTheory.SmallObject.functorMap_id, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₃, CategoryTheory.Iso.inv_hom_id_triangle_hom₃_assoc, HomotopicalAlgebra.fibration_op_iff, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_right, CategoryTheory.shiftFunctorZero_inv_app_obj_of_induced, CategoryTheory.Limits.Cones.postcomposeId_hom_app_hom, CategoryTheory.Comon.tensorObj_comul', CategoryTheory.Limits.Bicone.category_id_hom, CategoryTheory.Triangulated.SpectralObject.Hom.comm, CategoryTheory.Bicategory.iterated_mateEquiv_conjugateEquiv, CategoryTheory.LocalizerMorphism.LeftResolution.opFunctor_map_f, AlgebraicGeometry.Scheme.Hom.resLE_map_assoc, CategoryTheory.ShortComplex.opcyclesMap_smul, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d, SemimoduleCat.MonoidalCategory.triangle, CategoryTheory.Functor.relativelyRepresentable.pullback₃.snd_fst'_eq_p₁, CategoryTheory.Limits.kernelSubobjectMap_arrow_assoc, CategoryTheory.Limits.IsImage.e_isoExt_inv, CategoryTheory.Grp.Hom.hom_div, CategoryTheory.Over.associator_hom_left_snd_fst_assoc, AlgebraicGeometry.Γ_map_morphismRestrict, CategoryTheory.Adjunction.adjToComonadIso_inv_toNatTrans_app, SimplexCategoryGenRel.σ_comp_σ, CategoryTheory.MorphismProperty.LeftFraction.map_compatibility, CategoryTheory.Limits.pushoutIsoOpPullback_inr_hom_assoc, CategoryTheory.Limits.Fork.IsLimit.homIso_natural, CategoryTheory.CommSq.LiftStruct.op_l, CategoryTheory.Limits.Cocones.precompose_obj_ι, CategoryTheory.GrothendieckTopology.overMapPullbackId_hom_app_val_app, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyπ_comp_leftHomologyIso_hom, CategoryTheory.Grp.comp', CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_eq, SemiNormedGrp₁.comp_apply, CategoryTheory.CostructuredArrow.homMk'_id, CategoryTheory.InjectiveResolution.Hom.hom'_f, CategoryTheory.Pseudofunctor.mapComp'_naturality_1_assoc, CategoryTheory.Functor.whiskeringRightObjIdIso_hom_app_app, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π, AlgebraicGeometry.AffineSpace.map_Spec_map, AlgebraicGeometry.Scheme.Modules.pushforward_obj_presheaf_map, Action.forget_η, CategoryTheory.Join.pseudofunctorLeft_mapId_inv_toNatTrans_app, CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv_assoc, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₁, CategoryTheory.ShortComplex.toCycles_comp_homologyπ, Rep.resCoindHomEquiv_symm_apply_hom, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_fst, SimplicialObject.Splitting.cofan_inj_πSummand_eq_id_assoc, HomologicalComplex.pOpcycles_restrictionOpcyclesIso_hom_assoc, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_assoc, CategoryTheory.Functor.functorHomEquiv_apply_app, CategoryTheory.MonoidalCategory.tensor_left_unitality, CategoryTheory.Limits.Cocone.category_id_hom, CategoryTheory.Pseudofunctor.DescentData.isEquivalence_toDescentData_of_sieve_le, CategoryTheory.SimplicialObject.id_left_app, CategoryTheory.Bicategory.prod_whiskerLeft_snd, Rep.resCoindHomEquiv_apply_hom, CategoryTheory.Functor.eventualRange_eq_range_precomp, CategoryTheory.Limits.hasPullbackVertPaste, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_hom_right, CategoryTheory.sum.inrCompInverseAssociator_hom_app, CategoryTheory.Functor.FullyFaithful.homNatIsoMaxRight_inv_app, CategoryTheory.Over.prodLeftIsoPullback_hom_snd_assoc, SSet.Subcomplex.lift_ι, CommRingCat.HomTopology.isEmbedding_precomp_of_surjective, CategoryTheory.Functor.map_homCongr, CategoryTheory.Functor.CommShift.isoAdd_hom_app, CategoryTheory.ShortComplex.rightHomologyMap_id, PresheafOfModules.instIsRightAdjointPushforwardCompFunctorOppositeRingCatWhiskerLeftOp, CategoryTheory.Adjunction.compUliftCoyonedaIso_hom_app_app_down, SimplexCategory.δ_comp_δ', smoothSheafCommRing.ι_forgetStalk_inv, CategoryTheory.ShortComplex.toCycles_comp_homologyπ_assoc, AlgebraicTopology.DoldKan.PInfty_comp_PInftyToNormalizedMooreComplex, HomologicalComplex.eqToHom_f, CategoryTheory.SingleFunctors.postcompPostcompIso_hom_hom_app, CategoryTheory.ObjectProperty.isoModSerre_isInvertedBy_iff, ModuleCat.hom_zero, CommBialgCat.ofSelfIso_inv, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.hπ_assoc, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_map, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_hom_app_zero, CategoryTheory.GrpObj.lift_inv_comp_left, CategoryTheory.uliftCoyonedaEquiv_apply, CategoryTheory.Limits.eq_zero_of_mono_cokernel, CategoryTheory.MonoidalCategory.associator_naturality_middle_assoc, groupHomology.π_comp_H2Iso_hom_assoc, CategoryTheory.Limits.DiagramOfCones.id, CategoryTheory.PreOneHypercover.forkOfIsColimit_ι_map_inj_assoc, CategoryTheory.Limits.zero_of_from_zero, CategoryTheory.TwoSquare.equivNatTrans_symm_apply, AddCommGrpCat.image.lift_fac, CategoryTheory.BraidedCategory.braiding_naturality_right, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_hom_left, CategoryTheory.ShortComplex.Homotopy.h₀_f_assoc, CategoryTheory.Sum.natTransOfWhiskerLeftInlInr_app, SheafOfModules.pushforward_assoc, CategoryTheory.biproduct_ι_comp_leftDistributor_hom_assoc, CategoryTheory.Subobject.map_mk, CommRingCat.HomTopology.isClosedEmbedding_precomp_of_surjective, CategoryTheory.Presieve.ofArrows_eq_ofArrows_uncurry, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_inv_fac_app, AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality_assoc, CochainComplex.mappingConeCompTriangleh_comm₁_assoc, CategoryTheory.Limits.cokernelBiproductιIso_hom, Rep.invariantsAdjunction_homEquiv_symm_apply_hom, HomologicalComplex₂.totalAux.ιMapObj_D₁, CategoryTheory.Mat_.additiveObjIsoBiproduct_hom_π, CategoryTheory.Functor.PushoutObjObj.inr_ι, CategoryTheory.Groupoid.reverse_eq_inv, CategoryTheory.Functor.isoSum_inv_app_inl, CategoryTheory.Limits.Cone.toUnder_pt, CategoryTheory.Mon.id_hom, CategoryTheory.ShortComplex.LeftHomologyData.op_g', AddMagmaCat.coe_id, CategoryTheory.Types.instIsCorepresentableForgetTypeHom, AlgebraicGeometry.Proj.awayMap_awayToSection_assoc, HomologicalComplex.extendSingleIso_inv_f, CategoryTheory.Grothendieck.base_eqToHom, LightCondensed.free_internallyProjective_iff_tensor_condition, CategoryTheory.Equivalence.leftOp_unitIso_hom_app, CategoryTheory.Over.μ_pullback_left_snd', CategoryTheory.Monad.ForgetCreatesColimits.commuting, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_hom_app_val_app, CategoryTheory.WithTerminal.coneEquiv_unitIso_hom_app_hom_left, CategoryTheory.Functor.mapTriangleIdIso_inv_app_hom₃, CategoryTheory.Monad.monadMonEquiv_unitIso_inv_app_toNatTrans_app, CategoryTheory.Iso.prod_inv, CategoryTheory.Limits.limitConeOfUnique_cone_π, CategoryTheory.StrictPseudofunctorPreCore.map_id, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, CategoryTheory.ComposableArrows.opEquivalence_counitIso_inv_app_app, CategoryTheory.mateEquiv_counit_symm, HomologicalComplex.restrictionToTruncGE'_f_eq_iso_hom_pOpcycles_iso_inv, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom, BoolAlg.coe_id, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst_assoc, CategoryTheory.GrpObj.inv_hom, CategoryTheory.MonoidalCategory.DayConvolution.braidingHomCorepresenting_app, TopModuleCat.hom_zero, AlgebraicGeometry.Scheme.Hom.toPartialMap_hom, AlgebraicGeometry.descendsAlong_isOpenImmersion_surjective_inf_flat_inf_quasicompact', CategoryTheory.Bicategory.RightExtension.w_assoc, SemimoduleCat.Hom.hom₂_apply, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_apply, CategoryTheory.Functor.coreComp_hom_app_iso_inv, CategoryTheory.kernelCokernelCompSequence.snakeInput_v₀₁_τ₂, AlgebraicTopology.DoldKan.P_f_0_eq, CategoryTheory.Functor.natTransEquiv_apply_app, CategoryTheory.Functor.mapComposableArrowsObjMk₂Iso_inv_app, CategoryTheory.uliftCoyonedaIsoCoyoneda_hom_app_app, CategoryTheory.Pseudofunctor.DescentData.subtypeCompatibleHomEquiv_toCompatible_presheafHomObjHomEquiv, SimplexCategory.mkOfSucc_eq_id, CategoryTheory.LaxFunctor.mapComp'_whiskerRight_comp_mapComp', HomotopicalAlgebra.LeftHomotopyRel.postcomp, CategoryTheory.Limits.imageSubobject_arrow_assoc, CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc, CategoryTheory.coyonedaEquiv_symm_app_apply, CategoryTheory.Subobject.factorThru_right, CommAlgCat.comp_apply, CategoryTheory.Presheaf.instIsLocallySurjectiveHomWhiskerRightOppositeForget, CategoryTheory.Oplax.StrongTrans.Modification.vcomp_app, CategoryTheory.Sieve.pullback_apply, CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_right, HomologicalComplex.singleMapHomologicalComplex_hom_app_ne, CategoryTheory.StructuredArrow.map_map_right, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_adj, CategoryTheory.ModObj.one_smul_assoc, CategoryTheory.NatTrans.hcomp_id_app, CategoryTheory.ObjectProperty.isoModSerre_zero_iff, CategoryTheory.tensorLeftHomEquiv_symm_coevaluation_comp_whiskerLeft, CategoryTheory.Functor.OplaxMonoidal.δ_comp_tensorHom_η, CategoryTheory.eHom_whisker_cancel, CategoryTheory.Pi.eqToEquivalenceFunctorIso_hom, TopCat.PrelocalPredicate.res, CategoryTheory.PreGaloisCategory.mulAction_def, CategoryTheory.Pseudofunctor.map₂_associator_assoc, CategoryTheory.shiftFunctorAdd'_assoc_inv_app, CategoryTheory.instEffectiveEpiFamilyCompOfIsSplitEpi, CategoryTheory.Functor.partialRightAdjointHomEquiv_comp_symm, CategoryTheory.Limits.Multiequalizer.condition_assoc, CategoryTheory.IsPullback.of_id_fst, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst_assoc, CategoryTheory.IsHomLift.eqToHom_domain_lift_id, homotopyEquivalences_le_quasiIso, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionRight_unop, CategoryTheory.ShortComplex.SnakeInput.w₀₂_assoc, CategoryTheory.Sheaf.ΓHomEquiv_naturality_left_symm, TopologicalSpace.Opens.id_apply, CategoryTheory.preadditiveCoyonedaObj_map, FundamentalGroupoid.eqToHom_eq, CategoryTheory.Functor.LaxMonoidal.associativity_assoc, CategoryTheory.CosimplicialObject.δ_comp_δ_self_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.unit_actionHomRight_assoc, CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_p, CategoryTheory.BraidedCategory.yang_baxter', Rep.coe_linearization_obj_ρ, CategoryTheory.kernelUnopOp_inv, CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair_hom_app, CategoryTheory.Functor.OplaxMonoidal.associativity, AlgebraicTopology.DoldKan.Compatibility.equivalence₀_unitIso_hom_app, CategoryTheory.ObjectProperty.InheritedFromTarget.instMin, CategoryTheory.CommSq.fac_right_assoc, CategoryTheory.Idempotents.app_idem_assoc, CategoryTheory.PreZeroHypercover.inv_hom_h₀, CategoryTheory.Functor.homObjEquiv_apply_app, CategoryTheory.Limits.imageSubobjectCompIso_hom_arrow, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_three_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_left, ModuleCat.biproductIsoPi_inv_comp_π, CategoryTheory.ShortComplex.HomologyData.canonical_iso_hom, CategoryTheory.Limits.Bicone.π_of_isColimit, AlgebraicTopology.DoldKan.PInfty_f_add_QInfty_f, CategoryTheory.CatEnrichedOrdinary.id_hComp_heq, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app', CategoryTheory.Limits.inr_of_isLimit, CategoryTheory.sum_whiskerRight, CategoryTheory.SingleFunctors.Hom.comm, CategoryTheory.LaxFunctor.map₂_associator_assoc, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app, CategoryTheory.Localization.isLocalization_op, CategoryTheory.Functor.OfSequence.congr_f, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map, CategoryTheory.ShortComplex.homologyι_naturality, CategoryTheory.Limits.image.isIso_precomp_iso, CategoryTheory.GrothendieckTopology.toPlus_plusLift_assoc, CategoryTheory.CartesianMonoidalCategory.prodComparison_snd, CategoryTheory.Limits.coprod.inl_snd, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.ShortComplex.Homotopy.refl_h₀, CategoryTheory.CartesianMonoidalCategory.tensorδ_snd, CategoryTheory.Equivalence.sheafCongr.counitIso_hom_app_val_app, groupHomology.mapCycles₂_comp_assoc, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv_assoc, SimplexCategoryGenRel.standardσ_nil, CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux_fac, CategoryTheory.Functor.liftOfIsRightKanExtension_fac, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_appTop, LightProfinite.proj_comp_transitionMap, CategoryTheory.Limits.hasPushout_assoc, AlgebraicGeometry.Spec.map_eq_id, HomologicalComplex.dFrom_comp_xNextIsoSelf, AlgebraicGeometry.AffineSpace.map_toSpecMvPoly_assoc, CategoryTheory.Endofunctor.Coalgebra.id_f, CategoryTheory.Subobject.underlyingIso_hom_comp_eq_mk_assoc, SimplexCategory.Truncated.δ₂_two_comp_σ₂_one_assoc, CategoryTheory.Limits.biproduct.mapBiproduct_inv_map_desc, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp_inv_app_f, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo, TopologicalSpace.Opens.map_id_obj_unop, CategoryTheory.Preadditive.IsIso.comp_left_eq_zero, CochainComplex.HomComplex.Cochain.fromSingleMk_neg, CategoryTheory.Presieve.uncurry_bind, CategoryTheory.Localization.Monoidal.whiskerLeft_comp, CategoryTheory.LaxFunctor.whiskerLeft_mapComp'_comp_mapComp'_assoc, CategoryTheory.ShortComplex.homologyMap_smul, CategoryTheory.ObjectProperty.instIsClosedUnderLimitsOfShapeUnopOppositeOfIsClosedUnderColimitsOfShape, CategoryTheory.opHom_apply, CategoryTheory.MonoidalCategory.hom_inv_whiskerRight', CategoryTheory.NatTrans.prod'_app_snd, CategoryTheory.Join.inlCompFromSum_hom_app, LightProfinite.Extend.functorOp_obj, CategoryTheory.DifferentialObject.shiftFunctor_obj_d, CategoryTheory.ShortComplex.hasHomology_of_zeros, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_hom_inv_assoc, CategoryTheory.StructuredArrow.map_comp, CochainComplex.mappingCone.δ_inl, CategoryTheory.Limits.colimitHomIsoLimitYoneda_hom_comp_π, AlgebraicGeometry.Scheme.Modules.pushforwardId_inv_app_app, CochainComplex.mappingCone.inl_v_descCochain_v_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_naturality_assoc, HomotopicalAlgebra.PrepathObject.p_fst_assoc, TopCat.pullbackIsoProdSubtype_hom_fst, CategoryTheory.Limits.kernelIsoOfEq_trans, CategoryTheory.ShortComplex.SnakeInput.naturality_φ₁, CategoryTheory.IsPullback.isoIsPullback_inv_snd_assoc, AlgebraicGeometry.AffineSpace.map_reindex, CategoryTheory.Limits.CatCospanTransform.associator_hom_right_app, CategoryTheory.SmallObject.SuccStruct.prop.arrowIso_hom_left, CategoryTheory.Arrow.equivSigma_symm_apply_left, CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj_map_f, CategoryTheory.IsHomLift.comp_lift_id_right', CategoryTheory.Preadditive.hasKernel_of_hasEqualizer, CommRingCat.HomTopology.mvPolynomialHomeomorph_apply_snd, AlgebraicGeometry.IsAffineOpen.map_fromSpec_assoc, CategoryTheory.Retract.refl_r, CategoryTheory.NonPreadditiveAbelian.neg_sub', CategoryTheory.additive_yonedaObj, AlgebraicGeometry.IsAffineOpen.isLocalization_of_eq_basicOpen, CategoryTheory.conjugateEquiv_iso, CategoryTheory.ObjectProperty.le_limitsClosure, CategoryTheory.DinatTrans.dinaturality_assoc, CategoryTheory.Cat.Hom₂.comp_app, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_fst_assoc, AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_fst, CategoryTheory.Functor.rightKanExtensionUniqueOfIso_hom, CategoryTheory.ihom.coev_naturality, CategoryTheory.obj_ε_app_assoc, HomologicalComplex.rightUnitor'_inv, CategoryTheory.Monad.id_η_app, CategoryTheory.ShortComplex.fromOpcycles_naturality, AlgebraicGeometry.LocallyRingedSpace.residueFieldMap_comp, CategoryTheory.SimplicialObject.δ_comp_δ_self_assoc, CategoryTheory.ShortComplex.Homotopy.comm₁, HomologicalComplex.π_homologyIsoSc'_hom, CategoryTheory.MonoidalCategory.tensorμ_natural_assoc, CategoryTheory.Functor.mapHomologicalComplexIdIso_hom_app_f, CategoryTheory.ShortComplex.HomologyData.ofIso_right_p, CategoryTheory.Bicategory.Comonad.comul_assoc_flip, HomotopyCategory.quotient_map_out_comp_out, CategoryTheory.regularTopology.EqualizerCondition.bijective_mapToEqualizer_pullback', CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_hom_inv', CategoryTheory.ShortComplex.Homotopy.comp_h₃, CategoryTheory.Limits.limitUnopIsoUnopColimit_hom_comp_ι, CategoryTheory.ObjectProperty.instSmallUnopOfOpposite_1, CategoryTheory.ObjectProperty.colimitsOfShape_op, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_associator, AlgebraicGeometry.Scheme.Hom.germ_stalkMap_assoc, AlgebraicGeometry.IsProper.instCompScheme, groupCohomology.toCocycles_comp_isoCocycles₁_hom, CategoryTheory.Join.mapPairId_hom_app, CategoryTheory.Sheaf.instIsLocallySurjectiveHomToImage, TopCat.presheafToType_map, HomologicalComplex.mapBifunctor.ι_D₂, CategoryTheory.Functor.OplaxMonoidal.δ_natural_left_assoc, CategoryTheory.Functor.leftOpRightOpEquiv_functor_obj_map, TopCat.Sheaf.interUnionPullbackCone_snd, CategoryTheory.Limits.Types.Small.productIso_hom_comp_eval, CategoryTheory.linearCoyoneda_map_app, HomologicalComplex.homologyπ_extendHomologyIso_hom, AlgebraicGeometry.Scheme.Cover.gluedCoverT'_snd_snd_assoc, CategoryTheory.linearCoyoneda_obj_obj_carrier, CategoryTheory.MonoidalCategory.tensorμ_tensorδ_assoc, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_hom_hom, LightCondensed.isoFinYonedaComponents_hom_apply, CategoryTheory.ShortComplex.Splitting.op_r, SimplexCategoryGenRel.multiplicativeClosure_isGenerator_eq_top, CategoryTheory.Limits.biprod.lift_eq, CategoryTheory.ShortComplex.RightHomologyData.ι_g', CategoryTheory.ShortComplex.SnakeInput.op_δ, CategoryTheory.Limits.isLimitConeRightOpOfCocone_lift, CategoryTheory.ObjectProperty.isClosedUnderColimitsOfShape_iff_op, CategoryTheory.OplaxFunctor.id_mapComp, CategoryTheory.Limits.ConeMorphism.hom_inv_id, HomologicalComplex.mapBifunctor₁₂.ι_D₃_assoc, AlgebraicGeometry.Scheme.Spec_map_stalkMap_fromSpecStalk, DerivedCategory.right_fac, CategoryTheory.Limits.map_ι_comp_inv_sigmaComparison_assoc, CategoryTheory.Functor.rightDerivedNatTrans_id, Rep.MonoidalClosed.linearHomEquiv_symm_hom, CategoryTheory.Quiv.comp_eq_comp, AlgebraicGeometry.descendsAlong_universallyClosed_surjective_inf_flat_inf_quasicompact, CategoryTheory.Limits.wideCoequalizer.condition, CategoryTheory.BraidedCategory.braiding_tensor_right_hom, CategoryTheory.ShortComplex.SnakeInput.comp_f₃_assoc, CategoryTheory.Functor.LaxMonoidal.whiskerLeft_μ_comp_μ_assoc, SimplexCategory.eq_id_of_isIso, CategoryTheory.ShortComplex.cyclesOpIso_inv_op_iCycles_assoc, Action.leftRegularTensorIso_inv_hom, CategoryTheory.MorphismProperty.instHasOfPrecompPropertyOppositeOpOfHasOfPostcompProperty, CategoryTheory.CosimplicialObject.comp_app, CategoryTheory.composePath_comp', CategoryTheory.EnrichedOrdinaryCategory.homEquiv_comp, CategoryTheory.Comma.mapLeftEq_inv_app_right, CategoryTheory.Limits.PreservesPushout.inr_iso_inv_assoc, CategoryTheory.Functor.ι_colimitIsoOfIsLeftKanExtension_inv_assoc, CategoryTheory.Functor.shiftIso_add_inv_app, CategoryTheory.Comma.mapLeftIso_inverse_map_right, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_snd, CategoryTheory.Subobject.imageFactorisation_F_m, CategoryTheory.MonoidalCategory.DayConvolution.unit_naturality, AlgebraicGeometry.PresheafedSpace.stalkMap_germ, CategoryTheory.Iso.eHomCongr_inv_comp_assoc, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceInverseπ_hom_app, CategoryTheory.Square.category_id_τ₃, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_hom_app_eq, CategoryTheory.shiftFunctorComm_zero_hom_app, CategoryTheory.op_hom_leftUnitor, CategoryTheory.IsPullback.isoIsPullback_inv_snd, CategoryTheory.Grothendieck.ιCompMap_hom_app_fiber, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app, CategoryTheory.ShortComplex.cokernel_π_comp_cokernelToAbelianCoimage_assoc, CategoryTheory.NatTrans.rightDerived_comp_assoc, CategoryTheory.ShortComplex.pOpcycles_π_isoOpcyclesOfIsColimit_inv_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_assoc, CategoryTheory.Join.mapWhiskerLeft_app, HomologicalComplex₂.totalFlipIso_hom_f_D₁, AddCommGrpCat.comp_apply, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_map_left, CategoryTheory.Equivalence.comp_asNatTrans, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_naturality_assoc, CategoryTheory.MonoidalCategory.rightUnitor_monoidal_assoc, HomologicalComplex.singleMapHomologicalComplex_hom_app_self, HomologicalComplex.double_d_eq_zero₀, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_hom_app, CategoryTheory.Subobject.underlyingIso_arrow_assoc, CategoryTheory.Functor.mapConeMapCone_hom_hom, Action.neg_hom, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_two, CategoryTheory.Limits.coconeEquivalenceOpConeOp_unitIso, CategoryTheory.Limits.coprod.inl_fst, CategoryTheory.GradedObject.ι_mapBifunctorMapMap, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_hom_app_app_down, HomologicalComplex.πTruncGE_naturality_assoc, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.ShortComplex.homologyOpIso_hom_naturality, CategoryTheory.Abelian.PreservesCoimage.iso_hom_π_assoc, CategoryTheory.ComposableArrows.IsComplex.zero'_assoc, AddGrpCat.id_apply, CategoryTheory.Preadditive.commGrpEquivalence_functor_obj_grp_one, AlgebraicGeometry.Scheme.PartialMap.ext_iff, CategoryTheory.Functor.LeftExtension.precomp₂_obj_hom_app, PresheafOfModules.pullback_id_comp, HomologicalComplex.singleObjHomologySelfIso_hom_singleObjOpcyclesSelfIso_hom_assoc, AddMagmaCat.ofHom_comp, CategoryTheory.CostructuredArrow.map_comp, SSet.PtSimplex.RelStruct.δ_map_of_lt, CategoryTheory.isSeparating_unop_iff, SSet.Subcomplex.toRange_ι, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_inv_app_val_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.lift_fac, Bimod.TensorBimod.π_tensor_id_actRight, CategoryTheory.Limits.Cotrident.ofCocone_ι, CategoryTheory.Abelian.LeftResolution.karoubi.F_obj_p, TopCat.GlueData.preimage_image_eq_image, CategoryTheory.Linear.instMonoHSMulHomOfInvertible, CategoryTheory.ShortComplex.leftHomologyMap_comp, HomologicalComplex.mapBifunctor₁₂.d_eq, CategoryTheory.Limits.CatCospanTransform.whisker_exchange, CategoryTheory.NatTrans.unop_whiskerLeft, CategoryTheory.Localization.Preadditive.homEquiv_symm_apply, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_hom_inv, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_e, CategoryTheory.Functor.HomObj.comp_app, CategoryTheory.SmallObject.SuccStruct.prop.arrowIso_inv_left, CategoryTheory.e_comp_id, CategoryTheory.Limits.colimit.isoColimitCocone_ι_inv, CategoryTheory.Comma.opFunctor_obj, CategoryTheory.Functor.CommShift.isoAdd_inv_app, AlgebraicGeometry.Scheme.Hom.app_invApp'_assoc, Bimod.AssociatorBimod.hom_left_act_hom', CategoryTheory.MonoidalCategory.tensor_inv_hom_id_assoc, CategoryTheory.Classifier.SubobjectRepresentableBy.pullback_homEquiv_symm_obj_Ω₀, CategoryTheory.ReflQuiv.adj_homEquiv, CategoryTheory.ShortComplex.LeftHomologyMapData.unop_φQ, HomologicalComplex.singleObjCyclesSelfIso_hom_singleObjOpcyclesSelfIso_hom_assoc, AlgebraicGeometry.pointOfClosedPoint_comp_assoc, CategoryTheory.Join.pseudofunctorRight_mapComp_inv_toNatTrans_app, groupHomology.mapShortComplexH2_id, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_whiskerRight, CategoryTheory.CommMon.comp_hom, AlgebraicTopology.DoldKan.σ_comp_PInfty_assoc, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_id, CategoryTheory.StrictlyUnitaryLaxFunctor.id_map₂, CategoryTheory.IsPushout.id_horiz, CategoryTheory.Functor.opUnopIso_hom_app, Bimod.RightUnitorBimod.hom_right_act_hom', SimplicialObject.Splitting.IndexSet.epiComp_fst, CategoryTheory.FreeMonoidalCategory.mk_id, Action.inv_hom_hom_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app_assoc, CategoryTheory.MonoidalOpposite.tensorLeftMopIso_hom_app_unmop, CategoryTheory.SimplicialObject.δ_comp_δ''_assoc, CategoryTheory.NatTrans.rightDerivedToHomotopyCategory_id, HomologicalComplex.XIsoOfEq_hom_comp_XIsoOfEq_hom, HomologicalComplex.dFrom_eq_zero, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_comp_assoc, CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv'_assoc, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_fst, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv, CategoryTheory.Limits.Trident.app_zero, CategoryTheory.CosimplicialObject.δ_comp_δ_self', SimplexCategory.const_eq_id, AlgebraicGeometry.Scheme.Hom.quasiFiniteLocus_comp, CategoryTheory.ShortComplex.SnakeInput.naturality_δ, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_snd_snd_assoc, CategoryTheory.Pseudofunctor.map₂_associator_app_assoc, CategoryTheory.Functor.OplaxMonoidal.δ_comp_η_tensorHom_assoc, LightCondensed.ihomPoints_apply, CategoryTheory.MorphismProperty.isomorphisms_le_of_containsIdentities, CategoryTheory.MorphismProperty.comp_eq_top_iff, AlgebraicGeometry.Scheme.Pullback.Triplet.tensorCongr_trans_hom, CategoryTheory.MorphismProperty.isStableUnderLimitsOfShape_iff_limitsOfShape_le, TopCat.Presheaf.isSheaf_iff_isSheafUniqueGluing_types, AlgebraicGeometry.Scheme.app_eq, CochainComplex.mappingCone.inr_f_d_assoc, CategoryTheory.Limits.IsColimit.fac, CategoryTheory.shrinkYonedaEquiv_comp, CategoryTheory.Enriched.FunctorCategory.enriched_id_comp, Bimod.RightUnitorBimod.inv_hom_id, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_id_base, CategoryTheory.Subobject.ofLE_arrow, CategoryTheory.LocalizerMorphism.LeftResolution.id_f, CategoryTheory.ShortComplex.LeftHomologyData.unop_p, AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom_ι_assoc, LinearMap.id_fgModuleCat_comp, CategoryTheory.NatTrans.naturality_2, CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_snd_assoc, HomotopicalAlgebra.PrepathObject.p_snd, CategoryTheory.GrothendieckTopology.toSheafify_naturality_assoc, Bimod.LeftUnitorBimod.hom_right_act_hom', CategoryTheory.Square.category_comp_τ₂, CategoryTheory.Subfunctor.Subpresheaf.range_eq_ofSection', HomotopicalAlgebra.instWeakEquivalenceOppositeOp, CategoryTheory.ShortComplex.homologyMap_add, CategoryTheory.RegularMono.w_assoc, CategoryTheory.SmallObject.SuccStruct.extendToSucc_map_le_succ, ModuleCat.restrictScalarsId'App_inv_naturality_assoc, CategoryTheory.Grp.Hom.hom_hom_zpow, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberDesc, HomologicalComplex.opcyclesMap_comp, CategoryTheory.Functor.relativelyRepresentable.pullback₃.map_p₃_comp, CategoryTheory.MorphismProperty.RespectsIso.postcomp, CategoryTheory.Groupoid.invEquivalence_inverse_map, AlgebraicTopology.NormalizedMooreComplex.obj_d, CategoryTheory.Limits.biprod.braid_natural, CategoryTheory.CategoryOfElements.fromStructuredArrow_map, assoc, CategoryTheory.ObjectProperty.preservesLimitsOfShape_eq_iSup, ProfiniteGrp.ofHom_comp, CategoryTheory.BicartesianSq.of_is_biproduct₁, CategoryTheory.SimplicialObject.δ_comp_σ_of_gt, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_hom, CategoryTheory.ShortComplex.homology_π_ι_assoc, CategoryTheory.Limits.map_id_right_eq_curry_swap_map, Preord.ofHom_id, AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_inv_app, CategoryTheory.ShortComplex.SnakeInput.Hom.comm₂₃, CategoryTheory.ObjectProperty.essentiallySmall_unop_iff, CategoryTheory.Limits.coprod.symmetry, CategoryTheory.HasShift.Induced.add_inv_app_obj, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapId_hom_iso, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_ι_presheafHom, TopCat.isOpenEmbedding_iff_comp_isIso, CategoryTheory.Limits.pullback_inv_snd_fst_of_left_isIso, SimplexCategoryGenRel.δ_comp_δ_nat, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_inv_app_hom, CategoryTheory.Adjunction.Localization.ε_app, CategoryTheory.Mon_Class.mul_comp, CategoryTheory.FintypeCat.instPreservesFiniteLimitsActionFintypeCatForgetHomSubtypeHomCarrierV, CategoryTheory.Pseudofunctor.isEquivalence_toDescentData, CategoryTheory.FunctorToTypes.coprod.desc_inr, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_isLimit_lift, CategoryTheory.biproduct_ι_comp_rightDistributor_inv, CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_inv_comp_iCycles_assoc, HomologicalComplex.pOpcycles_opcyclesToCycles_iCycles_assoc, CategoryTheory.GrothendieckTopology.Cover.index_fst, CategoryTheory.sum_tensor, HomologicalComplex.truncLEMap_comp_assoc, CategoryTheory.Bicategory.conjugateEquiv_whiskerRight, AlgebraicGeometry.Proj.basicOpenIsoSpec_inv_ι_assoc, CategoryTheory.Oplax.OplaxTrans.Modification.whiskerRight_naturality, CategoryTheory.Adjunction.rightAdjointUniq_trans, CategoryTheory.Functor.LaxMonoidal.μ_natural_right, CategoryTheory.Functor.mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app_assoc, HomotopicalAlgebra.CofibrantObject.homRel_equivalence_of_isFibrant_tgt, CategoryTheory.Iso.comp_inv_eq, CategoryTheory.PullbackShift.adjunction_counit, CategoryTheory.CategoryOfElements.map_snd, CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom'_assoc, CategoryTheory.Functor.LaxMonoidal.right_unitality, CategoryTheory.Equivalence.unitIso_hom_app_comp_inverse_map_η_functor_assoc, CategoryTheory.SmallCategoryOfSet.id_def, CochainComplex.HomComplex.Cochain.δ_single, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_app_hom_assoc, CategoryTheory.Adjunction.unit_app_tensor_comp_map_δ_assoc, CategoryTheory.Functor.Monoidal.whiskerLeft_η_ε, Action.sum_hom, CategoryTheory.NonPreadditiveAbelian.diag_σ, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_left_app, CategoryTheory.Limits.colimit.eqToHom_comp_ι_assoc, CategoryTheory.MorphismProperty.IsLocalAtTarget.toRespects, CategoryTheory.Limits.hasPushout_of_right_factors_epi, CategoryTheory.Functor.Monoidal.whiskerLeft_app_fst_assoc, CategoryTheory.iterated_mateEquiv_conjugateEquiv, CategoryTheory.Bicategory.leftUnitor_inv_naturality_assoc, CategoryTheory.Limits.monoFactorisationZero_I, CategoryTheory.ExactPairing.evaluation_coevaluation, HomologicalComplex.pOpcycles_opcyclesIsoSc'_hom, CategoryTheory.GradedObject.mapTrifunctorMapFunctorObj_obj_map, CategoryTheory.Limits.Cone.ofTrident_π, CategoryTheory.Mon_Class.comp_mul, CategoryTheory.Functor.mapCommGrpCompIso_inv_app_hom_hom_hom, CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse, CategoryTheory.Limits.terminal.subsingleton_to, CategoryTheory.Sum.functorEquivFunctorCompFstIso_inv_app_app, CategoryTheory.IsPullback.isoPullback_inv_fst, CategoryTheory.ExactPairing.coevaluation_evaluation', CategoryTheory.ShortComplex.leftHomologyMap'_sub, CategoryTheory.Limits.biprod.inl_snd_assoc, AlgebraicGeometry.StructureSheaf.comap_id, AddMonCat.comp_apply, SimplicialObject.Splitting.IndexSet.id_fst, CategoryTheory.OverPresheafAux.unitAux_hom, CochainComplex.mappingConeCompTriangle_obj₂, CategoryTheory.Limits.BinaryBicone.inl_fst, CategoryTheory.Limits.fiberwiseColimit_map, CategoryTheory.MorphismProperty.LeftFractionRel.unop, CategoryTheory.CosimplicialObject.id_right_app, CategoryTheory.cocones_map_app_app, groupCohomology.π_comp_H0IsoOfIsTrivial_hom_assoc, CategoryTheory.MorphismProperty.FunctorialFactorizationData.i_mapZ_assoc, CategoryTheory.Over.iteratedSliceBackward_map, CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom, CategoryTheory.Lax.StrongTrans.vComp_naturality_hom, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_unitIso, CategoryTheory.Sieve.functor_obj, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_map_left_left, PresheafOfModules.add_app, AugmentedSimplexCategory.inr_comp_associator, CategoryTheory.IsPushout.of_is_bilimit', BddLat.hom_comp, CategoryTheory.Retract.refl_i, HomologicalComplex.pOpcycles_singleObjOpcyclesSelfIso_inv, CategoryTheory.ShortComplex.Homotopy.sub_h₀, FGModuleCat.hom_hom_id, CategoryTheory.monoidalOfHasFiniteCoproducts.whiskerLeft, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_app_snd_app, AlgebraicGeometry.Scheme.Hom.toNormalization_inl_normalizationCoprodIso_hom_assoc, CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp_inv_hom₁, CategoryTheory.MorphismProperty.hasOfPostcompProperty_iff_le_diagonal, CategoryTheory.InjectiveResolution.homotopyEquiv_inv_ι, CategoryTheory.Subfunctor.Subpresheaf.range_eq_ofSection, CategoryTheory.Limits.pullbackProdSndIsoProd_hom_snd, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_whiskerRight, quasiIsoAt_iff_comp_right, CategoryTheory.Bicategory.whiskerLeft_inv_hom, CategoryTheory.StrictlyUnitaryLaxFunctor.mapIdIso_hom, CategoryTheory.Over.associator_inv_left_snd, CategoryTheory.MorphismProperty.universally_inf, SSet.ι₀_snd_assoc, CategoryTheory.MorphismProperty.LeftFraction.ofInv_f, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_π_app, CategoryTheory.Limits.coprod.associator_naturality, CategoryTheory.GradedObject.ι_mapBifunctorMapObjDesc, SSet.Truncated.HomotopyCategory.descOfTruncation_comp, AlgebraicGeometry.Scheme.Hom.toNormalization_normalizationPullback_fst, CategoryTheory.NatIso.cancel_natIso_hom_right, AlgebraicGeometry.instLocallyQuasiFiniteCompSchemeιQuasiFiniteLocus, TopCat.Presheaf.coveringOfPresieve.iSup_eq_of_mem_grothendieck, CategoryTheory.Functor.sheafPushforwardContinuousComp'_inv_app_val_app, CategoryTheory.Limits.equalizerComparison_comp_π, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_leftUnitor, CategoryTheory.MonoidalCategory.whisker_exchange, CategoryTheory.SmallObject.ρFunctorObj_π_assoc, TopCat.Presheaf.germ_eq_of_isBasis, CategoryTheory.Functor.rightOp_map, SSet.Subcomplex.mem_ofSimplex_obj_iff, HasFibers.inducedMap_comp, CategoryTheory.MonoidalCategory.inv_hom_id_tensor_assoc, AlgebraicTopology.DoldKan.N₁_map_f, CategoryTheory.ShortComplex.homologyMap_zero, CategoryTheory.MorphismProperty.IsStableUnderCobaseChange.op, CategoryTheory.Bicategory.Prod.sectL_mapId_inv, CondensedMod.IsSolid.isIso_solidification_map, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app, CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_hom_inv_id, groupCohomology.cocyclesMap_id_comp_assoc, AlgebraicGeometry.IsAffineOpen.map_fromSpec, CategoryTheory.ExponentiableMorphism.homEquiv_symm_apply_eq, CategoryTheory.SimplicialThickening.SimplicialCategory.comp_id, CategoryTheory.Grp_Class.comp_inv, CategoryTheory.Pretriangulated.TriangleMorphism.comp_hom₂, CategoryTheory.Functor.leftDerivedNatTrans_fac_assoc, CategoryTheory.Functor.mapCommMon_obj_mon_mul, CategoryTheory.Limits.pullbackDiagonalMapIso.hom_fst, groupHomology.map₁_one, CategoryTheory.CartesianMonoidalCategory.associator_inv_fst_fst, CochainComplex.HomComplex.Cocycle.equivHom_symm_apply, CategoryTheory.eqToHom_comp_homOfLE_op, CategoryTheory.Functor.coe_mapLinearMap, CategoryTheory.whiskerLeft_coprod_inr_leftDistrib_inv, HomologicalComplex.homologyπ_restrictionHomologyIso_inv_assoc, CategoryTheory.CosimplicialObject.δ_comp_δ''_assoc, AlgebraicGeometry.Spec_Γ_naturality, Frm.coe_comp, CategoryTheory.isSeparator_coprod, AddCommGrpCat.hom_add, CategoryTheory.FunctorToTypes.functorHomEquiv_symm_apply_app_app, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_map, TopCat.Presheaf.Pushforward.id_inv_app, CategoryTheory.PreservesImage.factorThruImage_comp_hom, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₃, groupCohomology.d₀₁_comp_d₁₂, CategoryTheory.MorphismProperty.LeftFraction.op_map, CategoryTheory.iterated_mateEquiv_conjugateEquiv_symm, CategoryTheory.Limits.CatCospanTransform.comp_whiskerLeft_assoc, CategoryTheory.Limits.spanCompIso_inv_app_zero, CategoryTheory.Functor.map_mul, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_app_assoc, CategoryTheory.ObjectProperty.HasCardinalLT.sup, prevD_comp_left, CategoryTheory.Mon.forget_μ, CategoryTheory.WithInitial.opEquiv_unitIso_inv_app, CategoryTheory.Limits.bicone_ι_π_self_assoc, CategoryTheory.Limits.pushoutIsoOpPullback_inl_hom, CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsMin, CategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy.hg', CategoryTheory.Limits.CatCospanTransform.rightUnitor_inv_left_app, ModuleCat.freeHomEquiv_apply, CategoryTheory.Limits.Cocone.toOver_ι_app, CochainComplex.mappingCone.id, CategoryTheory.Idempotents.neg_def, CategoryTheory.Equivalence.counitIso_inv_app_comp_functor_map_η_inverse, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_fst_snd_assoc, CategoryTheory.Bicategory.whiskerRight_comp_assoc, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeftLift_snd, CategoryTheory.ShortComplex.π₁Toπ₂_comp_π₂Toπ₃_assoc, AlgebraicGeometry.Scheme.Opens.toSpecΓ_naturality, CategoryTheory.Limits.colimit.ι_pre_assoc, TopCat.Presheaf.germ_stalkPullbackHom, CategoryTheory.Under.postComp_inv_app_right, CategoryTheory.Bicategory.Prod.snd_map, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_assoc, Rep.coindResAdjunction_counit_app, CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_homEquiv_symm, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top, CategoryTheory.HalfBraiding.naturality_assoc, CategoryTheory.BraidedCategory.braiding_tensor_right_hom_assoc, CategoryTheory.Adjunction.map_ε_comp_counit_app_unit_assoc, AddCommGrpCat.ofHom_comp, AlgebraicGeometry.Scheme.Pullback.openCoverOfLeftRight_f, CategoryTheory.CosimplicialObject.δ_comp_δ_assoc, HomologicalComplex.opcyclesIsoSc'_inv_fromOpcycles, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom, SSet.modelCategoryQuillen.I_le_monomorphisms, AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_comp_assoc, AlgebraicGeometry.Scheme.comp_toLRSHom_assoc, HomologicalComplex.singleObjOpcyclesSelfIso_hom, AlgebraicGeometry.Scheme.restrictFunctorΓ_inv_app, CategoryTheory.ShortComplex.RightHomologyMapData.neg_φH, CategoryTheory.op_inv_associator, CategoryTheory.Limits.Multiequalizer.condition, CategoryTheory.Limits.ConeMorphism.inv_hom_id_assoc, HomologicalComplex.singleObjCyclesSelfIso_inv_iCycles, CategoryTheory.SimplicialObject.σ_naturality_assoc, CategoryTheory.Abelian.Pseudoelement.pseudoZero_def, CategoryTheory.Limits.walkingParallelPairOp_left, CategoryTheory.Bicategory.LeftExtension.w_assoc, TopCat.coe_of_of, CategoryTheory.Functor.isoSum_inv_app_inr, CategoryTheory.ShortComplex.LeftHomologyMapData.id_φK, CategoryTheory.Limits.WidePushout.arrow_ι, TopCat.Presheaf.stalkSpecializes_stalkPushforward, CategoryTheory.Functor.IsEventuallyConstantTo.coneπApp_eq, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_naturality, CategoryTheory.shrinkYonedaEquiv_symm_map_assoc, CategoryTheory.ModObj.mul_smul_assoc, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_counit_app_app, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_specStalkEquiv, CategoryTheory.Functor.OplaxMonoidal.left_unitality, AlgebraicGeometry.Scheme.Hom.inr_toNormalization_normalizationCoprodIso_inv, CategoryTheory.ShortComplex.op_g, CategoryTheory.MonoidalCategory.MonoidalRightAction.id_actionHom, CategoryTheory.Limits.MultispanIndex.inj_sndSigmaMapOfIsColimit, CategoryTheory.Limits.biprod.hom_ext'_iff, CategoryTheory.Limits.ι_comp_colimitOpIsoOpLimit_hom_assoc, CategoryTheory.Over.inv_left_hom_left_assoc, CategoryTheory.epi_iff_isPushout, CategoryTheory.Dial.leftUnitor_naturality, CategoryTheory.instHasFunctorialSurjectiveInjectiveFactorizationTypeHom, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₂, CategoryTheory.IsPullback.isoPullback_inv_snd_assoc, CategoryTheory.Comma.map_obj_hom, HomologicalComplex₂.totalShift₂Iso_hom_naturality_assoc, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_apply, CategoryTheory.coprod_inr_rightDistrib_hom_assoc, CategoryTheory.CatEnriched.id_hComp, SSet.horn.faceSingletonComplIso_inv_ι_assoc, CategoryTheory.Limits.pullbackSymmetry_inv_comp_snd_assoc, CategoryTheory.Bimon.ofMonComonObjX_mul, CategoryTheory.OplaxFunctor.map₂_associator, CategoryTheory.Bicategory.inv_hom_whiskerRight_whiskerRight_assoc, commBialgCatEquivComonCommAlgCat_unitIso_inv_app, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_left_assoc, CategoryTheory.CartesianMonoidalCategory.associator_hom_fst_assoc, AlgebraicTopology.DoldKan.MorphComponents.preComp_a, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_app_apply, CategoryTheory.Bicategory.mateEquiv_comp_id_right, AlgebraicGeometry.universallyClosedTypeComp, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_hom_eq_germ, CategoryTheory.Limits.parallelPairOpIso_inv_app_zero, CategoryTheory.shift_shift', AlgebraicGeometry.quasiSeparated_comp, CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_hom, CategoryTheory.Limits.HasColimit.isoOfEquivalence_inv_π, CategoryTheory.CatCenter.app_sub, CategoryTheory.HasLiftingProperty.unop, groupCohomology.cocyclesIso₀_hom_comp_f, CategoryTheory.InjectiveResolution.ι'_f_zero, CategoryTheory.CartesianMonoidalCategory.prodComparison_fst, Monoid.Foldl.ofFreeMonoid_apply, CategoryTheory.Pseudofunctor.StrongTrans.homCategory_comp_as_app, CategoryTheory.MonoidalCategory.whiskerLeft_eqToHom, CategoryTheory.ShortComplex.abelianImageToKernel_comp_kernel_ι_comp_cokernel_π_assoc, SheafOfModules.pushforwardNatIso_inv, CategoryTheory.Comonad.ComonadicityInternal.unitFork_π_app, CategoryTheory.ObjectProperty.instIsClosedUnderColimitsOfShapeOppositeOpOfIsClosedUnderLimitsOfShape, prodIsoPullback_inv_fst, AlgebraicGeometry.HasAffineProperty.affineAnd_le_affineAnd, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₁_W, CategoryTheory.StructuredArrow.w_prod_fst, CategoryTheory.Limits.Types.coequalizerIso_quot_comp_inv, CategoryTheory.Arrow.mapCechNerve_app, CategoryTheory.Bicategory.inv_hom_whiskerRight_assoc, CategoryTheory.Bicategory.whisker_exchange, CategoryTheory.Functor.CorepresentableBy.uniqueUpToIso_inv, CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_left, CategoryTheory.PreOneHypercover.forkOfIsColimit_pt, CategoryTheory.SingleFunctors.id_hom, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_eq_iff', CategoryTheory.Bicategory.inv_hom_whiskerRight, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_left_hom, TopModuleCat.hom_zero_apply, CochainComplex.mappingCone.liftCochain_v_snd_v_assoc, AlgebraicGeometry.Proj.fromOfGlobalSections_toSpecZero_assoc, CategoryTheory.Limits.ι_colimitCompWhiskeringLeftIsoCompColimit_hom_assoc, CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux_fac_assoc, HomologicalComplex.extend.d_comp_eq_zero_iff, CategoryTheory.finrank_hom_simple_simple_le_one, CategoryTheory.Functor.hom_map, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_symm_apply, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_comp, HomotopicalAlgebra.PrepathObject.trans_p₀, CategoryTheory.Functor.mapCommGrp_obj_grp_one, AlgebraicGeometry.morphismRestrict_ι_assoc, CategoryTheory.sum.inlCompInrCompInverseAssociator_hom_app_down_down, CategoryTheory.Functor.uliftCoyonedaCoreprXIso_hom_app, CochainComplex.augmentTruncate_inv_f_zero, CategoryTheory.LaxFunctor.map₂_leftUnitor_assoc, CategoryTheory.NatTrans.removeLeftOp_id, CategoryTheory.GrothendieckTopology.arrow_stable, CategoryTheory.Functor.isLimitConeOfIsRightKanExtension_lift, Action.ofMulAction_apply, CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.hg, CategoryTheory.Functor.OplaxRightLinear.δᵣ_unitality_inv, groupCohomology.eq_d₀₁_comp_inv, groupCohomology.H1π_comp_map_assoc, SimplexCategoryGenRel.δ_comp_σ_of_gt_assoc, CategoryTheory.eHomEquiv_id, CategoryTheory.SimplicialObject.comp_right, CategoryTheory.eval_map, CategoryTheory.Adjunction.mapMon_unit, Profinite.Extend.functorOp_map, CategoryTheory.Functor.Monoidal.tensorHom_app_fst_assoc, CategoryTheory.StructuredArrow.homMk'_comp, CategoryTheory.ObjectProperty.FullSubcategory.comp_hom_assoc, CategoryTheory.MonoidalCategory.leftUnitor_naturality, CategoryTheory.MorphismProperty.DescendsAlong.top, CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_fst_assoc, CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_left_app, CategoryTheory.Cat.associator_hom_app, CategoryTheory.kernelCokernelCompSequence.snakeInput_L₀_X₂, CategoryTheory.Limits.kernelBiprodSndIso_hom, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_point, CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_obj, CochainComplex.mappingCone.inr_f_fst_v, AlgebraicGeometry.Scheme.fromSpecStalk_toSpecΓ_assoc, CategoryTheory.InducedCategory.endEquiv_symm_apply_hom, CategoryTheory.Under.forgetMapInitial_inv_app, CategoryTheory.ShortComplex.Homotopy.smul_h₁, CategoryTheory.Bicategory.pentagon_inv, HomologicalComplex.biprod_inr_desc_f, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.hf, CategoryTheory.Grp.id', CategoryTheory.Limits.IsImage.lift_ι_assoc, CategoryTheory.ShortComplex.zero_assoc, CategoryTheory.Limits.equalizerSubobject_arrow'_assoc, CategoryTheory.MonoidalCategory.associator_inv_naturality_right_assoc, SSet.stdSimplex.faceSingletonIso_zero_hom_comp_ι_eq_δ, groupHomology.mapCycles₁_comp_apply, SemiNormedGrp₁.coe_id, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_hom_app_app, CategoryTheory.Arrow.hom_inv_id_right_assoc, CategoryTheory.GrothendieckTopology.OneHypercover.comp_h₁, AddMonCat.zeroHom_apply, CategoryTheory.GrpObj.lift_inv_right_eq, CategoryTheory.InducedCategory.endEquiv_apply, CategoryTheory.MorphismProperty.LeftFraction₂.map_add, CategoryTheory.ShortComplex.leftHomologyMap'_comp, CategoryTheory.RetractArrow.retract_left_assoc, CategoryTheory.ShortComplex.HomotopyEquiv.trans_hom, CategoryTheory.CostructuredArrow.w_assoc, AlgebraicGeometry.AffineSpace.SpecIso_hom_appTop, CategoryTheory.Functor.rightDerived_fac_app, CategoryTheory.Limits.HasLimit.isoOfNatIso_inv_π_assoc, CategoryTheory.Limits.Pi.hom_ext_iff, SimplexCategory.δ_comp_δ'', groupHomology.mapShortComplexH1_zero, CategoryTheory.MonoidalCategory.pentagon_hom_inv_assoc, groupCohomology.π_comp_H0Iso_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHomRight, CategoryTheory.instHomIsOverComp, CategoryTheory.MorphismProperty.LeftFraction.op_X', CategoryTheory.Comon.tensorObj_comul, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_map_app, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_app_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocIso_inv_naturality, CategoryTheory.op_tensorHom, FDRep.endRingEquiv_symm_comp_ρ, CategoryTheory.Limits.coprod.map_inl_inr_codiag, CategoryTheory.NatTrans.CommShiftCore.shift_app_comm, CategoryTheory.Limits.cokernelCompIsIso_hom, CategoryTheory.Functor.map_shiftFunctorComm_hom_app, CategoryTheory.OverPresheafAux.YonedaCollection.map₂_comp, CategoryTheory.ShortComplex.RightHomologyData.wp, CategoryTheory.Functor.Monoidal.whiskerLeft_μ_δ_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_hom_app_snd_app, SemiRingCat.comp_apply, HomotopicalAlgebra.Precylinder.i₁_π_assoc, CategoryTheory.Idempotents.functorExtension₂_map_app_f, HomologicalComplex.homotopyCofiber.inlX_fstX, CategoryTheory.IsKernelPair.comp_of_mono, ModuleCat.ofHom_comp, CategoryTheory.Adjunction.derivedε_fac_app_assoc, CategoryTheory.ShortComplex.RightHomologyData.ofAbelian_H, CategoryTheory.ShortComplex.mapOpcyclesIso_hom_naturality_assoc, SimplicialObject.Splitting.IndexSet.fac_pull_assoc, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₁, CategoryTheory.Limits.Fork.π_comp_hom, CategoryTheory.Bicategory.Adjunction.homEquiv₂_symm_apply, CategoryTheory.Monad.Algebra.unit_assoc, CategoryTheory.PreGaloisCategory.endEquivSectionsFibers_π, groupCohomology.π_comp_H1Iso_hom_assoc, CategoryTheory.PreOneHypercover.comp_s₀, CategoryTheory.Functor.OplaxRightLinear.δᵣ_naturality_right_assoc, CategoryTheory.MorphismProperty.RightFraction.leftFraction_fac, SSet.Subcomplex.fromPreimage_ι_assoc, CategoryTheory.Sieve.pushforward_apply, CategoryTheory.Bicategory.InducedBicategory.Hom.category_id_hom, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_rightHomologyIso_inv, CategoryTheory.ShortComplex.LeftHomologyMapData.id_φH, CategoryTheory.BimonObj.one_comul, CategoryTheory.LaxFunctor.comp_mapId, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app, CategoryTheory.ShiftedHom.mk₀_zero, CategoryTheory.Limits.CoconeMorphism.w, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_ι_inv, CategoryTheory.Limits.coprod.associator_inv, CategoryTheory.Limits.Pi.lift_π_assoc, FinBddDistLat.ofHom_comp, CategoryTheory.eHomWhiskerRight_comp, HomologicalComplex.biprod_lift_fst_f_assoc, CategoryTheory.Equivalence.rightOp_counitIso_inv_app, HomologicalComplex.mapBifunctor.ι_D₂_assoc, CategoryTheory.MonoidalCategory.tensorHom_comp_whiskerRight_assoc, CategoryTheory.Sheaf.toImage_ι_assoc, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_assoc, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_inv_eq_germ_assoc, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.comp, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_right, CategoryTheory.Limits.wideEqualizer.condition_assoc, CategoryTheory.MonadHom.app_μ, TopologicalSpace.OpenNhds.inclusionMapIso_hom, FintypeCat.uSwitch_map_uSwitch_map, CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_base, CategoryTheory.Quiv.pathsOf_pathComposition_toPrefunctor, HomologicalComplex.op_d, CategoryTheory.Functor.curryObjCompIso_hom_app_app, CategoryTheory.down_comp_assoc, CategoryTheory.Functor.unopOpIso_inv_app, CategoryTheory.Limits.image.compIso_hom_comp_image_ι, CategoryTheory.GrothendieckTopology.overMapPullback_comp_id, CategoryTheory.PreOneHypercover.Homotopy.wl, CategoryTheory.GradedObject.Monoidal.associator_naturality, CategoryTheory.MorphismProperty.RespectsIso.precomp, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_naturality, groupHomology.cyclesMap_id_comp, HomotopicalAlgebra.FibrantObject.homMk_homMk, CategoryTheory.Pseudofunctor.map₂_left_unitor_assoc, HomologicalComplex.homotopyCofiber.inrX_fstX_assoc, CategoryTheory.Over.rightUnitor_inv_left_fst_assoc, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_symm_apply_φ, CategoryTheory.GrothendieckTopology.Cover.Arrow.ext_iff, CategoryTheory.Functor.uncurryObjFlip_hom_app, HomologicalComplex.homologyι_singleObjOpcyclesSelfIso_inv_assoc, CategoryTheory.ShortComplex.leftHomologyMap_sub, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_id, CochainComplex.HomComplex.Cochain.fromSingleEquiv_fromSingleMk, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_fst, LightCondensed.ihomPoints_symm_comp, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_map_mkHom_id_homMk, HomologicalComplex.extendHomologyIso_hom_naturality, CategoryTheory.Limits.prod.lift_map, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_id, CategoryTheory.NonPreadditiveAbelian.add_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id_app, CategoryTheory.Retract.op_i, CategoryTheory.ShortComplex.RightHomologyData.p_comp_opcyclesIso_inv, CategoryTheory.yoneda_map_app, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom, Pointed.Hom.id_toFun', CategoryTheory.Functor.LaxLeftLinear.μₗ_naturality_right, CategoryTheory.Functor.WellOrderInductionData.map_succ, HomologicalComplex.opSymm_d, CategoryTheory.OplaxFunctor.map₂_associator_app, CategoryTheory.Oplax.LaxTrans.vComp_naturality_id, CategoryTheory.Functor.OplaxMonoidal.δ_snd_assoc, CategoryTheory.ShortComplex.RightHomologyData.wp_assoc, CategoryTheory.MorphismProperty.Over.hasPullbacks, CategoryTheory.Comma.mapLeft_map_left, groupHomology.mapShortComplexH2_zero, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_fst, SimplexCategory.Truncated.δ₂_zero_comp_σ₂_zero, CategoryTheory.StrictPseudofunctorCore.map₂_left_unitor, CategoryTheory.SmallObject.πObj_ιIteration_app_right, CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit_proj, groupCohomology.eq_d₁₂_comp_inv, CategoryTheory.unop_tensorHom, CompHausLike.pullback.condition, CategoryTheory.Limits.PreservesPushout.inr_iso_inv, CategoryTheory.MorphismProperty.HasCardinalLT.iSup, CategoryTheory.Bicategory.Lan.existsUnique, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_id_fiber, CategoryTheory.typeEquiv_functor_obj_val_obj, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_morphismRestrict_assoc, AlgebraicGeometry.Spec.map_surjective, CategoryTheory.CartesianMonoidalCategory.tensorδ_snd_assoc, CategoryTheory.TransportEnrichment.eId_eq, CategoryTheory.MonoidalClosed.ofEquiv_uncurry_def, CategoryTheory.Sum.functorEquiv_functor_map, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_whiskerRight_as_app, CategoryTheory.Oplax.OplaxTrans.Modification.vcomp_app, CategoryTheory.ShortComplex.opcyclesMap'_g', CategoryTheory.Limits.biproduct.fromSubtype_π_subtype, AlgebraicTopology.DoldKan.Γ₀NondegComplexIso_inv_f, AlgebraicGeometry.Scheme.Opens.topIso_inv, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀', CategoryTheory.Limits.biproduct.ι_π_assoc, CategoryTheory.curryingIso_hom_toFunctor_obj_map, SheafOfModules.sectionsMap_id, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition', CategoryTheory.CatCommSq.hInv_iso_inv_app, CategoryTheory.GrothendieckTopology.overMapPullbackId_inv_app_val_app, AlgebraicGeometry.Scheme.SpecToEquivOfField_eq_iff, CategoryTheory.Limits.ColimitPresentation.changeDiag_ι, CategoryTheory.Equivalence.leftOp_unitIso_inv_app, CategoryTheory.Limits.Cone.equiv_inv_pt, CategoryTheory.Preregular.exists_fac, PresheafOfModules.pullback_comp_id, AugmentedSimplexCategory.whiskerLeft_id_star, CategoryTheory.IsSplitEqualizer.bottom_rightRetraction, Homotopy.nullHomotopicMap_comp, HomologicalComplex.toCycles_i, CategoryTheory.Functor.LaxRightLinear.μᵣ_naturality_right_assoc, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_inverse, CategoryTheory.mop_comp, CategoryTheory.Sieve.ofArrows.fac, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_naturality_assoc, FundamentalGroupoid.conj_eqToHom_assoc, CategoryTheory.Limits.prod.pentagon_assoc, CategoryTheory.Grp_Class.comp_zpow, CategoryTheory.PreZeroHypercover.inv_hom_h₀_comp_f_assoc, CategoryTheory.Localization.isoOfHom_inv_hom_id, SSet.OneTruncation₂.nerveHomEquiv_id, CategoryTheory.Functor.Monoidal.RepresentableBy.tensorObj_homEquiv, CategoryTheory.Functor.descOfIsLeftKanExtension_fac_assoc, CategoryTheory.Limits.colimit.pre_post, ProfiniteGrp.ProfiniteCompletion.lift_eta, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality_assoc, CategoryTheory.Bicategory.RightLift.w_assoc, CategoryTheory.op_mono_of_epi, CategoryTheory.Limits.CategoricalPullback.comp_snd, CommRingCat.id_apply, CategoryTheory.Over.comp_left_assoc, CategoryTheory.MonObj.mul_assoc, CategoryTheory.Functor.mapTriangleRotateIso_inv_app_hom₂, groupCohomology.mapCocycles₂_comp_i, CategoryTheory.Comon.uniqueHomToTrivial_default_hom, CategoryTheory.Limits.MonoFactorisation.compMono_m, CategoryTheory.Bicategory.mateEquiv_vcomp, CategoryTheory.Pseudofunctor.StrongTrans.comp_app, CategoryTheory.ProjectiveResolution.lift_commutes_zero_assoc, CategoryTheory.Limits.BinaryFan.braiding_hom_snd_assoc, CategoryTheory.ObjectProperty.le_shiftClosure, CategoryTheory.InducedCategory.homLinearEquiv_apply, HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom_desc_hom_assoc, CategoryTheory.yonedaCommGrpGrpObj_map, TopCat.Presheaf.SheafConditionEqualizerProducts.piOpens.hom_ext_iff, CategoryTheory.Functor.WellOrderInductionData.Extension.ofLE_val, CategoryTheory.GrpObj.lift_inv_comp_left_assoc, CategoryTheory.MonoidalCategory.associator_naturality_assoc, CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj, CategoryTheory.ShortComplex.abelianImageToKernel_comp_kernel_ι, HomotopicalAlgebra.instWeakEquivalenceCompOfIsStableUnderCompositionWeakEquivalences, CategoryTheory.ShrinkHoms.id_def, AlgebraicTopology.DoldKan.identity_N₂, groupHomology.eq_d₃₂_comp_inv, CategoryTheory.Dial.rightUnitor_naturality, CategoryTheory.MonObj.ofIso_mul, AlgebraicGeometry.pointsPi_surjective_of_isAffine, CategoryTheory.EnrichedCat.leftUnitor_hom_out_app, CategoryTheory.ExponentiableMorphism.id_pushforward, CategoryTheory.Subobject.map_comp, CategoryTheory.MonoidalClosed.uncurry_natural_right, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHomRight, CategoryTheory.Pseudofunctor.mapComp'_hom_comp_whiskerLeft_mapComp'_hom, CategoryTheory.conjugateEquiv_symm_id, PresheafOfModules.comp_app, CategoryTheory.Limits.IsImage.lift_fac, CategoryTheory.Functor.shiftIso_hom_app_comp, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.IsTerminal.comm, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_right_symm, CategoryTheory.monoidalComp_refl, CategoryTheory.Bicategory.conjugateEquiv_adjunction_id_symm, AlgebraicTopology.DoldKan.PInfty_comp_QInfty, CategoryTheory.monoidalOfHasFiniteProducts.associator_inv_fst_snd, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom_assoc, TopCat.GlueData.ι_fromOpenSubsetsGlue, CategoryTheory.CartesianMonoidalCategory.lift_leftUnitor_hom_assoc, HomotopicalAlgebra.Precylinder.inr_i, CategoryTheory.ShortComplex.RightHomologyMapData.op_φH, SheafOfModules.pullbackPushforwardAdjunction_homEquiv_pullbackObjUnitToUnit, CategoryTheory.MorphismProperty.Over.instHasTerminalTopOfContainsIdentities, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_assoc, CochainComplex.IsKInjective.nonempty_homotopy_zero, CategoryTheory.nerve.functorOfNerveMap_map, CategoryTheory.Mon.hom_injective, HomotopicalAlgebra.FibrantBrownFactorization.i_r_assoc, CategoryTheory.Pretriangulated.shiftFunctorZero_op_inv_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_ι_app, CategoryTheory.Functor.prod'_μ_fst, CategoryTheory.PreOneHypercover.p₁_sigmaOfIsColimit_assoc, CategoryTheory.Iso.inv_hom_id_triangle_hom₂, CategoryTheory.Bicategory.Adj.comp_τl_assoc, CochainComplex.mappingCone.liftCochain_v_snd_v, CategoryTheory.ShortComplex.RightHomologyMapData.homologyMap_eq, CategoryTheory.MorphismProperty.instHasLeftCalculusOfFractionsUnopOfHasRightCalculusOfFractionsOpposite, CategoryTheory.StructuredArrow.mapIso_inverse_obj_hom, Bimod.whiskerLeft_hom, CategoryTheory.HasLiftingProperty.op, QuadraticModuleCat.toIsometry_comp, CategoryTheory.Limits.image.compIso_hom_comp_image_ι_assoc, CategoryTheory.StrictPseudofunctor.mk'_obj, CategoryTheory.Functor.mapMon_obj_mon_mul, CategoryTheory.Functor.isColimitCoconeOfIsLeftKanExtension_desc, CategoryTheory.Join.inclRightCompOpEquivInverse_inv_app_op, CategoryTheory.ShortComplex.exact_iff_iCycles_pOpcycles_zero, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_inv_app_hom, CategoryTheory.Abelian.LeftResolution.chainComplexMap_zero, CategoryTheory.Oplax.OplaxTrans.StrongCore.naturality_hom, CategoryTheory.Limits.BinaryBicone.ofLimitCone_inl, CategoryTheory.NatIso.naturality_1', CategoryTheory.Mon.forget_ε, CategoryTheory.Grp.trivial_grp_inv, CategoryTheory.ShortComplex.exact_iff_kernel_ι_comp_cokernel_π_zero, CategoryTheory.Functor.relativelyRepresentable.symmetry_symmetry, groupHomology.chainsMap_id, CategoryTheory.PreOneHypercover.Hom.w₁₁, CategoryTheory.Localization.liftNatTrans_add, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app_assoc, CategoryTheory.Limits.IsLimit.map_π, CategoryTheory.BraidedCategory.braiding_tensor_left_inv, CategoryTheory.Functor.biprodComparison_snd_assoc, HomologicalComplex.mapBifunctor.ι_D₁_assoc, HomologicalComplex.leftUnitor'_inv_comm, CategoryTheory.Endofunctor.Algebra.Hom.h_assoc, CategoryTheory.Limits.biproduct.lift_map, CategoryTheory.Limits.end_.map_π, CategoryTheory.MonoidalCategory.triangle_assoc_comp_left_inv, CategoryTheory.Functor.OplaxMonoidal.associativity_assoc, ContinuousMap.Homotopy.apply_zero_path, CategoryTheory.Abelian.Ext.mk₀_addEquiv₀_apply, CategoryTheory.cosimplicialSimplicialEquiv_counitIso_hom_app_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.comp_snd_app, CategoryTheory.MonoidalCategory.externalProductBifunctor_map_app, HomotopicalAlgebra.BifibrantObject.homMk_id, CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_inv_assoc, CategoryTheory.Over.hom_left_inv_left, CategoryTheory.Limits.BinaryBicone.toBiconeFunctor_obj_π, CategoryTheory.sum.inrCompInrCompInverseAssociator_hom_app_down, CategoryTheory.Limits.pullback.diagonal_snd_assoc, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id, SimplicialObject.Splitting.PInfty_comp_πSummand_id, CategoryTheory.Deterministic.discard_natural, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₃, LightCondSet.epi_iff_locallySurjective_on_lightProfinite, CategoryTheory.GrothendieckTopology.sheafifyMap_sheafifyLift_assoc, CategoryTheory.Limits.IsZero.unique_to, AlgebraicGeometry.Scheme.Cover.glued_cover_cocycle_fst, CategoryTheory.PreGaloisCategory.autMap_comp, CategoryTheory.Limits.opProdIsoCoprod_hom_snd_assoc, CategoryTheory.Limits.ColimitPresentation.comp_base, CategoryTheory.MonoidalCategory.whiskerRight_tensor_symm, CategoryTheory.Functor.mapTriangleCompIso_inv_app_hom₂, AlgebraicGeometry.IsSeparated.instIsClosedImmersionMapDescScheme, CategoryTheory.Presieve.CoverByImageStructure.fac, CategoryTheory.InjectiveResolution.self_ι, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_leftUnitor, ComplexShape.Embedding.liftExtend.comm_assoc, CategoryTheory.Functor.pi'CompEval_hom_app, CategoryTheory.Limits.biproduct.whiskerEquiv_inv, CategoryTheory.Limits.biproduct.map_desc, AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id_assoc, CategoryTheory.Functor.PreservesHomology.preservesKernels, CategoryTheory.Presieve.isSeparatedFor_singleton, Mathlib.Tactic.Monoidal.evalWhiskerLeft_of_cons, CategoryTheory.Over.monObjMkPullbackSnd_mul, CategoryTheory.Limits.image.lift_mk_factorThruImage, SSet.Subcomplex.range_eq_ofSimplex, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerRight, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app, CategoryTheory.IsHomLift.comp_eqToHom_lift_iff, CategoryTheory.CosimplicialObject.δ_comp_δ', AlgebraicGeometry.GeometricallyIrreducible.comp, CategoryTheory.MorphismProperty.Comma.eqToHom_left, TopCat.sigmaIsoSigma_hom_ι, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_fst_fst, CategoryTheory.Monad.Algebra.Hom.h, CategoryTheory.GrothendieckTopology.Point.id_hom, CategoryTheory.Oplax.OplaxTrans.homCategory_id_as_app, SimplexCategory.const_comp, CategoryTheory.Functor.leftOpRightOpEquiv_counitIso_inv_app_app, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp_assoc, CategoryTheory.Adjunction.compCoyonedaIso_inv_app_app, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_unitIso_hom_app_f, CategoryTheory.MorphismProperty.postcomp_iff, CategoryTheory.Subfunctor.Subpresheaf.equalizer.condition, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app, HomologicalComplex.dTo_eq_zero, CategoryTheory.Square.Hom.comm₂₄, CategoryTheory.Grothendieck.map_comp_eq, CategoryTheory.Limits.FormalCoproduct.isoOfComponents_inv_φ, AlgebraicGeometry.Scheme.Hom.iUnion_support_ker_openCover_map_comp, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_apply_f, CategoryTheory.isIso_unop_iff, CategoryTheory.ShortComplex.opcyclesMap_sub, CategoryTheory.Functor.comp_mapGrp_mul, HomologicalComplex₂.comm_f, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app_assoc, CategoryTheory.NonPreadditiveAbelian.add_def, CategoryTheory.Over.whiskerLeft_left, CategoryTheory.Monad.algebraFunctorOfMonadHomId_inv_app_f, CategoryTheory.MonoidalOpposite.mopFunctor_ε, CategoryTheory.unop_epi_of_mono, SSet.spine_map_subinterval, CategoryTheory.Abelian.image.fac, CategoryTheory.Dial.rightUnitorImpl_inv_f, CategoryTheory.Grpd.piIsoPi_hom_π, CategoryTheory.CartesianMonoidalCategory.whiskerLeft_toUnit_comp_rightUnitor_hom, HomologicalComplex.extendHomologyIso_hom_naturality_assoc, AddCommMonCat.coe_id, CategoryTheory.Over.forgetMapTerminal_hom_app, Opens.mayerVietorisSquare_X₃, AddMonCat.hom_zero, Rep.diagonalHomEquiv_symm_apply, CategoryTheory.Adjunction.leftAdjointUniq_refl, CategoryTheory.Limits.piComparison_comp_π, CategoryTheory.Equivalence.rightOp_functor_map, DerivedCategory.HomologySequence.comp_δ, CategoryTheory.eqToHom_iso_hom_naturality_assoc, SSet.PtSimplex.MulStruct.δ_map_of_gt, Bimod.TensorBimod.right_assoc', CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app, CategoryTheory.Limits.π_comp_cokernelIsoOfEq_hom_assoc, CategoryTheory.Functor.PreOneHypercoverDenseData.w_assoc, CategoryTheory.ParametrizedAdjunction.whiskerLeft_map_counit, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_associator, AlgebraicGeometry.diagonal_SpecMap, CategoryTheory.ULiftHom.down_map, CategoryTheory.Limits.image.map_id, CategoryTheory.CatCenter.naturality_assoc, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapCompIso_inv, AlgebraicGeometry.Scheme.inv_app, ProfiniteAddGrp.ofHom_id, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_map_app_app, CategoryTheory.GrothendieckTopology.ι_plusCompIso_hom_assoc, CategoryTheory.ShortComplex.opcyclesMap'_sub, CategoryTheory.ObjectProperty.le_isoClosure, CategoryTheory.GradedObject.singleObjApplyIso_inv_single_map, CategoryTheory.Functor.mapTriangle_obj, CategoryTheory.Functor.leftDerived_fac_app, CategoryTheory.Iso.eHomCongr_hom, groupCohomology.H0IsoOfIsTrivial_hom, AlgebraicGeometry.LocallyRingedSpace.id_toShHom', CategoryTheory.ObjectProperty.isDetecting_op_iff, CategoryTheory.rightDistributor_ext₂_right_iff, CategoryTheory.ObjectProperty.instContainsZeroOppositeOp, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_app_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.leftUnitor_inv_one_tensor_mul, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_hom_app, CategoryTheory.ShortComplex.RightHomologyMapData.neg_φQ, AddMonCat.ofHom_id, CategoryTheory.SplitEpi.id, AlgebraicGeometry.Scheme.Hom.id_appTop, CategoryTheory.Functor.RepresentableBy.homEquiv_eq, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_hom_inv_id, CategoryTheory.Functor.toPrefunctor_map, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_one, AlgebraicGeometry.ι_right_coprodIsoSigma_inv, CategoryTheory.LocalizerMorphism.RightResolution.comp_f_assoc, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_id, CategoryTheory.Abelian.LeftResolution.chainComplexMap_comp, CategoryTheory.CatCommSq.hId_iso_hom_app, CategoryTheory.linearYoneda_obj_map, CategoryTheory.Limits.coend.map_id, CategoryTheory.PreOneHypercover.multicospanIndex_fst, CategoryTheory.Functor.LeftExtension.postcomp₁_map_right_app, CategoryTheory.CostructuredArrow.IsUniversal.existsUnique, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_inv_hom, AlgebraicGeometry.ι_sigmaSpec, CategoryTheory.NatTrans.unop_comp_assoc, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_one, CategoryTheory.CountableCategory.countableHom, CategoryTheory.Functor.mapComposableArrowsObjMk₁Iso_inv_app, PresheafOfModules.homEquivOfIsLocallyBijective_symm_apply, CategoryTheory.Limits.widePullbackShapeUnop_map, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp_app, SimplexCategory.δ_comp_σ_of_gt'_assoc, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_comp_naturality_hom, inl_coprodIsoPushout_hom, HomotopicalAlgebra.Precylinder.inr_i_assoc, CommRingCat.HomTopology.instCompactSpaceHomOfIsTopologicalRingOfT1SpaceOfCarrier, CategoryTheory.CostructuredArrow.mkPrecomp_id, CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtension_map_leftKanExtensionObjIsoColimit_hom, CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_π_assoc, CategoryTheory.OplaxFunctor.mapComp_naturality_right_assoc, CategoryTheory.prodOpEquiv_inverse_map, CategoryTheory.right_comp_retraction, CategoryTheory.ShortComplex.LeftHomologyMapData.commf', AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_hom_app, HomotopyCategory.isZero_quotient_obj_iff, Action.Hom.comp_hom, CategoryTheory.Functor.Monoidal.η_ε_assoc, CategoryTheory.ShortComplex.opMap_τ₁, CategoryTheory.Preadditive.homSelfLinearEquivEndMulOpposite_apply, LinOrd.hom_id, CategoryTheory.Oplax.LaxTrans.naturality_naturality_assoc, CategoryTheory.CategoryOfElements.map_map_coe, SemiNormedGrp.hom_sub, CategoryTheory.Join.id_right, CategoryTheory.Functor.mapCoconePrecompose_inv_hom, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict, CategoryTheory.Linear.comp_apply, CategoryTheory.ShortComplex.HasLeftHomology.of_zeros, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left, CategoryTheory.simplicialCosimplicialEquiv_counitIso_inv_app_app, CategoryTheory.Iso.inv_hom_id, CategoryTheory.DifferentialObject.d_squared_apply, CategoryTheory.GrpObj.left_inv_assoc, CategoryTheory.Functor.mapGrp_id_mul, CategoryTheory.Limits.PushoutCocone.unop_π_app, CategoryTheory.EnrichedFunctor.forgetComp_inv_app, CategoryTheory.eqToHom_map_comp, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_inv_app, CategoryTheory.Functor.relativelyRepresentable.pullback₃.snd_snd_eq_p₃_assoc, CompHausLike.coe_id, CategoryTheory.Functor.homologySequence_comp_assoc, CategoryTheory.Limits.coprod.inl_map_assoc, CategoryTheory.GrothendieckTopology.plusMap_id, CategoryTheory.Limits.prod.rightUnitor_hom_naturality, CategoryTheory.MonoidalCategory.DayFunctor.equiv_unitIso_hom_app, CategoryTheory.Abelian.LeftResolution.chainComplexMap_id, CategoryTheory.Subfunctor.range_le_equalizer_iff, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom, CategoryTheory.CostructuredArrow.w_prod_fst, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app, CategoryTheory.StrictPseudofunctor.id_mapComp_hom, CategoryTheory.Limits.diagramIsoParallelFamily_inv_app, CompHausLike.finiteCoproduct.ι_desc, AlgebraicGeometry.Scheme.Hom.le_ker_comp, HomologicalComplex.restrictionMap_comp, AlgebraicGeometry.Spec.map_injective, CategoryTheory.Presheaf.functorToRepresentables_map, CategoryTheory.op_whiskerRight, CategoryTheory.MorphismProperty.LeftFraction.rightFraction_fac, CategoryTheory.comp_hom_eq_id, AlgebraicGeometry.coprodSpec_inr, CategoryTheory.Functor.mapGrpIdIso_hom_app_hom_hom, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_postcomp, CategoryTheory.ShortComplex.Homotopy.unop_h₂, CategoryTheory.Linear.smulOfRingMorphism_smul_eq', CategoryTheory.simplicialCosimplicialEquiv_inverse_map, CategoryTheory.Comonad.Coalgebra.comp_f, HomologicalComplex.mapBifunctor₂₃.ι_D₃, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_hom_app_hom_apply, CategoryTheory.Limits.biproduct.fromSubtype_π_subtype_assoc, CategoryTheory.Limits.inr_inl_pushoutRightPushoutInlIso_hom_assoc, AlgebraicTopology.DoldKan.PInfty_idem, ModuleCat.Iso.homCongr_eq_arrowCongr, AlgebraicTopology.DoldKan.homotopyPInftyToId_hom, AlgebraicGeometry.IsOpenImmersion.comp_lift_assoc, CategoryTheory.unop_inv_associator, CategoryTheory.Join.mapWhiskerRight_leftUnitor_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv, CategoryTheory.Limits.Multifork.isoOfι_hom_hom, SimplicialObject.opFunctor_obj_σ, CategoryTheory.braiding_tensorUnit_left_assoc, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp_symm_assoc, CategoryTheory.Limits.Fork.unop_ι_app_zero, CategoryTheory.WithInitial.down_id, CategoryTheory.Subobject.factorThru_eq_zero, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left, CategoryTheory.Localization.Monoidal.associator_hom_app, TopologicalSpace.OpenNhds.comp_apply, CategoryTheory.finrank_hom_simple_simple_eq_one_iff, CategoryTheory.Localization.Monoidal.pentagon_aux₁, AlgebraicGeometry.Scheme.stalkSpecializes_stalkMap, CategoryTheory.Limits.CatCospanTransform.rightUnitor_hom_left_app, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_snd_assoc, CategoryTheory.Adjunction.rightAdjointLaxMonoidal_μ, CategoryTheory.Limits.MulticospanIndex.multicospan_map, CategoryTheory.MonoidalCategory.leftUnitor_inv_comp_tensorHom_assoc, CategoryTheory.ObjectProperty.IsClosedUnderColimitsOfShape.colimitsOfShape_le, CategoryTheory.Functor.FullyFaithful.homMulEquiv_apply, CochainComplex.isoHomologyπ₀_inv_naturality_assoc, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_inv_app, CategoryTheory.Center.comp_f, CategoryTheory.Functor.inlCompSum'_inv_app, CategoryTheory.Limits.Cocone.ofCotrident_ι, CategoryTheory.Subgroupoid.full_arrow_eq_iff, CategoryTheory.ShortComplex.leftHomologyMap'_neg, CategoryTheory.kernelCokernelCompSequence.snakeInput_L₃_g, CochainComplex.mappingCone.homologySequenceδ_triangleh, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_pos_assoc, CategoryTheory.IsPullback.op, CategoryTheory.Limits.opCompYonedaSectionsEquiv_symm_apply_coe, CategoryTheory.Cat.Hom₂.eqToHom_toNatTrans, CategoryTheory.Yoneda.naturality, CategoryTheory.Adjunction.IsMonoidal.leftAdjoint_μ, CategoryTheory.prodFunctorToFunctorProd_map, CategoryTheory.Cat.Hom₂.id_app, CategoryTheory.Limits.WalkingReflexivePair.reflexion_comp_left, CategoryTheory.ObjectProperty.topEquivalence_counitIso, CategoryTheory.Adjunction.comp_homEquiv, groupHomology.comap_coinvariantsKer_pOpcycles_range_subtype_pOpcycles_eq_top, CategoryTheory.Grothendieck.ιNatTrans_app_fiber, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_comp_ι, CategoryTheory.CostructuredArrow.mapIso_functor_obj_hom, CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_self_succ, CategoryTheory.Functor.closedIhom_obj_map, CategoryTheory.ShortComplex.opcyclesMap'_g'_assoc, CategoryTheory.SingleFunctors.Hom.comp_hom, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_inv_naturality_assoc, CategoryTheory.ShortComplex.LeftHomologyData.ofEpiOfIsIsoOfMono'_i, LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition, CategoryTheory.Discrete.natIsoFunctor_hom_app, CategoryTheory.MonoidalCategory.externalProductCompDiagIso_hom_app_app, CategoryTheory.Limits.yonedaCompLimIsoCocones_inv_app, CategoryTheory.e_id_comp, CategoryTheory.MonoidalCategory.associator_inv_naturality_right, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_app_assoc, CategoryTheory.coyonedaEvaluation_map_down, CategoryTheory.nerve.homEquiv_edgeMk_map_nerveMap, CategoryTheory.Limits.LimitPresentation.w, CategoryTheory.Limits.FormalCoproduct.mapPower_id, FunctorToFintypeCat.naturality, AlgebraicGeometry.Scheme.Spec_map_stalkSpecializes_fromSpecStalk, CategoryTheory.Limits.biproduct.ι_map_assoc, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id_assoc, CategoryTheory.Limits.pullbackProdSndIsoProd_inv_fst_snd, CategoryTheory.Subobject.ofMkLEMk_comp_ofMkLEMk_assoc, CategoryTheory.Over.grpObjMkPullbackSnd_one, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition, groupHomology.cyclesMap_comp_isoCycles₂_hom, HomologicalComplex.mapBifunctor₂₃.d₂_eq, CategoryTheory.Functor.WellOrderInductionData.Extension.map_zero, CategoryTheory.Limits.biproduct.map_π_assoc, HeytAlg.hom_id, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_left_right, CategoryTheory.Limits.Multicoequalizer.condition, CategoryTheory.CartesianMonoidalCategory.associator_inv_snd, CategoryTheory.Iso.isoInverseComp_inv_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_hom_app_fst_app, AugmentedSimplexCategory.inr_comp_inl_comp_associator, CategoryTheory.Functor.Monoidal.coreMonoidalTransport_εIso_inv, CategoryTheory.Grothendieck.grothendieckTypeToCat_inverse_map_base, CategoryTheory.Abelian.Pseudoelement.comp_apply, Action.FunctorCategoryEquivalence.counitIso_inv_app_app, AlgebraicGeometry.HasRingHomProperty.comp_of_isOpenImmersion, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₁₂, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.g_app, CategoryTheory.MorphismProperty.ContainsIdentities.inf, CategoryTheory.Limits.prod.inl_snd, CategoryTheory.Endofunctor.algebraPreadditive_homGroup_neg_f, CategoryTheory.Functor.OplaxLeftLinear.δₗ_associativity_inv, HomotopicalAlgebra.LeftHomotopyClass.whitehead, CategoryTheory.Limits.pullbackAssoc_hom_snd_fst_assoc, CategoryTheory.Functor.commShift₂_comm, CategoryTheory.WithTerminal.map₂_app, CategoryTheory.Pseudofunctor.StrongTrans.leftUnitor_inv_as_app, AlgebraicGeometry.Scheme.ideal_ker_le_ker_ΓSpecIso_inv_comp, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_obj, SSet.Subcomplex.toImage_ι, CategoryTheory.δ_naturalityₗ_assoc, CategoryTheory.Comma.mapLeftIso_functor_map_left, SimplexCategory.instFiniteHom, CategoryTheory.Iso.refl_conj, CategoryTheory.Iso.map_inv_hom_id_app_assoc, CategoryTheory.MonoidalCategory.inv_hom_id_tensor'_assoc, AlgebraicGeometry.Scheme.stalkMap_congr_assoc, CategoryTheory.MonoidalCategory.leftUnitor_inv_whiskerRight, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_symm_assoc, HomologicalComplex.opcyclesOpIso_inv_naturality_assoc, CategoryTheory.Limits.inl_comp_pushoutComparison_assoc, CategoryTheory.isCodetecting_empty_of_groupoid, CategoryTheory.Limits.prod.map_swap_assoc, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_whiskerLeft_as_app, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_inverse_obj_str, CategoryTheory.Limits.MulticospanIndex.sndPiMap_π_assoc, CategoryTheory.Functor.Fiber.fiberInclusionCompIsoConst_inv_app, HomologicalComplex.opcyclesIsoSc'_inv_fromOpcycles_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id_assoc, CategoryTheory.Limits.KernelFork.condition_assoc, CategoryTheory.PreOneHypercover.trivial_p₁, groupHomology.comp_d₂₁_eq, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv, CategoryTheory.MorphismProperty.Over.map_obj_left, HomologicalComplex.inl_biprodXIso_inv_assoc, CategoryTheory.Functor.FullyFaithful.homEquiv_apply, CategoryTheory.Preadditive.sub_comp_assoc, SemiRingCat.hom_comp, CategoryTheory.Limits.zero_of_source_iso_zero, CategoryTheory.GrothendieckTopology.whiskerRight_toSheafify_sheafifyCompIso_hom_assoc, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_left, PresheafOfModules.limitPresheafOfModules_map, CategoryTheory.ShortComplex.rightHomologyι_naturality'_assoc, CategoryTheory.preadditiveYonedaObj_obj_carrier, CategoryTheory.Functor.pentagon, LightCondensed.finYoneda_map, CategoryTheory.Limits.Multicofork.π_comp_hom_assoc, CategoryTheory.Subobject.ofLEMk_comp_ofMkLEMk, CategoryTheory.Limits.Sigma.map_comp_map, SimplicialObject.Splitting.cofan_inj_epi_naturality_assoc, CategoryTheory.Monad.algebraPreadditive_homGroup_sub_f, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_inv_app_coe, HomologicalComplex.cyclesMap_comp_assoc, CategoryTheory.MonObj.ofIso_one, CategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSet_id, CategoryTheory.Functor.mapCoconeWhisker_hom_hom, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂_assoc, CategoryTheory.sheafificationNatIso_inv_app_val, CategoryTheory.tensorRightHomEquiv_symm_naturality, AddCommGrpCat.hom_zero, CategoryTheory.Limits.colimitCoyonedaHomIsoLimit'_π_apply, CategoryTheory.NatIso.cancel_natIso_inv_right_assoc, groupHomology.mapCycles₁_comp_assoc, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_map, CategoryTheory.η_naturality_assoc, Semigrp.hom_comp, AlgebraicGeometry.Scheme.isoSpec_inv_toSpecΓ, CategoryTheory.Limits.HasZeroObject.zeroIsoIsInitial_inv, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_assoc, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_inv_app_hom_apply, HomologicalComplex.biprod_inr_snd_f_assoc, CategoryTheory.ShortComplex.Splitting.s_g, CategoryTheory.Functor.cones_map_app, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inr_assoc, CategoryTheory.ShortComplex.LeftHomologyData.f'_π_assoc, CategoryTheory.ShortComplex.LeftHomologyData.unop_ι, MonObj.mopEquivCompForgetIso_hom_app_unmop, CategoryTheory.Types.instReflectsLimitsOfSizeForgetTypeHom, CategoryTheory.Over.grpObjMkPullbackSnd_mul, CategoryTheory.Functor.Monoidal.map_associator_inv_assoc, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃_tensorHom, CategoryTheory.Bimon.equivMonComonUnitIsoAppXAux_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_inv_app_app_hom_hom, SemiNormedGrp.hom_id, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι_assoc, CategoryTheory.μ_δ_app_assoc, CategoryTheory.Functor.Monoidal.toUnit_ε_assoc, CategoryTheory.IsRegularMono.w, Action.comp_hom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_inv_app_snd_app, CategoryTheory.PreOneHypercover.cylinderHom_h₁, CategoryTheory.NatTrans.leftOp_app, ContinuousMap.Homotopy.evalAt_eq, CochainComplex.IsKProjective.homotopyZero_def, groupHomology.toCycles_comp_isoCycles₂_hom_assoc, CategoryTheory.Limits.prod.rightUnitor_hom_naturality_assoc, CategoryTheory.Bicategory.pentagon_hom_hom_inv_hom_hom_assoc, CategoryTheory.coprod_inl_leftDistrib_hom, CommRingCat.moduleCatRestrictScalarsPseudofunctor_mapComp, SSet.horn.yonedaEquiv_ι, CategoryTheory.Functor.toPseudoFunctor'_obj, CategoryTheory.Pretriangulated.comp_hom₁_assoc, AlgebraicGeometry.pointsPi_injective, CategoryTheory.Oplax.OplaxTrans.categoryStruct_id_naturality, HomologicalComplex.biprod_inl_snd_f_assoc, SimplexCategory.Truncated.Hom.tr_comp, CategoryTheory.Localization.Construction.natTransExtension_hcomp, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app_apply, CategoryTheory.MonoidalCategory.rightUnitor_tensor_hom, CategoryTheory.Join.isoMkFunctor_hom_app, CategoryTheory.Pseudofunctor.mapId'_inv_naturality_assoc, CategoryTheory.Center.forget_η, CategoryTheory.LocalizerMorphism.homMap_id, CategoryTheory.Limits.FormalCoproduct.pullbackCone_fst_φ, CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_π, CategoryTheory.coevaluation_comp_leftAdjointMate_assoc, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy₂_homEquiv, CategoryTheory.IsPullback.of_prod_fst_with_id, CategoryTheory.Equivalence.leftOp_counitIso_inv_app, CategoryTheory.TransfiniteCompositionOfShape.fac_assoc, CategoryTheory.η_ε_app_assoc, CategoryTheory.NatTrans.unop_whiskerLeft_assoc, CategoryTheory.conjugateEquiv_symm_comp_assoc, CategoryTheory.Limits.coyonedaCompLimIsoCones_inv_app, CategoryTheory.Functor.Monoidal.map_associator_assoc, CategoryTheory.Arrow.comp_left, CategoryTheory.Subfunctor.ofSection_eq_range, Bimod.TensorBimod.whiskerLeft_π_actLeft, CategoryTheory.Limits.Cofork.ofCocone_ι, Homotopy.nullHomotopicMap_f_eq_zero, SemimoduleCat.Iso.homCongr_eq_arrowCongr, groupHomology.H0π_comp_map, CategoryTheory.MonoidalClosed.coev_app_comp_pre_app, CategoryTheory.Limits.inl_inr_pushoutAssoc_inv_assoc, TopologicalSpace.Opens.comp_apply, CategoryTheory.Dial.tensorHom_F, CategoryTheory.Pretriangulated.Triangle.eqToHom_hom₂, CategoryTheory.Localization.SmallHom.equiv_equiv_symm, CategoryTheory.kernelCokernelCompSequence.inl_π_assoc, CategoryTheory.OrthogonalReflection.D₁.ιLeft_comp_l, CategoryTheory.Functor.CommShift.isoZero_hom_app, CategoryTheory.ChosenPullbacksAlong.hom_ext_iff, CategoryTheory.Bicategory.LeftLift.w_assoc, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_inv_app_op_zero, CategoryTheory.Limits.BinaryBicone.inr_snd, HomotopicalAlgebra.instWeakEquivalenceIdOfContainsIdentitiesWeakEquivalences, AlgebraicTopology.AlternatingFaceMapComplex.ε_app_f_succ, HomologicalComplex.eq_liftCycles_homologyπ_up_to_refinements, HomologicalComplex₂.totalAux.d₂_eq, CategoryTheory.LocalizerMorphism.commShift_iso_hom_app, CategoryTheory.IsHomLift.eqToHom_comp_lift, CategoryTheory.ShortComplex.cyclesMap_neg, AlgebraicGeometry.ExistsHomHomCompEqCompAux.exists_eq, CategoryTheory.Limits.inl_comp_pushoutObjIso_hom, CategoryTheory.Comma.mapRightIso_counitIso_inv_app_left, CategoryTheory.ShortComplex.toCycles_comp_leftHomologyπ_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_hom_app, AlgebraicGeometry.Scheme.ι_toIso_inv, CategoryTheory.section_comp_left_assoc, CategoryTheory.MorphismProperty.RightFraction.map_ofInv_hom_id, CategoryTheory.Abelian.LeftResolution.karoubi.F'_map_f, CochainComplex.mappingCone.d_snd_v, HomologicalComplex.p_fromOpcycles, CategoryTheory.ShortComplex.mapCyclesIso_hom_iCycles_assoc, CategoryTheory.OverPresheafAux.YonedaCollection.map₂_yonedaEquivFst, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.natTrans_app_uliftYoneda_obj, CategoryTheory.Preadditive.isColimitCoforkOfCokernelCofork_desc, CategoryTheory.Limits.biprod.lift_snd, CategoryTheory.Equivalence.cancel_unit_right, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one, CategoryTheory.StrictlyUnitaryPseudofunctor.mk'_map, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_assoc, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_functor_obj, CategoryTheory.Limits.limitConstTerminal_inv_π_assoc, AlgebraicGeometry.Scheme.Hom.stalkSpecializes_stalkMap, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_right, CategoryTheory.Limits.Fork.isoForkOfι_hom_hom, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app, CategoryTheory.GradedObject.mapBifunctorObjObjSingle₀Iso_hom, CategoryTheory.IsCofiltered.bowtie, CategoryTheory.opOp_map, CategoryTheory.Limits.limitOpIsoOpColimit_hom_comp_ι_assoc, AlgebraicGeometry.tilde.map_id, CategoryTheory.GradedObject.mapTrifunctorMapObj_ext_iff, AugmentedSimplexCategory.inr_comp_inl_comp_associator_assoc, HomologicalComplex₂.D₂_totalShift₁XIso_hom_assoc, CategoryTheory.Functor.Monoidal.whiskerRight_app_fst_assoc, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₂, CochainComplex.HomComplex.Cochain.δ_fromSingleMk, CategoryTheory.ForgetEnrichment.equivFunctor_map, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_inv_assoc, TopologicalSpace.OpenNhds.val_apply, CategoryTheory.Limits.pushoutIsoUnopPullback_inr_hom, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct, CommSemiRingCat.hom_id, CategoryTheory.Comma.mapRightEq_hom_app_right, CategoryTheory.MonoidalCategory.hom_inv_id_tensor'_assoc, CategoryTheory.Limits.IsColimit.existsUnique, CategoryTheory.Functor.mapHomotopyEquiv_homotopyHomInvId, HomotopicalAlgebra.instFibrationOppositeOpOfCofibration, CategoryTheory.Limits.CatCospanTransform.triangle_assoc, CategoryTheory.MorphismProperty.pushouts_le, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_inv_app_snd_app, CategoryTheory.Limits.PullbackCone.condition, TopCat.Presheaf.Pushforward.comp_eq, CategoryTheory.Equalizer.firstObjEqFamily_inv, CategoryTheory.Limits.prod.inr_fst_assoc, CategoryTheory.CartesianMonoidalCategory.braiding_hom_snd_assoc, SheafOfModules.unitHomEquiv_symm_comp, CategoryTheory.Presieve.FunctorPushforwardStructure.fac, CategoryTheory.MonoidalPreadditive.whiskerLeft_add, CategoryTheory.unop_mono_iff, CategoryTheory.Limits.BinaryFan.braiding_hom_fst_assoc, CategoryTheory.yonedaEquiv_apply, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_hom, AlgebraicGeometry.Scheme.Hom.preimageIso_hom_ι_assoc, CategoryTheory.Monad.beckCoequalizer_desc, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_hom_iCycles_assoc, Rep.coinvariantsAdjunction_counit_app, CategoryTheory.Limits.isPullback_equalizer_prod, CategoryTheory.Limits.PreservesPushout.inr_iso_hom_assoc, SemiNormedGrp₁.hom_comp, CategoryTheory.coprodMonad_μ_app, CategoryTheory.ShortComplex.HomotopyEquiv.refl_homotopyHomInvId, AlgebraicGeometry.Scheme.IdealSheafData.ideal_le_comap_ideal, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftUnitor_actionHom_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app_assoc, AlgebraicTopology.DoldKan.QInfty_idem, CategoryTheory.ChosenPullbacksAlong.unit_pullbackComp_hom_assoc, CategoryTheory.MorphismProperty.Under.mk_hom, SimplexCategory.δ_comp_σ_self', HomologicalComplex.stupidTruncMap_comp, CategoryTheory.ShortComplex.mapHomologyIso_hom_naturality, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ₀_assoc, CategoryTheory.Limits.Sigma.ι_isoColimit_inv, CategoryTheory.ShortComplex.LeftHomologyData.π_comp_homologyIso_inv, SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_inv_app, CategoryTheory.Limits.PreservesKernel.iso_inv_ι, CategoryTheory.Functor.PullbackObjObj.π_fst, CategoryTheory.Functor.partialRightAdjointHomEquiv_symm_comp, CategoryTheory.RetractArrow.r_w_assoc, CategoryTheory.Functor.FullyFaithful.monObj_mul, CategoryTheory.CommComon.comp_hom, CategoryTheory.Comma.mapRightIso_counitIso_inv_app_right, CategoryTheory.CartesianMonoidalCategory.whiskerRight_snd_assoc, CategoryTheory.Bicategory.rightUnitor_inv_naturality, ChainComplex.isoHomologyι₀_inv_naturality_assoc, CategoryTheory.Enriched.FunctorCategory.isLimitConeFunctorEnrichedHom.fac, CategoryTheory.Functor.Monoidal.transport_μ, ProfiniteGrp.coe_id, CategoryTheory.Abelian.Ext.mk₀_id_comp, CategoryTheory.OplaxFunctor.mapComp_assoc_left_app_assoc, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂, CategoryTheory.Localization.LeftBousfield.galoisConnection, SimplicialObject.Split.comp_f, CategoryTheory.MorphismProperty.Comma.comp_right, CategoryTheory.Limits.BinaryBicone.inl_fst_assoc, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_unitIso, HomologicalComplex.biprodXIso_hom_fst, HomologicalComplex₂.D₂_totalShift₂XIso_hom_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_hom_app, CategoryTheory.sum.inlCompInrCompInverseAssociator_inv_app_down_down, CategoryTheory.Limits.biprod.inlCokernelCofork_π, CategoryTheory.ForgetEnrichment.equivInverse_map, CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoCofanPt_assoc, HomologicalComplex₂.d_f_comp_d_f, CategoryTheory.ObjectProperty.isomorphisms_le_isoModSerre, CategoryTheory.BraidedCategory.hexagon_reverse_assoc, CategoryTheory.Limits.kernelForkBiproductToSubtype_cone, CategoryTheory.StructuredArrow.map₂_map_right, Action.rightDual_ρ, CategoryTheory.PreOneHypercover.Hom.comp_h₀, CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal_ε_unmop_unmop, CategoryTheory.MonoidalCategory.whiskerLeft_dite, CategoryTheory.Functor.biproductComparison'_comp_biproductComparison, CategoryTheory.Pseudofunctor.CoGrothendieck.instIsEquivalenceαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor, TopologicalSpace.OpenNhds.inclusionMapIso_inv, CategoryTheory.IsPushout.of_id_snd, groupHomology.map_id, CategoryTheory.Functor.commShiftIso_comp_hom_app, AlgebraicGeometry.Scheme.isoOfEq_inv_ι, CategoryTheory.OverClass.asOverHom_comp_assoc, CategoryTheory.Comma.mapLeftEq_hom_app_left, CategoryTheory.HalfBraiding.naturality, CategoryTheory.Functor.coreId_hom_app_iso_hom, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₂_app, HomologicalComplex.add_f_apply, CategoryTheory.Monad.monadMonEquiv_counitIso_hom_app_hom, CategoryTheory.Subobject.ofMkLEMk_comp_ofMkLE, CategoryTheory.MonoOver.mapIso_unitIso, LinearMap.comp_id_fgModuleCat, CategoryTheory.MonObj.lift_comp_one_right, CategoryTheory.exactFunctor_le_additiveFunctor, CategoryTheory.CommGrp.id', HomologicalComplex.extend_op_d_assoc, CategoryTheory.CatEnriched.id_hComp_id, CategoryTheory.PreGaloisCategory.instEssSurjContActionFintypeCatHomCarrierAutFunctorFunctorToContAction, CategoryTheory.ComposableArrows.mk₁_eqToHom_comp, CategoryTheory.Limits.CatCospanTransform.rightUnitor_inv_base_app, CategoryTheory.constantCommuteCompose_hom_app_val, CategoryTheory.Square.op_f₁₂, CategoryTheory.CatCenter.smul_iso_inv_eq', HomotopicalAlgebra.Precylinder.LeftHomotopy.h₀_assoc, CategoryTheory.cokernelUnopUnop_inv, CategoryTheory.Limits.image.eq_fac, CategoryTheory.MonoidalCategory.MonoidalLeftAction.action_exchange, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.unit_app_ev_app_app_assoc, CategoryTheory.Bimon.trivial_comon_counit_hom, AlgebraicGeometry.instIsOpenImmersionLeftSchemeDiscretePUnitMapWalkingSpanOverTopMorphismPropertySpan, AlgebraicGeometry.StructureSheaf.exists_const, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight_apply, CategoryTheory.InducedCategory.homEquiv_apply, CategoryTheory.Endofunctor.Adjunction.Algebra.homEquiv_naturality_str, CategoryTheory.Limits.KernelFork.IsLimit.isZero_of_mono, CategoryTheory.Limits.Sigma.ι_desc_assoc, CategoryTheory.Bicategory.Adjunction.homEquiv₁_apply, CategoryTheory.StrictPseudofunctorCore.map₂_associator, CategoryTheory.Limits.desc_op_comp_opCoproductIsoProduct'_hom, CategoryTheory.Bicategory.Prod.swap_map₂, CategoryTheory.Functor.Monoidal.map_μ_δ_assoc, CategoryTheory.Equivalence.cancel_counit_right, CategoryTheory.ObjectProperty.eqToHom_hom, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict_assoc, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_inv_colimit_map_assoc, CategoryTheory.Limits.pullbackDiagonalMapIso.inv_fst_assoc, SimplicialObject.Splitting.ι_desc_assoc, CategoryTheory.Functor.relativelyRepresentable.hom_ext_iff, AlgebraicGeometry.StructureSheaf.toStalk_stalkSpecializes_assoc, CategoryTheory.Functor.Monoidal.lift_μ_assoc, CategoryTheory.Iso.inv_hom_id_triangle_hom₁, groupCohomology.cochainsMap_comp, AlgebraicGeometry.Scheme.Hom.toNormalization_inr_normalizationCoprodIso_hom, CategoryTheory.MorphismProperty.RightFraction.map_s_comp_map_assoc, CategoryTheory.Limits.colimit.desc_extend, CategoryTheory.InjectiveResolution.toRightDerivedZero'_comp_iCycles, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_associator, CategoryTheory.CosimplicialObject.σ_naturality_assoc, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃_tensorHom_assoc, CategoryTheory.monoidalOfHasFiniteProducts.associator_hom, AlgebraicGeometry.Scheme.Modules.Hom.zero_app, AlgebraicGeometry.tilde.map_sub, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_fac_app_assoc, CategoryTheory.Limits.colimit.homIso_hom, CategoryTheory.WithInitial.opEquiv_functor_map, CategoryTheory.MonadHom.comp_toNatTrans, CategoryTheory.Functor.mapConePostcompose_inv_hom, CategoryTheory.Limits.prod.associator_naturality_assoc, CategoryTheory.GlueData.ι_gluedIso_inv, CategoryTheory.BraidedCategory.braiding_inv_naturality_assoc, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_right_as, SemimoduleCat.hom_zsmul, CategoryTheory.tensorRightHomEquiv_whiskerLeft_comp_evaluation, CochainComplex.mappingConeCompTriangle_mor₃, CategoryTheory.Limits.prod.inr_snd_assoc, CategoryTheory.whiskerRight_coprod_inr_rightDistrib_inv_assoc, groupCohomology.comp_d₁₂_eq, CategoryTheory.IsHomLift.commSq, CategoryTheory.Idempotents.Karoubi.HomologicalComplex.comp_p_d, CategoryTheory.Join.mapWhiskerLeft_whiskerRight, CategoryTheory.Pseudofunctor.DescentData.isoMk_inv_hom, AlgebraicGeometry.Scheme.Cover.glued_cover_cocycle, CategoryTheory.Sheaf.isLocallySurjective_comp, CategoryTheory.Endofunctor.Algebra.functorOfNatTransId_inv_app_f, HomologicalComplex₂.d₁_eq_zero', CommRingCat.toAlgHom_comp, CategoryTheory.BasedCategory.comp_def, HomotopicalAlgebra.weakEquivalences_op, CategoryTheory.eqToIso.hom, CategoryTheory.Center.whiskerLeft_comm, AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom_ι, CategoryTheory.Localization.Monoidal.μ_inv_natural_right, CategoryTheory.Iso.op_inv, AlgebraicGeometry.Scheme.congr_app, CategoryTheory.unop_tensor_unop, AlgebraicGeometry.isImmersion_eq_inf, SimplicialObject.opFunctor_obj_map, HomologicalComplex₂.D₁_D₁_assoc, CategoryTheory.ShortComplex.Homotopy.compLeft_h₂, TopologicalSpace.Opens.infLELeft_apply_mk, CategoryTheory.Cat.Hom₂.comp_app_assoc, CategoryTheory.Subgroupoid.le_iff, CategoryTheory.Limits.PreservesCokernel.π_iso_hom_assoc, CategoryTheory.Functor.homologySequence_comp, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_right_hom, HomologicalComplex₂.total.mapAux.mapMap_D₁_assoc, CategoryTheory.Monad.algebraFunctorOfMonadHomId_hom_app_f, Bimod.actRight_one, CategoryTheory.kernelOpUnop_hom, CategoryTheory.Functor.Monoidal.whiskerRight_η_ε, CategoryTheory.prod.rightUnitor_map, CategoryTheory.Functor.IsCoverDense.isoOver_hom_app, CategoryTheory.CommGrp.comp', CategoryTheory.congrArg_cast_hom_right, CategoryTheory.Limits.limit.w_assoc, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_inv_comp_homologyι, AugmentedSimplexCategory.eqToHom_toOrderHom, SimplexCategory.δ_comp_δ_self', CategoryTheory.ShortComplex.SnakeInput.Hom.comp_f₁, Rep.linearization_single, SemiNormedGrp.coe_comp, CategoryTheory.Limits.ι_colimitPointwiseProductToProductColimit_π, CategoryTheory.ShortComplex.comp_τ₁, CategoryTheory.Functor.currying₃_unitIso_hom_app_app_app_app, CategoryTheory.Limits.image.map_comp, SSet.Subcomplex.homOfLE_refl, CategoryTheory.MorphismProperty.RightFraction.ofHom_s, CategoryTheory.Functor.FullyFaithful.compUliftCoyonedaCompWhiskeringLeft_hom_app_app_down, CategoryTheory.InjectiveResolution.of_def, CategoryTheory.Limits.inr_inr_pushoutRightPushoutInlIso_hom, CategoryTheory.Limits.limitIsoLimitCurryCompLim_hom_π_π_assoc, CategoryTheory.Functor.LaxRightLinear.μᵣ_unitality_inv_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHomRight, Homotopy.extend_hom_eq, CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_fst, FintypeCat.instFiniteHom, CochainComplex.HomComplex.Cochain.comp_id, SemimoduleCat.hom_nsmul, ModuleCat.extendRestrictScalarsAdj_homEquiv_apply, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_unit_app, Lat.coe_id, CategoryTheory.Localization.Construction.prodIsLocalization, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₁, CategoryTheory.Limits.prod.lift_fst_assoc, groupHomology.π_comp_H1Iso_inv, CategoryTheory.MorphismProperty.colimitsOfShape_le_coproducts, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_π_app, CategoryTheory.ShortComplex.Homotopy.op_h₀, CategoryTheory.IsSplitEqualizer.ι_leftRetraction, CategoryTheory.Coyoneda.objOpOp_inv_app, CategoryTheory.toOverPullbackIsoToOver_inv_app_left, SheafOfModules.freeHomEquiv_freeMap, AlgebraicGeometry.Scheme.preimage_comp, CategoryTheory.Comma.eqToHom_left, CategoryTheory.Functor.prod'_δ_snd, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_inv, CategoryTheory.Functor.opComp_inv_app, CategoryTheory.Equivalence.unitInv_naturality, CategoryTheory.CostructuredArrow.w_prod_fst_assoc, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom_assoc, PresheafOfModules.sectionsMap_comp, CategoryTheory.Idempotents.Karoubi.idem_assoc, CategoryTheory.Iso.homCongr_trans, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.lift_fac_assoc, CategoryTheory.CartesianMonoidalCategory.associator_inv_fst_snd, CategoryTheory.MonoidalCategory.tensorμ_natural_right_assoc, CategoryTheory.ProjectiveResolution.self_π, CategoryTheory.Bicategory.rightUnitor_inv_congr, CategoryTheory.Monad.id_μ_app, CategoryTheory.Functor.LeftExtension.precomp_map_right, CategoryTheory.Functor.LaxBraided.braided, CategoryTheory.Limits.hasPushoutVertPaste, CategoryTheory.Functor.LaxMonoidal.left_unitality_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_id, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_π_app_walkingParallelPair_one, SemimoduleCat.MonoidalCategory.associator_naturality, SSet.Truncated.Edge.CompStruct.d₂, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_leftUnitor, CategoryTheory.Functor.OplaxMonoidal.δ_snd, HomologicalComplex.homotopyCofiber.inrX_sndX_assoc, CategoryTheory.Functor.IsCartesian.map_self, CategoryTheory.Limits.isColimitCoconeLeftOpOfCone_desc, CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_app_app, CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_fst_snd_assoc, CategoryTheory.GradedObject.zero_apply, CategoryTheory.Equivalence.functor_unit_comp, AlgebraicGeometry.sourceLocalClosure.iff_forall_exists, CategoryTheory.IsPushout.zero_top, CategoryTheory.Limits.cokernelCoforkBiproductFromSubtype_isColimit, CategoryTheory.ProjectiveResolution.cochainComplex_d, CategoryTheory.Comonad.right_counit_assoc, HomotopicalAlgebra.CofibrantObject.homMk_homMk, CategoryTheory.Pseudofunctor.map₂_left_unitor, HomologicalComplex.singleObjCyclesSelfIso_inv_homologyπ, CategoryTheory.Pseudofunctor.CoGrothendieck.map_map_base, CategoryTheory.types_id, CategoryTheory.Limits.pushoutIsoUnopPullback_inl_hom_assoc, CategoryTheory.Limits.CatCospanTransform.category_id_left, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σ, CategoryTheory.Grpd.id_to_functor, CategoryTheory.Bicategory.Adj.forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map, CategoryTheory.Limits.Pi.ι_π_eq_id, CategoryTheory.nonempty_hom_of_preconnected_groupoid, CategoryTheory.types_id_apply, CategoryTheory.Limits.colimitCurrySwapCompColimIsoColimitCurryCompColim_ι_ι_hom, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app', CategoryTheory.MonoidalCategory.whiskerRight_tensor, CochainComplex.HomComplex.Cochain.toSingleMk_neg, CategoryTheory.FreeGroupoid.mapComp_hom_app, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap, CategoryTheory.GradedObject.Monoidal.pentagon, CategoryTheory.SimplicialObject.Augmented.w₀, CategoryTheory.Square.Hom.id_τ₂, CategoryTheory.Functor.RightExtension.coneAt_π_app, CategoryTheory.ShortComplex.homologyMap'_zero, SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_hom_app, CategoryTheory.CommSq.instHasLift, CategoryTheory.Preadditive.IsIso.comp_right_eq_zero, CategoryTheory.StrictPseudofunctor.mk''_mapId, CategoryTheory.Bicategory.associator_inv_naturality_middle, CategoryTheory.Comma.mapRightIso_functor_map_left, CategoryTheory.Limits.Sigma.ι_π_assoc, AlgebraicGeometry.Scheme.Pullback.Triplet.isPullback_SpecMap_tensor, CategoryTheory.Regular.frobeniusStrongEpiMonoFactorisation_I, CategoryTheory.μ_naturality₂_assoc, CategoryTheory.Equivalence.inv_fun_map, CochainComplex.HomComplex.Cochain.ofHom_v_comp_d, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₂_assoc, CategoryTheory.Functor.Monoidal.δ_μ, CategoryTheory.TwoSquare.guitartExact_id', AlgebraicTopology.AlternatingCofaceMapComplex.d_eq_unop_d, TopCat.Presheaf.pushforwardToOfIso_app, CategoryTheory.Idempotents.Karoubi.Biproducts.bicone_ι_f, CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_right, CategoryTheory.Bicategory.associator_naturality_right_assoc, CategoryTheory.ShortComplex.Hom.comm₁₂, CategoryTheory.Pseudofunctor.CoGrothendieck.map_map_fiber, CategoryTheory.MorphismProperty.IsInvertedBy.iff_map_le_isomorphisms, CategoryTheory.Limits.prod.rightUnitor_inv, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_right, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerLeft_naturality_assoc, groupHomology.coresNatTrans_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_hom_inv, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality, CategoryTheory.Functor.prod'CompSnd_inv_app, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁_assoc, HomologicalComplex.unopInverse_map, SimplexCategory.Truncated.δ₂_one_comp_σ₂_one, CategoryTheory.Presheaf.freeYonedaHomEquiv_comp, CategoryTheory.SimplicialObject.σ_naturality, CategoryTheory.OverPresheafAux.yonedaCollectionPresheaf_map, CategoryTheory.Limits.coprod.pentagon, CategoryTheory.Bicategory.hom_inv_whiskerRight_whiskerRight_assoc, CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_of_mono₂, CategoryTheory.StrictlyUnitaryLaxFunctor.mapId_isIso, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_comp, CategoryTheory.Limits.hasPushout_of_epi_comp, CategoryTheory.Groupoid.vertexGroup.inv_eq_inv, CategoryTheory.ShortComplex.RightHomologyData.unop_i, CategoryTheory.Limits.coprod.map_codiag, HomologicalComplex.Hom.next_eq, CategoryTheory.Comma.map_map_right, CategoryTheory.MonoidalCategory.DayConvolution.whiskerRight_comp_unit_app_assoc, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd_assoc, CategoryTheory.CartesianClosed.curry_id_eq_coev, CochainComplex.shiftShortComplexFunctorIso_add'_hom_app, CategoryTheory.Bicategory.triangle_assoc_comp_left, CommBialgCat.id_apply, CategoryTheory.Limits.pullbackProdFstIsoProd_hom_fst_assoc, CategoryTheory.Limits.IsColimit.homIso_hom, CategoryTheory.WithInitial.opEquiv_counitIso_hom_app, CategoryTheory.ShortComplex.Hom.comp_τ₃, AlgebraicGeometry.Scheme.Hom.isOver_iff, CategoryTheory.Adjunction.id_counit, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_hom_app, CategoryTheory.Limits.kernel.condition_apply, CategoryTheory.prodComonad_δ_app, Preord.coe_id, CategoryTheory.Limits.pullbackAssoc_inv_fst_snd, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.ofRestrict_invApp, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom, CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_inv_hom_id_assoc, CategoryTheory.ShortComplex.RightHomologyData.p_g'_assoc, AlgebraicGeometry.Scheme.PartialMap.fromSpecStalkOfMem_compHom, CategoryTheory.WithInitial.isColimitEquiv_symm_apply_desc, CategoryTheory.ShortComplex.homologyMap'_comp, CategoryTheory.Limits.equalizer_as_kernel, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_hom_app_hom, CochainComplex.cm5b.fac, CategoryTheory.Quotient.comp_natTransLift_assoc, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₃_assoc, CategoryTheory.WideSubcategory.id_def, SheafOfModules.instIsRightAdjointPushforwardCompSheafRingCatMapSheafPushforwardContinuous, HomologicalComplex.mapBifunctor₂₃.d₃_eq, CategoryTheory.Quotient.lift.isLift_hom, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_right, CategoryTheory.Bicategory.associator_inv_naturality_right, CategoryTheory.CostructuredArrow.unop_left_comp_ofMkLEMk_unop, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_point_assoc, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivLeft_symm_apply, HomologicalComplex.natIsoSc'_inv_app_τ₂, DerivedCategory.singleFunctorsPostcompQIso_inv_hom, PresheafOfModules.ι_fromFreeYonedaCoproduct, CategoryTheory.MonoidalCategory.id_whiskerLeft, CategoryTheory.Limits.multicospanIndexEnd_snd, AlgebraicGeometry.Spec.locallyRingedSpaceMap_id, CategoryTheory.GrpObj.comp_zpow, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι, CategoryTheory.Bimon.equivMonComonUnitIsoApp_hom_hom_hom, CategoryTheory.MonoidalCategory.id_tensorHom, CategoryTheory.leftAdjointOfStructuredArrowInitialsAux_apply, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_hom_app_hom_hom_app, CategoryTheory.Limits.colimitIsoSwapCompColim_hom_app, AlgebraicGeometry.descendsAlong_isomorphisms_surjective_inf_flat_inf_quasicompact, CochainComplex.HomComplex.Cochain.toSingleMk_v, groupCohomology.eq_d₂₃_comp_inv_assoc, HomologicalComplex.extend.d_none_eq_zero', CategoryTheory.Limits.BinaryBiconeMorphism.winr, CategoryTheory.ShortComplex.HomologyMapData.add_left, CategoryTheory.Localization.HasProductsOfShapeAux.adj_counit_app, CategoryTheory.Monad.algebraEquivOfIsoMonads_unitIso, CategoryTheory.Functor.Monoidal.whiskerLeft_μ_δ, groupCohomology.congr, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_hom_app_val_app, CategoryTheory.Functor.IsStronglyCocartesian.universal_property', CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_hom_comp_homologyIso_inv, CategoryTheory.Functor.mapTriangleCompIso_hom_app_hom₂, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₃, HomologicalComplex₂.D₁_D₁, CategoryTheory.Subfunctor.Subpresheaf.preimage_id, CategoryTheory.Limits.kernelSubobjectIsoComp_hom_arrow, CategoryTheory.Adjunction.compYonedaIso_hom_app_app, RingCat.hom_comp, PresheafOfModules.freeYonedaEquiv_symm_app, SSet.Subcomplex.toRange_ι_assoc, CommRingCat.coyoneda_map_app, AlgebraicGeometry.AffineSpace.map_over_assoc, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapCompIso_hom, CategoryTheory.Functor.currying_counitIso_hom_app_app, CategoryTheory.Limits.biproduct.matrixEquiv_symm_apply, AlgebraicGeometry.Scheme.IdealSheafData.inclusion_subschemeι_assoc, CategoryTheory.zero_map, CategoryTheory.Sheaf.isLocallySurjective_iff_epi, CategoryTheory.InjectiveResolution.complex_d_comp, CategoryTheory.MorphismProperty.Over.mapCongr_inv_app_left, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app_assoc, CategoryTheory.leftDistributor_hom, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.associator_hom_unit_unit, TopCat.Presheaf.germ_res', CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapComp_hom, CategoryTheory.Over.mapId_eq, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.w_app, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_fiber, HomologicalComplex.restrictionCyclesIso_hom_iCycles, CategoryTheory.MonoidalCategory.DayFunctor.ν_comp_unitDesc_assoc, CategoryTheory.Functor.RightExtension.postcomp₁_map_right, AlgebraicGeometry.IsClosedImmersion.comp, CategoryTheory.Limits.PushoutCocone.condition_assoc, CategoryTheory.MorphismProperty.monotone_map, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_l, CategoryTheory.epi_comp_iff_of_epi, CategoryTheory.ShortComplex.unopFunctor_map, CategoryTheory.Limits.PreservesCokernel.of_iso_comparison, CategoryTheory.Bicategory.whiskerLeft_comp, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompCoyoneda, CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_comp, TopologicalSpace.Opens.map_comp_obj_unop, CategoryTheory.Functor.Monoidal.map_rightUnitor_inv, CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_snd, CategoryTheory.Limits.colimit.ι_map, CategoryTheory.Functor.prod'CompSnd_hom_app, SSet.RelativeMorphism.Homotopy.h₀_assoc, HomologicalComplex.homotopyCofiber.desc_f', CategoryTheory.Subobject.ofMkLE_arrow, HomologicalComplex.single_obj_d, CategoryTheory.ObjectProperty.isCodetecting_bot_of_isGroupoid, CategoryTheory.Iso.isoInverseComp_hom_app, CategoryTheory.CategoryOfElements.homMk_coe, CategoryTheory.ForgetEnrichment.homOf_eId, CategoryTheory.Over.prodLeftIsoPullback_inv_snd, CategoryTheory.tensorLeftHomEquiv_naturality, CategoryTheory.Functor.mapActionComp_hom, CategoryTheory.whiskerLeft_coprod_inl_leftDistrib_inv, CategoryTheory.ShortComplex.leftRightHomologyComparison_fac, HomologicalComplex₂.D₂_D₁_assoc, CategoryTheory.BasedNatIso.id_hom, CochainComplex.IsKInjective.Qh_map_bijective, CategoryTheory.FinCategory.categoryAsType_comp, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionActionOfMonoidalFunctorToEndofunctorIso_inv_app_app, CategoryTheory.Limits.pushoutIsoUnopPullback_inr_hom_assoc, CategoryTheory.Limits.PreservesPullback.iso_inv_fst_assoc, CategoryTheory.IsPushout.inl_isoIsPushout_inv, CategoryTheory.eqToHom_heq_id_cod, CategoryTheory.Limits.piObjIso_hom_comp_π, HomotopicalAlgebra.cofibration_op_iff, CategoryTheory.leftAdjointOfStructuredArrowInitialsAux_symm_apply, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_left, CategoryTheory.MonoidalClosed.uncurry_natural_left_assoc, CategoryTheory.Limits.Cones.extendId_inv_hom, CategoryTheory.Pseudofunctor.ObjectProperty.ι_app_toFunctor, CategoryTheory.ShortComplex.Homotopy.op_h₂, TopCat.Sheaf.interUnionPullbackCone_fst, CategoryTheory.Iso.inv_comp_eq_id, CategoryTheory.GradedObject.mapMap_comp_assoc, CategoryTheory.kernelCokernelCompSequence.snakeInput_v₂₃_τ₃, Bimod.left_assoc_assoc, CategoryTheory.ObjectProperty.instIsClosedUnderColimitsOfShapeUnopOppositeOfIsClosedUnderLimitsOfShape, CategoryTheory.MonoidalCategory.tensorμ_natural_right, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_map_app, CategoryTheory.ShortComplex.SnakeInput.L₀X₂ToP_comp_pullback_snd, ModuleCat.restrictScalarsId'App_hom_naturality, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map, HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac', CategoryTheory.Bicategory.conjugateEquiv_symm_id, CategoryTheory.whiskerRight_coprod_inl_rightDistrib_inv, CategoryTheory.Discrete.sumEquiv_inverse_map, CategoryTheory.Limits.span_map_id, CategoryTheory.Over.iteratedSliceForwardIsoPost_inv_app, CategoryTheory.ShortComplex.SnakeInput.id_f₂, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.ShortComplex.LeftHomologyData.ofAbelian_H, CategoryTheory.IsSifted.factorization_prodComparison_colim, CategoryTheory.Comma.mapRight_obj_hom, CategoryTheory.NatIso.naturality_1, CategoryTheory.MorphismProperty.IsStableUnderComposition.unop, CategoryTheory.ShortComplex.ShortExact.comp_δ, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv, CategoryTheory.LaxBraidedFunctor.comp_hom, CategoryTheory.Comma.mapRightIso_inverse_map_right, CategoryTheory.ObjectProperty.hasCardinalLT_subtype_ofObj, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_le_transfiniteCompositions, ProfiniteGrp.ProfiniteCompletion.lift_eta_assoc, CategoryTheory.Grp.ε_def, CategoryTheory.MorphismProperty.RightFraction.map_hom_ofInv_id, AlgebraicGeometry.IsSeparated.instIsClosedImmersionLiftSchemeId, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app, AlgebraicGeometry.Scheme.Pullback.tensorCongr_SpecTensorTo, CategoryTheory.Limits.kernelBiprodFstIso_hom, CategoryTheory.MonoidalClosed.uncurry_pre_app_assoc, CategoryTheory.ShortComplex.RightHomologyData.copy_p, CategoryTheory.Oplax.StrongTrans.Modification.whiskerLeft_naturality, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_hom_assoc, CategoryTheory.Abelian.coimage_image_factorisation, AlgebraicGeometry.IsSeparated.eq_valuativeCriterion, CategoryTheory.Limits.Cocones.whiskeringEquivalence_unitIso, CommSemiRingCat.ofHom_comp, CategoryTheory.LaxFunctor.mapComp_naturality_left_app_assoc, CategoryTheory.Bicategory.conjugateEquiv_apply, CategoryTheory.Bicategory.prod_whiskerRight_fst, AlgebraicGeometry.Scheme.Hom.SpecMap_residueFieldMap_fromSpecResidueField_assoc, CategoryTheory.op_epi_iff, CategoryTheory.Iso.inv_hom_id_triangle_hom₂_assoc, CommRingCat.ofHom_id, CategoryTheory.Sheaf.comp_val, CategoryTheory.Limits.image.lift_fac_assoc, CategoryTheory.InjectiveResolution.desc_commutes_zero_assoc, CategoryTheory.Limits.monoFactorisationZero_e, CategoryTheory.Functor.FullyFaithful.map_bijective, CategoryTheory.Adjunction.eq_homEquiv_apply, CategoryTheory.Limits.Multifork.isoOfι_inv_hom, CategoryTheory.Functor.ShiftSequence.induced.isoZero_hom_app_obj, CategoryTheory.Sum.functorEquiv_unit_app_app_inr, CategoryTheory.Injective.comp_factorThru_assoc, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoColimitUncurryWhiskeringLeft₂_inv_assoc, CategoryTheory.Limits.colimitCurrySwapCompColimIsoColimitCurryCompColim_ι_ι_inv, CategoryTheory.Pseudofunctor.DescentData.comp_hom, CategoryTheory.Bicategory.whiskerRight_comp_symm, CategoryTheory.pathComposition_obj, Semigrp.ofHom_comp, CategoryTheory.Functor.LaxRightLinear.μᵣ_associativity_inv_assoc, CategoryTheory.Functor.IsCartesian.domainUniqueUpToIso_inv_isHomLift, CategoryTheory.Iso.conj_pow, CategoryTheory.Functor.shiftMap_comp', CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε, CategoryTheory.rightUnitor_inv_braiding, CategoryTheory.Limits.MonoFactorisation.compMono_I, CategoryTheory.GradedObject.Monoidal.rightUnitor_naturality_assoc, StalkSkyscraperPresheafAdjunctionAuxs.germ_fromStalk, CategoryTheory.MonoidalCategory.DayFunctor.id_natTrans, CategoryTheory.Limits.walkingParallelPairHom_id, SSet.stdSimplex.map_id, AlgebraicGeometry.IsImmersion.comp, HomologicalComplex.biprod_lift_fst_f, SSet.Subcomplex.lift_ι_assoc, HomologicalComplex.XIsoOfEq_hom_comp_d_assoc, CategoryTheory.Presieve.FamilyOfElements.compatible_singleton_iff, CategoryTheory.NatTrans.vcomp_app', CategoryTheory.Grothendieck.comp_base, CategoryTheory.Endofunctor.Algebra.ext_iff, CategoryTheory.monoidalOpOp_δ, CategoryTheory.Adjunction.Triple.rightToLeft_eq_units, HomologicalComplex.pOpcycles_opcyclesIsoSc'_inv_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv, SimplicialObject.Splitting.cofan_inj_eq, CategoryTheory.Bicategory.Pith.comp₂_iso_hom_assoc, CategoryTheory.Limits.inl_pushoutAssoc_inv_assoc, CategoryTheory.Limits.coker_map, Bimod.right_assoc, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_inv_app_left, DerivedCategory.subsingleton_hom_of_isStrictlyLE_of_isStrictlyGE, HomologicalComplex.ιTruncLE_naturality, CategoryTheory.MonObj.ofRepresentableBy_one, CategoryTheory.HasShift.Induced.zero_inv_app_obj, CategoryTheory.ReflQuiv.id_map, AlgebraicGeometry.Scheme.LocalRepresentability.instIsLocallySurjectiveHomYonedaGluedToSheafOfIsLocallySurjectiveZariskiTopologyDescFunctorOppositeType, SimplexCategoryGenRel.standardσ_simplicialInsert, CategoryTheory.Limits.Cocones.eta_inv_hom, CategoryTheory.ConcreteCategory.comp_apply, AlgebraicGeometry.Scheme.Hom.toNormalization_fromNormalization_assoc, CategoryTheory.StructuredArrow.eta_hom_right, CategoryTheory.Subobject.ofLE_arrow_assoc, CategoryTheory.ShortComplex.cyclesMap_sub, CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_inv, CategoryTheory.GradedObject.Monoidal.symmetry, CategoryTheory.IsPullback.inr_fst, HomologicalComplex₂.D₂_D₂, CategoryTheory.Cat.leftUnitor_hom_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.hom_inv_actionHomLeft'_assoc, CategoryTheory.Functor.curry₃_obj_obj_map_app, CategoryTheory.Bicategory.associator_eqToHom_hom_assoc, CategoryTheory.LocallyDiscrete.subsingleton2Hom, CategoryTheory.Limits.pullback_diagonal_map_snd_snd_fst_assoc, CommGrpCat.coe_comp, ModuleCat.exteriorPower.iso₀_hom_naturality, CategoryTheory.Limits.inr_inl_pushoutLeftPushoutInrIso_hom, CategoryTheory.shift_shift_neg', CategoryTheory.NatTrans.CommShift.shift_comm, CategoryTheory.NatTrans.naturality_2_assoc, CategoryTheory.ShortComplex.Homotopy.g_h₃_assoc, HomologicalComplex.truncLE'_d_eq_toCycles, CategoryTheory.GrpObj.lift_inv_comp_right, CategoryTheory.IsPullback.id_horiz, CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_snd, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_inv_app, CategoryTheory.CostructuredArrow.prodFunctor_map, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_left_right, CategoryTheory.Sum.functorEquiv_unitIso_inv_app_app_inl, CategoryTheory.Limits.kernelFactorThruImage_hom_comp_ι_assoc, CategoryTheory.Retract.retract, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimIso_aux_assoc, CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inr_assoc, CategoryTheory.LocalizerMorphism.commShift_iso_inv_app, CategoryTheory.FinCategory.asTypeToObjAsType_map, CategoryTheory.MonoidalCategory.id_tensor_comp_tensor_id, CategoryTheory.Bicategory.whiskerRight_id, CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv'_assoc, CategoryTheory.Grothendieck.isoMk_inv_fiber, CategoryTheory.GradedObject.ιMapBifunctor₁₂BifunctorMapObj_eq_assoc, Homotopy.prevD_succ_cochainComplex, CategoryTheory.Limits.prod.symmetry'_assoc, CategoryTheory.IsCardinalLocallyPresentable.iff_exists_isStrongGenerator, CategoryTheory.Limits.WalkingReflexivePair.leftCompReflexion_eq, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality_assoc, SimplexCategory.Truncated.δ₂_zero_comp_δ₂_two_assoc, CommMonCat.hom_comp, AlgebraicGeometry.IsClosedImmersion.eq_proper_inf_monomorphisms, SSet.exists_nonDegenerate, CategoryTheory.MonoOver.mapIso_counitIso, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_hom, CategoryTheory.Limits.PushoutCocone.op_snd, CategoryTheory.Limits.isColimitOfConeRightOpOfCocone_desc, CategoryTheory.HasShift.Induced.add_hom_app_obj, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_hom_fac_app, HomotopicalAlgebra.FibrantObject.HoCat.exists_resolution_map, HomologicalComplex.d_toCycles_assoc, CategoryTheory.Abelian.coim_map, CategoryTheory.Limits.coend.condition, CategoryTheory.kernel_zero_of_nonzero_from_simple, CategoryTheory.sheafToPresheaf_μ, ContinuousMap.Homotopy.heq_path_of_eq_image, CategoryTheory.NatTrans.mapHomologicalComplex_id, CategoryTheory.ExponentiableMorphism.comp_pushforward, CategoryTheory.biproduct_ι_comp_rightDistributor_hom, HasFibers.homLift, CategoryTheory.LocalizerMorphism.hasLeftResolutions_iff_op, HomologicalComplex₂.ιTotalOrZero_map_assoc, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₁_app, CategoryTheory.rightDistributor_hom_comp_biproduct_π_assoc, CategoryTheory.Cat.FreeRefl.homMk_id, CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLift_assoc, CategoryTheory.CatCommSq.hComp_iso_hom_app, CategoryTheory.pullbackShiftFunctorZero_inv_app, CategoryTheory.ShortComplex.Splitting.id, CategoryTheory.Subobject.ofMkLE_comp_ofLEMk_assoc, CategoryTheory.Functor.mapTriangleRotateIso_inv_app_hom₁, BddDistLat.hom_id, CategoryTheory.Under.liftCone_pt, TopCat.Presheaf.germ_res_apply, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompPointIso_hom_app, CategoryTheory.StructuredArrow.prodInverse_map, HomologicalComplex₂.ιTotal_map, CategoryTheory.Limits.biprod.inr_snd_assoc, CategoryTheory.Limits.PullbackCone.unop_inl, CategoryTheory.Iso.homFromEquiv_symm_apply, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app, CategoryTheory.MonObj.comp_mul_assoc, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivLeft_apply, CategoryTheory.NatTrans.rightOp_comp, groupHomology.π_comp_H0Iso_hom_assoc, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans, CategoryTheory.StructuredArrow.eta_inv_right, HomologicalComplex.xPrevIsoSelf_comp_dTo, CategoryTheory.isIso_comp_right_iff, CategoryTheory.Discrete.compNatIsoDiscrete_hom_app, CategoryTheory.uliftCoyonedaEquiv_uliftCoyoneda_map, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_hom_fac_app, SheafOfModules.unitHomEquiv_symm_freeHomEquiv_apply, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality, CategoryTheory.comul_eq_lift, CategoryTheory.MorphismProperty.IsMultiplicative.instTop, CochainComplex.homotopyUnop_hom_eq, CategoryTheory.Functor.RepresentableBy.coyoneda_homEquiv, CategoryTheory.CostructuredArrow.mapIso_unitIso_hom_app_left, CategoryTheory.TwoSquare.equivNatTrans_apply, CategoryTheory.CatCommSq.iso_inv_naturality, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_comp, Rep.resCoindAdjunction_unit_app_hom_hom, CategoryTheory.ShortComplex.Homotopy.add_h₁, CochainComplex.HomComplex.Cochain.toSingleMk_add, CategoryTheory.Dial.triangle, CategoryTheory.Kleisli.Adjunction.toKleisli_map, CategoryTheory.coyonedaEquiv_comp, HomologicalComplex₂.ι_totalShift₁Iso_hom_f_assoc, CategoryTheory.uliftYonedaEquiv_symm_apply_app, groupHomology.d₃₂_comp_d₂₁_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.hom_inv_actionHomLeft_assoc, CategoryTheory.Functor.mapProjectiveResolution_π, CategoryTheory.Limits.Cocones.whiskeringEquivalence_inverse, CategoryTheory.Adjunction.localization_unit_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_def'_assoc, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₂, CategoryTheory.NatTrans.app_naturality, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_left, HomologicalComplex.cyclesMap_id, CategoryTheory.CartesianMonoidalCategory.tensorμ_fst_assoc, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom, CategoryTheory.Limits.inr_opProdIsoCoprod_inv_assoc, CategoryTheory.Limits.isLimitOfCoconeOfConeRightOp_lift, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd_assoc, CategoryTheory.ObjectProperty.isoHom_inv_id_hom, CategoryTheory.Abelian.Ext.mk₀_neg, SimplexCategory.const_subinterval_eq, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₂, CategoryTheory.Limits.isoZeroOfEpiZero_hom, CategoryTheory.IsHomLift.comp_lift_id_right, AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimage, CategoryTheory.Oplax.LaxTrans.naturality_comp_assoc, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_π_assoc, CategoryTheory.Functor.Monoidal.map_leftUnitor_inv, CategoryTheory.EnrichedCat.associator_inv_out_app, CategoryTheory.Limits.PushoutCocone.isoMk_inv_hom, CategoryTheory.Limits.colimitYonedaHomIsoLimit'_π_apply, CategoryTheory.Prod.symmetry_hom_app, CategoryTheory.Limits.π_comp_colimitLeftOpIsoUnopLimit_inv, CategoryTheory.WithInitial.liftFromUnderComp_inv_app, HomologicalComplex.opcyclesOpIso_inv_naturality, CategoryTheory.NatTrans.Equifibered.comp, CategoryTheory.conjugateEquiv_symm_apply_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_id_assoc, AlgebraicGeometry.Scheme.ι_toIso_inv_assoc, HomologicalComplex.ι_mapBifunctorAssociatorX_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionActionOfMonoidalFunctorToEndofunctorMopIso_hom_app_unmop_app, CategoryTheory.Limits.WalkingParallelPair.inclusionWalkingReflexivePair_map, AlgebraicGeometry.Scheme.Hom.id_preimage, CategoryTheory.HopfObj.mul_antipode, HomologicalComplex.mapBifunctor₁₂.ι_D₁_assoc, CategoryTheory.Groupoid.invFunctor_map, ModuleCat.endRingEquiv_symm_apply_hom, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality, CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_snd_assoc, BddOrd.coe_id, CochainComplex.mappingCone.inr_f_d, CategoryTheory.Over.tensorObj_ext_iff, CategoryTheory.coreCategory_id_iso_inv, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_right, CategoryTheory.Join.mapWhiskerLeft_whiskerLeft, FGModuleCat.instFiniteHomModuleCatObjIsFG, CategoryTheory.Limits.Cone.toStructuredArrowCompProj_inv_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.inv_hom_actionHomLeft, HomologicalComplex.extend.XOpIso_hom_d_op, CategoryTheory.Limits.parallelPairOpIso_inv_app_one, CategoryTheory.RetractArrow.i_w, CategoryTheory.IsSplitEqualizer.condition_assoc, CategoryTheory.ε_η_app_assoc, CategoryTheory.Oplax.OplaxTrans.categoryStruct_comp_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_right_unitality_assoc, CategoryTheory.MorphismProperty.IsMultiplicative.inf, CategoryTheory.Join.inrCompFromSum_hom_app, CategoryTheory.CommGrp.comp_hom, AlgebraicGeometry.Scheme.Hom.toImage_imageι, CategoryTheory.ShortComplex.RightHomologyMapData.id_φH, CategoryTheory.Functor.PreservesRightKanExtension.preserves, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app', CategoryTheory.CostructuredArrow.toOver_map_right, CategoryTheory.Limits.FormalCoproduct.category_comp_f, AlgebraicGeometry.Scheme.IdealSheafData.ideal_le_ker_glueDataObjι, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_c_app, CategoryTheory.ReflQuiv.comp_map, CategoryTheory.OppositeShift.adjunction_unit, CategoryTheory.MonoidalPreadditive.add_whiskerRight, TopCat.Presheaf.germ_stalkPullbackInv_assoc, CategoryTheory.CostructuredArrow.map_obj_hom, CategoryTheory.LaxFunctor.id_mapId, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_snd_coe, CategoryTheory.ε_naturality_assoc, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_hom_whiskerRight_π_assoc, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_tensorDec, CategoryTheory.Localization.Monoidal.pentagon_aux₂, CategoryTheory.Comma.toPUnitIdEquiv_counitIso_hom_app, AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_pullbackHom, CategoryTheory.MonoidalCategory.rightUnitor_inv_comp_tensorHom_assoc, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagram_map, CategoryTheory.MonoidalCategory.id_tensor_rightUnitor_inv_assoc, CategoryTheory.coev_expComparison, CategoryTheory.MonoidalCategory.prodCompExternalProduct_inv_app, CategoryTheory.Equivalence.mkHom_id_inverse, CategoryTheory.nerve.homEquiv_apply, CategoryTheory.ShortComplex.leftRightHomologyComparison'_fac, AlgebraicGeometry.Scheme.eqToHom_c_app, CategoryTheory.Limits.FormalCoproduct.hom_ext_iff, CategoryTheory.FreeGroupoid.mapId_hom_app, CategoryTheory.MonoidalClosed.uncurry_natural_right_assoc, Rep.homEquiv_apply_hom, CategoryTheory.MorphismProperty.RespectsIso.unop, CategoryTheory.Functor.Monoidal.map_associator, HeytAlg.hom_comp, BddOrd.hom_id, HomologicalComplex₂.ι_D₁_assoc, CategoryTheory.MonoidalCategory.eqToHom_whiskerRight, CategoryTheory.Limits.IsColimit.ι_map, CategoryTheory.isIso_iff_coyoneda_map_bijective, CategoryTheory.Functor.mapMatComp_hom_app, CategoryTheory.Limits.colimit.ι_post, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π_assoc, CategoryTheory.Limits.Types.binaryCoproductCocone_ι_app, CategoryTheory.Sigma.mapComp_hom_app, CategoryTheory.conjugateEquiv_apply_app, CategoryTheory.StrictPseudofunctor.id_obj, CategoryTheory.Limits.biproductBiproductIso_hom, HomotopicalAlgebra.Cylinder.ofFactorizationData_i₀, CochainComplex.HomComplex.δ_v, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_left, CategoryTheory.CatCenter.mul_app, CategoryTheory.Monad.Algebra.assoc_assoc, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_id, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_inv_app_app_fst, CategoryTheory.Limits.biproduct.fromSubtype_toSubtype_assoc, AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_hom_π, CategoryTheory.SmallObject.SuccStruct.ofCocone_map_assoc, CategoryTheory.Groupoid.isThin_iff, CategoryTheory.Limits.kernelBiproductπIso_hom, CategoryTheory.Functor.partialLeftAdjointHomEquiv_symm_comp, AlgebraicGeometry.PresheafedSpace.componentwiseDiagram_map, groupCohomology.mapShortComplexH2_comp_assoc, AlgebraicGeometry.PresheafedSpace.stalkMap_germ_assoc, CategoryTheory.rightDistributor_ext₂_left_iff, Rep.FiniteCyclicGroup.chainComplexFunctor_obj, CategoryTheory.Abelian.tfae_epi, CategoryTheory.Idempotents.app_p_comp, CategoryTheory.MonoidalCategory.whiskerRight_id_symm_assoc, CategoryTheory.ShortComplex.SnakeInput.comp_f₀, CategoryTheory.Limits.kernelCompMono_hom, AlgebraicGeometry.Scheme.Cover.comp_app, CategoryTheory.toSheafify_sheafifyLift_assoc, CategoryTheory.Oplax.StrongTrans.homCategory_id_as_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom, AlgebraicGeometry.Proj.basicOpenToSpec_app_top, CategoryTheory.Limits.compYonedaSectionsEquiv_apply_app, CategoryTheory.exp.coev_ev, CategoryTheory.Idempotents.add_def, HomologicalComplex.d_comp_d_assoc, CategoryTheory.cokernelOpOp_hom, CategoryTheory.Endofunctor.Algebra.functorOfNatTransComp_hom_app_f, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_naturality, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.ofRestrict_invApp, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, CategoryTheory.Limits.biprod.symmetry, CategoryTheory.Comma.mapSnd_inv_app, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_naturality, CategoryTheory.ShortComplex.op_pOpcycles_opcyclesOpIso_hom, CategoryTheory.MonoidalOpposite.unmopEquiv_inverse_map_unmop, CategoryTheory.SimplicialObject.δ_comp_σ_succ'_assoc, CategoryTheory.ShortComplex.opcyclesMap'_id, ContinuousMap.Homotopy.eq_path_of_eq_image, CategoryTheory.SimplicialObject.δ_def, CategoryTheory.ShortComplex.HomologyMapData.neg_left, CochainComplex.HomComplex.Cochain.comp_v, CategoryTheory.Limits.WidePushout.hom_eq_desc, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp, HomologicalComplex.forgetEval_hom_app, HomologicalComplex.homologyι_singleObjOpcyclesSelfIso_inv, CategoryTheory.GradedObject.Monoidal.rightUnitor_inv_apply, CategoryTheory.ShortComplex.π_leftRightHomologyComparison'_ι, CategoryTheory.MorphismProperty.colimitsOfShape_le, HomologicalComplex₂.ιTotal_totalFlipIso_f_inv_assoc, AddCommGrpCat.coe_comp, CategoryTheory.MonoidalCategory.tensorμ_comp_μ_tensorHom_μ_comp_μ_assoc, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, AlgebraicGeometry.AffineSpace.homOverEquiv_symm_apply_coe, CategoryTheory.Limits.BinaryBicone.sndKernelFork_ι, CategoryTheory.Square.Hom.comm₁₃_assoc, CategoryTheory.Functor.homologySequenceδ_naturality, CategoryTheory.Functor.compConstIso_hom_app_app, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_app_assoc, CategoryTheory.Preadditive.commGrpEquivalence_unitIso_inv_app, CategoryTheory.Bicategory.InducedBicategory.eqToHom_hom, CochainComplex.fromSingle₀Equiv_apply_coe, CategoryTheory.ObjectProperty.unop_isoClosure, CategoryTheory.Functor.FullyFaithful.nonempty_iff_map_bijective, commBialgCatEquivComonCommAlgCat_unitIso_hom_app, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app, CategoryTheory.Limits.CategoricalPullback.id_fst, SimplexCategory.σ_injective, CategoryTheory.Functor.coreComp_hom_app_iso_hom, CategoryTheory.CatCommSq.vId_iso_hom_app, CategoryTheory.CategoryOfElements.to_comma_map_right, CategoryTheory.Pseudofunctor.Grothendieck.ext_iff, CategoryTheory.Functor.prod'_ε_fst, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_inv_app_snd_app, CategoryTheory.Limits.Cofork.unop_op_π, CategoryTheory.GradedObject.Monoidal.leftUnitor_inv_apply, Rep.coindFunctorIso_hom_app_hom_hom_apply_hom_hom_apply, CategoryTheory.Functor.imageSieve_eq_imageSieve, CategoryTheory.WithTerminal.opEquiv_counitIso_inv_app, CategoryTheory.frobeniusMorphism_mate, CategoryTheory.Functor.IsEventuallyConstantTo.isoMap_inv_hom_id, CategoryTheory.eHomWhiskerRight_comp_assoc, CategoryTheory.Subgroupoid.IsWide.eqToHom_mem, CochainComplex.HomComplex.Cochain.comp_zero_cochain_v, HomologicalComplex.dgoToHomologicalComplex_obj_d, CategoryTheory.NatIso.naturality_1'_assoc, CategoryTheory.Bicategory.lanLiftUnit_desc_assoc, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right', CategoryTheory.Localization.liftNatTrans_zero, CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.liftHom_fac_assoc, Lat.hom_comp, CategoryTheory.Adjunction.ε_comp_map_ε_assoc, CategoryTheory.Limits.BinaryFan.IsLimit.lift'_coe, CategoryTheory.tensorRightHomEquiv_whiskerRight_comp_evaluation, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_fst, CategoryTheory.toOverIsoToOverUnit_inv_app_left, CategoryTheory.MorphismProperty.IsLocalAtSource.inf, CategoryTheory.MorphismProperty.Over.mk_hom, CategoryTheory.ShortComplex.Homotopy.smul_h₂, CategoryTheory.Equivalence.sheafCongrPreregular_inverse_obj_val_map, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_inv_app_hom_left, PresheafOfModules.id_app, CategoryTheory.Codiscrete.natIsoFunctor_hom_app, CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.full, SimplicialObject.Split.comp_F, CategoryTheory.MorphismProperty.Over.pullback_obj_left, CategoryTheory.Subobject.inf_comp_left, CategoryTheory.Functor.flipping_counitIso_inv_app_app_app, CategoryTheory.Bicategory.whiskerLeft_hom_inv, CategoryTheory.Limits.colimit.map_desc, HomotopyCategory.quotient_map_eq_zero_iff, CochainComplex.mappingCone.inr_f_descShortComplex_f_assoc, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app, CategoryTheory.MorphismProperty.Over.map_map_left, CategoryTheory.Abelian.Pseudoelement.zero_eq_zero', CategoryTheory.Lax.LaxTrans.id_app, CategoryTheory.ShortComplex.RightHomologyMapData.op_φK, CommMonCat.coe_comp, CategoryTheory.Under.mapCongr_inv_app, CategoryTheory.Limits.Types.binaryProductIso_inv_comp_fst, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.presheafHom_naturality, CategoryTheory.instSmallHomOfLocallySmall, CategoryTheory.Subobject.factors_add, Bimod.id_whiskerLeft_bimod, CategoryTheory.StrictlyUnitaryLaxFunctor.id_obj, CategoryTheory.NatTrans.hcomp_app, CategoryTheory.ShortComplex.opMap_id, CochainComplex.HomComplex.Cochain.neg_v, CochainComplex.HomComplex.Cocycle.equivHomShift'_symm_apply, CategoryTheory.Limits.Pi.reindex_hom_π_assoc, CategoryTheory.ShortComplex.LeftHomologyMapData.op_φH, AlgebraicGeometry.Scheme.Opens.isoOfLE_hom_ι_assoc, CategoryTheory.Dial.braiding_naturality_right, CategoryTheory.Limits.CatCospanTransform.whiskerleft_id, CategoryTheory.Pseudofunctor.mapComp'_inv_naturality, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_map, CategoryTheory.Idempotents.Karoubi.comp_p, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_snd, prodIsoPullback_inv_fst_assoc, SimplexCategory.II_σ, CochainComplex.HomComplex.Cochain.sub_v, CategoryTheory.Functor.FullyFaithful.preimage_comp, CategoryTheory.Linear.units_smul_comp, CategoryTheory.SmallObject.SuccStruct.arrowMap_refl, CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.f', CategoryTheory.MonoidalCategory.tensor_whiskerLeft_symm_assoc, CategoryTheory.Bicategory.mateEquiv_id_comp_right, CategoryTheory.Limits.PullbackCone.op_pt, CategoryTheory.Discrete.id_def, CategoryTheory.Limits.Cocone.w_assoc, AlgebraicGeometry.Scheme.toSpecΓ_naturality_assoc, CategoryTheory.Adjunction.conjugateEquiv_leftAdjointCompIso_inv, CategoryTheory.Linear.leftComp_apply, CategoryTheory.ShortComplex.cyclesMap'_comp_assoc, CategoryTheory.Functor.OplaxMonoidal.δ_fst_assoc, CategoryTheory.Bicategory.leftUnitor_comp_inv, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_inv_π_assoc, CategoryTheory.MorphismProperty.RightFractionRel.unop, CategoryTheory.Functor.curryObjProdComp_hom_app_app, HomologicalComplex.XIsoOfEq_inv_naturality_assoc, CategoryTheory.Limits.Pi.reindex_hom_π, AlgebraicGeometry.Scheme.Modules.pushforwardComp_inv_app_app, CochainComplex.mappingCone.liftCochain_v_descCochain_v, CategoryTheory.GradedObject.CofanMapObjFun.inj_iso_hom, CategoryTheory.oppositeShiftFunctorAdd_inv_app, CategoryTheory.Idempotents.app_p_comm, AlgebraicGeometry.LocallyQuasiFinite.comp_iff, CategoryTheory.Functor.associator_hom_app, CategoryTheory.Functor.Linear.map_smul, Homotopy.nullHomotopicMap'_f_eq_zero, CategoryTheory.Presheaf.restrictedULiftYoneda_obj_map, CategoryTheory.Pseudofunctor.mapComp_id_left, SSet.Truncated.HomotopyCategory.multiplicativeClosure_morphismPropertyHomMk, CategoryTheory.Limits.inr_comp_pushoutObjIso_hom_assoc, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition_assoc, CategoryTheory.CopyDiscardCategory.copy_tensor, CategoryTheory.Limits.IsBilimit.total, CategoryTheory.Sieve.mem_ofObjects_iff, BddDistLat.coe_id, CategoryTheory.IsIso.inv_comp, CategoryTheory.Limits.pushoutIsoUnopPullback_inv_snd, CategoryTheory.BraidedCategory.braiding_tensor_left_hom, CategoryTheory.LocalizerMorphism.RightResolution.op_X₁, CategoryTheory.SemiadditiveOfBinaryBiproducts.comp_add, CategoryTheory.MonoOver.mkArrowIso_hom_hom_left, CategoryTheory.Limits.pushout.condition, AddMonCat.hom_comp, CategoryTheory.Functor.rightOpComp_hom_app, CategoryTheory.Localization.Monoidal.whiskerRight_comp, CochainComplex.mappingCone.lift_f_fst_v, SheafOfModules.GeneratingSections.epi, CategoryTheory.obj_zero_map_μ_app_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomLeft_action_assoc, CategoryTheory.braiding_inv_tensorUnit_right_assoc, CategoryTheory.MorphismProperty.instHasLeftCalculusOfFractionsOppositeOpOfHasRightCalculusOfFractions, CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_inv, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_map_app_app, AddGrpCat.hom_comp, GrpWithZero.hom_comp, CategoryTheory.IsGrothendieckAbelian.isomorphisms_le_pushouts_generatingMonomorphisms, CategoryTheory.Functor.isoShift_inv_naturality_assoc, CochainComplex.mappingCone.inl_v_triangle_mor₃_f, CategoryTheory.Limits.FormalCoproduct.Hom.fromIncl_asSigma, CategoryTheory.ShortComplex.Splitting.s_g_assoc, CategoryTheory.Limits.kernelSubobject_arrow_assoc, IsFreeGroupoid.SpanningTree.endIsFree, HomologicalComplex.extend.XOpIso_hom_d_op_assoc, CategoryTheory.ObjectProperty.isCoseparating_op_iff, CategoryTheory.ShortComplex.LeftHomologyMapData.smul_φH, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality_app, CategoryTheory.Comma.opFunctor_map, CategoryTheory.image_ι_op_comp_imageUnopOp_hom, CategoryTheory.Presheaf.comp_isLocallySurjective_iff, CategoryTheory.hom_id, CategoryTheory.EnrichedCat.rightUnitor_hom_out_app, HomologicalComplex₂.d₂_eq_zero, CategoryTheory.Limits.HasColimit.isoOfEquivalence_hom_π, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_pushouts_coproducts_le_llp_rlp, CategoryTheory.Idempotents.Karoubi.decompId_p_naturality, CategoryTheory.Functor.partialRightAdjointHomEquiv_comp_symm_assoc, SimplexCategory.δ_comp_σ_self_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_app, CategoryTheory.Mat_.ι_additiveObjIsoBiproduct_inv_assoc, CategoryTheory.Functor.ι_colimitIsoColimitGrothendieck_inv_assoc, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_whisker_right, AlgebraicTopology.DoldKan.PInfty_f_naturality_assoc, HomologicalComplex.mapBifunctorMapHomotopy.comm₁, CategoryTheory.StrictPseudofunctor.comp_mapComp_hom, CategoryTheory.Adjunction.Triple.adj₁_counit_app_rightToLeft_app, CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.hf', CategoryTheory.Biprod.unipotentLower_inv, HomologicalComplex₂.ι_totalShift₁Iso_inv_f, CategoryTheory.NatTrans.id_app', HomologicalComplex.extendSingleIso_inv_f_assoc, AlgebraicGeometry.IsFinite.comp_iff, Action.smul_hom, CategoryTheory.Functor.mapContActionComp_inv, CategoryTheory.Limits.WidePullback.π_arrow, CategoryTheory.ComposableArrows.IsComplex.opcyclesToCycles_fac_assoc, CategoryTheory.ShortComplex.cyclesMap'_sub, CategoryTheory.Functor.IsCoverDense.Types.appHom_valid_glue, CategoryTheory.Limits.inr_inl_pushoutRightPushoutInlIso_hom, CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_mapComp, CategoryTheory.Limits.Cofork.unop_π_app_one, AddSemigrp.coe_id, CategoryTheory.Limits.pullbackAssoc_inv_fst_snd_assoc, AlgebraicGeometry.HasRingHomProperty.respects_isOpenImmersion, CategoryTheory.Functor.rightOpLeftOpIso_hom_app, CategoryTheory.Functor.obj.ε_def_assoc, CategoryTheory.ShortComplex.homologyMap'_sub, CategoryTheory.Functor.Monoidal.ε_η, CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_ext_iff, CategoryTheory.Sieve.equalizer_apply, CategoryTheory.ShortComplex.Splitting.rightHomologyData_ι, CategoryTheory.Functor.rightDerived_fac_assoc, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_inl, CategoryTheory.LocalizerMorphism.LeftResolution.Hom.id_f, AlgebraicGeometry.PresheafedSpace.stalkMap.stalkSpecializes_stalkMap, CategoryTheory.Equalizer.firstObjEqFamily_hom, BddDistLat.ofHom_id, CategoryTheory.OrthogonalReflection.D₁.ι_comp_t_assoc, CategoryTheory.Subfunctor.Subpresheaf.ofSection_eq_range', AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap, CategoryTheory.Preadditive.commGrpEquivalence_unitIso_hom_app, CategoryTheory.ObjectProperty.ι_η, HomologicalComplex.XIsoOfEq_inv_comp_XIsoOfEq_inv, CochainComplex.ιTruncLE_naturality_assoc, CategoryTheory.eqToHom_map, CategoryTheory.Functor.toOplaxFunctor'_obj, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_hom_inv, Rep.coinvariantsAdjunction_homEquiv_symm_apply_hom, CategoryTheory.Limits.isLimitOfCoconeOfConeLeftOp_lift, AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_fst_assoc, HomologicalComplex₂.ι_totalDesc_assoc, CategoryTheory.IsIso.inv_comp_eq, AlgebraicGeometry.SheafedSpace.comp_hom_c_app, CategoryTheory.ShortComplex.hasHomology_of_hasCokernel, CategoryTheory.MonObj.lift_lift_assoc, CategoryTheory.Limits.image.preComp_epi_of_epi, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd, CategoryTheory.Comonad.ForgetCreatesColimits'.newCocone_ι_app, CategoryTheory.SplitEpi.comp_section_, HomotopicalAlgebra.LeftHomotopyClass.postcomp_mk, CategoryTheory.Limits.inl_opProdIsoCoprod_inv_assoc, CategoryTheory.Functor.Monoidal.map_whiskerRight, CategoryTheory.ObjectProperty.isClosedUnderLimitsOfShape_op_iff_unop, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app, GrpWithZero.coe_id, CategoryTheory.DifferentialObject.eqToHom_f, CategoryTheory.MorphismProperty.coproducts_monotone, AlgebraicGeometry.Scheme.isoOfEq_hom_ι, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_hom, LightCondSet.topCatAdjunctionUnit_val_app_apply, CategoryTheory.Functor.OplaxRightLinear.δᵣ_associativity_inv, CategoryTheory.OplaxFunctor.PseudoCore.mapCompIso_hom, CategoryTheory.StrictPseudofunctor.comp_mapId_hom, CategoryTheory.Limits.inl_comp_pushoutComparison, CategoryTheory.Idempotents.Karoubi.hom_eq_zero_iff, CategoryTheory.Square.Hom.comp_τ₂, CategoryTheory.CatCenter.smul_iso_inv_eq'_assoc, CategoryTheory.homOfLE_comp_eqToHom, CategoryTheory.Over.rightUnitor_inv_left_fst, HomologicalComplex.truncGEMap_comp_assoc, CategoryTheory.eHomWhiskerLeft_comp, CategoryTheory.Limits.piConst_map_app, Bimod.TensorBimod.actRight_one', GrpCat.hom_id, CategoryTheory.CostructuredArrow.homMk'_mk_id, CategoryTheory.Functor.mapMonCompIso_hom_app_hom, CategoryTheory.epi_comp', CategoryTheory.MonObj.instIsMonHomId, CategoryTheory.Limits.biprod.inr_fst, AlgebraicGeometry.RingedSpace.exists_res_eq_zero_of_germ_eq_zero, CategoryTheory.Subobject.ofMkLEMk_comp_ofMkLE_assoc, HomotopicalAlgebra.Cylinder.ofFactorizationData_i₁, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_symm_apply_right, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_fiber, CategoryTheory.nerve.edgeMk_id, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_def, AlgebraicGeometry.IsAffineHom.comp_iff, CategoryTheory.ShortComplex.Homotopy.sub_h₁, CategoryTheory.Functor.LeftExtension.coconeAtWhiskerRightIso_inv_hom, CategoryTheory.Preadditive.commGrpEquivalence_functor_obj_grp_mul, SSet.Subcomplex.image_id, CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_comm_f_assoc, CategoryTheory.Presieve.isSheafFor_singleton, CategoryTheory.Limits.IsBilimit.binary_total, CategoryTheory.MonObj.mul_leftUnitor, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_symm_apply_φ, CategoryTheory.Iso.eq_comp_inv, CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_right, TopCat.Sheaf.id_app, CategoryTheory.Adjunction.mapCommMon_unit, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality_assoc, HomologicalComplex.extendHomologyIso_hom_homologyι_assoc, CochainComplex.mappingCone.inr_triangleδ, CategoryTheory.Comonad.coassoc, AlgebraicGeometry.Scheme.comp_base, SimplicialObject.opFunctor_map_app, Bicategory.Opposite.unop2_id_bop, CategoryTheory.Functor.RightExtension.precomp_map_left, CategoryTheory.Localization.Construction.morphismProperty_eq_top', CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_snd_assoc, CategoryTheory.μ_naturalityᵣ_assoc, CategoryTheory.kernelCokernelCompSequence.ι_φ, CategoryTheory.Pretriangulated.TriangleMorphism.comm₃, AlgebraicGeometry.IsClosedImmersion.lift_fac_assoc, CochainComplex.HomComplex.Cochain.ofHoms_comp, CategoryTheory.LaxFunctor.mapComp_assoc_right_app, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_snd_fst, groupCohomology.cocyclesIso₀_inv_comp_iCocycles, CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_hom_assoc, CategoryTheory.Limits.Cocone.toCostructuredArrowCompProj_hom_app, HomologicalComplex.XIsoOfEq_inv_naturality, CommBialgCat.ofHom_comp, CategoryTheory.ShortComplex.rightHomologyMap'_id, CategoryTheory.Limits.pullbackObjIso_inv_comp_fst_assoc, CategoryTheory.Iso.hom_inv_id_app_app_assoc, CategoryTheory.Limits.coneOfIsSplitMono_ι, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.unit_app_ev_app_app, CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp_inv_hom₃, CategoryTheory.ShortComplex.homologyπ_naturality_assoc, SSet.spine_vertex, CategoryTheory.Oplax.OplaxTrans.associator_hom_as_app, CategoryTheory.Limits.HasZeroObject.zeroIsoTerminal_inv, MonCat.oneHom_apply, CategoryTheory.Idempotents.Karoubi.inclusionHom_apply, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_hom_hom₂, CategoryTheory.End.smul_left, HomologicalComplex.mapBifunctorFlipIso_hom_naturality_assoc, HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom, CategoryTheory.Preadditive.isSeparator_iff, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id, CategoryTheory.MonObj.lift_comp_one_right_assoc, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d, CategoryTheory.Iso.hom_inv_id_eval_assoc, CategoryTheory.GlueData.t_inv, HomologicalComplex.fromOpcycles_d_assoc, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_hom_inv_assoc, HomologicalComplex.restriction_d_eq, CategoryTheory.Limits.kernelSubobjectMap_comp, CategoryTheory.SimplicialObject.δ_comp_δ_assoc, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality', CategoryTheory.Pseudofunctor.toOplax_mapComp, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.ofRestrict_invApp_apply, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app_assoc, groupCohomology.mapCocycles₂_comp_i_assoc, CategoryTheory.StructuredArrow.id_right, CategoryTheory.Limits.coprod.inl_desc_assoc, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_right_app, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.const_s', HomotopicalAlgebra.FibrantBrownFactorization.mk'_i, SheafOfModules.GeneratingSections.opEpi_comp, HomologicalComplex.dTo_eq, CategoryTheory.eq_whisker, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over_assoc, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.left_triangle_components, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_μ_unmop_app, CategoryTheory.CartesianMonoidalCategory.lift_braiding_hom, CategoryTheory.Bimon.compatibility_assoc, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_unit_app, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ_ΓToStalk, CategoryTheory.Functor.Monoidal.whiskerRight_μ_δ_assoc, CategoryTheory.Functor.FullyFaithful.homNatIso_inv_app_down, CategoryTheory.Idempotents.Karoubi.eqToHom_f, CategoryTheory.ShortComplex.HomologyMapData.comp_left, IsFreeGroupoid.SpanningTree.functorOfMonoidHom_map, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_symm_apply, CategoryTheory.Limits.image.fac_lift, CategoryTheory.Limits.pullback.diagonal_snd, AlgebraicGeometry.IsZariskiLocalAtSource.iff_of_iSup_eq_top, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomLeft_action, CategoryTheory.Under.pushout_map, CategoryTheory.IsPushout.inr_isoPushout_inv_assoc, CategoryTheory.Grp.Hom.hom_zpow, Rep.ρ_hom, CategoryTheory.PreZeroHypercover.inv_hom_h₀_comp_f, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_app, AlgebraicTopology.DoldKan.comp_P_eq_self_iff, SimplexCategory.δ_zero_mkOfSucc, CategoryTheory.Functor.ranCounit_app_whiskerLeft_ranAdjunction_unit_app_assoc, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_ι, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_inv, CategoryTheory.Over.mapCongr_inv_app_left, CategoryTheory.Limits.kernelSubobject_comp_mono_isIso, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom, CategoryTheory.IsPullback.zero_top, CategoryTheory.ModObj.mul_smul'_assoc, CategoryTheory.Bicategory.inv_hom_whiskerRight_whiskerRight, CategoryTheory.Limits.Types.binaryCoproductIso_inl_comp_inv, CategoryTheory.ComonadHom.app_ε, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp, CategoryTheory.Limits.pushoutIsoUnopPullback_inv_fst, AlgebraicGeometry.Scheme.Hom.appLE_map', CategoryTheory.Functor.IsStronglyCartesian.map_self, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₃_assoc, CategoryTheory.IsComonHom.hom_comul, CategoryTheory.ComonObj.comul_counit, CategoryTheory.isPullback_of_cofan_isVanKampen, CategoryTheory.Functor.CorepresentableBy.ofIsoObj_homEquiv, CategoryTheory.instIsSplitMonoOppositeOpOfIsSplitEpi, CategoryTheory.Limits.biprod.map_snd, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.id_fst_app, AlgebraicGeometry.Scheme.isoSpec_hom_naturality, CategoryTheory.LocalizerMorphism.LeftResolution.unop_X₁, CategoryTheory.Bicategory.Prod.sectR_mapComp_inv, topCatOpToFrm_map, CategoryTheory.MorphismProperty.Over.Hom.ext_iff, CategoryTheory.Bicategory.Prod.fst_mapComp_hom, CategoryTheory.MonoidalCategory.prodMonoidal_whiskerRight, CategoryTheory.LocalizerMorphism.LeftResolution.Hom.comm, CategoryTheory.Limits.fiberwiseColimitLimitIso_hom_app, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTrans_obj_str, CategoryTheory.Limits.kernelIsoOfEq_hom_comp_ι, HomologicalComplex.instQuasiIsoAtMapOppositeSymmUnopFunctorOp, CochainComplex.πTruncGE_naturality, CategoryTheory.Limits.inr_pushoutLeftPushoutInrIso_inv, CategoryTheory.Pretriangulated.Triangle.eqToHom_hom₃, groupHomology.π_comp_H2Iso_inv_assoc, CategoryTheory.FreeMonoidalCategory.normalize_naturality, HomologicalComplex.homologyπ_extendHomologyIso_inv, CategoryTheory.MorphismProperty.LeftFraction.unop_X', CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHom_def_assoc, HomologicalComplex.homologyπ_restrictionHomologyIso_inv, CategoryTheory.Cat.freeMapIdIso_hom_app, AlgebraicGeometry.PresheafedSpace.comp_c_app, SemimoduleCat.ofHom₂_hom_apply_hom, CategoryTheory.Functor.curryingFlipEquiv_symm_apply_map_app, CategoryTheory.epi_comp, CategoryTheory.MorphismProperty.op_isomorphisms, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality', CategoryTheory.Limits.opCoproductIsoProduct'_comp_self, PresheafOfModules.map_comp_apply, CategoryTheory.MonoidalClosed.uncurry_pre_app, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_hom_inv_assoc, AlgebraicGeometry.Scheme.homOfLE_ι, CategoryTheory.IsFiltered.crown₄, CategoryTheory.HomOrthogonal.matrixDecomposition_id, CategoryTheory.Limits.biproduct.toSubtype_π_assoc, CategoryTheory.Limits.pullbackConeOfLeftIso_snd, CategoryTheory.Localization.comp_liftNatTrans, CategoryTheory.Limits.Multicoequalizer.ι_sigmaπ_assoc, CategoryTheory.IsHomLift.lift_comp_eqToHom, AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv_assoc, HomotopicalAlgebra.trivialCofibrations_sub_cofibrations, CategoryTheory.Functor.Final.extendCocone_obj_ι_app, CochainComplex.mappingCone.id_X, CategoryTheory.Functor.Full.map_surjective, AlgebraicGeometry.Scheme.Pullback.residueFieldCongr_inv_residueFieldMap_ofPoint, HomologicalComplex.truncGE'Map_comp, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.uliftCoyonedaEquiv_symm_apply_app, CategoryTheory.ShortComplex.leftHomologyMap_op, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃_associator_inv, CategoryTheory.InjectiveResolution.toRightDerivedZero_eq, CategoryTheory.Bicategory.id_whiskerLeft_symm, CategoryTheory.CartesianMonoidalCategory.braiding_inv_fst_assoc, CategoryTheory.ShortComplex.p_fromOpcycles, CategoryTheory.Pseudofunctor.mapComp'_naturality_1, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitIso_hom_naturality_assoc, CategoryTheory.Functor.representableByUliftFunctorEquiv_symm_apply_homEquiv, CategoryTheory.Functor.opId_hom_app, CommRingCat.HomTopology.continuous_precomp, CategoryTheory.Dial.associator_hom_F, CategoryTheory.ShortComplex.Homotopy.refl_h₃, CategoryTheory.LocalizerMorphism.RightResolution.unop_X₁, CochainComplex.HomComplex.Cochain.single_zero, CategoryTheory.ShortComplex.homologyMap'_add, CochainComplex.mappingCone.inr_descShortComplex_assoc, groupHomology.chainsMap_f_3_comp_chainsIso₃, CategoryTheory.actionAsFunctor_map, CategoryTheory.PreZeroHypercover.inv_inv_h₀_comp_f, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoColimitUncurryWhiskeringLeft₂_inv, CategoryTheory.ShortComplex.SnakeInput.δ_L₃_f, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_hom_app_fst_app, CategoryTheory.MorphismProperty.Comma.comp_left_assoc, groupHomology.mapCycles₁_id_comp_assoc, CategoryTheory.Limits.image.map_ι, CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_sub_f, CategoryTheory.Over.mapCongr_hom_app_left, AddCommGrpCat.asHom_injective, CategoryTheory.MorphismProperty.instHasTwoOutOfThreePropertyUnopOfOpposite, CategoryTheory.Pseudofunctor.isStackFor_ofArrows_iff, CategoryTheory.Limits.opCoproductIsoProduct'_hom_comp_proj, CategoryTheory.Abelian.Pseudoelement.pseudoZero_iff, CategoryTheory.MonoidalCategory.DayConvolution.unit_naturality_assoc, CategoryTheory.ProdPreservesConnectedLimits.forgetCone_π, CategoryTheory.Limits.biprod.symmetry'_assoc, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd, CategoryTheory.Functor.shift_map_op_assoc, CategoryTheory.Limits.coker.condition_assoc, CategoryTheory.Functor.isLeftAdjoint_iff_rightAdjointObjIsDefined_eq_top, AlgebraicGeometry.Scheme.Hom.resLE_map, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_π_app, CategoryTheory.strongMono_comp, CategoryTheory.Limits.ConeMorphism.w, CategoryTheory.CostructuredArrow.homMk'_right, CategoryTheory.LocalizerMorphism.LeftResolution.opEquivalence_unitIso, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_comp_assoc, CategoryTheory.Adjunction.leftAdjointCompNatTrans₀₁₃_eq_conjugateEquiv_symm, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app, CategoryTheory.Functor.opUnopIso_inv_app, CategoryTheory.Functor.IsFibered.comp, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι_assoc, CategoryTheory.MorphismProperty.colimitsOfShape_discrete_le_llp_rlp, AlgebraicGeometry.Scheme.Hom.comp_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality, HomotopicalAlgebra.PrepathObject.ι_p₁_assoc, groupHomology.eq_d₂₁_comp_inv, SemiNormedGrp₁.hom_id, CategoryTheory.Preadditive.nsmul_comp, CategoryTheory.Functor.IsCoverDense.Types.pushforwardFamily_def, CategoryTheory.LocalizerMorphism.instHasLeftResolutionsOppositeOpOpOfHasRightResolutions, SimplicialObject.Splitting.IndexSet.eqId_iff_len_eq, SimplexCategoryGenRel.σ_comp_σ_nat, CategoryTheory.MonoidalCategory.tensor_inv_hom_id', CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitIso_hom_naturality_assoc, CategoryTheory.Limits.equalizerSubobject_arrow_comp, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_inv_assoc, CategoryTheory.Functor.LeftLinear.μₗ_comp_δₗ_assoc, CategoryTheory.Limits.LimitPresentation.self_π, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_inv_app, CategoryTheory.Limits.CoconeMorphism.hom_inv_id_assoc, CategoryTheory.GrpObj.one_inv_assoc, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι_ι_eq_support_inter, CategoryTheory.Localization.Preadditive.add'_map, HomologicalComplex.pOpcycles_opcyclesIsoSc'_inv, HomotopicalAlgebra.RightHomotopyRel.precomp, CategoryTheory.Localization.Monoidal.triangle_aux₃, CategoryTheory.ShortComplex.homologyOpIso_inv_naturality, CategoryTheory.GrothendieckTopology.sheafifyMap_id, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_inv_app, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app', CategoryTheory.ihom.ev_coev_assoc, CategoryTheory.Limits.limit.lift_post, AlgebraicGeometry.Scheme.Pullback.left_affine_comp_pullback_hasPullback, CategoryTheory.Functor.OplaxRightLinear.δᵣ_unitality_hom_assoc, SimplicialObject.Splitting.IndexSet.ext', CategoryTheory.Limits.ι_comp_sigmaObjIso_inv, CategoryTheory.eqToHom_app, AlgebraicGeometry.Scheme.hom_base_inv_base, CategoryTheory.CosimplicialObject.δ_comp_σ_self', CategoryTheory.Bicategory.Pith.pseudofunctorToPith_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_of, CategoryTheory.MorphismProperty.RespectsIso.op, CategoryTheory.Limits.ι_colimitLimitIso_limit_π, CategoryTheory.Limits.BinaryBicone.inl_snd_assoc, CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_hom_app_unmop_unmop, CategoryTheory.Bicategory.LeftLift.IsKan.fac_assoc, CategoryTheory.ShortComplex.mapOpcyclesIso_inv_naturality, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr, CategoryTheory.IsPullback.of_id_snd, CategoryTheory.Localization.Monoidal.id_tensorHom, HomologicalComplex.cyclesOpIso_inv_naturality_assoc, CategoryTheory.MonoidalCategory.DayConvolution.whiskerLeft_comp_unit_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocIso_inv_naturality_assoc, CategoryTheory.Over.mapComp_hom_app_left, CategoryTheory.Functor.Final.ι_colimitIso_hom_assoc, SSet.Subcomplex.toImage_ι_assoc, CategoryTheory.kernelCokernelCompSequence.inr_π_assoc, CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_fst, CategoryTheory.BimonObj.mul_counit_assoc, CategoryTheory.instIsComonHomComp, AlgebraicGeometry.Scheme.Cover.comp_idx_apply, AlgebraicGeometry.IsLocalAtSource.iff_of_openCover, CategoryTheory.Functor.mapGrp_obj_grp_one, CategoryTheory.linearYoneda_obj_obj_carrier, CategoryTheory.Limits.walkingCospanOpEquiv_counitIso_hom_app, TopologicalSpace.Opens.mapId_hom_app, CategoryTheory.Preadditive.isSeparating_iff, AlgebraicGeometry.StructureSheaf.toStalk_stalkSpecializes, CategoryTheory.Pretriangulated.Triangle.smul_hom₂, CategoryTheory.MonoidalCategory.triangle_assoc_comp_left_inv_assoc, CategoryTheory.Functor.biprodComparison'_comp_biprodComparison_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_inv_hom, CategoryTheory.Limits.Cotrident.IsColimit.homIso_natural, CategoryTheory.Limits.LimitPresentation.changeDiag_π, CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_fst_fst_assoc, CategoryTheory.MonoidalCategory.rightUnitor_tensor_inv_assoc, CategoryTheory.Functor.mapTriangleInvRotateIso_inv_app_hom₃, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_app, CategoryTheory.ObjectProperty.limitsOfShape_op, CategoryTheory.Grothendieck.id_fiber, groupHomology.mapCycles₁_comp, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_inv, CategoryTheory.Limits.coequalizer.condition, CategoryTheory.GradedObject.ι_mapBifunctorComp₁₂MapObjIso_hom_assoc, CategoryTheory.Limits.prodComparison_natural_of_natTrans_assoc, CategoryTheory.Comma.equivProd_unitIso_hom_app_left, TopologicalSpace.Opens.mapComp_hom_app, SSet.Subcomplex.topIso_inv_ι, AlgebraicGeometry.Scheme.toSpecΓ_naturality, CategoryTheory.PreZeroHypercover.restrictIndexHom_h₀, CategoryTheory.Adjunction.mapCommMon_counit, CategoryTheory.Limits.biprod.mapBiprod_hom_desc, CategoryTheory.Functor.Monoidal.map_ε_η_assoc, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app_assoc, CategoryTheory.Limits.ι_colimitLimitToLimitColimit_π, CategoryTheory.SimplicialObject.Truncated.rightExtensionInclusion_hom_app, CategoryTheory.coprod_inl_rightDistrib_hom, CategoryTheory.MonoidalCategory.id_tensor_comp_assoc, CategoryTheory.CatCenter.naturality, CategoryTheory.ShortComplex.HomotopyEquiv.refl_hom, CategoryTheory.GradedObject.mapBifunctorMap_obj_map, AlgebraicTopology.DoldKan.QInfty_idem_assoc, CategoryTheory.Coyoneda.objOpOp_hom_app, CategoryTheory.Bicategory.Adj.Hom₂.conjugateEquiv_symm_τr, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst, PartOrd.coe_id, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_left, SimplexCategory.const_fac_thru_zero, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app, HomologicalComplex.singleObjHomologySelfIso_hom_singleObjOpcyclesSelfIso_hom, HomologicalComplex.mapBifunctor₁₂.hom_ext_iff, CategoryTheory.ShortComplex.Homotopy.unop_h₃, CategoryTheory.ShortComplex.iCycles_g, groupHomology.map_comp, CategoryTheory.PreZeroHypercover.Hom.id_h₀, CategoryTheory.Functor.unopId_inv_app, CategoryTheory.FreeBicategory.mk_vcomp, HomologicalComplex.mapBifunctor₂₃.ι_mapBifunctor₂₃Desc, CategoryTheory.Subobject.ofLE_comp_ofLEMk_assoc, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_inv, CategoryTheory.Square.Hom.id_τ₄, CategoryTheory.LaxFunctor.PseudoCore.mapCompIso_inv, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_map, OrderHom.equivalenceFunctor_counitIso_inv_app_app, Action.FunctorCategoryEquivalence.unitIso_inv_app_hom, CategoryTheory.Dial.associatorImpl_inv_F, CategoryTheory.Functor.mapCommGrpCompIso_hom_app_hom_hom_hom, CategoryTheory.Functor.congr_hom_assoc, CategoryTheory.Limits.π_comp_colimitUnopIsoOpLimit_inv, SSet.Subcomplex.ofSimplexProd_eq_range, smoothSheaf.ι_evalHom_assoc, CategoryTheory.nerve.homEquiv_edgeMk, CategoryTheory.Limits.Types.binaryProductFunctor_obj_map, CategoryTheory.Over.whiskerRight_left_fst, DerivedCategory.HomologySequence.mono_homologyMap_mor₁_iff, CategoryTheory.Join.pseudofunctorLeft_mapId_hom_toNatTrans_app, HomotopicalAlgebra.AttachCells.ofArrowIso_g₂, CategoryTheory.MorphismProperty.RightFraction.unop_s, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_app_assoc, CategoryTheory.Limits.colimit.toOver_ι_app, CategoryTheory.Functor.whiskeringRight₂_obj_obj_obj_map, CochainComplex.mappingConeCompHomotopyEquiv_comm₂_assoc, CategoryTheory.sheafComposeIso_hom_fac, CategoryTheory.Mathlib.Tactic.MonTauto.associator_inv_comp_tensorHom_tensorHom_assoc, AlgebraicGeometry.pointEquivClosedPoint_apply_coe, CategoryTheory.StrictlyUnitaryLaxFunctor.comp_mapId, CategoryTheory.CostructuredArrow.w_prod_snd_assoc, CategoryTheory.Over.postAdjunctionLeft_unit_app_left, CategoryTheory.Functor.mapActionComp_inv, CategoryTheory.Limits.fst_opProdIsoCoprod_hom_assoc, CategoryTheory.Limits.BiconeMorphism.wι, CategoryTheory.obj_μ_app, CategoryTheory.PreOneHypercover.Homotopy.wl_assoc, Action.FunctorCategoryEquivalence.functor_map_app, CategoryTheory.Idempotents.functorExtension₂CompWhiskeringLeftToKaroubiIso_hom_app_app_f, CategoryTheory.Limits.Multicofork.snd_app_right_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality, CategoryTheory.Functor.ι_colimitIsoColimitGrothendieck_hom, SheafOfModules.ιFree_mapFree_inv_assoc, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_naturality, ModuleCat.homLinearEquiv_symm_apply, CategoryTheory.Limits.limit.pre_post, CategoryTheory.μ_naturalityₗ, HomologicalComplex.truncGE'.d_comp_d, HomotopicalAlgebra.instWeakEquivalenceUnopOfOpposite, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_tensorHom_app, SimplexCategory.δ_comp_σ_succ_assoc, HomologicalComplex.Hom.sqFrom_comp, CategoryTheory.GradedObject.mapTrifunctorMapFunctorObj_map_app, CategoryTheory.Comonad.counit_naturality, HomotopicalAlgebra.PrepathObject.symm_p, CategoryTheory.MonoidalCategory.hom_inv_whiskerRight_assoc, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right_assoc, ModuleCat.hom_smul, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_counit_app, CochainComplex.mappingConeCompHomotopyEquiv_hom_inv_id, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp_val_app, CategoryTheory.IsPushout.inr_isoPushout_hom_assoc, CategoryTheory.GrothendieckTopology.sheafifyMap_sheafifyLift, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_inv_app, AlgebraicGeometry.Scheme.Hom.ι_toNormalization, CategoryTheory.Limits.cokernel.π_zero_isIso, CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_zero_f, CategoryTheory.MorphismProperty.isStableUnderRetracts_iff_retracts_le, CategoryTheory.Pseudofunctor.map₂_associator_app, CategoryTheory.Functor.leftDerivedNatTrans_comp_assoc, CategoryTheory.Equalizer.Sieve.w, CommSemiRingCat.ofHom_id, BoolAlg.ofHom_comp, CategoryTheory.BasedNatTrans.isHomLift', CategoryTheory.Limits.spanCompIso_hom_app_zero, CategoryTheory.Functor.homObjEquiv_symm_apply_app, CategoryTheory.Functor.const.opObjUnop_hom_app, CategoryTheory.Limits.Types.equalizerIso_inv_comp_ι, SemimoduleCat.MonoidalCategory.braiding_naturality_right, CategoryTheory.Pretriangulated.Triangle.eqToHom_hom₁, CategoryTheory.Limits.equalizer.condition, CategoryTheory.Comma.comp_right, AlgebraicGeometry.LocallyRingedSpace.Γ_Spec_left_triangle, CategoryTheory.Adjunction.mkOfHomEquiv_counit_app, CategoryTheory.Bicategory.Prod.snd_map₂, CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullback, CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsISup, CategoryTheory.Functor.prod'CompFst_hom_app, CategoryTheory.Functor.coreId_inv_app_iso_inv, SSet.PtSimplex.RelStruct.δ_castSucc_map, Condensed.isoFinYonedaComponents_hom_apply, CategoryTheory.CosimplicialObject.δ_comp_σ_self_assoc, CategoryTheory.MorphismProperty.IsStableUnderComposition.comp_mem, CategoryTheory.Functor.map_inv', CategoryTheory.MorphismProperty.multiplicativeClosure_monotone, CategoryTheory.Limits.PullbackCone.condition_assoc, CategoryTheory.PullbackShift.adjunction_unit, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_inv_app_hom_hom_app, CategoryTheory.Limits.kernelComparison_comp_ι, CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id, CategoryTheory.MonoidalCategory.inv_hom_whiskerRight_assoc, groupCohomology.π_map_assoc, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp_f, CategoryTheory.SmallObject.SuccStruct.extendToSuccObjIso_hom_naturality_assoc, Rep.MonoidalClosed.linearHomEquivComm_hom, CategoryTheory.MonoidalOpposite.tensorLeftUnmopIso_inv_app, CategoryTheory.Limits.Trident.condition, CategoryTheory.Lax.OplaxTrans.naturality_comp, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_inv_toNatTrans_app_val_app, SimplexCategory.δ_comp_δ_self, isoOfQuasiIsoAt_hom_inv_id, CategoryTheory.compEvaluation_hom_app, HomologicalComplex.extend.d_none_eq_zero, CategoryTheory.ShortComplex.cyclesOpIso_hom_naturality, ProfiniteGrp.hom_id, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_hom_π_π, CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHom_mk, CategoryTheory.Arrow.square_from_iso_invert, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, CategoryTheory.IsSplitCoequalizer.leftSection_bottom_assoc, SemimoduleCat.homLinearEquiv_apply, CategoryTheory.Functor.relativelyRepresentable.isomorphisms_le, CategoryTheory.Limits.coprodComparison_inl, Lat.comp_apply, HomologicalComplex.extendCyclesIso_inv_iCycles_assoc, AlgebraicGeometry.Spec.preimage_id, CategoryTheory.Localization.Preadditive.add'_comp_assoc, ModuleCat.smul_naturality, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv, CategoryTheory.Limits.inl_inl_pushoutLeftPushoutInrIso_hom_assoc, CategoryTheory.Over.preservesTerminalIso_pullback, CategoryTheory.Limits.CatCospanTransform.comp_whiskerRight_assoc, CategoryTheory.Iso.op_hom, groupCohomology.toCocycles_comp_isoCocycles₂_hom, CategoryTheory.NatTrans.mapHomotopyCategory_comp, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_tensorDesc_app, SheafOfModules.pullback_map_ιFree_comp_pullbackObjFreeIso_hom_assoc, CategoryTheory.Bicategory.leftUnitor_inv_whiskerRight_assoc, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_SpecMap_awayMap_right_assoc, HomologicalComplex.singleObjCyclesSelfIso_hom_naturality, HomologicalComplex.mapBifunctor₁₂.ι_mapBifunctor₁₂Desc, CategoryTheory.Projective.factorThru_comp_assoc, CategoryTheory.isSeparating_op_iff, ProfiniteAddGrp.hom_id, CategoryTheory.StructuredArrow.functor_map, HomologicalComplex.mapBifunctor₁₂.ι_D₂_assoc, CategoryTheory.Limits.prod.lift_fst, CategoryTheory.eHom_whisker_exchange_assoc, CategoryTheory.Functor.RepresentableBy.comp_homEquiv_symm, CategoryTheory.Bicategory.whiskerRight_comp_symm_assoc, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_hom_hom₁, CategoryTheory.Precoverage.ZeroHypercover.id_h₀, CategoryTheory.Limits.PushoutCocone.condition, HomologicalComplex.cylinder.πCompι₀Homotopy.nullHomotopicMap_eq, CategoryTheory.Oplax.StrongTrans.Modification.whiskerRight_naturality, CategoryTheory.ShortComplex.Homotopy.neg_h₁, CategoryTheory.Limits.Cofork.condition_assoc, CategoryTheory.Congruence.compRight, CategoryTheory.coprod_inr_rightDistrib_hom, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app_assoc, CochainComplex.HomComplex.Cochain.fromSingleMk_postcomp, CategoryTheory.MorphismProperty.DescendsAlong.inf, CategoryTheory.Limits.PullbackCone.unop_inr, HomologicalComplex.mapBifunctor₂₃.ιOrZero_eq_zero, HomologicalComplex.singleObjCyclesSelfIso_inv_naturality_assoc, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_naturality_assoc, CommGrpCat.hom_id, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv, SimplexCategory.mkOfSucc_subinterval_eq, CochainComplex.ConnectData.d_comp_d, CategoryTheory.NatTrans.app_nsmul, CategoryTheory.MorphismProperty.CodescendsAlong.inf, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_hom, HomologicalComplex.homotopyCofiber.inrX_d_assoc, CategoryTheory.Enriched.FunctorCategory.enrichedId_π_assoc, CategoryTheory.δ_naturalityᵣ_assoc, CategoryTheory.kernelCokernelCompSequence.ι_fst_assoc, HomologicalComplex.mapBifunctor.hom_ext_iff, HomologicalComplex.sub_f_apply, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict_assoc, CategoryTheory.Over.prodLeftIsoPullback_inv_fst, groupCohomology.map_comp, CochainComplex.mappingCone.d_snd_v'_assoc, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone_pt, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_comp_assoc, AddCommMonCat.coyonedaType_map_app, CategoryTheory.EnrichedFunctor.category_id_out, CategoryTheory.NatTrans.op_id, CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inl, CategoryTheory.CatCenter.mul_app', CategoryTheory.NatTrans.prod_app_fst, FGModuleCat.hom_comp, CategoryTheory.ι_preservesColimitIso_inv_assoc, CategoryTheory.Limits.MonoFactorisation.isoComp_e, HomologicalComplex.homotopyCofiber.descSigma_ext_iff, CategoryTheory.IsPushout.inr_isoPushout_inv, HomologicalComplex.ι_mapBifunctorDesc, CategoryTheory.FreeGroupoid.mapCompLift_inv_app, groupHomology.map_id_comp, AlgebraicGeometry.Scheme.comp_coeBase_assoc, CategoryTheory.Limits.Fork.ι_postcompose, CategoryTheory.Abelian.im_map, CategoryTheory.Comon.MonOpOpToComon_map_hom, CategoryTheory.Limits.MonoFactorisation.fac_assoc, CategoryTheory.MorphismProperty.FunctorsInverting.id_hom, ContinuousCohomology.I_obj_ρ_apply, ProfiniteAddGrp.ofHom_comp, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_inv_right, CategoryTheory.StructuredArrow.map₂_map_left, CategoryTheory.Limits.spanOp_hom_app, CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapId_inv, CategoryTheory.Limits.limitIsoSwapCompLim_hom_app, CategoryTheory.Limits.coprodComparison_inv_natural, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_assoc, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_coproductIsoSelf_inv_assoc, HeytAlg.coe_comp, CategoryTheory.Limits.pullbackProdSndIsoProd_hom_fst, AlgebraicGeometry.IsLocalIso.le_of_isZariskiLocalAtSource, ModuleCat.imageIsoRange_hom_subtype, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom, HomotopicalAlgebra.PrepathObject.p_fst, GrpWithZero.coe_comp, CategoryTheory.Iso.eHomCongr_comp_assoc, CategoryTheory.Limits.Multiequalizer.hom_ext_iff, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_coproductIsoSelf_inv, AlgebraicTopology.karoubi_alternatingFaceMapComplex_d, CategoryTheory.Adjunction.homEquiv_unit, CategoryTheory.Functor.LaxLeftLinear.μₗ_associativity_inv_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_hom_comp_π_assoc, CategoryTheory.MorphismProperty.retracts_le, Quiver.Hom.mop_inj, CategoryTheory.Under.postAdjunctionRight_unit_app_right, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_inv_app, CategoryTheory.NatTrans.shift_comm_assoc, CategoryTheory.Join.opEquiv_inverse_map_inclRight_op, CategoryTheory.ComposableArrows.Precomp.map_zero_succ_succ, Profinite.Extend.functorOp_obj, groupHomology.mapCycles₁_comp_i, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_left_hom, HomologicalComplex.d_pOpcycles, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapId_inv_iso_inv, SimplexCategoryGenRel.δ_comp_σ_self, CategoryTheory.Subfunctor.preimage_comp, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality, AlgebraicGeometry.Scheme.Hom.congr_app, CategoryTheory.Functor.CoreMonoidal.left_unitality, CategoryTheory.Functor.IsCartesian.of_iso_comp, CategoryTheory.Pseudofunctor.mapComp_id_right, CategoryTheory.Adjunction.mapCommGrp_unit, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app, CategoryTheory.Abelian.LeftResolution.π_naturality_assoc, CategoryTheory.Functor.curry₃ObjProdComp_inv_app_app_app, CategoryTheory.Preadditive.comp_neg, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_inv_colimit_map, CategoryTheory.CartesianMonoidalCategory.comp_lift, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.id_tensorHom_id, CategoryTheory.conjugateEquiv_leftUnitor_hom, CategoryTheory.Sum.functorEquiv_inverse_map, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_comp_assoc, CategoryTheory.MorphismProperty.instRespectsIsoTop, CategoryTheory.Limits.IsImage.ofIsoI_lift, CategoryTheory.WithTerminal.coneEquiv_counitIso_inv_app_hom, CategoryTheory.Functor.Final.ι_colimitIso_inv, CategoryTheory.ObjectProperty.isDetecting_bot_of_isGroupoid, CategoryTheory.Limits.isIsoZero_iff_source_target_isZero, CategoryTheory.shiftFunctorCompIsoId_add'_inv_app, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₃_app, CategoryTheory.Bicategory.comp_whiskerRight, CategoryTheory.shiftFunctorAdd_zero_add_hom_app, CategoryTheory.Limits.Pi.ι_π_of_ne, AlgebraicGeometry.Scheme.IdealSheafData.inclusion_subschemeι, CategoryTheory.EnrichedFunctor.forget_map, CategoryTheory.Presheaf.isLocallySurjective_toSheafify, CategoryTheory.Limits.FormalCoproduct.cofan_inj, CategoryTheory.ShortComplex.add_τ₃, CategoryTheory.Functor.mapGrp_id_one, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_naturality, CategoryTheory.Over.opEquivOpUnder_inverse_obj, PartOrdEmb.comp_apply, CategoryTheory.Limits.limitCompCoyonedaIsoCone_hom_app, CategoryTheory.MorphismProperty.IsStableUnderBaseChange.inf, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_symm, CategoryTheory.OrthogonalReflection.iteration_map_succ, CategoryTheory.MonoidalClosed.uncurry_eq, CategoryTheory.Pseudofunctor.mapComp'_inv_naturality_assoc, SimplexCategory.Truncated.Hom.tr_comp', CategoryTheory.Monad.Algebra.id_f, CategoryTheory.Aut.toEnd_apply, TopCat.ofHom_comp, TopologicalSpace.Opens.map_id_obj', CategoryTheory.Functor.OplaxMonoidal.id_δ, CategoryTheory.uliftYonedaEquiv_apply, CategoryTheory.Limits.ι_comp_colimitRightOpIsoUnopLimit_hom_assoc, HomologicalComplex₂.flipEquivalenceUnitIso_hom_app_f_f, AlgebraicGeometry.Scheme.Opens.toSpecΓ_naturality_assoc, CategoryTheory.Adjunction.leftAdjointUniq_hom_app_counit_assoc, AlgebraicGeometry.Scheme.ofRestrict_appLE, CategoryTheory.Monad.ForgetCreatesLimits.newCone_π_app, CategoryTheory.Iso.homCongr_comp, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_map, CategoryTheory.Functor.IsLocalization.prod, CategoryTheory.Functor.Monoidal.μ_comp_assoc, CategoryTheory.CostructuredArrow.mkPrecomp_left, CategoryTheory.NatTrans.comp_app_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id_app, CategoryTheory.Bicategory.comp_whiskerLeft_symm, CategoryTheory.GrpObj.η_whiskerRight_commutator_assoc, CategoryTheory.CosimplicialObject.id_app, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_assoc, AlgCat.id_apply, CategoryTheory.SingleFunctors.Hom.comm_assoc, CategoryTheory.CartesianMonoidalCategory.prodComparison_id, CategoryTheory.Limits.FormalCoproduct.powerBifunctor_map_app, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_app_π_assoc, CategoryTheory.Limits.Types.coproductIso_mk_comp_inv, CategoryTheory.CostructuredArrow.mapIso_functor_map_left, CategoryTheory.MonoidalCategory.rightUnitor_inv_naturality, CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapComp_inv, CategoryTheory.Bicategory.Pith.id₂_iso_inv, CategoryTheory.ι_preservesColimitIso_hom_assoc, AlgebraicGeometry.instSmoothOfRelativeDimensionOfNatNatCompScheme, CategoryTheory.Iso.comp_hom_eq_id, CategoryTheory.StructuredArrow.prodFunctor_map, CategoryTheory.shiftFunctorComm_hom_app_comp_shift_shiftFunctorAdd_hom_app, CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_comp_d_assoc, CategoryTheory.MorphismProperty.instFaithfulOverTopOverForget, CategoryTheory.Localization.Monoidal.μ_natural_right, CategoryTheory.Limits.CatCospanTransform.whiskerRight_id, AlgebraicGeometry.IsAffineOpen.isoSpec_inv, CategoryTheory.ShortComplex.Homotopy.refl_h₂, CategoryTheory.Arrow.equivSigma_apply_snd_snd, CategoryTheory.GrpObj.lift_comp_inv_right_assoc, CategoryTheory.bijection_natural, HomologicalComplex.fromOpcycles_eq_zero, AlgebraicTopology.DoldKan.PInfty_f_comp_QInfty_f_assoc, AlgebraicGeometry.Scheme.Hom.id_app, TopCat.Presheaf.comp_app, CategoryTheory.LocalizerMorphism.nonempty_rightResolution_iff_op, CategoryTheory.MorphismProperty.IsLocalAtSource.top, CategoryTheory.Functor.currying_inverse_obj_obj_map, ChainComplex.toSingle₀Equiv_apply_coe, HomologicalComplex.opcyclesMap_id, AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_self_assoc, CategoryTheory.Square.Hom.id_τ₃, HomologicalComplex.homologyι_opcyclesToCycles_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_left, CategoryTheory.Limits.Pi.reindex_inv_π_assoc, SSet.horn.faceSingletonComplIso_inv_ι, AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem_ι_assoc, HomologicalComplex.extendMap_f, CategoryTheory.is_coprod_iff_isPushout, CategoryTheory.Functor.FullyFaithful.homEquiv_symm_apply, CategoryTheory.left_unitality_app_assoc, HomologicalComplex₂.ι_totalShift₂Iso_inv_f_assoc, SimplexCategory.δ_comp_σ_of_gt', CategoryTheory.Monad.algebraPreadditive_homGroup_add_f, CategoryTheory.CartesianMonoidalCategory.lift_lift_associator_inv_assoc, PresheafOfModules.zsmul_app, CategoryTheory.GrothendieckTopology.Point.Hom.sheafFiber_comp_assoc, CategoryTheory.μ_naturality₂, AlgebraicGeometry.Scheme.kerAdjunction_unit_app, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom, Condensed.finYoneda_map, FDRep.instFiniteDimensionalHom, CategoryTheory.Sigma.mapComp_inv_app, CategoryTheory.NormalEpi.w, CategoryTheory.Pretriangulated.TriangleMorphism.comm₁_assoc, CategoryTheory.Limits.coequalizer_as_cokernel, CategoryTheory.Limits.limit.post_π, CategoryTheory.Localization.small_of_hasSmallLocalizedHom, CategoryTheory.Comon.id_hom, CategoryTheory.CartesianClosed.homEquiv_apply_eq, CategoryTheory.Classifier.SubobjectRepresentableBy.homEquiv_eq, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ, CategoryTheory.Pretriangulated.triangleMorphismId_hom₃, CategoryTheory.Over.prodLeftIsoPullback_inv_snd_assoc, CategoryTheory.Functor.diag_δ, SimplexCategory.instSubsingletonHomMkOfNatNat, CategoryTheory.Limits.prodComparison_comp, CategoryTheory.Limits.BinaryBiconeMorphism.winl_assoc, CategoryTheory.Over.rightUnitor_inv_left_snd, SimplexCategoryGenRel.δ_comp_σ_of_gt, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHom_comp_assoc, CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_hom, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_map_left, CategoryTheory.GradedObject.ι_mapBifunctor₁₂BifunctorDesc, AlgebraicTopology.DoldKan.P_f_idem_assoc, CategoryTheory.Limits.Cone.toStructuredArrowCompToUnderCompForget_hom_app, CategoryTheory.op_whiskerLeft, CategoryTheory.Bicategory.mateEquiv_symm_apply', CategoryTheory.Comma.equivProd_counitIso_hom_app, HomologicalComplex₂.d_comm, CategoryTheory.Subfunctor.image_comp, CategoryTheory.CartesianMonoidalCategory.braiding_hom_fst, SSet.Subcomplex.instSubsingletonHomToSSetBot, CategoryTheory.Oplax.LaxTrans.naturality_naturality, CategoryTheory.rightAdjointMate_comp_evaluation_assoc, CategoryTheory.ShortComplex.HomologyMapData.comp_right, CategoryTheory.Functor.mapCoconeOp_inv_hom, CategoryTheory.MonoidalCategory.whisker_assoc_assoc, CategoryTheory.Limits.PullbackCone.combine_π_app, CategoryTheory.Limits.spanCompIso_inv_app_left, CategoryTheory.MorphismProperty.IsStableUnderComposition.op, Action.FunctorCategoryEquivalence.functor_δ, CategoryTheory.Mat_.id_apply_self, TopCat.Presheaf.germ_stalkSpecializes_assoc, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone_isColimit_desc, CategoryTheory.Pseudofunctor.mapComp'_comp_id, CategoryTheory.Localization.homEquiv_eq, CategoryTheory.Oplax.StrongTrans.naturality_comp, MonObj.mopEquiv_functor_obj_mon_one_unmop, CategoryTheory.CategoryOfElements.CreatesLimitsAux.liftedCone_π_app_coe, AlgHom.toUnder_comp, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_id, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_hom_assoc, CategoryTheory.Grp.Hom.hom_hom_div, CategoryTheory.GrothendieckTopology.whiskerRight_toPlus_comp_plusCompIso_hom, CategoryTheory.WithTerminal.down_id, AlgebraicGeometry.Proj.pullbackAwayιIso_inv_snd_assoc, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberι_assoc, CategoryTheory.ObjectProperty.colimitsOfShape_le_of_final, CategoryTheory.Limits.HasZeroObject.zeroIsoTerminal_hom, CategoryTheory.OplaxFunctor.map₂_leftUnitor_assoc, CategoryTheory.prodOpEquiv_unitIso_hom_app, CategoryTheory.Bifunctor.map_id_comp, CategoryTheory.ShortComplex.Hom.comp_τ₂, CategoryTheory.leftUnitor_inv_braiding_assoc, CategoryTheory.NatTrans.op_whiskerRight_assoc, CategoryTheory.Functor.toPseudoFunctor'_map, CategoryTheory.Subobject.ofLEMk_comp, CategoryTheory.Bicategory.conjugateEquiv_id_comp_right_apply, CategoryTheory.Adjunction.leftAdjointUniq_trans_app_assoc, CategoryTheory.preadditiveYoneda_obj, CategoryTheory.CartesianMonoidalCategory.lift_lift_associator_inv, CategoryTheory.ShortComplex.comp_τ₂, CategoryTheory.Oplax.OplaxTrans.associator_inv_as_app, CategoryTheory.Functor.map_hom_inv, HomologicalComplex.pOpcycles_restrictionOpcyclesIso_inv, CategoryTheory.IsPushout.inl_snd', CategoryTheory.Functor.rightUnitor_hom_app, CategoryTheory.Comma.mapRightId_inv_app_left, CategoryTheory.EnrichedCategory.comp_id, CategoryTheory.mono_comp', CategoryTheory.PreGaloisCategory.toAut_surjective_isGalois_finite_family, HomologicalComplex.extend.mapX_some, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality', CategoryTheory.GradedObject.ιMapBifunctorBifunctor₂₃MapObj_eq_assoc, CategoryTheory.NatTrans.vcomp_app, CategoryTheory.SingleFunctors.comp_hom_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp_app, CategoryTheory.Pseudofunctor.presheafHom_obj, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.fromBiprod_δ_assoc, CategoryTheory.GradedObject.ιMapObjOrZero_mapMap, CategoryTheory.Functor.FullyFaithful.compUliftYonedaCompWhiskeringLeft_inv_app_app_down, CategoryTheory.ShortComplex.π₁Toπ₂_comp_π₂Toπ₃, CategoryTheory.Limits.IsColimit.ι_map_assoc, CompHausLike.LocallyConstant.incl_of_counitAppApp, CategoryTheory.Bicategory.Adjunction.homEquiv₂_apply, CategoryTheory.Functor.leftOpId_hom_app, CategoryTheory.Over.mapPullbackAdj_counit_app, CategoryTheory.Functor.ι_biproductComparison'_assoc, AlgebraicGeometry.Scheme.IdealSheafData.comapIso_hom_snd_assoc, CategoryTheory.Limits.MultispanIndex.ι_fstSigmaMap_assoc, CategoryTheory.WithTerminal.opEquiv_unitIso_hom_app, CategoryTheory.Limits.Pi.ι_π, CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoSelf_hom, CategoryTheory.Limits.CatCospanTransform.category_id_right, Rep.standardComplex.εToSingle₀_comp_eq, CategoryTheory.PreGaloisCategory.toAut_hom_app_apply, CategoryTheory.LocalizerMorphism.LeftResolution.Hom.comp_f, CategoryTheory.Functor.isoShift_inv_naturality, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_assoc, CategoryTheory.ShortComplex.RightHomologyMapData.commg'_assoc, HomologicalComplex.inr_biprodXIso_inv, CategoryTheory.Limits.Cofan.IsColimit.inj_desc, CategoryTheory.Equivalence.cancel_counitInv_right, CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_inv_hom, CategoryTheory.Comma.mapLeftId_hom_app_right, PartOrdEmb.hom_comp, CategoryTheory.Idempotents.Karoubi.HomologicalComplex.comp_p_d_assoc, CategoryTheory.braiding_rightUnitor_aux₁, SimplicialObject.Splitting.IndexSet.mk_snd_coe, CategoryTheory.ShortComplex.RightHomologyMapData.homologyMap_comm, AlgebraicGeometry.Scheme.Hom.app_appIso_inv_assoc, CompHausLike.sigmaComparison_eq_comp_isos, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict, CategoryTheory.Limits.Fork.hom_comp_ι, CategoryTheory.ShortComplex.SnakeInput.Hom.comm₁₂, CategoryTheory.rightDistributor_inv_comp_biproduct_π, CategoryTheory.Functor.CoreMonoidal.μIso_hom_natural_left, CategoryTheory.Localization.Monoidal.triangle_aux₁_assoc, CategoryTheory.μ_naturalityᵣ, CategoryTheory.Congruence.equivalence, CategoryTheory.Preadditive.smul_iso_hom, CategoryTheory.Oplax.StrongTrans.naturality_id_assoc, CategoryTheory.Functor.Monoidal.map_associator'_assoc, CategoryTheory.StrictlyUnitaryLaxFunctorCore.mapComp_naturality_right, CategoryTheory.Adjunction.compPreadditiveYonedaIso_inv_app_app_apply, CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.liftHom_fac, CategoryTheory.Join.mapWhiskerRight_comp, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₃, CochainComplex.HomComplex.Cochain.zero_cochain_comp_v, HomotopicalAlgebra.FibrantBrownFactorization.mk'_Z, CategoryTheory.Bicategory.Adj.forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj, CochainComplex.MappingConeCompHomotopyEquiv.hom_inv_id_assoc, CategoryTheory.MonoidalCategory.DayConvolution.hexagon_forward, CategoryTheory.Functor.leftOpRightOpEquiv_unitIso_inv_app, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_inv_app_unop, CategoryTheory.MorphismProperty.Over.map_comp, CategoryTheory.MonoidalCategory.associator_inv_naturality_left_assoc, FintypeCat.toProfinite_map_hom_hom_apply, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_comp, CategoryTheory.ShortComplex.mapLeftHomologyIso_hom_naturality, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_app, CategoryTheory.leftDistributor_hom_comp_biproduct_π, CategoryTheory.Adjunction.Triple.whiskerRight_rightToLeft_assoc, CategoryTheory.Equivalence.changeFunctor_unitIso_hom_app, CategoryTheory.WithTerminal.opEquiv_counitIso_hom_app, CategoryTheory.Limits.colimit.ι_inv_pre, CategoryTheory.Oplax.LaxTrans.naturality_id, CategoryTheory.HopfObj.one_antipode, TopCat.Presheaf.stalkPushforward_germ_assoc, CategoryTheory.Limits.pullback.comp_diagonal_assoc, AlgebraicGeometry.Scheme.IdealSheafData.comap_id, SSet.prodStdSimplex.objEquiv_naturality, TopCat.pullbackIsoProdSubtype_inv_fst_assoc, CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_inv_assoc, CategoryTheory.Preadditive.commGrpEquivalence_functor_obj_grp_inv, HomologicalComplex.stupidTruncMap_id, CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsOppositeOp, HomotopicalAlgebra.FibrantObject.HoCat.resolutionMap_fac, CategoryTheory.BicartesianSq.of_has_biproduct₂, CategoryTheory.IsFiltered.coeq₃_condition₃, Rep.coindVEquiv_symm_apply_coe, AlgebraicGeometry.Scheme.Pullback.range_fst_comp, CategoryTheory.ShortComplex.leftHomologyMap'_comp_assoc, CategoryTheory.BraidedCategory.unop_tensorμ, CategoryTheory.Square.Hom.comm₁₃, CategoryTheory.ComposableArrows.opEquivalence_unitIso_inv_app, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_left_unitor, AlgebraicGeometry.instDescendsAlongSchemeMinMorphismPropertySurjectiveFlatLocallyOfFinitePresentationOfQuasiCompactOfIsZariskiLocalAtTarget, CategoryTheory.ShortComplex.SnakeInput.naturality_φ₁_assoc, CategoryTheory.SimplicialObject.Augmented.const_obj_hom, HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom_desc_hom, CategoryTheory.instIsMonHomComp, CategoryTheory.Limits.prod.diag_map_fst_snd, CochainComplex.g_shortComplexTruncLEX₃ToTruncGE, AlgCat.ofHom_comp, HomologicalComplex₂.d_f_comp_d_f_assoc, CategoryTheory.Pseudofunctor.toLax_mapComp, TopologicalSpace.OpenNhds.op_map_id_obj, CategoryTheory.MorphismProperty.Comma.instFullTopCommaForget, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_restriction_assoc, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.associator_naturality, CategoryTheory.PreOneHypercover.multifork_ι, CategoryTheory.Dial.rightUnitorImpl_inv_F, FinBddDistLat.coe_id, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.counitIso_inv, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_inv_app, CategoryTheory.Mathlib.Tactic.MonTauto.associator_hom_comp_tensorHom_tensorHom_assoc, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_ihom_ev_app_assoc, AlgebraicGeometry.Proj.SpecMap_awayMap_awayι_assoc, CategoryTheory.nerve.nonempty_compStruct_iff, AlgebraicGeometry.Scheme.isoSpec_hom_naturality_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_hom_app, CategoryTheory.Limits.braid_natural_assoc, TopCat.prodIsoProd_hom_snd_assoc, CategoryTheory.isCommMonObj_iff_commutator_eq_toUnit_η, CategoryTheory.PreOneHypercover.trivial_toPreZeroHypercover, CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse_obj_hom, AlgebraicGeometry.pullbackSpecIso_inv_snd, AlgebraicGeometry.IsImmersion.instMapDescScheme, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₃, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι_ι, CommGrpCat.coyonedaType_map_app, HomologicalComplex.homotopyCofiber.inlX_sndX_assoc, CategoryTheory.ShortComplex.Homotopy.compRight_h₀, CategoryTheory.Pseudofunctor.isoMapOfCommSq_horiz_id, CategoryTheory.Types.instFullForgetTypeHom, CategoryTheory.Functor.Monoidal.μ_fst_assoc, CategoryTheory.Oplax.OplaxTrans.naturality_comp, HomotopicalAlgebra.trivialCofibrations_sub_weakEquivalences, CategoryTheory.Limits.PreservesKernel.iso_inv_ι_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.leftUnitor_inv_one_tensor_mul_assoc, CategoryTheory.Equivalence.map_η_comp_η, CategoryTheory.CommSq.shortComplex_f, CategoryTheory.CatEnriched.id_hComp_heq, CategoryTheory.MonObj.comp_one, AlgebraicGeometry.HasAffineProperty.affineAnd_eq_of_propertyIsLocal, CategoryTheory.CosimplicialObject.δ_comp_δ, CategoryTheory.NatTrans.removeLeftOp_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app_assoc, CategoryTheory.Localization.LeftBousfield.le_W_iff, CategoryTheory.CartesianMonoidalCategory.tensorHom_fst, AlgebraicGeometry.quasiCompact_comp, CategoryTheory.Limits.pullbackConeEquivBinaryFan_functor_map_hom, CategoryTheory.MonoidalCategory.DayConvolution.associator_inv_unit_unit, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_hom, HomologicalComplex.mapBifunctorAssociatorX_hom_D₂, CategoryTheory.ShortComplex.leftRightHomologyComparison'_eq_descH, CategoryTheory.Join.pseudofunctorLeft_mapComp_hom_toNatTrans_app, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural, CategoryTheory.Sheaf.toImage_ι, CategoryTheory.op_tensor_op, CategoryTheory.CommSq.HasLift.iff_op, CategoryTheory.Equivalence.counit_naturality_assoc, CategoryTheory.StructuredArrow.mapNatIso_functor_obj_hom, CategoryTheory.Limits.Types.Small.productIso_inv_comp_π, ModuleCat.restrictScalarsId'App_inv_naturality, CategoryTheory.CostructuredArrow.mapIso_unitIso_inv_app_left, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_inv_hom_assoc, CategoryTheory.Limits.biproduct.map_π, MonCat.ofHom_comp, CategoryTheory.Limits.FintypeCat.productEquiv_apply, CategoryTheory.MorphismProperty.RightFraction.map_hom_ofInv_id_assoc, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_inv_naturality, CategoryTheory.MonoidalCategory.DayConvolution.hexagon_reverse, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left, CategoryTheory.Discrete.instSubsingletonDiscreteHom, CategoryTheory.uliftYonedaEquiv_symm_map, CategoryTheory.Limits.ConeMorphism.map_w_assoc, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_hom_app, CategoryTheory.Functor.prod_ε_snd, CategoryTheory.MorphismProperty.le_ind, CategoryTheory.PreOneHypercover.id_h₀, CategoryTheory.Enriched.FunctorCategory.homEquiv_apply_π, HomologicalComplex.homologyι_comp_fromOpcycles, CategoryTheory.MorphismProperty.RightFraction.map_s_comp_map, AlgebraicGeometry.Etale.instHasOfPostcompPropertySchemeMinMorphismPropertyLocallyOfFiniteTypeFormallyUnramified, CategoryTheory.Functor.cones_obj, CategoryTheory.preadditiveYonedaMap_app, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app', CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_neg_f, groupCohomology.comp_d₂₃_eq, CategoryTheory.IsSplitCoequalizer.leftSection_top, CategoryTheory.Triangulated.TStructure.le_monotone, CategoryTheory.NonPreadditiveAbelian.sub_sub_sub, CategoryTheory.MonoidalCategory.DayFunctor.equiv_counitIso_inv_app, CategoryTheory.homOfLE_op_comp_eqToHom_assoc, CategoryTheory.Square.unop_f₁₂, CategoryTheory.Lax.LaxTrans.naturality_comp, AlgebraicGeometry.Spec.topMap_id, CategoryTheory.NonPreadditiveAbelian.σ_comp, CategoryTheory.Mon.tensorObj_one, CategoryTheory.Presieve.preZeroHypercover_I₀, SSet.comp_app_assoc, CondensedMod.isDiscrete_iff_isDiscrete_forget, CochainComplex.HomComplex.Cochain.toSingleMk_v_eq_zero, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_le, CategoryTheory.PreservesImage.factorThruImage_comp_hom_assoc, FintypeCat.comp_apply, HomotopicalAlgebra.weakEquivalences_op_iff, CategoryTheory.Adjunction.unit_app_shift_commShiftIso_inv_app, CategoryTheory.Limits.zero_of_target_iso_zero', AlgebraicGeometry.Proj.pullbackAwayιIso_inv_fst, CategoryTheory.Comma.mapRightComp_inv_app_right, CategoryTheory.Subobject.ofLEMk_comp_ofMkLE, CategoryTheory.Localization.SmallShiftedHom.comp_mk₀_id, CategoryTheory.Abelian.subobjectIsoSubobjectOp_apply, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_naturality_assoc, CategoryTheory.Limits.biprod.fstKernelFork_ι, CategoryTheory.Limits.biprod.symmetry', CategoryTheory.SingleFunctors.Hom.id_hom, CategoryTheory.IsMod_Hom.smul_hom, CategoryTheory.Limits.biproduct.matrix_desc_assoc, CategoryTheory.Limits.Multicofork.condition_assoc, quasiIsoAt_comp, HomotopicalAlgebra.trivialFibrations_sub_fibrations, CategoryTheory.Limits.BinaryFan.braiding_hom_snd, ProfiniteGrp.comp_apply, CategoryTheory.SemiCartesianMonoidalCategory.comp_toUnit_assoc, FintypeCat.uSwitchEquiv_naturality, AlgebraicGeometry.Scheme.hom_base_inv_base_assoc, CategoryTheory.Functor.whiskerRight_id', CategoryTheory.IsIso.inv_id, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_right_hom, CategoryTheory.Iso.inv_comp_eq, CategoryTheory.Monad.left_unit, AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex_homotopyHomInvId, HomologicalComplex₂.ι_D₂, AlgebraicTopology.DoldKan.QInfty_f_0, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom, CategoryTheory.GlueData.ι_gluedIso_inv_assoc, CategoryTheory.kernelUnopUnop_inv, HomologicalComplex.homologyMap_neg, CategoryTheory.ShortComplex.RightHomologyData.wι_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π, CategoryTheory.Iso.map_hom_inv_id_assoc, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_right, AddSemigrp.hom_id, CategoryTheory.ReflQuiv.comp_eq_comp, CategoryTheory.Functor.compFlipUncurryIso_inv_app, CategoryTheory.Functor.CommShift.ofIso_commShiftIso_hom_app, CategoryTheory.NatTrans.leftOp_id, CategoryTheory.Limits.limit.isoLimitCone_hom_π_assoc, CategoryTheory.Quotient.LiftCommShift.iso_hom_app, CategoryTheory.Enriched.FunctorCategory.diagram_map_app, CategoryTheory.Oplax.StrongTrans.id_naturality_inv, CategoryTheory.CosimplicialObject.comp_right_app, CategoryTheory.Functor.relativelyRepresentable.pullback₃.map_p₁_comp, CategoryTheory.Limits.pullback_symmetry_hom_of_epi_eq, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_comp, CategoryTheory.InjectiveResolution.Hom.ι_comp_hom_assoc, CategoryTheory.OplaxFunctor.mapComp_assoc_left_app, CategoryTheory.Pretriangulated.id_hom₃, CategoryTheory.ShortComplex.homology_π_ι, CategoryTheory.preservesColimitIso_inv_comp_desc, AlgebraicGeometry.IsFinite.eq_proper_inf_locallyQuasiFinite, Action.hom_inv_hom, FintypeCat.comp_hom, CategoryTheory.ShortComplex.homologyι_naturality_assoc, CategoryTheory.Functor.Monoidal.coreMonoidalTransport_μIso_hom, CategoryTheory.Limits.Cocone.category_comp_hom, CategoryTheory.NatTrans.IsMonoidal.unit, AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ, CategoryTheory.InjectiveResolution.ι_f_succ, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms_le_monomorphisms, CategoryTheory.Functor.lanUnit_app_app_lanAdjunction_counit_app_app, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_snd, CategoryTheory.RetractArrow.op_r_right, CategoryTheory.Adjunction.compUliftCoyonedaIso_inv_app_app_down, CategoryTheory.Lax.OplaxTrans.vComp_naturality_comp, CategoryTheory.MonoidalCategory.id_tensor_associator_inv_naturality, AlgebraicGeometry.AffineSpace.map_comp, CategoryTheory.MonObj.one_comp_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_assoc, CategoryTheory.LocalizerMorphism.LeftResolution.opEquivalence_inverse, FintypeCat.equivEquivIso_symm_apply_symm_apply, CategoryTheory.presheafHom_obj, CategoryTheory.FinCategory.categoryAsType_id, CategoryTheory.GradedObject.mapObj_ext_iff, CategoryTheory.PreGaloisCategory.evaluation_injective_of_isConnected, prevD_eq_toPrev_dTo, CategoryTheory.Limits.IsColimit.homEquiv_apply, ModuleCat.cokernel_π_cokernelIsoRangeQuotient_hom, ModuleCat.extendScalars_assoc_assoc, Alexandrov.principals_map, CategoryTheory.ShortComplex.cokernel_π_comp_cokernelToAbelianCoimage, CategoryTheory.Limits.comp_zero, CategoryTheory.ObjectProperty.topEquivalence_unitIso, CategoryTheory.Endofunctor.Coalgebra.Hom.h_assoc, CategoryTheory.MorphismProperty.instHasFactorizationOppositeOp, AlgebraicTopology.DoldKan.MorphComponents.preComp_b, CategoryTheory.Limits.monoFactorisationZero_m, CategoryTheory.CosimplicialObject.σ_naturality, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst, CategoryTheory.Limits.biprod.lift_mapBiprod, CategoryTheory.ObjectProperty.InheritedFromTarget.op, CategoryTheory.Limits.BinaryBiconeMorphism.winl, CategoryTheory.Preadditive.neg_iso_hom, CategoryTheory.Groupoid.vertexGroup_inv, CategoryTheory.Limits.PullbackCone.op_inr, CategoryTheory.MorphismProperty.Over.instPreservesFiniteLimitsTopPullback, CategoryTheory.homOfLE_refl, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_assoc, CategoryTheory.MonoidalCategory.id_tensor_rightUnitor_inv, CategoryTheory.Oplax.LaxTrans.id_app, CategoryTheory.NatTrans.app_add, CategoryTheory.e_comp_id_assoc, CategoryTheory.EnrichedCategory.id_comp, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_π_app, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_leftUnitor_inv_as_app, AlgebraicTopology.DoldKan.Γ₂_obj_p_app, SimplexCategory.eq_σ_comp_of_not_injective, CategoryTheory.Limits.ι_colimMap, prodIsoPullback_hom_fst_assoc, CategoryTheory.EnrichedFunctor.id_map, CategoryTheory.Over.prodLeftIsoPullback_hom_snd, CategoryTheory.Functor.lanUnit_app_whiskerLeft_lanAdjunction_counit_app, CategoryTheory.Functor.whiskerLeft_obj_map_bijective_of_isCoverDense, SemiRingCat.hom_id, ModuleCat.id_apply, CategoryTheory.Cat.HasLimits.homDiagram_map, CategoryTheory.Limits.parallelPairOpIso_hom_app_one, AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_comp_iff_of_isOpenImmersion, Homotopy.nullHomotopicMap'_comp, CategoryTheory.Limits.walkingCospanOpEquiv_counitIso_inv_app, CategoryTheory.Pseudofunctor.map₂_right_unitor_assoc, CategoryTheory.Functor.mapTriangleInvRotateIso_hom_app_hom₃, CategoryTheory.GrothendieckTopology.Cover.Arrow.Relation.ext_iff, CategoryTheory.monoidalOfHasFiniteProducts.associator_hom_snd_fst, CategoryTheory.GrpObj.inv_comp_assoc, CategoryTheory.Bicategory.Prod.sectL_mapComp_hom, CategoryTheory.Comon.comp_hom, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff, CategoryTheory.PreZeroHypercover.Hom.w₀, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc_assoc, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_assoc, CategoryTheory.Limits.IsColimit.desc_self, CategoryTheory.Limits.biprod.braiding_map_braiding_assoc, CategoryTheory.Limits.preservesKernel_zero, CategoryTheory.ThinSkeleton.thin, CategoryTheory.rightDistributor_ext_right_iff, CategoryTheory.Abelian.Ext.mk₀_smul, CategoryTheory.CostructuredArrow.mkPrecomp_right, HomotopicalAlgebra.AttachCells.cell_def, CategoryTheory.Limits.coprod.leftUnitor_hom, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso_inv_app_f, CategoryTheory.Bicategory.associator_inv_naturality_left, CategoryTheory.ShortComplex.opMap_τ₃, CategoryTheory.Functor.ι_colimitIsoOfIsLeftKanExtension_inv, CategoryTheory.Functor.map_zero, CategoryTheory.PreOneHypercover.multicospanIndex_snd, AlgebraicGeometry.Proj.basicOpenToSpec_SpecMap_awayMap, CategoryTheory.IsUniversalColimit.isPullback_prod_of_isColimit, CategoryTheory.GradedObject.Monoidal.tensorHom_comp_tensorHom, CategoryTheory.Limits.PreservesPullback.iso_inv_snd, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc, HomotopicalAlgebra.PrepathObject.trans_p₁, CategoryTheory.opEquiv_apply, CategoryTheory.Limits.limit.pre_π_assoc, CategoryTheory.Pseudofunctor.CoGrothendieck.instFullαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor, CategoryTheory.CommSq.toLoc, CategoryTheory.Limits.PullbackCone.op_ι_app, CategoryTheory.Limits.HasEqualizersOfHasPullbacksAndBinaryProducts.pullbackFst_eq_pullback_snd, CategoryTheory.ShortComplex.opcyclesOpIso_hom_naturality_assoc, AlgebraicGeometry.Scheme.Cover.ι_fromGlued_assoc, CategoryTheory.Functor.Monoidal.coreMonoidalTransport_εIso_hom, CategoryTheory.Iso.hom_inv_id_triangle_hom₂, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_hom_app, CategoryTheory.Functor.constComp_inv_app, CategoryTheory.Functor.Monoidal.map_δ_μ_assoc, CategoryTheory.coprodComparison_tensorRight_braiding_hom, SemiNormedGrp.zero_apply, AddMonCat.coe_comp, CategoryTheory.Limits.biprod.inl_desc_assoc, BoolAlg.hom_id, groupHomology.mapCycles₂_id_comp, CategoryTheory.Comon.forget_η, SSet.Truncated.spine_map_subinterval, CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_eq, CategoryTheory.Limits.hasImage_iso_comp, CategoryTheory.Limits.π_reflexiveCoequalizerIsoCoequalizer_inv_assoc, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_comp_mapComp'_inv, ProfiniteAddGrp.comp_apply, TopCat.Presheaf.presheafEquivOfIso_inverse_obj_map, TopCat.Presheaf.pushforwardEq_hom_app, CategoryTheory.isSeparator_sigma, CategoryTheory.Bimon.equivMonComonCounitIsoAppXAux_inv, CategoryTheory.ComonadHom.id_toNatTrans, CategoryTheory.MonoidalCategory.whiskerRight_id_symm, CategoryTheory.GradedObject.mapBifunctorRightUnitorCofan_inj, CategoryTheory.Limits.biprod.inl_map, SSet.PtSimplex.RelStruct.δ_castSucc_map_assoc, CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc, smoothSheafCommRing.forgetStalk_inv_comp_eval_assoc, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality_app, CategoryTheory.Functor.prod_η_snd, CategoryTheory.Iso.hom_inv_id_triangle_hom₂_assoc, SimplexCategoryGenRel.standardσ_comp_standardσ_assoc, CategoryTheory.Discrete.functor_map_id, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero_assoc, AlgebraicGeometry.Scheme.fromSpecStalk_appTop, AlgebraicTopology.AlternatingFaceMapComplex.d_squared, CategoryTheory.Square.op_f₂₄, CategoryTheory.Limits.inr_pushoutZeroZeroIso_hom, CategoryTheory.Limits.pushoutCoconeOfLeftIso_inl, CategoryTheory.Bicategory.leftUnitor_inv_naturality, CategoryTheory.ObjectProperty.IsLocal.inf, CategoryTheory.Comonad.delta_naturality_assoc, CategoryTheory.Endofunctor.Algebra.Initial.right_inv, CategoryTheory.Join.mapWhiskerRight_whiskerRight, CategoryTheory.ShortComplex.opcyclesMap_add, CategoryTheory.Presheaf.isLocallySurjective_comp_iff, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturality_assoc, CategoryTheory.ShiftMkCore.add_zero_hom_app, AlgebraicGeometry.Scheme.GlueData.glue_condition, CategoryTheory.ShortComplex.mapHomologyIso_hom_naturality_assoc, CategoryTheory.GradedObject.singleObjApplyIsoOfEq_inv_single_map, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_def', UniformSpaceCat.extension_comp_coe, CategoryTheory.StructuredArrow.IsUniversal.existsUnique, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_inv_hom, CategoryTheory.Limits.biprod.decomp_hom_to, CategoryTheory.Pseudofunctor.DescentData.nonempty_fullyFaithful_toDescentData_iff_of_sieve_eq, CategoryTheory.Biprod.inr_ofComponents, CategoryTheory.Functor.liftOfIsRightKanExtension_fac_app, CategoryTheory.Limits.opCoproductIsoProduct_hom_comp_π, CategoryTheory.Limits.pullbackConeEquivBinaryFan_counitIso, CategoryTheory.Limits.PreservesPullback.iso_inv_fst, AlgebraicGeometry.pullbackRestrictIsoRestrict_inv_fst, CategoryTheory.Functor.congr_hom, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_map_left, CategoryTheory.Sum.swapCompInl_hom_app, SSet.PtSimplex.MulStruct.δ_succ_succ_map_assoc, CategoryTheory.Equivalence.inverseFunctor_map, TopCat.presheafToTop_obj, CategoryTheory.Functor.OplaxMonoidal.oplax_right_unitality, CategoryTheory.Functor.Monoidal.map_whiskerLeft_assoc, CategoryTheory.ShiftedHom.comp_mk₀, CategoryTheory.StructuredArrow.mapNatIso_functor_map_right, CategoryTheory.GradedObject.Monoidal.symmetry_assoc, CategoryTheory.Oplax.OplaxTrans.Modification.whiskerLeft_naturality_assoc, CategoryTheory.Biprod.ofComponents_snd, CategoryTheory.Arrow.mk_injective, CategoryTheory.Functor.LaxLeftLinear.μₗ_naturality_right_assoc, CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono'_g'_τ₃, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc, ModuleCat.exteriorPower.iso₁_hom_naturality, Bimod.TensorBimod.middle_assoc', HomologicalComplex₂.total.mapAux.d₁_mapMap, CategoryTheory.ShortComplex.unop_f, CategoryTheory.Cat.associator_inv_app, CategoryTheory.Limits.pullback_diagonal_map_snd_fst_fst, CategoryTheory.Bicategory.associator_naturality_right, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counitIso_hom_app_tensor_assoc, CategoryTheory.MonoidalCategory.DayConvolution.pentagon, CategoryTheory.Limits.inr_pushoutLeftPushoutInrIso_inv_assoc, CategoryTheory.NonPreadditiveAbelian.sub_add, CategoryTheory.SmallObject.FunctorObjIndex.comm, CategoryTheory.IsSplitCoequalizer.leftSection_bottom, HomologicalComplex.singleObjHomologySelfIso_hom_singleObjHomologySelfIso_inv_assoc, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_hom_app_f, FundamentalGroupoid.instSubsingletonHomPUnit, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_apply, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc_assoc, groupHomology.cyclesMap_comp_assoc, CochainComplex.mappingCone.lift_f_fst_v_assoc, CategoryTheory.Limits.biproduct.lift_matrix_assoc, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_snd, CategoryTheory.ShortComplex.LeftHomologyMapData.homologyMap_comm, AlgebraicGeometry.PresheafedSpace.Γ_map_op, CategoryTheory.simplicialToCosimplicialAugmented_map_left, CategoryTheory.Limits.Cocones.extendId_hom_hom, CategoryTheory.Bicategory.Prod.sectL_obj, CategoryTheory.Limits.biproduct.lift_desc_assoc, CategoryTheory.NatTrans.leftDerivedToHomotopyCategory_comp_assoc, CategoryTheory.Cat.FreeRefl.multiplicativeClosure_morphismPropertyHomMk, HomologicalComplex.cyclesIsoSc'_inv_iCycles_assoc, CategoryTheory.Limits.prod.leftUnitor_inv_naturality_assoc, CategoryTheory.InducedCategory.comp_hom_assoc, AlgebraicGeometry.Scheme.Pullback.Triplet.Spec_map_tensor_isPullback, HomologicalComplex.mapBifunctorMapHomotopy.zero₁, CommAlgCat.ofHom_id, CategoryTheory.kernelCokernelCompSequence.ι_fst, CategoryTheory.Monad.comparisonForget_hom_app, DistLat.hom_id, CategoryTheory.Subgroupoid.coe_comp_coe, HomotopicalAlgebra.cofibrations_op, CategoryTheory.Monoidal.tensorUnit_map, CategoryTheory.OverPresheafAux.YonedaCollection.map₂_snd, AlgebraicGeometry.IsOpenImmersion.isoOfRangeEq_inv_fac_assoc, CategoryTheory.Preadditive.epi_iff_cancel_zero, CategoryTheory.Dial.comp_le_lemma, CategoryTheory.Limits.biprod.braiding_map_braiding, CategoryTheory.Sieve.comp_mem_iff, Homotopy.dNext_zero_chainComplex, HomologicalComplex.mapBifunctor₂₃.d₃_eq_zero, CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaObj, CategoryTheory.tensorRightHomEquiv_symm_coevaluation_comp_whiskerRight, CategoryTheory.MonoidalOpposite.tensorIso_hom_app_unmop, CategoryTheory.Over.whiskerRight_left_snd_assoc, CategoryTheory.Sheaf.ΓHomEquiv_naturality_left, CategoryTheory.Arrow.w_mk_right, CategoryTheory.Limits.biproduct.matrixEquiv_apply, CategoryTheory.ShortComplex.Homotopy.compRight_h₁, CategoryTheory.NatTrans.mapHomologicalComplex_comp, CategoryTheory.Monad.algebraFunctorOfMonadHomComp_hom_app_f, CategoryTheory.InjectiveResolution.ι_f_zero_comp_complex_d_assoc, FintypeCat.hom_ext_iff, DerivedCategory.to_singleFunctor_obj_eq_zero_of_injective, CategoryTheory.Cat.rightUnitor_hom_app, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_snd_snd, CategoryTheory.Functor.whiskerLeft_comp_whiskerRight_assoc, CategoryTheory.Functor.Monoidal.whiskerLeft_ε_η_assoc, CategoryTheory.kernelOpUnop_inv, CategoryTheory.Quiv.lift_obj, CategoryTheory.Under.eqToHom_right, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_right_app, CategoryTheory.Limits.Fork.unop_ι_app_one, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app_apply, AlgebraicGeometry.Scheme.id_appTop, AlgebraicGeometry.Scheme.Cover.gluedCoverT'_fst_fst, CategoryTheory.DifferentialObject.ext_iff, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.g'_eq, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerLeft_assoc, AlgebraicGeometry.pullbackSpecIso_hom_base, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_apply_f, CategoryTheory.Linear.smulOfRingMorphism_smul_eq, CategoryTheory.shiftComm_hom_comp_assoc, CategoryTheory.Limits.biproduct.ι_matrix, CategoryTheory.yonedaMon_naturality_assoc, CategoryTheory.Limits.IsInitial.to_self, CategoryTheory.Preadditive.comp_sum_assoc, HomologicalComplex₂.d₁_eq, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocIso_hom_naturality_assoc, CategoryTheory.SmallObject.SuccStruct.extendToSuccObjIso_hom_naturality, Bimod.LeftUnitorBimod.inv_hom_id, DerivedCategory.right_fac_of_isStrictlyLE_of_isStrictlyGE, CategoryTheory.Oplax.LaxTrans.id_naturality, CategoryTheory.Limits.hasPushout_assoc_symm, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_monotone, CategoryTheory.SmallObject.SuccStruct.prop.arrowIso_inv_right, AlgebraicGeometry.IsOpenImmersion.comp, CategoryTheory.Functor.OplaxMonoidal.δ_comp_whiskerLeft_δ_assoc, groupCohomology.π_comp_H0IsoOfIsTrivial_hom, CategoryTheory.kernelCokernelCompSequence.snakeInput_L₃_f, CategoryTheory.Limits.coprodComparison_inl_assoc, CategoryTheory.TwistShiftData.shiftFunctorZero_hom_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomLeft_tensor, ContinuousCohomology.Iobj_ρ_apply, CategoryTheory.Limits.inl_inl_pushoutLeftPushoutInrIso_hom, CategoryTheory.ProjectiveResolution.Hom.hom_comp_π_assoc, CategoryTheory.Comon.ComonToMonOpOp_map, SheafOfModules.pushforwardComp_inv_app_val_app, CategoryTheory.Enriched.FunctorCategory.enriched_id_comp_assoc, CategoryTheory.CartesianMonoidalCategory.lift_braiding_inv, MonCat.hom_one, GrpCat.SurjectiveOfEpiAuxs.comp_eq, CommRingCat.Colimits.cocone_naturality, CategoryTheory.Pseudofunctor.ObjectProperty.ι_naturality, CategoryTheory.Limits.prodComparison_fst, CategoryTheory.Functor.Monoidal.transport_ε, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_id, LightCondensed.internallyProjective_iff_tensor_condition, CategoryTheory.Limits.isPushout_coequalizer_coprod, CategoryTheory.CartesianClosed.curry_natural_right_assoc, CategoryTheory.Limits.kernelBiprodFstIso_inv, CategoryTheory.MorphismProperty.isStableUnderCobaseChange_iff_pushouts_le, CategoryTheory.Functor.leftDerived_fac_assoc, HomologicalComplex.cyclesMap_comp, CategoryTheory.CartesianMonoidalCategory.tensorHom_snd_assoc, CategoryTheory.endofunctorMonoidalCategory_associator_inv_app, AlgebraicGeometry.Scheme.Spec_map_presheaf_map_eqToHom, CategoryTheory.Limits.IsLimit.pullbackConeEquivBinaryFanFunctor_lift_left, AlgebraicGeometry.Scheme.Opens.toSpecΓ_appTop_assoc, AlgebraicGeometry.smooth_comp, CategoryTheory.NatTrans.app_homology, SSet.id_app, CategoryTheory.ShortComplex.Homotopy.smul_h₀, CochainComplex.HomComplex.Cochain.ofHom_neg, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_app_fst_app, CategoryTheory.PreGaloisCategory.instFullContActionFintypeCatHomCarrierAutFunctorFunctorToContAction, CategoryTheory.Pseudofunctor.mapComp_id_right_hom, CategoryTheory.Functor.currying_counitIso_inv_app_app, CategoryTheory.Functor.OplaxLeftLinear.δₗ_naturality_left_assoc, HomologicalComplex.opcyclesToCycles_iCycles_assoc, CategoryTheory.yonedaMonObj_map, Homotopy.prevD_chainComplex, CategoryTheory.CartesianMonoidalCategory.map_toUnit_comp_terminalComparison_assoc, CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_of_mono₃, CategoryTheory.MonoidalCategory.whiskerLeft_id_assoc, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_point_assoc, CategoryTheory.ShortComplex.homologyMap'_op, SSet.spine_arrow, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_unit_app, CategoryTheory.Oplax.StrongTrans.Modification.naturality_assoc, CategoryTheory.CostructuredArrow.eta_hom_left, CategoryTheory.eComp_eHomWhiskerRight, groupCohomology.comp_d₀₁_eq, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality_assoc, CategoryTheory.over_def, CategoryTheory.Limits.FormalCoproduct.eval_map_app, CategoryTheory.ShortComplex.Homotopy.smul_h₃, CategoryTheory.LaxFunctor.mapComp_naturality_right_app_assoc, CategoryTheory.Grothendieck.comp_fiber, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_inv_app_hom, CategoryTheory.instIsSplitMonoComp, CategoryTheory.Limits.kernelBiproductToSubtypeIso_hom, CategoryTheory.ShortComplex.HomologyData.ofIso_left_i, CategoryTheory.Adjunction.mapGrp_unit, CategoryTheory.Limits.imageMonoIsoSource_hom_self, CategoryTheory.Subgroupoid.mem_discrete_iff, CategoryTheory.Subfunctor.ofSection_obj, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_hom_fac_assoc, CategoryTheory.uliftYonedaEquiv_naturality, CategoryTheory.SimplicialObject.δ_comp_σ_self'_assoc, CategoryTheory.MonoidalCategory.hom_inv_whiskerRight, CategoryTheory.MonoidalCategory.comp_tensor_id_assoc, CategoryTheory.Dial.whiskerRight_f, CategoryTheory.ShortComplex.cyclesMap_smul, CategoryTheory.Over.associator_inv_left_fst_fst_assoc, CategoryTheory.IsFiltered.coeq₃_condition₁, CategoryTheory.MonoidalCategory.triangle_assoc, CategoryTheory.Comon.forget_δ, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_associator_hom_as_app, CategoryTheory.MonoidalCategory.tensor_left_iff, CategoryTheory.Functor.curry₃_obj_map_app_app, CategoryTheory.Functor.coreId_inv_app_iso_hom, HomologicalComplex.homologyπ_singleObjHomologySelfIso_hom_assoc, CategoryTheory.Grothendieck.map_map, CategoryTheory.GradedObject.categoryOfGradedObjects_id, CategoryTheory.IsIso.inv_hom_id, CategoryTheory.Lax.LaxTrans.vComp_naturality_naturality, CategoryTheory.Bicategory.prod_whiskerRight_snd, CategoryTheory.OrthogonalReflection.toSucc_surjectivity, CategoryTheory.Under.mapId_inv, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocIso_hom_naturality, CategoryTheory.Functor.isoShift_hom_naturality, CategoryTheory.Adjunction.map_restrictFullyFaithful_unit_app_assoc, CategoryTheory.Limits.image.factorThruImage_preComp, CategoryTheory.CatEnrichedOrdinary.hComp_id, HomologicalComplex.instQuasiIsoMapOppositeSymmUnopFunctorOp, CategoryTheory.MonObj.one_def, CategoryTheory.CatCenter.app_add, CategoryTheory.Limits.pullbackSymmetry_inv_comp_fst_assoc, CategoryTheory.MonoidalClosed.curry'_ihom_map, CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_inv, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.functorMap_comp, CategoryTheory.Limits.CokernelCofork.condition, CategoryTheory.GradedObject.ι_mapTrifunctorMapMap_assoc, CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_inv_desc_assoc, CategoryTheory.conjugateEquiv_counit_symm, CochainComplex.HomComplex.Cochain.zero_v, AlgebraicGeometry.Scheme.stalkMap_congr_point_assoc, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_base, SimplicialObject.Splitting.IndexSet.eqId_iff_mono, HomotopicalAlgebra.PrepathObject.RightHomotopy.refl_h, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.ev_naturality_app, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_inv_left, smoothSheafCommRing.forgetStalk_inv_comp_eval, CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoSelf_hom_assoc, CategoryTheory.Limits.Fork.unop_op_ι, CategoryTheory.CartesianMonoidalCategory.prodComparison_snd_assoc, CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_map₂, CategoryTheory.Limits.cokernel.condition, CategoryTheory.Functor.CommShift.isoZero'_inv_app, CategoryTheory.Grothendieck.ιCompMap_inv_app_fiber, CategoryTheory.Limits.IsLimit.ofIsoLimit_lift, CategoryTheory.StrictPseudofunctor.comp_mapId_inv, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_assoc, CategoryTheory.GradedObject.Monoidal.tensorHom_comp_tensorHom_assoc, TopCat.Sheaf.extend_hom_app, CategoryTheory.ObjectProperty.isSeparating_unop_iff, CategoryTheory.Functor.map_add, CategoryTheory.MonObj.mul_mul_mul_comm'_assoc, CategoryTheory.OverPresheafAux.YonedaCollection.yonedaEquivFst_eq, CategoryTheory.CatEnrichedOrdinary.hComp_comp, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_val_obj, CategoryTheory.conj_eqToHom_iff_heq', HomologicalComplex.biprod_inr_snd_f, CategoryTheory.NonPreadditiveAbelian.sub_zero, CategoryTheory.op_inv_braiding, CategoryTheory.Functor.map_hom_inv_assoc, CategoryTheory.PreZeroHypercover.inj_sigmaOfIsColimit_f_assoc, ContinuousMap.Homotopy.apply_one_path, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₁, HomologicalComplex.id_f, CategoryTheory.id_app, CategoryTheory.Localization.SmallShiftedHom.mk₀_id_comp, CategoryTheory.Functor.Monoidal.whiskerRight_η_ε_assoc, ModuleCat.restrictScalarsId'App_hom_naturality_assoc, CategoryTheory.Limits.opParallelPairIso_hom_app_zero, CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.g, CategoryTheory.Bicategory.Adj.id_τl, CategoryTheory.Localization.Monoidal.associator_naturality₃, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_inr, CategoryTheory.Over.associator_hom_left_fst, SimplexCategory.Truncated.δ₂_zero_comp_σ₂_zero_assoc, CategoryTheory.Limits.BinaryBiconeMorphism.wsnd, CategoryTheory.ShortComplex.cyclesMap'_comp, CategoryTheory.Bicategory.Adj.comp_τl, CategoryTheory.Limits.map_id_left_eq_curry_map, HomologicalComplex.singleMapHomologicalComplex_inv_app_self, AlgebraicGeometry.Scheme.fromSpecStalk_toSpecΓ, CategoryTheory.ShortComplex.leftHomologyMap_add, CategoryTheory.TwoSquare.guitartExact_id, SimplexCategoryGenRel.δ_comp_σ_succ, CategoryTheory.MonObj.one_mul_assoc, CategoryTheory.Functor.Initial.extendCone_obj_π_app', ModuleCat.homAddEquiv_symm_apply_hom, CategoryTheory.IsPushout.zero_bot, CategoryTheory.Limits.BinaryBicone.ofLimitCone_inr, CategoryTheory.Subfunctor.equalizer.ι_ι_assoc, TopCat.Presheaf.map_germ_eq_Γgerm, CategoryTheory.Limits.WidePullback.hom_ext_iff, MulEquiv.toSingleObjEquiv_unitIso_hom, HeytAlg.id_apply, CategoryTheory.Abelian.LeftResolution.karoubi.F_map_f, SimplexCategoryGenRel.δ_comp_σ_of_le_assoc, CategoryTheory.Preadditive.smul_iso_inv, CategoryTheory.IsPushout.zero_left, groupHomology.coinvariantsMk_comp_H0Iso_inv, CategoryTheory.GradedObject.ιMapObjOrZero_mapMap_assoc, CategoryTheory.ObjectProperty.EssentiallySmall.exists_small_le', CategoryTheory.Pseudofunctor.ObjectProperty.mapId_inv_app, CategoryTheory.Limits.ColimitPresentation.map_ι, CategoryTheory.Limits.PreservesLimitPair.iso_inv_fst_assoc, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_map_right_right, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_counitIso, CategoryTheory.Limits.inr_zeroCoprodIso_hom, CategoryTheory.Limits.Cocone.toCostructuredArrowCompToOverCompForget_inv_app, CategoryTheory.Limits.PreservesPushout.inl_iso_inv, CategoryTheory.PrelaxFunctor.mkOfHomFunctors_toPrelaxFunctorStruct, ModuleCat.image.lift_fac, CategoryTheory.Limits.CatCospanTransform.rightUnitor_inv_right_app, CategoryTheory.ShortComplex.Hom.id_τ₁, CategoryTheory.Bimon.ofMon_Comon_ObjX_one, CategoryTheory.Bicategory.Comonad.comul_assoc_flip_assoc, AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTrans, CategoryTheory.EnrichedFunctor.comp_map, CategoryTheory.BraidedCategory.braiding_tensor_left_inv_assoc, CategoryTheory.Limits.BinaryBicone.category_id_hom, HomologicalComplex.restrictionMap_f'_assoc, CategoryTheory.Limits.Fork.IsLimit.homIso_symm_apply, CategoryTheory.Adjunction.leftAdjointUniq_hom_counit, HomologicalComplex.opcyclesToCycles_naturality, HomotopicalAlgebra.RightHomotopyClass.mk_surjective, RingCat.Colimits.cocone_naturality, CategoryTheory.MorphismProperty.universally_le, CategoryTheory.Functor.CoreMonoidal.associativity_assoc, CategoryTheory.Limits.Cowedge.condition_assoc, HomologicalComplex.mapBifunctor₁₂.d₂_eq_zero, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_left, CategoryTheory.Biprod.unipotentUpper_hom, CategoryTheory.Functor.natTransEquiv_symm_apply_app, AddCommMonCat.comp_apply, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_1, CategoryTheory.CatCommSq.hId_iso_inv_app, CategoryTheory.DifferentialObject.comp_f, CategoryTheory.GrothendieckTopology.PreservesSheafification.le, CategoryTheory.MonoidalCategory.MonoidalLeftAction.id_actionHomLeft, CategoryTheory.Functor.homEquivOfIsLeftKanExtension_symm_apply, SSet.PtSimplex.MulStruct.δ_succ_succ_map, CategoryTheory.MonoidalCategory.associator_naturality_middle, CategoryTheory.Limits.map_inr_inv_coprodComparison_assoc, CategoryTheory.isIso_comp_left_iff, CategoryTheory.δ_μ_app, AlgebraicGeometry.IsAffineOpen.algebraMap_Spec_obj, CategoryTheory.OplaxFunctor.map₂_associator_app_assoc, CategoryTheory.StrictPseudofunctor.mk'_mapComp, CategoryTheory.Adjunction.unit_app_unit_comp_map_η, AlgebraicGeometry.Scheme.isMonHom_fst_id_right, CategoryTheory.Localization.Monoidal.map_hexagon_forward, CategoryTheory.Limits.limCompFlipIsoWhiskerLim_inv_app_app, CategoryTheory.Monad.adj_counit, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app_assoc, TopologicalSpace.Opens.map_id_obj, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp, CommRingCat.HomTopology.precompHomeomorph_apply, CategoryTheory.ShortComplex.Homotopy.ofEq_h₂, HomologicalComplex₂.XXIsoOfEq_hom_ιTotal_assoc, CategoryTheory.MonoidalClosed.assoc, FintypeCat.id_apply, AlgebraicGeometry.SheafedSpace.comp_base, CategoryTheory.Limits.prod_rightUnitor_inv_naturality_assoc, CategoryTheory.Presieve.preZeroHypercover_X, SheafOfModules.pushforwardNatTrans_id, AlgebraicGeometry.IsLocalIso.eq_iInf, CategoryTheory.LaxFunctor.map₂_associator_app_assoc, HomologicalComplex.extendSingleIso_hom_f_assoc, CategoryTheory.Presheaf.functorEnrichedHomCoyonedaObjEquiv_naturality, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_unit, CategoryTheory.Bicategory.conjugateEquiv_comp_id_right_apply, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_assoc, CategoryTheory.Functor.commShiftOfLocalization_iso_inv_app, CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id_app, CategoryTheory.Limits.ι_colimMap_assoc, SSet.Subcomplex.homOfLE_comp_assoc, HomologicalComplex.restrictionToTruncGE'.comm_assoc, CategoryTheory.Subobject.bot_factors_iff_zero, CategoryTheory.Functor.uncurry_map_app, CategoryTheory.Adjunction.map_restrictFullyFaithful_counit_app, CategoryTheory.e_assoc_assoc, CategoryTheory.Comma.comp_left, CategoryTheory.Limits.piConst_obj_map, CategoryTheory.Limits.diagramIsoParallelPair_hom_app, groupHomology.mapCycles₂_comp_i, AlgebraicGeometry.Scheme.Spec_map_stalkMap_fromSpecStalk_assoc, AugmentedSimplexCategory.inl_comp_inl_comp_associator_assoc, CommMonCat.ofHom_comp, AlgebraicGeometry.Scheme.PartialMap.equiv_toPartialMap_iff_of_isSeparated, CategoryTheory.MonoidalPreadditive.whiskerLeft_zero, CategoryTheory.MonoidalOpposite.mopMopEquivalence_inverse_map_unmop_unmop, CategoryTheory.Functor.CoreMonoidal.right_unitality_assoc, CategoryTheory.FinitaryPreExtensive.isIso_sigmaDesc_map, CategoryTheory.ShortComplex.unopMap_τ₁, CategoryTheory.HopfObj.antipode_left, CategoryTheory.PreGaloisCategory.functorToContAction_map, CategoryTheory.WithInitial.coconeEquiv_counitIso_inv_app_hom, CategoryTheory.ShortComplex.RightHomologyMapData.opcyclesMap_comm, CategoryTheory.ActionCategory.uncurry_map, CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans, HomotopicalAlgebra.AttachCells.hm_assoc, CategoryTheory.ObjectProperty.ι_ε, CategoryTheory.Lax.LaxTrans.id_naturality, CategoryTheory.Limits.colimit.ι_pre, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₃, groupCohomology.map_H0Iso_hom_f, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_inv_hom_id_assoc, AlgebraicTopology.DoldKan.Γ₀NondegComplexIso_hom_f, AlgebraicGeometry.AffineSpace.reindex_over, AlgebraicGeometry.Scheme.IdealSheafData.subschemeCover_map_subschemeι, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_comp_assoc, CategoryTheory.hom_comp_eq_id, SemiNormedGrp.id_apply, HomologicalComplex.iCycles_d, CategoryTheory.NatTrans.removeUnop_app, CategoryTheory.Functor.commShiftOfLocalization.iso_inv_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.whiskerLeft_actionHomLeft_assoc, HomologicalComplex.mapBifunctor₁₂.ιOrZero_eq_zero, AlgebraicGeometry.Scheme.Cover.gluedCoverT'_snd_fst, CategoryTheory.flipCompEvaluation_hom_app, AlgebraicGeometry.SheafedSpace.comp_c_app, CategoryTheory.ShortComplex.LeftHomologyMapData.op_φQ, CategoryTheory.NatTrans.removeOp_id, CategoryTheory.GrpObj.tensorHom_inv_inv_mul_assoc, CategoryTheory.Functor.obj.Δ_def_assoc, HomologicalComplex₂.totalAux.ιMapObj_D₂_assoc, CategoryTheory.ShortComplex.Homotopy.comm₃, CategoryTheory.NonPreadditiveAbelian.sub_comp, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_assoc, prevD_nat, CategoryTheory.Limits.pullbackZeroZeroIso_inv_fst, CategoryTheory.Bicategory.leftUnitor_inv_whiskerRight, CategoryTheory.MonoidalOpposite.mopFunctor_η, AlgebraicGeometry.AffineSpace.map_over, CategoryTheory.MorphismProperty.ContainsIdentities.unop, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd, TopCat.Presheaf.SheafConditionEqualizerProducts.w, CategoryTheory.InjectiveResolution.extMk_zero, CategoryTheory.Functor.OplaxRightLinear.δᵣ_naturality_left, CategoryTheory.CartesianClosed.curry_natural_left_assoc, CategoryTheory.Limits.coend.map_comp_assoc, CategoryTheory.ShortComplex.op_pOpcycles_opcyclesOpIso_hom_assoc, CategoryTheory.sheafifyMap_id, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_inv_assoc, CategoryTheory.MonoidalCategory.tensorμ_tensorδ, ModuleCat.ExtendScalars.map'_id, ChainComplex.mk_congr_succ_X₃, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality_assoc, CategoryTheory.IsIso.eq_inv_comp, CochainComplex.isoHomologyπ₀_inv_naturality, CategoryTheory.ShortComplex.homologyMap'_neg, CategoryTheory.CostructuredArrow.toStructuredArrow'_obj, CategoryTheory.ShortComplex.RightHomologyData.copy_ι, CategoryTheory.ObjectProperty.strictMap_singleton, CategoryTheory.GradedObject.Monoidal.pentagon_inv, CategoryTheory.Limits.IsImage.isoExt_inv_m, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_comp, CategoryTheory.coev_app_comp_pre_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.action_exchange_assoc, CategoryTheory.ShortComplex.RightHomologyData.p_comp_opcyclesIso_inv_assoc, CategoryTheory.isCoseparating_op_iff, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_associator, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top_assoc, CategoryTheory.Limits.kernelIsIsoComp_hom, AlgebraicGeometry.ExistsHomHomCompEqCompAux.exists_index, SSet.S.mk_map_eq_iff_of_mono, CategoryTheory.Abelian.Pseudoelement.pseudoApply_mk', CategoryTheory.MonoidalCategory.leftUnitor_inv_whiskerRight_assoc, CategoryTheory.Subobject.pullback_id, CategoryTheory.Localization.Monoidal.μ_natural_left_assoc, CategoryTheory.PreGaloisCategory.comp_autMap, CategoryTheory.WithInitial.commaFromUnder_map_left, CategoryTheory.Functor.RightLinear.μᵣ_comp_δᵣ, CategoryTheory.StructuredArrow.homMk'_mk_comp, CategoryTheory.Functor.map_zsmul, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₂_assoc, AlgebraicGeometry.liftCoborder_app, AlgebraicGeometry.topologically_iso_le, Action.resId_inv_app_hom, CategoryTheory.ShortComplex.leftHomologyIso_hom_naturality, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_whiskerLeft_app, CategoryTheory.IsPullback.isoPullback_inv_snd, CategoryTheory.SimplicialObject.Augmented.const_map_left, Semigrp.id_apply, CategoryTheory.CostructuredArrow.prodInverse_obj, CategoryTheory.simplicialCosimplicialEquiv_unitIso_hom_app, CategoryTheory.nerve.homEquiv_comp, CompHaus.lift_lifts, CategoryTheory.Adjunction.leftAdjointUniq_hom_app_counit, CategoryTheory.Limits.pullbackZeroZeroIso_hom_snd, CategoryTheory.Triangulated.SpectralObject.triangle_obj₂, FGModuleCat.instFiniteHom, CategoryTheory.Functor.LeftExtension.postcompose₂ObjMkIso_inv_right_app, CategoryTheory.Pretriangulated.Triangle.rotate_mor₃, CategoryTheory.Limits.MulticospanIndex.sndPiMap_π, CategoryTheory.isUnit_iff_isIso, groupCohomology.cochainsMap_zero, CategoryTheory.pseudofunctorOfIsLocallyDiscrete_obj, CategoryTheory.ShortComplex.homologyι_comp_fromOpcycles_assoc, CategoryTheory.Functor.CommShift.comp_commShiftIso_inv_app, isoOfQuasiIsoAt_inv_hom_id, CategoryTheory.ChosenPullbacksAlong.Over.tensorUnit_hom, CategoryTheory.Limits.CategoricalPullback.id_snd, CategoryTheory.Over.prodLeftIsoPullback_hom_fst_assoc, CategoryTheory.Limits.pullbackIsoOpPushout_inv_fst_assoc, HomologicalComplex.dTo_comp_dFrom, CategoryTheory.Abelian.Ext.singleFunctor_map_comp_hom, AlgebraicTopology.DoldKan.QInfty_f_comp_PInfty_f, AlgebraicGeometry.Scheme.Cover.trans_id, SSet.OneTruncation₂.HoRel₂.mk, SimplexCategory.mkOfSucc_δ_lt, CategoryTheory.CartesianClosed.curry_natural_right, CategoryTheory.MonoidalCategory.MonoidalLeftAction.id_actionHom, CategoryTheory.FreeBicategory.mk_id, CategoryTheory.Equivalence.counitInv_functor_comp, CategoryTheory.nerve.mk₁_homEquiv_apply, CategoryTheory.ShortComplex.LeftHomologyMapData.neg_φH, CategoryTheory.MonoidalCategory.whiskerRight_comp_tensorHom_assoc, CochainComplex.mappingConeCompHomotopyEquiv_comm₁, AlgebraicGeometry.sourceLocalClosure.property_coverMap_comp, CategoryTheory.Functor.sheafPushforwardContinuousCompSheafToPresheafIso_inv_app_app, CategoryTheory.yonedaMon_naturality, CategoryTheory.Comonad.coalgebraPreadditive_homGroup_neg_f, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_snd_assoc, CategoryTheory.MorphismProperty.MapFactorizationData.op_Z, CategoryTheory.Mon.limit_mon_mul, CategoryTheory.Preadditive.neg_comp_neg_assoc, CategoryTheory.MonoidalCategory.tensorμ_comp_μ_tensorHom_μ_comp_μ, CategoryTheory.Functor.toOplaxFunctor_obj, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_left, CategoryTheory.ComposableArrows.mk₁_comp_eqToHom, CategoryTheory.GlueData.t'_iji, groupCohomology.π_comp_H1Iso_hom, CategoryTheory.Limits.colimitYonedaHomIsoLimit_π_apply, CategoryTheory.NatTrans.rightOpWhiskerRight, CategoryTheory.Limits.FintypeCat.productEquiv_symm_comp_π_apply, CategoryTheory.Limits.Cotrident.condition_assoc, CategoryTheory.instIsCartesianCompOfIsFibered, CategoryTheory.Limits.BinaryFan.braiding_inv_snd, CategoryTheory.Functor.Monoidal.transport_δ, CategoryTheory.precoherentEffectiveEpiFamilyCompEffectiveEpis, CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_inv_π_π, CategoryTheory.MonoidalCategory.associator_monoidal, CategoryTheory.Bicategory.Prod.fst_map₂, HomologicalComplex₂.D₁_shape, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_hom, AlgebraicGeometry.SheafedSpace.id_hom_c_app, CategoryTheory.Functor.inlCompSum'_hom_app, CategoryTheory.cokernelUnopOp_hom, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, CategoryTheory.heq_comp_eqToHom_iff, CategoryTheory.Equivalence.sheafCongrPrecoherent_functor_obj_val_map, CategoryTheory.WithTerminal.liftToTerminal_map, CategoryTheory.Precoverage.mem_finite_iff, groupHomology.map_comp_assoc, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w, CategoryTheory.SmallObject.objMap_comp_assoc, CategoryTheory.ExponentiableMorphism.pushforwardId_hom_counit_assoc, CategoryTheory.GradedObject.ι_mapBifunctorRightUnitor_hom_apply, CategoryTheory.Functor.OplaxLeftLinear.δₗ_unitality_hom_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_app, CategoryTheory.Quotient.natTransLift_id, CategoryTheory.Limits.pullback_lift_diagonal_isPullback, CategoryTheory.Limits.walkingCospanOpEquiv_unitIso_inv_app, AlgebraicGeometry.Spec_map_localization_isIso, CategoryTheory.Join.mapPairComp_hom_app_right, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_hom, AlgebraicGeometry.Scheme.Hom.toImage_imageι_assoc, CategoryTheory.Functor.toPseudoFunctor_mapComp, CategoryTheory.unop_whiskerRight, LinOrd.id_apply, CategoryTheory.prodFunctor_map, CategoryTheory.Preadditive.neg_comp_neg, CategoryTheory.Abelian.Ext.mk₀_comp_mk₀_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_obj, BddDistLat.coe_comp, CategoryTheory.Oplax.OplaxTrans.categoryStruct_id_app, CategoryTheory.ShortComplex.mapRightHomologyIso_inv_naturality, CategoryTheory.Bicategory.InducedBicategory.forget_map, CategoryTheory.Idempotents.Karoubi.decomp_p, CategoryTheory.ComposableArrows.IsComplex.mono_cokerToKer', CategoryTheory.Pretriangulated.Triangle.sub_hom₁, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_assoc, CategoryTheory.ShortComplex.RightHomologyMapData.ofEpiOfIsIsoOfMono'_φH, CategoryTheory.Bicategory.associator_eqToHom_inv, CategoryTheory.Limits.CoconeMorphism.w_assoc, CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan_inj, CategoryTheory.comp_toNatTrans, HomologicalComplex.d_comp_eqToHom, CategoryTheory.Limits.coneOfCoconeLeftOp_π_app, CategoryTheory.ObjectProperty.instSmallOppositeOp, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₂, CommAlgCat.lift_unop_hom, CategoryTheory.Limits.Pi.lift_π, CategoryTheory.MonoOver.image_map, CategoryTheory.Localization.Preadditive.homEquiv_apply, CategoryTheory.Bifunctor.map_id, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app, CategoryTheory.MorphismProperty.iff_of_zeroHypercover_source, AlgebraicGeometry.ΓSpec.adjunction_counit_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_associator_assoc, SSet.S.le_iff, CategoryTheory.Limits.inr_pushoutAssoc_hom_assoc, CategoryTheory.Functor.CoreMonoidal.μIso_hom_natural_left_assoc, AddCommGrpCat.homAddEquiv_symm_apply_hom, CategoryTheory.ComonadHom.app_ε_assoc, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app_assoc, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj_condition_assoc, CategoryTheory.Arrow.equivSigma_apply_fst, CategoryTheory.Equivalence.rightOp_inverse_map, AlgebraicGeometry.StructureSheaf.algebraMap_self_map, CategoryTheory.Functor.map_conj, CategoryTheory.isCardinalPresentable_monotone, TopCat.prodIsoProd_inv_snd_assoc, CategoryTheory.GradedObject.Monoidal.ι_tensorObjDesc_assoc, FinPartOrd.hom_hom_comp, AlgebraicGeometry.Scheme.Hom.preimage_smoothLocus_eq, AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInfty_assoc, CategoryTheory.Adjunction.IsMonoidal.leftAdjoint_ε, CategoryTheory.ShortComplex.RightHomologyMapData.unop_φK, CategoryTheory.InducedCategory.homEquiv_symm_apply_hom, CategoryTheory.kernelCokernelCompSequence.φ_snd_assoc, CategoryTheory.Under.mapPushoutAdj_unit_app, HomologicalComplex.homologyIsoSc'_hom_ι_assoc, AlgebraicGeometry.Spec.map_id, CategoryTheory.Limits.isColimitOfConeOfCoconeLeftOp_desc, CategoryTheory.Limits.cokernelBiprodInlIso_inv, CategoryTheory.Limits.inl_pushoutRightPushoutInlIso_inv, HomologicalComplex.ιTruncLE_naturality_assoc, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₂, CategoryTheory.Limits.SequentialProduct.functorMap_commSq_aux, CategoryTheory.DifferentialObject.d_squared, CategoryTheory.preservesLimitIso_inv_π_assoc, AlgebraicGeometry.Scheme.stalkMap_hom_inv_assoc, CategoryTheory.Limits.ι_comp_sigmaComparison, CategoryTheory.ShortComplex.SnakeInput.Hom.comm₂₃_assoc, ProfiniteGrp.hom_comp, CategoryTheory.GradedObject.ι_mapBifunctorBifunctor₂₃Desc, CategoryTheory.Center.ofBraided_ε_f, CategoryTheory.Functor.leftOpRightOpIso_hom_app, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_inv_fac_assoc, CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_snd, ModuleCat.Tilde.toOpen_res, CategoryTheory.OverPresheafAux.counitForward_val_snd, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one_assoc, AddCommGrpCat.hom_sub, AddGrpCat.zero_apply, CategoryTheory.MonoidalCategory.MonoidalLeftAction.tensor_actionHomRight, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom, CategoryTheory.Comma.mapLeftComp_inv_app_left, SSet.stdSimplex.faceSingletonIso_zero_hom_comp_ι_eq_δ_assoc, CategoryTheory.ShiftedHom.mk₀_comp, CategoryTheory.MonoidalClosed.assoc_assoc, CategoryTheory.Presieve.uncurry_singleton, NonemptyFinLinOrd.hom_comp, CategoryTheory.shiftFunctorComm_hom_app_comp_shift_shiftFunctorAdd_hom_app_assoc, HomotopicalAlgebra.Precylinder.symm_i_assoc, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv_assoc, CategoryTheory.Mat_.embeddingLiftIso_hom_app, CategoryTheory.CartesianMonoidalCategory.lift_rightUnitor_hom_assoc, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj_assoc, CategoryTheory.Limits.FormalCoproduct.cofan_inj_φ, CategoryTheory.Join.mapWhiskerRight_app, CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.le_isCardinalPresentable, CategoryTheory.PrelaxFunctor.map₂_eqToHom, HomologicalComplex.restrictionToTruncGE'.comm, CategoryTheory.Limits.ImageMap.factor_map_assoc, AlgebraicGeometry.instHasOfPostcompPropertySchemeQuasiSeparatedTopMorphismProperty, CategoryTheory.Over.tensorUnit_hom, AlgebraicGeometry.germ_comp_stalkToFiberRingHom, TopCat.prodIsoProd_inv_fst_assoc, CategoryTheory.Over.opEquivOpUnder_inverse_map, AlgebraicGeometry.Proj.basicOpenIsoSpec_inv_ι, CategoryTheory.coreCategory_comp_iso_inv, CategoryTheory.SmallObject.SuccStruct.Iteration.subsingleton.MapEq.w, AlgebraicGeometry.Scheme.id.base, CategoryTheory.MonoidalCategory.whiskerLeft_comp, CategoryTheory.MorphismProperty.IsLocalAtSource.comp, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom, CategoryTheory.Equalizer.Presieve.isSheafFor_singleton_iff, CategoryTheory.NatTrans.rightDerived_comp, CategoryTheory.instEpiId, CategoryTheory.StructuredArrow.mkPostcomp_left, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_neg_assoc, CategoryTheory.Presheaf.isLocallyInjective_toSheafify, CategoryTheory.StructuredArrow.left_eq_id, AlgebraicGeometry.Scheme.Opens.toSpecΓ_appTop, CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_fst_assoc, CochainComplex.HomComplex.Cochain.fromSingleMk_v, CommAlgCat.mul_op_of_unop_hom, AlgebraicGeometry.Scheme.Hom.isoOpensRange_hom_ι_assoc, CategoryTheory.Limits.pullbackProdFstIsoProd_inv_fst, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_whiskerLeft, CategoryTheory.MonoidalClosed.curry_id_eq_coev, CategoryTheory.Bicategory.LanLift.existsUnique, CategoryTheory.IsComonHom.hom_comul_assoc, CategoryTheory.Functor.shiftIso_add_hom_app, CategoryTheory.ChosenPullbacksAlong.condition_assoc, CategoryTheory.ComposableArrows.map'_comp, CategoryTheory.MonoidalCategory.whiskerRight_comp_tensorHom, CategoryTheory.shiftFunctorAdd_inv_app_obj_of_induced, CategoryTheory.conjugateEquiv_symm_iso, CategoryTheory.ComposableArrows.IsComplex.zero_assoc, CategoryTheory.ObjectProperty.monoModSerre_zero_iff, CategoryTheory.Oplax.OplaxTrans.categoryStruct_comp_naturality, CategoryTheory.Join.mapWhiskerLeft_whiskerRight_assoc, CategoryTheory.ShortComplex.RightHomologyMapData.zero_φH, CategoryTheory.Limits.opParallelPairIso_hom_app_one, CategoryTheory.ObjectProperty.strictLimitsOfShape_le_limitsOfShape, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_rightHomologyIso_inv_assoc, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_hom_assoc, CategoryTheory.Equivalence.symmEquivFunctor_map, CochainComplex.HomComplex.Cochain.fromSingleMk_add, CategoryTheory.Limits.Cofork.IsColimit.homIso_apply_coe, CategoryTheory.finrank_endomorphism_eq_one, CategoryTheory.Over.leftUnitor_inv_left_fst, HomologicalComplex.restrictionHomologyIso_inv_homologyι_assoc, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.exists_d_comp_eq_d, CategoryTheory.Limits.cospanCompIso_inv_app_left, CategoryTheory.Limits.CatCospanTransform.associator_hom_left_app, CategoryTheory.Functor.mapTriangleCompIso_inv_app_hom₃, CategoryTheory.CatEnriched.hComp_id_heq, CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_fst, CategoryTheory.Functor.rightOpId_inv_app, AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_snd, AugmentedSimplexCategory.tensorObj_hom_ext_iff, CategoryTheory.Bicategory.Prod.sectR_mapId_inv, CategoryTheory.Limits.isLimitConeOfCoconeUnop_lift, CategoryTheory.Square.category_id_τ₄, CategoryTheory.Limits.instHasImageCompOfIsIso, CategoryTheory.Equivalence.sheafCongrPreregular_functor_obj_val_map, CategoryTheory.WithInitial.inclLiftToInitial_inv_app, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃_associator_inv_assoc, CategoryTheory.Functor.toPrefunctor_obj, CategoryTheory.Functor.partialRightAdjointHomEquiv_comp, AlgebraicGeometry.PresheafedSpace.stalkMap.congr, CategoryTheory.Iso.hom_inv_id, SimplexCategory.eq_id_of_epi, CategoryTheory.Limits.image.ι_zero, CategoryTheory.MorphismProperty.le_pushouts, CategoryTheory.Limits.isColimitOfConeUnopOfCocone_desc, CategoryTheory.Sieve.downward_closed, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_unit_app_left, CategoryTheory.Over.inv_left_hom_left, CategoryTheory.Abelian.Pseudoelement.zero_morphism_ext, CategoryTheory.Limits.kernel.ι_of_mono, CategoryTheory.Limits.inl_of_isLimit, CategoryTheory.Over.starPullbackIsoStar_hom_app_left, CategoryTheory.Limits.PushoutCocone.ofCocone_ι, CategoryTheory.eComp_eHomWhiskerLeft_assoc, CategoryTheory.StructuredArrow.mapNatIso_unitIso_hom_app_right, CategoryTheory.Limits.coend.condition_assoc, CategoryTheory.Pretriangulated.contractibleTriangle_mor₂, CategoryTheory.ShortComplex.SnakeInput.snd_δ, FGModuleCat.hom_id, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec_assoc, CategoryTheory.Functor.rightDerivedNatTrans_comp, CategoryTheory.Limits.limitBiconeOfUnique_bicone_π, CategoryTheory.Pi.evalCompEqToEquivalenceFunctor_hom, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_naturality, CategoryTheory.Abelian.Ext.mapExactFunctor_hom, CategoryTheory.MonObj.mul_mul_mul_comm, ModuleCat.lof_coprodIsoDirectSum_inv, HomologicalComplex₂.totalFlipIsoX_hom_D₂_assoc, CategoryTheory.ShortComplex.RightHomologyMapData.rightHomologyMap_eq, CategoryTheory.IsMonHom.one_hom_assoc, CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id, CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp_hom_hom₁, AlgebraicGeometry.Scheme.residue_descResidueField, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_app, smoothSheafCommRing.ι_evalHom, CategoryTheory.Adjunction.conjugateEquiv_leftAdjointIdIso_hom, CategoryTheory.Monad.adj_unit, CategoryTheory.CostructuredArrow.id_left, CategoryTheory.Subfunctor.ofSection_eq_range', CategoryTheory.MonObj.mul_comp, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left, CategoryTheory.simplicialCosimplicialEquiv_counitIso_hom_app_app, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_presheafMap, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zero, CategoryTheory.Comon.tensorObj_counit, HopfAlgCat.toBialgHom_comp, groupCohomology.map₁_one, CategoryTheory.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCocone_π_app_eq_sum, CategoryTheory.PrelaxFunctor.map₂_hom_inv, CategoryTheory.MonoidalCategory.id_tensor_associator_naturality, CategoryTheory.Limits.ι_colimitCompWhiskeringLeftIsoCompColimit_hom, CategoryTheory.Functor.mapTriangleCompIso_hom_app_hom₃, Rep.coindResAdjunction_unit_app, CategoryTheory.Limits.coneOfIsSplitMono_π_app, HomologicalComplex.XIsoOfEq_hom_comp_d, CategoryTheory.Limits.ι_comp_sigmaObjIso_hom, AlgebraicGeometry.Scheme.Hom.isoOpensRange_hom_ι, CategoryTheory.Localization.Monoidal.map_hexagon_reverse, CategoryTheory.Limits.biprod.associator_hom, CategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy.hf, CategoryTheory.GradedObject.mapBifunctorObjSingle₀ObjIso_hom, AugmentedSimplexCategory.inr_comp_associator_assoc, CategoryTheory.ShortComplex.SnakeInput.snd_δ_inr, CategoryTheory.Functor.partialRightAdjointHomEquiv_map, CategoryTheory.Functor.IsStronglyCartesian.comp, CategoryTheory.StrictlyUnitaryLaxFunctor.id_mapComp, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone_cocone_ι_app, CategoryTheory.OplaxFunctor.mapComp_assoc_right_app, CategoryTheory.NatTrans.CommShift.comp, CategoryTheory.Limits.pullback.map_id, AlgebraicGeometry.Scheme.Hom.app_eq, CategoryTheory.Abelian.LeftResolution.chainComplexMap_comp_assoc, CategoryTheory.linearYoneda_map_app, CategoryTheory.Join.isoMkFunctor_inv_app, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_map_base, HomotopicalAlgebra.PathObject.symm_p_assoc, CategoryTheory.IsHomLift.id, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_hom_eq_germ, TopModuleCat.hom_add, CategoryTheory.Pseudofunctor.StrongTrans.Modification.naturality, CategoryTheory.SimplicialObject.δ_naturality, AlgebraicGeometry.morphismRestrict_ι, LinOrd.ofHom_id, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_μ, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransId_inv_app_f, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_hom_app_app, CategoryTheory.Enriched.FunctorCategory.enriched_comp_id_assoc, CategoryTheory.ReflQuiv.adj.unit.map_app_eq, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp_app, AlgebraicGeometry.Scheme.Hom.preimageIso_inv_ι, CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse_obj_hom, CategoryTheory.IsSplitEpi.id, CategoryTheory.Limits.end_.condition, CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_comp_assoc, AlgebraicGeometry.Scheme.SpecMap_stalkSpecializes_fromSpecStalk, AlgebraicGeometry.Scheme.descResidueField_fromSpecResidueField, TopCat.Presheaf.germ_res_assoc, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec, CategoryTheory.Limits.Multicofork.ofSigmaCofork_π, CategoryTheory.SmallObject.SuccStruct.ofCoconeObjIso_hom_naturality, CategoryTheory.WithInitial.coconeEquiv_unitIso_hom_app_hom_right, CategoryTheory.MonoidalCategory.associator_inv_naturality, CategoryTheory.Functor.CorepresentableBy.homEquiv_eq, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_right, CategoryTheory.PreGaloisCategory.fiberBinaryProductEquiv_symm_fst_apply, CommRingCat.moduleCatRestrictScalarsPseudofunctor_map, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.iSup_W, CategoryTheory.ShortComplex.Splitting.g_s, HomologicalComplex.opcyclesOpIso_hom_naturality_assoc, CategoryTheory.Over.forgetMapTerminal_inv_app, CategoryTheory.ProjectiveResolution.Hom.hom'_f_assoc, AlgebraicGeometry.Scheme.Cover.Hom.w, CategoryTheory.Functor.shiftMap_comp, AlgebraicGeometry.LocallyRingedSpace.stalkMap_id, CategoryTheory.Abelian.LeftResolution.karoubi.F'_obj_p, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_hom_app, CategoryTheory.ShortComplex.HomologyData.comm_assoc, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i, AlgebraicGeometry.Spec.map_preimage_unop, CategoryTheory.Hom.mul_def, CategoryTheory.Limits.opCoproductIsoProduct'_inv_comp_inj, CochainComplex.IsKInjective.homotopyZero_def, CategoryTheory.MorphismProperty.Over.mapCongr_hom_app_left, CategoryTheory.Functor.shiftIso_add'_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app, CategoryTheory.ShortComplex.Homotopy.ofEq_h₀, CategoryTheory.Functor.Monoidal.transport_μ_assoc, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app, AlgebraicGeometry.Scheme.IdealSheafData.map_comp, CategoryTheory.MonoidalCategory.MonoidalRightAction.hom_inv_actionHomLeft', CochainComplex.mappingCone.ext_from_iff, CategoryTheory.section_comp_right, CategoryTheory.MorphismProperty.Prod.containsIdentities, CategoryTheory.Limits.limitBiconeOfUnique_isBilimit_isColimit, CategoryTheory.ShortComplex.HomologyMapData.zero_left, Semigrp.hom_id, CategoryTheory.Limits.pushout.hom_ext_iff, CategoryTheory.Abelian.full_comp_preadditiveCoyonedaObj, TopCat.Presheaf.germToPullbackStalk_stalkPullbackHom, CategoryTheory.Grp.Hom.hom_hom_inv, CategoryTheory.Limits.Pi.isoLimit_inv_π, CategoryTheory.comp_inv_eq_id, CategoryTheory.ObjectProperty.FullSubcategory.comp_def, HomologicalComplex.opcyclesToCycles_homologyπ, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_obj_obj_map, HomotopicalAlgebra.Precylinder.i₀_π, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app, CategoryTheory.ShortComplex.LeftHomologyData.π_comp_leftHomologyIso_inv_assoc, CategoryTheory.MonoidalCategory.dite_whiskerRight, ChainComplex.augmentTruncate_inv_f_succ, CategoryTheory.MorphismProperty.IsLocalAtTarget.top, CategoryTheory.preadditiveYonedaObj_obj_isModule, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_inv_app_app, CommRingCat.HomTopology.isEmbedding_pushout, AlgebraicGeometry.ΓSpecIso_obj_hom, CategoryTheory.Presieve.preZeroHypercover_f, CategoryTheory.Limits.CokernelCofork.mapIsoOfIsColimit_inv, ProfiniteAddGrp.id_apply, CategoryTheory.MonoidalCategory.rightUnitor_inv_naturality_assoc, groupHomology.mapCycles₁_id_comp_apply, CategoryTheory.ShortComplex.leftHomologyIso_hom_naturality_assoc, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom_assoc, CategoryTheory.Functor.LaxMonoidal.left_unitality, CategoryTheory.ULift.equivalence_unitIso_inv, CategoryTheory.Localization.SmallHom.equiv_mkInv, CategoryTheory.ComposableArrows.opEquivalence_functor_obj_map, SSet.Truncated.StrictSegal.spine_δ_arrow_lt, CategoryTheory.SimplicialObject.σ_def, CategoryTheory.MonoidalCategory.MonoidalRightAction.id_actionHomLeft_assoc, AlgebraicGeometry.IsOpenImmersion.isPullback_lift_id, CategoryTheory.Subfunctor.homOfLe_ι_assoc, CategoryTheory.Bicategory.pentagon_inv_inv_hom_hom_inv, CategoryTheory.Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor, AlgebraicGeometry.IsLocalIso.le_of_isLocalAtSource, CategoryTheory.Subfunctor.homOfLe_ι, CategoryTheory.Subgroupoid.mem_map_iff, CategoryTheory.NatTrans.naturality_app_app_assoc, TopologicalSpace.Opens.map_comp_map, Bimod.right_assoc_assoc, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₁, CategoryTheory.Adjunction.Triple.leftToRight_app_obj, SSet.ι₀_fst_assoc, SSet.ι₁_comp, CategoryTheory.Limits.Pi.map'_comp_map', CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit_proj, CategoryTheory.Pi.comp_apply, AlgebraicGeometry.Proj.pullbackAwayιIso_inv_snd, CategoryTheory.Adjunction.homAddEquiv_sub, CategoryTheory.Square.Hom.comm₃₄, AlgebraicGeometry.Proj.pullbackAwayιIso_inv_fst_assoc, CategoryTheory.tensorLeftHomEquiv_tensor, CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_of_epi₁, CategoryTheory.Preadditive.commGrpEquivalenceAux_hom_app_hom_hom_hom, CategoryTheory.Presheaf.restrictedULiftYoneda_map_app, Action.tensorUnit_ρ, HomologicalComplex.extendMap_comp_assoc, CategoryTheory.Pseudofunctor.StrongTrans.homCategory_id_as_app, CategoryTheory.StructuredArrow.eqToHom_right, CategoryTheory.ShiftedHom.mk₀_id_comp, groupCohomology.cochainsMap_id_comp, HomologicalComplex.restrictionMap_id, SSet.Subcomplex.yonedaEquiv_coe, CategoryTheory.Sum.natTransOfWhiskerLeftInlInr_id, CategoryTheory.Pseudofunctor.isPrestackFor_ofArrows_iff, AlgebraicGeometry.Scheme.IdealSheafData.inclusion_comp_assoc, CategoryTheory.ShortComplex.Hom.comm₁₂_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_naturality_assoc, AlgebraicGeometry.pullbackSpecIso_inv_fst'_assoc, CategoryTheory.ModObj.one_smul'_assoc, CategoryTheory.Functor.OplaxMonoidal.δ_comp_δ_whiskerRight_assoc, HomologicalComplex.cyclesIsoSc'_hom_iCycles_assoc, AlgebraicGeometry.Spec.germ_stalkMapIso_hom_assoc, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan_inv_app_app_apply_eq_id, HomologicalComplex₂.ι_D₂_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_assoc, CategoryTheory.Functor.LaxMonoidal.μ_natural_right_assoc, CategoryTheory.CosimplicialObject.Augmented.leftOp_left_map, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac, CategoryTheory.Discrete.functorComp_hom_app, CategoryTheory.Biprod.ofComponents_eq, CategoryTheory.eqToHom_iso_inv_naturality, CategoryTheory.ShortComplex.id_τ₁, CategoryTheory.BraidedCategory.braiding_naturality, CategoryTheory.MonObj.tensorObj.mul_def, CategoryTheory.OverClass.asOverHom_id, CategoryTheory.Limits.biprod.sndKernelFork_ι, CategoryTheory.ObjectProperty.le_strictLimitsClosureStep, ComplexShape.Embedding.AreComplementary.hom_ext, CategoryTheory.Limits.spanOp_inv_app, CategoryTheory.Presheaf.isSeparated_iff_subsingleton, TopCat.sigmaIsoSigma_hom_ι_assoc, CategoryTheory.Preadditive.forkOfKernelFork_pt, Mathlib.Tactic.Coherence.assoc_liftHom, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom, CategoryTheory.right_unitality_app_assoc, Preord.id_apply, CategoryTheory.Functor.mapCoconeMapCocone_hom_hom, AddCommGrpCat.hom_id, CategoryTheory.Factorisation.Hom.id_h, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app_assoc, CategoryTheory.GrothendieckTopology.toSheafify_comp_sheafifyCompIso_inv_assoc, HomologicalComplex.homologyπ_naturality, SimplicialObject.Splitting.IndexSet.mk_fst, CategoryTheory.Limits.PushoutCocone.eta_inv_hom, CategoryTheory.Equivalence.rightOp_unitIso_hom_app, CategoryTheory.Over.conePostIso_hom_app_hom, CategoryTheory.Functor.inl_biprodComparison', AddCommGrpCat.hom_nsmul, CategoryTheory.EnrichedCat.rightUnitor_inv_out_app, CategoryTheory.MorphismProperty.instIsStableUnderRetractsUnopOfOpposite, HomotopyCategory.quot_mk_eq_quotient_map, CategoryTheory.Join.pseudofunctorLeft_mapComp_inv_toNatTrans_app, groupCohomology.map_id, CategoryTheory.PreGaloisCategory.instIsEquivalenceContActionFintypeCatHomCarrierAutFunctorFunctorToContAction, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv_assoc, CategoryTheory.MorphismProperty.strictMap_multiplicativeClosure_le, CategoryTheory.eqToHom_comp_heq_iff, CochainComplex.HomComplex.Cocycle.toSingleMk_zero, SSet.Subcomplex.homOfLE_ι_assoc, CategoryTheory.IsIso.inv_comp_assoc, HomologicalComplex.units_smul_f_apply, CategoryTheory.Functor.obj.η_def_assoc, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv, HomologicalComplex.quasiIsoAt_unopFunctor_map_iff, inr_coprodIsoPushout_hom_assoc, CategoryTheory.RanIsSheafOfIsCocontinuous.fac_assoc, CategoryTheory.DifferentialObject.Hom.comm_assoc, groupCohomology.mapShortComplexH2_comp, CategoryTheory.Functor.shiftIso_inv_naturality, CategoryTheory.Limits.coprod.map_id_comp, HomologicalComplex.p_opcyclesMap, CategoryTheory.Preadditive.sum_comp, CategoryTheory.MonoidalCategory.MonoidalLeftAction.rightUnitor_actionHom, CategoryTheory.η_app_obj, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_assoc, AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zero, CategoryTheory.Over.eqToHom_left, CategoryTheory.CatEnrichedOrdinary.Hom.mk_comp, CategoryTheory.GradedObject.mapMap_comp, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_apply_fst, ModuleCat.ExtendScalars.map'_comp, AlgebraicGeometry.Scheme.Modules.restrict_map, CategoryTheory.ProjectiveResolution.pOpcycles_comp_fromLeftDerivedZero'_assoc, CategoryTheory.Pseudofunctor.CoGrothendieck.map_obj_fiber, TopCat.Sheaf.objSupIsoProdEqLocus_hom_fst, Preord.hom_id, CategoryTheory.Functor.partialLeftAdjointHomEquiv_map, CategoryTheory.ExactPairing.evaluation_coevaluation', CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_whiskerRight_app, CategoryTheory.Limits.ker.condition, CategoryTheory.CartesianMonoidalCategory.tensorμ_snd, HomologicalComplex.homotopyCofiber.inrX_fstX, CochainComplex.HomComplex.Cochain.leftUnshift_v, CategoryTheory.Limits.kernelIsIsoComp_inv, CategoryTheory.ShortComplex.SnakeInput.L₁_f_φ₁_assoc, CategoryTheory.MonoidalCategory.DayFunctor.equiv_counitIso_hom_app, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInrIso_inv_app_app, CategoryTheory.Localization.Monoidal.tensorHom_id, CategoryTheory.Limits.colimitLimitToLimitColimitCone_hom, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_awayι, CategoryTheory.MorphismProperty.IsStableUnderBaseChange.unop, CategoryTheory.GrothendieckTopology.plusMap_plusLift, CommAlgCat.fst_unop_hom, CategoryTheory.Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor_assoc, CategoryTheory.ShortComplex.RightHomologyMapData.ofEpiOfIsIsoOfMono'_φQ, CategoryTheory.Over.mapComp_eq, CategoryTheory.Limits.BinaryBicone.inr_fst_assoc, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_three, CategoryTheory.Limits.image.fac_lift_assoc, CategoryTheory.leftExactFunctor_le_additiveFunctor, CategoryTheory.Limits.wideCoequalizer.condition_assoc, SimplexCategoryGenRel.exists_P_σ_P_δ_factorization, AlgebraicGeometry.LocallyRingedSpace.residue_comp_residueFieldMap_eq_stalkMap_comp_residue, DerivedCategory.HomologySequence.comp_δ_assoc, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_id, CategoryTheory.Limits.Fork.op_pt, CategoryTheory.Comma.equivProd_inverse_map_left, ModuleCat.restrictScalarsComp'App_hom_naturality_assoc, CategoryTheory.BraidedCategory.hexagon_reverse_inv, CategoryTheory.Presieve.ofArrows_surj, Quiver.FreeGroupoid.lift_spec, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_map_assoc, CategoryTheory.Limits.map_inr_inv_coprodComparison, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapIdIso_inv, SheafOfModules.freeHomEquiv_symm_comp, CategoryTheory.MonoidalOpposite.mopMopEquivalenceFunctorMonoidal_μ, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyπ_comp_leftHomologyIso_hom_assoc, CategoryTheory.WithTerminal.map_map, CategoryTheory.MonoidalClosed.uncurry_pre, CategoryTheory.cokernel.π_unop, CategoryTheory.MorphismProperty.instRespectsLeftInd, CochainComplex.mappingConeCompHomotopyEquiv_comm₁_assoc, CategoryTheory.Functor.curry₃ObjProdComp_hom_app_app_app, CategoryTheory.Over.tensorHom_left_snd_assoc, CategoryTheory.Limits.Bicone.category_comp_hom, CategoryTheory.oplaxFunctorOfIsLocallyDiscrete_map, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_whiskerRight_assoc, HomotopicalAlgebra.PathObject.symm_p, HomologicalComplex.homologyπ_naturality_assoc, CategoryTheory.CosimplicialObject.cechConerveEquiv_symm_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality', CategoryTheory.Pseudofunctor.whiskerLeftIso_mapId, CategoryTheory.Limits.biprod.decomp_hom_from, CategoryTheory.MonObj.lift_comp_one_left, CategoryTheory.Functor.map_smul, CategoryTheory.Functor.whiskeringLeftObjIdIso_hom_app_app, Pointed.Hom.comp_toFun', CategoryTheory.Iso.homCongr_refl, CategoryTheory.Limits.prod.leftUnitor_hom_naturality_assoc, CategoryTheory.Functor.preimage_comp, CategoryTheory.Idempotents.Karoubi.id_f, CategoryTheory.FreeMonoidalCategory.mk_comp, CategoryTheory.Bicategory.Prod.swap_map, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_uliftYoneda_map, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.secondMap_app_app_app, SimplexCategory.δ_comp_σ_of_le, CategoryTheory.Grp.μ_def, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap_assoc, CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_hom_app, CategoryTheory.Functor.IsCartesian.of_comp_iso, CategoryTheory.Limits.ι_colimitFiberwiseColimitIso_hom_assoc, CategoryTheory.Adjunction.shift_counit_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_hom_app_hom_hom_app, CategoryTheory.Limits.Cone.ofPullbackCone_π, CategoryTheory.InitiallySmall.exists_small_weakly_initial_set, CategoryTheory.FunctorToTypes.coprod.desc_inl, CategoryTheory.Functor.Monoidal.map_rightUnitor_assoc, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_id_assoc, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom, CategoryTheory.Functor.map_shift_unop, CategoryTheory.Functor.Additive.map_add, CategoryTheory.NatTrans.toCatHom₂_id, CategoryTheory.LocalizerMorphism.LeftResolution.opFunctor_obj, CategoryTheory.ShortComplex.LeftHomologyData.copy_i, CategoryTheory.PreGaloisCategory.toAut_surjective_isGalois, CategoryTheory.GradedObject.ι_mapBifunctorComp₂₃MapObjIso_hom, CategoryTheory.CosimplicialObject.δ_naturality_assoc, CategoryTheory.Functor.OplaxMonoidal.lift_δ, CategoryTheory.Limits.hasCokernel_comp_iso, isoOfQuasiIsoAt_inv_hom_id_assoc, CategoryTheory.TwoSquare.whiskerVertical_app, CategoryTheory.Limits.ConeMorphism.map_w, CommAlgCat.hom_comp, SheafOfModules.Presentation.quasicoherentData_presentation, CategoryTheory.ObjectProperty.instIsSerreClassTop, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_counitIso, CategoryTheory.HopfObj.antipode_comul, CategoryTheory.sheafifyMap_sheafifyLift, CategoryTheory.mop_id, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_base, HomologicalComplex.singleObjCyclesSelfIso_hom_singleObjOpcyclesSelfIso_hom, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv, CategoryTheory.SmallObject.ε_app, CategoryTheory.Limits.prod.map_comp_id, CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_inv_app, TopologicalSpace.Opens.map_comp_obj', CategoryTheory.Center.forget_ε, CategoryTheory.Bicategory.Comonad.counit_comul_assoc, CategoryTheory.SmallObject.succStruct_prop_le_propArrow, CategoryTheory.ShortComplex.SnakeInput.φ₁_L₂_f_assoc, SSet.Truncated.id_app, CategoryTheory.OplaxFunctor.mapComp_assoc_left, CategoryTheory.curryingIso_inv_toFunctor_obj_map_app, CategoryTheory.Adjunction.leftAdjointUniq_trans_assoc, CategoryTheory.Join.opEquiv_functor_map_op_edge, groupCohomology.H2π_comp_map, CategoryTheory.ShortComplex.SnakeInput.L₀X₂ToP_comp_φ₁, CategoryTheory.Monad.assoc, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd_assoc, HomologicalComplex.mapBifunctor₂₃.ι_D₁, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_app, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_app, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp_assoc, HomologicalComplex.leftUnitor'_inv_comm_assoc, CategoryTheory.ShortComplex.Homotopy.compRight_h₂, groupCohomology.cochainsMap_comp_assoc, CategoryTheory.Limits.Pi.map'_comp_π_assoc, CategoryTheory.Adjunction.map_restrictFullyFaithful_counit_app_assoc, CategoryTheory.Iso.inv_hom_id_app_app, CategoryTheory.Subobject.factorThru_arrow_assoc, CategoryTheory.endofunctorMonoidalCategory_tensorMap_app, CategoryTheory.Functor.obj.η_def, CategoryTheory.yonedaMonObj_obj_coe, CategoryTheory.Functor.map_eq_zero_iff, CategoryTheory.Discrete.productEquiv_counitIso_hom_app, CategoryTheory.Functor.homologySequence_epi_shift_map_mor₁_iff, CategoryTheory.Functor.toPrefunctor_comp, SimplicialObject.Splitting.cofan_inj_comp_PInfty_eq_zero, groupHomology.π_comp_H2Iso_hom, CategoryTheory.Presheaf.app_localPreimage, CategoryTheory.Functor.LaxRightLinear.μᵣ_associativity_inv, CategoryTheory.Limits.limit.isoLimitCone_hom_π, CategoryTheory.Limits.LimitPresentation.ofIso_π, CategoryTheory.Functor.LeftExtension.postcompose₂_map_right_app, HomologicalComplex.opcyclesOpIso_hom_toCycles_op, CategoryTheory.GradedObject.singleObjApplyIso_inv_single_map_assoc, CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_snd, CategoryTheory.MonoidalCategory.tensor_right_iff, CategoryTheory.Grothendieck.fiber_eqToHom, SemiNormedGrp.hom_add, AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_snd_assoc, HomologicalComplex.mapBifunctor₂₃.ι_mapBifunctor₂₃Desc_assoc, CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_fst, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_comp_map, SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zero, CategoryTheory.Biprod.unipotentLower_hom, CategoryTheory.Limits.pullbackConeOfRightIso_π_app_right, CategoryTheory.Idempotents.Karoubi.p_comm_assoc, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map, CategoryTheory.ComposableArrows.Exact.opcyclesIsoCycles_hom_fac_assoc, CategoryTheory.Lax.LaxTrans.naturality_comp_assoc, CategoryTheory.Injective.injective_iff_preservesEpimorphisms_preadditive_yoneda_obj', HomologicalComplex.extendCyclesIso_hom_naturality_assoc, CategoryTheory.Join.mapIsoWhiskerRight_hom_app, CategoryTheory.ExponentiableMorphism.ev_coev, CategoryTheory.ShortComplex.Exact.leftHomologyDataOfIsLimitKernelFork_K, CategoryTheory.Under.map_obj_hom, CategoryTheory.CommaMorphism.w_assoc, CategoryTheory.Limits.FormalCoproduct.inj_comp_cofanPtIsoSelf_hom_assoc, Rep.indResAdjunction_counit_app_hom_hom, FDRep.hom_hom_action_ρ, CategoryTheory.Functor.mapAction_obj_ρ_apply, CategoryTheory.Limits.zero_of_to_zero, SimplexCategory.σ_comp_σ_assoc, CategoryTheory.Idempotents.app_p_comp_assoc, CategoryTheory.Adjunction.counit_naturality, CategoryTheory.unop_inv_leftUnitor, Action.FintypeCat.toEndHom_apply, CategoryTheory.Limits.Types.coequalizerIso_π_comp_hom, CategoryTheory.Bicategory.pentagon_assoc, CategoryTheory.MonoidalOpposite.mopMopEquivalenceFunctorMonoidal_ε, CategoryTheory.Functor.OplaxLeftLinear.δₗ_unitality_inv, CategoryTheory.Functor.Monoidal.whiskeringLeft_ε_app, CategoryTheory.Limits.prod.leftUnitor_inv, CategoryTheory.Limits.Cone.category_id_hom, Bimod.Hom.left_act_hom, CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.preservesInjectiveObjects, ContinuousMap.yonedaPresheaf_map, CategoryTheory.Functor.biproductComparison_π_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.comp, CategoryTheory.MorphismProperty.map_eq_iff_postcomp, CategoryTheory.Limits.biprod.lift_fst, CategoryTheory.ULift.equivalence_counitIso_hom_app, CategoryTheory.Limits.instHasPushoutComp, CategoryTheory.Functor.Monoidal.map_leftUnitor_inv_assoc, CategoryTheory.Localization.Monoidal.triangle_aux₁, CategoryTheory.IsPushout.of_id_fst, CategoryTheory.Functor.op_commShiftIso_hom_app_assoc, CategoryTheory.CartesianMonoidalCategory.whiskerLeft_snd_assoc, CategoryTheory.CommGrp.trivial_grp_one, CategoryTheory.Functor.FullyFaithful.compYonedaCompWhiskeringLeftMaxRight_inv_app_app, CategoryTheory.IsSplitMono.id_assoc, CategoryTheory.Paths.of_map, CategoryTheory.CartesianClosed.curry_eq, CategoryTheory.SingleObj.functor_map, CategoryTheory.NatTrans.IsMonoidal.tensor, CategoryTheory.pullbackShiftFunctorZero'_hom_app, CategoryTheory.isIso_op, CategoryTheory.Functor.OplaxMonoidal.oplax_associativity, AlgebraicGeometry.Scheme.Pullback.ofPointTensor_SpecTensorTo_assoc, CategoryTheory.Limits.Types.binaryCoproductIso_inr_comp_hom, CategoryTheory.WithInitial.prelaxfunctor_toPrelaxFunctorStruct_toPrefunctor_obj, HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac, CategoryTheory.yoneda_obj_obj, CategoryTheory.Join.opEquiv_functor_map_op_inclRight, CategoryTheory.Limits.pullback_factors_iff, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_inv_app, CategoryTheory.uliftYonedaEquiv_comp, CategoryTheory.Limits.biprod.desc_eq, CategoryTheory.CostructuredArrow.map_map_right, Bimod.comp_hom, CategoryTheory.MonoidalCategory.rightUnitor_tensor_hom_assoc, MagmaCat.coe_comp, SSet.stdSimplex.face_obj, CategoryTheory.Functor.Monoidal.whiskerRight_ε_η_assoc, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app_assoc, CategoryTheory.Limits.IsLimit.hom_lift, CategoryTheory.Over.leftUnitor_inv_left_snd, CategoryTheory.e_assoc', CategoryTheory.ShortComplex.SnakeInput.Hom.id_f₃, CategoryTheory.μ_naturality, CategoryTheory.CartesianMonoidalCategory.associator_inv_snd_assoc, CategoryTheory.SmallObject.SuccStruct.ofCoconeObjIso_hom_naturality_assoc, CategoryTheory.Bicategory.Adj.id_τr, CategoryTheory.Functor.sectionsEquivHom_naturality, Homotopy.nullHomotopicMap_f, CategoryTheory.sheafifyLift_id_toSheafify, CategoryTheory.Subgroupoid.IsWide.wide, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst_assoc, CategoryTheory.Limits.snd_of_isColimit, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_leftUnitor, CategoryTheory.Oplax.StrongTrans.Modification.id_app, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₃₁, groupHomology.mapCycles₂_comp, ModuleCat.comp_apply, AlgebraicGeometry.IsFinite.instCompScheme, CategoryTheory.Comonad.left_counit, TopCat.id_app, CategoryTheory.Bicategory.prod_rightUnitor_inv_fst, CategoryTheory.Limits.Cofork.op_π_app_zero, AddMonCat.coe_id, AlgebraicGeometry.Scheme.Γevaluation_naturality_assoc, CategoryTheory.Bimon.ofMon_Comon_ObjX_mul, AlgebraicGeometry.Scheme.kerAdjunction_counit_app, CategoryTheory.Limits.MonoFactorisation.compMono_e, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_of_epi₂, CategoryTheory.IsCofiltered.wideCospan, CategoryTheory.pullbackShiftFunctorZero_hom_app, CategoryTheory.ShortComplex.RightHomologyMapData.comp_φQ, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerLeft_assoc, CategoryTheory.Presheaf.freeYoneda_map, CategoryTheory.ObjectProperty.strictLimitsClosureIter_le_limitsClosure, CategoryTheory.Functor.shiftMap_comp'_assoc, PresheafOfModules.pullback_assoc, CategoryTheory.Monad.unit_naturality, TopologicalSpace.Opens.mapIso_inv_app, CategoryTheory.Arrow.w, CategoryTheory.Square.Hom.comm₂₄_assoc, CategoryTheory.StructuredArrow.homMk'_left, CategoryTheory.Limits.opSpan_hom_app, CategoryTheory.unmop_id, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHom_unop, CategoryTheory.Subgroupoid.isThin_iff, CategoryTheory.Limits.π_comp_colimitLeftOpIsoUnopLimit_inv_assoc, groupHomology.isoShortComplexH1_hom, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_comp_assoc, SimplexCategory.factor_δ_spec, CategoryTheory.MonoidalClosed.pre_comm_ihom_map, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃'_obj_map_app, CategoryTheory.obj_zero_map_μ_app, AlgebraicGeometry.IsClosedImmersion.comp_iff, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionActionOfMonoidalFunctorToEndofunctorMopIso_inv_app_unmop_app, CategoryTheory.Iso.compInverseIso_inv_app, CategoryTheory.Adjunction.restrictFullyFaithful_homEquiv_apply, CategoryTheory.Limits.pushout_inr_inv_inl_of_right_isIso_assoc, CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_hom, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_SpecMap_awayMap_right, CategoryTheory.Grothendieck.eqToHom_eq, CategoryTheory.ShortComplex.Homotopy.compRight_h₃, CategoryTheory.Limits.Cofork.IsColimit.π_desc_assoc, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac, CategoryTheory.Limits.biproduct.lift_desc, SSet.stdSimplex.map_apply, HomologicalComplex.d_toCycles, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_snd', AlgebraicGeometry.instIsOpenImmersionCompSchemeιQuasiFiniteLocusToNormalization, CategoryTheory.CatCenter.smul_iso_hom_eq'_assoc, FundamentalGroupoid.comp_eq, CategoryTheory.Limits.piObjIso_inv_comp_π, CategoryTheory.GrothendieckTopology.overMapPullback_assoc_assoc, CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id_app, CategoryTheory.MonoidalCategory.triangle_assoc_comp_right_inv, CategoryTheory.Limits.ColimitPresentation.Total.Hom.w, HomologicalComplex.mapBifunctorAssociatorX_hom_D₃_assoc, CategoryTheory.PreZeroHypercover.Hom.ext'_iff, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app_assoc, CategoryTheory.ShortComplex.homologyπ_comp_leftHomologyIso_inv, CategoryTheory.ObjectProperty.isoClosure_iSup, CategoryTheory.Limits.prod.lift_map_assoc, CategoryTheory.Functor.Monoidal.whiskeringLeft_μ_app, CategoryTheory.Limits.limMap_π_assoc, CategoryTheory.IsHomLift.fac', CategoryTheory.Limits.MultispanIndex.ι_sndSigmaMap, CategoryTheory.Comma.equivProd_unitIso_hom_app_right, CategoryTheory.MonoidalClosed.id_tensor_pre_app_comp_ev, CategoryTheory.Dial.leftUnitor_inv_f, CategoryTheory.ObjectProperty.instIsClosedUnderExtensionsTop, CategoryTheory.Limits.biprod.inl_fst, TopCat.Presheaf.presheafEquivOfIso_unitIso_hom_app_app, CategoryTheory.CartesianClosed.homEquiv_symm_apply_eq, CategoryTheory.PreOneHypercover.p₁_sigmaOfIsColimit, CategoryTheory.ObjectProperty.instEssentiallySmallMax, CategoryTheory.MorphismProperty.isoClosure_le_iff, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom, CategoryTheory.Limits.isColimitCoconeUnopOfCone_desc, CategoryTheory.Equivalence.unitInv_naturality_assoc, CochainComplex.HomComplex.Cochain.ofHom_sub, CategoryTheory.Bimon.one_comul, CategoryTheory.IsPushout.inr_isoIsPushout_hom_assoc, CategoryTheory.conjugateEquiv_whiskerRight, CategoryTheory.NatTrans.op_whiskerRight, LightCondensed.isoFinYonedaComponents_inv_comp, CategoryTheory.Limits.pullback.diagonal_fst, CategoryTheory.ComposableArrows.Exact.opcyclesIsoCycles_hom_fac, CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_π, HomologicalComplex.opFunctor_map_f, CategoryTheory.Functor.mapTriangle_map_hom₁, CategoryTheory.MonoidalCategory.tensor_associativity_assoc, CategoryTheory.ShortComplex.leftHomologyIso_inv_naturality_assoc, CategoryTheory.LocalizerMorphism.LeftResolution.unop_w, CategoryTheory.Oplax.LaxTrans.naturality_comp, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.inverse_map_app, groupCohomology.isoCocycles₂_hom_comp_i, CategoryTheory.SmallObject.objMap_id, CategoryTheory.ShortComplex.p_opcyclesMap', CategoryTheory.MonoidalClosed.curry_pre_app, CategoryTheory.WithInitial.prelaxfunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.bijection_symm_apply_id, CategoryTheory.Limits.Sigma.map_id, SSet.Truncated.spine_map_vertex, CategoryTheory.FunctorToTypes.rightAdj_map_app, CategoryTheory.MorphismProperty.instIsStableUnderCobaseChangeTop, HomologicalComplex.cyclesIsoSc'_inv_iCycles, CategoryTheory.Comonad.Coalgebra.Hom.h, CategoryTheory.MonoidalPreadditive.add_tensor, CategoryTheory.ShortComplex.fromOpcycles_naturality_assoc, CategoryTheory.SmallObject.SuccStruct.prop.arrowIso_hom_right, CategoryTheory.MonoidalCategory.comp_whiskerRight, CategoryTheory.Limits.ι_colimitFiberwiseColimitIso_inv_assoc, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_inv_π_π, AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, TopModuleCat.hom_zsmul, CategoryTheory.ShortComplex.opcyclesMap_neg, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app, CategoryTheory.Limits.id_zero, CategoryTheory.Functor.rightDerivedNatTrans_app_assoc, SheafOfModules.pullbackObjFreeIso_hom_naturality_assoc, CategoryTheory.types_comp, CategoryTheory.Free.single_comp_single, CategoryTheory.PreservesImage.hom_comp_map_image_ι, CategoryTheory.NatTrans.CommShiftCore.shift_app, CategoryTheory.Limits.pullbackDiagonalMapIso.hom_snd_assoc, CategoryTheory.Over.μ_pullback_left_fst_snd', SimplexCategory.id_toOrderHom, CategoryTheory.Functor.homObjFunctor_map_app, CategoryTheory.Functor.toPseudoFunctor_map, CategoryTheory.Limits.PreservesPushout.inl_iso_inv_assoc, CategoryTheory.Limits.cokernelBiprodInrIso_inv, SSet.ι₀_snd, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy₂'_homEquiv, CategoryTheory.NatTrans.whiskerLeft_app_tensor_app_assoc, CategoryTheory.IsPushout.inr_fst, CategoryTheory.Over.comp_left, CategoryTheory.Pretriangulated.contractible_distinguished₂, CategoryTheory.CartesianMonoidalCategory.rightUnitor_inv_fst, CategoryTheory.Limits.pullbackConeOfRightIso_fst, CategoryTheory.Precoverage.IsStableUnderComposition.comp_mem_coverings, IsFreeGroupoid.SpanningTree.loopOfHom_eq_id, CategoryTheory.CatCommSq.vInv_iso_hom_app, CategoryTheory.Over.mapPullbackAdj_unit_app, CategoryTheory.Functor.ShiftSequence.induced_shiftIso_hom_app_obj, CategoryTheory.eqToHom_map_comp_assoc, CategoryTheory.sheafToPresheaf_δ, CategoryTheory.Limits.lim_ε_π_assoc, CategoryTheory.prod.leftInverseUnitor_map, CategoryTheory.Limits.coprod.inr_snd, CategoryTheory.monoidalUnopUnop_ε, AlgebraicGeometry.Scheme.Opens.toSpecΓ_top, Rep.resIndAdjunction_homEquiv_symm_apply, Rep.coinvariantsFunctor_hom_ext_iff, CategoryTheory.MorphismProperty.LeftFraction.unop_f, AlgebraicGeometry.LocallyRingedSpace.comp_base, CategoryTheory.Functor.isRepresentedBy_iff, CategoryTheory.MorphismProperty.Over.forget_comp_forget_map, CategoryTheory.instIsSplitEpiOppositeOpOfIsSplitMono, CategoryTheory.ShortComplex.fromOpcycles_op_cyclesOpIso_inv_assoc, CochainComplex.mappingCone.inr_f_snd_v, CategoryTheory.Functor.Monoidal.map_associator_inv, CategoryTheory.Localization.homEquiv_comp, CategoryTheory.ShortComplex.leftHomologyπ_naturality_assoc, CategoryTheory.ShortComplex.Homotopy.symm_h₀, CategoryTheory.NatTrans.shift_comm, CategoryTheory.rightDistributor_inv, ProfiniteAddGrp.coe_id, CategoryTheory.quotientPathsTo_obj, SSet.PtSimplex.MulStruct.δ_succ_castSucc_map, CategoryTheory.lift_comp_preservesLimitIso_hom_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_hom_inv'_assoc, CategoryTheory.Limits.limitUnopIsoUnopColimit_inv_comp_π_assoc, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.hπ, CategoryTheory.ShortComplex.rightHomologyMap_comp, CategoryTheory.Limits.PushoutCocone.condition_zero, CategoryTheory.preservesLimitIso_inv_π, CategoryTheory.Abelian.PreservesImage.iso_hom_ι, CategoryTheory.Subobject.factors_comp_arrow, CategoryTheory.ShortComplex.toCycles_i_assoc, CategoryTheory.Localization.Preadditive.comp_add, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_fst, CategoryTheory.ObjectProperty.instSmallMin, CategoryTheory.Enriched.FunctorCategory.homEquiv_comp, TopCat.hom_id, CategoryTheory.whiskeringRightCompEvaluation_inv_app, Action.hom_injective, CategoryTheory.ShortComplex.Homotopy.equivSubZero_symm_apply, CategoryTheory.Functor.associator_inv_app, CochainComplex.mappingConeCompTriangle_mor₃_naturality, AlgebraicGeometry.Scheme.Pullback.openCoverOfRight_f, CategoryTheory.ShortComplex.mapHomologyIso'_hom_naturality, CategoryTheory.Limits.whiskeringLimYonedaIsoCones_inv_app_app, DistLat.id_apply, CategoryTheory.Oplax.StrongTrans.isoMk_hom_as_app, CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp, CategoryTheory.Functor.homologySequenceδ_comp_assoc, CategoryTheory.ComposableArrows.IsComplex.opcyclesToCycles_fac, CategoryTheory.LocalizerMorphism.homMap_apply, CategoryTheory.CostructuredArrow.mapNatIso_functor_obj_hom, CategoryTheory.NatTrans.unop_whiskerRight, CategoryTheory.Limits.limit.π_comp_eqToHom_assoc, Action.nsmul_hom, CategoryTheory.Subfunctor.lift_ι, groupHomology.comp_d₁₀_eq, classifyingSpaceUniversalCover_map, CategoryTheory.MorphismProperty.RightFractionRel.op, CategoryTheory.Over.mapId_inv_app_left, HomologicalComplex.d_pOpcycles_assoc, CategoryTheory.Comma.map_map_left, CategoryTheory.ShortComplex.LeftHomologyData.copy_π, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app'_assoc, CategoryTheory.Limits.biprod.inr_desc, CategoryTheory.Bicategory.conjugateIsoEquiv_apply_inv, CategoryTheory.MorphismProperty.instHasTwoOutOfThreePropertyOppositeOp, CategoryTheory.NatTrans.op_comp_assoc, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left_assoc, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id_app, CategoryTheory.SemiadditiveOfBinaryBiproducts.isUnital_leftAdd, CategoryTheory.CommSq.LiftStruct.fac_left, CategoryTheory.BraidedCategory.yang_baxter, CategoryTheory.Limits.BinaryBicone.category_comp_hom, CategoryTheory.CostructuredArrow.w_prod_snd, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_functor_map, CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_left, AlgebraicGeometry.instSurjectiveCompScheme, CategoryTheory.Functor.relativelyRepresentable.symmetry_symmetry_assoc, AlgebraicGeometry.germ_stalkClosedPointIso_hom_assoc, CategoryTheory.Idempotents.Karoubi.comp_f, CategoryTheory.ShortComplex.RightHomologyMapData.commg', CategoryTheory.ShortComplex.rightHomologyMap'_op, CategoryTheory.Comma.mapRightIso_functor_obj_hom, CategoryTheory.shift_equiv_triangle, CategoryTheory.CosimplicialObject.δ_comp_σ_succ_assoc, CommMonCat.comp_apply, CategoryTheory.Limits.imageSubobjectIso_comp_image_map, CategoryTheory.Functor.flipping_counitIso_hom_app_app_app, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_inv_app, CategoryTheory.IsPullback.inl_snd, AlgebraicGeometry.Scheme.Hom.iInf_ker_openCover_map_comp, CategoryTheory.BraidedCategory.braiding_naturality_left, CommRingCat.toAlgHom_id, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₁_assoc, CategoryTheory.Functor.leftDerivedNatTrans_comp, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_app_comp_π, CategoryTheory.ShortComplex.opcyclesOpIso_hom_toCycles_op_assoc, CategoryTheory.PrelaxFunctor.map₂_inv_hom_isIso, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_hom_assoc, CategoryTheory.Pseudofunctor.mapComp'_hom_naturality_assoc, CategoryTheory.Comma.toIdPUnitEquiv_unitIso_inv_app_right, CategoryTheory.ProjectiveResolution.of_def, CommRingCat.HomTopology.instT2SpaceHomOfCarrier, CategoryTheory.Pseudofunctor.mapComp'_naturality_2_assoc, CategoryTheory.Limits.kernelComparison_comp_ι_assoc, CategoryTheory.associator_inv, CategoryTheory.Pseudofunctor.Grothendieck.categoryStruct_id_fiber, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_inv_app_app, AddMagmaCat.coe_comp, CategoryTheory.Limits.PreservesPullback.iso_hom_fst, LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition', HomologicalComplex₂.totalAux.d₂_eq', CategoryTheory.IsCofiltered.inf_objs_exists, CategoryTheory.Limits.colimitCoyonedaHomIsoLimitUnop_π_apply, CategoryTheory.shiftFunctorZero_hom_app_obj_of_induced, SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_inv_app, CategoryTheory.Pseudofunctor.ObjectProperty.map_map_hom, CompHausLike.LocallyConstant.functorToPresheaves_map_app, HomotopicalAlgebra.CofibrantObject.exists_bifibrant_map, CategoryTheory.Dial.hexagon_reverse, CategoryTheory.Functor.corepresentableByUliftFunctorEquiv_apply_homEquiv, CategoryTheory.CommaMorphism.w, TopologicalSpace.OpenNhds.id_apply, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_assoc, CategoryTheory.Comma.toPUnitIdEquiv_unitIso_inv_app_left, CategoryTheory.factorThruImage_comp_imageUnopOp_inv, CategoryTheory.Functor.homologySequence_mono_shift_map_mor₁_iff, smoothSheafCommRing.forgetStalk_hom_comp_evalHom_assoc, AlgebraicGeometry.specTargetImageFactorization_comp_assoc, Homotopy.zero, CondensedSet.topCatAdjunctionUnit_val_app_apply, CategoryTheory.Limits.Fork.hom_comp_ι_assoc, AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_right, Rep.coindMap'_hom, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_naturality_app, CategoryTheory.ProjectiveResolution.π'_f_zero_assoc, CategoryTheory.HomRel.IsStableUnderPrecomp.comp_left, CategoryTheory.composePath_comp, CategoryTheory.TransfiniteCompositionOfShape.fac, HomologicalComplex.truncLE'Map_f_eq_cyclesMap, CategoryTheory.ShortComplex.SnakeInput.Hom.comm₁₂_assoc, CategoryTheory.Limits.imageSubobject_zero_arrow, CategoryTheory.PreGaloisCategory.exists_lift_of_mono_of_isConnected, CategoryTheory.Functor.isIso_ranAdjunction_unit_app_iff, CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_fst_snd, CategoryTheory.Limits.colimit.pre_pre, CategoryTheory.leftAdjointMate_id, CategoryTheory.Functor.map_sub, CategoryTheory.Localization.Construction.lift_map, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst, CategoryTheory.Join.mkFunctorLeft_hom_app, CategoryTheory.Functor.PreOneHypercoverDenseData.w, CategoryTheory.ProjectiveResolution.π_f_succ, HomotopicalAlgebra.PrepathObject.RightHomotopy.precomp_h, AlgebraicGeometry.AffineSpace.map_reindex_assoc, CategoryTheory.Functor.OplaxLeftLinear.δₗ_associativity, CategoryTheory.ShortComplex.rightHomologyι_comp_fromOpcycles_assoc, CategoryTheory.Adjunction.comp_counit, CategoryTheory.GradedObject.Monoidal.tensorHom_def, HomologicalComplex₂.totalAux.d₁_eq, CategoryTheory.Limits.limitRightOpIsoOpColimit_hom_comp_ι, ComplexShape.Embedding.homRestrict_precomp, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans, groupHomology.H0π_comp_map_assoc, CategoryTheory.CatEnriched.hComp_assoc, CategoryTheory.ShortComplex.opcyclesOpIso_hom_naturality, CategoryTheory.CatCommSq.iso_hom_naturality, CategoryTheory.yonedaEquiv_yoneda_map, CategoryTheory.Limits.opProdIsoCoprod_inv_inl, CategoryTheory.Limits.limit.π_comp_eqToHom, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_inv_app_unmop, Preorder.subsingleton_hom, CategoryTheory.OverPresheafAux.unitForward_naturality₂, CategoryTheory.Bicategory.pentagon_inv_inv_hom_inv_inv, CategoryTheory.Limits.FormalCoproduct.eval_obj_map, CategoryTheory.Equivalence.changeFunctor_counitIso_hom_app, CategoryTheory.PrelaxFunctor.map₂_inv_hom_isIso_assoc, CategoryTheory.Limits.isLimitOfCoconeLeftOpOfCone_lift, AlgebraicGeometry.IsLocalAtSource.comp, CategoryTheory.Over.leftUnitor_inv_left_snd_assoc, CategoryTheory.Localization.Monoidal.map_hexagon_reverse_assoc, CategoryTheory.kernelCokernelCompSequence.inr_φ_fst_assoc, CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt_assoc, CategoryTheory.RetractArrow.r_w, CategoryTheory.CatCenter.mul_app_assoc, HomotopicalAlgebra.fibrations_eq_unop, CategoryTheory.IsPushout.of_hasBinaryCoproduct, CategoryTheory.Limits.biproduct.ι_matrix_assoc, CategoryTheory.Idempotents.zero_def, CategoryTheory.Limits.CatCospanTransform.category_comp_left, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s₀_comp_δ₁_assoc, CategoryTheory.Subgroupoid.IsNormal.generatedNormal_le, HomologicalComplex₂.D₁_totalShift₂XIso_hom_assoc, AlgebraicGeometry.Scheme.stalkMap_germ_assoc, CategoryTheory.Pseudofunctor.CoGrothendieck.Hom.congr, HomologicalComplex.homotopyCofiber.sndX_inrX_assoc, CategoryTheory.GlueData.diagramIso_inv_app_left, CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc, TopCat.Presheaf.SheafConditionEqualizerProducts.piInters.hom_ext_iff, CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom, CategoryTheory.Iso.map_inv_hom_id_app, CategoryTheory.LocalizerMorphism.RightResolution.Hom.id_f, CategoryTheory.Abelian.Ext.mk₀_add, CategoryTheory.Limits.biproduct.matrix_map_assoc, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app_assoc, CategoryTheory.Subfunctor.Subpresheaf.image_comp, CategoryTheory.IsPullback.of_hasBinaryProduct, CategoryTheory.LaxBraidedFunctor.comp_hom_assoc, CategoryTheory.MorphismProperty.IsStableUnderBaseChange.op, CategoryTheory.Functor.OplaxRightLinear.δᵣ_associativity, CategoryTheory.Limits.BinaryFan.unop_mk, CategoryTheory.Quotient.functor_homRel_eq_compClosure_eqvGen, CategoryTheory.Functor.LeftLinear.δₗ_comp_μₗ, CategoryTheory.Iso.hom_inv_id_app, CategoryTheory.Limits.imageSubobject_zero, CategoryTheory.MonoidalCategory.associator_inv_naturality_middle_assoc, CategoryTheory.ShortComplex.homologyπ_naturality, AddSemigrp.comp_apply, CategoryTheory.Limits.HasLimit.isoOfEquivalence_hom_π, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_app, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_inv_hom, CategoryTheory.MorphismProperty.coproducts_le_iff, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π, CategoryTheory.Limits.limitConstTerminal_inv_π, CategoryTheory.ComonObj.counit_comul_assoc, CategoryTheory.Limits.KernelFork.mapIsoOfIsLimit_inv, CategoryTheory.LocalizerMorphism.instIsLocalizedEquivalenceOppositeOpOp, CategoryTheory.NatIso.naturality_1_assoc, CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_hom, CategoryTheory.CartesianMonoidalCategory.rightUnitor_inv_snd_assoc, HomologicalComplex.xPrevIso_comp_dTo, AlgebraicGeometry.SheafedSpace.ofRestrict_hom_c_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_invApp, CategoryTheory.Limits.pullbackProdSndIsoProd_inv_fst_snd_assoc, CategoryTheory.unit_conjugateEquiv_symm, CategoryTheory.Adjunction.mapMon_counit, CategoryTheory.CategoryOfElements.comp_val, CategoryTheory.Localization.Preadditive.comp_add'_assoc, CategoryTheory.GrothendieckTopology.Point.Hom.sheafFiber_comp, CategoryTheory.ComonObj.counit_comul_hom, CategoryTheory.Localization.Monoidal.μ_natural_left, CategoryTheory.CatEnrichedOrdinary.Hom.id_eq, CategoryTheory.ShortComplex.quasiIso_iff_comp_right, finGaloisGroupMap.map_id, Homotopy.extend.hom_eq_zero₁, CommRingCat.hom_comp, CategoryTheory.PreGaloisCategory.evaluation_aut_bijective_of_isGalois, CategoryTheory.Limits.opCompYonedaSectionsEquiv_apply_app, Mathlib.Tactic.Monoidal.structuralIsoOfExpr_comp, CategoryTheory.MorphismProperty.instHasOfPostcompPropertyOppositeOpOfHasOfPrecompProperty, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom'_assoc, TopCat.Presheaf.whiskerIsoMapGenerateCocone_inv_hom, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app_assoc, CategoryTheory.Pretriangulated.preadditiveYoneda_homologySequenceδ_apply, SSet.StrictSegal.spineToSimplex_interval, HomologicalComplex.homologyMap_id, CategoryTheory.ShortComplex.LeftHomologyMapData.homologyMap_eq, CategoryTheory.Grpd.freeForgetAdjunction_homEquiv_symm_apply, CategoryTheory.Mon_Class.mul_eq_mul, CategoryTheory.Functor.NatTrans.hcomp_eq_whiskerLeft_comp_whiskerRight, CategoryTheory.Lax.LaxTrans.naturality_id_assoc, CategoryTheory.Groupoid.vertexGroup_one, CategoryTheory.comp_leftAdjointMate_assoc, CategoryTheory.Iso.map_hom_inv_id, CategoryTheory.PreservesImage.inv_comp_image_ι_map, CategoryTheory.Limits.pullbackProdFstIsoProd_inv_snd_snd, CategoryTheory.Functor.RightLinear.δᵣ_comp_μᵣ, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_map_hom, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_naturality_assoc, CategoryTheory.IsSplitCoequalizer.leftSection_top_assoc, AlgebraicGeometry.SurjectiveOnStalks.comp, CategoryTheory.LaxFunctor.mapComp_naturality_right_assoc, CategoryTheory.MorphismProperty.instHasPullbackHomDiscretePUnitOfHasPullbacksAlong, CategoryTheory.ChosenPullbacksAlong.iso_pullback_obj, CategoryTheory.MonoidalCategory.leftUnitor_monoidal, CategoryTheory.kernelCokernelCompSequence.snakeInput_v₂₃_τ₂, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp_assoc, CategoryTheory.ObjectProperty.shiftClosure_le_iff, CategoryTheory.Limits.BinaryFan.rightUnitor_inv, CategoryTheory.Functor.ι_colimitIsoColimitGrothendieck_hom_assoc, AlgebraicGeometry.Scheme.Hom.appIso_inv_app, CategoryTheory.kernelCokernelCompSequence.ι_snd, CategoryTheory.Subfunctor.Subpresheaf.range_comp, prevD_eq, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_inv, AlgebraicGeometry.Scheme.Cover.id_idx_apply, CategoryTheory.WideSubcategory.comp_def, SSet.Subcomplex.image_comp, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app_assoc, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom, CategoryTheory.MorphismProperty.MapFactorizationData.fac, CategoryTheory.Preadditive.comp_neg_assoc, CategoryTheory.FreeBicategory.preinclusion_map₂, CategoryTheory.OplaxFunctor.mapComp'_comp_mapComp'_whiskerRight, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_inv_iso_inv, HomologicalComplex.mapBifunctor.d₂_eq, CategoryTheory.Bicategory.prod_whiskerLeft_fst, CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit_proj_assoc, groupHomology.toCycles_comp_isoCycles₁_hom_assoc, MulEquiv.toSingleObjEquiv_counitIso_hom, CategoryTheory.Oplax.OplaxTrans.rightUnitor_hom_as_app, CategoryTheory.Limits.kernelSubobjectIsoComp_inv_arrow, CommRingCat.HomTopology.precompHomeomorph_symm_apply, CategoryTheory.MorphismProperty.LeftFraction.op_f, TopCat.Presheaf.map_germ_eq_Γgerm_assoc, AlgebraicGeometry.Scheme.stalkMap_congr_hom_assoc, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom, CategoryTheory.Limits.pushoutIsoOpPullback_inv_fst, CategoryTheory.unit_conjugateEquiv, CategoryTheory.Limits.pullbackAssoc_hom_snd_snd, HomologicalComplex.instQuasiIsoAtOppositeMapSymmOpFunctorOp, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_ι_inv_assoc, TopologicalSpace.Opens.op_map_id_obj, CategoryTheory.Abelian.Ext.comp_mk₀_id, PartOrd.coe_comp, CategoryTheory.OplaxFunctor.map₂_associator_assoc, CategoryTheory.Dial.braiding_inv_F, AlgebraicTopology.DoldKan.P_f_idem, DerivedCategory.left_fac_of_isStrictlyLE_of_isStrictlyGE, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct_assoc, CategoryTheory.GradedObject.mapBifunctorObjSingle₀ObjIso_inv, CategoryTheory.GlueData.t_fac, CategoryTheory.unmop_comp, CategoryTheory.SimplicialObject.δ_comp_σ_of_gt'_assoc, AlgebraicTopology.AlternatingCofaceMapComplex.d_squared, CategoryTheory.SmallObject.ιObj_naturality, CategoryTheory.NatTrans.rightDerivedToHomotopyCategory_comp_assoc, CategoryTheory.Free.embedding_map, CategoryTheory.Limits.biprod.total, CategoryTheory.Limits.cokernel.π_of_zero, CategoryTheory.Grothendieck.grothendieckTypeToCatFunctor_map_coe, CategoryTheory.SmallObject.ιFunctorObj_naturality, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone_ι_app, CategoryTheory.ShortComplex.RightHomologyData.unop_f', CategoryTheory.Pseudofunctor.map₂_whisker_left, CategoryTheory.Limits.BinaryFan.op_mk, CategoryTheory.Sieve.uliftNatTransOfLe_comm, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_pt, HomologicalComplex₂.ι_totalDesc, CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_inv, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionActionOfMonoidalFunctorToEndofunctorIso_hom_app_app, CategoryTheory.Functor.op_iff, CategoryTheory.TransfiniteCompositionOfShape.map_isColimit, CategoryTheory.Join.mapWhiskerLeft_associator_hom, CochainComplex.mappingCone.ext_to_iff, CategoryTheory.uliftYoneda_obj_map, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_right, TopCat.Sheaf.interUnionPullbackConeLift_right, CategoryTheory.Limits.coprod.map_map_assoc, CategoryTheory.Quiv.adj_homEquiv, AlgebraicTopology.DoldKan.PInfty_idem_assoc, CategoryTheory.Triangulated.TStructure.zero, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_inv_app_app, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_ι_assoc, CategoryTheory.Groupoid.isoEquivHom_apply, HomologicalComplex₂.total.mapAux.d₂_mapMap_assoc, CategoryTheory.Enriched.FunctorCategory.homEquiv_id, CategoryTheory.regularTopology.mapToEqualizer_eq_comp, CategoryTheory.MonoidalClosed.curry_eq, CategoryTheory.Groupoid.invEquivalence_functor_map, CategoryTheory.Endofunctor.Coalgebra.Terminal.left_inv, CompHausLike.ofHom_id, HomologicalComplex.ι_mapBifunctorFlipIso_inv_assoc, CategoryTheory.Groupoid.isoEquivHom_symm_apply_hom, CategoryTheory.RelCat.Hom.rel_id_apply₂, CategoryTheory.Functor.mapTriangleRotateIso_hom_app_hom₂, HomologicalComplex.extend_single_d, CategoryTheory.Equivalence.counitInv_app_comp_functor_map_η_inverse_assoc, CategoryTheory.LaxFunctor.mapComp'_whiskerRight_comp_mapComp'_assoc, SheafOfModules.pullback_comp_id, CategoryTheory.SmallObject.ιFunctorObj_πFunctorObj_assoc, CategoryTheory.GradedObject.mapTrifunctorMap_map_app_app, CategoryTheory.projective_iff_llp_epimorphisms_zero, AlgebraicGeometry.Scheme.Hom.map_appLE_assoc, CategoryTheory.Under.postComp_hom_app_right, CategoryTheory.MonoidalCategory.inv_hom_id_tensor, CategoryTheory.ComposableArrows.opEquivalence_functor_map_app, Rep.applyAsHom_comm_assoc, CategoryTheory.FunctorToTypes.binaryProductIso_hom_comp_snd, HomologicalComplex.mapBifunctor.d₁_eq_zero, CategoryTheory.Functor.LaxMonoidal.id_ε, CategoryTheory.Functor.mapCommMonCompIso_inv_app_hom_hom, CategoryTheory.GrothendieckTopology.map_yonedaEquiv', CategoryTheory.Pseudofunctor.StrongTrans.isoMk_hom_as_app, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_comp_base, CategoryTheory.Limits.colimit_obj_ext_iff, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_symm_apply_φ, CategoryTheory.MonoidalCategory.MonoidalRightAction.action_exchange_assoc, CategoryTheory.Adjunction.Triple.rightToLeft_eq_counits, HomologicalComplex.singleObjHomologySelfIso_inv_homologyι_assoc, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_assoc, CategoryTheory.Functor.comp_mapMon_mul, AlgebraicGeometry.Scheme.Modules.pseudofunctor_right_unitality, CategoryTheory.ProjectiveResolution.Hom.hom'_comp_π', CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_assoc, CategoryTheory.Limits.image.lift_fac, SSet.Truncated.Edge.src_eq, CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id_app_assoc, CategoryTheory.EnrichedOrdinaryCategory.homEquiv_id, CategoryTheory.Sieve.natTransOfLe_comm, CategoryTheory.Pi.η_def, CategoryTheory.PreGaloisCategory.instFiniteHomOfIsConnected, CategoryTheory.Idempotents.toKaroubi_map_f, CategoryTheory.Localization.homEquiv_symm_apply, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app, CategoryTheory.ObjectProperty.galoisConnection_isColocal, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τl, TopologicalSpace.OpenNhds.map_id_obj_unop, CategoryTheory.kernelUnopOp_hom, CategoryTheory.Limits.Sigma.ι_isoColimit_hom_assoc, Rep.freeLiftLEquiv_apply, CategoryTheory.Functor.curry₃_obj_obj_obj_map, CategoryTheory.SimplicialObject.Augmented.rightOp_right_map, CategoryTheory.Limits.prod.map_map, CategoryTheory.Subfunctor.preimage_id, CategoryTheory.ShortComplex.rightHomologyMap'_add, CategoryTheory.Groupoid.invEquiv_apply, HomologicalComplex₂.d₁_eq_zero, CategoryTheory.MorphismProperty.map_inverseImage_le, CategoryTheory.IsPushout.paste_vert, CategoryTheory.ShortComplex.LeftHomologyData.f'_i, CategoryTheory.Lax.StrongTrans.toLax_naturality, CategoryTheory.Functor.mapComposableArrowsObjMk₂Iso_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.ShortComplex.LeftHomologyMapData.commπ, CategoryTheory.LocalizerMorphism.commShift_iso_hom_app_assoc, CommRingCat.HomTopology.isClosedEmbedding_hom, CategoryTheory.WithInitial.coconeEquiv_functor_map_hom, CategoryTheory.Cat.HasLimits.limit_π_homDiagram_eqToHom, HomologicalComplex.zsmul_f_apply, groupCohomology.mapCocycles₁_one, CategoryTheory.NatTrans.op_whiskerLeft_assoc, CategoryTheory.ObjectProperty.epiModSerre_zero_iff, HomologicalComplex.cyclesMap_i_assoc, CategoryTheory.TwoSquare.hId_app, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_right, CategoryTheory.Subgroupoid.hom.faithful, CategoryTheory.BraidedCategory.hexagon_forward_inv_assoc, CategoryTheory.Functor.RightExtension.coneAtWhiskerRightIso_inv_hom, CategoryTheory.eHomFunctor_map_app, CategoryTheory.Arrow.comp_right_assoc, CategoryTheory.HomOrthogonal.matrixDecompositionLinearEquiv_symm_apply, CategoryTheory.CosimplicialObject.δ_comp_σ_succ'_assoc, CategoryTheory.EnrichedCat.comp_whiskerRight, CategoryTheory.CosimplicialObject.δ_comp_δ_self'_assoc, CategoryTheory.Functor.liftOfIsRightKanExtension_fac_app_assoc, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_inv_hom₁, CategoryTheory.Functor.Monoidal.map_associator_inv', AlgebraicGeometry.IsAffineOpen.isoSpec_inv_toSpecΓ, SemimoduleCat.MonoidalCategory.tensorHom_comp_tensorHom, CategoryTheory.ProjectiveResolution.Hom.hom'_f, CategoryTheory.unitCompPartialBijective_natural, CategoryTheory.IsHomLift.id_comp_lift, AddSemigrp.hom_comp, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_right, CategoryTheory.MonoidalCategory.tensorHom_def, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInlIso_hom_app_app, CategoryTheory.MorphismProperty.le_isLocal_isLocal, CategoryTheory.ShortComplex.homologyMap'_id, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id, CategoryTheory.WithTerminal.ofCommaMorphism_app, CochainComplex.singleFunctor_obj_d, CategoryTheory.uliftYoneda_obj_obj, CategoryTheory.typeEquiv_counitIso_inv_app_val_app, CategoryTheory.Comonad.id_δ_app, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_inv_app_left, CategoryTheory.ShortComplex.homologyOpIso_hom_naturality_assoc, AlgebraicGeometry.Scheme.comp_base_assoc, CategoryTheory.CosimplicialObject.δ_comp_σ_of_le, CategoryTheory.Pseudofunctor.toOplax_mapId, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, CategoryTheory.Functor.LeftExtension.postcomp₁_obj_hom_app, CategoryTheory.MorphismProperty.IsMultiplicative.op, CategoryTheory.biconeCategoryStruct_id, CategoryTheory.IsHomLift.comp, CategoryTheory.dite_comp, AlgebraicGeometry.Scheme.stalkMap_id, groupCohomology.cocyclesMap_comp, CategoryTheory.Endofunctor.algebraPreadditive_homGroup_zsmul_f, CategoryTheory.ShortComplex.LeftHomologyData.f'_π, CategoryTheory.MonoidalCategory.MonoidalLeftAction.hom_inv_actionHomLeft'_assoc, CategoryTheory.SmallObject.functorMapSrc_functorObjTop, HomologicalComplex.biprod_lift_snd_f, CategoryTheory.Functor.mapCommMonIdIso_hom_app_hom_hom, AlgebraicGeometry.LocallyRingedSpace.comp_toShHom, CategoryTheory.Limits.CokernelCofork.mapIsoOfIsColimit_hom, CategoryTheory.FinCategory.objAsTypeToAsType_map, AlgebraicGeometry.Scheme.Hom.map_appLE'_assoc, CategoryTheory.Functor.whiskerLeft_comp, CategoryTheory.ShortComplex.cyclesMap_comp, SimplexCategory.eq_comp_δ_of_not_surjective', CategoryTheory.isCoseparator_prod, TopologicalSpace.Opens.overEquivalence_unitIso_hom_app_left, CategoryTheory.MorphismProperty.LeftFraction.map_hom_ofInv_id_assoc, Mathlib.Tactic.Reassoc.eq_whisker', CategoryTheory.Subobject.mk_eq_bot_iff_zero, AlgebraicGeometry.Scheme.Spec.residue_residueFieldIso_hom_assoc, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_left, CategoryTheory.Iso.inv_hom_id_app_app_app, CategoryTheory.preservesFiniteColimits_preadditiveYonedaObj_of_injective, CategoryTheory.Localization.SmallHom.equiv_mk, groupHomology.H2π_comp_map_assoc, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app', AlgebraicGeometry.IsAffineOpen.toSpecΓ_isoSpec_inv, CategoryTheory.IsIso.comp_isIso, CategoryTheory.Limits.pullbackConeOfLeftIso_fst, AlgebraicGeometry.Scheme.Hom.appIso_inv_naturality, CompHausLike.ofHom_comp, AlgebraicGeometry.tilde.map_comp_assoc, CategoryTheory.Limits.Fork.ofCone_π, CategoryTheory.ObjectProperty.instIsStableUnderShiftByMin, CategoryTheory.InducedCategory.comp_hom, HomotopicalAlgebra.Precylinder.LeftHomotopy.refl_h, CategoryTheory.MorphismProperty.gc_llp_rlp, CategoryTheory.MonoOver.map_obj_arrow, CategoryTheory.kernelCokernelCompSequence.ι_snd_assoc, CategoryTheory.SimplicialObject.δ_comp_δ'_assoc, CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_left, CategoryTheory.ProjectiveResolution.pOpcycles_comp_fromLeftDerivedZero', CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_fst_assoc, CategoryTheory.GrpObj.one_inv, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal, CategoryTheory.SmallObject.functorObj_comm, CategoryTheory.Equivalence.cancel_unitInv_right, CategoryTheory.eqToHom_comp_heq, CategoryTheory.Limits.WalkingReflexivePair.Hom.id_eq, CategoryTheory.Preadditive.instMonoNegHom, AlgebraicGeometry.SheafedSpace.id_hom_base, HomologicalComplex.mapBifunctor₂₃.ι_D₂, AlgebraicTopology.DoldKan.N₂Γ₂_inv_app_f_f, CategoryTheory.Bicategory.prod_associator_inv_fst, CategoryTheory.Limits.opProductIsoCoproduct'_comp_self, HomologicalComplex.homologyMap_add, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_inv, SSet.stdSimplex.faceSingletonIso_one_hom_comp_ι_eq_δ, CategoryTheory.MonoidalClosed.curry_natural_left, CategoryTheory.PrelaxFunctor.map₂_hom_inv_assoc, Mathlib.Tactic.Bicategory.evalWhiskerLeft_of_cons, CategoryTheory.tensorRightHomEquiv_symm_coevaluation_comp_whiskerLeft, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map, CategoryTheory.Limits.HasZeroObject.zeroIsoIsTerminal_hom, CategoryTheory.SimplicialObject.δ_comp_σ_self', CategoryTheory.Functor.LaxMonoidal.right_unitality_inv, CategoryTheory.Limits.π_comp_colimitOpIsoOpLimit_inv_assoc, HomotopicalAlgebra.LeftHomotopyClass.mk_surjective, CategoryTheory.ShortComplex.homologyMap_mapNatTrans, CategoryTheory.comp_rightAdjointMate, CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsMax, CategoryTheory.Functor.rightKanExtension_hom_ext_iff, CategoryTheory.EnrichedFunctor.map_id, CategoryTheory.Limits.DiagramOfCocones.comp, CategoryTheory.Pretriangulated.Triangle.neg_hom₁, CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom_assoc, CategoryTheory.Arrow.inv_hom_id_right, Action.forget_δ, AlgebraicGeometry.Scheme.Hom.comp_app_assoc, CategoryTheory.StrictlyUnitaryLaxFunctor.mapId_eq_eqToHom, CategoryTheory.Arrow.w_mk_right_assoc, CategoryTheory.SmallObject.SuccStruct.iterationFunctor_map_succ_assoc, CategoryTheory.MorphismProperty.FunctorialFactorizationData.i_mapZ, SheafOfModules.freeHomEquiv_comp_apply, AlgebraicGeometry.Scheme.comp_app, ContinuousCohomology.MultiInd.d_comp_d_assoc, Action.FunctorCategoryEquivalence.inverse_obj_ρ_apply, CategoryTheory.yonedaMon_map_app, CategoryTheory.MorphismProperty.instHasOfPostcompPropertyUnopOfHasOfPrecompPropertyOpposite, HomologicalComplex.cylinder.ι₁_π, SimplexCategory.Truncated.morphismProperty_eq_top, ModuleCat.biprodIsoProd_inv_comp_snd, SemiNormedGrp.hom_neg, CategoryTheory.shrinkYonedaEquiv_naturality, SimplexCategory.eqToHom_toOrderHom, CategoryTheory.Functor.pointwiseLeftKanExtensionUnit_app, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_unit_app, CategoryTheory.BraidedCategory.hexagon_reverse, CategoryTheory.ComonadHom.app_δ_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_rightUnitor, AlgebraicGeometry.Scheme.zeroLocus_map, CategoryTheory.Functor.OfSequence.map_comp_assoc, CategoryTheory.Endofunctor.Coalgebra.Terminal.right_inv, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id, TopCat.Presheaf.stalk_hom_ext_iff, CategoryTheory.Equivalence.unitIso_hom_app_comp_inverse_map_η_functor, CategoryTheory.CostructuredArrow.mapIso_counitIso_hom_app_left, CategoryTheory.OplaxFunctor.mapComp_naturality_left_app, CategoryTheory.MonoidalCategory.associator_naturality_left, CochainComplex.HomComplex.Cochain.rightUnshift_v, CategoryTheory.Limits.pullbackConeEquivBinaryFan_functor_obj, AlgebraicGeometry.Scheme.AffineZariskiSite.coequifibered_iff_forall_isLocalizationAway, HomologicalComplex.singleObjCyclesSelfIso_inv_homologyπ_assoc, AlgebraicGeometry.AffineSpace.homOfVector_toSpecMvPoly_assoc, AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInfty, HomologicalComplex.biprod_inl_fst_f_assoc, HomotopicalAlgebra.trivialFibrations_sub_weakEquivalences, CategoryTheory.Center.ofBraided_δ_f, AlgebraicGeometry.Scheme.evaluation_naturality, AlgebraicGeometry.Spec.sheafedSpaceMap_comp, CategoryTheory.Presieve.ofArrows.eq_eqToHom_comp_hom_idx, CategoryTheory.SmallObject.functorMap_π_assoc, AlgebraicGeometry.Scheme.Cover.glued_cover_cocycle_snd, CategoryTheory.ShortComplex.rightHomologyIso_inv_naturality_assoc, CategoryTheory.GrothendieckTopology.toPlus_comp_plusCompIso_inv, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.right_triangle_components, Action.id_hom, CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_snd_assoc, CategoryTheory.Presheaf.imageSieve_apply, CategoryTheory.Enriched.FunctorCategory.functorEnriched_id_comp, CategoryTheory.Limits.coprod.functor_map_app, CategoryTheory.Iso.compInverseIso_hom_app, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_hom_app_app, HomologicalComplex.extend_d_to_eq_zero, TopCat.coe_id, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_inv_app_fst_app, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_hom_assoc, CategoryTheory.yonedaEquiv_naturality', AlgebraicGeometry.Scheme.Hom.normalizationPullback_snd_assoc, Condensed.comp_val, CategoryTheory.Localization.Monoidal.rightUnitor_naturality, AlgebraicGeometry.Scheme.Cover.trans_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_hom_app_snd_app, CategoryTheory.StrictlyUnitaryLaxFunctor.map_id, AlgebraicGeometry.ΓSpec.left_triangle, CategoryTheory.CartesianMonoidalCategory.inv_prodComparison_map_fst_assoc, CategoryTheory.FunctorToTypes.prod.lift_fst, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerLeft_naturality, CategoryTheory.ProjectiveResolution.Hom.hom_f_zero_comp_π_f_zero_assoc, Action.sub_hom, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app_assoc, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac, CategoryTheory.OverPresheafAux.restrictedYonedaObj_map, AlgebraicGeometry.AffineSpace.comp_homOfVector, CategoryTheory.Limits.colimitIsoSwapCompColim_inv_app, CategoryTheory.CartesianMonoidalCategory.prodComparison_comp, FintypeCat.toLightProfinite_map_hom_hom_apply, CategoryTheory.Limits.FormalCoproduct.category_comp_φ, CategoryTheory.HopfObj.antipode_comul₂, CategoryTheory.Over.map_obj_hom, SimplexCategory.revCompRevIso_inv_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app, CategoryTheory.monoidalUnopUnop_δ, CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj_inv_app, AlgebraicGeometry.ι_left_coprodIsoSigma_inv, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_functor_obj, CategoryTheory.Subgroupoid.mem_ker_iff, CategoryTheory.oplaxFunctorOfIsLocallyDiscrete_obj, CategoryTheory.Types.instPreservesLimitsOfSizeForgetTypeHom, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_hom_app_fst_app, SSet.ι₁_snd_assoc, SimplicialObject.Splitting.ofIso_isColimit', PresheafOfModules.toSheaf_map_sheafificationHomEquiv_symm, CategoryTheory.Functor.LaxLeftLinear.μₗ_unitality_assoc, CategoryTheory.Limits.walkingSpanOpEquiv_counitIso_hom_app, CategoryTheory.Functor.map₂HomologicalComplex_map_app, CategoryTheory.Limits.WidePushout.hom_ext_iff, CategoryTheory.GrothendieckTopology.plusMap_comp_assoc, CategoryTheory.Limits.Cofork.π_precompose, CategoryTheory.Functor.mapZeroObject_inv, CategoryTheory.Bicategory.comp_whiskerRight_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_one, CategoryTheory.Functor.cocones_obj, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero, CategoryTheory.Limits.ReflexiveCofork.condition, CategoryTheory.Functor.IsEventuallyConstantTo.coneπApp_eq_id, CategoryTheory.Over.associator_hom_left_snd_fst, CategoryTheory.CommSq.fac_right, CategoryTheory.Limits.PreservesLimitPair.iso_inv_snd, CategoryTheory.Dial.associator_inv_f, CategoryTheory.Limits.compCoyonedaSectionsEquiv_symm_apply_coe, CategoryTheory.tensorHom_def, CategoryTheory.Enriched.Functor.functorHom_whiskerLeft_natTransEquiv_symm_app, CategoryTheory.Limits.coker.condition, CategoryTheory.cokernel.π_op, CategoryTheory.Functor.constCompWhiskeringLeftIso_hom_app_app, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply', CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app_assoc, HomologicalComplex.nsmul_f_apply, CategoryTheory.Types.instIsEquivalenceForgetTypeHom, CategoryTheory.Limits.colimit.hom_ext_iff, SimplexCategory.diag_subinterval_eq, CategoryTheory.ShortComplex.LeftHomologyMapData.ofEpiOfIsIsoOfMono'_φK, CategoryTheory.NatTrans.mapElements_map_coe, HomologicalComplex.g_shortComplexTruncLEX₃ToTruncGE, Frm.hom_comp, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv, CategoryTheory.Limits.imageMonoIsoSource_inv_ι, CategoryTheory.ObjectProperty.instSmallOppositeOp_1, CategoryTheory.Limits.WalkingReflexivePair.reflexion_comp_right, CategoryTheory.Over.postComp_inv_app_left, CategoryTheory.CosimplicialObject.Augmented.const_map_right, CategoryTheory.TwoSquare.whiskerBottom_app, CategoryTheory.Limits.biprod.lift_fst_assoc, CategoryTheory.ObjectProperty.prop_sup_iff, AlgebraicGeometry.Scheme.homOfLE_appTop, CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_hom, CategoryTheory.Pretriangulated.comp_hom₃_assoc, CategoryTheory.Limits.FormalCoproduct.inj_comp_cofanPtIsoSelf_hom, HomologicalComplex.homotopyCofiber.inr_desc, CategoryTheory.comp_eqToHom_heq_iff, CategoryTheory.Bicategory.hom_inv_whiskerRight_whiskerRight, CategoryTheory.Limits.biproduct.matrix_map, CategoryTheory.Limits.Sigma.map_comp_map', CategoryTheory.monoidalOfHasFiniteProducts.associator_inv_snd, Rep.FiniteCyclicGroup.chainComplexFunctor_map_f, CategoryTheory.Bicategory.LeftExtension.whiskerIdCancel_right, CategoryTheory.MorphismProperty.instHasOfPrecompPropertyTop, CategoryTheory.Bicategory.prod_rightUnitor_inv_snd, CategoryTheory.IsMonHom.mul_hom, CategoryTheory.Pretriangulated.Triangle.neg_hom₃, CategoryTheory.MorphismProperty.HasCardinalLT.sup, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.functorMap_id, CategoryTheory.Limits.π_comp_cokernelIsoOfEq_inv_assoc, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counit_app_assoc, CategoryTheory.ReflQuiv.comp_obj, CategoryTheory.NatTrans.app_zero, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_app, CategoryTheory.NatTrans.prod'_app_fst, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_cofanPtIsoSelf_inv_assoc, CategoryTheory.BraidedCategory.braiding_tensor_left_hom_assoc, CategoryTheory.cosimplicialSimplicialEquiv_functor_map_app, HomotopicalAlgebra.PathObject.ofFactorizationData_p₁, CategoryTheory.Limits.isLimitConeUnopOfCocone_lift, CategoryTheory.Limits.Cocones.extendComp_hom_hom, HomologicalComplex.truncGE'_d_eq, CategoryTheory.Linear.comp_units_smul, CategoryTheory.Limits.prod.triangle, CategoryTheory.kernelCokernelCompSequence.snakeInput_L₀_g, CategoryTheory.Mathlib.Tactic.MonTauto.rightUnitor_inv_tensor_one_mul_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_right, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_functor_obj_d_f, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_fst, CategoryTheory.ShiftedHom.mk₀_comp_mk₀, CategoryTheory.Functor.ShiftSequence.induced.shiftIso_hom_app_obj, CategoryTheory.IsHomLift.lift_id_comp, AlgebraicGeometry.Scheme.isoSpec_inv_naturality_assoc, CategoryTheory.Equivalence.inverseFunctorObjIso_inv, AlgebraicGeometry.PresheafedSpace.stalkMap.id, CategoryTheory.Abelian.Ext.hom_comp_singleFunctor_map_shift, CategoryTheory.Monad.mu_naturality, AlgebraicGeometry.Spec.map_comp_assoc, CategoryTheory.Functor.coreCompInclusionIso_hom_app, CategoryTheory.Localization.SmallShiftedHom.mk₀Inv_comp_mk₀, CategoryTheory.comp_rightAdjointMate_assoc, CategoryTheory.ShortComplex.Homotopy.refl_h₁, CategoryTheory.lift_comp_preservesLimitIso_hom, CategoryTheory.RanIsSheafOfIsCocontinuous.fac', AlgebraicGeometry.IsImmersion.isImmersion_iff_exists, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self, AlgebraicGeometry.Spec.toPresheafedSpace_map_op, CategoryTheory.Over.toOverSectionsAdj_unit_app, CategoryTheory.Limits.image.fac, CategoryTheory.GradedObject.mapBifunctorRightUnitor_inv_naturality_assoc, CategoryTheory.Equivalence.changeInverse_counitIso_inv_app, CategoryTheory.MorphismProperty.instIsStableUnderRetractsMin, CategoryTheory.Functor.Monoidal.coreMonoidalTransport_μIso_inv, CategoryTheory.kernelCokernelCompSequence.inl_φ, CategoryTheory.ShortComplex.Exact.shortExact, CategoryTheory.Functor.diag_μ, ModuleCat.range_mkQ_cokernelIsoRangeQuotient_inv, CategoryTheory.Functor.toPreimages_map, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_0, CategoryTheory.Functor.commShiftIso_hom_naturality_assoc, CategoryTheory.Limits.IndObjectPresentation.yoneda_isColimit_desc, ModuleCat.exteriorPower.iso₀_hom_naturality_assoc, groupCohomology.resNatTrans_app, CategoryTheory.Comma.mapRightEq_inv_app_left, AlgebraicGeometry.Scheme.homOfLE_homOfLE_assoc, CategoryTheory.Iso.inv_hom_id_app_app_assoc, CategoryTheory.BimonObj.mul_comul_assoc, CategoryTheory.monoidalOfHasFiniteProducts.associator_hom_snd_snd, CategoryTheory.Limits.coprod.map_swap, CategoryTheory.Limits.biprod.map_fst, CategoryTheory.Functor.FullyFaithful.mulEquivEnd_symm_apply, CategoryTheory.Limits.KernelFork.condition, SSet.OneTruncation₂.nerveEquiv_symm_apply_map, HomotopicalAlgebra.CofibrantBrownFactorization.s_p, AlgebraicGeometry.IsLocalAtSource.respectsLeft_isOpenImmersion, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_inv_f_f, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_def_assoc, CategoryTheory.Functor.comp_mapCommMon_mul, CategoryTheory.Comonad.Coalgebra.coassoc, CategoryTheory.MorphismProperty.Comma.comp_right_assoc, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app, CategoryTheory.Limits.opCospan_hom_app, CategoryTheory.MorphismProperty.retracts_transfiniteComposition_pushouts_coproducts_le_llp_rlp, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict, CategoryTheory.Presheaf.FamilyOfElementsOnObjects.IsCompatible.familyOfElements_apply, CategoryTheory.Adjunction.comp_counit_app, CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_hom_comp_i_assoc, SSet.Truncated.StrictSegal.spine_δ_arrow_gt, CategoryTheory.cancel_mono, AlgebraicGeometry.isLocalIso_iff, CategoryTheory.Limits.biproduct.fromSubtype_π, CategoryTheory.ShortComplex.quasiIso_iff_comp_left, AlgebraicGeometry.Spec.preimage_comp_assoc, CategoryTheory.instMonoId, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_assoc, CategoryTheory.Grothendieck.map_id_eq, CategoryTheory.OrthogonalReflection.D₁.ιLeft_comp_t, CategoryTheory.SingleFunctors.shiftIso_add_inv_app, PartOrdEmb.hom_id, AlgebraicGeometry.IsClosedImmersion.lift_fac, Bimod.middle_assoc_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app'_assoc, CategoryTheory.whiskerLeft_coprod_inl_leftDistrib_inv_assoc, CategoryTheory.Functor.unopOpIso_hom_app, CategoryTheory.uliftYonedaEquiv_uliftYoneda_map, CategoryTheory.Comon.MonOpOpToComonObj_comon_comul, CategoryTheory.Functor.ShiftSequence.induced_shiftIso_hom_app_obj_assoc, CategoryTheory.Localization.SmallShiftedHom.equiv_shift', CategoryTheory.Limits.kernel.ι_of_zero, CategoryTheory.Pretriangulated.triangleCategory_id, AlgebraicGeometry.AffineSpace.hom_ext_iff, CategoryTheory.CostructuredArrow.eta_inv_left, PartOrdEmb.ofHom_id, prevD_eq_zero, CategoryTheory.ShortComplex.rightHomologyIso_hom_comp_homologyι, UniformSpaceCat.coe_comp, CategoryTheory.BraidedCategory.braiding_inv_naturality_right_assoc, CategoryTheory.finrank_hom_simple_simple_eq_zero_iff, CategoryTheory.ShortComplex.mapRightHomologyIso_hom_naturality, CategoryTheory.MonObj.one_comp, groupCohomology.π_comp_H0Iso_hom_assoc, CategoryTheory.yoneda_obj_map, CategoryTheory.Dial.rightUnitor_inv_f, CategoryTheory.MonObj.tensorObj.one_def, CategoryTheory.kernelCokernelCompSequence.inr_π, CategoryTheory.Quotient.compClosure.congruence, AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk_assoc, CategoryTheory.CosimplicialObject.δ_comp_δ_self, CategoryTheory.Iso.cancel_iso_inv_left, CategoryTheory.Cat.opFunctorInvolutive_hom_app_toFunctor_map, CategoryTheory.GradedObject.Monoidal.hexagon_reverse, CategoryTheory.Functor.OplaxMonoidal.δ_natural_left, CategoryTheory.Lax.LaxTrans.naturality_id, AlgebraicGeometry.ΓSpec.unop_locallyRingedSpaceAdjunction_counit_app', CategoryTheory.CartesianClosed.uncurry_natural_right, CategoryTheory.ForgetEnrichment.homOf_comp, groupCohomology.π_map, CategoryTheory.Limits.Sigma.ι_map, AlgebraicGeometry.LocallyRingedSpace.stalkMap_germ_assoc, CategoryTheory.ShortComplex.exact_and_epi_g_iff_g_is_cokernel, CategoryTheory.Limits.PreservesPullback.iso_inv_snd_assoc, AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_pullbackHom_assoc, CategoryTheory.Functor.IsCartesian.universal_property, CategoryTheory.Mat_.isoBiproductEmbedding_hom, CategoryTheory.Monad.mu_naturality_assoc, CategoryTheory.functorProdFunctorEquivUnitIso_hom_app, CategoryTheory.Pseudofunctor.DescentData.ofObj_obj, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_inv_app_hom, CategoryTheory.Functor.ι_colimitIsoOfIsLeftKanExtension_hom, CategoryTheory.ShortComplex.opcyclesMap'_comp_assoc, CategoryTheory.SmallObject.ιFunctorObj_eq, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_functor_map_f, CategoryTheory.Functor.commShiftIso_comp_inv_app, CategoryTheory.MonoidalClosed.curry_pre_app_assoc, CategoryTheory.Limits.IsImage.isoExt_hom_m, CategoryTheory.StructuredArrow.mkPostcomp_comp, CategoryTheory.Adjunction.mkOfHomEquiv_unit_app, CategoryTheory.Lax.StrongTrans.naturality_comp_assoc, CategoryTheory.Bicategory.associator_naturality_left_assoc, Semigrp.comp_apply, CategoryTheory.Localization.SmallHom.comp_mk_id, CategoryTheory.finrank_hom_simple_simple_eq_zero_of_not_iso, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_map_right, HomologicalComplex.inl_biprodXIso_inv, CategoryTheory.Limits.biproduct.ι_desc, ModuleCat.imageIsoRange_hom_subtype_assoc, SemiNormedGrp.explicitCokernel_hom_ext_iff, CategoryTheory.Functor.Monoidal.toUnit_ε, CategoryTheory.StrictPseudofunctorCore.map₂_right_unitor, CategoryTheory.Functor.Monoidal.whiskerRight_app_fst, Condensed.epi_iff_locallySurjective_on_compHaus, AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjMap_glueDataObjι_assoc, instIsMonHomOppositeCommAlgCatOpOfHomToAlgHomBialgHom, CategoryTheory.Groupoid.inv_comp, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_rightUnitor_inv_as_app, CategoryTheory.CartesianMonoidalCategory.inv_prodComparison_map_snd_assoc, AlgebraicGeometry.stalkMap_toStalk, groupCohomology.mapShortComplexH2_zero, CategoryTheory.Bicategory.prod_leftUnitor_inv_fst, AlgebraicTopology.DoldKan.QInfty_f_naturality_assoc, CategoryTheory.Functor.mapComon_obj_comon_comul, CategoryTheory.ShortComplex.RightHomologyMapData.rightHomologyMap_comm, CategoryTheory.Limits.spanCompIso_inv_app_right, AlgebraicTopology.DoldKan.MorphComponents.postComp_a, CategoryTheory.GlueData.diagramIso_inv_app_right, CategoryTheory.ShiftedHom.mk₀_comp_mk₀_assoc, CategoryTheory.Limits.BiconeMorphism.wι_assoc, CategoryTheory.Bicategory.triangle_assoc_comp_right_inv_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_app_assoc, CategoryTheory.Limits.limit.conePointUniqueUpToIso_hom_comp_assoc, CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyonedaObj, CategoryTheory.MonoidalCategory.whiskerLeft_comp_tensorHom, AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv, HomologicalComplex.fromOpcycles_op_cyclesOpIso_inv_assoc, CategoryTheory.Limits.MonoFactorisation.ofCompIso_m, comp_id, CategoryTheory.EnrichedFunctor.forgetId_inv_app, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagramOfIsLimit_map, CategoryTheory.NonPreadditiveAbelian.add_zero, SSet.Truncated.HomotopyCategory.homMk_id, CategoryTheory.Pretriangulated.TriangleMorphism.comp_hom₁, CategoryTheory.RetractArrow.retract_left, CategoryTheory.Limits.Fork.IsLimit.homIso_apply_coe, CategoryTheory.Adjunction.instMonoCoeEquivHomObjHomEquivOfReflectsMonomorphisms, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₂, CategoryTheory.Bicategory.hom_inv_whiskerRight, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_symm_app, CategoryTheory.InducedCategory.homAddEquiv_symm_apply_hom, CategoryTheory.PreZeroHypercover.inter_f, CategoryTheory.WithTerminal.inclLiftToTerminal_inv_app, SSet.stdSimplex.faceSingletonComplIso_hom_ι, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app, CategoryTheory.Bicategory.prod_rightUnitor_hom_fst, CategoryTheory.HopfObj.antipode_left_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.associator_hom_comp_tensorHom_tensorHom, CategoryTheory.Limits.HasLimit.isoOfNatIso_inv_π, CategoryTheory.Adjunction.leftAdjointCompIso_inv_app, CategoryTheory.Bicategory.Adjunction.left_triangle, CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_comp, CochainComplex.mappingCone.map_inr, CategoryTheory.CatCommSq.vComp_iso_hom_app, CategoryTheory.Functor.mapCochainComplexShiftIso_inv_app_f, DerivedCategory.HomologySequence.epi_homologyMap_mor₁_iff, HomologicalComplex.homotopyCofiber.inr_desc_assoc, CategoryTheory.ObjectProperty.instIsClosedUnderLimitsOfShapeOppositeOpOfIsClosedUnderColimitsOfShape_1, CategoryTheory.Under.mapCongr_hom_app, CategoryTheory.PreOneHypercover.id_s₁, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_fst, CategoryTheory.LocalizerMorphism.commShift_iso_inv_app_assoc, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_ε, CategoryTheory.GlueData.t'_comp_eq_pullbackSymmetry_assoc, CategoryTheory.GradedObject.Monoidal.id_tensorHom_id, CategoryTheory.Limits.ColimitPresentation.id_base, Quiver.FreeGroupoid.congr_comp_reverse, CategoryTheory.cokernelOpUnop_inv, CategoryTheory.LocalizerMorphism.equiv_smallHomMap', CategoryTheory.Functor.map_shiftFunctorCompIsoId_inv_app_assoc, Rep.resIndAdjunction_homEquiv_apply, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id_val_app, CategoryTheory.Limits.image.preComp_ι, HomologicalComplex.mapBifunctorFlipIso_hom_naturality, AlgebraicGeometry.Scheme.Pullback.tensorCongr_SpecTensorTo_assoc, CommRingCat.HomTopology.mvPolynomialHomeomorph_symm_apply_hom, HeytAlg.ofHom_id, CategoryTheory.coyonedaEquiv_naturality, CategoryTheory.Limits.Sigma.eqToHom_comp_ι_assoc, SheafOfModules.id_val, CategoryTheory.SimplicialObject.δ_comp_δ', CategoryTheory.CategoryOfElements.fromCostructuredArrow_obj_snd, CategoryTheory.CartesianMonoidalCategory.map_toUnit_comp_terminalComparison, Opens.mayerVietorisSquare_X₂, CategoryTheory.PreZeroHypercover.inv_hom_h₀_assoc, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheaf_map, CategoryTheory.SingleFunctors.inv_hom_id_hom_assoc, CategoryTheory.Sieve.pushforward_comp, CategoryTheory.Functor.leftDerivedNatTrans_app_assoc, CategoryTheory.Comma.eqToHom_right, LightCondensed.isLocallySurjective_iff_locallySurjective_on_lightProfinite, CategoryTheory.Limits.prod.map_snd, AlgebraicGeometry.Scheme.IdealSheafData.comapIso_inv_subschemeι_assoc, CategoryTheory.Pseudofunctor.CoGrothendieck.ext_iff, CategoryTheory.GrothendieckTopology.yonedaEquiv_comp, HomologicalComplex₂.D₁_totalShift₁XIso_hom_assoc, HomologicalComplex.truncLEMap_comp, CategoryTheory.oppositeShiftFunctorZero_inv_app, CategoryTheory.IsMod_Hom.smul_hom_assoc, CategoryTheory.MonoidalCategory.externalProductCompDiagIso_inv_app_app, CategoryTheory.SemiadditiveOfBinaryBiproducts.add_comp, CategoryTheory.Functor.prod'CompFst_inv_app, CategoryTheory.HomOrthogonal.matrixDecompositionLinearEquiv_apply, Homotopy.extend.homAux_eq, CategoryTheory.coyonedaEquiv_apply, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom_assoc, CochainComplex.mappingCone.liftCochain_v_fst_v, CategoryTheory.MonoidalCategory.triangle_assoc_comp_right, CategoryTheory.Lax.OplaxTrans.naturality_naturality, CategoryTheory.Idempotents.Karoubi.decompId_i_f, PresheafOfModules.pushforward_obj_map_apply, CategoryTheory.InjectiveResolution.ι_f_zero_comp_complex_d, CategoryTheory.Arrow.squareToSnd_left, AugmentedSimplexCategory.inl_comp_tensorHom, CategoryTheory.ObjectProperty.isDetecting_unop_iff, AlgebraicGeometry.AffineSpace.map_toSpecMvPoly, CategoryTheory.CostructuredArrow.mapIso_functor_map_right, CategoryTheory.Comonad.comparisonForget_inv_app, HomologicalComplex.cylinder.inrX_π_assoc, CategoryTheory.Equivalence.changeInverse_unitIso_inv_app, CochainComplex.HomComplex.CohomologyClass.equiv_toSmallShiftedHom_mk, groupCohomology.H2π_comp_map_assoc, CategoryTheory.Limits.compCoyonedaSectionsEquiv_apply_app, CategoryTheory.Limits.kernelOrderHom_coe, SemimoduleCat.homAddEquiv_apply, SSet.ι₁_snd, CategoryTheory.Functor.isoSum_hom_app_inl, CategoryTheory.Functor.IsStronglyCocartesian.comp, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_id, CategoryTheory.Limits.Fork.IsLimit.lift_ι, CategoryTheory.op_comp_assoc, CategoryTheory.Idempotents.Karoubi.p_comp, CategoryTheory.ShortComplex.SnakeInput.comp_f₂, CategoryTheory.IsCoreflexivePair.common_retraction, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_SpecMap_awayMap_left, AddGrpCat.ofHom_injective, CategoryTheory.PreZeroHypercover.shrink_X, CategoryTheory.Functor.biprodComparison_fst_assoc, AlgebraicGeometry.Scheme.Hom.app_invApp', CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_hom_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_id, CategoryTheory.ShortComplex.LeftHomologyMapData.ofEpiOfIsIsoOfMono'_φH, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right, CategoryTheory.Functor.PreservesHomology.preservesCokernels, CategoryTheory.Limits.hasPullback_of_right_factors_mono, CategoryTheory.ShortComplex.leftHomologyπ_naturality', groupHomology.d₁₀_comp_coinvariantsMk, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompPointIso_inv_app, AlgebraicGeometry.LocallyRingedSpace.Hom.ext_iff, CategoryTheory.ShortComplex.HasLeftHomology.of_hasCokernel, CategoryTheory.Over.rightUnitor_inv_left_snd_assoc, CategoryTheory.Subfunctor.Subpresheaf.toRange_ι, CategoryTheory.Preadditive.cokernelCoforkOfCofork_π, CategoryTheory.LaxFunctor.whiskerLeft_mapComp'_comp_mapComp', CategoryTheory.MonoidalCategory.MonoidalLeftAction.id_actionHomLeft_assoc, CategoryTheory.Limits.biproduct.toSubtype_fromSubtype, CategoryTheory.Functor.rightOpLeftOpIso_inv_app, CategoryTheory.Bicategory.Prod.fst_mapId_hom, CategoryTheory.Bicategory.triangle_assoc_comp_right_inv, CategoryTheory.Functor.mapMon_obj_mon_one, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso_inv_app_f, CategoryTheory.Enriched.FunctorCategory.enrichedComp_π_assoc, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂, CategoryTheory.Bicategory.associator_naturality_middle, CategoryTheory.Functor.IsStronglyCartesian.universal_property', CategoryTheory.Over.toOverSectionsAdj_counit_app, CategoryTheory.Functor.relativelyRepresentable.symmetry_fst, CategoryTheory.DinatTrans.compNatTrans_app, AlgebraicGeometry.Scheme.Hom.inl_normalizationCoprodIso_hom_fromNormalization_assoc, CategoryTheory.MonObj.comp_pow, HomologicalComplex.homologyOp_hom_naturality_assoc, CategoryTheory.Functor.mapMonIdIso_hom_app_hom, CategoryTheory.Presheaf.isLocallyInjective_forget_iff, CategoryTheory.Functor.comp_homologySequenceδ, CategoryTheory.regularTopology.isLocallySurjective_iff, HomologicalComplex.homologyMap_comp, CategoryTheory.StructuredArrow.toCostructuredArrow_map, CategoryTheory.Limits.ImageMap.factor_map, CategoryTheory.Limits.kernelIsoOfEq_hom_comp_ι_assoc, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_snd, CategoryTheory.Limits.Types.equalizerIso_hom_comp_subtype, CategoryTheory.MonoidalCategory.triangle_assoc_comp_right_inv_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app, CategoryTheory.Join.mapPairComp_inv_app_right, groupHomology.mapCycles₂_comp_apply, HomologicalComplex.mapBifunctor₁₂.ι_D₁, DerivedCategory.HomologySequence.mono_homologyMap_mor₂_iff, CategoryTheory.Limits.cokernelBiprodInrIso_hom, CategoryTheory.Limits.Types.pullbackIsoPullback_inv_snd, CategoryTheory.Center.Hom.comm, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocIso_hom_naturality, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_inv_naturality_assoc, CategoryTheory.Functor.Fiber.fiberInclusion_homMk, AlgebraicGeometry.Scheme.Hom.stalkSpecializes_stalkMap_assoc, CategoryTheory.Limits.kernel.condition, AddCommMonCat.coe_comp, CategoryTheory.ShortComplex.cyclesOpIso_inv_naturality, CategoryTheory.CartesianClosed.uncurry_eq, CategoryTheory.MonoOver.w, HomologicalComplex.homotopyCofiber.inlX_desc_f_assoc, CategoryTheory.Functor.map_shiftFunctorComm_assoc, HomologicalComplex.biprod_inl_fst_f, CategoryTheory.IsPushout.inl_isoIsPushout_hom_assoc, CategoryTheory.MonoOver.bot_arrow_eq_zero, CategoryTheory.ShortComplex.LeftHomologyData.wπ_assoc, CategoryTheory.WithInitial.equivComma_inverse_map_app, CategoryTheory.Biprod.column_nonzero_of_iso, CategoryTheory.GradedObject.CofanMapObjFun.ιMapObj_iso_inv, Bimod.one_actLeft_assoc, SimplicialObject.Splitting.πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty, CategoryTheory.kernel.ι_unop, CategoryTheory.Pseudofunctor.Grothendieck.map_obj_fiber, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_right_assoc, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp'_X, CategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy.g', CategoryTheory.ShortComplex.smul_τ₃, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_hom_app_coe, CategoryTheory.Comma.left_hom_inv_right, CategoryTheory.prodComonad_map, CochainComplex.HomComplex.Cochain.fromSingleMk_zero, CategoryTheory.HasClassifier.comm, CategoryTheory.Functor.ShiftSequence.induced_isoShiftZero_hom_app_obj_assoc, CategoryTheory.Oplax.LaxTrans.vComp_naturality_comp, CategoryTheory.ShortComplex.Splitting.unop_r, CategoryTheory.MorphismProperty.FunctorsInverting.comp_hom_assoc, CategoryTheory.Localization.Monoidal.whiskerRight_id, CategoryTheory.IsSplitCoequalizer.rightSection_π, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompYoneda, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp_assoc, CategoryTheory.MonObj.mul_one, CategoryTheory.forgetAdjToOver_unit_app, CategoryTheory.ShortComplex.homologyMap_neg, CategoryTheory.IsComonHom.hom_counit, CategoryTheory.Functor.OplaxMonoidal.right_unitality_hom, CategoryTheory.Adjunction.adjToComonadIso_hom_toNatTrans_app, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, CategoryTheory.Cat.FreeRefl.quotientFunctor_map_id, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp_assoc, CategoryTheory.Functor.Monoidal.map_associator_inv'_assoc, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp, CochainComplex.mappingCone.decomp_from, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp, CategoryTheory.IsSplitCoequalizer.rightSection_π_assoc, CategoryTheory.Subgroupoid.IsWide.id_mem, CochainComplex.mappingCone.inl_v_triangle_mor₃_f_assoc, AlgebraicGeometry.pullbackSpecIso_inv_fst, CategoryTheory.Limits.pushout_inr_iso_of_right_factors_epi, CategoryTheory.EnrichedCat.associator_hom_out_app, CategoryTheory.Comma.unopFunctor_obj, AlgebraicTopology.DoldKan.P_succ, FinBddDistLat.comp_apply, CategoryTheory.ShortComplex.RightHomologyMapData.ofEpiOfIsIsoOfMono_φH, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd, CategoryTheory.Limits.colimitHomIsoLimitYoneda_hom_comp_π_assoc, CategoryTheory.Limits.Types.binaryProductFunctor_map_app, CategoryTheory.Mathlib.Tactic.MonTauto.associator_inv_comp_tensorHom_tensorHom_comp, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_inv_left_app, CategoryTheory.Bicategory.prod_leftUnitor_inv_snd, CategoryTheory.Presheaf.w, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_app_assoc, CategoryTheory.Over.iteratedSliceEquivOverMapIso_inv_app_left_left, SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁_hom_app_f_f, CategoryTheory.Limits.Cone.mapConeToUnder_inv_hom, HomologicalComplex.homotopyCofiber.d_fstX, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_map, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_functor_map, CategoryTheory.unop_neg, CategoryTheory.Limits.inr_comp_pushoutSymmetry_inv_assoc, CategoryTheory.Limits.initial.to_comp_assoc, CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.essentiallyLarge_top, CategoryTheory.Functor.map_shiftFunctorCompIsoId_hom_app_assoc, CategoryTheory.StrictPseudofunctor.comp_map, CategoryTheory.ShiftMkCore.assoc_inv_app_assoc, CategoryTheory.Functor.IsCartesian.fac_assoc, ModuleCat.smulNatTrans_apply_app, AddMonCat.hom_id, FGModuleCat.ihom_obj, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₁, CategoryTheory.Over.iteratedSliceEquivOverMapIso_hom_app_left_left, CategoryTheory.Bicategory.LeftExtension.IsKan.fac_assoc, TopModuleCat.hom_id, SimplicialObject.Splitting.cofan_inj_πSummand_eq_id, CategoryTheory.Comma.mapLeftComp_inv_app_right, CategoryTheory.Idempotents.Karoubi.comp_proof, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_pt, CategoryTheory.Comma.equivProd_counitIso_inv_app, CategoryTheory.CategoryOfElements.ext_iff, AlgebraicGeometry.RingedSpace.isUnit_res_of_isUnit_germ, CategoryTheory.WithTerminal.isLimitEquiv_symm_apply_lift, CategoryTheory.instIsIsoEqToHom, CategoryTheory.CostructuredArrow.map₂_map_right, CategoryTheory.GlueData.glue_condition, CategoryTheory.endofunctorMonoidalCategory_rightUnitor_inv_app, CategoryTheory.pre_id, CategoryTheory.Limits.terminal.comp_from, CategoryTheory.Comma.toIdPUnitEquiv_unitIso_hom_app_right, CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono_g', CategoryTheory.Limits.biprod.inl_snd, AlgebraicGeometry.Spec.locallyRingedSpaceMap_comp, CategoryTheory.Limits.Wedge.condition, PartOrd.comp_apply, CategoryTheory.Limits.IsInitial.to_comp, CategoryTheory.Limits.HasCoequalizersOfHasPushoutsAndBinaryCoproducts.pushoutInl_eq_pushout_inr, CategoryTheory.ShortComplex.Exact.rightHomologyDataOfIsColimitCokernelCofork_Q, CategoryTheory.Functor.Braided.braided, CategoryTheory.Limits.CatCospanTransform.rightUnitor_hom_base_app, CochainComplex.mappingConeCompTriangle_mor₁, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_obj_fiber, CategoryTheory.RetractArrow.retract_right_assoc, AddMonCat.FilteredColimits.cocone_naturality, CategoryTheory.Abelian.extFunctor_map_app, CochainComplex.mappingCone.inr_triangleδ_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_map_app_app, CochainComplex.cm5b.instIsStrictlyGEBiprodIntMappingConeIdIOfHAddOfNat, CategoryTheory.Grothendieck.id_base, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_left, CategoryTheory.ShortComplex.LeftHomologyMapData.comp_φH, CategoryTheory.SmallCategoryOfSet.comp_def, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counitIso_hom_app, groupHomology.chainsMap_id_comp, CategoryTheory.PrelaxFunctor.map₂_inv, CategoryTheory.Precoverage.ZeroHypercover.id_s₀, CategoryTheory.Iso.unop_hom_inv_id_app, CategoryTheory.Coyoneda.naturality, MulEquiv.toSingleObjEquiv_unitIso_inv, CategoryTheory.Biprod.ofComponents_comp, CategoryTheory.StrictPseudofunctorPreCore.map_comp, HomologicalComplex.homologyπ_restrictionHomologyIso_hom, CategoryTheory.ShortComplex.HomologyMapData.zero_right, HomologicalComplex.comp_f, CategoryTheory.Limits.limit.existsUnique, CategoryTheory.Localization.Preadditive.add_comp, CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsUnopOfOpposite, CochainComplex.mappingCone.inl_v_snd_v_assoc, AlgebraicGeometry.AffineSpace.homOfVector_over_assoc, AugmentedSimplexCategory.id_star_whiskerRight, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHomLeft_op, CategoryTheory.Iso.inv_hom_id_assoc, CategoryTheory.ShortComplex.Homotopy.symm_h₃, CategoryTheory.NatTrans.IsMonoidal.comp, CategoryTheory.regularTopology.parallelPair_pullback_initial, CategoryTheory.Limits.Cones.extendComp_inv_hom, CategoryTheory.StrictPseudofunctor.mk''_map, MonCat.comp_apply, HomologicalComplex.cylinder.inlX_π, CategoryTheory.monoidalOpOp_μ, HomologicalComplex.cylinder.ι₀_π, CategoryTheory.MorphismProperty.RightFraction.map_ofInv_hom_id_assoc, CategoryTheory.Join.mapPairLeft_inv_app, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_inverse_map, CategoryTheory.Grp_Class.zpow_comp, CategoryTheory.cosimplicialSimplicialEquiv_counitIso_inv_app_app, SimplexCategoryGenRel.standardσ_cons, CategoryTheory.ObjectProperty.instContainsZeroTopOfHasZeroObject, CategoryTheory.Codiscrete.natIsoFunctor_inv_app, Rep.leftRegularHomEquiv_symm_apply, CategoryTheory.Functor.commShiftIso_hom_naturality, CategoryTheory.overToCoalgebra_map_f, CategoryTheory.Oplax.StrongTrans.naturality_naturality_assoc, CategoryTheory.Comonad.adj_counit, CategoryTheory.Functor.CommShift.comp_commShiftIso_hom_app, CategoryTheory.composePath_nil, CategoryTheory.Limits.biprod.associator_natural_assoc, CategoryTheory.BraidedCategory.yang_baxter_assoc, CategoryTheory.ShortComplex.SnakeInput.w₁₃_assoc, CategoryTheory.Limits.biprod.associator_inv_natural_assoc, CategoryTheory.MonoidalCategory.leftUnitor_naturality_assoc, CategoryTheory.GlueData.diagram_snd, CategoryTheory.Pseudofunctor.isStackFor_iff, AlgebraicGeometry.morphismRestrict_comp, HomologicalComplex.XIsoOfEq_hom_comp_XIsoOfEq_inv_assoc, CategoryTheory.Adjunction.homAddEquiv_add, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatTrans_comp, HomologicalComplex.ι_mapBifunctorAssociatorX_hom_assoc, CategoryTheory.Limits.pushoutIsoUnopPullback_inl_hom, CategoryTheory.Localization.Monoidal.whisker_exchange, CategoryTheory.endomorphism_simple_eq_smul_id, CategoryTheory.Bicategory.Prod.sectL_mapId_hom, CategoryTheory.MonoidalCategory.associator_monoidal_assoc, CategoryTheory.ComposableArrows.opEquivalence_unitIso_hom_app, AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_comp, AlgebraicGeometry.Scheme.SpecMap_stalkSpecializes_fromSpecStalk_assoc, CategoryTheory.ObjectProperty.ι_δ, CategoryTheory.ProjectiveResolution.Hom.hom'_comp_π'_assoc, CategoryTheory.PreZeroHypercover.bind_f, CategoryTheory.Limits.Sigma.ι_π, CategoryTheory.cancel_epi_assoc_iff, CategoryTheory.Limits.equalizer.condition_assoc, CategoryTheory.StructuredArrow.IsUniversal.hom_desc, HomologicalComplex.singleObjOpcyclesSelfIso_inv_naturality, HomologicalComplex.ιOrZero_mapBifunctorAssociatorX_hom, CategoryTheory.eHom_whisker_cancel_assoc, CategoryTheory.TwoSquare.hComp_app, CategoryTheory.MonoidalCategory.id_whiskerLeft_assoc, CategoryTheory.eq_conj_eqToHom, TopologicalSpace.Opens.coe_id, CategoryTheory.ShortComplex.mapToComposableArrows_comp, CategoryTheory.Mon.tensorObj_mul, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right_assoc, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_id_naturality_hom, CategoryTheory.CatCenter.smul_eq', CategoryTheory.ShortComplex.LeftHomologyMapData.add_φH, TopCat.presheafToTypes_map, CommRingCat.HomTopology.isEmbedding_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.unit_actionHomRight_assoc, CategoryTheory.SimplicialObject.isCoskeletal_iff, CategoryTheory.Limits.Cocone.toOver_pt, SkyscraperPresheafFunctor.map'_comp, CategoryTheory.NatTrans.whiskerRight_app_tensor_app, CategoryTheory.Functor.mapComposableArrowsObjMk₁Iso_hom_app, CategoryTheory.Pseudofunctor.isoMapOfCommSq_vert_id, CategoryTheory.Limits.hasPullback_assoc, CategoryTheory.Limits.Multifork.condition, CategoryTheory.Pseudofunctor.isPrestackFor_iff_isSheafFor, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_left_app, CategoryTheory.η_naturality, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_app_app_germToPullbackStalk_assoc, CategoryTheory.MonoidalClosed.curry'_comp, CategoryTheory.ShortComplex.unopMap_τ₂, HomologicalComplex.extend.rightHomologyData.d_comp_desc_eq_zero_iff, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.leftUnitor_naturality, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerRight, HomologicalComplex.cyclesOpIso_inv_naturality, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.lift_fac_assoc, CategoryTheory.yonedaGrp_naturality_assoc, CategoryTheory.Limits.WalkingReflexivePair.reflexion_comp_left_assoc, AddCommMonCat.coyoneda_map_app, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_hom_app_app_hom_hom, CategoryTheory.Limits.CategoricalPullback.Hom.w_assoc, CategoryTheory.Sheaf.ΓRes_map_assoc, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_snd_assoc, AlgebraicGeometry.Scheme.Cover.LocallyDirected.trans_comp, groupCohomology.mapShortComplexH1_id, MagmaCat.id_apply, AlgebraicTopology.DoldKan.N₂Γ₂_compatible_with_N₁Γ₀, CommRingCat.moduleCatExtendScalarsPseudofunctor_map, CategoryTheory.Mon_Class.one_eq_one, CategoryTheory.Grp.Hom.hom_pow, CategoryTheory.CartesianMonoidalCategory.lift_lift_associator_hom, CategoryTheory.Functor.prod'_δ_fst, AlgebraicGeometry.Scheme.ΓSpecIso_naturality, CategoryTheory.Under.mapFunctor_map, CategoryTheory.ShortComplex.HomotopyEquiv.refl_inv, CategoryTheory.Grp.δ_def, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv, CategoryTheory.Functor.prod'_μ_snd, CategoryTheory.Bimon.ofMonComon_toMonComon_obj_counit, CategoryTheory.Center.Hom.comm_assoc, CategoryTheory.surjective_up_to_refinements_of_epi, CategoryTheory.MorphismProperty.map_le_iff, CategoryTheory.ShortComplex.HomologyMapData.id_right, CategoryTheory.GrpObj.whiskerLeft_η_commutator, CategoryTheory.Limits.Fork.op_π, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp'_f, Frm.id_apply, quasiIso_iff_comp_left, HomologicalComplex.biprod_inr_fst_f, CategoryTheory.Limits.piObjIso_hom_comp_π_assoc, CategoryTheory.ShiftedHom.comp_mk₀_id, CategoryTheory.Square.category_id_τ₁, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_fst_assoc, CategoryTheory.LocalizerMorphism.RightResolution.id_f, AlgebraicGeometry.Scheme.restrictFunctorΓ_hom_app, CategoryTheory.MonoidalCategory.whisker_exchange_assoc, AddCommGrpCat.zero_apply, CategoryTheory.Pseudofunctor.bijective_toDescentData_map_iff, CategoryTheory.Limits.inv_prodComparison_map_fst, AlgebraicGeometry.Scheme.stalkMap_congr_hom, CategoryTheory.ShortComplex.LeftHomologyMapData.leftHomologyMap_comm, CategoryTheory.Limits.limit.conePointUniqueUpToIso_inv_comp_assoc, CategoryTheory.Limits.CatCospanTransform.triangle_inv, CategoryTheory.Functor.uncurryObjFlip_inv_app, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_inv_app_hom, CategoryTheory.Groupoid.CategoryTheory.Functor.mapVertexGroup_apply, CategoryTheory.Limits.pullbackAssoc_hom_snd_fst, CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_id, CategoryTheory.MonoidalCategory.tensorHom_comp_whiskerLeft_assoc, CategoryTheory.Bicategory.mateEquiv_symm_apply, CategoryTheory.Functor.Elements.initialOfCorepresentableBy_snd, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_hom_app_app, CategoryTheory.MonoidalCategory.id_whiskerLeft_symm_assoc, CategoryTheory.Pseudofunctor.map₂_whisker_left_assoc, CategoryTheory.IsPullback.isoIsPullback_hom_fst_assoc, CategoryTheory.Limits.cokernel.condition_assoc, CategoryTheory.CatCommSq.iso_inv_naturality_assoc, CategoryTheory.Limits.CatCospanTransform.leftUnitor_inv_right_app, CategoryTheory.Under.liftCone_π_app, ModuleCat.ExtendRestrictScalarsAdj.homEquiv_symm_apply, CategoryTheory.GrpObj.lift_commutator_eq_mul_mul_inv_inv, CategoryTheory.Limits.Cocone.ofCofork_ι, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τr, AlgebraicGeometry.Scheme.Γ_map_op, AlgebraicGeometry.Scheme.Pullback.range_snd_comp, HomologicalComplex.opcyclesOpIso_hom_naturality, CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_hom_assoc, PresheafOfModules.homEquivOfIsLocallyBijective_apply, TopModuleCat.comp_cokerπ, CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_left, CategoryTheory.Limits.kernelSubobject_arrow_comp_apply, HomologicalComplex₂.total.mapAux.mapMap_D₁, CategoryTheory.Limits.WalkingMulticospan.Hom.comp_eq_comp, CategoryTheory.isoCartesianComon_hom_hom, CategoryTheory.Presieve.FamilyOfElements.isAmalgamation_iff_ofArrows, CategoryTheory.Limits.pullbackProdFstIsoProd_inv_snd_fst, CategoryTheory.Bicategory.leftUnitor_whiskerRight, CategoryTheory.preservesFiniteColimits_preadditiveCoyonedaObj_of_projective, CategoryTheory.Limits.IsZero.unique_from, CategoryTheory.Localization.Monoidal.whisker_exchange_assoc, CategoryTheory.MonoidalCategory.tensorHom_def', HomotopicalAlgebra.PathObject.trans_p₀, CategoryTheory.Over.pullback_map_left, CategoryTheory.Limits.MonoFactorisation.ofIsoComp_e, Bicategory.Opposite.homCategory_comp_unop2, CategoryTheory.Functor.sheafPushforwardContinuous_obj_val_map, AddCommGrpCat.id_apply, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id, groupHomology.mapShortComplexH1_id_comp, HasFibers.Fib.mkIsoSelfIsHomLift, TopCat.Presheaf.stalkSpecializes_stalkFunctor_map_assoc, TopCat.Sheaf.comp_app, CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_inv_assoc, CategoryTheory.Functor.rightDerivedNatTrans_fac, CategoryTheory.Localization.liftNatTrans_app, CategoryTheory.NatTrans.naturality_app_assoc, groupHomology.mapShortComplexH1_comp, CategoryTheory.Cat.FreeRefl.quotientFunctor_map_nil, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_inv_app_app, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_left, CategoryTheory.ShortComplex.leftHomologyπ_naturality'_assoc, HomologicalComplex.homotopyCofiber.eq_desc, CategoryTheory.ULift.equivalence_unitIso_hom, HomologicalComplex.truncLE'Map_id, CategoryTheory.ShortComplex.Splitting.ofIso_s, CategoryTheory.Limits.biproduct.lift_π_assoc, PresheafOfModules.unitHomEquiv_apply_coe, CategoryTheory.Iso.cancel_iso_hom_right_assoc, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.counitIso_hom_app_app_hom, CategoryTheory.Mat_.embeddingLiftIso_inv_app, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_counitIso_inv_app_f, AlgebraicGeometry.Scheme.Opens.isoOfLE_hom_ι, CategoryTheory.Limits.pullback.condition_assoc, CategoryTheory.Join.pseudofunctorRight_mapId_hom_toNatTrans_app, CategoryTheory.Under.forgetMapInitial_hom_app, CochainComplex.HomComplex.Cochain.ofHoms_v_comp_d, CategoryTheory.ObjectProperty.instIsClosedUnderColimitsOfShapeUnopOfIsClosedUnderLimitsOfShapeOpposite, CategoryTheory.Limits.FormalCoproduct.cochainComplexFunctor_obj_d, Rep.coindResAdjunction_homEquiv_apply, CochainComplex.mappingCone.inr_f_triangle_mor₃_f, CategoryTheory.Functor.triangle, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_map_fiber, PartOrdEmb.coe_comp, groupCohomology.inhomogeneousCochains.d_comp_d, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftUnitor_actionHom, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp_assoc, CategoryTheory.sum.inrCompInrCompInverseAssociator_inv_app_down, HomologicalComplex.π_homologyIsoSc'_hom_assoc, CategoryTheory.PreGaloisCategory.exists_autMap, AlgebraicGeometry.SheafedSpace.Γ_map, HeytAlg.comp_apply, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_hom_π, AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem_ι, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_pt, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_fst_assoc, CategoryTheory.Limits.Multicoequalizer.ι_sigmaπ, CategoryTheory.LocalizerMorphism.LeftResolution.comp_f_assoc, CategoryTheory.Limits.colimCompFlipIsoWhiskerColim_hom_app_app, AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id, CategoryTheory.Functor.mapHomologicalComplexIdIso_inv_app_f, CategoryTheory.Endofunctor.Algebra.id_f, CategoryTheory.conjugateEquiv_symm_comp, CategoryTheory.StrictPseudofunctor.toFunctor_obj, assoc', CategoryTheory.PreZeroHypercover.comp_s₀, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_functor_map_hom, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_fst, CategoryTheory.Comma.mapRightIso_functor_map_right, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.Sieve.functorInclusion_app, CategoryTheory.GradedObject.mapBifunctor₁₂BifunctorMapObj_ext_iff, SheafOfModules.ιFree_freeMap, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_snd, HomologicalComplex.homotopyCofiber.inrX_desc_f, CategoryTheory.Pretriangulated.shiftFunctorZero_op_hom_app, Opens.coe_mayerVietorisSquare_X₁, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_app_apply, CategoryTheory.Paths.lift_spec, SSet.comp_app, AlgebraicGeometry.Scheme.Modules.pushforwardComp_hom_app_app, CategoryTheory.Oplax.StrongTrans.naturality_id, CategoryTheory.Equivalence.cancel_counitInv_right_assoc, Homotopy.compRight_hom, CategoryTheory.Abelian.factorThruImage_comp_coimageIsoImage'_inv, CategoryTheory.instIsMod_HomComp, CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_homEquiv, CategoryTheory.Comma.limitAuxiliaryCone_π_app, CategoryTheory.MonoidalCategory.associator_conjugation_assoc, CochainComplex.cm5b.fac_assoc, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_inv_hom'_assoc, CategoryTheory.Bicategory.associator_eqToHom_inv_assoc, AlgebraicTopology.DoldKan.Hσ_eq_zero, CategoryTheory.ObjectProperty.isClosedUnderColimitsOfShape_iff, CochainComplex.ConnectData.d₀_comp, CategoryTheory.Subobject.underlyingIso_arrow, MonCat.coe_comp, CategoryTheory.StrictPseudofunctor.map_comp, CategoryTheory.Limits.Trident.IsLimit.homIso_apply_coe, CategoryTheory.SimplicialObject.δ_comp_σ_succ', CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_fst, CategoryTheory.ObjectProperty.le_isLocal_iff, CategoryTheory.Pseudofunctor.presheafHom_map, CategoryTheory.MonoidalCategory.pentagon_hom_inv, CategoryTheory.Limits.limit.post_π_assoc, CategoryTheory.Functor.toOplaxFunctor'_map, AlgebraicTopology.AlternatingFaceMapComplex.obj_d_eq, CategoryTheory.FreeMonoidalCategory.inclusion_map, CategoryTheory.prodOpEquiv_unitIso_inv_app, CategoryTheory.Localization.comp_liftNatTrans_assoc, HomologicalComplex.tensor_unit_d₂, ComplexShape.Embedding.homRestrict_comp_extendMap_assoc, AlgebraicGeometry.Scheme.iso_inv_base_hom_base, CategoryTheory.Sheaf.ΓObjEquivHom_naturality_symm, AlgebraicGeometry.Scheme.Hom.inl_normalizationCoprodIso_hom_fromNormalization, AlgebraicGeometry.germ_stalkClosedPointIso_hom, CategoryTheory.Functor.relativelyRepresentable.pullback₃.map_p₁_comp_assoc, CategoryTheory.Join.opEquiv_inverse_map_inclLeft_op, CategoryTheory.Bicategory.prod_leftUnitor_hom_snd, CategoryTheory.GradedObject.mapBifunctorRightUnitor_inv_apply, CategoryTheory.GradedObject.ι_mapBifunctorComp₁₂MapObjIso_inv, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply, fintypeToFinBoolAlgOp_map, CategoryTheory.Grothendieck.toTransport_fiber, CategoryTheory.Idempotents.Karoubi.Hom.comm, CategoryTheory.Limits.WidePullback.π_arrow_assoc, CategoryTheory.ChosenPullbacksAlong.pullbackId_hom_counit, GrpCat.coe_comp, AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv, CategoryTheory.MorphismProperty.LeftFraction.op_s, CategoryTheory.ι_colimitCompWhiskeringRightIsoColimitComp_hom, CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_inv_hom_id, CommMonCat.coe_id, ChainComplex.mk'_congr_succ'_d, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_hom_app_hom_left, CategoryTheory.Subobject.ofLE_comp_ofLE_assoc, CategoryTheory.tensorRightHomEquiv_naturality, CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor, CategoryTheory.SplitEpi.id_assoc, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_fst, CategoryTheory.IsReflexivePair.common_section, CategoryTheory.Limits.cokernelBiproductιIso_inv, CategoryTheory.Functor.ranObjObjIsoLimit_inv_π_assoc, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_assoc, AlgebraicGeometry.Scheme.Hom.comp_apply, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_hom_f_f, CategoryTheory.Limits.pullbackConeOfRightIso_snd, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_hom_app_app, CategoryTheory.OplaxFunctor.mapComp_assoc_right_app_assoc, CochainComplex.IsKProjective.nonempty_homotopy_zero, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π_assoc, Traversable.foldl.unop_ofFreeMonoid, CategoryTheory.Limits.piPiIso_hom, CategoryTheory.GradedObject.ι_mapBifunctorMapObjDesc_assoc, CategoryTheory.Cat.HasLimits.id_def, CategoryTheory.Functor.PullbackObjObj.ofHasPullback_π, groupCohomology.toCocycles_comp_isoCocycles₁_hom_assoc, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_inv, CategoryTheory.Subgroupoid.Map.arrows_iff, SimplicialObject.Splitting.IndexSet.fac_pull, CategoryTheory.Groupoid.vertexGroupIsomOfMap_apply, CategoryTheory.Quiv.pathComposition_naturality, CategoryTheory.rightDistributor_ext_left_iff, Frm.coe_id, AlgebraicGeometry.Scheme.homOfLE_homOfLE, HomologicalComplex.biprodXIso_hom_fst_assoc, CategoryTheory.HalfBraiding.monoidal_assoc, Rep.resIndAdjunction_counit_app, ContAction.resComp_hom, CategoryTheory.GrpObj.lift_inv_left_eq, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_assoc, CategoryTheory.StrictlyUnitaryPseudofunctor.mapId_eq_eqToIso, CategoryTheory.Functor.comp_mapCommGrp_mul, CategoryTheory.Center.whiskerRight_comm, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_inv_π_assoc, CategoryTheory.MorphismProperty.IsInvertedBy.leftOp, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_hom_hom, SimplicialObject.Split.cofan_inj_naturality_symm_assoc, CategoryTheory.Limits.fiberwiseColimitLimitIso_inv_app, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv_desc_assoc, CategoryTheory.e_id_comp_assoc, AlgebraicGeometry.Proj.awayι_toSpecZero, CategoryTheory.Subobject.ofMkLEMk_comp, CategoryTheory.MonoidalOpposite.tensorRightUnmopIso_inv_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_id_assoc, CategoryTheory.MorphismProperty.Comma.ext_iff, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_assoc, Action.Hom.id_hom, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_assoc, CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom', HomologicalComplex₂.flipEquivalenceUnitIso_inv_app_f_f, CategoryTheory.StrictlyUnitaryPseudofunctor.id_obj, CategoryTheory.MorphismProperty.le_coproducts, CommAlgCat.snd_unop_hom, CategoryTheory.ProjectiveResolution.lift_commutes_zero, SimplicialObject.Splitting.ofIso_ι, CategoryTheory.ShortComplex.HomotopyEquiv.ext_iff, TopCat.pullbackIsoProdSubtype_inv_fst, CategoryTheory.Limits.biprod.ext_to_iff, CategoryTheory.Limits.pullbackIsoOpPushout_inv_fst, CategoryTheory.Square.fac, CategoryTheory.MonadHom.app_η_assoc, CategoryTheory.ObjectProperty.isoClosure_le_iff, CategoryTheory.Bicategory.whiskerLeft_inv_hom_whiskerRight_assoc, CategoryTheory.Idempotents.whiskeringLeft_obj_preimage_app, AlgebraicGeometry.PresheafedSpace.GlueData.f_invApp_f_app_assoc, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy_homEquiv_symm_apply, CategoryTheory.Limits.cospanCompIso_inv_app_right, CategoryTheory.Cat.freeMapCompIso_hom_app, CategoryTheory.Equivalence.sheafCongr.unitIso_hom_app_val_app, CategoryTheory.monoidalOpOp_η, CategoryTheory.Pseudofunctor.StrongTrans.isoMk_inv_as_app, CategoryTheory.Grp.id_hom, groupCohomology.isoCocycles₁_inv_comp_iCocycles, CategoryTheory.Bicategory.whisker_exchange_assoc, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.isoAux_hom_app, CategoryTheory.AsSmall.up_map_down, typeToBoolAlgOp_map, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_fst, CategoryTheory.Limits.inr_pushoutAssoc_hom, CategoryTheory.op_inv_leftUnitor, CategoryTheory.CartesianMonoidalCategory.tensorδ_fst_assoc, CategoryTheory.tensorRightHomEquiv_tensor, CategoryTheory.biproduct_ι_comp_leftDistributor_hom, groupHomology.π_comp_H0IsoOfIsTrivial_hom, CategoryTheory.Hom.mulEquivCongrRight_symm_apply, CategoryTheory.ShortComplex.LeftHomologyMapData.leftHomologyMap_eq, CategoryTheory.MonObj.mul_comp_assoc, CategoryTheory.BimonObj.one_counit_assoc, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_rightUnitor_hom_as_app, CategoryTheory.Functor.relativelyRepresentable.pullback₃.snd_snd_eq_p₃, CategoryTheory.Iso.map_hom_inv_id_app, CategoryTheory.Functor.op_commShiftIso_inv_app_assoc, HomologicalComplex.mapBifunctorAssociatorX_hom_D₂_assoc, StalkSkyscraperPresheafAdjunctionAuxs.unit_app, CategoryTheory.CostructuredArrow.toStructuredArrow'_map, CategoryTheory.Limits.kernelBiproductπIso_inv, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₂, CategoryTheory.HasLiftingProperty.of_comp_left, CategoryTheory.MonoidalCategory.MonoidalRightAction.action_actionHomRight_assoc, CategoryTheory.ShortComplex.mapRightHomologyIso_inv_naturality_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_id, CategoryTheory.Dial.associatorImpl_hom_F, CategoryTheory.RetractArrow.op_i_right, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_hom_app_snd_app, CategoryTheory.Pretriangulated.binaryProductTriangle_mor₁, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_symm_apply_f_coe, CategoryTheory.MorphismProperty.instFullUnderTopUnderForget, CategoryTheory.prod.prodFunctorToFunctorProdAssociator_inv_app_app, SSet.comp_const, CategoryTheory.Functor.mapGrpCompIso_hom_app_hom_hom, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_map_mkHom_homMk_id, HomologicalComplex.homologyι_comp_fromOpcycles_assoc, CategoryTheory.Functor.map_shiftFunctorCompIsoId_hom_app, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom_assoc, CategoryTheory.Subfunctor.range_eq_ofSection', CategoryTheory.Limits.cokernelBiproductFromSubtypeIso_hom, AlgebraicTopology.DoldKan.QInfty_comp_PInfty, SimplicialObject.opFunctor_obj_δ, CategoryTheory.unop_add, AlgebraicTopology.DoldKan.Q_idem, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃'_tensorHom_assoc, CategoryTheory.Functor.mapTriangleInvRotateIso_inv_app_hom₂, CategoryTheory.IsSplitEqualizer.bottom_rightRetraction_assoc, Action.leftRegularTensorIso_hom_hom, groupHomology.eq_d₂₁_comp_inv_assoc, CategoryTheory.Square.category_comp_τ₃, HomologicalComplex.opcyclesMap_comp_assoc, CategoryTheory.GlueData.t_fac_assoc, HomologicalComplex.restrictionHomologyIso_hom_homologyι, CategoryTheory.Functor.FullyFaithful.homNatIso'_hom_app_down, CategoryTheory.SimplicialObject.Augmented.const_map_right, CategoryTheory.Factorisation.initial_ι, CategoryTheory.Limits.sigmaConst_obj_map, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv, ModuleCat.imageIsoRange_inv_image_ι, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom, CategoryTheory.Preadditive.kernelForkOfFork_ι, CategoryTheory.Bicategory.pentagon, CategoryTheory.CatEnrichedOrdinary.Hom.base_comp, CategoryTheory.ShortComplex.Homotopy.comp_h₁, CategoryTheory.ULiftHom.up_map_down, CategoryTheory.Oplax.OplaxTrans.homCategory_comp_as_app, CategoryTheory.Functor.leftOpId_inv_app, CategoryTheory.MonoidalCategory.pentagon_inv_hom, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanMap_app, CategoryTheory.Functor.Initial.extendCone_map_hom, CategoryTheory.Pretriangulated.Triangle.zero_hom₁, CategoryTheory.Bicategory.Prod.snd_obj, HomologicalComplex.cylinder.inlX_π_assoc, CategoryTheory.SimplicialObject.σ_comp_σ, CategoryTheory.Comonad.comparisonForget_hom_app, CategoryTheory.Limits.pullbackIsoOpPushout_inv_snd, CategoryTheory.isSeparator_iff_of_isColimit_cofan, SheafOfModules.conjugateEquiv_pullbackComp_inv, CategoryTheory.NatTrans.CommShiftCore.shift_app_assoc, CategoryTheory.MonoidalCategory.tensor_hom_inv_id_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_inv_app_snd_app, AlgebraicTopology.DoldKan.whiskerLeft_toKaroubi_N₂Γ₂_hom, SimplexCategory.Truncated.Hom.tr_id, CategoryTheory.kernelCokernelCompSequence.instEpiπ, PresheafOfModules.ι_fromFreeYonedaCoproduct_assoc, CategoryTheory.typeEquiv_functor_obj_val_map, SSet.const_app, CategoryTheory.EnrichedCat.leftUnitor_inv_out_app, TopCat.Presheaf.Pushforward.comp_inv_app, AlgebraicGeometry.Scheme.toIso_inv_ι_assoc, CategoryTheory.braiding_rightUnitor_assoc, CategoryTheory.Types.instPreservesColimitsOfSizeForgetTypeHom, TopCat.Presheaf.covering_presieve_eq_self, CommSemiRingCat.hom_comp, CategoryTheory.WithTerminal.liftFromOverComp_hom_app, CategoryTheory.Functor.relativelyRepresentable.pullback₃.hom_ext_iff, CategoryTheory.Functor.coe_mapAddHom, CategoryTheory.ShortComplex.SnakeInput.L₀_g_δ, CategoryTheory.Localization.Construction.morphismProperty_is_top', CategoryTheory.Functor.LaxMonoidal.tensorHom_ε_comp_μ_assoc, CategoryTheory.Limits.colimit.map_post, CategoryTheory.Functor.corepresentableByUliftFunctorEquiv_symm_apply_homEquiv, CategoryTheory.ForgetEnrichment.homTo_comp, HomologicalComplex₂.d₂_eq_zero', CategoryTheory.IsHomLift.lift_eqToHom_comp_iff, CategoryTheory.Functor.RepresentableBy.equivUliftYonedaIso_symm_apply_homEquiv, CategoryTheory.shiftFunctorCompIsoId_add'_hom_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_inv_hom', CategoryTheory.MorphismProperty.MapFactorizationData.op_i, CategoryTheory.Bicategory.rightUnitor_naturality_assoc, CategoryTheory.MonoidalCategory.DayConvolution.triangle, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_comp, CategoryTheory.ProjectiveResolution.leftDerived_app_eq, CategoryTheory.MonadHom.app_μ_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_assoc, groupHomology.cyclesMap_comp_isoCycles₂_hom_assoc, CategoryTheory.Over.tensorHom_left, CategoryTheory.CostructuredArrow.w, CategoryTheory.preservesHomology_preadditiveCoyonedaObj_of_projective, CategoryTheory.Limits.colimitFlipIsoCompColim_hom_app, CategoryTheory.Dial.Hom.le, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_inv_app_snd_app, HomologicalComplex.homologyπ_extendHomologyIso_inv_assoc, HomologicalComplex₂.ι_totalShift₁Iso_inv_f_assoc, CategoryTheory.monoidalOfHasFiniteCoproducts.associator_hom, HomologicalComplex₂.ιTotal_totalFlipIso_f_hom_assoc, CategoryTheory.ShortComplex.Splitting.leftHomologyData_π, CategoryTheory.MorphismProperty.instIsLeftAdjointOverTopMapOfHasPullbacksAlongOfIsStableUnderBaseChangeAlong, CategoryTheory.IsPushout.paste_horiz, CategoryTheory.Limits.pullbackLeftPullbackSndIso_hom_snd_assoc, CategoryTheory.Limits.colimit.isoColimitCocone_ι_inv_assoc, CategoryTheory.Monad.Algebra.assoc, CategoryTheory.Abelian.Ext.mk₀_sum, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.leftUnitor_hom_unit_app, CategoryTheory.RetractArrow.retract_right, CategoryTheory.Cokleisli.Adjunction.fromCokleisli_map, CategoryTheory.Lax.OplaxTrans.vComp_naturality_naturality, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_app_app, CategoryTheory.Limits.end_.map_id, CategoryTheory.IsPushout.unop, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_obj, AlgebraicGeometry.Scheme.Hom.appIso_inv_naturality_assoc, CategoryTheory.leftDualFunctor_map, CategoryTheory.Limits.prod.inl_snd_assoc, FintypeCat.equivEquivIso_symm_apply_apply, AlgebraicTopology.DoldKan.MorphComponents.id_φ, CategoryTheory.MonoidalCategory.MonoidalLeftAction.associator_actionHom_assoc, CategoryTheory.Types.hom_eq_coe, AlgebraicGeometry.Scheme.Cover.id_app, AlgebraicGeometry.Scheme.Hom.appLE_map_assoc, CategoryTheory.Limits.PullbackCone.eta_inv_hom, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₂, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_inv_app_zero, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_two, CategoryTheory.SimplicialObject.δ_comp_δ'', AlgebraicGeometry.Scheme.Hom.resLE_id, CategoryTheory.Idempotents.app_p_comm_assoc, CategoryTheory.MonoidalCategory.id_whiskerRight, CategoryTheory.toOverIteratedSliceForwardIsoPullback_hom_app_left, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.unitIso_hom_app_hom_app, HomologicalComplex.d_comp_d', CategoryTheory.Limits.bicone_ι_π_ne_assoc, CategoryTheory.Limits.inl_comp_pushoutSymmetry_inv, CategoryTheory.StructuredArrow.homMk'_id, CategoryTheory.Functor.CommShift₂.comm, CategoryTheory.Triangulated.SpectralObject.triangle_mor₂, CategoryTheory.Limits.Fork.π_comp_hom_assoc, MonObj.mopEquiv_counitIso_hom_app_hom_unmop, CategoryTheory.regularTopology.isLocallySurjective_sheaf_of_types, CategoryTheory.pullbackShiftFunctorAdd'_hom_app, CategoryTheory.Limits.IsColimit.homEquiv_symm_naturality, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeftLift_fst, CategoryTheory.Prod.snd_map, CategoryTheory.ObjectProperty.instIsTriangulatedClosed₂MinOfIsClosedUnderIsomorphisms, CategoryTheory.MorphismProperty.le_pullbacks, BoolAlg.hom_comp, imageToKernel_epi_of_zero_of_mono, CategoryTheory.Under.mapComp_hom, CategoryTheory.Limits.HasZeroMorphisms.zero_comp, HomologicalComplex.zero_f, CategoryTheory.Functor.limitIsoOfIsRightKanExtension_hom_π_assoc, CategoryTheory.EnrichedCat.whisker_exchange, CategoryTheory.BraidedCategory.braiding_naturality_assoc, CategoryTheory.ShortComplex.SnakeInput.snd_δ_assoc, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_ι_assoc, CategoryTheory.Presheaf.isLocallySurjective_iff_range_sheafify_eq_top', CategoryTheory.Dial.whiskerRight_F, CategoryTheory.CatEnrichedOrdinary.id_hComp, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₂₃, CategoryTheory.OplaxFunctor.map₂_rightUnitor_assoc, CategoryTheory.Equivalence.induced_inverse_map, CategoryTheory.ε_naturality, HomologicalComplex₂.total.mapAux.mapMap_D₂, CategoryTheory.Presieve.FamilyOfElements.singletonEquiv_symm_apply, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom, CategoryTheory.ObjectProperty.epimorphisms_le_epiModSerre, groupHomology.cyclesIso₀_inv_comp_iCycles, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_rightUnitor_assoc, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv_assoc, CategoryTheory.MorphismProperty.IsInvertedBy.prod, CategoryTheory.ComonObj.comul_assoc_flip, CategoryTheory.MorphismProperty.antitone_rlp, CategoryTheory.ProjectiveResolution.lift_commutes, CategoryTheory.Functor.IsLocalization.op_iff, CategoryTheory.nerve.homEquiv_id, AlgebraicGeometry.Scheme.stalkMap_comp, CategoryTheory.CartesianMonoidalCategory.associator_hom_fst, HomologicalComplex₂.XXIsoOfEq_inv_ιTotal_assoc, CochainComplex.MappingConeCompHomotopyEquiv.hom_inv_id, CategoryTheory.MonoidalCategory.inv_hom_id_tensor', TopologicalSpace.Opens.mapId_inv_app, CategoryTheory.StructuredArrow.w_prod_snd, CategoryTheory.MorphismProperty.LeftFraction.unop_s, CategoryTheory.MorphismProperty.IsLocalAtSource.iff_of_zeroHypercover, CategoryTheory.Localization.Monoidal.μ_inv_natural_left_assoc, HomologicalComplex.cylinder.ι₀_π_assoc, CategoryTheory.id_apply, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_inv_app, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_counitIso_inv_app_right_app, CategoryTheory.MonoidalCategory.tensor_inv_hom_id'_assoc, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_id, HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom_eq_zero, CategoryTheory.Limits.BinaryBicone.toBiconeFunctor_map_hom, CategoryTheory.MorphismProperty.bijective_eq_sup, CategoryTheory.ConcreteCategory.hom_injective, CategoryTheory.Prod.fac'_assoc, CategoryTheory.Bimon.ofMon_Comon_toMon_Comon_obj_comul, AlgebraicTopology.DoldKan.Q_idem_assoc, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_snd_fst_assoc, AlgebraicGeometry.Scheme.IdealSheafData.comapIso_inv_subschemeι, CategoryTheory.Limits.MultispanIndex.inj_fstSigmaMapOfIsColimit_assoc, AlgebraicGeometry.PresheafedSpace.comp_c_app_assoc, CategoryTheory.ExponentiableMorphism.ev_coev_assoc, CategoryTheory.OrthogonalReflection.D₁.ιLeft_comp_l_assoc, CompHausLike.finiteCoproduct.ι_desc_assoc, CategoryTheory.Functor.isIso_ranAdjunction_homEquiv_iff, CategoryTheory.Presheaf.isLocallySurjective_iff_whisker_forget, CategoryTheory.LocallyDiscrete.mkPseudofunctor_map, CochainComplex.mappingCone.d_snd_v_assoc, CategoryTheory.Lax.LaxTrans.vComp_naturality_id, CategoryTheory.Limits.bicone_ι_π_self, CategoryTheory.shiftFunctorZero_inv_app_shift, CategoryTheory.MorphismProperty.IsStableUnderTransfiniteCompositionOfShape.le, CategoryTheory.ShortComplex.LeftHomologyData.ofEpiOfIsIsoOfMono'_f', CategoryTheory.Functor.ofOpSequence_map_homOfLE_succ, CategoryTheory.Bimon.equivMonComonUnitIsoAppXAux_inv, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.map_f', CategoryTheory.MorphismProperty.instHasOfPrecompPropertyUnopOfHasOfPostcompPropertyOpposite, CategoryTheory.Under.opEquivOpOver_functor_obj, CategoryTheory.CechNerveTerminalFrom.wideCospan.limitIsoPi_inv_comp_pi, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHomLeft_unop, CategoryTheory.HomOrthogonal.matrixDecomposition_comp, CategoryTheory.ShortComplex.RightHomologyMapData.id_φQ, CategoryTheory.Limits.coprod.map_comp_id, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_hom_c_app, Representation.coind'_apply_apply, CategoryTheory.Monoidal.InducingFunctorData.tensorHom_eq, CategoryTheory.Limits.Cones.eta_inv_hom, CategoryTheory.ComposableArrows.naturality', AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjMap_glueDataObjι, groupCohomology.d₁₂_comp_d₂₃_assoc, AlgebraicGeometry.Scheme.Hom.comp_appIso, ChainComplex.isoHomologyι₀_inv_naturality, CategoryTheory.Quiv.freeMap_pathsOf_pathComposition, CategoryTheory.eComp_op_eq_assoc, HomologicalComplex.cylinder.ι₁_π_assoc, CategoryTheory.MonObj.Mon_tensor_mul_one, CategoryTheory.Adjunction.commShiftIso_inv_app_counit_app_assoc, CategoryTheory.Oplax.OplaxTrans.Modification.naturality_assoc, CategoryTheory.Limits.Multicofork.map_ι_app, CochainComplex.shiftFunctor_map_f, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_map, CategoryTheory.Functor.leftKanExtension_hom_ext_iff, CategoryTheory.ObjectProperty.instEssentiallySmallISupOfSmall, CategoryTheory.Enriched.Functor.natTransEquiv_symm_app_app_apply, CategoryTheory.Limits.Pi.ι_π_eq_id_assoc, CategoryTheory.Limits.CatCospanTransform.associator_inv_left_app, CategoryTheory.Functor.CommShift.id_commShiftIso_inv_app, CategoryTheory.Lax.OplaxTrans.id_naturality, CategoryTheory.Limits.inl_pushoutLeftPushoutInrIso_inv, CategoryTheory.isCommMonObj_iff_isMulCommutative, CategoryTheory.DifferentialObject.id_f, CategoryTheory.ShortComplex.cyclesMap'_zero, CategoryTheory.Functor.LaxMonoidal.ε_tensorHom_comp_μ_assoc, CategoryTheory.unop_mono_of_epi, CategoryTheory.Functor.curryingFlipEquiv_symm_apply_obj_map, CategoryTheory.Limits.WalkingReflexivePair.reflexion_comp_right_assoc, CategoryTheory.Limits.Sigma.map'_comp_map', CategoryTheory.Limits.limit.post_post, CochainComplex.mappingCone.d_snd_v', CategoryTheory.StructuredArrow.mapNatIso_inverse_obj_hom, CategoryTheory.Over.associator_inv_left_fst_snd, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_apply, AlgebraicGeometry.IsOpenImmersion.range_pullback_to_base_of_left, CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_iff_epi₁, CategoryTheory.Functor.commShiftIso_inv_naturality_assoc, CategoryTheory.ShortComplex.zero_τ₃, HomologicalComplex.extend_op_d, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₃, SSet.Truncated.HomotopyCategory.descOfTruncation_map_homMk, CategoryTheory.Limits.Fan.IsLimit.fac_assoc, CategoryTheory.Endofunctor.Algebra.functorOfNatTransEq_inv_app_f, CategoryTheory.FreeGroupoid.eq_mk, CategoryTheory.ShortComplex.HasRightHomology.of_hasCokernel, CategoryTheory.NatTrans.IsMonoidal.id, CategoryTheory.Limits.biproduct.ι_π_ne, CategoryTheory.CoreSmallCategoryOfSet.functor_map, CategoryTheory.Pretriangulated.contractibleTriangleFunctor_map_hom₃, CategoryTheory.Limits.CatCospanTransform.whiskerRight_comp, CategoryTheory.Limits.CatCospanTransform.leftUnitor_hom_left_app, CategoryTheory.Functor.whiskerLeft_twice, CategoryTheory.Functor.OneHypercoverDenseData.SieveStruct.fac, CategoryTheory.GrothendieckTopology.uliftYonedaIsoYoneda_hom_app_val_app, MulEquiv.toSingleObjEquiv_counitIso_inv, CategoryTheory.NatTrans.op_app, AlgebraicTopology.DoldKan.Γ₀_map_app, CategoryTheory.uliftYoneda_obj_map_down, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence, CategoryTheory.braiding_leftUnitor_aux₂, CategoryTheory.Functor.obj.ε_def, CategoryTheory.braiding_tensorUnit_left, CategoryTheory.BimonObj.mul_counit, CategoryTheory.SimplicialObject.comp_left_app, CategoryTheory.BimonObj.one_comul_assoc, CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv', AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_right, CategoryTheory.Limits.PushoutCocone.op_π_app, CategoryTheory.PrelaxFunctor.mapFunctor_map, CategoryTheory.ObjectProperty.leftOrthogonal.map_bijective_of_isTriangulated, HomologicalComplex.extend.rightHomologyData_p, CategoryTheory.ShortComplex.Homotopy.sub_h₃, CategoryTheory.Bicategory.whiskerRight_congr, CategoryTheory.Limits.biproduct.fromSubtype_π_assoc, AlgebraicGeometry.Scheme.Hom.appIso_inv_appLE_assoc, CategoryTheory.Oplax.StrongTrans.categoryStruct_comp_naturality, CategoryTheory.NatTrans.op_comp, CategoryTheory.shiftFunctorAdd'_assoc_inv_app_assoc, CategoryTheory.Functor.LeftExtension.postcompose₂ObjMkIso_hom_right_app, AlgebraicGeometry.Proj.homOfLE_toBasicOpenOfGlobalSections_ι_assoc, CategoryTheory.MonoidalCategory.tensorHom_def'_assoc, CategoryTheory.CartesianMonoidalCategory.lift_whiskerLeft, CategoryTheory.CechNerveTerminalFrom.wideCospan.limitIsoPi_hom_comp_pi_assoc, LightCondensed.free_internallyProjective_iff_tensor_condition', CategoryTheory.MonoidalOpposite.unmopEquiv_counitIso_hom_app, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp, SimplexCategory.Truncated.δ₂_zero_comp_δ₂_two, CategoryTheory.IsHomLift.comp_of_lift_id, CategoryTheory.coprod_inl_leftDistrib_hom_assoc, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_map_mkHom_homMk_homMk, CategoryTheory.Comonad.ForgetCreatesLimits'.newCone_π, CategoryTheory.mateEquiv_symm_apply, CategoryTheory.Functor.sheafPushforwardContinuousComp_inv_app_val_app, CategoryTheory.Iso.map_inv_hom_id, SemiNormedGrp₁.coe_comp, HomologicalComplex.Hom.comm_to, CategoryTheory.exp.ev_coev, CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois_apply, CategoryTheory.section_comp_left, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap_assoc, CategoryTheory.comp_apply', CategoryTheory.Limits.limit.lift_π_app, CategoryTheory.MonObj.Mon_tensor_one_mul, CategoryTheory.Limits.limit_obj_ext_iff, ProfiniteGrp.profiniteCompletion_map, AlgebraicGeometry.Scheme.Modules.Hom.id_app, SSet.RelativeMorphism.comm_assoc, CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_π_assoc, CategoryTheory.Limits.Cone.equiv_inv_π, CategoryTheory.rightDualFunctor_map, CategoryTheory.biconeMk_map, SimplexCategoryGenRel.σ_comp_σ_assoc, CategoryTheory.ShortComplex.Homotopy.trans_h₂, Action.FintypeCat.quotientToEndHom_mk, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_assoc, CategoryTheory.ShortComplex.leftRightHomologyComparison_eq, CategoryTheory.ShortComplex.kernel_ι_comp_cokernel_π_comp_cokernelToAbelianCoimage, CategoryTheory.CartesianMonoidalCategory.associator_inv_fst_snd_assoc, CategoryTheory.Limits.BinaryBiconeMorphism.wfst_assoc, CategoryTheory.ObjectProperty.HasCardinalLT.iSup, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_assoc, CategoryTheory.Functor.rightDerivedNatTrans_comp_assoc, CategoryTheory.Equivalence.cancel_unit_right_assoc, CategoryTheory.MorphismProperty.instIsStableUnderBaseChangeTop, CategoryTheory.Bicategory.LeftLift.whisker_unit, CategoryTheory.Limits.CategoricalPullback.Hom.w', CompHausLike.LocallyConstant.adjunction_left_triangle, CategoryTheory.Functor.ranCounit_app_app_ranAdjunction_unit_app_app_assoc, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app, CategoryTheory.CartesianMonoidalCategory.lift_fst_snd, CategoryTheory.Limits.image.factorThruImage_preComp_assoc, AlgebraicTopology.DoldKan.Q_f_0_eq, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight_symm_apply, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_left, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_hom_app_app_snd, CategoryTheory.Triangulated.TStructure.zero_of_isLE_of_isGE, CategoryTheory.Adjunction.ε_comp_map_ε, smoothSheafCommRing.forgetStalk_hom_comp_evalHom, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_assoc, CategoryTheory.IsFiltered.coeq_condition_assoc, CategoryTheory.ShortComplex.RightHomologyData.wι, CategoryTheory.Functor.LaxRightLinear.μᵣ_naturality_right, CategoryTheory.coreCategory_comp_iso, CategoryTheory.Oplax.OplaxTrans.naturality_id_assoc, CategoryTheory.Limits.coprodComparison_inr_assoc, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map_assoc, CategoryTheory.Limits.pullbackProdFstIsoProd_inv_snd_snd_assoc, CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero, Mathlib.Tactic.CategoryTheory.CancelIso.hom_inv_id_of_eq_assoc, CategoryTheory.IsIso.hom_inv_id_assoc, CategoryTheory.Limits.π_comp_colimitOpIsoOpLimit_inv, CategoryTheory.Functor.curryingEquiv_symm_apply_map_app, CategoryTheory.Functor.leftOpRightOpEquiv_inverse_map, CategoryTheory.Limits.hasPullback_assoc_symm, CategoryTheory.Limits.IsImage.e_isoExt_hom, HomotopicalAlgebra.weakEquivalences_unop_iff, CategoryTheory.SimplicialObject.Truncated.trunc_obj_map, HomologicalComplex.mapBifunctor.d_eq, CategoryTheory.Join.InclLeftCompRightOpOpEquivFunctor_hom_app, CategoryTheory.PreGaloisCategory.FibreFunctor.end_isUnit, HomologicalComplex.cylinder.ι₀_desc, CategoryTheory.Iso.isoFunctorOfIsoInverse_inv_app, CategoryTheory.Cat.opFunctorInvolutive_inv_app_toFunctor_map, CategoryTheory.Functor.leftOpRightOpEquiv_unitIso_hom_app, CategoryTheory.ObjectProperty.strictMap_le_map, CategoryTheory.IsMonHom.one_hom, CategoryTheory.ProjectiveResolution.Hom.hom_comp_π, CategoryTheory.CostructuredArrow.mapNatIso_inverse_obj_hom, CategoryTheory.Dial.hexagon_forward, HomologicalComplex.unopSymm_d, CategoryTheory.IsPullback.zero_left, CategoryTheory.Precoverage.ZeroHypercover.comp_s₀, CategoryTheory.MorphismProperty.MapFactorizationData.fac_assoc, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_comp_π_assoc, CategoryTheory.Functor.Final.extendCocone_obj_ι_app', CategoryTheory.Presheaf.uliftYonedaAdjunction_homEquiv_app, CategoryTheory.Sheaf.isLocallyInjective_forget, CategoryTheory.ShortComplex.iCycles_g_assoc, CategoryTheory.MonoidalCategory.DayConvolution.symmetry, CategoryTheory.Adjunction.leftAdjointUniq_trans_app, CategoryTheory.Equivalence.counitInv_app_comp_functor_map_η_inverse, CategoryTheory.Bicategory.prod_homCategory_id_fst, CategoryTheory.rightUnitor_inv_braiding_assoc, groupHomology.map_id_comp_H0Iso_hom_assoc, SheafOfModules.pullback_id_comp, HomologicalComplex.biprodXIso_hom_snd, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w, CategoryTheory.OplaxFunctor.map₂_leftUnitor, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₁_assoc, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_appLE_assoc, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id_assoc, HomologicalComplex.stupidTruncMap_stupidTruncXIso_hom_assoc, SimplexCategory.δ_comp_δ_self'_assoc, CategoryTheory.Conv.one_eq, CategoryTheory.Sieve.uliftNatTransOfLe_app_down_coe, CategoryTheory.Bicategory.conjugateEquiv_symm_comp, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIso_inv_app_hom, CategoryTheory.Limits.MulticospanIndex.fstPiMap_π_assoc, AlgebraicGeometry.Scheme.IdealSheafData.inclusion_comp, HomologicalComplex.XIsoOfEq_inv_comp_XIsoOfEq_hom_assoc, CategoryTheory.WithInitial.equivComma_inverse_obj_map, SimplicialObject.Split.Hom.comm, AlgebraicGeometry.Scheme.Γ_map, CategoryTheory.Limits.Types.binaryCoproductIso_inr_comp_inv, CategoryTheory.ShortComplex.Exact.mono_g_iff, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_hom_app_val_app, CategoryTheory.PreOneHypercover.comp_s₁, CategoryTheory.ShortComplex.LeftHomologyData.homologyπ_comp_homologyIso_hom_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.action_exchange, CategoryTheory.Limits.WidePullbackCone.condition_assoc, ModuleCat.hom_sum, CategoryTheory.Limits.lim_ε_π, CategoryTheory.Localization.Monoidal.associator_naturality₂, CategoryTheory.ShortComplex.SnakeInput.w₀₂, CategoryTheory.BraidedCategory.hexagon_forward, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerRight_assoc, CategoryTheory.Join.mapWhiskerRight_associator_hom, CategoryTheory.ShortComplex.rightHomologyMap_zero, CategoryTheory.Limits.Sigma.hom_ext_iff, CategoryTheory.CartesianClosed.uncurry_id_eq_ev, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, CategoryTheory.Functor.CoreMonoidal.associativity, CategoryTheory.ShortComplex.exact_iff_i_p_zero, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_assoc, CategoryTheory.Limits.Bicone.ofLimitCone_ι, CategoryTheory.IsPushout.id_vert, CategoryTheory.MorphismProperty.Over.w_assoc, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst_assoc, CategoryTheory.Bicategory.pentagon_hom_hom_inv_inv_hom_assoc, CategoryTheory.CommSq.right_adjoint_hasLift_iff, Homotopy.nullHomotopicMap_f_of_not_rel_right, CategoryTheory.toOverPullbackIsoToOver_hom_app_left, CategoryTheory.Limits.biprod.map_eq, TopCat.prodIsoProd_hom_snd, ModuleCat.restrictScalarsComp'App_hom_naturality, CochainComplex.homotopyOp_hom_eq, CategoryTheory.Abelian.PreservesImage.iso_inv_ι_assoc, CategoryTheory.Functor.RightExtension.postcomp₁_map_left_app, CochainComplex.mappingCone.inr_f_descCochain_v_assoc, CategoryTheory.cones_obj_map_app, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π_assoc, CategoryTheory.PreGaloisCategory.fiberBinaryProductEquiv_symm_snd_apply, CategoryTheory.Limits.sigmaConst_map_app, CategoryTheory.Comma.toIdPUnitEquiv_counitIso_hom_app, AlgCat.ofHom_id, AlgebraicTopology.DoldKan.QInfty_f_naturality, CategoryTheory.Limits.walkingSpanOpEquiv_unitIso_inv_app, CategoryTheory.StrictPseudofunctor.mk'_map, CategoryTheory.ShortComplex.RightHomologyData.pOpcycles_comp_opcyclesIso_hom, CategoryTheory.NatTrans.removeRightOp_app, CategoryTheory.shiftComm', CategoryTheory.CopyDiscardCategory.discard_unit, CategoryTheory.SmallObject.πObj_ιIteration_app_right_assoc, CategoryTheory.Abelian.Pseudoelement.zero_morphism_ext', CategoryTheory.Limits.pullbackProdSndIsoProd_inv_fst_fst, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_right, CategoryTheory.Bicategory.mateEquiv_hcomp, HomologicalComplex.natIsoSc'_hom_app_τ₂, TopCat.Presheaf.germ_res_apply', CategoryTheory.LocalizerMorphism.homMap_apply_assoc, CategoryTheory.StrictlyUnitaryLaxFunctor.mk'_obj, CategoryTheory.subsingleton_of_unop, HomologicalComplex₂.totalAux.ιMapObj_D₂, CategoryTheory.Iso.homCongr_apply, TopCat.Presheaf.stalkSpecializes_comp, CategoryTheory.toSheafify_plusPlusIsoSheafify_hom, CategoryTheory.Subobject.ofMkLE_comp_ofLEMk, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_right_assoc, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.WithTerminal.ofCommaObject_map, CategoryTheory.Lax.LaxTrans.naturality_naturality, CategoryTheory.Functor.LaxMonoidal.associativity_inv, CategoryTheory.ShortComplex.SnakeInput.L₁_f_φ₁, AlgebraicGeometry.Scheme.LocalRepresentability.yoneda_toGlued_yonedaGluedToSheaf_assoc, CategoryTheory.Square.opFunctor_map_τ₁, CategoryTheory.Limits.coprodComparison_inr, CommRingCat.moduleCatExtendScalarsPseudofunctor_obj, CategoryTheory.Limits.opCospan_inv_app, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc, CategoryTheory.Quiv.lift_map, CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_idem, MagmaCat.coe_id, CategoryTheory.ShortComplex.rightHomologyι_naturality', AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀'_assoc, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_hom, CategoryTheory.PreGaloisCategory.card_hom_le_card_fiber_of_connected, CategoryTheory.coalgebraToOver_obj, CategoryTheory.Limits.Types.isPullback_iff, CategoryTheory.Over.associator_hom_left_snd_snd_assoc, CategoryTheory.preservesColimitIso_inv_comp_desc_assoc, CategoryTheory.Bicategory.whiskerLeft_eqToHom, CategoryTheory.Comma.mapRightComp_hom_app_left, CategoryTheory.ShortComplex.HomotopyEquiv.trans_homotopyHomInvId, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_left, CategoryTheory.Limits.limitRightOpIsoOpColimit_hom_comp_ι_assoc, CategoryTheory.ExponentiableMorphism.pushforwardComp_hom_counit_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_inv_app_snd_app, CategoryTheory.ObjectProperty.isClosedUnderColimitsOfShape_op_iff_unop, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_app, CategoryTheory.MonoidalClosed.id_tensor_pre_app_comp_ev_assoc, Homotopy.ofEq_hom, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_comp, CategoryTheory.Functor.WellOrderInductionData.Extension.map_succ, AlgebraicGeometry.Scheme.Pullback.Triplet.tensorCongr_trans_hom_assoc, CategoryTheory.sum.inlCompAssociator_hom_app, AlgebraicGeometry.Proj.awayι_toSpecZero_assoc, groupCohomology.mapShortComplexH2_id_comp_assoc, SSet.Subcomplex.homOfLE_ι, CategoryTheory.Bicategory.Pith.id₂_iso_hom, CategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSet_comp, CategoryTheory.MorphismProperty.le_llp_rlp, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₂, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_inv_app_val_app, CategoryTheory.Limits.biprod.map_lift_mapBiprod, CategoryTheory.LocalizerMorphism.RightResolution.unopFunctor_obj, CategoryTheory.ShortComplex.π_leftRightHomologyComparison_ι_assoc, groupHomology.mapCycles₂_id_comp_assoc, CategoryTheory.braiding_tensorUnit_right_assoc, HomologicalComplex₂.D₂_shape, CategoryTheory.Adjunction.homEquiv_naturality_right_square_iff, CategoryTheory.conjugateEquiv_counit, CategoryTheory.NatTrans.CommShiftCore.shift_app_comm_assoc, CategoryTheory.Mon.Hom.hom_mul, CategoryTheory.Bicategory.associator_hom_congr, AlgebraicGeometry.Scheme.Hom.inr_normalizationCoprodIso_hom_fromNormalization_assoc, CochainComplex.IsKProjective.Qh_map_bijective, Condensed.isoFinYonedaComponents_inv_comp, AlgebraicGeometry.HasRingHomProperty.inf, CategoryTheory.whiskerRight_ι_colimitCompWhiskeringRightIsoColimitComp_inv_assoc, CategoryTheory.LocalizerMorphism.smallHomMap'_mk, Rep.coindIso_inv_hom_hom, CochainComplex.mappingCone.d_fst_v_assoc, CategoryTheory.EnrichedFunctor.category_comp_out, CategoryTheory.Functor.Initial.limit_cone_comp_aux, HomologicalComplex₂.total.mapAux.mapMap_D₂_assoc, AlgebraicGeometry.Scheme.Hom.residueFieldMap_congr, CategoryTheory.Functor.mapCommMon_id_mul, CategoryTheory.Localization.Construction.morphismProperty_eq_top, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_left, CategoryTheory.ObjectProperty.le_isLocal_isLocal, CategoryTheory.tensor_sum, CategoryTheory.Functor.sheafPushforwardCocontinuousCompSheafToPresheafIso_inv, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.triangle, CategoryTheory.Preadditive.mono_iff_isZero_kernel', CategoryTheory.ShortComplex.LeftHomologyData.wi, CategoryTheory.Functor.FullyFaithful.monObj_one, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂'_map_app_app, CategoryTheory.Limits.CatCospanTransform.comp_whiskerRight, HomologicalComplex.π_homologyIsoSc'_inv_assoc, Action.zero_hom, CategoryTheory.Hom.inv_def, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_whiskerLeft, CategoryTheory.monoidalOfHasFiniteCoproducts.whiskerRight, CategoryTheory.Limits.WalkingMultispan.instSubsingletonHomRight, CategoryTheory.Limits.prod.symmetry_assoc, CategoryTheory.MonoidalCategory.whiskerRight_tensor_symm_assoc, CategoryTheory.Prod.fac_assoc, ModuleCat.hom_nsmul, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_comp, CategoryTheory.Limits.inr_comp_pushoutSymmetry_hom_assoc, CategoryTheory.Functor.prod_map, TopCat.pullbackIsoProdSubtype_hom_snd, CategoryTheory.Mathlib.Tactic.MonTauto.eq_mul_one, AddMonCat.id_apply, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_inl, SimplicialObject.Splitting.IndexSet.id_snd_coe, AlgebraicGeometry.Scheme.Opens.ι_appTop, CategoryTheory.MorphismProperty.comp_mem, CategoryTheory.ShortComplex.Exact.leftHomologyDataOfIsLimitKernelFork_π, CategoryTheory.MorphismProperty.instHasOfPostcompPropertyTop, CategoryTheory.Adjunction.rightAdjointUniq_trans_app_assoc, AlgebraicGeometry.Scheme.Modules.Hom.comp_app, CategoryTheory.unopHom_apply, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_inv_comp_homologyι_assoc, CategoryTheory.Bicategory.pentagon_inv_inv_hom_inv_inv_assoc, groupHomology.mapShortComplexH2_comp, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_counitIso_hom, AlgebraicGeometry.IsOpenImmersion.lift_fac_assoc, CategoryTheory.Functor.ranges_directed, CategoryTheory.Functor.ranObjObjIsoLimit_hom_π_assoc, CommMonCat.hom_id, CategoryTheory.Functor.sheafPushforwardContinuousComp_hom_app_val_app, HomologicalComplex.cyclesOpIso_hom_naturality_assoc, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatTrans_id, CategoryTheory.ComonObj.instTensorUnit_counit, CategoryTheory.Limits.isLimitConeOfAdj_lift, CategoryTheory.Functor.toOplaxFunctor_mapComp, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_assoc, CategoryTheory.Preadditive.isCoseparating_iff, CategoryTheory.InducedCategory.homAddEquiv_apply, CategoryTheory.Adjunction.compPreadditiveYonedaIso_hom_app_app_apply, CategoryTheory.Limits.ι_colimitLimitIso_limit_π_assoc, CategoryTheory.Limits.IndObjectPresentation.yoneda_ι_app, TopologicalSpace.Opens.overEquivalence_counitIso_inv_app, CategoryTheory.Arrow.mapCechConerve_app, CategoryTheory.leftAdjointMate_comp_evaluation, CategoryTheory.uncurry_pre, CategoryTheory.MonoidalPreadditive.tensor_zero, HomotopicalAlgebra.instFibrationUnopOfCofibrationOpposite, SimplexCategoryGenRel.δ_comp_σ_of_le, CategoryTheory.Functor.LaxMonoidal.tensorUnit_whiskerLeft_comp_leftUnitor_hom, Bimod.comp_hom', CategoryTheory.Functor.Monoidal.whiskerRight_app_snd_assoc, HomotopicalAlgebra.Precylinder.LeftHomotopy.h₁_assoc, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidalObj_map, CategoryTheory.IsHomLift.comp_lift_id_left', CategoryTheory.Bicategory.Comonad.comul_assoc, CategoryTheory.GradedObject.mapBifunctorRightUnitor_naturality, CategoryTheory.SimplicialObject.δ_comp_δ_self, groupCohomology.subtype_comp_d₀₁_assoc, CategoryTheory.sum.inrCompInlCompAssociator_inv_app_down_down, CategoryTheory.CartesianMonoidalCategory.braiding_inv_snd, Bimod.AssociatorBimod.hom_inv_id, CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_hom_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom, CategoryTheory.Limits.Cofork.condition, CategoryTheory.Square.category_comp_τ₁, CategoryTheory.Functor.OplaxRightLinear.δᵣ_unitality_hom, CategoryTheory.whiskeringRightCompEvaluation_hom_app, CategoryTheory.shiftFunctorAdd_assoc_hom_app_assoc, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_right, HomologicalComplex₂.ι_totalShift₂Iso_hom_f_assoc, SemimoduleCat.id_apply, SheafOfModules.ιFree_freeMap_assoc, CategoryTheory.Limits.BinaryFan.braiding_inv_fst_assoc, SimplexCategory.δ_comp_σ_of_gt, CategoryTheory.nerve.δ₁_mk₂_eq, CategoryTheory.Limits.pullback_map_diagonal_isPullback, CategoryTheory.Functor.partialLeftAdjointHomEquiv_map_comp, CategoryTheory.NatTrans.mapHomologicalComplex_naturality, AlgebraicGeometry.Scheme.residueFieldCongr_fromSpecResidueField, ChainComplex.augmentTruncate_hom_f_succ, CochainComplex.mappingCone.map_id, CategoryTheory.Limits.PreservesPushout.inl_iso_hom_assoc, CategoryTheory.SmallObject.πObj_naturality_assoc, CategoryTheory.eHomWhiskerLeft_id, CategoryTheory.Bicategory.comp_whiskerLeft, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₁, CategoryTheory.preservesLimits_preadditiveYonedaObj, CategoryTheory.MorphismProperty.le_llp_iff_le_rlp, CategoryTheory.Adjunction.homAddEquiv_symm_zero, CategoryTheory.NatTrans.CommShiftCore.shift_comm, CategoryTheory.Subobject.ofMkLEMk_comp_ofMkLEMk, SimplexCategory.Truncated.δ₂_zero_comp_σ₂_one_assoc, HomologicalComplex.XIsoOfEq_hom_naturality_assoc, CategoryTheory.ConcreteCategory.forget₂_comp_apply, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app, CategoryTheory.ihom.coev_naturality_assoc, CategoryTheory.Limits.end_.hom_ext_iff, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd, TopCat.Presheaf.presieveOfCovering.indexOfHom_spec, CategoryTheory.coprod_inr_leftDistrib_hom, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst, CategoryTheory.Limits.isLimitOfCoconeRightOpOfCone_lift, CategoryTheory.ShortComplex.sub_τ₁, CategoryTheory.Functor.RepresentableBy.homEquiv_comp, HomologicalComplex.HomologySequence.δ_naturality_assoc, CategoryTheory.Limits.ConeMorphism.w_assoc, MonCat.FilteredColimits.cocone_naturality, AlgebraicGeometry.Scheme.map_basicOpen, CategoryTheory.MorphismProperty.coproducts_le, CategoryTheory.OplaxFunctor.mapComp_naturality_left, HomologicalComplex.biprodXIso_hom_snd_assoc, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₁, CategoryTheory.Limits.prod.symmetry', groupHomology.toCycles_comp_isoCycles₂_hom, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_inv_π, CategoryTheory.Pi.id_apply, CategoryTheory.conjugateEquiv_rightUnitor_hom, SemiNormedGrp.hom_comp, CategoryTheory.LocalizerMorphism.equiv_smallShiftedHomMap, CategoryTheory.FreeGroupoid.mapComp_inv_app, CategoryTheory.Lax.StrongTrans.naturality_id, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₁, CategoryTheory.Adjunction.unit_app_shift_commShiftIso_inv_app_assoc, TopologicalSpace.Opens.adjunction_counit_map_functor, CategoryTheory.Mat_.add_apply, groupCohomology.map_id_comp_H0Iso_hom, CategoryTheory.Functor.commShiftOfLocalization.iso_inv_app_assoc, CategoryTheory.OrthogonalReflection.iteration_map_succ_assoc, CategoryTheory.Limits.PullbackCone.unop_ι_app, CategoryTheory.Triangulated.SpectralObject.Hom.comm_assoc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_inv_app_hom, quasiIso_comp, CategoryTheory.Functor.Monoidal.whiskeringLeft_η_app, CategoryTheory.Square.unop_f₁₃, CategoryTheory.Limits.pullbackDiagonalMapIso.hom_snd, CategoryTheory.Functor.Fiber.instIsHomLiftIdMapFiberInclusion, ComplexShape.Embedding.liftExtend.comm, SSet.Truncated.StrictSegal.spineToSimplex_vertex, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality_assoc, CategoryTheory.Bicategory.prod_associator_hom_fst, CategoryTheory.Grp_Class.inv_comp, CategoryTheory.exists_equivalence_iff_of_locallySmall, CategoryTheory.SymmetricCategory.symmetry_assoc, CategoryTheory.MorphismProperty.precomp_iff, CategoryTheory.CategoryOfElements.π_map, CategoryTheory.IsPushout.of_isBilimit, PresheafOfModules.neg_app, CategoryTheory.exp.ev_coev_assoc, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_hom_right_app, CategoryTheory.Localization.Monoidal.μ_inv_natural_right_assoc, CategoryTheory.Limits.FormalCoproduct.evalOp_map_app, CategoryTheory.Bicategory.LeftExtension.ofCompId_hom, CategoryTheory.Functor.prod_ε_fst, CategoryTheory.Limits.Multifork.toPiFork_π_app_one, CategoryTheory.Idempotents.Karoubi.decompId, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_leftUnitor_hom_as_app, CategoryTheory.CartesianMonoidalCategory.tensorHom_snd, CategoryTheory.Bimon.equivMonComonCounitIsoAppX_hom_hom, CategoryTheory.SingleFunctors.hom_inv_id_hom, GrpCat.ofHom_comp, CategoryTheory.SmallObject.SuccStruct.Iteration.mapObj_trans_assoc, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_inv_app, CategoryTheory.Functor.IsCocartesian.of_iso_comp, AlgebraicGeometry.Scheme.Hom.preimageIso_hom_ι, CategoryTheory.Functor.LaxMonoidal.id_μ, CategoryTheory.ShortComplex.leftHomologyπ_naturality, CategoryTheory.ForgetEnrichment.homTo_id, CategoryTheory.ShortComplex.opMap_τ₂, CategoryTheory.CatEnrichedOrdinary.id_eq_eqToHom, CategoryTheory.Limits.Pi.π_comp_eqToHom_assoc, CategoryTheory.cosimplicialSimplicialEquiv_unitIso_hom_app, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_hom_naturality_assoc, CategoryTheory.Functor.relativelyRepresentable.w'_assoc, CategoryTheory.Join.inclRightCompOpEquivInverse_hom_app_op, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.tensorHom_id, AugmentedSimplexCategory.inl_comp_inl_comp_associator, CategoryTheory.Bicategory.prod_homCategory_comp_fst, groupHomology.mapCycles₁_id_comp, StalkSkyscraperPresheafAdjunctionAuxs.germ_fromStalk_assoc, SimplicialObject.Splitting.cofan_inj_πSummand_eq_zero, CategoryTheory.MonoidalCategory.leftUnitor_whiskerRight_assoc, CategoryTheory.Over.μ_pullback_left_fst_fst', CategoryTheory.instIsMonHomInvHomOfIsCommMonObj, HomologicalComplex.homotopyCofiber.inlX_sndX, CategoryTheory.Functor.RepresentableBy.isRepresentedBy, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₂, AlgebraicGeometry.Scheme.isoOfEq_hom_ι_assoc, CategoryTheory.Functor.LaxMonoidal.μ_natural_left_assoc, CategoryTheory.Limits.pullbackObjIso_hom_comp_fst, AlgebraicGeometry.instRespectsSchemeLocallyQuasiFiniteIsOpenImmersion, CategoryTheory.ProjectiveResolution.π'_f_zero, CategoryTheory.CosimplicialObject.δ_comp_σ_succ', CategoryTheory.Linear.homCongr_apply, CategoryTheory.Pseudofunctor.toLax_mapId', CategoryTheory.Lax.StrongTrans.categoryStruct_id_naturality, CategoryTheory.StrictlyUnitaryLaxFunctor.id_map, CategoryTheory.ShortComplex.Homotopy.add_h₀, CategoryTheory.Limits.π_comp_cokernelComparison_assoc, CategoryTheory.Limits.cospanOp_hom_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w_apply, CategoryTheory.CartesianClosed.uncurry_natural_left_assoc, AlgebraicGeometry.Scheme.isoSpec_inv_naturality, CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_snd_snd_assoc, Homotopy.ofExtend_hom, CategoryTheory.Precoverage.comp_mem_coverings, CategoryTheory.shiftFunctorZero_hom_app_shift, HomologicalComplex.truncGE'.d_comp_d_assoc, AlgebraicGeometry.IsAffineOpen.toSpecΓ_fromSpec_assoc, AlgebraicGeometry.Scheme.Hom.ker_comp_of_isIso, CategoryTheory.ShortComplex.SnakeInput.comp_f₀_assoc, HomologicalComplex.leftUnitor'_inv, CategoryTheory.ShortComplex.cyclesMap_zero, HomologicalComplex₂.totalFlipIso_hom_f_D₂, CategoryTheory.Limits.asEmptyCocone_ι_app, CategoryTheory.MonadHom.app_η, AlgebraicGeometry.Scheme.Pullback.openCoverOfRight_X, CategoryTheory.Over.μ_pullback_left_fst_snd, CategoryTheory.Over.whiskerRight_left, CategoryTheory.Subobject.eq_of_comp_arrow_eq_iff, ModuleCat.homEquiv_extendScalarsComp, CategoryTheory.Equivalence.changeFunctor_unitIso_inv_app, CategoryTheory.ShortComplex.leftRightHomologyComparison'_eq_leftHomologpMap'_comp_iso_hom_comp_rightHomologyMap', CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_hom_inv_id_assoc, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_apply_snd, CategoryTheory.IsPushout.inr_isoIsPushout_inv, dNext_comp_left, CategoryTheory.CommSq.left_adjoint_hasLift_iff, CategoryTheory.Limits.biproduct.hom_ext'_iff, CategoryTheory.Pseudofunctor.mapComp_id_left_inv, CategoryTheory.ShortComplex.cyclesMap'_smul, TopCat.Sheaf.objSupIsoProdEqLocus_inv_snd, CategoryTheory.CostructuredArrow.homMk'_left, CategoryTheory.Over.monObjMkPullbackSnd_one, AlgebraicTopology.DoldKan.P_f_naturality_assoc, CategoryTheory.Limits.Pi.reindex_inv_π, CategoryTheory.unitOfTensorIsoUnit_inv_app, CategoryTheory.Limits.imageSubobjectCompIso_inv_arrow_assoc, CochainComplex.mappingCone.inl_v_fst_v, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_hom_naturality, TopologicalSpace.Opens.overEquivalence_unitIso_inv_app_left, CategoryTheory.Idempotents.Karoubi.sum_hom, CategoryTheory.ShortComplex.comp_homologyMap_comp_assoc, CategoryTheory.StructuredArrow.homMk'_right, CategoryTheory.Arrow.id_left, CategoryTheory.Functor.LaxMonoidal.associativity_inv_assoc, CategoryTheory.SplitMono.id_assoc, SemimoduleCat.hom_zero, CategoryTheory.ShortComplex.LeftHomologyMapData.zero_φH, Profinite.lift_lifts_assoc, CategoryTheory.Limits.CatCospanTransform.pentagon_assoc, TopCat.pullbackIsoProdSubtype_inv_snd, CategoryTheory.Limits.Cones.eta_hom_hom, CategoryTheory.WithInitial.pseudofunctor_mapId, CategoryTheory.ObjectProperty.limitsOfShape_eq_unop_colimitsOfShape, CategoryTheory.epi_comp_iff_of_isIso, CategoryTheory.NatTrans.naturality_app, CategoryTheory.biproduct_ι_comp_rightDistributor_hom_assoc, CategoryTheory.Functor.relativelyRepresentable.pullback₃.fst_snd_eq_p₂_assoc, BoolAlg.ofHom_id, CategoryTheory.sum.inlCompInlCompAssociator_inv_app_down, AlgebraicGeometry.Scheme.Hom.id_appIso, AlgebraicGeometry.Scheme.isoOfEq_inv_ι_assoc, CategoryTheory.InjectiveResolution.desc_commutes, CategoryTheory.op_hom_braiding, CategoryTheory.MorphismProperty.rightFractionRel_op_iff, CategoryTheory.GrothendieckTopology.diagram_map, CategoryTheory.Subfunctor.Subpresheaf.range_le_equalizer_iff, CategoryTheory.Functor.biprodComparison'_comp_biprodComparison, CategoryTheory.Sieve.uliftFunctorInclusion_app, CategoryTheory.OverPresheafAux.YonedaCollection.map₂_id, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_counitIso, smoothSheafCommRing.ι_forgetStalk_inv_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.inv_hom_actionHomLeft_assoc, CategoryTheory.Adjunction.CommShift.compatibilityCounit_left, AlgebraicGeometry.Scheme.Hom.preimageIso_inv_ι_assoc, CategoryTheory.Functor.flipping_unitIso_hom_app_app_app, CategoryTheory.Triangulated.SpectralObject.id_hom, CategoryTheory.Equivalence.inverseFunctorObj'_hom_app, CategoryTheory.PreZeroHypercover.hom_inv_h₀_assoc, CategoryTheory.Limits.coconeOfIsSplitEpi_pt, CategoryTheory.Limits.pullbackSymmetry_hom_of_mono_eq, HomotopicalAlgebra.RightHomotopyClass.precomp_mk, HomologicalComplex.xPrevIso_comp_dTo_assoc, CategoryTheory.StructuredArrow.pre_map_left, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τr, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_comp_homologyIso_inv_assoc, CategoryTheory.Join.pseudofunctorRight_mapId_inv_toNatTrans_app, CategoryTheory.Functor.op_commShiftIso_inv_app, AlgebraicGeometry.Scheme.Cover.gluedCoverT'_snd_fst_assoc, CategoryTheory.Comma.unopFunctorCompSnd_inv_app, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_whisker_left, CategoryTheory.Limits.Fan.IsLimit.fac, PresheafOfModules.map_comp, CategoryTheory.ShortComplex.LeftHomologyMapData.cyclesMap_comm, PartOrdEmb.id_apply, CategoryTheory.conjugateEquiv_mateEquiv_vcomp, CategoryTheory.cocones_obj_map_app, CategoryTheory.Functor.LaxRightLinear.μᵣ_associativity_assoc, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberι, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_tensorDesc_app_assoc, SSet.Subcomplex.image_eq_range, CategoryTheory.Functor.Monoidal.map_associator', CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_iso, CategoryTheory.obj_η_app_assoc, HomologicalComplex.homotopyCofiber.inlX_d, CategoryTheory.isIso_unop, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃'_map_app_app, CategoryTheory.Sieve.mem_functorPushforward_inverse, CategoryTheory.Sieve.pullback_comp, CategoryTheory.Comma.inv_left_hom_right, HomologicalComplex.mapBifunctor₂₃.d₁_eq, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right, CategoryTheory.GradedObject.mapMap_id, CategoryTheory.Functor.map_braiding_assoc, SSet.RelativeMorphism.comm, CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_inv_desc, CategoryTheory.ObjectProperty.le_isColocal_iff, CategoryTheory.ShortComplex.SnakeInput.naturality_δ_assoc, SSet.Truncated.StrictSegal.spine_δ_vertex_ge, CategoryTheory.coevaluation_comp_rightAdjointMate, CategoryTheory.ShiftedHom.opEquiv'_symm_apply, CategoryTheory.Limits.imageSubobjectMap_arrow, CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom_assoc, CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_fst_assoc, CategoryTheory.Comonad.coassoc_assoc, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_ihom_ev_app, AlgebraicGeometry.PresheafedSpace.map_id_c_app, CategoryTheory.Conv.mul_eq, CategoryTheory.ObjectProperty.instEssentiallySmallTopOfEssentiallySmall, SSet.StrictSegal.spineToSimplex_edge, CategoryTheory.GrpObj.div_comp_assoc, CategoryTheory.SemiadditiveOfBinaryBiproducts.add_eq_right_addition, AlgebraicGeometry.specTargetImageFactorization_comp, CategoryTheory.ExponentiableMorphism.ev_naturality_assoc, CategoryTheory.Limits.inv_piComparison_comp_map_π, CategoryTheory.Limits.colimitPointwiseProductToProductColimit_app, CategoryTheory.Idempotents.DoldKan.η_inv_app_f, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.IsTerminal.prop_id, CategoryTheory.ConcreteCategory.hom_bijective, CategoryTheory.Bicategory.Comonad.counit_def, AlgebraicGeometry.Scheme.comp_appTop_assoc, CategoryTheory.NonPreadditiveAbelian.lift_sub_lift, CategoryTheory.Limits.imageSubobjectMap_arrow_assoc, CategoryTheory.Limits.inr_pushoutRightPushoutInlIso_inv, CategoryTheory.Functor.mapTriangleIdIso_hom_app_hom₃, Homotopy.comp_nullHomotopicMap, RingCat.moduleCatRestrictScalarsPseudofunctor_map, AddCommGrpCat.kernelIsoKer_inv_comp_ι, CategoryTheory.MonoidalCategory.MonoidalLeftAction.hom_inv_actionHomLeft_assoc, CategoryTheory.LaxFunctor.map₂_associator, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, CategoryTheory.Adjunction.Triple.adj₁_counit_app_rightToLeft_app_assoc, CategoryTheory.Limits.limit.map_post, CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id_app_assoc, CategoryTheory.IsFinitelyPresentable.exists_hom_of_isColimit, AlgebraicGeometry.SheafedSpace.GlueData.ι_isoPresheafedSpace_inv, AddCommGrpCat.image.fac, CategoryTheory.Over.opEquivOpUnder_counitIso, CategoryTheory.Bicategory.associator_inv_naturality_left_assoc, CategoryTheory.Monad.algebraPreadditive_homGroup_zsmul_f, TopCat.Presheaf.SheafConditionEqualizerProducts.res_π, CategoryTheory.ShortComplex.HasRightHomology.of_hasKernel, SSet.PtSimplex.MulStruct.δ_map_of_lt, CategoryTheory.Grp_Class.comp_div, HomologicalComplex.extend.rightHomologyData_g', CategoryTheory.OplaxFunctor.mapComp_id_right_assoc, LinearMap.id_moduleCat_comp, TopCat.Presheaf.germ_res, CommGrpCat.hom_comp, CategoryTheory.CostructuredArrow.prodFunctor_obj, CategoryTheory.IsFiltered.tulip, HomotopicalAlgebra.trivialCofibrations_op, CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_mapId, CategoryTheory.Limits.pullback_snd_iso_of_left_factors_mono, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_SpecMap_awayMap_left_assoc, CategoryTheory.SmallObject.SuccStruct.iterationFunctor_map_succ, ModuleCat.restrictScalarsComp'App_inv_naturality, CategoryTheory.Oplax.StrongTrans.naturality_comp_assoc, AlgebraicGeometry.PresheafedSpace.GlueData.f_invApp_f_app, TopCat.prodIsoProd_inv_fst, CategoryTheory.Functor.OplaxMonoidal.δ_comp_whiskerLeft_δ, AlgebraicGeometry.Scheme.Hom.resLE_comp_resLE_assoc, AlgebraicGeometry.IsZariskiLocalAtSource.respectsLeft_isOpenImmersion, CategoryTheory.Functor.LeftExtension.coconeAtWhiskerRightIso_hom_hom, CategoryTheory.Comma.equivProd_inverse_map_right, CategoryTheory.GrpObj.whiskerLeft_η_commutator_assoc, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_hom_app_left, CategoryTheory.Pretriangulated.comp_hom₂_assoc, CategoryTheory.plusPlusAdjunction_counit_app_val, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_left, CategoryTheory.Dial.associator_naturality, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapComp_hom, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_σ, CategoryTheory.InjectiveResolution.desc_commutes_assoc, HomologicalComplex.single_map_f_self_assoc, SSet.Truncated.StrictSegal.spineToSimplex_edge, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocIso_inv_naturality_assoc, CategoryTheory.Localization.SmallHom.mk_comp_mk, CategoryTheory.MorphismProperty.instFaithfulCostructuredArrowTopOverToOver, CategoryTheory.Limits.IsTerminal.comp_from, CategoryTheory.Square.Hom.comp_τ₁, CategoryTheory.NatTrans.CommShiftCore.shift_comm_assoc, CategoryTheory.Limits.coprod.map_comp_id_assoc, CategoryTheory.MorphismProperty.op_inverseImage, groupHomology.eq_d₁₀_comp_inv, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_symm_apply, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_comp_π, CategoryTheory.mateEquiv_conjugateEquiv_vcomp, CategoryTheory.CommSq.LiftStruct.opEquiv_symm_apply, CategoryTheory.OplaxFunctor.mapComp_assoc_right, CategoryTheory.GrpObj.isPullback, TopologicalSpace.Opens.adjunction_counit_app_self, CategoryTheory.Bicategory.mateEquiv_eq_iff, SSet.Truncated.spine_arrow, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_app, HomologicalComplex.ι_mapBifunctorMap_assoc, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_inv_app_f, CategoryTheory.ModObj.one_smul', HomologicalComplex.ιMapBifunctorOrZero_eq_zero, CategoryTheory.coreCategory_id_iso_hom, CategoryTheory.uncurry_expComparison, CategoryTheory.Arrow.equivSigma_symm_apply_hom, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_obj_hom_app, CategoryTheory.CategoryOfElements.fromCostructuredArrow_map_coe, CategoryTheory.RegularMono.w, CategoryTheory.Preadditive.comp_sum, CategoryTheory.Adjunction.adjToMonadIso_inv_toNatTrans_app, CategoryTheory.MonoidalCategory.hom_inv_whiskerRight'_assoc, CategoryTheory.Pretriangulated.binaryProductTriangle_mor₃, CategoryTheory.Equivalence.leftOp_inverse_map, CategoryTheory.Limits.WidePushoutShape.wideSpan_map, CategoryTheory.Limits.prod.associator_hom, AlgebraicGeometry.AffineSpace.reindex_comp, CategoryTheory.ShortComplex.SnakeInput.id_f₁, CategoryTheory.Functor.sheafPushforwardCocontinuousCompSheafToPresheafIso_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHom_id, CategoryTheory.cancel_epi_id, CategoryTheory.Limits.biproduct.fromSubtype_eq_lift, CategoryTheory.Limits.pullback_diagonal_map_snd_fst_fst_assoc, CategoryTheory.forget₂_comp_apply, CategoryTheory.Limits.limit.isoLimitCone_inv_π_assoc, AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_self, CategoryTheory.CartesianClosed.uncurry_natural_left, CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_inv_apply, CategoryTheory.Limits.BinaryFan.braiding_hom_fst, CategoryTheory.CatCenter.smul_iso_inv_eq_assoc, CategoryTheory.Functor.prod_μ_fst, CategoryTheory.GrothendieckTopology.OneHypercover.id_s₁, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_inv_naturality_assoc, CategoryTheory.Idempotents.KaroubiUniversal₁.counitIso_hom_app_app_f, CategoryTheory.Functor.CommShift.id_commShiftIso_hom_app, Preord.hom_comp, groupHomology.isoShortComplexH1_inv, CategoryTheory.FunctorToTypes.map_comp_apply, AlgebraicGeometry.AffineSpace.map_SpecMap, CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_p_assoc, CategoryTheory.OplaxFunctor.mapComp_assoc_left_assoc, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_whiskerLeft, CategoryTheory.Limits.CatCospanTransform.associator_inv_base_app, SSet.horn.faceι_ι, CategoryTheory.Square.opFunctor_map_τ₂, Action.res_map_hom, HomologicalComplex.extend.homologyData'_right_p, HomologicalComplex.extendCyclesIso_hom_iCycles, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₃, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionRight_op, CategoryTheory.Adjunction.commShiftIso_hom_app_counit_app_shift_assoc, CategoryTheory.SingleFunctors.hom_inv_id_hom_app_assoc, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_ε_assoc, AlgebraicTopology.DoldKan.degeneracy_comp_PInfty_assoc, CategoryTheory.GrothendieckTopology.dense_covering, CategoryTheory.Bicategory.InducedBicategory.forget_mapId_inv, CategoryTheory.Pretriangulated.id_hom₂, CategoryTheory.SmallObject.FunctorObjIndex.w_assoc, CategoryTheory.Functor.FullyFaithful.homMulEquiv_symm_apply, CategoryTheory.NatTrans.prod_app_snd, CategoryTheory.LocalizerMorphism.homMap_comp, CategoryTheory.Functor.Monoidal.transport_η_assoc, CategoryTheory.Pseudofunctor.ObjectProperty.IsClosedUnderMapObj.map_obj, CategoryTheory.Limits.Cotrident.IsColimit.homIso_symm_apply, CategoryTheory.Limits.ColimitPresentation.w_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_app_assoc, SheafOfModules.pushforwardComp_hom_app_val_app, CategoryTheory.RetractArrow.unop_r_right, CategoryTheory.Projective.factorThru_comp, CategoryTheory.Arrow.id_right, CategoryTheory.Limits.kernelSubobject_arrow, CategoryTheory.Pretriangulated.triangleMorphismId_hom₂, CategoryTheory.Limits.Cones.postcompose_obj_π, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_inv_app, Bicategory.Opposite.op2_comp, CategoryTheory.Limits.colimit.ι_post_assoc, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_unitIso_inv_app_f, CategoryTheory.Paths.lift_cons, groupHomology.eq_d₁₀_comp_inv_assoc, CategoryTheory.Functor.OplaxMonoidal.comp_η, CategoryTheory.Bicategory.pentagon_inv_assoc, SimplexCategory.δ_comp_δ, CategoryTheory.Pseudofunctor.mapComp'_hom_naturality, groupCohomology.d₁₂_comp_d₂₃, CategoryTheory.Idempotents.KaroubiUniversal₁.counitIso_inv_app_app_f, CategoryTheory.GlueData.t'_inv, CategoryTheory.Subfunctor.Subpresheaf.range_id, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app, CategoryTheory.StructuredArrow.map_map_left, CategoryTheory.GradedObject.CofanMapObjFun.inj_iso_hom_assoc, CategoryTheory.GradedObject.mapBifunctorObjObjSingle₀Iso_inv, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_left, CategoryTheory.yonedaGrpObj_map, CategoryTheory.Iso.map_hom_inv_id_eval_assoc, CategoryTheory.Functor.unop_map, CategoryTheory.PreOneHypercover.id_s₀, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitIso_inv_naturality_assoc, CategoryTheory.Limits.coprod.inl_desc, TopCat.Presheaf.Pushforward.id_hom_app, CategoryTheory.MonoidalClosed.uncurry_ihom_map, CategoryTheory.Limits.eq_zero_of_epi_kernel, CategoryTheory.Pseudofunctor.StrongTrans.Modification.id_app, Bimod.comp_whiskerRight_bimod, CategoryTheory.Adjunction.rightAdjointUniq_hom_counit_assoc, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_id_assoc, CategoryTheory.Limits.isLimitConeOfCoconeRightOp_lift, CategoryTheory.Presheaf.isLocallySurjective_comp, CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_comp_d, Representation.linHom.invariantsEquivRepHom_symm_apply_coe, CategoryTheory.Limits.ColimitPresentation.Total.Hom.comp_base, TopCat.Presheaf.pullback_obj_obj_ext_iff, CategoryTheory.Limits.biprod.map_snd_assoc, BddOrd.id_apply, CategoryTheory.Bicategory.whiskerRight_comp, CategoryTheory.ObjectProperty.isLocal.homEquiv_apply, CategoryTheory.ShortComplex.π_leftRightHomologyComparison'_ι_assoc, CategoryTheory.Limits.pullbackProdSndIsoProd_inv_fst_fst_assoc, CategoryTheory.MorphismProperty.RightFraction.op_f, CategoryTheory.Limits.IsZero.map, AlgebraicGeometry.Scheme.GlueData.oneHypercover_p₂, FintypeCat.homMk_eq_id_iff, CategoryTheory.CatCenter.smul_eq, CategoryTheory.Endofunctor.Algebra.functorOfNatTrans_map_f, CategoryTheory.Limits.PreservesPushout.inr_iso_hom, CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_id, Rep.linearization_obj_ρ, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd, CategoryTheory.Functor.RepresentableBy.homEquiv_unop_comp, CategoryTheory.Functor.flipIsoCurrySwapUncurry_hom_app_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso_hom_app_app, CondensedMod.LocallyConstant.instFaithfulSheafCompHausCoherentTopologyTypeConstantSheaf, AlgebraicGeometry.Scheme.IdealSheafData.isLocalization_away, CategoryTheory.Pseudofunctor.StrongTrans.associator_inv_as_app, CategoryTheory.Idempotents.Karoubi.coe_p, Homotopy.symm_hom, groupHomology.chainsMap_f_1_comp_chainsIso₁_assoc, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_map_left_right, AlgebraicGeometry.isOpenImmersion_eq_inf, CategoryTheory.SingleFunctors.postcomp_shiftIso_inv_app, CategoryTheory.shiftFunctorAdd_assoc_inv_app_assoc, CpltSepUniformSpace.hom_comp, CategoryTheory.Limits.Multicofork.isoOfπ_hom_hom, CategoryTheory.MonoidalCategory.MonoidalRightAction.id_actionHomLeft, CategoryTheory.Dial.tensorHomImpl_F, CategoryTheory.Subobject.ofLE_refl, SSet.N.le_iff_exists_mono, CategoryTheory.Functor.mapCone₂_π_app, AlgebraicGeometry.Scheme.ofRestrict_toLRSHom_c_app, CategoryTheory.yonedaGrpObjIsoOfRepresentableBy_hom, CategoryTheory.Limits.PreservesLimitPair.iso_inv_snd_assoc, CategoryTheory.Regular.frobeniusStrongEpiMonoFactorisation_e, CategoryTheory.GradedObject.Monoidal.braiding_naturality_left, CategoryTheory.IsPullback.isoPullback_hom_fst, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc, CategoryTheory.Limits.pullbackDiagonalMapIso.inv_snd_fst, CategoryTheory.Limits.MonoFactorisation.ofCompIso_I, CategoryTheory.StructuredArrow.mkPostcomp_right, CategoryTheory.Linear.comp_smul, ModuleCat.restrictScalarsComp'App_inv_naturality_assoc, CategoryTheory.MonoidalClosed.uncurry_injective, CategoryTheory.LocalizerMorphism.RightResolution.comp_f, CategoryTheory.Bicategory.Comonad.comul_counit_assoc, HomologicalComplex.extend.homologyData'_left_i, CategoryTheory.Functor.OplaxMonoidal.δ_comp_η_tensorHom, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHom_unop, CategoryTheory.Subfunctor.lift_ι_assoc, CategoryTheory.CartesianMonoidalCategory.whiskerLeft_toUnit_comp_rightUnitor_hom_assoc, CategoryTheory.rightDistributor_assoc, CategoryTheory.Limits.pullbackProdFstIsoProd_inv_fst_assoc, CategoryTheory.FreeGroupoid.mapId_inv_app, HomologicalComplex.truncGE'_d_eq_fromOpcycles, CategoryTheory.Subobject.ofMkLEMk_refl, CategoryTheory.Functor.obj.μ_def, CategoryTheory.Limits.limitFlipIsoCompLim_inv_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_hom_app, CategoryTheory.regularTopology.equalizerCondition_iff_isIso_lift, CategoryTheory.MonObj.one_leftUnitor, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_app_hom, CategoryTheory.GlueData.t_inv_assoc, CochainComplex.mappingCone.inr_f_descCochain_v, CategoryTheory.Limits.CatCospanTransform.whisker_exchange_assoc, CategoryTheory.toOverIsoToOverUnit_hom_app_left, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃'_associator_hom, CategoryTheory.rightAdjointOfCostructuredArrowTerminalsAux_apply, CategoryTheory.Functor.IsCocartesian.universal_property, CategoryTheory.Bicategory.congr_whiskerLeft, CategoryTheory.Adjunction.compYonedaIso_inv_app_app, CategoryTheory.GlueData.t'_jii, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f, CategoryTheory.PreOneHypercover.w, CategoryTheory.MarkovCategory.discard_natural, CategoryTheory.SmallObject.ρFunctorObj_π, AlgebraicGeometry.Surjective.comp_iff, CategoryTheory.yonedaGrpObjIsoOfRepresentableBy_inv, CategoryTheory.ShortComplex.RightHomologyData.ofAbelian_ι, CategoryTheory.Mon.uniqueHomFromTrivial_default_hom, CategoryTheory.eqToHom_comp_homOfLE, CategoryTheory.ComposableArrows.isComplex₂_iff, CategoryTheory.Functor.FullyFaithful.map_surjective, SimplexCategory.Truncated.δ₂_one_comp_σ₂_zero, CategoryTheory.ShortComplex.RightHomologyMapData.comp_φH, CategoryTheory.ObjectProperty.instSmallOfObjOfSmall, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_inv_hom, CategoryTheory.MonoidalClosed.uncurry_id_eq_ev, prodIsoPullback_hom_snd, TopCat.Presheaf.id_pushforward, CategoryTheory.DifferentialObject.Hom.id_f, CategoryTheory.Preadditive.comp_zsmul, CategoryTheory.Equivalence.changeInverse_counitIso_hom_app, CochainComplex.cm5b.instQuasiIsoIntP, CategoryTheory.Limits.colimit.pre_desc_assoc, CategoryTheory.Over.w, CategoryTheory.Pseudofunctor.toLax_mapId, CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_zsmul_f, SemimoduleCat.MonoidalCategory.hexagon_forward, CategoryTheory.Limits.MonoCoprod.mono_map'_of_injective, CategoryTheory.Functor.leftUnitor_inv_app, CategoryTheory.Limits.HasLimit.isoOfNatIso_hom_π_assoc, CategoryTheory.ShiftedHom.mk₀_add, SimplicialObject.Splitting.IndexSet.instEpiSimplexCategoryE, CategoryTheory.CartesianMonoidalCategory.whiskerLeft_snd, HomologicalComplex.XIsoOfEq_hom_comp_XIsoOfEq_hom_assoc, CategoryTheory.Limits.Cones.extendId_hom_hom, HomologicalComplex.restrictionHomologyIso_hom_homologyι_assoc, CategoryTheory.Functor.mapTriangleRotateIso_hom_app_hom₁, CategoryTheory.Limits.pushout_inl_iso_of_left_factors_epi, SheafOfModules.Presentation.map_relations_I, FGModuleCat.Iso.conj_eq_conj, HomologicalComplex₂.D₁_totalShift₁XIso_hom, CategoryTheory.MorphismProperty.CostructuredArrow.toOver_map, CategoryTheory.Functor.coreCompInclusionIso_inv_app, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv, CategoryTheory.Localization.Monoidal.associator_naturality₁_assoc, CategoryTheory.ObjectProperty.FullSubcategory.id_def, TopCat.Presheaf.Pushforward.id_eq, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_inv, CategoryTheory.Functor.hom_obj, groupCohomology.cocyclesIso₀_hom_comp_f_assoc, CategoryTheory.Sheaf.adjunction_unit_app_val, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.sq, CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_assoc, CategoryTheory.Limits.sigmaComparison_map_desc_assoc, AlgebraicGeometry.instHasCoproductsOfShapeOverSchemeTopMorphismPropertyOfSmall, SSet.Truncated.HomotopyCategory.homToNerveMk_app_one, CategoryTheory.Functor.shiftMap_zero, HomologicalComplex.πTruncGE_naturality, groupHomology.lsingle_comp_chainsMap_f, CategoryTheory.Functor.ι_biproductComparison', AlgebraicGeometry.Proj.fromOfGlobalSections_toSpecZero, HomologicalComplex₂.D₂_totalShift₁XIso_hom, CategoryTheory.Coyoneda.colimitCoconeIsColimit_desc, AlgebraicTopology.DoldKan.P_idem, CategoryTheory.Comma.mapLeftEq_hom_app_right, CategoryTheory.mono_comp, CategoryTheory.Subgroupoid.mem_sInf, MonObj.mopEquiv_functor_map_hom_unmop, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_pos, CategoryTheory.Functor.const_map_app, CategoryTheory.Endofunctor.Algebra.functorOfNatTransId_hom_app_f, CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_hom_desc_assoc, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_comp_assoc, CategoryTheory.GradedObject.ι_mapBifunctorMapMap_assoc, CategoryTheory.Functor.opInv_map, CategoryTheory.Limits.colimit.pre_desc, CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono_p, CategoryTheory.Subfunctor.toRange_ι_assoc, BoolAlg.coe_comp, CategoryTheory.Localization.homEquiv_apply, CategoryTheory.DifferentialObject.objEqToHom_d, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv, CategoryTheory.Equivalence.fun_inv_map, CategoryTheory.StructuredArrow.mapIso_unitIso_inv_app_right, ComplexShape.Embedding.homEquiv_symm_apply, CategoryTheory.Oplax.OplaxTrans.isoMk_hom_as_app, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_m, HomotopicalAlgebra.Precylinder.LeftHomotopy.h₀, CategoryTheory.StructuredArrow.prodFunctor_obj, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_hom_assoc, SSet.prodStdSimplex.objEquiv_map_apply, AlgebraicGeometry.Scheme.iso_hom_base_inv_base, CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_left, CategoryTheory.Bicategory.whiskerLeft_inv_hom_whiskerRight, SheafOfModules.instIsLeftAdjointOverOverRingCatPushforwardIdSheafOver, AlgebraicGeometry.Scheme.stalkMap_congr_point, ComplexShape.Embedding.homRestrict.comm_assoc, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π_assoc, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app_assoc, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_π_app, CategoryTheory.MonoidalOpposite.tensorLeftUnmopIso_hom_app, CategoryTheory.Bicategory.Adj.comp_τr_assoc, CategoryTheory.MonoidalCategory.DayConvolution.braidingInvCorepresenting_app, ModuleCat.imageIsoRange_inv_image_ι_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitIso_inv_naturality, CategoryTheory.CartesianMonoidalCategory.associator_inv_fst_fst_assoc, CategoryTheory.ShortComplex.toCycles_comp_leftHomologyπ, Bimod.id'_hom, HomologicalComplex₂.comm_f_assoc, HomologicalComplex.cylinder.inrX_π, CategoryTheory.MonoidalCategory.MonoidalLeftAction.tensor_actionHomRight_assoc, CategoryTheory.Bicategory.whisker_assoc_assoc, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.δ_toBiprod_assoc, CategoryTheory.GradedObject.ι_mapBifunctor₁₂BifunctorDesc_assoc, HomologicalComplex.d_comp_XIsoOfEq_inv_assoc, CategoryTheory.Preadditive.add_comp, CategoryTheory.Limits.PreservesPullback.iso_hom_snd_assoc, CategoryTheory.Limits.spanCompIso_hom_app_right, SSet.stdSimplex.objEquiv_symm_mem_nonDegenerate_iff_mono, CategoryTheory.Abelian.PreservesCoimage.iso_inv_π, CategoryTheory.Subfunctor.Subpresheaf.homOfLe_ι, CategoryTheory.CommSq.LiftStruct.fac_right, SSet.Truncated.Edge.mk'_edge, NonemptyFinLinOrd.hom_hom_id, SimplicialObject.Splitting.cofan_inj_comp_app, AlgebraicGeometry.AffineSpace.SpecIso_inv_over_assoc, CategoryTheory.MorphismProperty.le_retracts, CategoryTheory.Functor.lanUnit_app_whiskerLeft_lanAdjunction_counit_app_assoc, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_three, TopCat.range_pullback_to_prod, HomologicalComplex.mapBifunctor₂₃.ι_eq, CategoryTheory.Subobject.factorThru_self, CategoryTheory.NatTrans.whiskerLeft_app_tensor_app, CategoryTheory.Limits.prodComparison_snd, CategoryTheory.Limits.limitOpIsoOpColimit_inv_comp_π_assoc, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₂_assoc, CategoryTheory.DifferentialObject.eqToHom_f', CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_hom_π_π_assoc, CategoryTheory.MorphismProperty.Comma.Hom.comp_left, CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_inv_assoc, CategoryTheory.MorphismProperty.instHasOfPrecompPropertyMin, CategoryTheory.Subobject.ofLEMk_comp_ofMkLEMk_assoc, CategoryTheory.comp_app, LightProfinite.Extend.functorOp_map, CategoryTheory.Limits.imageSubobject_comp_le, PresheafOfModules.sub_app, CategoryTheory.GrpObj.comp_div, TopCat.Sheaf.interUnionPullbackConeLift_left, AlgebraicTopology.NormalizedMooreComplex.d_squared, CategoryTheory.Limits.Sigma.map'_comp_map, AlgebraicGeometry.sourceLocalClosure.instRespectsLeftSchemeOfIsStableUnderBaseChange, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality_assoc, CategoryTheory.PreOneHypercover.Hom.id_h₀, HomologicalComplex.homologyMap_sub, CategoryTheory.PreZeroHypercover.inv_inv_h₀_comp_f_assoc, CategoryTheory.instIsComonHomId, CategoryTheory.Functor.const.opObjOp_hom_app, groupHomology.cyclesMap_comp_cyclesIso₀_hom, HomotopicalAlgebra.cofibrations_eq_unop, MonObj.mopEquivCompForgetIso_inv_app_unmop, CategoryTheory.Functor.relativelyRepresentable.w_assoc, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_counitIso, HomologicalComplex₂.totalFlipIso_hom_f_D₁_assoc, CategoryTheory.Limits.kernelSubobject_factors_iff, Homotopy.comp_nullHomotopicMap', CategoryTheory.Functor.isIso_lanAdjunction_homEquiv_symm_iff, CategoryTheory.Preadditive.add_comp_assoc, CategoryTheory.CostructuredArrow.comp_left, AlgebraicGeometry.Scheme.stalkMap_hom_inv, CategoryTheory.DifferentialObject.Hom.comp_f, TopCat.subpresheafToTypes_map_coe, CategoryTheory.MonObj.one_braiding, CategoryTheory.CartesianMonoidalCategory.whiskerRight_toUnit_comp_leftUnitor_hom, AlgebraicGeometry.IsClosedImmersion.eq_inf, CategoryTheory.Functor.rightDerivedNatTrans_app, CategoryTheory.GradedObject.single_map_singleObjApplyIsoOfEq_hom, CategoryTheory.NatTrans.tensor_naturality_assoc, CategoryTheory.Functor.mapCommGrp_id_one, CategoryTheory.MorphismProperty.RightFraction.op_map, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_fst_assoc, PresheafOfModules.colimitPresheafOfModules_map, CategoryTheory.ShortComplex.opcyclesOpIso_inv_naturality, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_assoc, groupCohomology.cochainsMap_f, CategoryTheory.MonoidalCategory.pentagon_inv_assoc, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s₀_comp_δ₁, AlgebraicGeometry.Scheme.monObjAsOverPullback_mul, HomologicalComplex.XIsoOfEq_inv_comp_d, CategoryTheory.Iso.map_inv_hom_id_assoc, CategoryTheory.ProjectiveResolution.complex_d_succ_comp, AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c, CategoryTheory.Prod.fac, AddMagmaCat.ofHom_id, CategoryTheory.MorphismProperty.isLocal_iff, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_hom_app_fst_app, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app_assoc, CategoryTheory.CartesianMonoidalCategory.lift_braiding_hom_assoc, CategoryTheory.Bicategory.associator_eqToHom_hom, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality, CategoryTheory.Mon_Class.comp_pow, CategoryTheory.MorphismProperty.IsInvertedBy.op, Alexandrov.lowerCone_π_app, CategoryTheory.ShortComplex.SnakeInput.φ₁_L₂_f, CategoryTheory.ObjectProperty.isoHom_inv_id_hom_assoc, CategoryTheory.SimplicialObject.δ_comp_σ_of_le, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_fst, AlgebraicTopology.DoldKan.Γ₀.map_app, CategoryTheory.Limits.Cofan.IsColimit.inj_desc_assoc, CategoryTheory.Bicategory.whisker_assoc_symm, ComplexShape.Embedding.homEquiv_apply_coe, CategoryTheory.extendCofan_ι_app, CategoryTheory.LocallySmall.hom_small, CategoryTheory.Join.mapWhisker_exchange, CategoryTheory.Limits.ι_comp_colimitRightOpIsoUnopLimit_hom, CategoryTheory.IsComonHom.hom_counit_assoc, CategoryTheory.Mod_.comp_hom', CategoryTheory.Comma.opFunctorCompSnd_hom_app, CategoryTheory.Localization.Monoidal.associator_naturality_assoc, Homotopy.dNext_succ_chainComplex, CategoryTheory.nerve.σ₀_mk₀_eq, CategoryTheory.MonoidalClosed.pre_id, CategoryTheory.Lax.StrongTrans.naturality_naturality_assoc, CategoryTheory.ShortComplex.homologyMap_comp, HomologicalComplex.XIsoOfEq_inv_comp_d_assoc, CategoryTheory.MonObj.Mon_tensor_mul_assoc, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π, CategoryTheory.Localization.SmallShiftedHom.equiv_shift, CategoryTheory.op_hom_associator, CategoryTheory.Center.id_f, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.inverse_obj_map, topToLocale_map, CategoryTheory.Functor.OplaxMonoidal.left_unitality_hom, CategoryTheory.Functor.LaxLeftLinear.μₗ_associativity, CategoryTheory.TransportEnrichment.eComp_eq, CategoryTheory.Functor.shiftIso_hom_naturality_assoc, CommGrpCat.coe_id, TopologicalSpace.Opens.map_comp_eq, HomologicalComplex.homotopyCofiber.shape, CategoryTheory.CommSq.right_adjoint, CategoryTheory.GlueData.cocycle_assoc, CategoryTheory.Bicategory.Prod.sectL_mapComp_inv, CategoryTheory.WithInitial.opEquiv_counitIso_inv_app, CategoryTheory.ObjectProperty.monomorphisms_le_monoModSerre, HomotopicalAlgebra.Cylinder.symm_i, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac', CategoryTheory.ShiftMkCore.add_zero_inv_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_obj, PartOrd.ofHom_id, CommGrpCat.id_apply, HomotopicalAlgebra.Cylinder.trans_i₀, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_comp, CategoryTheory.Limits.equalizerSubobject_factors_iff, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_snd_coe, CategoryTheory.Limits.Fork.condition, CategoryTheory.Functor.sectionsEquivHom_naturality_symm, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id_assoc, CategoryTheory.MorphismProperty.CostructuredArrow.toOver_obj, CategoryTheory.IsHomLift.lift_eqToHom_comp, CategoryTheory.HasShift.Induced.zero_hom_app_obj, groupHomology.chainsMap_comp, TopCat.Presheaf.stalkSpecializes_stalkFunctor_map, CategoryTheory.Functor.IsEventuallyConstantFrom.coconeιApp_eq, CategoryTheory.NatTrans.unop_id, AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv_assoc, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_two_assoc, CategoryTheory.IsPushout.inl_isoPushout_inv, CategoryTheory.Pretriangulated.contractibleTriangle_mor₁, CategoryTheory.Equalizer.Presieve.w, CategoryTheory.Limits.imageSubobject_arrow, CategoryTheory.Functor.Monoidal.tensorHom_app_fst, CategoryTheory.Endofunctor.algebraPreadditive_homGroup_sub_f, CategoryTheory.MorphismProperty.Under.w, CategoryTheory.Limits.coneLeftOpOfCocone_π_app, HomologicalComplex₂.XXIsoOfEq_inv_ιTotal, AlgebraicGeometry.Scheme.Modules.pseudofunctor_obj_obj, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_assoc, groupHomology.d₂₁_comp_d₁₀, HomotopicalAlgebra.FibrantObject.homRel_equivalence_of_isCofibrant_src, AlgebraicGeometry.Scheme.homOfLE_app, CategoryTheory.InjectiveResolution.Hom.ι_f_zero_comp_hom_f_zero, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.δ_toBiprod, PresheafOfModules.Elements.fromFreeYoneda_app_apply, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_comp_assoc, CategoryTheory.MorphismProperty.pretopology_inf, CategoryTheory.Iso.refl_inv, CategoryTheory.StructuredArrow.mapIso_functor_map_left, CategoryTheory.ShortComplex.RightHomologyMapData.smul_φH, CategoryTheory.Limits.imageSubobject_comp_le_epi_of_epi, CategoryTheory.Limits.Types.productIso_hom_comp_eval, CategoryTheory.eComp_eHomWhiskerRight_assoc, CategoryTheory.Equivalence.congrLeftFunctor_map, CategoryTheory.Bicategory.id_whiskerLeft_assoc, CategoryTheory.Functor.eqToHom_proj, CategoryTheory.Functor.sheafPushforwardContinuousId_hom_app_val_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.rightUnitor_actionHom_assoc, AlgebraicGeometry.targetAffineLocally_affineAnd_eq_affineLocally, CategoryTheory.ShortComplex.exact_iff_exact_up_to_refinements, CategoryTheory.ShortComplex.LeftHomologyData.wπ, CategoryTheory.Abelian.coimage.fac, CategoryTheory.ShortComplex.LeftHomologyData.π_comp_homologyIso_inv_assoc, CategoryTheory.Functor.flipping_unitIso_inv_app_app_app, HomologicalComplex.cylinder.πCompι₀Homotopy.inrX_nullHomotopy_f, HomologicalComplex.homologyπ_singleObjHomologySelfIso_hom, SSet.Truncated.comp_app_assoc, SSet.Subcomplex.homOfLE_comp, AlgebraicGeometry.Scheme.Hom.comp_preimage, CategoryTheory.CatEnriched.hComp_assoc_heq, CategoryTheory.Bicategory.LeftLift.IsKan.fac, CategoryTheory.unop_epi_iff, CategoryTheory.liftedLimitMapsToOriginal_inv_map_π, CategoryTheory.Adjunction.homAddEquiv_symm_neg, CategoryTheory.Bimon.equivMonComonUnitIsoApp_inv_hom_hom, ModuleCat.HasColimit.coconePointSMul_apply, SheafOfModules.ιFree_mapFree_inv, CategoryTheory.Bimon.ofMon_Comon_toMon_Comon_obj_counit, CategoryTheory.Projective.factors, CategoryTheory.Adjunction.CoreUnitCounit.right_triangle, CategoryTheory.Abelian.Ext.mk₀_zero, CategoryTheory.Comonad.coalgebraPreadditive_homGroup_nsmul_f, CategoryTheory.Limits.FormalCoproduct.cech_map, CategoryTheory.Iso.hom_inv_id_triangle_hom₁, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_inv_app_one, CategoryTheory.EnrichedFunctor.map_comp_assoc, CategoryTheory.Comonad.Coalgebra.Hom.h_assoc, CategoryTheory.Adjunction.shift_unit_app, CategoryTheory.Limits.inl_inl_pushoutAssoc_hom, CategoryTheory.Join.inclLeftCompOpEquivInverse_inv_app_op, CategoryTheory.IsCofiltered.cospan, CategoryTheory.Limits.biprod.inr_map, CategoryTheory.Abelian.OfCoimageImageComparisonIsIso.imageMonoFactorisation_e', ModuleCat.kernelIsoKer_hom_ker_subtype, CategoryTheory.Functor.mapHomotopyEquiv_homotopyInvHomId, SSet.Truncated.StrictSegal.spineToSimplex_arrow, CategoryTheory.Adjunction.map_η_comp_η_assoc, AlgebraicGeometry.Scheme.Hom.naturality_assoc, CategoryTheory.MonoidalCategory.prodMonoidal_whiskerLeft, CategoryTheory.Functor.PushoutObjObj.inl_ι_assoc, CategoryTheory.Limits.coconeOfIsSplitEpi_π, SheafOfModules.Presentation.mapRelations_mapGenerators, AlgebraicGeometry.IsZariskiLocalAtSource.iff_of_openCover, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app_assoc, HomologicalComplex₂.total.map_comp, CategoryTheory.ChosenPullbacksAlong.pullbackId_hom_counit_assoc, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self_apply, CategoryTheory.op_mono_iff, HomologicalComplex.cyclesOpIso_hom_naturality, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_hom_inv'_assoc, CategoryTheory.Comonad.Coalgebra.coassoc_assoc, groupHomology.chainsMap_f_3_comp_chainsIso₃_assoc, CategoryTheory.SmallObject.SuccStruct.prop.fac_assoc, CategoryTheory.Bicategory.InducedBicategory.forget_mapComp_inv, CategoryTheory.Adjunction.unit_app_commShiftIso_hom_app_assoc, AlgebraicGeometry.AffineSpace.reindex_comp_assoc, ModuleCat.hom_add, CochainComplex.mappingConeCompHomotopyEquiv_comm₂, AlgebraicGeometry.Scheme.Hom.iInf_ker_openCover_map_comp_apply, Bicategory.Opposite.op2_id, CommRingCat.HomTopology.continuous_apply, CategoryTheory.IsPushout.inr_fst', HomotopicalAlgebra.CofibrantObject.HoCat.exists_resolution_map, CategoryTheory.Abelian.PreservesImage.iso_hom_ι_assoc, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_hom_assoc, CategoryTheory.Functor.OplaxLeftLinear.δₗ_unitality_hom, CategoryTheory.Endofunctor.Algebra.comp_f, CategoryTheory.op_hom_rightUnitor, CategoryTheory.Pseudofunctor.IsStack.essSurj_of_sieve, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₂₃_assoc, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.sheafCondition_iff_bijective_toPullbackObj, HomotopicalAlgebra.PrepathObject.symm_p_assoc, CategoryTheory.Monad.algebraEquivOfIsoMonads_counitIso, CategoryTheory.Subobject.imageFactorisation_F_I, CategoryTheory.Limits.pullbackDiagonalMapIdIso_hom_fst_assoc, HomotopicalAlgebra.CofibrantObject.HoCat.resolutionMap_fac, SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero_assoc, CategoryTheory.Sigma.inclCompMap_hom_app, CategoryTheory.GrpObj.comp_zpow_assoc, CategoryTheory.Subobject.factors_of_factors_right, CategoryTheory.Bicategory.toNatTrans_mateEquiv, CategoryTheory.Limits.KernelFork.app_one, CategoryTheory.Functor.RepresentableBy.uniqueUpToIso_hom, CondensedSet.topCatAdjunctionUnit_val_app, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac'_assoc, CategoryTheory.eqToHom_op, AlgebraicGeometry.Scheme.homOfLE_appLE, CategoryTheory.CartesianMonoidalCategory.lift_snd, CategoryTheory.SimplicialObject.δ_comp_σ_self, CategoryTheory.Factorisation.terminal_π, CategoryTheory.CostructuredArrow.homMk'_mk_comp, CategoryTheory.Functor.sheafPushforwardContinuousId'_inv_app_val_app, CategoryTheory.MorphismProperty.inf, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_hom_fac, CategoryTheory.IsHomLift.isoOfIsoLift_hom_inv_id, CategoryTheory.OplaxFunctor.map₂_rightUnitor, prodIsoPullback_hom_snd_assoc, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso_hom_app_f, CategoryTheory.Limits.limitBiconeOfUnique_isBilimit_isLimit, FGModuleCat.hom_hom_comp, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff, CategoryTheory.Over.associator_inv_left_fst_fst, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app_assoc, CategoryTheory.Functor.Final.exists_coeq, CategoryTheory.uliftYoneda_map_app, AlgebraicGeometry.Scheme.Hom.normalizationCoprodIso_inv_coprodDesc_fromNormalization, CategoryTheory.Limits.Cones.postcomposeComp_inv_app_hom, CategoryTheory.MonoidalCategory.comp_whiskerRight_assoc, CategoryTheory.Functor.IsEventuallyConstantTo.isoMap_hom_inv_id, CategoryTheory.Functor.prod'_η_snd, CategoryTheory.Preadditive.commGrpEquivalenceAux_inv_app_hom_hom_hom, CategoryTheory.ShortComplex.RightHomologyData.ι_g'_assoc, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_obj_hom_app, CategoryTheory.Comma.mapLeftIso_inverse_obj_hom, CategoryTheory.Localization.SmallHom.equiv_chgUniv, AlgebraicGeometry.pullbackSpecIso_inv_snd_assoc, CategoryTheory.ShortComplex.abelianImageToKernel_comp_kernel_ι_assoc, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop, CategoryTheory.tensorHom_eComp_op_eq_assoc, AlgebraicGeometry.Scheme.Cover.pushforwardIso_f, CategoryTheory.Limits.CatCospanTransform.category_id_base, CategoryTheory.Iso.unop_inv, CategoryTheory.SimplicialThickening.SimplicialCategory.assoc, CategoryTheory.Functor.Monoidal.whiskerLeft_app_snd, CategoryTheory.CostructuredArrow.right_eq_id, CategoryTheory.Functor.whiskerRight_zero, CategoryTheory.Functor.mapConePostcomposeEquivalenceFunctor_inv_hom, CategoryTheory.Limits.prod.map_fst_assoc, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_assoc, CategoryTheory.Functor.uliftYonedaReprXIso_hom_app, TopCat.Presheaf.pushforward_obj_map, CategoryTheory.OrthogonalReflection.D₁.ιLeft_comp_t_assoc, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_unitIso, CategoryTheory.Limits.Sigma.ι_isoColimit_hom, CategoryTheory.Limits.opProdIsoCoprod_hom_fst, SSet.Subcomplex.topIso_inv_ι_assoc, CategoryTheory.Limits.map_π_preserves_coequalizer_inv_assoc, CategoryTheory.StructuredArrow.comp_right, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.single_P, CategoryTheory.NatTrans.naturality_1_assoc, HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac_assoc, HomologicalComplex.mapBifunctor₁₂.ι_D₃, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_leftUnitor_assoc, CategoryTheory.Pretriangulated.TriangleMorphism.comm₃_assoc, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_hom_fac, CategoryTheory.IsCommMonObj.mul_comm'_assoc, Action.ρ_self_inv_apply, CategoryTheory.MorphismProperty.coproducts_le_llp_rlp, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app, CategoryTheory.Limits.kernel.ι_zero_isIso, AddCommGrpCat.coe_id, HomotopicalAlgebra.Precylinder.inl_i_assoc, CategoryTheory.equivYoneda_hom_app, CategoryTheory.isCoseparator_pi, CochainComplex.HomComplex.δ_zero_cochain_v, CochainComplex.HomComplex.Cochain.units_smul_v, CategoryTheory.NonPreadditiveAbelian.neg_add_cancel, CommSemiRingCat.comp_apply, CommGrpCat.comp_apply, CategoryTheory.GrpObj.inv_eq_inv, CategoryTheory.Limits.ColimitPresentation.Total.Hom.comp_hom, CategoryTheory.Functor.Monoidal.μ_comp, CategoryTheory.NatTrans.mapHomotopyCategory_id, CochainComplex.HomComplex.Cochain.δ_toSingleMk, CategoryTheory.Limits.Pi.whiskerEquiv_hom, HomologicalComplex.smul_f_apply, CompHausLike.pullback.condition_assoc, groupCohomology.map_id_comp_assoc, CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp_hom_hom₃, ModuleCat.ι_coprodIsoDirectSum_hom, TopCat.Presheaf.presheafEquivOfIso_unitIso_inv_app_app, CategoryTheory.Limits.coend.map_comp, CategoryTheory.StrictlyUnitaryLaxFunctorCore.mapComp_naturality_left, CategoryTheory.unit_mateEquiv_symm, CategoryTheory.Functor.prod'_map, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_comp_ι_assoc, CategoryTheory.ObjectProperty.InheritedFromSource.instMin, CategoryTheory.Limits.isLimitOfCoconeOfConeUnop_lift, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_right, CategoryTheory.Limits.inr_inr_pushoutRightPushoutInlIso_hom_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁'_obj_map_app, CategoryTheory.Comma.mapLeftId_hom_app_left, CochainComplex.cm5b.instMonoFIntI, CategoryTheory.Limits.pullbackConeOfRightIso_π_app_left, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_left_assoc, CategoryTheory.Limits.FintypeCat.instPreservesFiniteColimitsFintypeCatForgetHomCarrier, CategoryTheory.MonoidalOpposite.mopMopEquivalence_counitIso_inv_app, CategoryTheory.WithTerminal.prelaxfunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.Abelian.coimage_image_factorisation_assoc, SemiNormedGrp.explicitCokernelIso_hom_π, CategoryTheory.Limits.walkingCospanOpEquiv_functor_map, AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff, AlgebraicGeometry.IsProper.comp_iff, CategoryTheory.Iso.homToEquiv_apply, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd, CategoryTheory.SimplicialObject.δ_comp_σ_of_gt_assoc, CochainComplex.HomComplex.CohomologyClass.toHom_bijective, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp, CategoryTheory.Functor.Monoidal.whiskerRight_μ_δ, CategoryTheory.Limits.Cone.toStructuredArrowCompProj_hom_app, CategoryTheory.ShortComplex.LeftHomologyMapData.zero_φK, CategoryTheory.Grpd.id_eq_id, Compactum.continuous_of_hom, CategoryTheory.IsCofiltered.eq_condition_assoc, CategoryTheory.Limits.Trident.ofCone_π, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop_assoc, CategoryTheory.Limits.ImageMap.map_ι, CategoryTheory.SmallObject.functorMap_comm, CategoryTheory.Functor.curryingEquiv_apply_map, CommSemiRingCat.id_apply, CategoryTheory.Presieve.FamilyOfElements.compPresheafMap_comp, CategoryTheory.Bifunctor.diagonal, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₂, CategoryTheory.ShortComplex.HomologyMapData.add_right, CompHausLike.pullback.cone_π, CategoryTheory.Limits.Cocone.w, CategoryTheory.NatTrans.app_sum, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv, CategoryTheory.Limits.pushoutIsoOpPullback_inr_hom, CategoryTheory.GradedObject.Monoidal.ι_tensorObjDesc, CategoryTheory.Limits.PreservesEqualizer.iso_inv_ι, CategoryTheory.CostructuredArrow.prodInverse_map, Rep.linearizationTrivialIso_inv_hom, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_fst_assoc, CategoryTheory.Functor.initial_iff_of_isCofiltered, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_naturality_assoc, CategoryTheory.Grp.comp_hom_hom, CategoryTheory.Adjunction.Triple.epi_rightToLeft_app_iff, CategoryTheory.Join.mapPairId_inv_app, CategoryTheory.Functor.const.opObjOp_inv_app, CategoryTheory.Pseudofunctor.map₂_left_unitor_app, CategoryTheory.ShortComplex.f'_cyclesMap', BddDistLat.id_apply, CategoryTheory.LocalizerMorphism.RightResolution.Hom.comm, HomologicalComplex.mapBifunctorAssociatorX_hom_D₁, CategoryTheory.Functor.LaxMonoidal.tensorUnit_whiskerLeft_comp_leftUnitor_hom_assoc, CategoryTheory.Limits.biproduct.matrix_π, CategoryTheory.Presheaf.isLocallyInjective_comp_iff, CategoryTheory.Limits.biproduct.total, CategoryTheory.Limits.prodComparison_natural_of_natTrans, CategoryTheory.Functor.CorepresentableBy.equivUliftCoyonedaIso_symm_apply_homEquiv, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ_assoc, CategoryTheory.Bicategory.associator_inv_naturality_right_assoc, CategoryTheory.Adjunction.rightAdjointUniq_hom_counit, CategoryTheory.ShortComplex.LeftHomologyData.homologyIso_hom_comp_leftHomologyIso_inv_assoc, CategoryTheory.Functor.map_comp_assoc, groupHomology.chainsMap_f_0_comp_chainsIso₀_assoc, CategoryTheory.Preadditive.coforkOfCokernelCofork_π, AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap, CategoryTheory.ShortComplex.SnakeInput.L₀X₂ToP_comp_φ₁_assoc, CategoryTheory.Limits.cokernelEpiComp_inv, AlgebraicGeometry.Scheme.Spec_map_stalkSpecializes_fromSpecStalk_assoc, CategoryTheory.Equivalence.cancel_unit_right_assoc', CategoryTheory.FunctorToTypes.functorHomEquiv_apply_app, CategoryTheory.Iso.hom_inv_id_triangle_hom₃, AlgebraicTopology.DoldKan.MorphComponents.preComp_φ, CategoryTheory.Bimon.id_hom', CategoryTheory.GrpObj.zpow_comp, CategoryTheory.Limits.biprod.inrCokernelCofork_π, CategoryTheory.Comma.mapLeftId_inv_app_left, CategoryTheory.Limits.IsTerminal.subsingleton_to, AlgebraicGeometry.morphismRestrict_appTop, CategoryTheory.Functor.commShiftOfLocalization.iso_hom_app, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_right, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp, AlgebraicGeometry.Scheme.IdealSheafData.ofIdealTop_ideal, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_self_assoc, CategoryTheory.Comonad.delta_naturality, AlgebraicGeometry.AffineTargetMorphismProperty.cancel_right_of_respectsIso, CategoryTheory.MonObj.mul_mul_mul_comm', CategoryTheory.ShortComplex.rightHomologyMap_sub, CategoryTheory.Functor.mapMonIdIso_inv_app_hom, CategoryTheory.ShortComplex.LeftHomologyData.op_p, CategoryTheory.CartesianMonoidalCategory.lift_snd_assoc, CategoryTheory.Functor.fun_inv_map, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π, CategoryTheory.StrictPseudofunctor.toFunctor_map, Bimod.one_actLeft, CategoryTheory.GlueData'.cocycle_assoc, CategoryTheory.Bicategory.Prod.snd_mapId_hom, CategoryTheory.Iso.isoCompInverse_inv_app, CategoryTheory.LocalizerMorphism.LeftResolution.comp_f, CategoryTheory.NatTrans.app_shift_assoc, CochainComplex.HomComplex.Cochain.fromSingleMk_precomp, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality, CategoryTheory.Bicategory.hom_inv_whiskerRight_assoc, CategoryTheory.MonObj.pow_comp_assoc, CategoryTheory.Presieve.IsSheafFor.functorInclusion_comp_extend, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_app_assoc, CategoryTheory.Bicategory.triangle, CategoryTheory.HopfObj.mul_antipode₁, CategoryTheory.GradedObject.comapEq_hom_app, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_unitIso, CategoryTheory.Functor.mapConePostcomposeEquivalenceFunctor_hom_hom, CompHausLike.const_comp, CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_inv, CategoryTheory.Pseudofunctor.StrongTrans.leftUnitor_hom_as_app, CategoryTheory.MonoidalCategory.associator_naturality, CategoryTheory.sum.inrCompAssociator_hom_app_down_down, CategoryTheory.Limits.limit.conePointUniqueUpToIso_hom_comp, CategoryTheory.cosimplicialSimplicialEquiv_unitIso_inv_app, AlgebraicTopology.DoldKan.Q_f_naturality_assoc, HomologicalComplex.mapBifunctor₂₃.ι_D₁_assoc, CategoryTheory.Limits.pullbackObjIso_hom_comp_fst_assoc, CategoryTheory.Limits.Pi.ι_π_assoc, CategoryTheory.ObjectProperty.EssentiallySmall.exists_small_le, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_inv_hom', CategoryTheory.Comma.fromProd_map_right, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_limit_map, CategoryTheory.FunctorToTypes.map_id_apply, CategoryTheory.Triangulated.SpectralObject.triangle_mor₁, CategoryTheory.Limits.ι_comp_coequalizerComparison_assoc, TopCat.Presheaf.stalkPushforward_germ, CategoryTheory.Arrow.inv_hom_id_left_assoc, CategoryTheory.Bimon.trivialTo_hom, CategoryTheory.Localization.Preadditive.add_eq, CategoryTheory.Limits.prod.associator_inv, SSet.Truncated.spine_vertex, CategoryTheory.Limits.isoZeroOfMonoZero_inv, CategoryTheory.ε_app_obj, CategoryTheory.ShortComplex.ShortExact.δ_comp_assoc, CategoryTheory.Functor.toSheafify_pullbackSheafificationCompatibility, HomologicalComplex.singleObjCyclesSelfIso_inv_iCycles_assoc, AlgebraicGeometry.PresheafedSpace.id_base, groupHomology.inhomogeneousChains.ext_iff, CategoryTheory.Limits.BinaryCofan.op_mk, CategoryTheory.Over.tensorHom_left_fst, CategoryTheory.Sheaf.ΓHomEquiv_naturality_right_symm, AlgebraicGeometry.SheafedSpace.comp_hom_c_app', CategoryTheory.Functor.map_units_smul, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_right_assoc, SimplexCategory.revCompRevIso_hom_app, CategoryTheory.MonoidalCategory.whisker_assoc_symm_assoc, Action.ρ_one, CategoryTheory.Functor.IsCoverDense.Types.naturality_apply, CategoryTheory.Limits.biprod.inr_desc_assoc, Homotopy.compLeftId_hom, SemimoduleCat.ofHom_id, CategoryTheory.Iso.hom_inv_id_app_assoc, CategoryTheory.MonoidalOpposite.tensorRightIso_hom_app_unmop, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_symm_apply_f, SimplicialObject.opFunctorCompOpFunctorIso_hom_app_app, CategoryTheory.Equivalence.induced_unitIso, CategoryTheory.Equivalence.sheafCongr.functor_obj_val_map, CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_snd, Bimod.TensorBimod.left_assoc', CategoryTheory.Limits.limit_map_limitObjIsoLimitCompEvaluation_hom_assoc, CategoryTheory.CatEnrichedOrdinary.Hom.comp_eq, CategoryTheory.MorphismProperty.Over.mk_left, SSet.range_eq_iSup_sigma_ι, CategoryTheory.GlueData'.cocycle, CategoryTheory.Triangulated.TStructure.ge_antitone, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapId_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.whiskerLeft_actionHomLeft, CategoryTheory.instIsMod_HomId, HomologicalComplex.singleObjOpcyclesSelfIso_hom_naturality_assoc, CochainComplex.HomComplex.Cocycle.fromSingleMk_zero, CategoryTheory.CosimplicialObject.δ_comp_σ_succ, AlgebraicGeometry.ΓSpecIso_hom_stalkClosedPointIso_inv, MonObj.mopEquiv_unitIso_hom_app_hom, CategoryTheory.Pseudofunctor.ObjectProperty.mapId_hom_app, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_assoc, CategoryTheory.IsPullback.paste_vert, CategoryTheory.Over.whiskerRight_left_snd, TopCat.Presheaf.stalkPushforward.id, germ_skyscraperPresheafStalkOfSpecializes_hom_assoc, AlgebraicGeometry.Scheme.instIsOverFstOverInferInstanceOverClassId, CategoryTheory.NatTrans.rightOpWhiskerRight_assoc, CategoryTheory.CartesianMonoidalCategory.braiding_hom_fst_assoc, CategoryTheory.Iso.isoInverseOfIsoFunctor_inv_app, CategoryTheory.SmallObject.SuccStruct.ofCocone_map_to_top, CategoryTheory.Limits.CatCospanTransform.id_whiskerLeft_assoc, SSet.Subcomplex.range_comp, HomologicalComplex.zero_f_apply, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_apply, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃_eq, CategoryTheory.DifferentialObject.shiftFunctor_map_f, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_π_app, CategoryTheory.Functor.commShiftIso_id_hom_app, CategoryTheory.Grothendieck.ιCompMap_inv_app_base, CategoryTheory.Dial.comp_F, CategoryTheory.Over.conePostIso_inv_app_hom, CategoryTheory.Bicategory.Prod.sectR_map₂, CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair_inv_app, CategoryTheory.Square.Hom.comp_τ₄, CategoryTheory.Limits.colimit.desc_cocone, CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id_app, CategoryTheory.PreGaloisCategory.fiber_in_connected_component, CategoryTheory.instSmallHomDerivedCategoryObjSingleFunctorOfHasExt, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_mapPullbackAdj_unit_app, CategoryTheory.congrArg_mpr_hom_left, AlgebraicGeometry.Scheme.descResidueField_stalkClosedPointTo_fromSpecResidueField, CategoryTheory.GrpObj.eq_lift_inv_right, CategoryTheory.Functor.shiftIso_hom_app_comp_assoc, CategoryTheory.Preadditive.hasCokernel_of_hasCoequalizer, CategoryTheory.Limits.biprod.add_eq_lift_desc_id, CategoryTheory.Mon.trivial_mon_one, CategoryTheory.FreeMonoidalCategory.instSubsingletonHomCompDiscreteNormalMonoidalObject, CategoryTheory.strongEpi_comp, CategoryTheory.ShortComplex.Splitting.g_s_assoc, CategoryTheory.Functor.LaxLeftLinear.μₗ_naturality_left, CategoryTheory.Limits.biprod.inl_desc, CategoryTheory.ObjectProperty.instSmallPair, CategoryTheory.WithInitial.map_map, CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_hom_π_π, CategoryTheory.ShortComplex.SnakeInput.id_f₀, SSet.stdSimplex.objEquiv_symm_comp, CategoryTheory.SimplicialObject.Augmented.w₀_assoc, CategoryTheory.Limits.Multiequalizer.ιPi_π, CategoryTheory.Functor.Fiber.inducedFunctorCompIsoSelf_hom_app, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃_assoc, CategoryTheory.StrictPseudofunctorPreCore.map₂_whisker_right, CategoryTheory.ProjectiveResolution.extMk_zero, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj_condition, AlgebraicGeometry.IsOpenImmersion.isoOfRangeEq_hom_fac, HopfAlgCat.toBialgHom_id, CategoryTheory.Functor.curryObjCompIso_inv_app_app, CategoryTheory.Adjunction.Triple.leftToRight_app_map_adj₁_unit_app_assoc, CategoryTheory.leftDistributor_rightDistributor_assoc, CategoryTheory.Limits.coprod.map_codiag_assoc, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapIdIso_inv, CategoryTheory.PrelaxFunctor.id_toPrelaxFunctorStruct, CategoryTheory.ChosenPullbacksAlong.pullbackComp_hom_counit, TopCat.Presheaf.germ_stalkPullbackHom_assoc, CategoryTheory.Equivalence.inv_fun_map_assoc, CategoryTheory.ShortComplex.Homotopy.equivSubZero_apply, CategoryTheory.Limits.inl_inr_pushoutAssoc_inv, CategoryTheory.PresheafOfGroups.OneCochain.ev_precomp, CategoryTheory.ShortComplex.Splitting.f_r_assoc, CategoryTheory.ShortComplex.homologyπ_comp_leftHomologyIso_inv_assoc, CategoryTheory.Limits.pullbackComparison_comp_snd_assoc, CategoryTheory.Functor.biprodComparison_snd, CategoryTheory.Limits.CatCospanTransform.pentagon, CategoryTheory.GradedObject.mapBifunctorMap_map_app, TopCat.Presheaf.whiskerIsoMapGenerateCocone_hom_hom, CategoryTheory.comp_apply, CategoryTheory.Subobject.factorThru_ofLE, AlgebraicGeometry.coprodSpec_inr_assoc, CategoryTheory.Equivalence.inverse_counitInv_comp_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd_assoc, Action.add_hom, CategoryTheory.Functor.mapCommGrpIdIso_hom_app_hom_hom_hom, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_inv_app_val_app, ModuleCat.ihom_map_apply, CategoryTheory.MonObj.mul_mul_mul_comm_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd, CategoryTheory.Presieve.factorsThruAlong_id, CategoryTheory.FreeBicategory.normalize_naturality, HomologicalComplex.d_comp_XIsoOfEq_hom_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom, FintypeCat.comp_hom_assoc, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransEq_hom_app_f, CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_inv, CategoryTheory.WithTerminal.subsingleton_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocIso_hom_naturality_assoc, CategoryTheory.rightAdjointMate_id, CategoryTheory.StrictPseudofunctor.id_map₂, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_hom, CategoryTheory.Limits.biproduct.lift_map_assoc, CategoryTheory.Limits.pullbackDiagonalMapIso.inv_fst, SheafOfModules.sectionsMap_comp, CategoryTheory.Sheaf.ΓObjEquivHom_naturality, CategoryTheory.obj_μ_inv_app, AlgebraicGeometry.IsClosedImmersion.Spec_iff, Action.ρAut_apply_hom, CategoryTheory.Limits.Cocones.extendComp_inv_hom, CategoryTheory.Limits.sigmaSigmaIso_inv, SimplexCategory.δ_injective, CategoryTheory.HomOrthogonal.matrixDecomposition_apply, HomologicalComplex.pOpcycles_extendOpcyclesIso_hom_assoc, CategoryTheory.Limits.colimit.ι_desc, CategoryTheory.Bicategory.Prod.sectL_map, CategoryTheory.NatTrans.appHom_apply, HomologicalComplex.toCycles_eq_zero, CategoryTheory.End.smul_right, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_left_symm, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app, CategoryTheory.LocallyDiscrete.mkPseudofunctor_mapComp, CategoryTheory.CommSq.unop, CategoryTheory.Functor.IsRepresentedBy.uliftYonedaIso_hom, CategoryTheory.IsHomLift.id_lift_eqToHom_domain, CategoryTheory.Bicategory.conjugateIsoEquiv_apply_hom, AlgebraicGeometry.isPreimmersion_eq_inf, AlgebraicGeometry.Scheme.Hom.comp_toLRSHom, CategoryTheory.Limits.end_.map_comp, CategoryTheory.NonPreadditiveAbelian.neg_add, CategoryTheory.Functor.OplaxMonoidal.associativity_inv, CategoryTheory.Monad.algebraPreadditive_homGroup_zero_f, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_σ_assoc, CategoryTheory.monoidalOfHasFiniteCoproducts.rightUnitor_hom, CategoryTheory.GrothendieckTopology.isoToPlus_inv, AlgebraicGeometry.AffineSpace.map_id, CategoryTheory.Sheaf.ΓRes_map, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_self, CategoryTheory.Bicategory.id_whiskerRight, CategoryTheory.MorphismProperty.CostructuredArrow.mk_left, CategoryTheory.NatTrans.leftDerived_comp_assoc, SimplexCategory.δ_comp_δ_self_assoc, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv, CategoryTheory.functorProdToProdFunctor_map, SheafOfModules.pushforwardCongr_symm, CategoryTheory.Functor.mapCommMon_obj_mon_one, CategoryTheory.Functor.Monoidal.μ_fst, CategoryTheory.Limits.biproduct.whiskerEquiv_hom, CategoryTheory.NatTrans.CommShift₂.instCompFunctor, CategoryTheory.Functor.const.unop_functor_op_obj_map, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_inv_fac, CategoryTheory.Bicategory.conjugateIsoEquiv_symm_apply_hom, HomologicalComplex.homotopyCofiber.inlX_d'_assoc, CategoryTheory.kernelUnopUnop_hom, CategoryTheory.Functor.leftOpComp_inv_app, CochainComplex.mappingCone.inr_f_fst_v_assoc, CategoryTheory.NatTrans.tensor_naturality, CategoryTheory.Pseudofunctor.mapComp'_inv_comp_mapComp'_hom, CategoryTheory.Limits.biproduct.matrix_desc, CategoryTheory.IsPullback.of_hasBinaryBiproduct, CategoryTheory.Functor.CommShift.ofIso_commShiftIso_inv_app, groupHomology.π_map_assoc, CategoryTheory.MonObj.ofRepresentableBy_mul, Homotopy.add_hom, CategoryTheory.Comma.opFunctorCompFst_hom_app, CategoryTheory.Limits.Cofork.IsColimit.homIso_natural, CategoryTheory.LocalizerMorphism.homMap_comp_assoc, CategoryTheory.Localization.homEquiv_refl, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_π_assoc, groupHomology.congr, CategoryTheory.CommComon.trivial_comon_counit, CategoryTheory.IsPushout.inl_snd, CategoryTheory.Lax.StrongTrans.naturality_id_assoc, CategoryTheory.DifferentialObject.objEqToHom_refl, groupCohomology.mapCocycles₁_comp_i_assoc, CategoryTheory.Limits.prod.inl_fst_assoc, CategoryTheory.InjectiveResolution.ι'_f_zero_assoc, CategoryTheory.ShortComplex.homologyOpIso_inv_naturality_assoc, CategoryTheory.monoidalOpOp_ε, CategoryTheory.Limits.pullbackAssoc_hom_snd_snd_assoc, CategoryTheory.CatCenter.mul_app'_assoc, CategoryTheory.underToAlgebra_obj_a, CategoryTheory.Comma.toPUnitIdEquiv_unitIso_hom_app_left, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit_assoc, CategoryTheory.ChosenPullbacksAlong.pullbackMap_id, HomologicalComplex₂.totalFlipIsoX_hom_D₁, Rep.applyAsHom_comm, Action.trivial_ρ, CategoryTheory.Limits.WalkingParallelFamily.hom_id, CategoryTheory.Functor.Fiber.homMk_comp, CategoryTheory.ShortComplex.id_τ₂, CategoryTheory.CatCommSq.vInv_iso_inv_app, CategoryTheory.CartesianMonoidalCategory.braiding_inv_fst, CochainComplex.mappingCone.inl_v_d_assoc, CategoryTheory.regularTopology.equalizerCondition_w', CategoryTheory.MarkovCategory.discard_natural_assoc, AlgebraicGeometry.Scheme.Pullback.openCoverOfBase'_f, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_naturality₂, CategoryTheory.Localization.homEquiv_trans, CommAlgCat.toUnit_unop_hom, CochainComplex.mappingCone.cocycleOfDegreewiseSplit_triangleRotateShortComplexSplitting_v, Bimod.whisker_assoc_bimod, CategoryTheory.Limits.ι_colimitOfIsReflexivePairIsoCoequalizer_hom, CategoryTheory.Limits.Multicofork.fst_app_right, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse_assoc, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_cofanPtIsoSelf_inv, SSet.ι₀_comp_assoc, AlgebraicGeometry.pullbackSpecIso_inv_fst_assoc, CategoryTheory.ShortComplex.LeftHomologyData.ofAbelian_π, AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_naturality_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_comp, SimplicialObject.Splitting.PInfty_comp_πSummand_id_assoc, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv', CategoryTheory.MorphismProperty.ContainsIdentities.eqToHom, CategoryTheory.IsPullback.of_is_bilimit', CategoryTheory.Functor.constCompEvaluationObj_inv_app, CategoryTheory.oppositeShiftFunctorZero_hom_app, CategoryTheory.IsIso.eq_comp_inv, CategoryTheory.Comma.mapRightIso_unitIso_hom_app_left, HomologicalComplex.inr_biprodXIso_inv_assoc, AlgebraicGeometry.Scheme.Pullback.ofPointTensor_SpecTensorTo, HomologicalComplex.truncLE'_d_eq, ChainComplex.mk'_d, CategoryTheory.Limits.limitCompYonedaIsoCocone_inv, HomologicalComplex.singleMapHomologicalComplex_inv_app_ne, PresheafOfModules.Hom.naturality_assoc, CategoryTheory.MonoidalOpposite.tensorRightIso_inv_app_unmop, RingCat.ofHom_id, CategoryTheory.Limits.asEmptyCone_π_app, CategoryTheory.Localization.Monoidal.whiskerRight_comp_assoc, CategoryTheory.Quotient.inv_mk, CategoryTheory.Limits.fiberwiseColimCompEvaluationIso_hom_app, CategoryTheory.Functor.LaxRightLinear.μᵣ_unitality, CategoryTheory.nerve_map, CategoryTheory.Limits.Fork.op_ι_app, AlgebraicGeometry.Scheme.Hom.id_base, AlgebraicGeometry.AffineSpace.functor_map_app, CategoryTheory.Limits.biproduct.matrix_π_assoc, HomologicalComplex.pOpcycles_extendOpcyclesIso_inv, CategoryTheory.Comma.fromProd_map_left, CategoryTheory.Functor.LaxMonoidal.μ_whiskerRight_comp_μ_assoc, CategoryTheory.Idempotents.Karoubi.decompId_i_toKaroubi, CategoryTheory.SimplicialObject.cechNerveEquiv_symm_apply, CategoryTheory.Mathlib.Tactic.MonTauto.associator_inv_comp_tensorHom_tensorHom_comp_assoc, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counitIso_hom_app_assoc, SheafOfModules.add_val, CategoryTheory.IsFiltered.crown₃, CategoryTheory.ShortComplex.HasLeftHomology.of_hasKernel, AlgebraicGeometry.Scheme.Modules.Hom.sub_app, CategoryTheory.functorProdFunctorEquivCounitIso_inv_app_app, CategoryTheory.ShortComplex.mapCyclesIso_hom_naturality_assoc, CategoryTheory.ι_preservesColimitIso_hom, CategoryTheory.ObjectProperty.le_colimitsClosure, CategoryTheory.ShortComplex.rightHomologyMap_op, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id_assoc, HomologicalComplex.truncLE'ToRestriction_naturality_assoc, AlgebraicGeometry.Scheme.LocalRepresentability.yoneda_toGlued_yonedaGluedToSheaf, CategoryTheory.Limits.pullbackLeftPullbackSndIso_hom_snd, CategoryTheory.Functor.Monoidal.tensorHom_app_snd, CategoryTheory.Functor.prod_δ_snd, CategoryTheory.Bicategory.iterated_mateEquiv_conjugateEquiv_symm, CategoryTheory.conjugateEquiv_comp_assoc, HomologicalComplex.dgoToHomologicalComplex_map_f, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.iso_hom_naturality_assoc, CompHaus.lift_lifts_assoc, CategoryTheory.Limits.BinaryBicone.inrCokernelCofork_π, groupHomology.eq_d₃₂_comp_inv_assoc, AlgebraicGeometry.LocallyRingedSpace.restrict_presheaf_map, CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_hom_assoc, CategoryTheory.algebraToUnder_obj, CategoryTheory.Limits.biproduct.π_comp_eqToHom_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.inv_hom_actionHomLeft'_assoc, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_incl, CategoryTheory.Limits.Types.binaryProductIso_inv_comp_snd, CategoryTheory.MonoidalClosed.curry_natural_left_assoc, CategoryTheory.ObjectProperty.ι_μ, CategoryTheory.associativity_app_assoc, CategoryTheory.Oplax.OplaxTrans.naturality_id, CategoryTheory.Limits.equalizerSubobject_arrow, Semigrp.ofHom_id, CategoryTheory.Limits.coprod.inr_map_assoc, CategoryTheory.coyonedaEquiv_coyoneda_map, CategoryTheory.Limits.ColimitPresentation.Total.Hom.w_assoc, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv_desc, CategoryTheory.TwoSquare.whiskerLeft_app, CategoryTheory.Functor.pointwiseRightKanExtensionCounit_app, CategoryTheory.CatCenter.smul_iso_hom_eq_assoc, CategoryTheory.endofunctorMonoidalCategory_leftUnitor_hom_app, AlgebraicGeometry.isProper_eq, CategoryTheory.Limits.pullbackZeroZeroIso_hom_fst, CategoryTheory.Limits.Types.binaryProductIso_hom_comp_fst, CategoryTheory.Idempotents.KaroubiKaroubi.idem_f, CategoryTheory.ShortComplex.Homotopy.op_h₃, CategoryTheory.IsUniversalColimit.isPullback_of_isColimit_right, CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp_inv_hom₂, CategoryTheory.Bicategory.rightUnitor_comp, CategoryTheory.Bicategory.whiskerRight_id_symm, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_naturality, AlgebraicGeometry.ΓSpec.adjunction_homEquiv_apply, CategoryTheory.Iso.cancel_iso_hom_left, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_fst, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_app, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_assoc, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_hom_inv, CategoryTheory.ConcreteCategory.coe_id, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_inv_comp_π, CategoryTheory.sheafifyMap_comp, CategoryTheory.Groupoid.vertexGroupIsomOfMap_symm_apply, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f, AlgebraicGeometry.SheafedSpace.comp_hom_base, CategoryTheory.StrictlyUnitaryPseudofunctor.mk'_obj, CategoryTheory.CartesianClosed.uncurry_natural_right_assoc, HomologicalComplex.ι_mapBifunctorDesc_assoc, CategoryTheory.Limits.map_lift_piComparison_assoc, CategoryTheory.ObjectProperty.retractClosure_le_iff, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_assoc, CategoryTheory.GrpObj.left_inv, HomologicalComplex.homology_π_ι_assoc, CategoryTheory.Limits.coneOfSectionCompYoneda_π, CategoryTheory.ShortComplex.sub_τ₂, CategoryTheory.OplaxFunctor.mapComp_id_right, CategoryTheory.CosimplicialObject.σ_comp_σ, CategoryTheory.Equivalence.map_η_comp_η_assoc, CategoryTheory.op_add, CategoryTheory.Limits.pullback.comp_diagonal, CategoryTheory.Comma.opFunctorCompFst_inv_app, CategoryTheory.Functor.OplaxMonoidal.δ_fst, AddGrpCat.ofHom_comp, CategoryTheory.Limits.hasEqualizer_precomp_of_equalizer, CategoryTheory.eComp_eHomWhiskerLeft, CategoryTheory.Limits.imageSubobject_arrow_comp_assoc, CategoryTheory.braiding_rightUnitor_aux₂, CategoryTheory.SymmetricCategory.symmetry, CategoryTheory.shiftZero', CategoryTheory.Limits.coend.ι_map, CategoryTheory.Limits.cospan_map_id, CategoryTheory.ShortComplex.LeftHomologyData.f'_i_assoc, CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_hom, CategoryTheory.Limits.Cocones.eta_hom_hom, AlgebraicGeometry.Scheme.Opens.isoOfLE_inv_ι, CategoryTheory.SmallObject.functorMapSrc_functorObjTop_assoc, CategoryTheory.Bicategory.triangle_assoc_comp_right, CategoryTheory.CostructuredArrow.toStructuredArrow_obj, CategoryTheory.Limits.prod.map_map_assoc, CategoryTheory.GrothendieckTopology.sheafifyMap_comp, AlgebraicGeometry.Scheme.Hom.ι_toNormalization_assoc, CategoryTheory.Monoidal.InducingFunctorData.whiskerRight_eq, CategoryTheory.ShortComplex.Homotopy.trans_h₃, HomotopicalAlgebra.RightHomotopyRel.postcomp, CategoryTheory.Limits.FormalCoproduct.mapPower_comp, CategoryTheory.Limits.Pi.map_eq_prod_map, CategoryTheory.MonoidalCategory.tensor_map, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.fac_assoc, CategoryTheory.Pseudofunctor.toDescentData_obj, CategoryTheory.Limits.isIso_kernelSubobject_zero_arrow, CategoryTheory.Limits.ι_comp_sigmaObjIso_hom_assoc, CategoryTheory.Mat_.ι_additiveObjIsoBiproduct_inv, HomotopicalAlgebra.trivialFibrations_eq_unop, AlgebraicGeometry.instQuasiCompactLiftSchemeIdOfQuasiSeparatedSpaceCarrierCarrierCommRingCat, CategoryTheory.Bicategory.comp_whiskerLeft_assoc, CategoryTheory.ShortComplex.rightHomologyMap'_comp, CategoryTheory.Limits.diagramIsoParallelFamily_hom_app, CategoryTheory.Functor.coreId_hom_app_iso_inv, AlgebraicGeometry.Scheme.Hom.Spec_map_residueFieldMap_fromSpecResidueField_assoc, CategoryTheory.Bicategory.InducedBicategory.forget_mapComp_hom, CategoryTheory.Presheaf.isStrongGenerator, CategoryTheory.Bimon.mul_counit, AugmentedSimplexCategory.tensor_id, SSet.Truncated.Edge.id_edge, CategoryTheory.ShortComplex.rightHomologyMap'_sub, CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_hom, CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ, CategoryTheory.ParametrizedAdjunction.unit_whiskerRight_map_assoc, CategoryTheory.MonoidalCategory.tensor_whiskerLeft_assoc, CategoryTheory.Over.star_map_left, CategoryTheory.Presieve.bind_comp, CategoryTheory.SimplicialObject.δ_naturality_assoc, CategoryTheory.MonoidalCategory.rightUnitor_naturality_assoc, CategoryTheory.Functor.mapTriangleCompIso_inv_app_hom₁, CategoryTheory.Pseudofunctor.mapComp_id_right_inv, CategoryTheory.ShortComplex.Homotopy.neg_h₃, CategoryTheory.StrictlyUnitaryPseudofunctor.id_map₂, SimplexCategory.Truncated.δ₂_two_comp_σ₂_zero, groupCohomology.π_comp_H2Iso_hom_assoc, AlgebraicGeometry.PresheafedSpace.toRestrictTop_c, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inl, SSet.ι₀_comp, CategoryTheory.ModObj.assoc_flip, CategoryTheory.ShortComplex.Homotopy.unop_h₁, CategoryTheory.Limits.colimit.post_post, CategoryTheory.Bicategory.whiskerLeft_inv_hom_assoc, CategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy.f, CategoryTheory.Comma.unopFunctor_map, CategoryTheory.Limits.pushout.desc_inl_inr, CategoryTheory.Over.tensorHom_left_fst_assoc, CategoryTheory.Functor.pi'CompEval_inv_app, CategoryTheory.Mon.tensorUnit_one, CategoryTheory.MonoidalCategory.DayFunctor.comp_natTrans, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd_assoc, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_app_assoc, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc, TopCat.Presheaf.germ_stalkPullbackInv, CategoryTheory.Limits.Sigma.ι_map_assoc, groupCohomology.H1InfRes_g, CategoryTheory.Monad.algebraFunctorOfMonadHom_obj_a, CategoryTheory.CartesianMonoidalCategory.rightUnitor_inv_snd, HomotopicalAlgebra.FibrantObject.homMk_homMk_assoc, Action.Hom.comm_assoc, CategoryTheory.Join.mapWhiskerRight_whiskerLeft, AlgebraicTopology.DoldKan.Q_succ, CategoryTheory.preservesHomology_preadditiveYonedaObj_of_injective, CategoryTheory.forgetAdjToOver.homEquiv_symm, CategoryTheory.Functor.map_inv_hom_assoc, CommBialgCat.ofSelfIso_hom, CategoryTheory.ShortComplex.homologyMap_sub, CategoryTheory.Limits.MultispanIndex.inj_sndSigmaMapOfIsColimit_assoc, CategoryTheory.Localization.Monoidal.associator_naturality₂_assoc, CategoryTheory.tensorHom_eComp_op_eq, CategoryTheory.preservesLimitIso_hom_π_assoc, HomologicalComplex.cyclesMap_zero, CondensedSet.isDiscrete_tfae, CategoryTheory.Limits.Types.binaryProductIso_hom_comp_snd, CategoryTheory.ShortComplex.leftRightHomologyComparison'_eq_liftH, CategoryTheory.linearCoyoneda_obj_map, AlgebraicGeometry.Flat.comp, AlgebraicGeometry.Scheme.Cover.Hom.sigma_h₀, Rep.standardComplex.d_comp_ε, CategoryTheory.Limits.CatCospanTransform.category_comp_base, groupCohomology.toCocycles_comp_isoCocycles₂_hom_assoc, prodIsoPullback_hom_fst, HomologicalComplex.single_map_f_self, AlgebraicGeometry.Scheme.Hom.fromNormalization_app_assoc, CategoryTheory.IsHomLift.comp_lift_id_left, CategoryTheory.Dial.isoMk_inv_F, AlgebraicGeometry.Scheme.isoSpec_inv_toSpecΓ_assoc, CategoryTheory.IsCardinalFiltered.wideSpan, CategoryTheory.simplicialCosimplicialEquiv_functor_map_app, CategoryTheory.ShortComplex.toCycles_naturality_assoc, AlgebraicGeometry.Proj.fromOfGlobalSections_morphismRestrict, ChainComplex.fromSingle₀Equiv_symm_apply_f_zero, CategoryTheory.Functor.leftOpRightOpEquiv_counitIso_hom_app_app, CochainComplex.HomComplex.Cocycle.equivHomShift'_apply, CategoryTheory.MorphismProperty.LeftFraction.map_ofInv_hom_id_assoc, AlgebraicGeometry.Scheme.Cover.LocallyDirected.trans_id, CategoryTheory.ChosenPullbacksAlong.condition, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_assoc, CategoryTheory.ObjectProperty.ι_map_top, HomologicalComplex.homologyπ_extendHomologyIso_hom_assoc, CategoryTheory.CatCommSq.hComp_iso_inv_app, CategoryTheory.OverPresheafAux.MakesOverArrow.app, CategoryTheory.ShortComplex.SnakeInput.Hom.id_f₀, CategoryTheory.Pseudofunctor.map₂_whisker_right_app_assoc, FDRep.simple_iff_end_is_rank_one, ContinuousMap.piComparison_fac, CategoryTheory.Limits.isColimitOfConeLeftOpOfCocone_desc, CategoryTheory.Limits.walkingSpanOpEquiv_functor_map, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app_apply, CategoryTheory.Functor.isLeftKanExtension_iff_postcomp₁, CategoryTheory.InjectiveResolution.Hom.ι'_comp_hom'_assoc, AlgebraicGeometry.Scheme.Hom.isoImage_inv_ι, CategoryTheory.Limits.WalkingMultispan.Hom.id_eq_id, CategoryTheory.ShortComplex.Hom.comm₂₃, CategoryTheory.HopfObj.antipode_right_assoc, CategoryTheory.Subfunctor.equalizer.condition, CategoryTheory.Limits.unop_zero, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_π_app, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp, CategoryTheory.ShortComplex.SnakeInput.comp_f₁_assoc, AlgebraicGeometry.AffineSpace.map_comp_assoc, CategoryTheory.Square.unop_f₂₄, CategoryTheory.shiftFunctorAdd_add_zero_inv_app, CategoryTheory.Functor.IsLocalization.unop, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_hom_inv', CategoryTheory.Grp.Hom.hom_mul, AlgebraicGeometry.Scheme.isSeparated_iff_isClosedImmersion_prod_lift, TopologicalSpace.Opens.leSupr_apply_mk, CategoryTheory.Bicategory.mateEquiv_square, CategoryTheory.Dial.associator_inv_F, CategoryTheory.Idempotents.Karoubi.p_comp_assoc, HomotopicalAlgebra.BifibrantObject.homMk_homMk, CategoryTheory.SimplicialObject.δ_comp_σ_succ, CategoryTheory.Presieve.BindStruct.fac_assoc, CategoryTheory.Adjunction.leftAdjointUniq_hom_counit_assoc, PresheafOfModules.comp_toPresheaf_map_sheafifyHomEquiv'_symm_hom, CategoryTheory.Pretriangulated.binaryBiproductTriangle_mor₃, CategoryTheory.Limits.HasZeroObject.zeroIsoInitial_inv, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃_assoc, CategoryTheory.extendFan_π_app, AlgebraicGeometry.PresheafedSpace.comp_base, HomologicalComplex.homologyMap_zero, AlgebraicGeometry.Scheme.GlueData.ι_isoCarrier_inv, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInrIso_hom_app_app, CategoryTheory.Over.prodLeftIsoPullback_inv_fst_assoc, CategoryTheory.Pseudofunctor.StrongTrans.Modification.naturality_assoc, CategoryTheory.ShortComplex.Homotopy.trans_h₀, CategoryTheory.PreZeroHypercover.comp_h₀, CategoryTheory.Limits.lim_μ_π_assoc, CategoryTheory.Lax.LaxTrans.naturality_naturality_assoc, CategoryTheory.ShortComplex.opcyclesMap_zero, CategoryTheory.Bicategory.Adj.forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.Limits.CatCospanTransform.category_comp_right, CategoryTheory.Bicategory.rightUnitor_naturality, CategoryTheory.MonoidalCategory.leftAssocTensor_map, CategoryTheory.Functor.currying_unitIso_inv_app_app_app, CategoryTheory.CountableCategory.instCountableHomHomAsType, CategoryTheory.MonoidalClosed.curry_natural_right_assoc, CategoryTheory.MonoidalCategory.inv_hom_whiskerRight, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_hom_left, CategoryTheory.PreGaloisCategory.exists_hom_from_galois_of_fiber, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_hom_app_hom, CategoryTheory.OverPresheafAux.OverArrows.app_val, AddCommMonCat.ofHom_comp, CategoryTheory.StrictlyUnitaryPseudofunctor.id_map, CategoryTheory.CommMon.trivial_mon_one, CategoryTheory.Localization.Monoidal.tensor_comp_assoc, CategoryTheory.Subobject.bot_arrow, CategoryTheory.Presieve.FamilyOfElements.isAmalgamation_singleton_iff, CategoryTheory.ShortComplex.opcyclesMap_comp, CategoryTheory.Mon.Hom.hom_pow, CategoryTheory.GrpObj.mul_inv_rev_assoc, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map_val_app, CategoryTheory.ShortComplex.neg_τ₂, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_δ_unmop_app, CategoryTheory.Bicategory.whiskerLeft_comp_assoc, AlgebraicGeometry.Scheme.Hom.isoImage_inv_ι_assoc, AlgebraicTopology.NormalizedMooreComplex.map_f, CategoryTheory.Functor.Monoidal.map_μ_δ, CategoryTheory.MonoidalCategory.whiskerLeft_id, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_obj_obj_map, CategoryTheory.Functor.currying_unitIso_hom_app_app_app, CategoryTheory.yonedaCommGrpGrpObj_obj_coe, CategoryTheory.kernelCokernelCompSequence.δ_fac, SemimoduleCat.Iso.conj_eq_conj, CategoryTheory.Subfunctor.range_eq_ofSection, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_iso, CategoryTheory.evaluationUncurried_map, CategoryTheory.orderDualEquivalence_counitIso, CategoryTheory.ConcreteCategory.id_apply, CategoryTheory.Limits.PullbackCone.eta_hom_hom, CategoryTheory.Pseudofunctor.Grothendieck.categoryStruct_id_base, CategoryTheory.Limits.IsZero.iff_isSplitEpi_eq_zero, CategoryTheory.Discrete.productEquiv_counitIso_inv_app, CategoryTheory.FinallySmall.exists_small_weakly_terminal_set, CategoryTheory.Equivalence.counitIso_inv_app_comp_functor_map_η_inverse_assoc, CategoryTheory.ShortComplex.HomologyData.exact_iff_i_p_zero, CategoryTheory.left_comp_retraction, CategoryTheory.CosimplicialObject.Augmented.const_map_left, CategoryTheory.Join.pseudofunctorRight_mapComp_hom_toNatTrans_app, HomologicalComplex.toCycles_comp_homologyπ, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_whiskerRight_assoc, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isoBot_inv, CategoryTheory.Iso.unop_hom_inv_id_app_assoc, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapIdIso_hom, CochainComplex.ConnectData.d_comp_d_assoc, CategoryTheory.CosimplicialObject.δ_comp_δ'', CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_snd, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_assoc, CategoryTheory.Functor.mapCoconeWhisker_inv_hom, CategoryTheory.Adjunction.Triple.leftToRight_eq_counits, CategoryTheory.Monad.MonadicityInternal.comparisonAdjunction_unit_f_aux, CategoryTheory.Limits.coprod.desc_inl_inr, CategoryTheory.MonObj.comp_mul, CategoryTheory.MonoidalCategory.triangle, CategoryTheory.CommSq.op, CategoryTheory.Limits.colimit.pre_map', CategoryTheory.MorphismProperty.Under.Hom.ext_iff, AlgebraicGeometry.Scheme.Modules.pushforwardId_hom_app_app, AddCommGrpCat.ofHom_id, Homotopy.compRightId_hom, HomotopicalAlgebra.instCofibrationCompOfIsStableUnderCompositionCofibrations, CategoryTheory.LocallyDiscrete.eqToHom_toLoc, CategoryTheory.CartesianMonoidalCategory.comp_lift_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_assoc, CategoryTheory.Pretriangulated.binaryProductTriangleIsoBinaryBiproductTriangle_inv_hom₃, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_ι, CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id_app, CommAlgCat.one_op_of_unop_hom, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app, CategoryTheory.GradedObject.Monoidal.braiding_naturality_right, CategoryTheory.WithInitial.inclLiftToInitial_hom_app, CategoryTheory.Limits.coprodComparison_inv_natural_assoc, AlgebraicGeometry.Scheme.Hom.germ_stalkMap, CategoryTheory.SmallObject.SuccStruct.ofCocone.map_comp, HeytAlg.ofHom_comp, CategoryTheory.LaxFunctor.map₂_rightUnitor_assoc, CategoryTheory.Pi.sum_obj_map, CategoryTheory.Lax.StrongTrans.naturality_comp, CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt'_assoc, AlgebraicGeometry.Scheme.Hom.ker_comp, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_inv_assoc, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.fromBiprod_biprodIsoProd_inv_apply, CategoryTheory.ShiftedHom.opEquiv_symm_apply_comp, CategoryTheory.instIsMonHomId, CategoryTheory.Limits.pullback.diagonal_fst_assoc, CategoryTheory.braiding_rightUnitor, CategoryTheory.IsHomLift.lift_comp_eqToHom_iff, CategoryTheory.yonedaPairing_map, CategoryTheory.Monad.MonadicityInternal.comparisonAdjunction_counit, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst, CategoryTheory.Localization.isoOfHom_hom_inv_id, CategoryTheory.Lax.OplaxTrans.naturality_id_assoc, CochainComplex.HomComplex.Cochain.smul_v, CategoryTheory.Over.η_pullback_left, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_hom_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.Functor.toOplaxFunctor_map, CategoryTheory.MorphismProperty.Comma.comp_left, CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt, AlgebraicGeometry.ExistsHomHomCompEqCompAux.ha, HomologicalComplex₂.D₂_D₂_assoc, AlgebraicGeometry.Scheme.toOpen_eq, groupCohomology.mapShortComplexH1_id_comp, FintypeCat.hom_apply, CategoryTheory.Functor.IsCocartesian.map_isHomLift, CategoryTheory.GradedObject.mapBifunctorMapObj_ext_iff, CategoryTheory.Pretriangulated.Triangle.isZero₂_iff, AlgebraicGeometry.IsOpenImmersion.range_pullback_to_base_of_right, HomologicalComplex.homotopyCofiber.d_sndX, CategoryTheory.Presieve.CoverByImageStructure.fac_assoc, CategoryTheory.GrothendieckTopology.toSheafify_comp_sheafifyCompIso_inv, CategoryTheory.Limits.pullbackProdFstIsoProd_inv_snd_fst_assoc, CategoryTheory.Pseudofunctor.map₂_whisker_right, CategoryTheory.Functor.relativelyRepresentable.w', CategoryTheory.Sigma.inclCompMap_inv_app, CategoryTheory.Limits.cokernelIsoOfEq_trans, AlgebraicGeometry.Spec.toSheafedSpace_map, CategoryTheory.Join.mapWhiskerRight_whiskerLeft_assoc, CategoryTheory.MonoidalClosed.comp_id_assoc, TopCat.isOpenEmbedding_iff_isIso_comp, CategoryTheory.Bicategory.whiskerRight_id_assoc, CategoryTheory.GrothendieckTopology.overMapPullback_comp_id_assoc, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_π, AlgebraicGeometry.Scheme.IdealSheafData.comapIso_hom_snd, CategoryTheory.Functor.rightOpComp_inv_app, CategoryTheory.Limits.CategoricalPullback.Hom.w, CategoryTheory.Mon_Class.pow_comp, CategoryTheory.Limits.cospanCompIso_inv_app_one, CategoryTheory.Bicategory.Prod.sectR_obj, HomologicalComplex.extendMap_add, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_apply, CategoryTheory.MonoidalCategory.tensorδ_tensorμ, CategoryTheory.IsCommComonObj.comul_comm_assoc, CategoryTheory.MorphismProperty.limitsOfShape_le, CategoryTheory.ExponentiableMorphism.coev_ev_assoc, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_inv_app_hom_hom_hom, CategoryTheory.ObjectProperty.IsLocal.top, CategoryTheory.InjectiveResolution.Hom.hom'_f_assoc, CategoryTheory.ObjectProperty.colimitsClosure_eq_unop_limitsClosure, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_inv_app_fst_app, Mathlib.Tactic.Monoidal.eval_of, CategoryTheory.Functor.FullyFaithful.hasShift.map_add_hom_app, CategoryTheory.IsPullback.inl_snd', CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₂_assoc, SSet.horn.faceι_ι_assoc, CategoryTheory.Bicategory.whisker_assoc_symm_assoc, HomologicalComplex.xPrevIsoSelf_comp_dTo_assoc, CategoryTheory.BimonObj.one_counit, groupCohomology.cocyclesMap_comp_assoc, CategoryTheory.GrothendieckTopology.Point.comp_hom, CategoryTheory.Under.hom_right_inv_right, CategoryTheory.uliftYoneda_map_app_down, CategoryTheory.MorphismProperty.instHasRightCalculusOfFractionsUnopOfHasLeftCalculusOfFractionsOpposite, CategoryTheory.Preadditive.sum_comp_assoc, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left, CategoryTheory.Over.id_left, CategoryTheory.Iso.inv_hom_id_eval_assoc, CategoryTheory.ShortComplex.HomologyMapData.comm, CategoryTheory.MorphismProperty.Comma.id_hom, CategoryTheory.Join.mapPairComp_hom_app_left, CategoryTheory.Functor.opId_inv_app, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_assoc, HomotopicalAlgebra.CofibrantBrownFactorization.mk'_s, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom.w_assoc, CategoryTheory.MonoOver.top_arrow, CategoryTheory.HomOrthogonal.matrixDecompositionAddEquiv_symm_apply, CategoryTheory.unit_mateEquiv, Bimod.comp_whiskerLeft_bimod, CategoryTheory.conjugateEquiv_associator_hom, SimplicialObject.Splitting.decomposition_id, CategoryTheory.Functor.OplaxRightLinear.δᵣ_associativity_inv_assoc, CategoryTheory.PreGaloisCategory.surjective_on_fiber_of_epi, CategoryTheory.ComonObj.comul_counit_hom_assoc, CategoryTheory.Sigma.SigmaHom.comp_def, SSet.Truncated.Path.arrow_src, CategoryTheory.Functor.mapTriangle_map_hom₃, SemiNormedGrp₁.mkHom_comp, CategoryTheory.GrpObj.inv_comp, CategoryTheory.Limits.limitConeOfUnique_isLimit_lift, CategoryTheory.IsSplitEqualizer.top_rightRetraction, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app, CategoryTheory.Localization.Monoidal.pentagon_aux₃, CategoryTheory.Bicategory.conjugateEquiv_apply', CategoryTheory.Square.Hom.comm₁₂_assoc, SSet.spine_map_vertex, Bimod.left_assoc, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₃, CategoryTheory.sum.inrCompInlCompAssociator_hom_app_down_down, CategoryTheory.Limits.spanCompIso_hom_app_left, OrderHom.equivalenceFunctor_counitIso_hom_app_app, LinOrd.ofHom_comp, HomologicalComplex.mapBifunctor₁₂.d₃_eq_zero, CategoryTheory.ShortComplex.HomologyMapData.comm_assoc, CategoryTheory.Arrow.iso_w, CategoryTheory.Limits.BinaryBiconeMorphism.wfst, groupHomology.isoCycles₂_inv_comp_iCycles_assoc, CategoryTheory.Enriched.FunctorCategory.enriched_assoc_assoc, Action.forget_ε, CategoryTheory.Presieve.ofArrows.hom_idx, CategoryTheory.Limits.BiconeMorphism.wπ_assoc, CategoryTheory.Functor.leftKanExtensionUniqueOfIso_inv, CategoryTheory.MorphismProperty.Under.mk_left, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_right, ModuleCat.mkOfSMul_smul, CategoryTheory.endofunctorMonoidalCategory_associator_hom_app, CategoryTheory.Iso.cancel_iso_inv_right, CategoryTheory.Functor.RepresentableBy.ext_iff, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom, CategoryTheory.Limits.pullback.hom_ext_iff, CategoryTheory.Bicategory.mateEquiv_conjugateEquiv_vcomp, CategoryTheory.Under.mapId_hom, CochainComplex.HomComplex.Cochain.fromSingleMk_sub, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_inv_app_app_snd, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturality, CategoryTheory.Arrow.comp_left_assoc, AlgebraicGeometry.smoothOfRelativeDimension_comp, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_hom_assoc, CategoryTheory.Functor.const.opObjUnop_inv_app, CategoryTheory.Over.postComp_hom_app_left, CategoryTheory.ShortComplex.RightHomologyMapData.zero_φQ, CategoryTheory.GrothendieckTopology.OneHypercover.id_h₀, CochainComplex.toSingle₀Equiv_symm_apply_f_succ, CategoryTheory.OplaxFunctor.mapComp_assoc_right_assoc, CategoryTheory.Abelian.PreservesImage.iso_inv_ι, CategoryTheory.Limits.imageSubobject_iso_comp, CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_π_0, CategoryTheory.Limits.coprod.map_comp_inl_inr_codiag, CategoryTheory.Limits.zero_of_source_iso_zero', BoolAlg.comp_apply, CategoryTheory.ShortComplex.homologyMap'_smul, CochainComplex.mappingCone.inl_v_descShortComplex_f_assoc, CategoryTheory.MonObj.comp_one_assoc, groupHomology.isoShortComplexH2_hom, SSet.RelativeMorphism.Homotopy.h₁_assoc, Rep.coindResAdjunction_homEquiv_symm_apply, CategoryTheory.MonoidalCategory.triangle_assoc_comp_right_assoc, CategoryTheory.Limits.IsZero.eq_zero_of_tgt, CategoryTheory.MonoidalCategory.tensor_id_comp_id_tensor_assoc, CategoryTheory.FreeMonoidalCategory.subsingleton_hom, CategoryTheory.Mat.comp_apply, CategoryTheory.Equivalence.rightOp_counitIso_hom_app, CategoryTheory.Pretriangulated.Triangle.neg_hom₂, HomologicalComplex.toCycles_cyclesIsoSc'_hom_assoc, CategoryTheory.Functor.Monoidal.map_tensor_assoc, Profinite.lift_lifts, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom'', SemiRingCat.ofHom_id, CategoryTheory.Subfunctor.fromPreimage_ι, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_unit_app_app, CategoryTheory.Functor.Monoidal.whiskerLeft_app_fst, CategoryTheory.Limits.limit.lift_pre, CategoryTheory.Functor.OplaxMonoidal.oplax_left_unitality, CategoryTheory.Adjunction.homAddEquiv_zero, CategoryTheory.Discrete.id_def', CategoryTheory.Pseudofunctor.StrongTrans.rightUnitor_inv_as_app, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_app_assoc, CategoryTheory.Over.whiskerLeft_left_fst, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply, CategoryTheory.Idempotents.app_comp_p, CategoryTheory.Iso.trans_hom, CategoryTheory.Functor.mapComon_obj_comon_counit, ChainComplex.augmentTruncate_hom_f_zero, DerivedCategory.from_singleFunctor_obj_eq_zero_of_projective, CategoryTheory.ProjectiveResolution.lift_commutes_assoc, CategoryTheory.InducedCategory.id_hom, CategoryTheory.op_sum, CategoryTheory.Limits.CoconeMorphism.hom_inv_id, CategoryTheory.MorphismProperty.retracts_le_iff, CategoryTheory.Limits.WidePullback.hom_eq_lift, AddCommGrpCat.biprodIsoProd_inv_comp_desc, CategoryTheory.Endofunctor.Coalgebra.Hom.h, TopModuleCat.hom_sub, CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtensionObjIsoColimit_hom, AlgebraicTopology.DoldKan.MorphComponents.postComp_b, HomologicalComplex₂.ιTotalOrZero_map, CategoryTheory.Limits.BinaryCofan.unop_mk, HomologicalComplex.truncGE'Map_f_eq_opcyclesMap, CategoryTheory.SmallObject.πFunctorObj_eq, CategoryTheory.μ_δ_app, TopCat.Presheaf.restrictOpenCommRingCat_apply, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality_assoc, HomologicalComplex.restrictionMap_comp_assoc, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_iff_epi₂, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerRight_assoc, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_hom_app_unmop, NonemptyFinLinOrd.id_apply, CategoryTheory.Limits.Multicoequalizer.hom_ext_iff, CategoryTheory.LaxFunctor.map₂_leftUnitor, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.functorMap_comp_assoc, HasFibers.inducedMap_comp_assoc, CategoryTheory.StructuredArrow.mapNatIso_counitIso_hom_app_right, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_id_naturality_inv, ModuleCat.exteriorPower.iso₁_hom_naturality_assoc, CategoryTheory.ObjectProperty.instIsClosedUnderLimitsOfShapeOppositeOpOfIsClosedUnderColimitsOfShape, CategoryTheory.Limits.biproduct.map_matrix_assoc, CategoryTheory.expComparison_ev, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality, CategoryTheory.Mathlib.Tactic.MonTauto.rightUnitor_inv_tensor_one_mul, CategoryTheory.Limits.biprod.associator_natural, CategoryTheory.MonoOver.inf_map_app, CategoryTheory.Biprod.ofComponents_fst, CategoryTheory.SingleFunctors.postcompPostcompIso_inv_hom_app, Bimod.Hom.left_act_hom_assoc, CategoryTheory.ShortComplex.Splitting.op_s, CategoryTheory.Sum.functorEquivFunctorCompSndIso_inv_app_app, CategoryTheory.MorphismProperty.LeftFraction.map_hom_ofInv_id, CategoryTheory.MonoOver.isThin, CategoryTheory.Biprod.unipotentUpper_inv, CategoryTheory.Limits.CategoricalPullback.comp_fst_assoc, CategoryTheory.typeEquiv_counitIso_hom_app_val_app, CategoryTheory.Discrete.compNatIsoDiscrete_inv_app, CategoryTheory.Limits.Pi.map_comp_map, AlgebraicGeometry.universallyClosed_eq_universallySpecializing, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_aux_one, CategoryTheory.Functor.prod_η_fst, CategoryTheory.Limits.Fork.op_ι_app_one, CategoryTheory.IsPullback.of_has_biproduct, CategoryTheory.ShortComplex.leftHomologyMap'_id, SheafOfModules.unitHomEquiv_comp_apply, CategoryTheory.MorphismProperty.instHasPullbacksAlongCompOfIsStableUnderBaseChangeAlong, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_inv_inv, CategoryTheory.CategoryOfElements.toCostructuredArrow_obj, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_symm_apply_f, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitIso_hom_naturality, CategoryTheory.ShortComplex.mapCyclesIso_inv_naturality_assoc, CategoryTheory.LaxFunctor.mapComp_assoc_left_app, CategoryTheory.Comma.mapRightId_hom_app_right, SemiNormedGrp.completion.lift_comp_incl, CategoryTheory.Functor.IsCocartesian.fac_assoc, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_le_llp_rlp, CategoryTheory.Adjunction.unit_naturality, CategoryTheory.preadditiveYonedaObj_obj_isAddCommGroup, CategoryTheory.Limits.Cone.w, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_comp_map_assoc, CategoryTheory.leftDistributor_ext₂_left_iff, CategoryTheory.ShortComplex.SnakeInput.Hom.id_f₁, CategoryTheory.Limits.kernelFactorThruImage_inv_comp_ι, CategoryTheory.Presheaf.uliftYonedaAdjunction_unit_app_app, CategoryTheory.MonoidalCategory.id_tensorHom_id, CategoryTheory.ShiftedHom.opEquiv'_symm_add, CategoryTheory.Functor.IsCocartesian.map_self, AlgebraicGeometry.ΓSpecIso_inv_ΓSpec_adjunction_homEquiv, CategoryTheory.Limits.Pi.map_id, AddMonCat.ofHom_comp, CategoryTheory.Mathlib.Tactic.MonTauto.associator_inv_comp_tensorHom_tensorHom, CategoryTheory.PreGaloisCategory.PointedGaloisObject.comp_val, CategoryTheory.NonPreadditiveAbelian.add_neg, SimplexCategoryGenRel.eq_or_len_le_of_P_δ, CategoryTheory.Mon_Class.comp_one, CategoryTheory.Bicategory.conjugateEquiv_adjunction_id, HomologicalComplex.restrictionToTruncGE'.f_eq_iso_hom_pOpcycles_iso_inv, SSet.Truncated.HomotopyCategory.BinaryProduct.associativity'Iso_hom_app, CategoryTheory.Grothendieck.transportIso_inv_fiber, CategoryTheory.GradedObject.single_map_singleObjApplyIso_hom, CategoryTheory.MonoidalCategory.tensorμ_natural, CategoryTheory.PreZeroHypercover.inj_sigmaOfIsColimit_f, CategoryTheory.Sum.functorEquiv_unitIso_inv_app_app_inr, CochainComplex.cm5b.instMonoIntI, CategoryTheory.LocalizerMorphism.op_functor, CategoryTheory.isCodetecting_op_iff, QuadraticModuleCat.toIsometry_id, CategoryTheory.MonoidalCategory.whiskerLeft_comp_assoc, CategoryTheory.SmallObject.objMap_comp, CategoryTheory.left_unitality_app, CategoryTheory.braiding_inv_tensorUnit_left_assoc, CategoryTheory.Limits.image.preComp_mono, CategoryTheory.Cat.rightUnitor_inv_app, CategoryTheory.Limits.coprod.inr_map, AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zero, CategoryTheory.Functor.map_id, CategoryTheory.BraidedCategory.braiding_inv_naturality_left_assoc, CategoryTheory.Limits.PullbackCone.ofCone_π, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app, CategoryTheory.unop_inv, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app_assoc, AlgebraicGeometry.StructureSheaf.algebraMap_germ_assoc, CategoryTheory.Functor.Monoidal.whiskerLeft_δ_μ, CategoryTheory.ShortComplex.Homotopy.compLeft_h₃, CategoryTheory.ExactPairing.evaluation_coevaluation_assoc, groupHomology.chainsMap_f_1_comp_chainsIso₁, AlgebraicGeometry.StructureSheaf.res_apply, Rep.coindVEquiv_apply_hom, CategoryTheory.ObjectProperty.instIsClosedUnderQuotientsTop, groupCohomology.mapShortComplexH1_comp, SimplexCategory.eq_σ_comp_of_not_injective', CategoryTheory.Functor.Final.ι_colimitIso_inv_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.unit_actionHomRight, CategoryTheory.Pseudofunctor.Grothendieck.Hom.ext_iff, CategoryTheory.Limits.coprod.inl_fst_assoc, CategoryTheory.OverPresheafAux.YonedaCollection.mk_snd, CategoryTheory.Limits.inl_comp_pushoutObjIso_inv, CategoryTheory.Equivalence.counitInv_functor_comp_assoc, CategoryTheory.Functor.LeftExtension.postcompose₂_map_left, CategoryTheory.Limits.pullbackObjIso_inv_comp_fst, CategoryTheory.Functor.OplaxLeftLinear.δₗ_naturality_right, CategoryTheory.Functor.uncurry_obj_map, CategoryTheory.CosimplicialObject.Augmented.const_obj_hom, CategoryTheory.CartesianMonoidalCategory.inv_prodComparison_map_snd, AlgebraicGeometry.Scheme.LocalRepresentability.instIsLocallyInjectiveHomYonedaGluedToSheaf, CategoryTheory.Limits.CategoricalPullback.comp_fst, CategoryTheory.Bicategory.Prod.snd_mapId_inv, CategoryTheory.Iso.comp_inv_eq_id, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_app_assoc, AlgebraicGeometry.Scheme.Modules.Hom.add_app, CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc_assoc, CategoryTheory.Limits.LimitPresentation.map_π, CategoryTheory.Presieve.Arrows.toCompatible_coe, CategoryTheory.Functor.Monoidal.whiskerLeft_ε_η, CategoryTheory.NatTrans.id_hcomp_app, SSet.stdSimplex.yonedaEquiv_map, CategoryTheory.Limits.pullbackAssoc_inv_snd_assoc, CategoryTheory.LocalizerMorphism.nonempty_leftResolution_iff_op, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_counit_app_left, CategoryTheory.Join.inclLeftCompOpEquivInverse_hom_app_op, CategoryTheory.Presheaf.coconeOfRepresentable_naturality, CategoryTheory.Abelian.Ext.mk₀_comp_mk₀, CategoryTheory.Functor.OplaxLeftLinear.δₗ_associativity_assoc, CategoryTheory.Groupoid.isIsomorphic_iff_nonempty_hom, CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_left, CategoryTheory.IsSplitEqualizer.top_rightRetraction_assoc, CategoryTheory.Subobject.ofLE_comp_ofLEMk, AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_naturality, CommBialgCat.comp_apply, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.kernel_ι_d_comp_d, Preord.coe_comp, CategoryTheory.EnrichedFunctor.map_comp, CategoryTheory.CatEnrichedOrdinary.homEquiv_comp, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_naturality, CategoryTheory.NatTrans.app_naturality_assoc, CategoryTheory.Limits.Pi.map'_comp_map, CategoryTheory.eHomWhiskerRight_id, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_assoc, SemiNormedGrp.completion.map_zero, CategoryTheory.Adjunction.map_μ_comp_counit_app_tensor, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_as_app, CategoryTheory.Limits.PullbackCone.op_inl, CategoryTheory.NatTrans.rightOp_app, CategoryTheory.MonoOver.mkArrowIso_inv_hom_left, CategoryTheory.Bicategory.InducedBicategory.bicategory_homCategory_comp_hom, CategoryTheory.GradedNatTrans.naturality_assoc, CategoryTheory.Limits.PreservesKernel.of_iso_comparison, SSet.RelativeMorphism.Homotopy.ofEq_h, CategoryTheory.Arrow.inv_left_hom_right, CategoryTheory.Enriched.Functor.natTransEquiv_symm_whiskerRight_functorHom_app, AlgebraicTopology.DoldKan.P_add_Q, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counit_app, CategoryTheory.Adjunction.compCoyonedaIso_hom_app_app, CategoryTheory.Kleisli.Adjunction.fromKleisli_map, CategoryTheory.ComposableArrows.Exact.cokerIsoKer_hom_fac_assoc, CategoryTheory.GrothendieckTopology.Point.Hom.sheafFiber_id, CategoryTheory.Functor.currying₃_unitIso_inv_app_app_app_app, CategoryTheory.ReflQuiv.id_eq_id, CategoryTheory.Functor.mapConeWhisker_hom_hom, CategoryTheory.Limits.prodZeroIso_iso_inv_snd, AddCommGrpCat.biprodIsoProd_inv_comp_snd, CategoryTheory.Equivalence.fun_inv_map_assoc, groupHomology.isoCycles₁_inv_comp_iCycles_assoc, CategoryTheory.ShortComplex.pOpcycles_π_isoOpcyclesOfIsColimit_inv, CategoryTheory.inv_eqToHom, CategoryTheory.Cat.Hom.toNatTrans_id, AlgebraicTopology.DoldKan.hσ'_eq, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_hom_fac_assoc, CategoryTheory.Functor.whiskeringLeftObjIdIso_inv_app_app, HomologicalComplex₂.d₂_eq, CategoryTheory.CommSq.left_adjoint, CategoryTheory.MorphismProperty.instRespectsOfIsStableUnderComposition, groupHomology.π_comp_H1Iso_hom_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_inv_app_app, CategoryTheory.comp_over_assoc, CategoryTheory.Limits.Cocone.toCostructuredArrowCompToOverCompForget_hom_app, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac, OrderHom.equivalenceFunctor_unitIso_hom_app, CategoryTheory.IsPullback.id_vert, AlgebraicGeometry.ExistsHomHomCompEqCompAux.hab, CategoryTheory.Functor.Monoidal.transport_η, CategoryTheory.Iso.symm_self_conj, CategoryTheory.ShortComplex.p_opcyclesMap_assoc, CategoryTheory.Iso.hom_inv_id_eval, CategoryTheory.unop_comp_assoc, AlgebraicGeometry.Proj.basicOpenToSpec_SpecMap_awayMap_assoc, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_as_app, Lat.hom_id, CategoryTheory.Equivalence.ε_comp_map_ε, CategoryTheory.Functor.mapCocone₂_ι_app, AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_comp_assoc, groupHomology.chainsMap_f_2_comp_chainsIso₂, CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv', CategoryTheory.Limits.pullback_inv_snd_fst_of_left_isIso_assoc, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv, CategoryTheory.NatTrans.leftOpWhiskerRight, CategoryTheory.Lax.StrongTrans.naturality_naturality, CategoryTheory.Limits.limitCompCoyonedaIsoCone_inv, CategoryTheory.MorphismProperty.Over.instPreservesFiniteLimitsTopOverForget, CategoryTheory.ShortComplex.rightHomologyIso_hom_naturality_assoc, AlgebraicGeometry.AffineSpace.homOfVector_over, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_left, CategoryTheory.Limits.Cofork.unop_π_app_zero, CategoryTheory.Monad.algebraPreadditive_homGroup_nsmul_f, CategoryTheory.CanonicallyOverClass.over_def, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_inv_ι_assoc, Action.resComp_inv_app_hom, CategoryTheory.biproduct_ι_comp_rightDistributor_inv_assoc, HomologicalComplex.extend_d_from_eq_zero, HomotopicalAlgebra.RightHomotopyRel.equivalence, CategoryTheory.NonPreadditiveAbelian.lift_map_assoc, CategoryTheory.Localization.lift₃NatTrans_app_app_app, CategoryTheory.ShiftedHom.opEquiv'_zero_add_symm, CategoryTheory.Functor.whiskerLeft_comp_assoc, CategoryTheory.ObjectProperty.instIsClosedUnderLimitsOfShapeUnopOfIsClosedUnderColimitsOfShapeOpposite, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_right_right, CategoryTheory.MonoidalClosed.uncurry_natural_left, CategoryTheory.GrpObj.tensorHom_inv_inv_mul, groupHomology.pOpcycles_comp_opcyclesIso_hom, CategoryTheory.Subobject.bot_eq_zero, CategoryTheory.GrothendieckTopology.OneHypercover.id_s₀, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_hom_assoc, SheafOfModules.pullback_assoc, AlgebraicGeometry.Scheme.Hom.map_appLE', Homotopy.extend.hom_eq_zero₂, CategoryTheory.Functor.toPseudoFunctor_mapId, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv_assoc, AddMagmaCat.hom_id, CategoryTheory.Functor.ranCounit_app_app_ranAdjunction_unit_app_app, CategoryTheory.Oplax.OplaxTrans.naturality_naturality, CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inl_assoc, CategoryTheory.ShortComplex.zero, Bimod.whiskerRight_id_bimod, CategoryTheory.Subobject.top_eq_id, CategoryTheory.Comma.mapRightId_hom_app_left, groupHomology.H2π_comp_map, Homotopy.nullHomotopicMap'_f_of_not_rel_left, CategoryTheory.ShortComplex.Hom.comp_τ₁, CategoryTheory.Pseudofunctor.isPrestackFor_iff, CategoryTheory.CommMon.id_hom, CategoryTheory.Limits.IsColimit.hom_desc, CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_fst_assoc, CategoryTheory.Functor.Final.colimit_cocone_comp_aux, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionRight_op, CategoryTheory.SmallObject.SuccStruct.prop.fac, CategoryTheory.ShiftedHom.opEquiv'_symm_op_opShiftFunctorEquivalence_counitIso_inv_app_op_shift, CategoryTheory.LaxMonoidalFunctor.comp_hom, CategoryTheory.Functor.relativelyRepresentable.symmetry_snd_assoc, CategoryTheory.GlueData'.t_inv, CategoryTheory.Functor.RightExtension.precomp_map_right, CategoryTheory.CosimplicialObject.δ_comp_δ'_assoc, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_assoc, SimplexCategory.δ_one_mkOfSucc, CategoryTheory.Presheaf.imageSieve_whisker_forget, CategoryTheory.MonoidalClosed.homEquiv_symm_apply_eq, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.exists_pushouts, AlgebraicGeometry.Flat.surjective_descendsAlong_surjective_inf_flat_inf_quasicompact, CategoryTheory.ProjectiveResolution.leftDerivedToHomotopyCategory_app_eq, CategoryTheory.composePath_cons, CategoryTheory.Subgroupoid.IsNormal.conjugation_bij, CategoryTheory.Equivalence.comp_asNatTrans_assoc, TopModuleCat.hom_nsmul, CategoryTheory.StructuredArrow.map_mk, CategoryTheory.ShortComplex.Exact.rightHomologyDataOfIsColimitCokernelCofork_ι, CategoryTheory.GrpObj.lift_commutator_eq_mul_mul_inv_inv_assoc, CategoryTheory.Over.mapId_hom_app_left, CategoryTheory.Comma.mapLeftEq_inv_app_left, Mathlib.Tactic.Elementwise.forget_hom_Type, CategoryTheory.bicategoricalComp_refl, AlgebraicGeometry.Scheme.PartialMap.restrict_hom, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_right, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_hom_app_unop_assoc, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_apply, CategoryTheory.NatTrans.naturality, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_hom_π_π_assoc, CategoryTheory.ObjectProperty.IsStableUnderShiftBy.le_shift, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv, groupHomology.cyclesIso₀_inv_comp_cyclesMap_assoc, CategoryTheory.WithInitial.map₂_app, CategoryTheory.MonoidalCategory.tensorHom_comp_whiskerLeft, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp_assoc, CategoryTheory.Iso.eHomCongr_comp, CategoryTheory.NatTrans.CommShift₂.instIdFunctor, groupHomology.π_comp_H2Iso_inv, CategoryTheory.Limits.prod.inr_snd, CategoryTheory.MorphismProperty.retracts_transfiniteCompositionsOfShape_pushouts_coproducts_le_llp_rlp, CategoryTheory.NatTrans.rightDerivedToHomotopyCategory_comp, HomologicalComplex.homotopyCofiber.inlX_d', CategoryTheory.Center.ofBraided_μ_f, CategoryTheory.Limits.imageSubobject_arrow'_assoc, CategoryTheory.Bicategory.LeftLift.ofIdComp_hom, CategoryTheory.CartesianMonoidalCategory.lift_whiskerRight_assoc, AlgebraicTopology.DoldKan.PInfty_f_0, CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id_assoc, Homotopy.nullHomotopicMap_f_of_not_rel_left, CategoryTheory.Limits.biprod.isIso_inl_iff_id_eq_fst_comp_inl, CategoryTheory.Subobject.factorThru_arrow, AlgebraicGeometry.Scheme.Hom.toNormalization_inr_normalizationCoprodIso_hom_assoc, CategoryTheory.ShortComplex.Homotopy.neg_h₀, CategoryTheory.WithTerminal.commaFromOver_map_right, CategoryTheory.functorMapReverse, CategoryTheory.Limits.biproduct.map_matrix, CategoryTheory.Functor.IsRepresentedBy.map_bijective, CategoryTheory.PreGaloisCategory.endEquivAutGalois_mul, SheafOfModules.Presentation.of_isIso_relations, CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_right, CategoryTheory.braiding_leftUnitor_assoc, groupCohomology.eq_d₂₃_comp_inv, CategoryTheory.Limits.Cotrident.app_one, HomologicalComplex.truncLEMap_id, CategoryTheory.MonoOver.w_assoc, CategoryTheory.CostructuredArrow.map_map_left, Frm.ofHom_comp, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'_inv, CategoryTheory.Limits.FormalCoproduct.mapPower_powerMap, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_hom_app_app_down, CategoryTheory.Pseudofunctor.StrongTrans.associator_hom_as_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom.w, AlgebraicGeometry.pullbackSpecIso_hom_fst, AlgebraicGeometry.IsProper.eq_valuativeCriterion, HomologicalComplex.toCycles_comp_homologyπ_assoc, CategoryTheory.Endofunctor.Algebra.Hom.h, CategoryTheory.Functor.mapEnd_apply, CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_hom_assoc, CategoryTheory.ShortComplex.Hom.id_τ₃, CategoryTheory.MonoidalCategory.tensorHom_comp_whiskerRight, CategoryTheory.Pretriangulated.comp_hom₂, CategoryTheory.CostructuredArrow.map₂_map_left, CategoryTheory.Functor.PullbackObjObj.ofHasPullback_snd, CategoryTheory.Limits.image.preComp_comp, CategoryTheory.Limits.prod.diag_map_fst_snd_comp_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomLeft_tensor_assoc, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε_assoc, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_presheafHom_uliftYoneda_obj, CategoryTheory.Functor.OfSequence.map_comp, CategoryTheory.Pseudofunctor.map₂_right_unitor, CategoryTheory.ShortComplex.exact_and_mono_f_iff_f_is_kernel, CategoryTheory.Bimon.ofMonComonObjX_one, CategoryTheory.Functor.representableByUliftFunctorEquiv_apply_homEquiv, CategoryTheory.Functor.shift_map_op, CategoryTheory.MorphismProperty.Under.forget_comp_forget_map, CategoryTheory.Lax.LaxTrans.StrongCore.naturality_hom, CategoryTheory.ShiftedHom.homEquiv_apply, CategoryTheory.Limits.limitIsoSwapCompLim_inv_app, CategoryTheory.Limits.coprod.map_comp_inl_inr_codiag_assoc, HomologicalComplex₂.D₂_D₁, CategoryTheory.Functor.LaxRightLinear.μᵣ_naturality_left_assoc, CategoryTheory.Functor.LaxLeftLinear.μₗ_associativity_inv, AlgebraicGeometry.locallyOfFinitePresentation_comp, CategoryTheory.ε_η_app, CategoryTheory.MonoidalCategory.whiskerRight_id, CategoryTheory.GradedObject.eqToHom_proj, CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_fst_snd, CategoryTheory.Bicategory.rightUnitor_comp_inv, Action.FunctorCategoryEquivalence.unitIso_hom_app_hom, CategoryTheory.Limits.colimit.pre_map, LightCondensed.ihomPoints_symm_apply, CategoryTheory.Pretriangulated.Triangle.add_hom₂, CategoryTheory.Sum.swapCompInl_inv_app, CategoryTheory.MorphismProperty.IsInvertedBy.iff_le_inverseImage_isomorphisms, CategoryTheory.Pseudofunctor.IsStackFor.isEquivalence, CategoryTheory.MonoidalCategory.MonoidalLeftAction.unit_actionHomRight, CategoryTheory.GrothendieckTopology.OneHypercover.comp_s₁, CategoryTheory.GlueData'.t_inv_assoc, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv, CategoryTheory.Triangulated.TStructure.le_zero_le, HomologicalComplex.truncGE.rightHomologyMapData_φH, CategoryTheory.CommSq.fac_left_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_inv_app_fst_app, CategoryTheory.Localization.Monoidal.leftUnitor_naturality, AddCommGrpCat.hom_comp, CategoryTheory.MonoidalCategory.MonoidalRightAction.comp_actionHomLeft_assoc, CategoryTheory.Functor.LaxLeftLinear.μₗ_unitality_inv, AlgebraicGeometry.IsClosedImmersion.eq_isFinite_inf_mono, CategoryTheory.EnrichedFunctor.forgetId_hom_app, CategoryTheory.Adjunction.comp_unit_app_assoc, CategoryTheory.CartesianMonoidalCategory.hom_ext_iff, CategoryTheory.ShortComplex.SnakeInput.comp_f₃, CategoryTheory.Limits.ι_comp_colimitOpIsoOpLimit_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHom_op, CategoryTheory.NatTrans.id_comm, CategoryTheory.homOfLE_comp, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp_assoc, CategoryTheory.Limits.biproduct.hom_ext_iff, CategoryTheory.GlueData.t_id, AlgebraicGeometry.AffineSpace.reindex_over_assoc, CategoryTheory.Limits.inr_comp_pushoutObjIso_inv, AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality, CategoryTheory.Localization.isoOfHom_hom_inv_id_assoc, CategoryTheory.Limits.IsLimit.fac_assoc, groupCohomology.isoShortComplexH1_hom, groupHomology.mapShortComplexH1_id, AlgebraicGeometry.Scheme.IdealSheafData.comapIso_hom_fst_assoc, TopCat.GlueData.image_inter, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app, CategoryTheory.Limits.Types.pullbackIsoPullback_inv_fst, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy_homEquiv_apply_app, CategoryTheory.Limits.prod.diag_map, CategoryTheory.Pretriangulated.shiftFunctor_op_map, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp_X, CategoryTheory.Idempotents.functorExtension₂CompWhiskeringLeftToKaroubiIso_inv_app_app_f, CategoryTheory.Limits.CokernelCofork.condition_assoc, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_inv_comp_π, AlgebraicTopology.DoldKan.PInfty_f_naturality, HomologicalComplex₂.total.map_comp_assoc, CategoryTheory.Functor.Monoidal.whiskerRight_δ_μ, CategoryTheory.InjectiveResolution.cochainComplex_d_assoc, CategoryTheory.Localization.hasSmallLocalizedHom_iff, groupHomology.H1π_comp_map_assoc, CategoryTheory.Limits.BinaryFan.braiding_inv_fst, SemimoduleCat.MonoidalCategory.leftUnitor_naturality, AlgebraicGeometry.Spec.topMap_comp, CategoryTheory.ShortComplex.RightHomologyData.op_f', CategoryTheory.Subgroupoid.coe_inv_coe', CategoryTheory.MorphismProperty.instFullOverTopOverForget, CategoryTheory.Bicategory.whiskerLeft_hom_inv_assoc, CategoryTheory.CatCenter.smul_iso_inv_eq, AlgebraicTopology.DoldKan.hσ'_eq_zero, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_whiskerRight, CategoryTheory.Localization.Monoidal.triangle, CategoryTheory.Limits.Sigma.ι_reindex_hom, SimplexCategory.mkOfSucc_δ_gt, CategoryTheory.Limits.cospanCompIso_hom_app_left, AlgebraicGeometry.Spec.map_comp, groupCohomology.map_id_comp, CategoryTheory.Limits.BinaryFan.assoc_snd, CategoryTheory.ShortComplex.add_τ₂, Action.hom_inv_hom_assoc, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_unitIso, CategoryTheory.Adjunction.rightAdjointUniq_trans_app, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_comp_naturality_inv, CategoryTheory.NormalMono.w, CategoryTheory.IsHomLift.lift_id_inv_isIso, CategoryTheory.SimplicialObject.equivalenceRightToLeft_left, CategoryTheory.ShortComplex.rightHomologyMap'_comp_assoc, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceFunctorProj_hom_app, SimplexCategory.δ_comp_σ_of_gt_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_hom_inv_assoc, CategoryTheory.initiallySmall_iff_exists_small_weakly_initial_set, CategoryTheory.uliftCoyonedaEquiv_naturality, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_assoc, AlgebraicTopology.DoldKan.HigherFacesVanish.of_comp, CategoryTheory.Pseudofunctor.CoGrothendieck.instEssSurjαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor, CategoryTheory.exp.coev_ev_assoc, CategoryTheory.MonObj.mul_associator, CategoryTheory.Over.whiskerLeft_left_fst_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_app_assoc, HeytAlg.coe_id, CategoryTheory.IsFiltered.bowtie, CategoryTheory.Functor.RightExtension.postcompose₂ObjMkIso_inv_left_app, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_assoc, SimplicialObject.opFunctorCompOpFunctorIso_inv_app_app, HomologicalComplex₂.shape_f, CategoryTheory.prod_map_pre_app_comp_ev, Frm.ofHom_id, CategoryTheory.Limits.opProdIsoCoprod_hom_fst_assoc, BddOrd.hom_comp, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app_assoc, CategoryTheory.PreZeroHypercover.sumInr_h₀, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π_assoc, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app, CategoryTheory.MorphismProperty.isomorphisms_le_pushouts, CategoryTheory.op_inv_rightUnitor, CategoryTheory.Equivalence.unit_naturality_assoc, CategoryTheory.Pretriangulated.Triangle.zero_hom₃, CategoryTheory.GrpObj.mul_inv, CategoryTheory.Limits.inr_comp_pushoutSymmetry_inv, SemiNormedGrp₁.zero_apply, CategoryTheory.shiftComm_hom_comp, CategoryTheory.OverPresheafAux.YonedaCollection.map₁_comp, CategoryTheory.Pretriangulated.Triangle.add_hom₃, CategoryTheory.Endofunctor.Algebra.functorOfNatTransEq_hom_app_f, CategoryTheory.Join.mapWhiskerLeft_associator_hom_assoc, AlgebraicTopology.DoldKan.PInfty_f_idem_assoc, CategoryTheory.Under.mapId_eq, CategoryTheory.Limits.isLimitConeLeftOpOfCocone_lift, ComplexShape.Embedding.liftExtend_f, CategoryTheory.Equivalence.unit_app_tensor_comp_inverse_map_δ_functor_assoc, CategoryTheory.NatTrans.shift_app_assoc, Action.inv_hom_hom, AlgebraicTopology.DoldKan.Compatibility.υ_hom_app, RingCat.moduleCatRestrictScalarsPseudofunctor_obj, CategoryTheory.CatCenter.app_neg_one_zpow, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict_assoc, CategoryTheory.cokernelUnopUnop_hom, CategoryTheory.NatIso.cancel_natIso_inv_right, CategoryTheory.Limits.CatCospanTransform.leftUnitor_inv_left_app, CategoryTheory.GradedObject.ι_mapBifunctorLeftUnitor_hom_apply, CategoryTheory.Sheaf.id_val, FinPartOrd.comp_apply, groupCohomology.isoCocycles₂_inv_comp_iCocycles, CategoryTheory.Limits.biproduct.ι_fromSubtype_assoc, CategoryTheory.IsCommMonObj.mul_comm, CategoryTheory.MorphismProperty.Comma.hasColimitsOfShape_of_closedUnderColimitsOfShape, CategoryTheory.MonoidalPreadditive.zero_tensor, CategoryTheory.sheafComposeIso_inv_fac_assoc, CategoryTheory.pseudofunctorOfIsLocallyDiscrete_map, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_inv_app_eq, AlgebraicGeometry.Scheme.Cover.gluedCoverT'_fst_snd_assoc, HomotopicalAlgebra.CofibrantBrownFactorization.mk'_p, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp_app, CategoryTheory.SimplicialObject.IsCoskeletal.isRightKanExtension, CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_inv_app_unmop_unmop, CondensedSet.LocallyConstant.instFaithfulCondensedTypeDiscrete, SSet.stdSimplex.objEquiv_toOrderHom_apply, CategoryTheory.Localization.SmallHom.equiv_comp, CategoryTheory.NatIso.naturality_2'_assoc, CategoryTheory.Limits.fst_of_isColimit, CategoryTheory.IsGrothendieckAbelian.instInjectiveZMonomorphismsRlpMonoMapFactorizationDataRlpOfNatHom, CategoryTheory.Functor.inrCompSum'_inv_app, CategoryTheory.ShortComplex.rightHomologyMap_add, CategoryTheory.ShortComplex.comp_τ₂_assoc, CategoryTheory.CartesianMonoidalCategory.inv_prodComparison_map_fst, CategoryTheory.Limits.biproduct.eqToHom_comp_ι_assoc, CategoryTheory.Functor.constComp_hom_app, HomologicalComplex.homotopyCofiber.inlX_fstX_assoc, CategoryTheory.MorphismProperty.Over.w, CategoryTheory.Adjunction.derivedη_fac_app, Frm.hom_id, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_left, CategoryTheory.Localization.Monoidal.associator_naturality, CategoryTheory.IsPushout.inl_isoPushout_hom, CategoryTheory.NonPreadditiveAbelian.add_comp, CategoryTheory.Pseudofunctor.Grothendieck.Hom.congr, CategoryTheory.Grpd.freeForgetAdjunction_homEquiv_apply, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom_assoc, CategoryTheory.Limits.biproduct.π_comp_eqToHom, CategoryTheory.Limits.coprod.diag_comp, CategoryTheory.Limits.coprod.inr_fst_assoc, GrpCat.ofHom_id, AugmentedSimplexCategory.tensorHom_id, CategoryTheory.DinatTrans.precompNatTrans_app, CategoryTheory.RelCat.Hom.rel_comp_apply₂, CategoryTheory.Functor.obj.μ_def_assoc, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ₀, AlgebraicGeometry.Scheme.Hom.stalkMap_comp, CategoryTheory.Limits.FormalCoproduct.powerMap_comp_assoc, CategoryTheory.Pretriangulated.productTriangle_mor₃, SSet.ι₁_fst, SSet.const_comp, CategoryTheory.PrelaxFunctor.map₂_comp, CategoryTheory.nerve.σ_zero_nerveEquiv_symm, CategoryTheory.Presieve.uncurry_ofArrows, CategoryTheory.SmallObject.SuccStruct.extendToSucc_map, CategoryTheory.Adjunction.rightAdjointUniq_hom_app_counit, CategoryTheory.Functor.homEquivOfIsRightKanExtension_symm_apply, Bicategory.Opposite.unop2_comp, CategoryTheory.OplaxFunctor.mapComp_naturality_left_assoc, CategoryTheory.Limits.imageSubobjectCompIso_hom_arrow_assoc, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.const_s, CategoryTheory.simplicialCosimplicialEquiv_unitIso_inv_app, Action.res_obj_ρ, CategoryTheory.MorphismProperty.IsStableUnderComposition.inf, CategoryTheory.Adjunction.derivedη_fac_app_assoc, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_inv_comp_π_assoc, CategoryTheory.Limits.inr_pushoutZeroZeroIso_inv, CategoryTheory.Regular.frobeniusMorphism_isPullback, CategoryTheory.NatTrans.toCatHom₂_comp, CategoryTheory.ShortComplex.leftHomology_ext_iff, CategoryTheory.Functor.RightExtension.postcompose₂_map_left_app, CategoryTheory.CosimplicialObject.σ_comp_σ_assoc, CategoryTheory.Equivalence.unit_naturality, HomologicalComplex.homologyι_naturality, CategoryTheory.Limits.Bicone.ι_π, AlgebraicGeometry.UniversallyClosed.eq_valuativeCriterion, CategoryTheory.Limits.prod.diag_map_fst_snd_assoc, CategoryTheory.ComposableArrows.isoMk₀_inv_app, CategoryTheory.GradedObject.CofanMapObjFun.ιMapObj_iso_inv_assoc, CategoryTheory.IsHomLift.comp_id_lift, CategoryTheory.StrictlyUnitaryLaxFunctor.mk'_map₂, CategoryTheory.isoSheafify_inv, CategoryTheory.GrpObj.div_comp, CategoryTheory.Limits.coprod.map_id_comp_assoc, HomotopicalAlgebra.instCofibrationOppositeOpOfFibration, CategoryTheory.Limits.limit.homIso_hom, CategoryTheory.Functor.prod'_ε_snd, CategoryTheory.Limits.Cone.category_comp_hom, HomotopicalAlgebra.CofibrantBrownFactorization.s_p_assoc, CategoryTheory.Limits.biprod.inr_fst_assoc, CategoryTheory.sum.inrCompAssociator_inv_app_down_down, CategoryTheory.Iso.hom_inv_id_app_app, CategoryTheory.Sieve.mem_functorPushforward_functor, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_hom_app_app, AlgebraicGeometry.StructureSheaf.algebraMap_germ, CochainComplex.cm5b.i_f_comp, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom, ModuleCat.FilteredColimits.ι_colimitDesc, CategoryTheory.Functor.LaxMonoidal.right_unitality_assoc, CategoryTheory.Equivalence.functor_unitIso_comp, CategoryTheory.Limits.colimit.existsUnique, CategoryTheory.Factorisation.Hom.ι_h, CategoryTheory.PrelaxFunctor.mapFunctor_obj, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.pentagon, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_apply, CategoryTheory.Limits.pullbackDiagonalMapIso.inv_snd_fst_assoc, CategoryTheory.Bimon.equivMonComonCounitIsoAppX_inv_hom, CategoryTheory.Comma.mapFst_hom_app, CategoryTheory.Functor.curry_obj_obj_map, CategoryTheory.Limits.wideCoequalizer.hom_ext_iff, CommAlgCat.hom_id, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_val_map, CategoryTheory.ComonObj.counit_comul_hom_assoc, CategoryTheory.Limits.inl_pushoutLeftPushoutInrIso_inv_assoc, CategoryTheory.GrothendieckTopology.overMapPullbackComp_inv_app_val_app, CategoryTheory.Limits.Cocone.ofPushoutCocone_ι, CategoryTheory.Pseudofunctor.Grothendieck.map_map_fiber, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₃_app, ComplexShape.Embedding.homRestrict.comm, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.comp, SemiNormedGrp₁.id_apply, CategoryTheory.MonObj.one_associator, CategoryTheory.eHom_whisker_cancel_inv_assoc, CategoryTheory.uliftYonedaIsoYoneda_hom_app_app, CategoryTheory.IsCodetecting.isIso_iff_of_epi, CategoryTheory.RetractArrow.op_r_left, CochainComplex.mappingCone.inr_snd, CommRingCat.comp_apply, CategoryTheory.ObjectProperty.isoClosure_sup, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv_assoc, CategoryTheory.Functor.IsEventuallyConstantFrom.coconeιApp_eq_id, CategoryTheory.MonoidalClosed.curry'_whiskerRight_comp_assoc, CategoryTheory.Limits.limit.map_pre', CategoryTheory.Preadditive.homSelfLinearEquivEndMulOpposite_symm_apply, CategoryTheory.Functor.Monoidal.map_whiskerRight_assoc, LinOrd.coe_id, CategoryTheory.ReflQuiv.id_obj, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app, CategoryTheory.NatTrans.CommShiftCore.app_shift, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullback_cone_of_left_condition, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_iso_hom, CategoryTheory.Pseudofunctor.StrongTrans.rightUnitor_hom_as_app, CategoryTheory.Functor.FullyFaithful.compUliftYonedaCompWhiskeringLeft_hom_app_app_down, CategoryTheory.Pseudofunctor.map₂_whisker_left_app_assoc, CategoryTheory.Join.mapWhiskerLeft_rightUnitor_hom, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.trans_app_left, CategoryTheory.Functor.LaxRightLinear.μᵣ_associativity, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_α, CategoryTheory.Functor.whiskeringRightObjCompIso_hom_app_app, AlgebraicGeometry.IsSeparated.instCompScheme, CategoryTheory.IsHomLift.id_lift_eqToHom_codomain, CategoryTheory.Functor.Monoidal.map_leftUnitor, CategoryTheory.Functor.whiskerLeft_id', CategoryTheory.Limits.isLimitConeOfCoconeLeftOp_lift, CategoryTheory.Limits.WalkingReflexivePair.rightCompReflexion_eq, CochainComplex.mappingCone.decomp_to, CategoryTheory.Bicategory.lanUnit_desc, CategoryTheory.Functor.leftDerived_fac, SemiNormedGrp.explicitCokernelDesc_zero, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst, CategoryTheory.eqToHom_down, CategoryTheory.Limits.inr_pushoutRightPushoutInlIso_inv_assoc, CategoryTheory.equivYoneda_inv_app, CategoryTheory.CommSq.shortComplex'_g, CategoryTheory.Functor.relativelyRepresentable.symmetry_fst_assoc, CategoryTheory.uliftCoyonedaEquiv_symm_map_assoc, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_obj, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.lift_fac, CategoryTheory.StructuredArrow.preEquivalenceInverse_map_right_right, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app, SimplexCategoryGenRel.δ_comp_δ_assoc, CategoryTheory.Iso.map_hom_inv_id_eval_app_assoc, HomologicalComplex.extendCyclesIso_hom_naturality, Rep.leftRegularHomEquiv_symm_single, CategoryTheory.PreGaloisCategory.comp_autMap_apply, CategoryTheory.Triangulated.SpectralObject.comp_hom, CategoryTheory.Comma.mapLeft_map_right, CommMonCat.coyoneda_map_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_right, CategoryTheory.ShortComplex.comp_τ₃, CategoryTheory.ObjectProperty.le_kernel_of_isoModSerre_isInvertedBy, CategoryTheory.Limits.ι_colimitFiberwiseColimitIso_hom, AlgebraicGeometry.Spec.homEquiv_apply, CategoryTheory.Subgroupoid.IsNormal.vertexSubgroup, HomologicalComplex.extend.leftHomologyData_i, CategoryTheory.Skeleton.comp_hom, CategoryTheory.StrictPseudofunctor.comp_mapComp_inv, CategoryTheory.Bicategory.whiskerLeft_id, inhomogeneousCochains.d_eq, CategoryTheory.Adjunction.homAddEquiv_symm_apply, CategoryTheory.Limits.pullbackSymmetry_inv_comp_fst, CategoryTheory.Functor.Faithful.map_injective, CategoryTheory.Limits.pullback.diagonal_comp, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_symm_apply_f, HomologicalComplex.extend.comp_d_eq_zero_iff, CategoryTheory.NatTrans.appLinearMap_apply, AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex_homotopyInvHomId, CategoryTheory.Functor.relativelyRepresentable.pullback₃.map_p₂_comp_assoc, CategoryTheory.unop_inv_braiding, ProfiniteAddGrp.coe_comp, HomologicalComplex.restrictionCyclesIso_inv_iCycles_assoc, CategoryTheory.CostructuredArrow.IsUniversal.fac, CategoryTheory.MorphismProperty.le_leftBousfieldW_isLocal, CategoryTheory.MonoidalClosed.curry_injective, CategoryTheory.Mon.mul_def, CategoryTheory.Limits.biproduct.whiskerEquiv_inv_eq_lift, CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_snd_fst_assoc, CategoryTheory.Pseudofunctor.Grothendieck.categoryStruct_comp_base, CategoryTheory.ObjectProperty.isCoseparating_unop_iff, CategoryTheory.GradedObject.mapBifunctorRightUnitor_naturality_assoc, CategoryTheory.Functor.Monoidal.map_ε_η, CategoryTheory.GradedObject.Monoidal.hexagon_forward, CategoryTheory.op_inv, CategoryTheory.Comonad.coalgebraPreadditive_homGroup_zsmul_f, CategoryTheory.ShortComplex.homologyIsoImageICyclesCompPOpcycles_ι, CategoryTheory.Localization.Construction.liftToPathCategory_map, BialgCat.toBialgHom_id, CategoryTheory.Limits.Trident.IsLimit.homIso_symm_apply, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_inv_assoc, CategoryTheory.ActionCategory.comp_val, CategoryTheory.Adjunction.localization_counit_app, AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom_appTop, CategoryTheory.Functor.mapGrpIdIso_inv_app_hom_hom, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₂, CategoryTheory.Comma.unopFunctorCompFst_inv_app, CategoryTheory.Abelian.Pseudoelement.zero_eq_zero, CategoryTheory.Lax.StrongTrans.vComp_naturality_inv, CategoryTheory.Limits.inl_comp_pushoutObjIso_inv_assoc, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIso_hom_app_hom, Mathlib.Tactic.Bicategory.eval_of, CochainComplex.mappingCone.inl_fst, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_fst_assoc, CategoryTheory.ShortComplex.HomotopyEquiv.trans_inv, CategoryTheory.Over.prodComparisonIso_pullback_Spec_inv_left_fst_fst', CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_restriction, CategoryTheory.HasLiftingProperty.iff_op, CategoryTheory.Presieve.FamilyOfElements.comp_of_compatible, CategoryTheory.LaxFunctor.mapComp_assoc_right_assoc, AlgebraicGeometry.coprodSpec_inl_assoc, AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem_toSpecΓ, AlgebraicGeometry.SheafedSpace.id_hom, CategoryTheory.shift_zero_eq_zero, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_awayι_assoc, CategoryTheory.Functor.Final.zigzag_of_eqvGen_colimitTypeRel, CategoryTheory.ShortComplex.eq_liftCycles_homologyπ_up_to_refinements, SSet.PtSimplex.MulStruct.δ_castSucc_castSucc_map_assoc, CategoryTheory.Iso.inv_hom_id_triangle_hom₁_assoc, CategoryTheory.CostructuredArrow.map_mk, SemiNormedGrp₁.mkHom_id, CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit_proj_assoc, CategoryTheory.Limits.ConeMorphism.hom_inv_id_assoc, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_hom, CategoryTheory.Limits.BinaryBicone.inlCokernelCofork_π, CategoryTheory.Pseudofunctor.mapComp'_naturality_2, ModuleCat.piIsoPi_hom_ker_subtype, CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id_app_assoc, CategoryTheory.Groupoid.invEquiv_symm_apply, CategoryTheory.Limits.opProdIsoCoprod_inv_inr, HomologicalComplex.singleObjHomologySelfIso_hom_naturality, AlgebraicGeometry.Spec.coe_toTop_map_hom_apply_asIdeal, AlgebraicGeometry.Scheme.Opens.toScheme_presheaf_map, CategoryTheory.IsPullback.zero_bot, CategoryTheory.Limits.prod.map_id_comp_assoc, PartOrdEmb.ofHom_comp, LightDiagram.id_hom_hom_hom_apply, CategoryTheory.Oplax.StrongTrans.vcomp_naturality_hom, AlgebraicGeometry.Scheme.instLocallyCoverDenseOverTopMorphismPropertyOverForgetOverGrothendieckTopology, CategoryTheory.Limits.coequalizer.isoTargetOfSelf_hom, CategoryTheory.ObjectProperty.rightOrthogonal.map_bijective_of_isTriangulated, CategoryTheory.Limits.pullbackObjIso_hom_comp_snd_assoc, CategoryTheory.MorphismProperty.CodescendsAlong.top, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_apply, CategoryTheory.Pi.evalCompEqToEquivalenceFunctor_inv, CategoryTheory.Functor.PreservesLeftKanExtension.preserves, CategoryTheory.orderDualEquivalence_functor_map, CategoryTheory.Localization.Monoidal.id_tensorHom_id, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_inv_app_app, CategoryTheory.toSkeletonFunctor_map_hom, CategoryTheory.Monad.algebraFunctorOfMonadHomComp_inv_app_f, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_obj_base, CategoryTheory.Functor.CorepresentableBy.homEquiv_comp, CategoryTheory.Limits.BinaryFan.braiding_inv_snd_assoc, CategoryTheory.Abelian.imageIsoImage_hom_comp_image_ι, CategoryTheory.PreZeroHypercover.hom_inv_h₀, CategoryTheory.ComonObj.comul_counit_assoc, CategoryTheory.CatEnrichedOrdinary.hComp_id_heq, CategoryTheory.ObjectProperty.isCodetecting_unop_iff, CategoryTheory.ShortComplex.LeftHomologyMapData.unop_φH, HomologicalComplex₂.D₁_D₂_assoc, CategoryTheory.IsSplitEpi.id_assoc, ModuleCat.hom_id, CategoryTheory.MorphismProperty.colimitsOfShape_le_of_final, CategoryTheory.Functor.FullyFaithful.compUliftCoyonedaCompWhiskeringLeft_inv_app_app_down, CategoryTheory.ModObj.one_smul, CategoryTheory.Adjunction.homAddEquiv_symm_add, Homotopy.trans_hom, CategoryTheory.Sum.natTransOfWhiskerLeftInlInr_comp, CategoryTheory.MonoidalCategory.leftUnitor_inv_naturality, CategoryTheory.Limits.PreservesLimitPair.iso_inv_fst, ComplexShape.Embedding.liftExtend.f_eq, CategoryTheory.Join.mapWhiskerRight_id, CategoryTheory.Limits.CatCospanTransform.associator_inv_right_app, CategoryTheory.Lax.StrongTrans.id_naturality_inv, CategoryTheory.Limits.ι_comp_sigmaObjIso_inv_assoc, CategoryTheory.ShortComplex.LeftHomologyMapData.commi_assoc, CategoryTheory.Limits.pushoutIsoOpPullback_inl_hom_assoc, ModuleCat.extendScalars_id_comp_assoc, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.eq_id_of_D₂_W, SimplexCategory.δ_comp_σ_succ', CategoryTheory.Limits.colimit.ι_coconeMorphism, CategoryTheory.Comma.equivProd_unitIso_inv_app_right, CategoryTheory.Over.whiskerLeft_left_snd_assoc, CategoryTheory.LocalizerMorphism.equiv_smallHomMap, CategoryTheory.Limits.BiconeMorphism.wπ, CategoryTheory.ShortComplex.π_homologyMap_ι_assoc, CategoryTheory.Monad.beckAlgebraCofork_ι_app, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_comp, TopCat.Sheaf.objSupIsoProdEqLocus_hom_snd, CategoryTheory.Idempotents.Karoubi.complement_p, CategoryTheory.Functor.Monoidal.tensorHom_app_snd_assoc, CategoryTheory.Sheaf.instIsLocallySurjectiveHomMapTypeSheafComposeForget, CategoryTheory.ite_comp, SSet.Truncated.StrictSegal.spine_δ_arrow_eq, CategoryTheory.Adjunction.CommShift.compatibilityUnit_right, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_inv_app_fst_app, CategoryTheory.Limits.biprod.lift_snd_assoc, CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_inv_hom_assoc, SemiNormedGrp.comp_explicitCokernelπ, CategoryTheory.Functor.CommShift.isoAdd'_hom_app, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_app, CategoryTheory.Limits.Fan.IsLimit.lift_proj, CategoryTheory.Limits.hasPullback_of_left_factors_mono, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app_assoc, SimplexCategory.Truncated.δ₂_two_comp_σ₂_zero_assoc, CategoryTheory.Oplax.OplaxTrans.naturality_naturality_assoc, CategoryTheory.GrpObj.inv_def, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_norm, CategoryTheory.Limits.IsColimit.pushoutCoconeEquivBinaryCofanFunctor_desc_right, CategoryTheory.braiding_inv_tensorUnit_right, CategoryTheory.Functor.IsCoverDense.homOver_app, CategoryTheory.NatIso.naturality_2', CategoryTheory.Iso.cancel_iso_hom_right, CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal_δ_unmop_unmop, CategoryTheory.Limits.Sigma.ι_π_of_ne_assoc, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_inv_app_app, SimplexCategory.δ_comp_σ_self, CategoryTheory.CartesianMonoidalCategory.lift_comp_fst_snd, CategoryTheory.Limits.kernelSubobject_comp_mono, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w_assoc, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app, CategoryTheory.Join.mapWhiskerRight_rightUnitor_hom, CategoryTheory.Limits.equalizerSubobject_arrow', CategoryTheory.Limits.FormalCoproduct.powerMap_comp, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionRight_unop, CochainComplex.mappingCone.liftCochain_v_fst_v_assoc, HomologicalComplex.cylinder.ι₁_desc_assoc, CategoryTheory.Limits.prod.pentagon, CategoryTheory.PreGaloisCategory.instFaithfulContActionFintypeCatHomCarrierAutFunctorFunctorToContAction, CategoryTheory.Limits.hasImage_comp_iso, CategoryTheory.IsIso.comp_inv_eq, AlgebraicGeometry.Spec.map_eqToHom, CategoryTheory.Limits.Cone.ofFork_π, CategoryTheory.Functor.CorepresentableBy.uniqueUpToIso_hom, CategoryTheory.Limits.colimit.ι_map_assoc, CategoryTheory.Limits.MultispanIndex.parallelPairDiagramOfIsColimit_map, CategoryTheory.ShortComplex.cyclesMap'_i_assoc, CategoryTheory.Limits.CatCospanTransform.whiskerLeft_comp, CategoryTheory.Functor.mapTriangleCompIso_hom_app_hom₁, AlgebraicGeometry.Scheme.Hom.comp_toLRSHom_assoc, CategoryTheory.ComonadHom.app_δ, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom, CategoryTheory.Retract.trans_r, HomotopicalAlgebra.Precylinder.LeftHomotopy.h₁, CategoryTheory.Bicategory.InducedBicategory.forget_obj, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left_assoc, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_hom_app_f, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHomRight, CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_idem_assoc, CategoryTheory.FunctorToTypes.rightAdj_obj_map_app, CategoryTheory.PreZeroHypercover.id_h₀, CategoryTheory.CosimplicialObject.δ_comp_σ_self, CategoryTheory.imageUnopOp_hom_comp_image_ι, CategoryTheory.ShortComplex.SnakeInput.Hom.comm₀₁, CategoryTheory.SimplicialObject.δ_comp_σ_of_gt', CategoryTheory.Adjunction.Triple.map_rightToLeft_app, CategoryTheory.Localization.Preadditive.add'_comp, CategoryTheory.IsFiltered.crown, TopCat.Sheaf.objSupIsoProdEqLocus_inv_eq_iff, CategoryTheory.Pi.eqToEquivalenceFunctorIso_inv, CategoryTheory.Limits.isColimitCoconeRightOpOfCone_desc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_associator, HomologicalComplex.instQuasiIsoOppositeMapSymmOpFunctorOp, CategoryTheory.CartesianMonoidalCategory.lift_whiskerRight, CategoryTheory.Limits.limitUnopIsoUnopColimit_hom_comp_ι_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app_assoc, CategoryTheory.Limits.isColimitCoconeOfConeRightOp_desc, CategoryTheory.Subobject.underlying_arrow_assoc, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_comp, groupHomology.H1π_comp_map, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_app, CategoryTheory.Limits.desc_op_comp_opCoproductIsoProduct_hom, HomologicalComplex.homologyIsoSc'_inv_ι, CategoryTheory.Localization.lift₂NatTrans_app_app, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles, HomologicalComplex.restrictionHomologyIso_inv_homologyι, CategoryTheory.Equivalence.sheafCongrPrecoherent_inverse_obj_val_map, CategoryTheory.Limits.CokernelCofork.map_condition, SimplicialObject.Split.id_f, CategoryTheory.MonoidalOpposite.tensorRightMopIso_inv_app_unmop, CategoryTheory.Limits.FormalCoproduct.powerMap_id, CategoryTheory.Limits.biproduct.lift_matrix, CategoryTheory.Adjunction.eq_unit_comp_map_iff, ModuleCat.extendScalars_assoc', CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₃₁_assoc, HomologicalComplex.restrictionToTruncGE'_naturality_assoc, HomologicalComplex.singleObjHomologySelfIso_hom_naturality_assoc, FinBddDistLat.hom_comp, AddSemigrp.coe_comp, CategoryTheory.IsPullback.isoIsPullback_inv_fst_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_id, ModuleCat.piIsoPi_inv_kernel_ι, CategoryTheory.MonoidalCategory.dite_tensor, CategoryTheory.Limits.Types.Pushout.condition, CategoryTheory.NatTrans.mapHomologicalComplex_naturality_assoc, CategoryTheory.LocalizerMorphism.map, HomologicalComplex.singleObjHomologySelfIso_inv_naturality_assoc, AlgebraicGeometry.isomorphisms_eq_isOpenImmersion_inf_surjective, CategoryTheory.Limits.pullback_snd_iso_of_right_factors_mono, NonemptyFinLinOrd.comp_apply, CategoryTheory.MonObj.pow_comp, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_hom_app_val_app, CategoryTheory.Pretriangulated.triangleCategory_comp, CategoryTheory.StrictPseudofunctor.id_map, CategoryTheory.Functor.constCompEvaluationObj_hom_app, CategoryTheory.Functor.leftKanExtensionIsoFiberwiseColimit_hom_app, CategoryTheory.Limits.biprod.symmetry_assoc, CategoryTheory.Pseudofunctor.toDescentData_map_hom, CategoryTheory.CountableCategory.instCountableHomObjAsType, CategoryTheory.MonoidalCategory.tensor_inv_hom_id, CategoryTheory.Monad.comparisonForget_inv_app, CategoryTheory.ShortComplex.RightHomologyMapData.commι, CategoryTheory.ShortComplex.HomologyMapData.neg_right, smoothSheafCommRing.ι_forgetStalk_hom_assoc, CategoryTheory.Pseudofunctor.map₂_associator, CategoryTheory.CosimplicialObject.equivalenceRightToLeft_right_app, CategoryTheory.ShortComplex.toCycles_i, CategoryTheory.CommSq.LiftStruct.unop_l, CategoryTheory.Functor.LaxMonoidal.comp_ε, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_assoc, CategoryTheory.MorphismProperty.ContainsIdentities.op, CategoryTheory.IsSplitMono.id, CategoryTheory.shiftFunctorAdd_add_zero_hom_app, AlgebraicGeometry.Proj.awayMap_awayToSection, CategoryTheory.Groupoid.invEquivalence_counitIso, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, CategoryTheory.Limits.MonoFactorisation.ofIsoI_m, CategoryTheory.LocalizerMorphism.RightResolution.Hom.comp_f, CategoryTheory.Limits.π_comp_cokernelComparison, CategoryTheory.ShortComplex.homologyι_comp_fromOpcycles, CategoryTheory.Bicategory.conjugateEquiv_associator_hom, CategoryTheory.ShortComplex.SnakeInput.id_f₃, CategoryTheory.Bicategory.Prod.swap_obj, CategoryTheory.HasLiftingProperty.iff_unop, CategoryTheory.StructuredArrow.mapIso_unitIso_hom_app_right, CategoryTheory.epi_from_simple_zero_of_not_iso, CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ', AlgebraicGeometry.Scheme.Hom.map_resLE, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_app_app, CategoryTheory.Limits.Sigma.ι_reindex_inv, CategoryTheory.Equivalence.cancel_counitInv_right_assoc', CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_fst, CategoryTheory.MonoidalCategory.tensor_associativity, CategoryTheory.Limits.MultispanIndex.ι_fstSigmaMap, CategoryTheory.Free.lift_map_single, DerivedCategory.right_fac_of_isStrictlyLE, CategoryTheory.Square.opFunctor_map_τ₃, CategoryTheory.Idempotents.Karoubi.zsmul_hom, CategoryTheory.Presheaf.map_comp_uliftYonedaEquiv_down_assoc, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_obj, CategoryTheory.homOfLE_op_comp_eqToHom, CategoryTheory.MonoidalOpposite.mopMopEquivalenceFunctorMonoidal_δ, CategoryTheory.isCoseparating_unop_iff, HomologicalComplex₂.ι_totalShift₂Iso_inv_f, CategoryTheory.Abelian.coimage.comp_π_eq_zero, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_hom, CategoryTheory.Idempotents.Karoubi.idem, CategoryTheory.Functor.id_mapMon_mul, CategoryTheory.Prod.sectL_map, CategoryTheory.StructuredArrow.w, CategoryTheory.Join.opEquiv_inverse_map_edge_op, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_inv_hom'_assoc, CategoryTheory.ObjectProperty.homMk_surjective, groupHomology.pOpcycles_comp_opcyclesIso_hom_assoc, CategoryTheory.MonObj.mul_braiding, CategoryTheory.MorphismProperty.instHasOfPostcompPropertyMin, CategoryTheory.IsPushout.inl_isoPushout_hom_assoc, CategoryTheory.PrelaxFunctor.map₂_hom_inv_isIso, CategoryTheory.Functor.curryingFlipEquiv_apply_map, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_assoc, CochainComplex.ConnectData.map_id, Bimod.triangle_bimod, CategoryTheory.ObjectProperty.instIsStableUnderShiftMin, CategoryTheory.Limits.coconeLeftOpOfCone_ι_app, CategoryTheory.MorphismProperty.RightFraction.unop_f, CategoryTheory.Limits.π_comp_colimitRightOpIsoUnopLimit_inv, CategoryTheory.Limits.ι_comp_colimitUnopIsoOpLimit_hom_assoc, AlgebraicTopology.DoldKan.PInfty_f_idem, CategoryTheory.isCoseparator_iff_faithful_preadditiveYonedaObj, CategoryTheory.Limits.zero_of_target_iso_zero, CategoryTheory.EnrichedFunctor.forgetComp_hom_app, CategoryTheory.CommGrp.id_hom, CategoryTheory.Functor.CoreMonoidal.μIso_hom_natural_right, Rep.ofHom_ρ, CategoryTheory.inv_comp_eq_id, CategoryTheory.ShortComplex.Homotopy.add_h₂, CategoryTheory.yonedaGrpObj_obj_coe, CategoryTheory.LocalizerMorphism.RightResolution.unop_w, AlgebraicGeometry.Proj.SpecMap_awayMap_awayι, CategoryTheory.conjugateEquiv_id, CategoryTheory.Functor.mapAddHom_apply, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_fac_app, CategoryTheory.Functor.constCompWhiskeringLeftIso_inv_app_app, CategoryTheory.Dial.pentagon, CategoryTheory.Functor.RightExtension.postcompose₂_map_right, AlgebraicGeometry.basicOpenIsoSpecAway_inv_homOfLE_assoc, CategoryTheory.Abelian.Ext.smul_eq_comp_mk₀, AlgebraicTopology.DoldKan.N₂_obj_p_f, inr_coprodIsoPushout_hom, CategoryTheory.NatTrans.leftOpWhiskerRight_assoc, CategoryTheory.ShortComplex.Splitting.r_f, ModuleCat.extendScalars_id_comp, SheafOfModules.GeneratingSections.ofEpi_π, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.single_W, CategoryTheory.Oplax.OplaxTrans.Modification.whiskerRight_naturality_assoc, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_inv_inv_assoc, CategoryTheory.Functor.leftOpComp_hom_app, CategoryTheory.PreOneHypercover.trivial_p₂, CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit_assoc, CategoryTheory.Square.Hom.comm₃₄_assoc, SSet.Truncated.HomotopyCategory.BinaryProduct.square, CategoryTheory.Limits.cospanCompIso_hom_app_one, CategoryTheory.Pseudofunctor.ObjectProperty.IsClosedUnderIsomorphisms.isClosedUnderIsomorphisms, RingCat.hom_id, CategoryTheory.Over.leftUnitor_inv_left_fst_assoc, CategoryTheory.Limits.ι_comp_coequalizerComparison, CochainComplex.ConnectData.shape, CategoryTheory.Triangulated.TStructure.zero', CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv, HomologicalComplex.pOpcycles_opcyclesIsoSc'_hom_assoc, CategoryTheory.Functor.OneHypercoverDenseData.SieveStruct.fac_assoc, CondensedSet.LocallyConstant.instFullCondensedTypeDiscrete, CategoryTheory.Functorial.map_comp, CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero, CategoryTheory.Limits.inr_inl_pushoutAssoc_hom, AlgebraicGeometry.tilde.map_add, CategoryTheory.Idempotents.app_comp_p_assoc, CategoryTheory.Subobject.ofLE_comp_ofLE, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_app_snd_app, CategoryTheory.Functor.RepresentableBy.uniqueUpToIso_inv, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_hom_comp_map_π, CategoryTheory.whiskerRight_coprod_inl_rightDistrib_inv_assoc, RingCat.moduleCatRestrictScalarsPseudofunctor_mapComp, CategoryTheory.Limits.CatCospanTransform.associator_hom_base_app, CategoryTheory.Functor.Initial.exists_eq, CategoryTheory.Functor.CommShift.isoZero_inv_app, CategoryTheory.Limits.IsImage.lift_fac_assoc, Action.FintypeCat.quotientToQuotientOfLE_hom_mk, CategoryTheory.TwoSquare.whiskerTop_app, CategoryTheory.IsPullback.zero_right, HomologicalComplex.eqToHom_comp_d, CochainComplex.HomComplex.Cochain.leftShift_v, AlgebraicGeometry.isIso_SpecMap_stakMap_localization, CategoryTheory.Limits.coend.hom_ext_iff, CochainComplex.mappingCone.d_fst_v'_assoc, CategoryTheory.WithTerminal.inclLiftToTerminal_hom_app, CategoryTheory.Functor.sheafPushforwardContinuousCompSheafToPresheafIso_hom_app_app, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitIso_inv_naturality_assoc, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left, AlgebraicGeometry.Scheme.residue_residueFieldMap_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHomLeft, CategoryTheory.Limits.equalizerSubobject_arrow_comp_assoc, CategoryTheory.StrictPseudofunctor.id_mapId_hom, groupHomology.H1CoresCoinfOfTrivial_f, CategoryTheory.kernelCokernelCompSequence.snakeInput_v₀₁_τ₁, CategoryTheory.Bicategory.InducedBicategory.Hom.category_comp_hom, CategoryTheory.Mat.id_apply_of_ne, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_counitIso_hom_app_f, LightCondMod.epi_iff_locallySurjective_on_lightProfinite, CategoryTheory.Subobject.ofMkLE_comp_ofLE, CategoryTheory.Bicategory.Prod.fst_map, CategoryTheory.ExactPairing.coevaluation_evaluation, CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_hom_comp_i, CategoryTheory.Functor.commShiftIso_inv_naturality, CategoryTheory.Limits.pullback_diagonal_map_snd_snd_fst, CategoryTheory.Limits.kernelSubobject_arrow'_assoc, CategoryTheory.Limits.limitIsoLimitCurryCompLim_inv_π, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_app, CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_comp, AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit_map, CategoryTheory.Limits.colimit.ι_desc_assoc, CategoryTheory.Adjunction.left_triangle, SSet.stdSimplex.ofSimplex_yonedaEquiv_δ, SheafOfModules.comp_val_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app_assoc, groupHomology.cyclesIso₀_comp_H0π_assoc, CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_inv, CategoryTheory.Idempotents.Karoubi.decompId_assoc, CategoryTheory.Bicategory.Adj.Hom₂.conjugateEquiv_τl, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_id, AlgebraicTopology.DoldKan.σ_comp_PInfty, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_iso_inv, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapCompIso_inv, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_mul, CategoryTheory.WithTerminal.liftFromOver_obj_map, CochainComplex.HomComplex.Cochain.toSingleMk_zero, CategoryTheory.Bicategory.eqToHom_whiskerRight, CategoryTheory.GrothendieckTopology.Point.comp_hom_assoc, CategoryTheory.Functor.relativelyRepresentable.pullback₃.map_p₂_comp, AlgebraicTopology.DoldKan.Compatibility.τ₁_hom_app, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj, CategoryTheory.Functor.LeftExtension.precomp_map_left, CategoryTheory.Limits.prod.map_snd_assoc, CategoryTheory.IsFiltered.span, CategoryTheory.Comma.mapLeftIso_functor_obj_hom, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_inv_fac, CategoryTheory.Equivalence.unit_app_comp_inverse_map_η_functor, CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_hom_assoc, CategoryTheory.Cat.FreeRefl.morphismProperty_eq_top, UniformSpaceCat.hom_id, CategoryTheory.Preadditive.comp_add, LightCondensed.ihom_map_val_app, CategoryTheory.Dial.comp_f, AlgebraicGeometry.Scheme.comp_toLRSHom, prodIsoPullback_inv_snd, CategoryTheory.Oplax.OplaxTrans.rightUnitor_inv_as_app, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_assoc, CategoryTheory.PreOneHypercover.Hom.w₁₂_assoc, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_hom_f_f, groupHomology.mapCycles₂_comp_i_assoc, CategoryTheory.Limits.Multicoequalizer.condition_assoc, CategoryTheory.PreZeroHypercover.Hom.w₀_assoc, CategoryTheory.Functor.mapGrp_obj_grp_mul, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.unitIso_inv, CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsTop, CategoryTheory.LaxFunctor.map₂_rightUnitor_app_assoc, CategoryTheory.Functor.LaxLeftLinear.μₗ_unitality, CategoryTheory.Abelian.Pseudoelement.pseudoZero_aux, CategoryTheory.MorphismProperty.RightFraction.leftFraction_fac_assoc, CategoryTheory.Functor.mapCommpGrp_id_mul, SheafOfModules.map_ιFree_mapFree_hom, CategoryTheory.Abelian.Ext.addEquiv₀_symm_apply, LinearMap.id_semiModuleCat_comp, CategoryTheory.rightDistributor_inv_comp_biproduct_π_assoc, CategoryTheory.sheafToPresheaf_η, CategoryTheory.Dial.id_f, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_right, CategoryTheory.Enriched.FunctorCategory.enriched_assoc, CategoryTheory.ShortComplex.Homotopy.eq_add_nullHomotopic, CategoryTheory.GradedObject.mapBifunctorRightUnitorCofan_inj_assoc, CategoryTheory.Limits.kernelZeroIsoSource_hom, groupCohomology.isoCocycles₁_hom_comp_i, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_hom_app_app_hom, TopCat.Presheaf.presheafEquivOfIso_counitIso_inv_app_app, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk, CategoryTheory.Presieve.FamilyOfElements.isAmalgamation_map_localPreimage, CategoryTheory.Iso.map_hom_inv_id_app_assoc, HomotopyCategory.homologyFunctor_shiftMap_assoc, CategoryTheory.Presheaf.isLocallySurjective_toPlus, AlgebraicGeometry.PresheafedSpace.stalkMap.congr_hom, dNext_eq_dFrom_fromNext, GrpWithZero.hom_id, AddCommGrpCat.biproductIsoPi_inv_comp_π, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanIndex_fst, CochainComplex.augmentTruncate_inv_f_succ, CategoryTheory.Functor.whiskerRight_comp_assoc, AlgebraicGeometry.ι_sigmaSpec_assoc, CategoryTheory.Subobject.underlyingIso_inv_top_arrow_assoc, HomologicalComplex.double_d, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_hom_app_left, CategoryTheory.rightDistributor_hom_comp_biproduct_π, CategoryTheory.Preadditive.sum_comp'_assoc, CategoryTheory.ι_colimitCompWhiskeringRightIsoColimitComp_hom_assoc, HomologicalComplex₂.totalShift₂Iso_hom_naturality, CochainComplex.mappingCone.inl_v_d, Bimod.RightUnitorBimod.hom_left_act_hom', CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_app_assoc, CategoryTheory.Linear.homCongr_symm_apply, CategoryTheory.DifferentialObject.Hom.comm, Action.FunctorCategoryEquivalence.inverse_map_hom, AlgebraicGeometry.PresheafedSpace.Γ_map, CategoryTheory.OplaxFunctor.mapComp'_comp_whiskerLeft_mapComp', CategoryTheory.Iso.hom_inv_id_assoc, AlgebraicGeometry.Scheme.IdealSheafData.subSchemeCover_map_inclusion_assoc, CategoryTheory.Pretriangulated.contractibleTriangle_mor₃, CategoryTheory.ShortComplex.Homotopy.comp_h₀, CategoryTheory.Adjunction.homAddEquiv_neg, MonObj.mopEquiv_functor_obj_mon_mul_unmop, AlgebraicGeometry.SheafedSpace.id_hom_c, CategoryTheory.Bicategory.Pith.comp₂_iso_hom, CategoryTheory.Limits.biproduct.desc_eq, CategoryTheory.Bicategory.lanLiftUnit_desc, CategoryTheory.Bicategory.leftUnitor_naturality_assoc, CategoryTheory.exactFunctor_le_leftExactFunctor, CategoryTheory.Limits.inl_comp_pushoutSymmetry_inv_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.whiskerRight_actionHomLeft, CategoryTheory.Bicategory.conjugateEquiv_id, CategoryTheory.Lax.StrongTrans.id_naturality_hom, AlgebraicGeometry.ΓSpec.right_triangle, CategoryTheory.Limits.Pi.π_comp_eqToHom, AddGrpCat.comp_apply, DistLat.ofHom_id, CategoryTheory.ObjectProperty.instEssentiallySmallOppositeOp, CategoryTheory.Enriched.FunctorCategory.functorEnriched_id_comp_assoc, CategoryTheory.Limits.colimit.ι_desc_app_assoc, CategoryTheory.TwoSquare.whiskerRight_app, CategoryTheory.Localization.liftNatTrans_id, CategoryTheory.Functor.CoreMonoidal.right_unitality, TopologicalSpace.Opens.op_map_comp_obj, CategoryTheory.Adjunction.homEquiv_symm_id, AlgebraicGeometry.SheafedSpace.id_c_app, CategoryTheory.isIso_iff_yoneda_map_bijective, AlgebraicGeometry.instIsAffineXSchemeCoverOfIsIsoIsOpenImmersionId, CategoryTheory.Limits.π_colimitOfIsReflexivePairIsoCoequalizer_inv, Rep.Action_ρ_eq_ρ, SSet.Truncated.Path₁.arrow_tgt, CategoryTheory.TwistShiftData.shiftFunctorAdd'_inv_app, CategoryTheory.Limits.PullbackCone.combine_pt_map, CategoryTheory.StrictlyUnitaryLaxFunctor.mk'_map, CategoryTheory.Limits.pushout.congrHom_hom, CategoryTheory.Bicategory.whisker_assoc, CategoryTheory.Square.op_f₁₃, CategoryTheory.Limits.equalizerSubobject_arrow_assoc, CategoryTheory.wideSubcategoryInclusion.map, CategoryTheory.Lax.OplaxTrans.naturality_id, CategoryTheory.Functor.OplaxRightLinear.δᵣ_naturality_left_assoc, CategoryTheory.Iso.unop_hom, CategoryTheory.comp_ite, CategoryTheory.Limits.Fork.IsLimit.lift_ι_assoc, CategoryTheory.MorphismProperty.RightFraction.exists_leftFraction, CategoryTheory.MorphismProperty.LeftFraction.exists_rightFraction, AlgebraicGeometry.Scheme.residue_residueFieldCongr, CategoryTheory.ShortComplex.ShortExact.δ_comp, CategoryTheory.Subgroupoid.coe_inv_coe, CochainComplex.HomComplex.Cochain.shift_v, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom, CategoryTheory.MonoidalCategory.tensor_right_unitality, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₃, CategoryTheory.CartesianMonoidalCategory.prodComparison_fst_assoc, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_of_eq, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counit_app_tensor_assoc, CategoryTheory.SemiCartesianMonoidalCategory.default_eq_toUnit, CategoryTheory.Join.mapPairComp_inv_app_left, CategoryTheory.Arrow.hom_inv_id_left, CategoryTheory.StructuredArrow.w_prod_fst_assoc, CategoryTheory.WithInitial.coconeEquiv_inverse_map_hom_right, AlgebraicGeometry.StructureSheaf.comap_id_eq_map, CategoryTheory.MonoidalClosed.internalHom_map, AlgebraicGeometry.Scheme.Hom.appIso_hom, HomotopicalAlgebra.fibrations_op, CategoryTheory.MonoidalCategory.MonoidalRightAction.inv_hom_actionHomLeft', CategoryTheory.Limits.colimit.eqToHom_comp_ι, CategoryTheory.ShortComplex.HomologyMapData.smul_right, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_inv_comp_rightHomologyι_assoc, CategoryTheory.Limits.opProdIsoCoprod_hom_snd, CategoryTheory.Limits.biprod.lift_desc_assoc, CategoryTheory.Limits.coprod.inr_snd_assoc, CategoryTheory.Functor.isMittagLeffler_iff_subset_range_comp, CategoryTheory.Sigma.mapId_hom_app, CategoryTheory.toSheafify_sheafifyLift, CategoryTheory.Functor.Monoidal.map_whiskerLeft, CategoryTheory.Functor.limitIsoOfIsRightKanExtension_inv_π_assoc, CategoryTheory.ProjectiveResolution.Hom.hom_f_zero_comp_π_f_zero, CategoryTheory.ShortComplex.leftRightHomologyComparison'_naturality_assoc, CategoryTheory.Comonad.counit_naturality_assoc, HomologicalComplex.pOpcycles_singleObjOpcyclesSelfIso_inv_assoc, CategoryTheory.Preadditive.isLimitForkOfKernelFork_lift, CategoryTheory.SimplicialObject.δ_comp_σ_self_assoc, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.IsTerminal.comm_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_inv_assoc, CategoryTheory.ShiftedHom.opEquiv'_symm_comp, CategoryTheory.Preadditive.epi_iff_isZero_cokernel', groupCohomology.cochainsMap_f_0_comp_cochainsIso₀, CategoryTheory.PreOneHypercover.sieve₁_apply, CategoryTheory.Functor.closedSieves_map_coe, CategoryTheory.leftDistributor_ext_right_iff, CategoryTheory.Functor.unopComp_inv_app, CategoryTheory.δ_naturality_assoc, CategoryTheory.CatCommSq.vComp_iso_inv_app, AlgebraicGeometry.instIsAffineHomCompScheme, FinPartOrd.hom_id, SimplicialObject.Splitting.IndexSet.epiComp_snd_coe, CategoryTheory.Limits.CokernelCofork.map_π, CategoryTheory.Bicategory.Adj.comp_τr, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, CategoryTheory.ShortComplex.LeftHomologyMapData.smul_φK, CategoryTheory.MorphismProperty.transfiniteCompositions_le, CategoryTheory.Limits.limit.hom_ext_iff, FintypeCat.inv_hom_id_apply, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd_assoc, SimplicialObject.Split.Hom.comm_assoc, CochainComplex.mappingCone.inr_f_snd_v_assoc, CategoryTheory.Over.liftCocone_ι_app, CategoryTheory.OplaxFunctor.PseudoCore.mapIdIso_hom, CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.pullHom_id, SemiNormedGrp.coe_id, CategoryTheory.Adjunction.homEquiv_naturality_left_square_iff, CategoryTheory.Pretriangulated.TriangleMorphism.comm₁, CategoryTheory.Limits.image.fac_assoc, SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_hom_app, CategoryTheory.IsPushout.inl_isoPushout_inv_assoc, CategoryTheory.comp_eqToHom_iff, CategoryTheory.cancel_mono_id, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm, CategoryTheory.Limits.inr_comp_pushoutComparison_assoc, HomologicalComplex.truncGE'Map_comp_assoc, CategoryTheory.Limits.ι_colimitFiberwiseColimitIso_inv, ModuleCat.hom_zsmul, CategoryTheory.Sieve.ofArrows.exists, TopCat.comp_app, CategoryTheory.eHom_whisker_cancel_inv, CategoryTheory.Limits.PullbackCone.unop_pt, CategoryTheory.Iso.map_inv_hom_id_eval, CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_π_succ, AlgebraicTopology.DoldKan.N₁Γ₀_hom_app, CategoryTheory.GrpObj.mul_inv_rev, HomotopicalAlgebra.FibrantBrownFactorization.mk'_r, CategoryTheory.Preadditive.inv_def, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_εIso_inv, CategoryTheory.NatTrans.IsMonoidal.unit_assoc, CategoryTheory.coprod_inr_leftDistrib_hom_assoc, CategoryTheory.SplitMono.comp_retraction, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_apply, CategoryTheory.Endofunctor.Coalgebra.ext_iff, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHom, CategoryTheory.GrpObj.mulRight_hom, HomologicalComplex.mapBifunctorMapHomotopy.comm₁_aux, CategoryTheory.MorphismProperty.FunctorsInverting.comp_hom, CategoryTheory.Functor.PullbackObjObj.π_snd_assoc, MonCat.ofHom_id, CategoryTheory.Limits.biprod.inl_map_assoc, CategoryTheory.Adjunction.homEquiv_naturality_right_symm, InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj, CategoryTheory.Functor.LaxMonoidal.μ_natural_left, CategoryTheory.Functor.mapMonCompIso_inv_app_hom, CategoryTheory.SmallObject.functorMap_π, AlgebraicGeometry.instHasOfPostcompPropertySchemeIsSeparatedTopMorphismProperty, CategoryTheory.Presheaf.instIsLocallySurjectiveHomToRangeSheafify, groupHomology.mapCycles₂_id_comp_apply, CategoryTheory.NatIso.naturality_2, ChainComplex.linearYonedaObj_d, CategoryTheory.Functor.opComp_hom_app, AlgebraicGeometry.Scheme.residue_residueFieldMap, CategoryTheory.ExponentiableMorphism.coev_naturality_assoc, CategoryTheory.ShortComplex.unop_g, CategoryTheory.Functor.rightDerived_fac_app_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_left, CategoryTheory.ShortComplex.Homotopy.symm_h₂, Action.zsmul_hom, SimplicialObject.Splitting.ι_desc, HomologicalComplex.Hom.comm_assoc, AlgCat.comp_apply, CategoryTheory.PreGaloisCategory.instEssSurjContActionFintypeCatHomCarrierAutFunctorFunctorToContActionOfFiberFunctor, CategoryTheory.Mon_Class.one_comp, CategoryTheory.StructuredArrow.mapIso_functor_obj_hom, CategoryTheory.cokernelOpUnop_hom, CategoryTheory.Preadditive.neg_comp, HomologicalComplex.truncGE'Map_id, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_fst, CategoryTheory.MorphismProperty.Comma.hasColimit_of_closedUnderColimitsOfShape, CategoryTheory.GradedObject.Monoidal.pentagon_inv_assoc, CategoryTheory.Limits.Cocone.mapCoconeToOver_inv_hom, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_left, CategoryTheory.StructuredArrow.mapNatIso_unitIso_inv_app_right, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc, HomotopicalAlgebra.PrepathObject.RightHomotopy.h₀, CategoryTheory.Subfunctor.Subpresheaf.preimage_comp, CategoryTheory.BasedNatIso.id_inv, CategoryTheory.Limits.coprod.map_desc_assoc, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_functor_obj_d_f, CategoryTheory.ShortComplex.mapCyclesIso_hom_iCycles, CategoryTheory.Congruence.compLeft, CategoryTheory.Bicategory.conjugateEquiv_symm_iso, CategoryTheory.Limits.limit.lift_π_assoc, CategoryTheory.Limits.FormalCoproduct.category_id_f, CategoryTheory.Functor.ranObjObjIsoLimit_hom_π, Compactum.str_hom_commute, Homotopy.smul_hom, AlgebraicGeometry.Scheme.evaluation_naturality_assoc, CategoryTheory.Dial.isoMk_hom_F, Homotopy.prevD_zero_cochainComplex, AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom, CategoryTheory.IsCardinalFilteredGenerator.of_isDense, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.toBiprod_fromBiprod_assoc, CategoryTheory.Equivalence.rightOp_unitIso_inv_app, CategoryTheory.Functor.LaxLeftLinear.μₗ_unitality_inv_assoc, HomotopicalAlgebra.RightHomotopyClass.whitehead, CategoryTheory.Functor.OplaxLeftLinear.δₗ_unitality_inv_assoc, CategoryTheory.Bicategory.Prod.sectR_mapComp_hom, SSet.Quasicategory.hornFilling, CategoryTheory.Limits.MonoFactorisation.kernel_ι_comp, CategoryTheory.HomOrthogonal.eq_zero, CategoryTheory.Limits.pullback_inv_fst_snd_of_right_isIso, CategoryTheory.StrictPseudofunctor.mapComp_eq_eqToIso, AlgebraicGeometry.Scheme.Hom.resLE_comp_ι_assoc, CategoryTheory.Mat_.isoBiproductEmbedding_inv, AlgebraicGeometry.tilde.toOpen_res, CategoryTheory.Pretriangulated.Triangle.add_hom₁, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_map, CategoryTheory.MonoidalCategory.leftUnitor_inv_comp_tensorHom, AlgebraicGeometry.tilde.toOpen_res_assoc, CategoryTheory.PreservesImage.hom_comp_map_image_ι_assoc, AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap_assoc, AlgebraicGeometry.PresheafedSpace.stalkMap.comp, CategoryTheory.PrelaxFunctor.map₂_comp_assoc, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv_assoc, CategoryTheory.Functor.rightKanExtensionUniqueOfIso_inv, CategoryTheory.kernelCokernelCompSequence.snakeInput_v₀₁_τ₃, AlgebraicGeometry.geometrically_inf, CategoryTheory.Dial.symmetry, CategoryTheory.Adjunction.Triple.whiskerRight_rightToLeft, CategoryTheory.Limits.biproduct.toSubtype_eq_desc, CategoryTheory.Equivalence.id_asNatTrans, CategoryTheory.LaxFunctor.mapComp_naturality_right, AlgebraicGeometry.Scheme.Hom.ι_fromNormalization_assoc, SimplexCategory.δ_comp_σ_of_le_assoc, CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_two_symm, CategoryTheory.Idempotents.natTrans_eq, CategoryTheory.Functor.FullyFaithful.homNatIso'_inv_app_down, HomologicalComplex.mapBifunctor.ι_D₁, CategoryTheory.Functor.isoShift_hom_naturality_assoc, CategoryTheory.Mat.add_apply, DistLat.coe_id, CategoryTheory.Functor.Monoidal.map_δ_μ, AlgebraicGeometry.LocallyRingedSpace.iso_inv_base_hom_base, RingCat.ofHom_comp, CategoryTheory.SplitMono.id, CategoryTheory.GrothendieckTopology.whiskerRight_toPlus_comp_plusCompIso_hom_assoc, CategoryTheory.Limits.CategoricalPullback.Hom.w'_assoc, CategoryTheory.ShortComplex.LeftHomologyMapData.ofEpiOfIsIsoOfMono_φK, HomologicalComplex₂.total.mapAux.d₂_mapMap, CategoryTheory.NatTrans.leftDerivedToHomotopyCategory_comp, FinBddDistLat.coe_comp, CategoryTheory.Preadditive.mul_def, AlgebraicGeometry.Scheme.Cover.trans_comp, Rep.MonoidalClosed.linearHomEquiv_hom, CategoryTheory.ObjectProperty.preservesColimitsOfShape_eq_iSup, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_id, CategoryTheory.ShortComplex.Homotopy.sub_h₂, TopCat.pullbackIsoProdSubtype_inv_snd_assoc, CategoryTheory.Abelian.Ext.mk₀_eq_zero_iff, CategoryTheory.congrArg_cast_hom_left, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_fst_fst_assoc, CategoryTheory.CommComon.id_hom, CategoryTheory.SingleFunctors.inv_hom_id_hom_app_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_as_app, CategoryTheory.StrictPseudofunctorPreCore.map₂_whisker_left, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃, Rep.invariantsAdjunction_homEquiv_apply_hom, CategoryTheory.MonoidalClosed.whiskerLeft_curry_ihom_ev_app, CategoryTheory.ObjectProperty.instIsClosedUnderColimitsOfShapeOppositeOpOfIsClosedUnderLimitsOfShape_1, CategoryTheory.Limits.Sigma.ι_comp_map'_assoc, CategoryTheory.SemiadditiveOfBinaryBiproducts.add_eq_left_addition, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_snd, CategoryTheory.Functor.IsRepresentedBy.iff_isIso_uliftYonedaEquiv, HomologicalComplex.restrictionMap_f', CategoryTheory.Limits.pullbackSymmetry_hom_comp_snd_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_hom_comp_π, HomologicalComplex.homotopyCofiber.inrX_d, CategoryTheory.Limits.widePushoutShapeUnop_map, CategoryTheory.kernel.ι_op, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj_hom_ext_iff, CategoryTheory.underToAlgebra_map_f, CategoryTheory.Join.InclLeftCompRightOpOpEquivFunctor_inv_app, CategoryTheory.Functor.OfSequence.map_id, CategoryTheory.ULift.equivalence_counitIso_inv_app, CategoryTheory.GrothendieckTopology.diagramNatTrans_app, CategoryTheory.Limits.Bicone.ofColimitCocone_π, CategoryTheory.Sum.swapCompInr_hom_app, AlgebraicGeometry.basicOpenIsoSpecAway_inv_homOfLE, CategoryTheory.Limits.prodComparison_natural, AlgebraicGeometry.Scheme.Hom.map_resLE_assoc, CategoryTheory.ShortComplex.HomologyData.canonical_iso_inv, MonCat.coe_id, TopCat.Presheaf.stalkSpecializes_comp_assoc, AlgebraicGeometry.IsLocalIso.exists_isOpenImmersion, AlgebraicGeometry.Scheme.Hom.comp_base_assoc, CategoryTheory.Meq.mk_apply, AlgebraicTopology.DoldKan.MorphComponents.postComp_φ, CategoryTheory.SimplicialObject.Augmented.rightOp_hom_app, CategoryTheory.Limits.Sigma.eqToHom_comp_ι, CategoryTheory.NatTrans.naturality', AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_map, CategoryTheory.yonedaEquiv_naturality, CategoryTheory.ComonObj.comul_assoc, TopCat.prodIsoProd_hom_fst, SimplicialObject.Splitting.πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty_assoc, SSet.Truncated.StrictSegal.spineToSimplex_interval, CategoryTheory.ShortComplex.SnakeInput.comp_f₂_assoc, CategoryTheory.Adjunction.homEquiv_apply, CategoryTheory.Abelian.preadditiveCoyonedaObj_map_surjective, CategoryTheory.MonoidalLinear.smul_whiskerRight, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_symm_apply, CategoryTheory.Limits.limit.pre_eq, CategoryTheory.ShortComplex.rightHomologyIso_hom_comp_homologyι_assoc, RingCat.comp_apply, CategoryTheory.unopUnop_map, CategoryTheory.Grp.trivial_grp_one, CategoryTheory.coalgebraToOver_map, AlgebraicGeometry.coprodSpec_inl, HomotopicalAlgebra.fibration_unop_iff, CategoryTheory.Limits.limit.lift_map, SimplexCategory.Truncated.δ₂_one_comp_σ₂_one_assoc, CategoryTheory.MorphismProperty.CostructuredArrow.Hom.ext_iff, SheafOfModules.pushforwardNatTrans_app_val_app, CategoryTheory.Subgroupoid.inv_mem_iff, HomotopicalAlgebra.PrepathObject.p_snd_assoc, CategoryTheory.Mat_.comp_apply, CategoryTheory.Functor.relativelyRepresentable.pullback₃.fst_fst'_eq_p₁_assoc, CategoryTheory.Functor.relativelyRepresentable.hom_ext'_iff, AlgebraicGeometry.IsImmersion.instHasOfPostcompPropertySchemeTopMorphismProperty, CategoryTheory.Limits.pullbackSymmetry_hom_comp_snd, CategoryTheory.WithTerminal.pseudofunctor_mapId, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_assoc, CategoryTheory.kernelCokernelCompSequence.φ_π, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_left, CategoryTheory.PreGaloisCategory.evaluation_aut_surjective_of_isGalois, CategoryTheory.MorphismProperty.retracts_le_llp_rlp, HomologicalComplex₂.ιTotal_totalFlipIso_f_hom, CategoryTheory.Limits.hasEqualizer_precomp_of_hasEqualizer, CategoryTheory.Iso.self_symm_conj, SimplicialObject.Split.natTransCofanInj_app, CategoryTheory.MonoidalLinear.whiskerLeft_smul, AlgebraicGeometry.Scheme.IdealSheafData.subSchemeCover_map_inclusion, CategoryTheory.Endofunctor.Algebra.functorOfNatTransComp_inv_app_f, CategoryTheory.Bicategory.associator_inv_congr, BddLat.comp_apply, CochainComplex.ConnectData.d₀_comp_assoc, CategoryTheory.Limits.Fan.IsLimit.lift_proj_assoc, CategoryTheory.ExponentiableMorphism.pushforwardComp_hom_counit, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackId_hom, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_id_app, CategoryTheory.Iso.isoCompInverse_hom_app, CategoryTheory.Functor.IsCartesian.fac, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app_assoc, CategoryTheory.Limits.FormalCoproduct.cosimplicialObjectFunctor_obj_map, CategoryTheory.Comonad.Coalgebra.counit_assoc, ModuleCat.Hom.hom₂_apply, ChainComplex.fromSingle₀Equiv_apply, CategoryTheory.braiding_leftUnitor, CategoryTheory.Iso.isoInverseOfIsoFunctor_hom_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app_assoc, CategoryTheory.Limits.ColimitPresentation.ofIso_ι, CategoryTheory.Bimon.equivMonComonCounitIsoApp_hom_hom_hom, CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app, CochainComplex.mappingCone.d_fst_v', CategoryTheory.MonoidalCategory.comp_tensor_id, CategoryTheory.Bimon.one_comul_assoc, CategoryTheory.Endofunctor.Algebra.functorOfNatTrans_obj_str, CategoryTheory.Limits.coequalizer.hom_ext_iff, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv_assoc, CategoryTheory.ComposableArrows.opEquivalence_inverse_map, PresheafOfModules.sectionsMap_id, CategoryTheory.Pseudofunctor.IsStackFor.essSurj, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_inv_hom, CategoryTheory.Limits.colimit.map_desc_assoc, CategoryTheory.Limits.prod.symmetry, CategoryTheory.MonoidalOpposite.mopMopEquivalenceFunctorMonoidal_η, CategoryTheory.InjectiveResolution.desc_commutes_zero, CategoryTheory.δ_naturality, CategoryTheory.ShortComplex.LeftHomologyMapData.neg_φK, CategoryTheory.MonoidalCategory.DayConvolution.associator_naturality, TopModuleCat.hom_smul, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.counitIso_inv, CategoryTheory.NonPreadditiveAbelian.add_comm, CondensedMod.epi_iff_locallySurjective_on_compHaus, CategoryTheory.LocalizerMorphism.LeftResolution.op_w, HomotopicalAlgebra.CofibrantObject.homMk_homMk_assoc, CategoryTheory.Limits.isoZeroOfEpiZero_inv, CategoryTheory.ComposableArrows.Exact.cokerIsoKer_hom_fac, CategoryTheory.StrictPseudofunctor.mk'_map₂, HomologicalComplex.singleObjCyclesSelfIso_hom_assoc, CategoryTheory.Comonad.right_counit, CategoryTheory.Bimon.ofMonComon_toMonComon_obj_comul, CategoryTheory.Limits.coprod.rightUnitor_hom, CategoryTheory.Limits.PushoutCocone.op_pt, CategoryTheory.GrpObj.lift_comp_inv_left_assoc, CategoryTheory.Functor.comp_mapCommGrp_one, CategoryTheory.Limits.π_reflexiveCoequalizerIsoCoequalizer_inv, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_α, AddCommGrpCat.biprodIsoProd_inv_comp_fst, CategoryTheory.Subobject.underlyingIso_inv_top_arrow, CategoryTheory.SimplicialObject.δ_comp_δ_self', CategoryTheory.Functor.toPseudoFunctor'_mapId, CategoryTheory.Limits.pushout.mapLift_comp, CategoryTheory.GrothendieckTopology.isoSheafify_inv, Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply, CategoryTheory.CatCenter.smul_iso_hom_eq', CategoryTheory.ObjectProperty.InheritedFromSource.op, CategoryTheory.WithInitial.prelaxfunctor_toPrelaxFunctorStruct_toPrefunctor_map, SimplexCategory.Truncated.Hom.tr_comp_assoc, AlgebraicGeometry.ΓSpec.adjunction_homEquiv_symm_apply, CategoryTheory.BraidedCategory.braiding_naturality_left_assoc, CategoryTheory.Over.associator_inv_left_fst_snd_assoc, CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id, CategoryTheory.IsPullback.isoPullback_hom_snd_assoc, CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_hom_inv_id_assoc, AugmentedSimplexCategory.id_tensorHom, CategoryTheory.Comma.mapRight_map_left, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_apply, AlgebraicTopology.DoldKan.P_zero, SemiNormedGrp.hom_zero, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_inv, CategoryTheory.Limits.Multifork.ofPiFork_π_app_right, CochainComplex.mappingCone.inl_v_descCochain_v, SSet.RelativeMorphism.Homotopy.h₀, CategoryTheory.Monoidal.InducingFunctorData.whiskerLeft_eq, CategoryTheory.Limits.kernel.condition_assoc, ComplexShape.Embedding.homRestrict_precomp_assoc, CategoryTheory.Arrow.inv_hom_id_left, CategoryTheory.GrothendieckTopology.covering_iff_covers_id, CategoryTheory.Iso.map_inv_hom_id_eval_app, CategoryTheory.DifferentialObject.eqToHom_f'_assoc, CategoryTheory.GrpObj.comp_inv_assoc, CategoryTheory.GrothendieckTopology.toPlus_naturality_assoc, CategoryTheory.PrelaxFunctor.map₂_isIso, AlgebraicGeometry.Spec_Γ_naturality_assoc, CategoryTheory.types_hom, CategoryTheory.Abelian.PreservesCoimage.hom_coimageImageComparison, AlgebraicGeometry.Scheme.Hom.appLE_map'_assoc, CategoryTheory.IsKernelPair.pullback, AlgebraicGeometry.RingedSpace.isUnit_res_basicOpen, CategoryTheory.Limits.Multicofork.snd_app_right, HomologicalComplex.d_comp_XIsoOfEq_hom, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_inv_right_app, CategoryTheory.Comma.mapRightId_inv_app_right, CategoryTheory.SmallObject.SuccStruct.Iteration.congr_map, CategoryTheory.Functor.LeftExtension.postcomp₁_map_left, CategoryTheory.Bicategory.mateEquiv_leftUnitor_hom_rightUnitor_inv, TopCat.Presheaf.germ_res'_assoc, CategoryTheory.Adjunction.rightAdjointUniq_trans_assoc, AlgebraicGeometry.Scheme.Opens.ι_app_self, CategoryTheory.Bicategory.LeftExtension.whisker_unit, CategoryTheory.Bicategory.conjugateEquiv_mateEquiv_vcomp, CategoryTheory.ShortComplex.mapCyclesIso_inv_naturality, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_π_app_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_app, CategoryTheory.mono_comp_iff_of_mono, HomotopicalAlgebra.trivialCofibrations_eq_unop, CategoryTheory.Adjunction.CoreUnitCounit.left_triangle, CategoryTheory.Iso.map_hom_inv_id_eval, CategoryTheory.Functor.mapConeOp_inv_hom, Homotopy.comm, groupCohomology.H1Map_id, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHomLeft, CategoryTheory.Limits.ι_reflexiveCoequalizerIsoCoequalizer_hom, TopologicalSpace.Opens.mapComp_inv_app, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_symm_apply, CategoryTheory.Limits.Cotrident.condition, CategoryTheory.isDetecting_op_iff, CategoryTheory.Functor.WellOrderInductionData.Extension.compatibility, HomologicalComplex.singleObjCyclesSelfIso_inv_naturality, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_hom_apply, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_hom_app_hom_hom_hom, HomotopicalAlgebra.AttachCells.cell_def_assoc, quasiIsoAt_iff_comp_left, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_inv, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackComp_inv, TopCat.toSheafCompHausLike_val_map, CategoryTheory.Functor.map_shift_unop_assoc, CategoryTheory.toQuotientPaths_obj_as, CategoryTheory.NatTrans.naturality_app_app, CategoryTheory.Limits.Types.productIso_inv_comp_π, HomotopicalAlgebra.LeftHomotopyRel.precomp, CategoryTheory.ActionCategory.id_val, CategoryTheory.ShiftMkCore.zero_add_hom_app, IsFreeGroupoid.endIsFreeOfConnectedFree, CategoryTheory.ShortComplex.Homotopy.trans_h₁, CategoryTheory.PreOneHypercover.Hom.id_h₁, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_comp, CategoryTheory.Pseudofunctor.mapComp'_id_comp, HomotopicalAlgebra.BifibrantObject.homMk_homMk_assoc, AlgebraicGeometry.StructureSheaf.toOpen_germ, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_assoc, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality, HomologicalComplex.mapBifunctor.d₁_eq', AlgebraicGeometry.PresheafedSpace.comp_base_assoc, CategoryTheory.Over.rightUnitor_hom_left, CategoryTheory.Limits.FormalCoproduct.pullbackCone_condition, Bimod.actRight_one_assoc, HomologicalComplex.Hom.comm_from, AlgebraicGeometry.Scheme.smallGrothendieckTopology_eq_toGrothendieck_smallPretopology, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₃_assoc, CategoryTheory.monoidalUnopUnop_μ, CategoryTheory.Functor.Monoidal.whiskerRight_ε_η, CategoryTheory.Limits.biproduct.ι_π_self_assoc, AlgebraicGeometry.Scheme.Hom.naturality, CochainComplex.augmentTruncate_hom_f_succ, CategoryTheory.MorphismProperty.Over.pullback_map_left, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₁_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.comp_actionHomLeft, CategoryTheory.Limits.cokernelBiprodInlIso_hom, CategoryTheory.Limits.pullbackProdSndIsoProd_hom_snd_assoc, CategoryTheory.Comma.mapRightComp_hom_app_right, CategoryTheory.Iso.conjAut_hom, CategoryTheory.Functor.diag_η, CategoryTheory.Comma.opFunctorCompSnd_inv_app, CategoryTheory.Iso.homCongr_symm_apply, NonemptyFinLinOrd.hom_hom_comp, CategoryTheory.IsCofilteredOrEmpty.cone_maps, AlgebraicGeometry.IsFinite.eq_isProper_inf_isAffineHom, CategoryTheory.MorphismProperty.antitone_llp, CategoryTheory.Functor.mapCommGrpIdIso_inv_app_hom_hom_hom, CategoryTheory.NatTrans.id_app, CategoryTheory.whiskerRight_coprod_inr_rightDistrib_inv, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app, CategoryTheory.ShortComplex.mapLeftHomologyIso_hom_naturality_assoc, CategoryTheory.yonedaCommGrpGrp_map_app, CategoryTheory.Limits.kernelIsoOfEq_inv_comp_ι, CategoryTheory.Limits.Multifork.ofPiFork_π_app_left, CategoryTheory.regularTopology.equalizerCondition_w, CategoryTheory.Functor.mapConePostcompose_hom_hom, SSet.Truncated.Path.arrow_tgt, CategoryTheory.StrictPseudofunctor.comp_map₂, CategoryTheory.Functor.whiskeringRightObjIdIso_inv_app_app, CategoryTheory.Functor.inv_fun_map, CategoryTheory.Limits.pullbackComparison_comp_fst, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_counitIso_inv, CategoryTheory.Bicategory.prod_homCategory_id_snd, CategoryTheory.IsHomLift.lift_id_inv, CategoryTheory.MonoidalCategory.tensorμ_natural_left, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_hom_iCycles, CategoryTheory.ShortComplex.Homotopy.comm₂, CategoryTheory.leftAdjointMate_comp_evaluation_assoc, CategoryTheory.Pi.δ_def, CategoryTheory.Injective.comp_factorThru, CategoryTheory.Limits.biproduct.ι_π, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_assoc, CategoryTheory.RetractArrow.op_i_left, CategoryTheory.ShortComplex.cyclesMap'_id, HomologicalComplex.d_comp_d, CategoryTheory.Functor.partialRightAdjointHomEquiv_symm_comp_assoc, CategoryTheory.ihom.ev_naturality, CategoryTheory.PreZeroHypercover.sumLift_h₀, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_naturality_assoc, AlgebraicGeometry.Scheme.Hom.resLE_comp_ι, ChainComplex.mk_congr_succ_d₂, Bimod.middle_assoc, CommRingCat.HomTopology.isHomeomorph_precomp, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app, CategoryTheory.ShortComplex.op_f, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_hom_comp_map_π_assoc, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃, SSet.mem_degenerate_iff, CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_inv, CategoryTheory.Limits.zeroProdIso_inv_snd, SSet.S.le_iff_nonempty_hom, CategoryTheory.Bicategory.InducedBicategory.forget_map₂, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_app_assoc, CategoryTheory.Abelian.image.ι_comp_eq_zero, CategoryTheory.Functor.LaxMonoidal.associativity, CategoryTheory.Equivalence.sheafCongr.inverse_obj_val_map, CategoryTheory.MonoidalCategory.tensor_left_unitality_assoc, TopCat.Presheaf.isGluing_iff_pairwise, CategoryTheory.MonoidalCategory.whisker_assoc_symm, AlgebraicGeometry.Scheme.Hom.liftCoborder_ι_assoc, CategoryTheory.GrpObj.comp_div_assoc, CategoryTheory.Subobject.underlyingIso_top_hom, CategoryTheory.OrthogonalReflection.D₁.ι_comp_t, CategoryTheory.monoidalOfHasFiniteCoproducts.leftUnitor_hom, AlgebraicGeometry.targetAffineLocally_affineAnd_le, CategoryTheory.ShortComplex.cyclesMap_id, CategoryTheory.Mat.comp_def, Bicategory.Opposite.bicategory_homCategory_id_unop2, CategoryTheory.Comonad.Coalgebra.id_f, CategoryTheory.Dial.whiskerLeft_f, CategoryTheory.Functor.isRightKanExtension_iff_precomp, CategoryTheory.Limits.MonoFactorisation.ofIsoComp_I, CategoryTheory.Functor.relativelyRepresentable.pullback₃.fst_snd_eq_p₂, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_assoc, CategoryTheory.IsPushout.of_hasBinaryBiproduct, CategoryTheory.composePath_id, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_cone_π_app, AlgebraicGeometry.Scheme.Pullback.Triplet.Spec_ofPointTensor_SpecTensorTo, CategoryTheory.MorphismProperty.HasRightCalculusOfFractions.exists_rightFraction, HomologicalComplex.XIsoOfEq_inv_comp_XIsoOfEq_hom, HomologicalComplex.mapBifunctor.d₂_eq_zero, CategoryTheory.ShortComplex.Splitting.s_r, CategoryTheory.Arrow.cechNerve_map, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π_assoc, CategoryTheory.ShortComplex.π_leftRightHomologyComparison_ι, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, CategoryTheory.Limits.colimit.isoColimitCocone_ι_hom_assoc, CategoryTheory.Over.sections_map, CommMonCat.id_apply, CategoryTheory.LocalizerMorphism.RightResolution.unopFunctor_map_f, CochainComplex.HomComplex.Cocycle.equivHomShift_comp, groupHomology.inhomogeneousChains.d_comp_d, CategoryTheory.ShortComplex.SnakeInput.naturality_φ₂, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_fst, AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_naturality, ChainComplex.chainComplex_d_succ_succ_zero, CategoryTheory.Limits.pullbackComparison_comp_snd, CategoryTheory.Adjunction.rightAdjointUniq_hom_app_counit_assoc, CategoryTheory.MonoidalCategory.rightAssocTensor_map, CategoryTheory.Functor.relativelyRepresentable.pullback₃.fst_fst'_eq_p₁, CategoryTheory.Functor.RightExtension.coneAtWhiskerRightIso_hom_hom, CategoryTheory.Subgroupoid.mem_full_iff, CochainComplex.cm5b.i_f_comp_assoc, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_inv_assoc, CategoryTheory.CartesianMonoidalCategory.lift_fst, HomologicalComplex.singleObjOpcyclesSelfIso_inv_naturality_assoc, CategoryTheory.Bicategory.LeftLift.whiskerIdCancel_right, CategoryTheory.Comma.mapRightIso_inverse_obj_hom, SSet.stdSimplex.faceSingletonComplIso_hom_ι_assoc, CategoryTheory.TwistShiftData.shiftFunctorAdd'_hom_app, AlgebraicGeometry.Scheme.restrict_presheaf_map, CategoryTheory.Cat.HasLimits.comp_def, CategoryTheory.PrelaxFunctor.comp_toPrelaxFunctorStruct, Action.FunctorCategoryEquivalence.counitIso_hom_app_app, AlgebraicGeometry.Scheme.IdealSheafData.inclusion_id_assoc, CategoryTheory.Sheaf.ΓHomEquiv_naturality_right, HomologicalComplex.d_eqToHom_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.hom_inv_actionHomLeft, HomologicalComplex.quasiIso_opFunctor_map_iff, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_inv_assoc, CategoryTheory.Subobject.ofMkLE_comp_ofLE_assoc, CategoryTheory.MonoidalCategory.hom_inv_id_tensor', CategoryTheory.MonoidalClosed.curryHomEquiv'_symm_apply, CategoryTheory.ShortComplex.unopMap_id, CategoryTheory.Limits.Pi.map_π_assoc, CategoryTheory.ShortComplex.sub_τ₃, PresheafOfModules.pushforward_assoc, SimplexCategory.concreteCategoryHom_id, CategoryTheory.PrelaxFunctor.map₂_inv_hom_assoc, CategoryTheory.Limits.Pi.ι_π_of_ne_assoc, CategoryTheory.PreGaloisCategory.PointedGaloisObject.Hom.comp, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_hom_app_app, CategoryTheory.ExponentiableMorphism.coev_naturality, CategoryTheory.map_yonedaEquiv, groupHomology.π_comp_H0Iso_hom, Homotopy.comp_hom, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.ofRestrict_invApp, CategoryTheory.Oplax.StrongTrans.isoMk_inv_as_app, CategoryTheory.CatEnrichedOrdinary.hComp_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict, CategoryTheory.Bicategory.Prod.fst_mapComp_inv, CategoryTheory.ShortComplex.abelianImageToKernel_comp_kernel_ι_comp_cokernel_π, dNext_eq, CategoryTheory.Limits.IsImage.lift_ι, CategoryTheory.ComposableArrows.IsComplex.epi_cokerToKer', CategoryTheory.Oplax.StrongTrans.Modification.naturality, CategoryTheory.Limits.prod.comp_lift, CategoryTheory.rightAdjointOfCostructuredArrowTerminalsAux_symm_apply, CategoryTheory.Limits.inl_comp_pushoutObjIso_hom_assoc, TopologicalSpace.Opens.map_comp_obj, PresheafOfModules.map_id, CategoryTheory.tensorLeftHomEquiv_symm_coevaluation_comp_whiskerRight, CategoryTheory.op_zsmul, CategoryTheory.Sieve.natTransOfLe_app_coe, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv, CategoryTheory.StructuredArrow.mapIso_inverse_map_right, CategoryTheory.eHomEquiv_comp, CategoryTheory.BraidedCategory.hexagon_reverse_inv_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom, CategoryTheory.Square.Hom.comm₁₂, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app_assoc, CategoryTheory.MonoidalCategory.pentagon_inv, CategoryTheory.Limits.kernelIsoOfEq_inv_comp_ι_assoc, CommRingCat.moduleCatExtendScalarsPseudofunctor_mapComp, CategoryTheory.Limits.coprod.inl_map, CategoryTheory.sum.inlCompInverseAssociator_inv_app_down_down, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoColimitUncurryWhiskeringLeft₂_hom_assoc, CategoryTheory.Functor.shiftIso_hom_app_comp_shiftMap, CochainComplex.shiftFunctor_obj_d', CategoryTheory.Pretriangulated.Triangle.smul_hom₃, Mathlib.Tactic.CategoryTheory.CancelIso.hom_inv_id_of_eq, HomotopicalAlgebra.PrepathObject.RightHomotopy.h₀_assoc, CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois_symm_fiber, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_comp, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_hom, CategoryTheory.Hom.one_def, CategoryTheory.Mon.comp_hom', CategoryTheory.NonPreadditiveAbelian.neg_sub, CategoryTheory.Over.μ_pullback_left_snd, groupCohomology.mapShortComplexH1_id_comp_assoc, CategoryTheory.Functor.partialLeftAdjointHomEquiv_symm_comp_assoc, CategoryTheory.Subfunctor.Subpresheaf.fromPreimage_ι, CategoryTheory.Ind.isSeparating_range_yoneda, Preord.ofHom_comp, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.ShortComplex.homologyMap_op, CategoryTheory.Limits.BinaryCofan.IsColimit.desc'_coe, CategoryTheory.Adjunction.Triple.whiskerLeft_leftToRight_assoc, CategoryTheory.Functor.shiftIso_add'_inv_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_naturality₂, CategoryTheory.Limits.opProdIsoCoprod_inv_inr_assoc, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, groupCohomology.mapShortComplexH1_zero, SheafOfModules.pullbackPushforwardAdjunction_homEquiv_symm_unitToPushforwardObjUnit, CategoryTheory.Functor.biprodComparison_fst, CategoryTheory.Under.mapPushoutAdj_counit_app, CategoryTheory.WithTerminal.pseudofunctor_mapComp, CategoryTheory.Limits.combineCocones_ι_app_app, CategoryTheory.FunctorToTypes.binaryProductCone_π_app, CategoryTheory.Over.iteratedSliceBackward_obj, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right, ModuleCat.binaryProductLimitCone_isLimit_lift, CategoryTheory.Comonad.beckEqualizer_lift, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.tensorHom_comp_tensorHom, ProfiniteGrp.ofHom_id, CategoryTheory.Limits.CatCospanTransform.triangle_inv_assoc, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_α, CategoryTheory.Localization.SmallHom.mk_comp_mkInv, CategoryTheory.Comonad.id_ε_app, SSet.ι₀_fst, CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_fst, HomologicalComplex.biprod_inl_desc_f, CategoryTheory.PreGaloisCategory.autEmbedding_range, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom_assoc, HomologicalComplex.π_homologyIsoSc'_inv, HomologicalComplex.singleObjHomologySelfIso_inv_naturality, CategoryTheory.CostructuredArrow.homMk'_comp, CochainComplex.ιTruncLE_naturality, AlgebraicGeometry.Scheme.Modules.pseudofunctor_left_unitality, CategoryTheory.Adjunction.Triple.map_adj₂_counit_app_leftToRight_app, Bimod.id_whiskerRight_bimod, CategoryTheory.NonPreadditiveAbelian.comp_add, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen', CategoryTheory.Adjunction.Triple.map_rightToLeft_app_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.comp_actionHomLeft_assoc, CategoryTheory.Regular.frobeniusStrongEpiMonoFactorisation_m, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_hom_app_app, CategoryTheory.conjugateIsoEquiv_apply_hom, TopCat.prodIsoProd_inv_snd, CategoryTheory.WithTerminal.prelaxfunctor_toPrelaxFunctorStruct_toPrefunctor_obj, HomologicalComplex.cyclesIsoSc'_hom_iCycles, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_assoc, CategoryTheory.GrpObj.inv_hom_assoc, CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_iff_epi₃, Bimod.AssociatorBimod.inv_hom_id, CategoryTheory.Under.mapComp_eq, CategoryTheory.Limits.pullbackLeftPullbackSndIso_hom_fst_assoc, CategoryTheory.Limits.coprod.inr_desc_assoc, CategoryTheory.Comma.id_left, CategoryTheory.GradedObject.ι_mapBifunctorBifunctor₂₃Desc_assoc, AlgebraicGeometry.Scheme.Hom.isoOpensRange_inv_comp_assoc, CategoryTheory.isCoseparator_iff_of_isLimit_fan, CategoryTheory.Functor.leftDerived_fac_app_assoc, CategoryTheory.op_epi_of_mono, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom, HomotopicalAlgebra.Cylinder.trans_i₁, Bicategory.Opposite.unop2_id, CategoryTheory.HopfObj.antipode_comul₁, AlgebraicTopology.DoldKan.N₂_obj_X_d, CategoryTheory.Limits.FormalCoproduct.evalOp_obj_map, AlgebraicGeometry.Scheme.Modules.pseudofunctor_associativity_assoc, CategoryTheory.Limits.Multicofork.sigma_condition, CategoryTheory.Limits.WalkingMultispan.instIsEmptyHomRightLeft, CategoryTheory.BicartesianSq.of_is_biproduct₂, CategoryTheory.MonoidalCategory.DayConvolution.whiskerLeft_comp_unit_app_assoc, CategoryTheory.Adjunction.unit_app_tensor_comp_map_δ, LinOrd.hom_comp, CategoryTheory.Idempotents.Karoubi.coe_X, ModuleCat.homLinearEquiv_apply, CategoryTheory.Functor.isRightAdjoint_iff_leftAdjointObjIsDefined_eq_top, groupCohomology.mapShortComplexH1_comp_assoc, CategoryTheory.Limits.MonoFactorisation.ofIsoI_e, CategoryTheory.WithTerminal.coneEquiv_unitIso_inv_app_hom_left, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃_eq_assoc, groupHomology.cyclesIso₀_inv_comp_cyclesMap, CategoryTheory.ShortComplex.RightHomologyMapData.add_φH, CategoryTheory.Limits.Sigma.ι_desc, CategoryTheory.PreOneHypercover.sieve₁'_cylinder, CochainComplex.HomComplex.Cocycle.equivHom_apply, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_π, CategoryTheory.GradedObject.mapBifunctorBifunctor₂₃MapObj_ext_iff, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_f, CategoryTheory.Pi.sum_map_app, CategoryTheory.Localization.structuredArrowEquiv_symm_apply, CategoryTheory.ObjectProperty.isClosedUnderColimitsOfShape_op_iff_op, CategoryTheory.BasedFunctor.instIsHomLiftObjPIdObj, AlgebraicGeometry.ProjectiveSpectrum.Proj.stalkMap_toSpec, CategoryTheory.Functor.mapMatId_hom_app, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_app, CategoryTheory.Triangulated.instNonemptyOctahedron, AlgebraicGeometry.pullbackSpecIso_hom_base_assoc, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_toSpecΓ_assoc, CategoryTheory.Limits.CatCospanTransform.id_whiskerLeft, AlgebraicGeometry.Scheme.Cover.gluedCoverT'_snd_snd, CategoryTheory.Dial.braiding_hom_F, CategoryTheory.Limits.coprod.hom_ext_iff, CategoryTheory.InducedCategory.eqToHom_hom, CategoryTheory.ObjectProperty.strictMap_ofObj, AlgebraicGeometry.instIsLocallyDirectedCompSchemeOverOverTopMorphismPropertyForgetForgetForget, CategoryTheory.Join.InclRightCompRightOpOpEquivFunctor_inv_app, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_hom_app_f, BddDistLat.ofHom_comp, CategoryTheory.Limits.Sigma.whiskerEquiv_inv, CategoryTheory.Functor.OplaxLeftLinear.δₗ_naturality_left, CategoryTheory.RanIsSheafOfIsCocontinuous.fac, CategoryTheory.Limits.Cofork.op_unop_π, CategoryTheory.GrpObj.ofIso_inv, AlgebraicGeometry.Scheme.Hom.normalizationCoprodIso_inv_coprodDesc_fromNormalization_assoc, TopCat.piIsoPi_inv_π, AlgebraicGeometry.Scheme.IdealSheafData.comapIso_hom_fst, CategoryTheory.Limits.limit.isoLimitCone_inv_π, CategoryTheory.Pretriangulated.Triangle.sub_hom₃, AlgebraicGeometry.AffineSpace.homOverEquiv_apply, CategoryTheory.GrothendieckTopology.toPlus_naturality, CategoryTheory.coevaluation_comp_leftAdjointMate, CategoryTheory.Functor.FullyFaithful.hasShift.map_add_inv_app, CategoryTheory.ShortComplex.rightHomologyMap_neg, CategoryTheory.IsSplitCoequalizer.condition, CategoryTheory.Sieve.pullback_ofArrows_of_iso, CategoryTheory.ObjectProperty.op_isoClosure, CategoryTheory.IsFiltered.coeq_condition, CategoryTheory.Bicategory.prod_leftUnitor_hom_fst, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_inv_hom₂, CategoryTheory.Functor.Monoidal.μ_snd, SimplicialObject.Splitting.cofan_inj_πSummand_eq_zero_assoc, AlgebraicGeometry.pullbackRestrictIsoRestrict_inv_fst_assoc, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberDesc_assoc, CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj_hom_app, CategoryTheory.Limits.pullbackZeroZeroIso_inv_snd, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_left, CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_fst_snd_assoc, CategoryTheory.Functor.IsCoverDense.isoOver_inv_app, CategoryTheory.Limits.inl_pushoutAssoc_inv, CategoryTheory.Limits.KernelFork.mapIsoOfIsLimit_hom, CategoryTheory.Limits.pullbackLeftPullbackSndIso_hom_fst, HomologicalComplex.restrictionToTruncGE'_naturality, CategoryTheory.CommSq.instHasLift_1, HomotopicalAlgebra.PathObject.ofFactorizationData_p₀, CategoryTheory.ShortComplex.LeftHomologyData.homologyIso_hom_comp_leftHomologyIso_inv, CategoryTheory.Functor.OplaxMonoidal.δ_comp_tensorHom_η_assoc, groupHomology.H0π_comp_H0Iso_hom, CategoryTheory.ExponentiableMorphism.unit_pushforwardId_hom, CategoryTheory.Functor.FullyFaithful.grpObj_mul, CategoryTheory.Iso.cancel_iso_inv_right_assoc, CategoryTheory.Limits.IsImage.fac_lift, AlgebraicGeometry.Scheme.GlueData.ι_isoLocallyRingedSpace_inv, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_app_assoc, CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app_assoc, groupHomology.isoCycles₁_hom_comp_i_assoc, AlgebraicGeometry.Scheme.IdealSheafData.map_id, CategoryTheory.MonoidalCategory.DayConvolution.associator_inv_unit_unit_assoc, CategoryTheory.Limits.limitOpIsoOpColimit_inv_comp_π, CategoryTheory.Limits.biproduct.lift_eq, CategoryTheory.BicartesianSq.of_has_biproduct₁, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_fst, CategoryTheory.Localization.Monoidal.triangle_aux₂, Rep.homEquiv_symm_apply_hom, CategoryTheory.Limits.coprod.triangle, AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem_toSpecΓ_assoc, AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp, CategoryTheory.Subobject.arrow_congr, HomotopicalAlgebra.LeftHomotopyRel.equivalence, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberToSpecResidueField, CategoryTheory.MorphismProperty.LeftFraction.rightFraction_fac_assoc, CategoryTheory.Grp_Class.inv_eq_inv, Bimod.id_hom', TopologicalSpace.Opens.mapIso_hom_app, CategoryTheory.Mon.forget_η, Rep.FiniteCyclicGroup.leftRegular.range_norm_eq_ker_applyAsHom_sub, TopCat.Sheaf.objSupIsoProdEqLocus_inv_fst, CategoryTheory.Limits.equalizerComparison_comp_π_assoc, smoothSheaf.ι_evalHom, CategoryTheory.OverPresheafAux.YonedaCollection.map₁_id, CategoryTheory.ShortComplex.LeftHomologyMapData.comp_φK, CategoryTheory.Dial.leftUnitor_inv_F, CategoryTheory.Functor.isoSum_hom_app_inr, CategoryTheory.Limits.inl_inl_pushoutAssoc_hom_assoc, CategoryTheory.Limits.isColimitOfConeOfCoconeRightOp_desc, GrpCat.ofHom_injective, CategoryTheory.Functor.OplaxMonoidal.id_η, HomotopicalAlgebra.CofibrantBrownFactorization.mk'_Z, CategoryTheory.GlueData.ι_gluedIso_hom, CategoryTheory.conjugateIsoEquiv_apply_inv, CategoryTheory.Endofunctor.algebraPreadditive_homGroup_zero_f, HomologicalComplex.mapBifunctor₂₃.d_eq, CategoryTheory.Localization.Preadditive.comp_add', CategoryTheory.Limits.CoconeMorphism.inv_hom_id, CategoryTheory.ShortComplex.cyclesMap_i_assoc, HomologicalComplex.HomologySequence.δ_naturality, CategoryTheory.Grpd.comp_eq_comp, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τl, AlgebraicGeometry.locallyOfFiniteType_comp, ProfiniteGrp.coe_comp, CochainComplex.mappingCone.inr_descShortComplex, CategoryTheory.MorphismProperty.leftFractionRel_op_iff, CategoryTheory.Equivalence.mkHom_id_functor, CategoryTheory.Functor.whiskerLeft_comp_whiskerRight, HomotopicalAlgebra.instCofibrationUnopOfFibrationOpposite, ModuleCat.Iso.conj_eq_conj, AlgebraicGeometry.Scheme.comp_appTop, CategoryTheory.Limits.fiberwiseColimCompEvaluationIso_inv_app, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π, CategoryTheory.WithInitial.liftFromUnderComp_hom_app, smoothSheafCommRing.ι_evalHom_assoc, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_inv_assoc, CategoryTheory.Oplax.OplaxTrans.naturality_comp_assoc, CategoryTheory.MonoidalCategory.whiskerLeft_comp_tensorHom_assoc, CategoryTheory.ShortComplex.RightHomologyMapData.smul_φQ, CategoryTheory.Limits.kernelZeroIsoSource_inv, CategoryTheory.Equivalence.counitInv_naturality, groupHomology.map_id_comp_H0Iso_hom, CategoryTheory.Bicategory.Adjunction.comp_left_triangle_aux, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom_assoc, CategoryTheory.Functor.CommShift.OfComp.map_iso_hom_app_assoc, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_hom_assoc, CategoryTheory.SimplicialObject.σ_comp_σ_assoc, CategoryTheory.Bicategory.whiskerLeft_hom_inv_whiskerRight, CategoryTheory.Limits.BinaryBicone.toBiconeFunctor_obj_ι, CategoryTheory.yonedaEvaluation_map_down, AddSemigrp.ofHom_comp, CategoryTheory.CartesianMonoidalCategory.lift_leftUnitor_hom, CategoryTheory.Limits.DiagramOfCones.comp, CategoryTheory.SemiCartesianMonoidalCategory.toUnit_unit, CategoryTheory.CartesianClosed.uncurry_injective, CategoryTheory.GrpObj.mulRight_inv, CategoryTheory.Functor.rightDerivedNatTrans_fac_assoc, CommRingCat.HomTopology.mvPolynomialHomeomorph_apply_fst, CategoryTheory.Limits.biproduct.eqToHom_comp_ι, CochainComplex.ι_mapBifunctorShift₁Iso_hom_f_assoc, groupCohomology.isoShortComplexH2_hom, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity, CategoryTheory.MonoidalCategory.DayConvolutionUnit.corepresentableByLeft_homEquiv, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_hom, CategoryTheory.Mat.id_apply, CategoryTheory.GlueData'.t_fac, CategoryTheory.Monad.monadMonEquiv_counitIso_inv_app_hom, CategoryTheory.Functor.Monoidal.map_η_ε_assoc, TopCat.Presheaf.Pushforward.comp_hom_app, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w_assoc, CategoryTheory.Functor.LaxMonoidal.whiskerRight_tensorUnit_comp_rightUnitor_hom, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_comp_assoc, CategoryTheory.Iso.homToEquiv_symm_apply, CategoryTheory.Functor.mapCoconeOp_hom_hom, CategoryTheory.PreGaloisCategory.surjective_of_nonempty_fiber_of_isConnected, CategoryTheory.Mod_.scalarRestriction_smul, CategoryTheory.sheafToPresheaf_ε, CategoryTheory.Limits.prod.lift_snd, CategoryTheory.preservesLimitIso_hom_π, CategoryTheory.Limits.PullbackCone.condition_one, MonObj.mopEquiv_counitIso_inv_app_hom_unmop, CategoryTheory.unitCompPartialBijective_symm_natural, CategoryTheory.Limits.piComparison_comp_π_assoc, CategoryTheory.ShortComplex.rightHomologyIso_inv_naturality, CategoryTheory.NatTrans.app_smul, CategoryTheory.GrothendieckTopology.coneCompEvaluationOfConeCompDiagramFunctorCompEvaluation_π_app, CategoryTheory.ObjectProperty.FullSubcategory.comp_hom, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_inv_app_hom_app, CategoryTheory.FunctorToTypes.binaryCoproductCocone_ι_app, CategoryTheory.Subfunctor.range_comp, CategoryTheory.Subgroupoid.mem_iff, AddCommGrpCat.coyoneda_map_app, CategoryTheory.Functor.sectionsEquivHom_apply_app, CochainComplex.cm5b.I_d, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inr, CategoryTheory.Functor.toPseudoFunctor'_mapComp, CategoryTheory.Limits.inl_pushoutRightPushoutInlIso_hom, CategoryTheory.Functor.Fiber.homMk_id, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocIso_inv_naturality, CategoryTheory.Pseudofunctor.DescentData.exists_equivalence_of_sieve_eq, CategoryTheory.Limits.inr_inr_pushoutAssoc_inv_assoc, CategoryTheory.Limits.limitIsoLimitCurryCompLim_inv_π_assoc, CategoryTheory.Subobject.inf_comp_left_assoc, CategoryTheory.ShortComplex.Homotopy.ofEq_h₁, CategoryTheory.ComposableArrows.map'_self, CategoryTheory.IsPullback.of_isBilimit, CategoryTheory.ComposableArrows.Exact.isIso_cokerToKer', CategoryTheory.Limits.prod.map_id_id, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_germ, CategoryTheory.StrictlyUnitaryPseudofunctor.map_id, CategoryTheory.Iso.homFromEquiv_apply, CategoryTheory.GrothendieckTopology.Cover.Arrow.precomp_f, CategoryTheory.Dial.associatorImpl_inv_f, CategoryTheory.Presieve.piComparison_fac, CategoryTheory.Equivalence.unit_inverse_comp, CategoryTheory.CostructuredArrow.eqToHom_left, CochainComplex.mappingCone.mapHomologicalComplexXIso'_hom, AlgebraicGeometry.Scheme.stalkMap_inv_hom, AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp_assoc, groupHomology.d₁₀_eq_zero_of_isTrivial, CategoryTheory.Functor.map_comp, CategoryTheory.SmallObject.ιObj_πObj, ContinuousMap.yonedaPresheaf'_map, CategoryTheory.PreGaloisCategory.mulAction_naturality, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst, inl_coprodIsoPushout_inv, CategoryTheory.prodOpEquiv_functor_map, CategoryTheory.MorphismProperty.StableUnderInverse.op, CategoryTheory.NatTrans.op_whiskerLeft, CategoryTheory.Comon.ComonToMonOpOpObj_mon_mul, AlgebraicGeometry.Etale.etale_comp, CategoryTheory.Localization.Monoidal.β_hom_app, CategoryTheory.GrpObj.mul_inv_assoc, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app, CategoryTheory.sheafificationAdjunction_counit_app_val, AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_map_assoc, CategoryTheory.Limits.HasZeroObject.zeroIsoIsInitial_hom, Traversable.foldl.ofFreeMonoid_comp_of, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_inv_app_app, CategoryTheory.Adjunction.right_triangle_components, CategoryTheory.Pretriangulated.triangleMorphismId_hom₁, CategoryTheory.Limits.pullbackObjIso_inv_comp_snd_assoc, CategoryTheory.WithInitial.coconeEquiv_counitIso_hom_app_hom, Bicategory.Opposite.bicategory_homCategory_comp_unop2, CategoryTheory.ihom.ev_naturality_assoc, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_hom_whiskerLeft_π_assoc, HomotopicalAlgebra.CofibrantObject.HoCat.resolutionMap_fac_assoc, CategoryTheory.ShortComplex.Homotopy.op_h₁, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc, CategoryTheory.GrpObj.comp_inv, AlgebraicGeometry.Scheme.comp_base_apply, CategoryTheory.ObjectProperty.isClosedUnderLimitsOfShape_op_iff_op, Action.FunctorCategoryEquivalence.functor_μ, CategoryTheory.Limits.Cone.toUnder_π_app, CategoryTheory.isIso_iff_isIso_coyoneda_map, AlgebraicGeometry.Scheme.fromSpecStalk_app, CategoryTheory.IsIso.hom_inv_id, HomologicalComplex.homotopyCofiber.inlX_d_assoc, HomologicalComplex.pOpcycles_extendOpcyclesIso_hom, AlgebraicGeometry.SpecMap_residueFieldIsoBase_inv, CategoryTheory.Limits.kernelBiprodSndIso_inv, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id_app, CategoryTheory.Limits.colimitCoyonedaHomIsoLimit_π_apply, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_inv_f_f, CochainComplex.HomComplex.Cochain.d_comp_ofHom_v, groupCohomology.d₀₁_comp_d₁₂_assoc, CategoryTheory.Comma.id_right, CategoryTheory.Iso.conj_id, groupCohomology.cocyclesMap_id, CategoryTheory.CartesianMonoidalCategory.whiskerLeft_fst, CategoryTheory.ObjectProperty.instContainsZeroMinOfIsClosedUnderIsomorphisms, AlgebraicTopology.DoldKan.karoubi_PInfty_f, CategoryTheory.ParametrizedAdjunction.unit_whiskerRight_map, CategoryTheory.Adjunction.unit_app_commShiftIso_hom_app, CategoryTheory.LocallyDiscrete.mkPseudofunctor_obj, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counitIso_hom_app_tensor, SSet.modelCategoryQuillen.J_le_monomorphisms, CategoryTheory.Under.inv_right_hom_right, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom, CategoryTheory.Functor.whiskerRight_comp, CategoryTheory.Limits.biproduct.ι_toSubtype_subtype_assoc, CategoryTheory.IsPullback.unop, CategoryTheory.IsCommMonObj.mul_comm_assoc, AlgebraicGeometry.Scheme.PartialMap.isOver_iff, CategoryTheory.Functor.prod'_η_fst, CategoryTheory.ShortComplex.mapOpcyclesIso_inv_naturality_assoc, CategoryTheory.Limits.inl_pushoutZeroZeroIso_inv, CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_iff_mono₂, CategoryTheory.Limits.inl_pushoutRightPushoutInlIso_hom_assoc, CategoryTheory.MonoidalClosed.homEquiv_apply_eq, Lat.id_apply, CategoryTheory.Limits.coneOfSectionCompCoyoneda_π, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isColimit, CategoryTheory.CechNerveTerminalFrom.wideCospan.limitIsoPi_inv_comp_pi_assoc, HomologicalComplex.mapBifunctorAssociatorX_hom_D₃, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_comp, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac, CategoryTheory.conjugateEquiv_whiskerLeft, CategoryTheory.ActionCategory.stabilizerIsoEnd_apply, HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_symm_apply, CategoryTheory.composePath_toPath, HomotopicalAlgebra.PrepathObject.ι_p₀, HomologicalComplex.stupidTruncMap_comp_assoc, CategoryTheory.Functor.commShiftIso_id_inv_app, Action.tensor_ρ, CategoryTheory.Limits.DiagramOfCocones.id, CategoryTheory.MorphismProperty.isStableUnderTransfiniteCompositionOfShape_iff, AlgebraicGeometry.tilde.map_zero, CategoryTheory.Arrow.arrow_mk_comp_eqToHom, CategoryTheory.Iso.homCongr_symm, AlgebraicGeometry.SpecMap_residueFieldIsoBase_inv_assoc, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp_assoc, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_hom_π_assoc, BddLat.id_apply, CategoryTheory.Limits.pushout_inl_inv_inr_of_right_isIso_assoc, CategoryTheory.Functor.Monoidal.μ_snd_assoc, CategoryTheory.Functor.rightOpId_hom_app, CategoryTheory.Subfunctor.fromPreimage_ι_assoc, HomologicalComplex.homotopyCofiber.desc_f, CategoryTheory.Localization.Monoidal.whiskerLeft_id, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_inv_app_hom_hom_app, CategoryTheory.Limits.pullbackDiagonalMapIso.inv_snd_snd_assoc, FundamentalGroupoid.conj_eqToHom, CategoryTheory.Functor.Monoidal.map_η_ε, AlgebraicGeometry.Scheme.Hom.toNormalization_normalizationPullback_fst_assoc, SimplexCategory.Truncated.δ₂_zero_comp_σ₂_one, CategoryTheory.CostructuredArrow.mapNatIso_functor_map_left, CategoryTheory.Limits.Multicofork.condition, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_comp, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app_assoc, CategoryTheory.Functor.HomObj.naturality_assoc, HomologicalComplex.extendCyclesIso_inv_iCycles, CategoryTheory.Limits.IsColimit.ofIsoColimit_desc, CategoryTheory.Limits.CoconeMorphism.map_w_assoc, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_hom_app_hom, CategoryTheory.Functor.Monoidal.map_tensor, CategoryTheory.IsCardinalPresentable.exists_hom_of_isColimit, CategoryTheory.coprodMonad_map, CochainComplex.ConnectData.comp_d₀, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_left, CategoryTheory.Limits.coprod.desc_comp_assoc, CategoryTheory.MorphismProperty.LeftFraction.map_comp_map_s, CategoryTheory.Presieve.IsSheafFor.functorInclusion_comp_extend_assoc, HomotopyCategory.homologyShiftIso_hom_app, CategoryTheory.Presheaf.map_comp_uliftYonedaEquiv_down, CategoryTheory.Limits.limCompFlipIsoWhiskerLim_hom_app_app, CategoryTheory.Free.lift_map, CategoryTheory.BraidedCategory.op_tensorμ, CategoryTheory.Limits.limitIsoLimitCurryCompLim_hom_π_π, ChainComplex.augmentTruncate_inv_f_zero, CategoryTheory.Limits.prodComparison_natural_assoc, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_assoc, AlgebraicGeometry.AffineSpace.homOfVector_toSpecMvPoly, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHom, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app, HomologicalComplex.restrictionCyclesIso_hom_iCycles_assoc, Opens.mayerVietorisSquare'_toSquare, AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_comp, CategoryTheory.Lax.LaxTrans.vComp_naturality_comp, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_apply, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_obj_hom, Rep.norm_comm_assoc, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv_assoc, CategoryTheory.Idempotents.isIdempotentComplete_iff_hasEqualizer_of_id_and_idempotent, CategoryTheory.WithInitial.liftFromUnder_map_app, CategoryTheory.Functor.WellOrderInductionData.map_lift, CategoryTheory.obj_μ_app_assoc, HomologicalComplex.ι_mapBifunctorFlipIso_hom, groupCohomology.mapShortComplexH2_id_comp, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_left, Bimod.whisker_exchange_bimod, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIdIso_inv_app_hom, CategoryTheory.Bicategory.id_whiskerLeft, SSet.RelativeMorphism.Homotopy.h₁, groupHomology.π_comp_H0IsoOfIsTrivial_hom_assoc, CategoryTheory.Quiv.pathsOf_freeMap_toPrefunctor, CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_hom_app, CategoryTheory.GrothendieckTopology.whiskerRight_toSheafify_sheafifyCompIso_hom, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_counit_app, CategoryTheory.Limits.inr_opProdIsoCoprod_inv, CategoryTheory.Functor.Monoidal.whiskerRight_app_snd, smoothSheafCommRing.ι_forgetStalk_hom, CategoryTheory.MorphismProperty.Over.pullback_obj_hom, CategoryTheory.GrothendieckTopology.overMapPullbackComp_hom_app_val_app, SimplicialObject.Splitting.comp_PInfty_eq_zero_iff, AlgebraicTopology.DoldKan.homotopyPToId_eventually_constant, CategoryTheory.GrpObj.η_whiskerRight_commutator, CategoryTheory.Quotient.lift.isLift_inv, CategoryTheory.ShortComplex.SnakeInput.L₀X₂ToP_comp_pullback_snd_assoc, CategoryTheory.Sigma.mapId_inv_app, AlgebraicGeometry.Spec.sheafedSpaceMap_id, CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_snd_assoc, CategoryTheory.conjugateIsoEquiv_symm_apply_inv, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_germ, CategoryTheory.Limits.hasPullback_of_comp_mono, CategoryTheory.ShortComplex.rightHomologyMap'_neg, CategoryTheory.ComonObj.comul_assoc_assoc, CategoryTheory.Limits.limitCompYonedaIsoCocone_hom_app, CategoryTheory.GrothendieckTopology.Cover.index_snd, ModuleCat.biprodIsoProd_inv_comp_fst, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_snd, CategoryTheory.MonoidalCategory.tensor_hom_inv_id'_assoc, CategoryTheory.Iso.inverseCompIso_inv_app, SemiNormedGrp.ofHom_id, CategoryTheory.Limits.fst_opProdIsoCoprod_hom, HomologicalComplex.homology_π_ι, CategoryTheory.comp_leftAdjointMate, CategoryTheory.MonoidalCategory.MonoidalLeftAction.inv_hom_actionHomLeft'_assoc, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_obj_map, CategoryTheory.SimplicialObject.cechNerveEquiv_apply, MonObj.mopMonObj_one_unmop, AlgebraicGeometry.pullbackSpecIso_hom_fst'_assoc, CategoryTheory.Bicategory.whiskerLeft_hom_inv_whiskerRight_assoc, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_right, CategoryTheory.Limits.coconeOfConeLeftOp_ι_app, CategoryTheory.StructuredArrow.projectSubobject_factors, Opens.coe_mayerVietorisSquare_X₄, HomologicalComplex.truncLE'Map_comp, CategoryTheory.Pseudofunctor.mapComp_id_left_hom, CategoryTheory.Limits.Sigma.ι_π_eq_id, CondensedMod.LocallyConstant.instFullSheafCompHausCoherentTopologyTypeConstantSheaf, ContinuousCohomology.MultiInd.d_comp_d, AlgebraicGeometry.Scheme.GlueData.glue_condition_assoc, CategoryTheory.Functor.OplaxMonoidal.δ_natural, CategoryTheory.Functor.LaxLeftLinear.μₗ_naturality_left_assoc, AlgebraicGeometry.PresheafedSpace.congr_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict_assoc, CategoryTheory.Functor.IsRepresentedBy.iff_of_isoObj, CategoryTheory.MonoidalPreadditive.zero_whiskerRight, CategoryTheory.Bicategory.prod_associator_inv_snd, CategoryTheory.Dial.whiskerLeft_F, CategoryTheory.pullbackShiftFunctorZero'_inv_app, CategoryTheory.ShortComplex.leftHomologyIso_inv_naturality, CategoryTheory.Limits.limit.coneMorphism_π, CategoryTheory.CartesianMonoidalCategory.lift_fst_assoc, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_unitIso_hom_app_right_app, CategoryTheory.Limits.end_.map_comp_assoc, TopCat.Presheaf.presheafEquivOfIso_counitIso_hom_app_app, CategoryTheory.Abelian.FunctorCategory.imageObjIso_hom, CategoryTheory.OplaxFunctor.id_mapId, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv, CategoryTheory.Join.mkFunctorRight_inv_app, CategoryTheory.Limits.coprod.inr_desc, CategoryTheory.FreeGroupoid.instIsLocalizationOfTopMorphismProperty, HomologicalComplex.biprod_inr_desc_f_assoc, CategoryTheory.Functor.map_neg, CategoryTheory.Idempotents.DoldKan.Γ_map_app, CategoryTheory.MorphismProperty.instHasTwoOutOfThreePropertyTop, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitIso_hom_naturality, CategoryTheory.MorphismProperty.le_isColocal_isColocal, CommGrpCat.one_apply, AlgebraicGeometry.IsAffineOpen.SpecMap_appLE_fromSpec_assoc, CategoryTheory.Subobject.underlyingIso_hom_comp_eq_mk, CategoryTheory.Limits.ι_colimitPointwiseProductToProductColimit_π_assoc, CategoryTheory.Functor.OplaxMonoidal.δ_natural_right, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_snd, CategoryTheory.Oplax.LaxTrans.naturality_id_assoc, CategoryTheory.endofunctorMonoidalCategory_rightUnitor_hom_app, Rep.resIndAdjunction_unit_app, CategoryTheory.Subobject.pullback_comp, CategoryTheory.Functor.homMonoidHom_apply, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd, CategoryTheory.Limits.KernelFork.map_condition, CategoryTheory.Abelian.Ext.mk₀_linearEquiv₀_apply, groupHomology.d₃₂_comp_d₂₁, CategoryTheory.Limits.pullbackAssoc_hom_fst, CategoryTheory.Under.mapComp_inv, HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_apply, CategoryTheory.Pseudofunctor.map₂_whisker_left_app, DistLat.coe_comp, CategoryTheory.MorphismProperty.RightFraction.ofInv_f, CategoryTheory.IsGrothendieckAbelian.instIsLeftAdjointModuleCatMulOppositeEndTensorObj, SheafOfModules.pushforward_comp_id, CategoryTheory.Limits.coend.ι_map_assoc, CategoryTheory.Functor.mapContActionComp_hom, CategoryTheory.MonoidalCategory.rightUnitor_inv_comp_tensorHom, CategoryTheory.overToCoalgebra_obj_a, CategoryTheory.Limits.PreservesPullback.iso_hom_fst_assoc, CategoryTheory.Iso.trans_conj, CategoryTheory.Endofunctor.Adjunction.Algebra.toCoalgebraOf_map_f, CategoryTheory.Adjunction.homEquiv_naturality_left_symm, HomologicalComplex.opcyclesToCycles_homologyπ_assoc, CategoryTheory.Enriched.FunctorCategory.homEquiv_apply_π_assoc, Bimod.TensorBimod.one_act_left', CategoryTheory.Functor.map₂HomologicalComplex_obj_map, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_rightUnitor, CommGrpCat.ofHom_id, CategoryTheory.Limits.colimitYonedaHomIsoLimitOp_π_apply, CategoryTheory.Idempotents.KaroubiKaroubi.idem_f_assoc, CategoryTheory.Limits.IsLimit.lift_self, CategoryTheory.Pseudofunctor.DescentData.isEquivalence_toDescentData_iff_of_sieve_eq, HomologicalComplex₂.totalShift₁Iso_hom_naturality_assoc, CategoryTheory.Limits.imageSubobjectCompIso_inv_arrow, CategoryTheory.NatTrans.congr, CategoryTheory.Pseudofunctor.CoGrothendieck.comp_const, ModuleCat.extendScalars_comp_id_assoc, CategoryTheory.ObjectProperty.le_isColocal_isColocal, CategoryTheory.GrpObj.inv_comp_inv_assoc, AlgebraicTopology.DoldKan.Γ₂N₁.natTrans_app_f_app, CategoryTheory.WithTerminal.prelaxfunctor_toPrelaxFunctorStruct_toPrefunctor_map, CategoryTheory.SimplicialObject.id_right, CategoryTheory.CartesianMonoidalCategory.lift_lift_associator_hom_assoc, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_inv_π, CategoryTheory.braiding_tensorUnit_right, CategoryTheory.Functor.OplaxRightLinear.δᵣ_associativity_assoc, CategoryTheory.BraidedCategory.braiding_inv_naturality_left, CategoryTheory.NatIso.naturality_2_assoc, CategoryTheory.Limits.inl_comp_pushoutSymmetry_hom_assoc, CategoryTheory.shiftFunctorComm_hom_app_of_add_eq_zero, CategoryTheory.Pretriangulated.comp_hom₃, CategoryTheory.Limits.PushoutCocone.isoMk_hom_hom, CategoryTheory.Over.μ_pullback_left_fst_fst, CategoryTheory.MonoidalClosed.compTranspose_eq, CategoryTheory.Limits.biprod.add_eq_lift_id_desc, CategoryTheory.Limits.CatCospanTransform.whiskerRight_comp_assoc, CategoryTheory.IsCommComonObj.comul_comm, CategoryTheory.PreGaloisCategory.IsNaturalSMul.naturality, CategoryTheory.StrictlyUnitaryLaxFunctor.ext_iff, CategoryTheory.Bicategory.Prod.snd_mapComp_hom, CategoryTheory.Iso.isoFunctorOfIsoInverse_hom_app, CochainComplex.mappingCone.inl_v_descShortComplex_f, CategoryTheory.Groupoid.isoEquivHom_symm_apply_inv, CategoryTheory.ObjectProperty.isCodetecting_op_iff, AlgebraicGeometry.SpecToEquivOfLocalRing_symm_apply, SimplexCategory.comp_toOrderHom, CategoryTheory.Under.hom_right_inv_right_assoc, HomotopicalAlgebra.bifibrantObjects_le_fibrantObject, CategoryTheory.ShiftedHom.opEquiv_symm_apply, CategoryTheory.Limits.pullback_inv_fst_snd_of_right_isIso_assoc, CategoryTheory.prodOpEquiv_counitIso_hom_app, CategoryTheory.Over.starPullbackIsoStar_inv_app_left, CategoryTheory.Bicategory.leftUnitor_hom_congr, HomologicalComplex.truncLE'Map_comp_assoc, CategoryTheory.Comma.mapSnd_hom_app, BddOrd.comp_apply, CategoryTheory.Join.mapWhiskerLeft_whiskerLeft_assoc, CategoryTheory.Subgroupoid.subset_generated, CategoryTheory.Oplax.StrongTrans.Modification.whiskerLeft_naturality_assoc, CategoryTheory.Limits.Sigma.ι_π_of_ne, AddCommGrpCat.kernelIsoKer_hom_comp_subtype, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_functor_obj_str, CategoryTheory.Limits.FintypeCat.jointly_surjective, CategoryTheory.Limits.coconeEquivalenceOpConeOp_counitIso, CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero_assoc, CategoryTheory.Center.whiskerRight_comm_assoc, CategoryTheory.Limits.Fork.op_ι_app_zero, CategoryTheory.Functor.descOfIsLeftKanExtension_fac_app_assoc, CategoryTheory.ComonObj.comul_counit_hom, AlgebraicGeometry.Scheme.Hom.stalkMap_congr, HomologicalComplex.homotopyCofiber.sndX_inrX, CategoryTheory.ActionCategory.homOfPair.val, CategoryTheory.ShortComplex.homologyMap_id, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_snd, FDRep.of_ρ, HomologicalComplex₂.ι_D₁, CategoryTheory.Limits.end_.map_π_assoc, CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapId_hom, CategoryTheory.Limits.coprod.map_desc, HomologicalComplex₂.flipEquivalenceCounitIso_inv_app_f_f, CategoryTheory.ShortComplex.Splitting.r_f_assoc, CategoryTheory.Functor.mapTriangleIdIso_inv_app_hom₁, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left, HomologicalComplex.homologyFunctorIso_hom_app, CategoryTheory.simplicialToCosimplicialAugmented_map_right, CategoryTheory.Localization.morphismProperty_eq_top, CategoryTheory.Limits.imageMonoIsoSource_inv_ι_assoc, CategoryTheory.Sieve.functor_map_coe, AlgebraicTopology.DoldKan.degeneracy_comp_PInfty, CategoryTheory.Limits.FormalCoproduct.category_id_φ, HomologicalComplex.mapBifunctor₁₂.d₁_eq_zero, CategoryTheory.Adjunction.rightAdjointLaxMonoidal_ε, CategoryTheory.Limits.kernelSubobject_arrow_comp_assoc, CategoryTheory.Mon.comp_hom, CategoryTheory.Functor.FullyFaithful.preimage_comp_assoc, CategoryTheory.Functor.mapGrpCompIso_inv_app_hom_hom, CategoryTheory.Limits.cospanOp_inv_app, CochainComplex.HomComplex.Cochain.d_comp_ofHoms_v, TopCat.prodIsoProd_hom_fst_assoc, CochainComplex.HomComplex.Cochain.toSingleMk_postcomp, CategoryTheory.Presheaf.freeYonedaHomEquiv_comp_assoc, CategoryTheory.GrothendieckTopology.overMapPullback_id_comp_assoc, CategoryTheory.coreCategory_comp_iso_hom, CategoryTheory.PreZeroHypercover.sumInl_h₀, CategoryTheory.Quotient.comp_left, CategoryTheory.Functor.Final.exists_coeq_of_locally_small, CategoryTheory.SmallObject.ιObj_πObj_assoc, CategoryTheory.Subgroupoid.mem_im_iff, CategoryTheory.ShortComplex.mapRightHomologyIso_hom_naturality_assoc, CategoryTheory.kernelOpOp_inv, CategoryTheory.coyonedaPairing_map, CategoryTheory.IsPushout.zero_right, CategoryTheory.Adjunction.homEquiv_counit, CategoryTheory.leftDistributor_inv, CategoryTheory.Localization.SmallHom.mk_id_comp, CochainComplex.HomComplex.Cochain.ofHom_add, CategoryTheory.Localization.Monoidal.μ_natural_right_assoc, CategoryTheory.kernelCokernelCompSequence.snakeInput_L₀_f, CategoryTheory.Limits.ker.condition_assoc, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_hom_app, AlgebraicGeometry.pullbackSpecIso_inv_fst', CategoryTheory.Limits.cospanCompIso_hom_app_right, CategoryTheory.Limits.pullbackDiagonalMapIdIso_hom_snd_assoc, SemiNormedGrp.comp_apply, CategoryTheory.WithTerminal.down_comp, CategoryTheory.Pretriangulated.Triangle.sub_hom₂, CategoryTheory.MorphismProperty.instHasRightCalculusOfFractionsOppositeOpOfHasLeftCalculusOfFractions, CategoryTheory.GrpObj.right_inv, CategoryTheory.Functor.IsCocartesian.of_comp_iso, AlgebraicGeometry.PresheafedSpace.id_c_app, CategoryTheory.PreOneHypercover.toPullback_cylinder, CategoryTheory.Linear.instEpiHSMulHomOfInvertible, SemiNormedGrp.comp_explicitCokernelπ_assoc, CategoryTheory.PrelaxFunctor.map₂_id, CategoryTheory.Functor.mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app, CategoryTheory.Limits.hasCoequalizer_epi_comp, CategoryTheory.Functor.LaxRightLinear.μᵣ_unitality_assoc, CategoryTheory.CommSq.vert_comp, CategoryTheory.CostructuredArrow.pre_map_right, CategoryTheory.Bicategory.rightUnitor_inv_naturality_assoc, CategoryTheory.HomIsOver.comp_over, CategoryTheory.Equivalence.unit_app_comp_inverse_map_η_functor_assoc, CategoryTheory.Localization.Preadditive.add'_zero, CategoryTheory.Functor.LaxMonoidal.ε_tensorHom_comp_μ, CategoryTheory.Limits.coprod.inr_fst, CategoryTheory.NatTrans.removeUnop_id, CategoryTheory.Limits.pullbackSymmetry_hom_comp_fst_assoc, CochainComplex.mappingCone.triangleRotateShortComplexSplitting_s, CategoryTheory.Dial.associator_hom_f, HomologicalComplex.extendCyclesIso_hom_iCycles_assoc, HomologicalComplex.mapBifunctor.d₂_eq_zero', CategoryTheory.Limits.zero_app, CategoryTheory.Functor.map_injective, CategoryTheory.Limits.isoZeroOfMonoZero_hom, CategoryTheory.Limits.opProdIsoCoprod_inv_inl_assoc, CategoryTheory.Pseudofunctor.CoGrothendieck.compIso_inv_app, CategoryTheory.Oplax.OplaxTrans.isoMk_inv_as_app, CategoryTheory.StrictlyUnitaryLaxFunctor.comp_map, AlgebraicGeometry.Scheme.Hom.comp_appTop, CochainComplex.mappingCone.inr_f_descShortComplex_f, CategoryTheory.StrictPseudofunctor.mk''_mapComp, CategoryTheory.CosimplicialObject.Augmented.leftOp_hom_app, HomologicalComplex.Hom.comm_from_assoc, CategoryTheory.Join.mapWhiskerLeft_id, CategoryTheory.ShiftedHom.opEquiv'_apply, CategoryTheory.Limits.CatCospanTransform.leftUnitor_inv_base_app, CategoryTheory.Presheaf.equalizerSieve_apply, CochainComplex.toSingle₀Equiv_apply, CategoryTheory.Limits.biproduct.fromSubtype_toSubtype, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₁_assoc, CategoryTheory.MonoidalCategory.rightUnitor_tensor_inv, CategoryTheory.LocalizerMorphism.LeftResolution.op_X₁, CategoryTheory.Limits.colimit.post_desc, CategoryTheory.SmallObject.ιFunctorObj_naturality_assoc, CategoryTheory.ShortComplex.LeftHomologyMapData.commf'_assoc, CategoryTheory.Functor.LaxMonoidal.whiskerLeft_μ_comp_μ, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app_assoc, CategoryTheory.Limits.BinaryBicone.fstKernelFork_ι, CategoryTheory.Adjunction.id_unit, AlgebraicGeometry.IsAffineOpen.Spec_map_appLE_fromSpec, CategoryTheory.Cat.HasLimits.limitConeLift_toFunctor, CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_fst_fst, CategoryTheory.Limits.braid_natural, CategoryTheory.Adjunction.leftAdjointCompNatTrans₀₂₃_eq_conjugateEquiv_symm, CategoryTheory.Functor.leftOp_map, CategoryTheory.Functor.toOplaxFunctor_mapId, CategoryTheory.CatCommSq.iso_hom_naturality_assoc, CategoryTheory.Prod.fac', CategoryTheory.Prod.symmetry_inv_app, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_left, CategoryTheory.Adjunction.counit_naturality_assoc, CategoryTheory.Equivalence.leftOp_counitIso_hom_app, CategoryTheory.Functor.obj.ι_def_assoc, CategoryTheory.Limits.Trident.app_zero_assoc, CategoryTheory.GrpObj.lift_comp_inv_left, CategoryTheory.MorphismProperty.Under.w_assoc, CochainComplex.HomComplex.Cochain.id_comp, CategoryTheory.braiding_leftUnitor_aux₁, CategoryTheory.Arrow.square_to_iso_invert, CategoryTheory.CommSq.w, CategoryTheory.constantSheafAdj_counit_w, AlgCat.hom_id, CategoryTheory.Limits.colimit_map_colimitObjIsoColimitCompEvaluation_hom, ComplexShape.Embedding.homRestrict_f, HomologicalComplex.opcyclesToCycles_naturality_assoc, Rep.leftRegularHomEquiv_apply, CategoryTheory.Limits.pullbackDiagonalMapIso.hom_fst_assoc, HomologicalComplex.singleObjCyclesSelfIso_hom_naturality_assoc, CategoryTheory.GradedObject.ι_descMapObj, CommGrpCat.ofHom_comp, CategoryTheory.sheafCompose_id, SSet.stdSimplex.mem_nonDegenerate_iff_mono, CategoryTheory.Endofunctor.Adjunction.Algebra.toCoalgebraOf_obj_str, CategoryTheory.oppositeShiftFunctorAdd'_hom_app, CategoryTheory.Pretriangulated.binaryProductTriangleIsoBinaryBiproductTriangle_inv_hom₁, AlgebraicGeometry.Scheme.Cover.gluedCoverT'_fst_snd, SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero, CategoryTheory.Limits.terminal.comp_from_assoc, PresheafOfModules.pushforward_obj_map_apply', CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.presheafHom_naturality_assoc, CategoryTheory.GrpObj.eq_lift_inv_left, CategoryTheory.sum.inlCompInlCompAssociator_hom_app_down, CategoryTheory.Functor.curry_obj_map_app, CategoryTheory.Endofunctor.algebraPreadditive_homGroup_add_f, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_comp_assoc, CategoryTheory.Grp.Hom.hom_inv, CategoryTheory.Comma.toPUnitIdEquiv_counitIso_inv_app, CategoryTheory.unop_hom_rightUnitor, CategoryTheory.MorphismProperty.instFullCostructuredArrowTopOverToOver, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec, CategoryTheory.SingleFunctors.hom_inv_id_hom_assoc, groupHomology.isoCycles₁_inv_comp_iCycles, CategoryTheory.IsPushout.hom_eq_add_up_to_refinements, AlgebraicGeometry.LocallyRingedSpace.stalkSpecializes_stalkMap, CategoryTheory.Limits.Cocones.extendId_inv_hom, CategoryTheory.HalfBraiding.monoidal, groupHomology.chainsMap_zero, CochainComplex.HomComplex.Cochain.single_v_eq_zero', CategoryTheory.toOverIteratedSliceForwardIsoPullback_inv_app_left, CategoryTheory.Functor.mapCoconePrecompose_hom_hom, CategoryTheory.Limits.CatCospanTransform.whiskerRight_id_assoc, CategoryTheory.Over.hom_left_inv_left_assoc, CategoryTheory.BasedCategory.id_def, CategoryTheory.Join.mapWhiskerRight_whiskerRight_assoc, CategoryTheory.Bicategory.Comonad.comul_assoc_assoc, CategoryTheory.tensorLeftHomEquiv_whiskerLeft_comp_evaluation, CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_comm_f, CategoryTheory.Functor.PullbackObjObj.π_snd, CategoryTheory.Presheaf.coconeOfRepresentable_ι_app, CategoryTheory.Preadditive.comp_nsmul, HomologicalComplex.homologyι_opcyclesToCycles, CompHausLike.LocallyConstant.sigmaComparison_comp_sigmaIso, CategoryTheory.Limits.coconeOfCoconeFiberwiseColimit_ι_app, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂'_obj_obj_map, CategoryTheory.Limits.pushoutIsoOpPullback_inv_snd, CategoryTheory.Limits.combineCones_pt_map, CategoryTheory.LocalizerMorphism.LeftResolution.Hom.comm_assoc, HomologicalComplex.extend.d_eq, CategoryTheory.Comonad.ComonadicityInternal.comparisonAdjunction_counit, CategoryTheory.SmallObject.functorObj_comm_assoc, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counit_app_tensor, CategoryTheory.Adjunction.Triple.leftToRight_app, AlgebraicGeometry.Scheme.residue_residueFieldCongr_assoc, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₃, CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_of_epi₃, CategoryTheory.Limits.PreservesPushout.inl_iso_hom, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIdIso_hom_app_hom, CategoryTheory.Limits.prod.map_id_comp, CategoryTheory.Mon.limit_mon_one, CategoryTheory.PreGaloisCategory.exists_lift_of_mono, CategoryTheory.Limits.Cofork.op_π_app_one, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_right_app, CategoryTheory.Preadditive.forkOfKernelFork_ι, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₁, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceInverseπ_inv_app, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_assoc, CategoryTheory.Limits.PreservesCokernel.π_iso_hom, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_assoc, CategoryTheory.Mat_.id_apply, CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm_assoc, AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom_comp_assoc, AlgebraicGeometry.IsImmersion.instLiftSchemeId, CategoryTheory.Quotient.LiftCommShift.iso_inv_app, CategoryTheory.ShortComplex.cycles_ext_iff, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_hom_right, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app, Action.resId_hom_app_hom, CategoryTheory.pre_map, CochainComplex.HomComplex.Cochain.ofHom_zero, HomotopicalAlgebra.Precylinder.i₀_π_assoc, UniformSpaceCat.coe_id, CategoryTheory.CartesianMonoidalCategory.lift_snd_comp_fst_comp_assoc, CategoryTheory.Limits.limit.conePointUniqueUpToIso_inv_comp, CategoryTheory.Join.mapWhiskerLeft_leftUnitor_hom, AlgebraicGeometry.Scheme.Hom.appLE_comp_appLE_assoc, CategoryTheory.Functor.descOfIsLeftKanExtension_fac, AlgebraicGeometry.Scheme.Hom.liftCoborder_ι, AlgebraicGeometry.Scheme.IsLocallyDirected.exists_of_pullback_V_V, groupHomology.cyclesMap_comp_isoCycles₁_hom_assoc, AlgebraicGeometry.Scheme.SpecMap_presheaf_map_eqToHom, HomologicalComplex.mapBifunctor.d₂_eq', CochainComplex.g_shortComplexTruncLEX₃ToTruncGE_assoc, CategoryTheory.Limits.IsLimit.map_π_assoc, AlgebraicGeometry.Scheme.mem_smallGrothendieckTopology, AlgebraicGeometry.Scheme.Modules.pseudofunctor_left_unitality_assoc, CategoryTheory.ShortComplex.Homotopy.compLeft_h₀, CochainComplex.mappingCone.inr_f_triangle_mor₃_f_assoc, PresheafOfModules.Hom.naturality, CategoryTheory.ChosenPullbacksAlong.iso_pullback_map, CategoryTheory.Comonad.Coalgebra.counit, CategoryTheory.conjugateEquiv_adjunction_id_symm, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_morphismRestrict, CategoryTheory.Limits.Cone.mapConeToUnder_hom_hom, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_symm_apply, CategoryTheory.Monad.right_unit, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_naturality_assoc, groupHomology.mapShortComplexH2_id_comp, GrpCat.one_apply, CategoryTheory.CartesianMonoidalCategory.lift_map, Homotopy.compLeft_hom, AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom_comp, CategoryTheory.Functor.OplaxMonoidal.δ_natural_assoc, CategoryTheory.ShortComplex.mapHomologyIso_inv_naturality, CategoryTheory.Functor.isStrongGenerator_of_isDense, Mathlib.Tactic.BicategoryCoherence.assoc_liftHom₂, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom', CategoryTheory.hasExt_iff, CategoryTheory.Bicategory.lanUnit_desc_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_assoc, CategoryTheory.Limits.ColimitPresentation.w, AddGrpCat.coe_comp, CategoryTheory.IsPushout.op, CategoryTheory.Idempotents.Karoubi.decompId_p_f, CategoryTheory.Functor.LaxMonoidal.right_unitality_inv_assoc, CategoryTheory.GradedObject.ι_descMapObj_assoc, CategoryTheory.Oplax.LaxTrans.vComp_naturality_naturality, CategoryTheory.Bicategory.associator_naturality_left, CategoryTheory.Limits.Cofork.IsColimit.π_desc, CategoryTheory.MonObj.lift_comp_one_left_assoc, CategoryTheory.CategoryOfElements.id_val, CategoryTheory.Limits.image_map_comp_imageSubobjectIso_inv, groupHomology.isoShortComplexH2_inv, CategoryTheory.Grothendieck.map_map_fiber, skyscraperPresheafCoconeOfSpecializes_ι_app, CategoryTheory.Sheaf.comp_val_assoc, HomotopicalAlgebra.cofibration_unop_iff, CategoryTheory.Functor.IsCartesian.domainUniqueUpToIso_hom_isHomLift, CategoryTheory.NatTrans.rightDerived_id, CategoryTheory.Under.opEquivOpOver_inverse_obj, HomotopicalAlgebra.FibrantObject.homMk_id, CategoryTheory.Limits.opProductIsoCoproduct'_inv_comp_lift, CategoryTheory.HopfObj.mul_antipode₂, CategoryTheory.instHomIsOverId, TopologicalSpace.Opens.apply_mk, CategoryTheory.PresheafHom.IsSheafFor.exists_app, CochainComplex.cochainComplex_d_succ_succ_zero, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompCoyoneda, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_inv_hom_assoc, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃'_tensorHom, TopologicalSpace.Opens.infLELeft_apply, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_app, CategoryTheory.ShrinkHoms.comp_def, HomologicalComplex.truncLE'Map_f_eq, groupHomology.toCycles_comp_isoCycles₁_hom, SimplexCategory.eq_id_of_mono, CategoryTheory.Limits.pullbackIsoOpPushout_inv_snd_assoc, CategoryTheory.SingleFunctors.inv_hom_id_hom_app, CategoryTheory.Limits.FormalCoproduct.coproductIsoSelf_inv_φ, CategoryTheory.Limits.BinaryFan.leftUnitor_inv, AlgebraicGeometry.SheafedSpace.id_c, CategoryTheory.ShortComplex.LeftHomologyMapData.ofEpiOfIsIsoOfMono_φH, AlgebraicGeometry.LocallyRingedSpace.comp_toHom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHom_def, CategoryTheory.Limits.IsTerminal.from_self, CategoryTheory.Abelian.tfae_mono, CategoryTheory.Limits.piObjIso_inv_comp_π_assoc, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_hom_eq_germ_assoc, Action.forget_μ, CategoryTheory.Iso.unop_inv_hom_id_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_hom_toNatTrans_app_val_app, prevD_comp_right, CategoryTheory.Functor.isLeftKanExtension_iff_precomp, HomologicalComplex.Hom.comm', HomologicalComplex₂.ι_totalShift₂Iso_hom_f, AlgebraicTopology.DoldKan.N₁Γ₀_inv_app, CategoryTheory.Bicategory.Pith.comp₂_iso_inv_assoc, CategoryTheory.OverClass.asOverHom_comp, CategoryTheory.MorphismProperty.map_top_eq_top_of_essSurj_of_full, CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_snd_snd, AlgebraicGeometry.Scheme.Hom.inl_toNormalization_normalizationCoprodIso_inv_assoc, CategoryTheory.ShortComplex.Homotopy.g_h₃, CategoryTheory.Coyoneda.fullyFaithful_preimage, SheafOfModules.pullbackObjFreeIso_hom_naturality, CategoryTheory.IsPushout.of_has_biproduct, CategoryTheory.Functor.ranObjObjIsoLimit_inv_π, SSet.yonedaEquiv_comp, LightCondSet.topCatAdjunctionUnit_val_app, LightDiagram.comp_hom_hom_hom_apply, CategoryTheory.Iso.eHomCongr_inv, AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_inv_ι_app, CategoryTheory.MorphismProperty.RightFraction₂.exists_leftFraction₂, CategoryTheory.MorphismProperty.id_mem, CategoryTheory.MonoidalCategory.rightUnitor_monoidal, CategoryTheory.Iso.hom_inv_id_triangle_hom₃_assoc, AlgebraicGeometry.Scheme.IdealSheafData.inclusion_id, CategoryTheory.MonoidalOpposite.tensorLeftIso_hom_app_unmop, CategoryTheory.StrictlyUnitaryPseudofunctor.mk'_map₂, CategoryTheory.Limits.FintypeCat.instPreservesFiniteLimitsFintypeCatForgetHomCarrier, CategoryTheory.IsCofiltered.eq_condition, HomologicalComplex.dFrom_comp_xNextIso_assoc, CategoryTheory.Abelian.Ext.mk₀_bijective, CategoryTheory.Limits.colimit_map_colimitObjIsoColimitCompEvaluation_hom_assoc, SSet.op_map, CategoryTheory.Iso.inverseCompIso_hom_app, CategoryTheory.Preadditive.isCoseparator_iff, HomologicalComplex.toCycles_cyclesIsoSc'_hom, CategoryTheory.Limits.isColimitCoconeOfConeLeftOp_desc, CategoryTheory.Sieve.ofArrows.fac_assoc, CategoryTheory.Mat.id_apply_self, CategoryTheory.Comon.trivial_comon_counit, CategoryTheory.MonObj.mul_assoc_assoc, CategoryTheory.GrothendieckTopology.toSheafify_naturality, SimplicialObject.Splitting.IndexSet.eqId_iff_eq, CategoryTheory.ObjectProperty.isColocal.homEquiv_apply, CategoryTheory.Functor.mapConeOp_hom_hom, CategoryTheory.Adjunction.right_triangle, CategoryTheory.leftUnitor_inv_braiding, CategoryTheory.Functor.OplaxMonoidal.left_unitality_assoc, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.inverse_obj, CategoryTheory.MonoidalCategory.tensor_whiskerLeft, CategoryTheory.HasLiftingProperty.transfiniteComposition.sqFunctor_map, CategoryTheory.Limits.biproduct.ι_desc_assoc, Frm.comp_apply, CategoryTheory.Limits.coequalizer.condition_assoc, CategoryTheory.Limits.Cocone.toCostructuredArrowCompProj_inv_app, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_app_apply, HomologicalComplex.fromOpcycles_op_cyclesOpIso_inv, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_hom_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHom_def', CategoryTheory.Limits.Types.Pushout.cocone_ι_app, CategoryTheory.leftDistributor_inv_comp_biproduct_π_assoc, CategoryTheory.EnrichedCat.whiskerRight_out_app, Bimod.whiskerRight_hom, CategoryTheory.MonoidalCategory.leftUnitor_monoidal_assoc, CategoryTheory.Bicategory.prod_homCategory_comp_snd, CategoryTheory.GradedObject.ι_mapMap_assoc, CategoryTheory.MorphismProperty.instHasTwoOutOfThreePropertyMin, AlgebraicGeometry.Scheme.germ_residue_assoc, CategoryTheory.unop_hom_braiding, CategoryTheory.Functor.prod_μ_snd, HomologicalComplex₂.total_d, Lat.ofHom_comp, CategoryTheory.ShortComplex.comp_τ₃_assoc, CategoryTheory.Limits.colimit.w_assoc, CategoryTheory.Idempotents.Karoubi.Biproducts.bicone_π_f, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq, CategoryTheory.Functor.IsEventuallyConstantTo.isoMap_hom_inv_id_assoc, CategoryTheory.InjectiveResolution.Hom.ι_f_zero_comp_hom_f_zero_assoc, CategoryTheory.Limits.KernelFork.map_ι, SSet.Quasicategory.hornFilling', SemimoduleCat.MonoidalCategory.braiding_naturality, CategoryTheory.MarkovCategory.instSubsingletonHomTensorUnit, CategoryTheory.IsPushout.inl_isoIsPushout_inv_assoc, CategoryTheory.Prod.sectR_map, CategoryTheory.GrothendieckTopology.ι_plusCompIso_hom, CategoryTheory.RetractArrow.unop_i_left, CategoryTheory.MorphismProperty.instHasPullbackSndHomDiscretePUnitOfHasPullbacksAlongOfIsStableUnderBaseChangeAlong, AlgebraicGeometry.IsAffineOpen.Spec_map_appLE_fromSpec_assoc, groupHomology.chainsMap_f_2_comp_chainsIso₂_assoc, CategoryTheory.Functor.leftDerivedNatTrans_app, CategoryTheory.Oplax.StrongTrans.id_naturality_hom, CategoryTheory.Bicategory.leftUnitor_naturality, CategoryTheory.Limits.zero_comp, CategoryTheory.PreGaloisCategory.functorToContAction_obj_obj, CategoryTheory.Localization.hasSmallLocalizedShiftedHom_iff, CategoryTheory.obj_μ_zero_app, CategoryTheory.Limits.inl_comp_pushoutSymmetry_hom, CategoryTheory.Limits.coprod.associator_hom, CategoryTheory.Functor.mapTriangleIdIso_inv_app_hom₂, CategoryTheory.Dial.leftUnitorImpl_inv_f, CategoryTheory.Bicategory.InducedBicategory.bicategory_homCategory_id_hom, CategoryTheory.ExponentiableMorphism.unit_pushforwardId_hom_assoc, CategoryTheory.CatEnrichedOrdinary.id_hComp_id, CategoryTheory.IsCommMonObj.mul_comm', CategoryTheory.IsPushout.inr_isoIsPushout_hom, CategoryTheory.cosimplicialToSimplicialAugmented_map, Bimod.pentagon_bimod, CategoryTheory.IsPullback.isoIsPullback_hom_fst, CategoryTheory.StrictlyUnitaryLaxFunctor.mk'_mapId, CategoryTheory.Mon.forget_δ, CategoryTheory.MonoidalCategory.MonoidalRightAction.whiskerRight_actionHomLeft, CategoryTheory.GrothendieckTopology.instWEqualsLocallyBijectiveTypeHom, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst_assoc, HomologicalComplex.pOpcycles_opcyclesToCycles_iCycles, AlgebraicGeometry.LocallyRingedSpace.residueFieldMap_id, CategoryTheory.ExponentiableMorphism.ev_naturality, HomologicalComplex.extend_d_eq, AlgebraicGeometry.diagonal_Spec_map, CategoryTheory.Comma.mapRightEq_hom_app_left, SSet.OneTruncation₂.nerveHomEquiv_apply, CochainComplex.HomComplex.CohomologyClass.toHom_mk_eq_zero_iff, CategoryTheory.Limits.Pi.isoLimit_hom_π, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_ι_inv, FintypeCat.uSwitchEquiv_symm_naturality, TopCat.Presheaf.Γgerm_res_apply, AlgebraicGeometry.Spec.toPresheafedSpace_map, CategoryTheory.MonoOver.initialTo_b_eq_zero, CategoryTheory.Functor.commShiftOfLocalization_iso_hom_app, AlgebraicTopology.DoldKan.QInfty_f_idem_assoc, CategoryTheory.Pretriangulated.Triangle.isZero₃_iff, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_left, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₂, CategoryTheory.Paths.lift_toPath, CategoryTheory.Join.inrCompFromSum_inv_app, CategoryTheory.eqToHom_iso_inv_naturality_assoc, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv, FintypeCat.homMk_eq_comp_iff, CategoryTheory.Functor.OplaxRightLinear.δᵣ_unitality_inv_assoc, CategoryTheory.ShrinkHoms.inverse_map, CategoryTheory.WithTerminal.liftFromOverComp_inv_app, CategoryTheory.Functor.OplaxLeftLinear.δₗ_naturality_right_assoc, CategoryTheory.ShortComplex.Hom.comm₂₃_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_right, CategoryTheory.Monad.algebraPreadditive_homGroup_neg_f, HomologicalComplex.mapBifunctor.d₁_eq_zero', CategoryTheory.WithInitial.liftToInitial_map, CategoryTheory.Comma.mapRightEq_inv_app_right, CategoryTheory.ShortComplex.Homotopy.comp_h₂, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_map_app_assoc, CategoryTheory.ShortComplex.Homotopy.ofEq_h₃, CategoryTheory.StructuredArrow.mapIso_functor_map_right, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_hom_assoc, CategoryTheory.Limits.ι_colimitConstInitial_hom, CategoryTheory.Bifunctor.diagonal', CategoryTheory.BraidedCategory.hexagon_forward_inv, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_assoc, CategoryTheory.Limits.π_comp_colimitRightOpIsoUnopLimit_inv_assoc, CategoryTheory.SingleFunctors.comp_hom, CategoryTheory.LaxFunctor.mapComp_assoc_left, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τl, CategoryTheory.Adjunction.map_restrictFullyFaithful_unit_app, CategoryTheory.Sheaf.sheafifyCocone_ι_app_val_assoc, commBialgCatEquivComonCommAlgCat_inverse_map_unop_hom, CategoryTheory.Bicategory.Comonad.counit_comul, HomologicalComplex.extendMap_comp, CategoryTheory.IsPushout.inr_isoIsPushout_inv_assoc, CategoryTheory.LocalizerMorphism.LeftResolution.opEquivalence_counitIso, CategoryTheory.Functor.curryObjProdComp_inv_app_app, CategoryTheory.MonoidalCategory.rightUnitor_naturality, ModuleCat.ofHom₂_hom_apply_hom, CategoryTheory.unop_zsmul, SheafOfModules.conjugateEquiv_pullbackId_hom, CategoryTheory.GrothendieckTopology.OneHypercover.comp_h₀, CategoryTheory.MonoidalCategory.tensorHom_def_assoc, CategoryTheory.Sheaf.Hom.add_app, CategoryTheory.PreZeroHypercover.Hom.comp_h₀, CategoryTheory.Dial.braiding_naturality_left, CategoryTheory.Under.costar_map_left, CategoryTheory.Dial.associatorImpl_hom_f, CategoryTheory.PreGaloisCategory.endEquivAutGalois_π, CategoryTheory.ActionCategory.π_map, CategoryTheory.CatEnriched.eqToHom_hComp_eqToHom, CategoryTheory.Monad.unit_naturality_assoc, CategoryTheory.Prod.swap_map, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapId_inv_iso_hom, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.firstMap_app_app_app, CategoryTheory.NatTrans.app_units_zsmul, CategoryTheory.ShortComplex.cyclesMap'_add, CategoryTheory.Limits.CatCospanTransform.whiskerLeft_comp_assoc, CategoryTheory.Presieve.extension_iff_amalgamation, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_whiskerRight, groupCohomology.subtype_comp_d₀₁, BialgCat.toBialgHom_comp, HomologicalComplex.quasiIso_unopFunctor_map_iff, CategoryTheory.OplaxFunctor.map₂_rightUnitor_app, SSet.StrictSegalCore.map_mkOfSucc_zero_spineToSimplex, CategoryTheory.ShortComplex.mapHomologyIso'_hom_naturality_assoc, CategoryTheory.MonoidalCategory.tensorμ_natural_left_assoc, CategoryTheory.CatEnrichedOrdinary.eqToHom_hComp_eqToHom, CategoryTheory.Subgroupoid.mem_top, CategoryTheory.MonoidalClosed.pre_map, BddOrd.ofHom_comp, CategoryTheory.NonPreadditiveAbelian.diag_σ_assoc, CategoryTheory.Over.whiskerRight_left_fst_assoc, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_right_unitor, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.SheafCondition.bijective_toPullbackObj, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_assoc, ComplexShape.Embedding.homRestrict.f_eq, CategoryTheory.CartesianClosed.curry_natural_left, CategoryTheory.PreOneHypercover.Hom.w₁₂, CategoryTheory.Functor.LaxMonoidal.tensorHom_ε_comp_μ, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_app, CategoryTheory.Cat.Hom.toNatTrans_comp, CategoryTheory.Limits.Multifork.hom_comp_ι, CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv_assoc, CategoryTheory.ShortComplex.RightHomologyData.op_i, CategoryTheory.ShortComplex.id_τ₃, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_left_map, AlgebraicTopology.DoldKan.QInfty_f_idem, CategoryTheory.LaxFunctor.mapComp_naturality_right_app, groupHomology.isoCycles₂_hom_comp_i, CategoryTheory.WithTerminal.equivComma_inverse_map_app, HomologicalComplex.restrictionToTruncGE'.f_eq_iso_hom_iso_inv, CategoryTheory.TwoSquare.vComp_app, CategoryTheory.GrothendieckTopology.diagramNatTrans_id, Action.isContinuous_def, CategoryTheory.Sum.functorEquiv_unit_app_app_inl, CategoryTheory.Functor.LaxMonoidal.comp_μ, CategoryTheory.Join.mkFunctorLeft_inv_app, CategoryTheory.ComonObj.counit_comul, SemiRingCat.id_apply, SSet.RelativeMorphism.Homotopy.rel, CategoryTheory.MonoidalClosed.curryHomEquiv'_apply, CategoryTheory.SmallObject.FunctorObjIndex.comm_assoc, AlgebraicGeometry.Scheme.stalkMap_inv_hom_assoc, CategoryTheory.LaxFunctor.mapComp_assoc_right, CategoryTheory.Functor.leftKanExtensionUniqueOfIso_hom, AlgebraicGeometry.tilde.toOpen_map_app_assoc, CategoryTheory.Limits.biproduct.ι_toSubtype, CategoryTheory.MonoidalOpposite.unmopEquiv_counitIso_inv_app, CategoryTheory.CartesianMonoidalCategory.lift_map_assoc, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d_1_0, CategoryTheory.ComposableArrows.mk₀_map, CategoryTheory.Limits.isLimitOfCoconeUnopOfCone_lift, CategoryTheory.Limits.limitFlipIsoCompLim_hom_app, CategoryTheory.shiftFunctorAdd_assoc_hom_app, groupHomology.π_comp_H1Iso_hom, CategoryTheory.Discrete.functor_map, CochainComplex.mappingCone.inl_v_snd_v, CategoryTheory.Discrete.sumEquiv_functor_map, CategoryTheory.CategoryOfElements.fromCostructuredArrow_obj_mk, CategoryTheory.Bicategory.mateEquiv_apply, CategoryTheory.whiskerLeft_sum, CategoryTheory.Limits.prod.comp_diag, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_hom_π_π, CategoryTheory.SmallObject.ιFunctorObj_πFunctorObj, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_right, CategoryTheory.Types.instReflectsColimitsOfSizeForgetTypeHom, CategoryTheory.GradedObject.Monoidal.rightUnitor_naturality, CategoryTheory.Limits.image.lift_mk_factorThruImage_assoc, CategoryTheory.HasClassifier.comm_assoc, CategoryTheory.Over.tensorHom_left_snd, CategoryTheory.WithInitial.ofCommaObject_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_rightUnitor, CategoryTheory.Limits.pullback.mapDesc_comp, HomologicalComplex.p_fromOpcycles_assoc, CategoryTheory.StrictlyUnitaryLaxFunctor.comp_mapComp, CategoryTheory.Abelian.DoldKan.comparisonN_hom_app_f, CategoryTheory.eHomEquiv_comp_assoc, CategoryTheory.ShortComplex.RightHomologyMapData.commp_assoc, CategoryTheory.Oplax.StrongTrans.naturality_naturality, CategoryTheory.Subobject.inf_comp_right, CategoryTheory.ShortComplex.neg_τ₁, groupHomology.isoCycles₂_inv_comp_iCycles, CategoryTheory.MonoidalOpposite.tensorRightMopIso_hom_app_unmop, CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv', CategoryTheory.ObjectProperty.isClosedUnderColimitsOfShape_iff_unop, CategoryTheory.Under.opEquivOpOver_counitIso, FinBddDistLat.id_apply, CategoryTheory.Functor.mapAction_map_hom, CategoryTheory.HopfObj.antipode_counit, AddMagmaCat.comp_apply, CategoryTheory.MorphismProperty.precoverage_inf, CategoryTheory.Functor.LaxMonoidal.whiskerRight_tensorUnit_comp_rightUnitor_hom_assoc, CategoryTheory.Functor.IsDenseSubsite.map_eq_of_eq, HomologicalComplex.extendHomologyIso_inv_homologyι, CategoryTheory.StructuredArrow.toUnder_map_left, CategoryTheory.Localization.SmallHom.mkInv_comp_mk, HomologicalComplex.unit_tensor_d₁, CategoryTheory.StructuredArrow.w_prod_snd_assoc, HomologicalComplex₂.XXIsoOfEq_hom_ιTotal, CategoryTheory.Grp.η_def, CategoryTheory.kernelCokernelCompSequence.inl_φ_assoc, CategoryTheory.WithTerminal.equivComma_inverse_obj_map, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_hom_left, SSet.Truncated.HomotopyCategory.BinaryProduct.associativityIso_hom_app, SheafOfModules.pullback_map_ιFree_comp_pullbackObjFreeIso_hom, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanIndex_snd, CategoryTheory.StructuredArrow.prodInverse_obj, AugmentedSimplexCategory.inr_comp_tensorHom, CategoryTheory.Subfunctor.Subpresheaf.range_comp_le, CategoryTheory.Bicategory.pentagon_hom_hom_inv_inv_hom, CategoryTheory.Limits.IsZero.eq_zero_of_src, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerLeft, CategoryTheory.Triangulated.SpectralObject.comp_hom_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_inv_app_app, CategoryTheory.MonObj.mul_one_assoc, AddCommMonCat.id_apply, CategoryTheory.SemiadditiveOfBinaryBiproducts.isUnital_rightAdd, CategoryTheory.Functor.toEssImageCompι_inv_app, CategoryTheory.IsFiltered.sup_exists, CategoryTheory.PrelaxFunctor.map₂Iso_hom, ModuleCat.hom_sub, CategoryTheory.MonoidalCategory.MonoidalRightAction.comp_actionHomLeft, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapIdIso_hom, TopologicalSpace.OpenNhds.map_id_obj, CategoryTheory.ShortComplex.LeftHomologyMapData.add_φK, CategoryTheory.MorphismProperty.Comma.eqToHom_right, AlgebraicGeometry.HasAffineProperty.affineAnd_le_isAffineHom, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition'_assoc, AlgebraicGeometry.PresheafedSpace.id_c, CategoryTheory.NonPreadditiveAbelian.sub_def, CategoryTheory.ShortComplex.Splitting.ofIso_r, AlgebraicGeometry.Scheme.Opens.ι_appLE, CategoryTheory.DifferentialObject.d_squared_assoc, CategoryTheory.conjugateEquiv_adjunction_id, CategoryTheory.Yoneda.fullyFaithful_preimage, CategoryTheory.Limits.prodComparison_fst_assoc, CategoryTheory.ShortComplex.SnakeInput.Hom.comm₀₁_assoc, inr_coprodIsoPushout_inv, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_π, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHom_op, CategoryTheory.Limits.prod.inl_fst, SSet.stdSimplex.faceSingletonIso_one_hom_comp_ι_eq_δ_assoc, CategoryTheory.Subobject.ofLEMk_comp_ofMkLE_assoc, AlgebraicGeometry.Scheme.ΓSpecIso_naturality_assoc, CategoryTheory.Oplax.OplaxTrans.leftUnitor_hom_as_app, AddMagmaCat.id_apply, CategoryTheory.GradedObject.Monoidal.leftUnitor_naturality, SSet.StrictSegal.spineToSimplex_arrow, CategoryTheory.MonObj.mul_assoc_flip_assoc, CategoryTheory.Limits.biproduct.ι_toSubtype_assoc, CategoryTheory.Functor.final_iff_of_isFiltered, AlgebraicGeometry.ExistsHomHomCompEqCompAux.hb, CategoryTheory.coyonedaEquiv_symm_map, HomologicalComplex₂.totalShift₁Iso_hom_naturality, CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id_app_assoc, groupCohomology.cocyclesMap_id_comp, CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.preservesFiniteLimits, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ_assoc, groupCohomology.isoCocycles₁_inv_comp_iCocycles_assoc, CategoryTheory.Functor.opHom_map_app, CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_hom_assoc, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom, CategoryTheory.Limits.opCoproductIsoProduct_hom_comp_π_assoc, AlgebraicGeometry.Scheme.Hom.comp_image, CategoryTheory.Comma.toIdPUnitEquiv_counitIso_inv_app, CategoryTheory.Abelian.FunctorCategory.functor_category_isIso_coimageImageComparison, CategoryTheory.Functor.FullyFaithful.mulEquivEnd_apply, CategoryTheory.SmallObject.SuccStruct.ofCocone_map, CategoryTheory.Limits.proj_comp_opProductIsoCoproduct'_hom, CommRingCat.hom_id, CategoryTheory.GradedObject.Monoidal.ιTensorObj₄_eq, CategoryTheory.Functor.cocones_map_app, CategoryTheory.MorphismProperty.IsStableUnderCobaseChange.inf, CategoryTheory.ShortComplex.unopMap_τ₃, AlgebraicGeometry.Spec.toLocallyRingedSpace_map, AlgebraicGeometry.Scheme.appLE_comp_appLE, CategoryTheory.MonoidalCategory.DayFunctor.equiv_unitIso_inv_app, CategoryTheory.Enriched.FunctorCategory.functorEnriched_comp_id_assoc, CategoryTheory.Limits.coprod.functor_obj_map, CategoryTheory.CommSq.w_assoc, CategoryTheory.ShiftMkCore.assoc_hom_app, CategoryTheory.rightDistributor_hom, ModuleCat.ofHom₂_compr₂, CategoryTheory.Functor.Monoidal.map_leftUnitor_assoc, CochainComplex.mappingConeCompTriangle_mor₃_naturality_assoc, CategoryTheory.PrelaxFunctor.map₂Iso_inv, SSet.Truncated.HomotopyCategory.homMk_comp_homMk_assoc, CategoryTheory.Functor.RightExtension.postcomp₁_obj_hom_app, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_map, CategoryTheory.leftAdjointMate_comp, CategoryTheory.eqToHom_trans_assoc, CategoryTheory.Limits.Multicofork.sigma_condition_assoc, ModuleCat.extendScalars_comp_id, CategoryTheory.Limits.colimit.w, CategoryTheory.Functor.OplaxMonoidal.right_unitality_assoc, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app, CategoryTheory.Bicategory.Pith.inclusion_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map, BddDistLat.comp_apply, HomologicalComplex₂.total.mapAux.d₁_mapMap_assoc, CategoryTheory.ObjectProperty.isSeparating_op_iff, CategoryTheory.functorProdFunctorEquivUnitIso_inv_app, CategoryTheory.Adjunction.adjToMonadIso_hom_toNatTrans_app, CategoryTheory.SmallObject.ιObj_naturality_assoc, CategoryTheory.Limits.pullbackProdFstIsoProd_hom_snd_assoc, CategoryTheory.Limits.HasZeroObject.zeroIsoIsTerminal_inv, CategoryTheory.Pretriangulated.comp_hom₁, CategoryTheory.Precoherent.pullback, CategoryTheory.Limits.PushoutCocone.unop_pt, AlgebraicGeometry.Scheme.Hom.resLE_comp_resLE, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_hom_app_val_app, CategoryTheory.ObjectProperty.colimitsOfShape_eq_unop_limitsOfShape, LightCondensed.id_val, TopCat.Presheaf.germ_stalkSpecializes, CategoryTheory.ShortComplex.Homotopy.neg_h₂, CategoryTheory.Functor.leftDerivedNatTrans_id, AlgebraicGeometry.Scheme.residue_descResidueField_assoc, CategoryTheory.ProjectiveResolution.liftFOne_zero_comm, CategoryTheory.Functor.FullyFaithful.grpObj_one, CategoryTheory.Enriched.FunctorCategory.functorEnriched_assoc_assoc, CategoryTheory.Functor.commShiftOfLocalization.iso_hom_app_assoc, AlgebraicGeometry.IsLocalAtSource.iff_of_iSup_eq_top, CategoryTheory.Limits.Multifork.pi_condition_assoc, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_hom, CategoryTheory.Limits.SequentialProduct.cone_π_app, CategoryTheory.Functor.biproductComparison_π, PresheafOfModules.freeYonedaEquiv_comp, AlgebraicGeometry.ΓSpec_adjunction_homEquiv_eq, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_assoc, CategoryTheory.ObjectProperty.le_ind, CategoryTheory.ShortComplex.leftRightHomologyComparison'_naturality, CochainComplex.ConnectData.comp_d₀_assoc, CategoryTheory.MonoidalPreadditive.tensor_add, AlgebraicGeometry.Scheme.Cover.LocallyDirected.w, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_assoc, CategoryTheory.endofunctorMonoidalCategory_leftUnitor_inv_app, AlgebraicGeometry.Scheme.Opens.ι_app, IsFreeGroupoid.SpanningTree.treeHom_root, CategoryTheory.toSheafify_naturality_assoc, CategoryTheory.WithInitial.liftFromUnder_obj_map, CategoryTheory.finrank_endomorphism_simple_eq_one, AlgebraicTopology.DoldKan.PInfty_f_comp_QInfty_f, CategoryTheory.PreOneHypercover.comp_h₀, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₃, CategoryTheory.ShortComplex.HasRightHomology.of_zeros, CategoryTheory.Limits.IsZero.iff_id_eq_zero, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₂, BddDistLat.hom_comp, CategoryTheory.Limits.PushoutCocone.eta_hom_hom, CategoryTheory.RetractArrow.unop_i_right, CategoryTheory.Limits.limit.lift_π_app_assoc, CategoryTheory.Limits.ImageMap.map_ι_assoc, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_inv_app_app, CategoryTheory.NatTrans.app_shift, CategoryTheory.MorphismProperty.monotone_isoClosure, CategoryTheory.Lax.OplaxTrans.naturality_comp_assoc, CategoryTheory.ShortComplex.LeftHomologyData.homologyπ_comp_homologyIso_hom, CategoryTheory.GradedObject.eqToHom_apply, CategoryTheory.Functor.leftDerivedNatTrans_fac, CategoryTheory.Pseudofunctor.DescentData.id_hom, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv_assoc, HomologicalComplex₂.d₂_eq', BddOrd.ofHom_id, CategoryTheory.Limits.limitRightOpIsoOpColimit_inv_comp_π_assoc, CategoryTheory.Functor.ι_colimitIsoOfIsLeftKanExtension_hom_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app_assoc, CategoryTheory.Functor.homologySequenceδ_naturality_assoc, CategoryTheory.eqToHom_comp_iff, CategoryTheory.Factorisation.Hom.h_π, CategoryTheory.NatTrans.comp_app, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id, CategoryTheory.ShortComplex.zero_τ₁, CategoryTheory.Functor.IsCartesian.map_isHomLift, CategoryTheory.Limits.Cone.w_assoc, CategoryTheory.IsFiltered.sup_objs_exists, CategoryTheory.CatCenter.localization_mul, CategoryTheory.LaxFunctor.mapComp_naturality_left_app, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right_assoc, CategoryTheory.ShortComplex.Exact.rightHomologyDataOfIsColimitCokernelCofork_p, AlgebraicGeometry.Scheme.Hom.isoImage_hom_ι, CategoryTheory.Bicategory.pentagon_inv_inv_hom_hom_inv_assoc, CategoryTheory.Join.mapPairLeft_hom_app, CategoryTheory.Localization.SmallShiftedHom.mk₀_comp_mk₀Inv, CategoryTheory.ShortComplex.smul_τ₁, Semigrp.coe_id, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransId_hom_app_f, CategoryTheory.Limits.cokernel.π_of_epi, CategoryTheory.Functor.flipIsoCurrySwapUncurry_inv_app_app, CategoryTheory.cones_map_app_app, CategoryTheory.IsPullback.isoPullback_inv_fst_assoc, AlgebraicGeometry.AffineSpace.SpecIso_inv_over, CategoryTheory.Limits.BinaryBiconeMorphism.winr_assoc, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_hom_assoc, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_hom_comp_ι_assoc, CategoryTheory.ObjectProperty.instIsTriangulatedMinOfIsClosedUnderIsomorphisms, CochainComplex.HomComplex.Cochain.fromSingleMk_v_eq_zero, CategoryTheory.MonoidalCategory.associator_inv_naturality_assoc, SSet.Truncated.Edge.CompStruct.d₀, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp, CategoryTheory.Limits.image.compIso_inv_comp_image_ι_assoc, CategoryTheory.OplaxFunctor.mapComp_id_left_assoc, CategoryTheory.comp_over, AlgebraicGeometry.SheafedSpace.id_base, CategoryTheory.StrictPseudofunctor.mk'_mapId, FintypeCat.hom_inv_id_apply, CategoryTheory.CartesianMonoidalCategory.lift_fst_comp_snd_comp, CategoryTheory.ShortComplex.Splitting.f_r, HomotopicalAlgebra.weakEquivalences_eq_unop, CategoryTheory.MorphismProperty.Comma.comp_hom, CategoryTheory.WithTerminal.liftFromOver_map_app, CompHausLike.LocallyConstant.incl_comap, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality, CategoryTheory.MonoidalClosed.coev_app_comp_pre_app_assoc, CategoryTheory.whiskerRight_ι_colimitCompWhiskeringRightIsoColimitComp_inv, AlgebraicGeometry.Scheme.Hom.toNormalization_fromNormalization, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_of_mono₁, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapCompIso_hom, CategoryTheory.isDetecting_unop_iff, CategoryTheory.Functor.relativelyRepresentable.w, DerivedCategory.singleFunctorsPostcompQIso_hom_hom, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₂, AlgCat.hom_comp, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_inv_comp_rightHomologyι, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.toBiprod_fromBiprod, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃'_eq, CategoryTheory.GradedObject.ιMapBifunctor₁₂BifunctorMapObj_eq, CategoryTheory.Presieve.FamilyOfElements.compPresheafMap_id, CategoryTheory.preadditiveCoyonedaObj_obj_carrier, SSet.Truncated.comp_app, groupCohomology.mapShortComplexH2_id, CategoryTheory.Functor.sheafPushforwardContinuousId_inv_app_val_app, CategoryTheory.ChosenPullbacksAlong.unit_pullbackComp_hom, SemimoduleCat.ofHom_comp, CategoryTheory.Limits.π_colimitOfIsReflexivePairIsoCoequalizer_inv_assoc, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app_assoc, AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id_assoc, LinearMap.comp_id_semiModuleCat, Homotopy.dNext_cochainComplex, CategoryTheory.MonoidalCategory.leftUnitor_inv_naturality_assoc, CategoryTheory.associativity_app, Quiver.FreeGroupoid.of_eq, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_precomp, DistLat.comp_apply, CategoryTheory.PreOneHypercover.Homotopy.wr, Homotopy.nullHomotopicMap'_f, CategoryTheory.Bicategory.Prod.swap_mapComp_hom, AlgebraicGeometry.Scheme.toIso_inv_ι, SemimoduleCat.MonoidalCategory.hexagon_reverse, AlgebraicGeometry.SheafedSpace.congr_hom_app, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_right, CategoryTheory.Enriched.FunctorCategory.homEquiv_comp_assoc, CategoryTheory.Dial.rightUnitor_inv_F, CategoryTheory.Presieve.uncurry_pullbackArrows, quasiIso_iff_comp_right, CategoryTheory.Limits.pullbackSymmetry_inv_comp_snd, CategoryTheory.Pseudofunctor.StrongTrans.Modification.vcomp_app, CategoryTheory.Presieve.IsSheafFor.valid_glue, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformPrecomposeObjSquare_iso_hom_comp, CategoryTheory.Mathlib.Tactic.MonTauto.associator_hom_comp_tensorHom_tensorHom_comp_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHom, CategoryTheory.Limits.limit.map_pre, CategoryTheory.Pseudofunctor.DescentData.isoMk_hom_hom, AddSemigrp.id_apply, AlgebraicGeometry.Scheme.Spec_map, CategoryTheory.WithTerminal.coneEquiv_inverse_map_hom_left, AlgebraicGeometry.Scheme.residueFieldCongr_trans_hom, CategoryTheory.CatEnrichedOrdinary.hComp_assoc_heq, CategoryTheory.Iso.inv_hom_id_app_app_app_assoc, CategoryTheory.Functor.mapCochainComplexShiftIso_hom_app_f, CategoryTheory.Functor.LaxMonoidal.μ_whiskerRight_comp_μ, CategoryTheory.NatTrans.IsMonoidal.tensor_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_assoc, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_inv_app_unop_assoc, CategoryTheory.Functor.OplaxMonoidal.δ_comp_δ_whiskerRight, CategoryTheory.StrictPseudofunctor.id_mapId_inv, CategoryTheory.Iso.inv_hom_id_app, HomologicalComplex₂.totalFlipIsoX_hom_D₂, CategoryTheory.SingleFunctors.shiftIso_add_hom_app, AlgebraicGeometry.Scheme.Hom.toNormalization_inl_normalizationCoprodIso_hom, CategoryTheory.Arrow.left_hom_inv_right, CategoryTheory.Idempotents.Karoubi.decompId_p_toKaroubi, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_apply_app, SSet.Subcomplex.fromPreimage_ι, Action.leftDual_ρ, AlgebraicGeometry.Scheme.Hom.opensRange_comp_of_isIso, CategoryTheory.ShortComplex.exact_iff_of_forks, CategoryTheory.Sieve.mem_ofArrows_iff, CategoryTheory.isDetecting_empty_of_groupoid, CategoryTheory.MonoidalClosed.curry'_id, CategoryTheory.MorphismProperty.IsStableUnderCobaseChange.unop, CategoryTheory.cosimplicialSimplicialEquiv_inverse_map, CategoryTheory.OppositeShift.adjunction_counit, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_inv_naturality, CategoryTheory.Functor.bifunctorComp₁₂Iso_inv_app_app_app, PresheafOfModules.sheafificationAdjunction_homEquiv_apply, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_inv_app, CategoryTheory.Adjunction.representableBy_homEquiv, AlgebraicGeometry.instRespectsSchemeSmoothIsOpenImmersion, CategoryTheory.shiftFunctorCompIsoId_zero_zero_hom_app, CategoryTheory.Functor.LeftLinear.μₗ_comp_δₗ, CategoryTheory.GradedObject.ι_mapBifunctorComp₂₃MapObjIso_inv, CategoryTheory.ShortComplex.HomotopyEquiv.trans_homotopyInvHomId, CategoryTheory.Functor.PushoutObjObj.inr_ι_assoc, CategoryTheory.Functor.Elements.initialOfRepresentableBy_snd, CategoryTheory.Equivalence.inverseFunctorObjIso_hom, CategoryTheory.epi_iff_surjective_up_to_refinements, AlgebraicGeometry.isomorphisms_eq_stalkwise, TopCat.Presheaf.germ_eq, CategoryTheory.Limits.image.preComp_ι_assoc, CategoryTheory.Functor.PreservesHomology.preservesCokernel, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one, CategoryTheory.MorphismProperty.cancel_left_of_respectsIso, CategoryTheory.Arrow.hom_inv_id_right, CategoryTheory.SimplicialObject.δ_comp_σ_of_le_assoc, CategoryTheory.SimplicialObject.δ_comp_δ, CategoryTheory.obj_μ_inv_app_assoc, AlgebraicGeometry.Scheme.homOfLE_ι_assoc, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.f'_eq, CategoryTheory.MonObj.one_rightUnitor, CategoryTheory.Limits.prod.functor_map_app, CategoryTheory.Functor.CorepresentableBy.ext_iff, ProfiniteGrp.id_apply, CategoryTheory.ShortComplex.smul_τ₂, CategoryTheory.IsCoreflexivePair.common_retraction', CategoryTheory.Functor.toEssImageCompι_hom_app, CategoryTheory.Limits.imageSubobject_arrow_comp, HomologicalComplex.extend.leftHomologyData.lift_d_comp_eq_zero_iff, CategoryTheory.e_assoc'_assoc, CategoryTheory.Limits.BinaryBicone.inl_snd, CategoryTheory.GrothendieckTopology.Cover.Arrow.base_f, CategoryTheory.Functor.CorepresentableBy.homEquiv_symm_comp, prodIsoPullback_inv_snd_assoc, AlgebraicGeometry.Scheme.residueFieldCongr_fromSpecResidueField_assoc, CategoryTheory.δ_naturalityₗ, AlgebraicGeometry.Scheme.Hom.inr_toNormalization_normalizationCoprodIso_inv_assoc, CategoryTheory.StrictlyUnitaryLaxFunctor.mapIdIso_inv, HomologicalComplex.mapBifunctor₂₃.ι_D₃_assoc, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_assoc, AlgebraicGeometry.Scheme.germ_residue, CategoryTheory.InjectiveResolution.toRightDerivedZero'_comp_iCycles_assoc, CategoryTheory.Abelian.Ext.linearEquiv₀_symm_apply, CategoryTheory.Limits.ColimitPresentation.comp_hom, AlgebraicGeometry.Scheme.instIsClosedImmersionLiftIdOfIsSeparated, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_as, CategoryTheory.MorphismProperty.transfiniteCompositions_pushouts_coproducts_le_llp_rlp, CategoryTheory.Mod_.assoc_flip, CommBialgCat.ofHom_id, CategoryTheory.Functor.PushoutObjObj.hom_ext_iff, AlgebraicGeometry.IsOpenImmersion.le_monomorphisms, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHomLeft, CategoryTheory.Limits.Cofan.IsColimit.fac_assoc, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_comp, CategoryTheory.Under.mkIdInitial_to_right, AlgebraicGeometry.Scheme.Hom.normalizationPullback_snd, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁, CategoryTheory.SmallObject.FunctorObjIndex.w, CategoryTheory.GradedObject.Monoidal.ι_tensorHom_assoc, CategoryTheory.TwoSquare.vComp'_app, SSet.Truncated.HomotopyCategory.homMk_comp_homMk, CategoryTheory.ShiftedHom.mk₀_neg, CommRingCat.isLocalHom_comp, CategoryTheory.Limits.walkingSpanOpEquiv_unitIso_hom_app, CategoryTheory.Join.mapIsoWhiskerLeft_inv_app, CategoryTheory.SmallObject.SuccStruct.ofCocone.map_id, CategoryTheory.Functor.relativelyRepresentable.pullback₃.map_p₃_comp_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_inv_app', CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app_assoc, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_left, AlgebraicGeometry.PresheafedSpace.GlueData.ιInvApp_π, HomologicalComplex.pOpcycles_opcyclesToCycles, CategoryTheory.MonoidalCategory.id_tensor_associator_inv_naturality_assoc, CategoryTheory.ShortComplex.quasiIso_comp, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_left, CategoryTheory.Equivalence.inverseFunctorObj'_inv_app, CategoryTheory.Enriched.FunctorCategory.enrichedComp_π, groupHomology.cyclesIso₀_comp_H0π, HomologicalComplex.homologyIsoSc'_inv_ι_assoc, CategoryTheory.Limits.prod.map_comp_id_assoc, SemimoduleCat.hom_comp, Bimod.whiskerLeft_id_bimod, CategoryTheory.ShortComplex.RightHomologyData.pOpcycles_comp_opcyclesIso_hom_assoc, CategoryTheory.Functor.rightUnitor_inv_app, CategoryTheory.Functor.leftUnitor_hom_app, AlgebraicGeometry.Scheme.Hom.opensRange_comp, CategoryTheory.eqToHom_comp_homOfLE_op_assoc, MonCat.hom_comp, AugmentedSimplexCategory.inl_comp_tensorHom_assoc, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality, AlgebraicGeometry.IsFinite.eq_inf, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_comp_assoc, CategoryTheory.Grothendieck.ιCompMap_hom_app_base, CategoryTheory.coprod_inl_rightDistrib_hom_assoc, CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ι_assoc, CategoryTheory.Idempotents.Karoubi.comp_p_assoc, SSet.RelativeMorphism.Homotopy.refl_h, AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_id, AlgebraicGeometry.Scheme.Hom.ι_fromNormalization, CategoryTheory.Functor.toPreimages_obj, CategoryTheory.ConcreteCategory.coe_comp, SimplexCategory.mkOfSucc_δ_eq, CategoryTheory.Bicategory.rightUnitor_comp_assoc, CategoryTheory.HomOrthogonal.matrixDecomposition_symm_apply, CategoryTheory.Limits.WidePullbackShape.wideCospan_map, CategoryTheory.Over.ConstructProducts.conesEquivInverseObj_π_app, CategoryTheory.NonPreadditiveAbelian.lift_map, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_inv, Bimod.Hom.right_act_hom, CategoryTheory.Localization.Preadditive.comp_add_assoc, CategoryTheory.GradedObject.comapEq_inv_app, CategoryTheory.CartesianMonoidalCategory.braiding_inv_snd_assoc, CategoryTheory.Functor.mapConeMapCone_inv_hom, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_inv_eq_germ, CategoryTheory.GrothendieckTopology.liftToPlusObjLimitObj_fac, AlgebraicGeometry.Scheme.Hom.comp_base, CategoryTheory.LaxMonoidalFunctor.comp_hom_assoc, AlgebraicGeometry.exists_finite_imageι_comp_morphismRestrict_of_finite_image_preimage, CategoryTheory.MorphismProperty.pushouts_le_llp_rlp, CategoryTheory.Adjunction.right_triangle_components_assoc, CategoryTheory.Limits.CatCospanTransform.leftUnitor_hom_base_app, CategoryTheory.Arrow.inv_hom_id_right_assoc, CategoryTheory.ComposableArrows.Precomp.map_comp, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom, CategoryTheory.Dial.id_F, CategoryTheory.FreeBicategory.locally_thin, CategoryTheory.TransfiniteCompositionOfShape.map_incl, SheafOfModules.map_ιFree_mapFree_hom_assoc, CategoryTheory.Functor.homEquivOfIsRightKanExtension_apply_app, CategoryTheory.Endofunctor.Adjunction.Coalgebra.toAlgebraOf_obj_str, Mathlib.Tactic.Bicategory.evalComp_nil_cons, Rep.diagonalHomEquiv_apply, AlgebraicGeometry.affineLocally_le, CategoryTheory.Limits.Multicofork.isoOfπ_inv_hom, CategoryTheory.ShortComplex.rightHomology_ext_iff, CategoryTheory.Mon.one_def, CategoryTheory.Limits.combineCocones_pt_map, CategoryTheory.Adjunction.comp_unit, CategoryTheory.ExponentiableMorphism.unit_pushforwardComp_hom, CategoryTheory.Dial.id_tensorHom_id, CategoryTheory.Limits.IsLimit.homEquiv_symm_naturality, Homotopy.nullHomotopicMap'_f_of_not_rel_right, CategoryTheory.Limits.inr_inl_pushoutLeftPushoutInrIso_hom_assoc, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₁, CategoryTheory.Pseudofunctor.mapId'_hom_naturality, CategoryTheory.IsDiscrete.subsingleton, CategoryTheory.conjugateIsoEquiv_symm_apply_hom, CategoryTheory.Retract.retract_assoc, CategoryTheory.toSheafify_plusPlusIsoSheafify_hom_assoc, AlgebraicGeometry.Scheme.IdealSheafData.comap_comp, CategoryTheory.HomOrthogonal.matrixDecompositionAddEquiv_apply, Mathlib.Tactic.Bicategory.evalWhiskerRightAux_of, CategoryTheory.coprodComparison_tensorLeft_braiding_hom, CategoryTheory.Limits.IsZero.iff_isSplitMono_eq_zero, CategoryTheory.Endofunctor.algebraPreadditive_homGroup_nsmul_f, dNext_comp_right, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_hom, HomologicalComplex.homotopyCofiber.inlX_desc_f, CategoryTheory.Pseudofunctor.DescentData.comp_hom_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_app, CategoryTheory.Functor.ranCounit_app_whiskerLeft_ranAdjunction_unit_app, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_app, AlgebraicTopology.DoldKan.QInfty_comp_PInfty_assoc, AlgebraicGeometry.instLocallyQuasiFiniteCompScheme, AlgebraicGeometry.Scheme.Hom.map_appLE, AlgebraicGeometry.tilde.map_comp, CategoryTheory.Bicategory.LeftExtension.IsKan.fac, TopologicalSpace.Opens.apply_def, CategoryTheory.ShortComplex.SnakeInput.Hom.comp_f₃, HomologicalComplex.fromOpcycles_d, CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_mapId, CategoryTheory.Functor.shiftIso_inv_naturality_assoc, CategoryTheory.conj_eqToHom_iff_heq, SSet.PtSimplex.RelStruct.δ_succ_map, CategoryTheory.Oplax.StrongTrans.categoryStruct_id_naturality, CategoryTheory.DifferentialObject.objEqToHom_d_assoc, CategoryTheory.Adjunction.homAddEquiv_apply, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_inv_hom_assoc, CategoryTheory.biproduct_ι_comp_leftDistributor_inv, CategoryTheory.Functor.PullbackObjObj.ofHasPullback_pt, HomologicalComplex.iCycles_d_assoc, CategoryTheory.Limits.op_zero, CategoryTheory.Iso.conj_comp, CategoryTheory.Functor.linear_iff, CategoryTheory.Iso.unop_inv_hom_id_app_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHomLeft_op, CategoryTheory.ShortComplex.opcyclesOpIso_hom_toCycles_op, inl_coprodIsoPushout_hom_assoc, HomotopyCategory.quotient_map_out, CategoryTheory.ShortComplex.rightHomologyι_comp_fromOpcycles, CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ι, MagmaCat.hom_comp, CategoryTheory.kernelCokernelCompSequence.snakeInput_v₂₃_τ₁, CategoryTheory.Functor.LeftExtension.coconeAt_ι_app, CategoryTheory.Pseudofunctor.ObjectProperty.map_obj_obj, AddCommMonCat.ofHom_id, CategoryTheory.ShortComplex.RightHomologyMapData.opcyclesMap_eq, AlgebraicGeometry.Scheme.Γevaluation_naturality, CategoryTheory.Limits.coconeOfIsSplitEpi_ι_app, CategoryTheory.CosimplicialObject.δ_naturality, CategoryTheory.Comma.equivProd_functor_map, CategoryTheory.Adjunction.unit_app_unit_comp_map_η_assoc, SheafOfModules.Presentation.IsFinite.finite_relations, CategoryTheory.CatCenter.instIsMulCommutative, SemimoduleCat.hom_add, CategoryTheory.ShortComplex.rightHomologyIso_hom_naturality, AlgebraicGeometry.GeometricallyIntegral.eq_geometricallyReduced_inf_geometricallyIrreducible, LightProfinite.proj_comp_transitionMapLE, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₃, CategoryTheory.hom_comp, AlgebraicGeometry.Scheme.residueFieldMap_id, CategoryTheory.ShortComplex.Homotopy.add_h₃, HomologicalComplex₂.d₁_eq', CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst_assoc, CategoryTheory.Limits.π_comp_colimitUnopIsoOpLimit_inv_assoc, CategoryTheory.Localization.isoOfHom_inv_hom_id_assoc, CategoryTheory.Bicategory.Comonad.comul_counit, CategoryTheory.Limits.kernelFactorThruImage_hom_comp_ι, CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_add_f, Rep.freeLiftLEquiv_symm_apply, CategoryTheory.ShortComplex.LeftHomologyData.ofEpiOfIsIsoOfMono_i, CategoryTheory.Adjunction.leftAdjointCompIso_hom_app, groupHomology.inhomogeneousChains.d_eq, CategoryTheory.NatTrans.shift_app_comm_assoc, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse, HomologicalComplex.cyclesMap_i, CategoryTheory.ObjectProperty.rightOrthogonal_iff, CategoryTheory.Limits.pullback.condition, CategoryTheory.Preadditive.one_def, CategoryTheory.Over.lift_left, CategoryTheory.Functor.whiskerRight_twice, CategoryTheory.Functor.toOplaxFunctor'_mapComp, CategoryTheory.homOfLE_comp_eqToHom_assoc, SheafOfModules.pushforwardNatTrans_app_val_app_apply, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_id, HomologicalComplex.truncLE'ToRestriction_naturality, CategoryTheory.IsRegularEpi.w, CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_iff_mono₃, CategoryTheory.Limits.ColimitPresentation.id_hom, AlgebraicGeometry.Spec.germ_stalkMapIso_hom, CategoryTheory.Mat_.id_def, AlgebraicTopology.DoldKan.Γ₂_map_f_app, CategoryTheory.Bicategory.Adjunction.comp_right_triangle_aux, BddLat.hom_id, CategoryTheory.Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone_ι_app_eq_sum, AlgebraicGeometry.Proj.homOfLE_toBasicOpenOfGlobalSections_ι, CategoryTheory.Functor.Monoidal.whiskeringLeft_δ_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.associator_actionHom, CategoryTheory.MonoidalOpposite.unmopFunctor_η, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_apply, CategoryTheory.NatTrans.shift_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app, CategoryTheory.ShortComplex.cyclesMap'_neg, CategoryTheory.Limits.pullbackProdSndIsoProd_inv_snd_assoc, CategoryTheory.DifferentialObject.d_squared_apply_assoc, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_naturality_app, CategoryTheory.Limits.prod.diag_map_fst_snd_comp, CategoryTheory.Limits.biproduct.toSubtype_fromSubtype_assoc, CategoryTheory.Limits.biproduct.lift_π, SSet.Truncated.HomotopyCategory.homToNerveMk_comp, CategoryTheory.MorphismProperty.map_eq_iff_precomp, CategoryTheory.MonoidalCategory.id_tensor_comp_tensor_id_assoc, CategoryTheory.Abelian.LeftResolution.π_naturality, CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoCofanPt, CategoryTheory.Under.postAdjunctionRight_counit_app_right, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_counitIso, CategoryTheory.ObjectProperty.instSmallMax, CategoryTheory.Limits.inr_comp_pushoutObjIso_inv_assoc, CategoryTheory.Functor.ShiftSequence.induced_shiftMap, CategoryTheory.monoidalOfHasFiniteCoproducts.associator_inv, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_app_assoc, CategoryTheory.Limits.biprod.associator_inv_natural, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_comp_fiber, CochainComplex.HomComplex.Cochain.equivHomotopy_symm_apply_hom, groupHomology.d₁₀_comp_coinvariantsMk_assoc, CategoryTheory.op_neg, CategoryTheory.IsHomLift.comp_eqToHom_lift, CategoryTheory.Limits.cokernelCompIsIso_inv, CategoryTheory.Limits.CokernelCofork.map_condition_assoc, CategoryTheory.unitCompPartialBijectiveAux_symm_apply, CategoryTheory.Pretriangulated.TriangleMorphism.comm₂_assoc, CategoryTheory.Limits.inr_comp_pushoutObjIso_hom, AugmentedSimplexCategory.inr_comp_tensorHom_assoc, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.counitIso_hom, AlgebraicTopology.DoldKan.decomposition_Q, CategoryTheory.MonoidalCategory.id_whiskerRight_assoc, CategoryTheory.Limits.hasPullback_over_zero, CategoryTheory.IsPullback.isoPullback_hom_snd, CategoryTheory.Functorial.map_id, CategoryTheory.Limits.colimitCoconeOfUnique_cocone_ι, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, CategoryTheory.MonoidalCategory.id_tensor_associator_naturality_assoc, HomologicalComplex.extendMap_zero, CategoryTheory.Idempotents.KaroubiKaroubi.p_comm_f, HomologicalComplex.extendMap_f_eq_zero, CategoryTheory.Subfunctor.Subpresheaf.equalizer.ι_ι, CategoryTheory.isCardinalFiltered_iff, CategoryTheory.Bicategory.Prod.sectL_map₂, CategoryTheory.μ_naturality_assoc, CategoryTheory.IsPullback.isoIsPullback_hom_snd_assoc, CategoryTheory.Functor.mapCommMonIdIso_inv_app_hom_hom, CategoryTheory.ObjectProperty.prop_inf_iff, CategoryTheory.Oplax.StrongTrans.toOplax_naturality, CategoryTheory.ShortComplex.RightHomologyData.unop_π, CategoryTheory.Pseudofunctor.mapId'_hom_naturality_assoc, CategoryTheory.CopyDiscardCategory.discard_tensor, CategoryTheory.Limits.Pi.isoLimit_hom_π_assoc, CategoryTheory.Limits.BinaryFan.assocInv_snd, CategoryTheory.shiftFunctorAdd_hom_app_obj_of_induced, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_succ_succ, CategoryTheory.ShortComplex.opcyclesMap'_add, CategoryTheory.ShortComplex.cyclesMap_i, CategoryTheory.Comma.mapLeftIso_inverse_map_left, CategoryTheory.Dial.tensorHom_comp_tensorHom, CategoryTheory.Limits.biprod.mapBiprod_inv_map_desc, CategoryTheory.ShortComplex.Exact.isZero_X₂_iff, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left_assoc, CategoryTheory.LocalizerMorphism.RightResolution.op_w, HomotopicalAlgebra.Precylinder.symm_i, CategoryTheory.Functor.map_shiftFunctorComm, CategoryTheory.OplaxFunctor.mapComp_naturality_right_app_assoc, CategoryTheory.Functor.LaxRightLinear.μᵣ_naturality_left, CategoryTheory.IsPullback.isoIsPullback_inv_fst, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.unitIso_hom, CategoryTheory.ShortComplex.SnakeInput.naturality_φ₂_assoc, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₃_W, CategoryTheory.IsUniversalColimit.isPullback_of_isColimit_left, CategoryTheory.Arrow.w_assoc, CategoryTheory.IsFiltered.coeq₃_condition₂, CommMonCat.ofHom_id, CategoryTheory.Functor.op_commShiftIso_hom_app, CategoryTheory.SmallObject.ιFunctorObj_extension, CategoryTheory.Limits.biproduct.mapBiproduct_hom_desc, AlgebraicGeometry.Scheme.IdealSheafData.subschemeMap_subschemeι_assoc, groupHomology.isoCycles₁_hom_comp_i, SheafOfModules.comp_val, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_app_fst_app, CategoryTheory.instSmallHomFunctorOppositeTypeColimitCompYoneda, CategoryTheory.StructuredArrow.map_obj_hom, CategoryTheory.leftDistributor_hom_comp_biproduct_π_assoc, CategoryTheory.CostructuredArrow.preEquivalence.inverse_map_left_left, CategoryTheory.CartesianMonoidalCategory.whiskerRight_fst, AlgebraicTopology.DoldKan.σ_comp_P_eq_zero, CategoryTheory.Groupoid.invEquivalence_unitIso, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_inv_naturality, CategoryTheory.MorphismProperty.isStableUnderColimitsOfShape_iff_colimitsOfShape_le, AlgebraicGeometry.Spec.fromSpecStalk_eq, HomologicalComplex.mapBifunctor₁₂.ι_eq, CategoryTheory.Limits.coconeEquivalenceOpConeOp_inverse_map_hom, CategoryTheory.GlueData.cocycle, CategoryTheory.Limits.biprod.map_fst_assoc, CategoryTheory.Functor.PushoutObjObj.inl_ι, CategoryTheory.Limits.pullbackProdFstIsoProd_hom_fst, CategoryTheory.Abelian.Pseudoelement.comp_comp, CategoryTheory.Limits.coprod.symmetry'_assoc, CategoryTheory.ObjectProperty.instSmallMin_1, CategoryTheory.Idempotents.FunctorExtension₁.map_app_f, CategoryTheory.Bicategory.Adjunction.homEquiv₁_symm_apply, CochainComplex.HomComplex.Cocycle.equivHomShift_comp_shift, CategoryTheory.Oplax.StrongTrans.Modification.whiskerRight_naturality_assoc, HomotopyCategory.homologyFunctor_shiftMap, CoalgCat.toCoalgHom_id, CategoryTheory.Bicategory.toNatTrans_conjugateEquiv, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over, CategoryTheory.MorphismProperty.StableUnderInverse.unop, CategoryTheory.NatTrans.vcomp_eq_comp, CategoryTheory.Functor.bifunctorComp₁₂Iso_hom_app_app_app, CategoryTheory.GradedObject.ιMapBifunctorBifunctor₂₃MapObj_eq, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_inv_hom_id, CategoryTheory.BimonObj.mul_comul, CategoryTheory.Lax.StrongTrans.categoryStruct_comp_naturality, CategoryTheory.Equivalence.mkHom_comp, CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm, CategoryTheory.Over.opEquivOpUnder_functor_map, CategoryTheory.Limits.prodComparison_inv_natural_assoc, CategoryTheory.op_sub, CategoryTheory.Subfunctor.to_sheafifyLift, CategoryTheory.Functor.Fiber.inducedFunctorCompIsoSelf_inv_app, CategoryTheory.Limits.PullbackCone.isoMk_hom_hom, CategoryTheory.ShortComplex.rightHomologyMap'_smul, CategoryTheory.NonPreadditiveAbelian.add_neg_cancel, SSet.S.mk_map_le, CategoryTheory.Presieve.isSheafFor_singleton_iso, CategoryTheory.ShortComplex.Homotopy.unop_h₀, HasFibers.inducedFunctor_map_coe, CategoryTheory.MonoidalCategory.whiskerRight_id_assoc, CategoryTheory.Localization.Monoidal.whiskerLeft_comp_assoc, CategoryTheory.Functor.descOfIsLeftKanExtension_fac_app, CategoryTheory.FreeBicategory.lift_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.Subobject.factors_zero, CategoryTheory.Limits.CatCospanTransform.leftUnitor_hom_right_app, CategoryTheory.CatCommSq.hInv_iso_hom_app, CategoryTheory.IsMonHom.mul_hom_assoc, TopCat.Presheaf.stalkSpecializes_refl, CategoryTheory.IsPullback.inr_fst', CategoryTheory.Comma.mapLeftComp_hom_app_left, CategoryTheory.Comonad.ForgetCreatesLimits'.commuting, CategoryTheory.Limits.coprod.desc_comp_inl_comp_inr, CategoryTheory.Pseudofunctor.comp_mapComp, AlgebraicGeometry.Scheme.Hom.stalkMap_id, AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_π, CategoryTheory.MonoidalCategory.DayFunctor.ν_comp_unitDesc, CategoryTheory.Sheaf.instIsLocallyInjectiveHomImageι, CategoryTheory.MorphismProperty.toSet_max, CategoryTheory.δ_naturalityᵣ, CategoryTheory.Presheaf.instIsLeftKanExtensionFunctorOppositeTypeIdCompUliftYonedaOfPreservesColimitsOfSizeOfHasPointwiseLeftKanExtension, TopCat.Presheaf.stalkFunctor_map_germ, CategoryTheory.PresheafHom.isAmalgamation_iff, CategoryTheory.Limits.SequentialProduct.functorMap_commSq_succ, CategoryTheory.ComposableArrows.mkOfObjOfMapSucc_exists, CategoryTheory.ShortComplex.mapHomologyIso_inv_naturality_assoc, CategoryTheory.ComposableArrows.isoMk₀_hom_app, CategoryTheory.Limits.Cofan.IsColimit.fac, CategoryTheory.Bicategory.Prod.swap_mapComp_inv, CategoryTheory.preadditiveCoyonedaObj_obj_isModule, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_comp_homologyIso_inv, CategoryTheory.Functor.CoreMonoidal.μIso_hom_natural_right_assoc, CategoryTheory.Limits.pullbackProdSndIsoProd_inv_snd, CategoryTheory.Monad.MonadicityInternal.counitCofork_ι_app, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app, CategoryTheory.Limits.Multifork.ofPiFork_ι, CategoryTheory.Comon.monoidal_tensorUnit_comon_counit, CategoryTheory.IsFilteredOrEmpty.cocone_maps, PresheafOfModules.pullbackObjIsDefined_eq_top, CategoryTheory.PrelaxFunctor.map₂Iso_eqToIso, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp, CategoryTheory.Functor.bifunctorComp₂₃Iso_hom_app_app_app, CategoryTheory.Limits.Cofork.IsColimit.homIso_symm_apply, CategoryTheory.Adjunction.Triple.rightToLeft_app_adj₂_unit_app, CategoryTheory.Limits.isColimitOfConeOfCoconeUnop_desc, CategoryTheory.Limits.inr_pushoutLeftPushoutInrIso_hom_assoc, CategoryTheory.ShortComplex.LeftHomologyData.wi_assoc, CategoryTheory.ShortComplex.mapOpcyclesIso_hom_naturality, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality, CategoryTheory.Functor.PullbackObjObj.π_fst_assoc, CategoryTheory.Limits.BinaryBicone.inr_snd_assoc, CategoryTheory.Pretriangulated.Triangle.isZero₁_iff, CategoryTheory.ShortComplex.SnakeInput.Hom.comp_f₂, CategoryTheory.cokernelUnopOp_inv, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_assoc, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₁, CochainComplex.mappingCone.lift_f_snd_v, CategoryTheory.Subgroupoid.id_mem_of_nonempty_isotropy, CategoryTheory.Functor.Initial.extendCone_obj_π_app, MonObj.mopEquiv_unitIso_inv_app_hom, CategoryTheory.PreGaloisCategory.PointedGaloisObject.comp_val_assoc, CategoryTheory.CartesianMonoidalCategory.lift_snd_comp_fst_comp, CategoryTheory.Limits.Fork.op_unop_ι, CategoryTheory.NatIso.cancel_natIso_hom_right_assoc, CategoryTheory.Functor.IsRepresentedBy.of_isoObj, CategoryTheory.Localization.SmallHom.equiv_shift, CategoryTheory.FunctorToTypes.prod.lift_snd, CategoryTheory.Subobject.inf_comp_right_assoc, CategoryTheory.Limits.Fork.condition_assoc, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₃, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp, TopCat.Presheaf.germToPullbackStalk_stalkPullbackHom_assoc, CategoryTheory.Limits.opProductIsoCoproduct_inv_comp_lift, CategoryTheory.CartesianClosed.curry_injective, CategoryTheory.Functor.IsCocartesian.fac, CategoryTheory.MorphismProperty.le_isoClosure, HomologicalComplex₂.ιTotalOrZero_eq_zero, CommRingCat.ofHom_comp, HomologicalComplex.double_d_eq_zero₁, CategoryTheory.CommGrp.trivial_grp_inv, HomologicalComplex.unop_d, CategoryTheory.FunctorToTypes.comp, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₁, groupHomology.H0π_comp_H0Iso_hom_assoc, CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_mapComp, groupCohomology.H1π_comp_map, CategoryTheory.Limits.ι_comp_colimitLeftOpIsoUnopLimit_hom_assoc, AlgebraicGeometry.IsAffineOpen.app_basicOpen_eq_away_map, CategoryTheory.ShortComplex.cyclesMap'_i, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv_assoc, HomologicalComplex.XIsoOfEq_hom_comp_XIsoOfEq_inv, AlgebraicGeometry.IsPreimmersion.comp_iff, CategoryTheory.uliftYonedaMap_app_apply, CategoryTheory.IsIso.comp_isIso', CategoryTheory.Pseudofunctor.toOplax_mapId', SheafOfModules.pushforward_id_comp, CategoryTheory.Functor.inrCompSum'_hom_app, CategoryTheory.Functor.WellOrderInductionData.Extension.map_limit, CategoryTheory.Limits.biproduct.ι_toSubtype_subtype, CategoryTheory.ShortComplex.Exact.epi_f_iff, CategoryTheory.Functor.whiskeringLeftObjCompIso_hom_app_app, TopModuleCat.hom_comp, CategoryTheory.GrothendieckTopology.OneHypercover.comp_s₀, CategoryTheory.Comon.forget_μ, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.rightUnitor_hom_unit_app, CategoryTheory.Functor.LeftExtension.precomp₂_map_left, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_inv_app_assoc, Action.Iso.conj_ρ, CategoryTheory.Limits.HasLimit.isoOfNatIso_hom_π, CategoryTheory.Preadditive.zsmul_comp, HomologicalComplex.truncGE'.homologyι_truncGE'XIsoOpcycles_inv_d, CategoryTheory.MonoidalClosed.curry'_whiskerRight_comp, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_inv_app_hom_hom, CategoryTheory.subterminals_thin, CategoryTheory.IsHomLift.eqToHom_comp_lift_iff, AlgebraicGeometry.pullbackSpecIso_hom_fst', CategoryTheory.Quotient.comp_right, CategoryTheory.Limits.HasBiproductsOfShape.colimIsoLim_hom_app, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_obj_map_app, AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjι_ι, CategoryTheory.MonoidalOpposite.unmopFunctor_ε, CategoryTheory.Limits.Wedge.condition_assoc, groupHomology.cyclesMap_comp, CategoryTheory.Limits.inv_prodComparison_map_snd_assoc, Quiver.Hom.unmop_inj, LightCondensed.internallyProjective_iff_tensor_condition', CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_symm_assoc, CategoryTheory.opEquiv_symm_apply, CategoryTheory.Functor.LaxLeftLinear.μₗ_associativity_assoc, CategoryTheory.Limits.CokernelCofork.π_eq_zero, CategoryTheory.Limits.bicone_ι_π_ne, CategoryTheory.Limits.pullbackDiagonalMapIdIso_hom_snd, CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac_assoc, AlgebraicGeometry.IsOpenImmersion.isoOfRangeEq_hom_fac_assoc, CategoryTheory.ObjectProperty.galoisConnection_isLocal, CategoryTheory.Factorisation.ι_π, CategoryTheory.ShortComplex.LeftHomologyData.π_comp_leftHomologyIso_inv, CategoryTheory.InducedWideCategory.category_comp_coe, CategoryTheory.Functor.Final.extendCocone_map_hom, SemiNormedGrp.explicitCokernelIso_inv_π, SimplexCategory.δ_comp_σ_succ'_assoc, CategoryTheory.congrArg_mpr_hom_right, HomotopicalAlgebra.Precylinder.LeftHomotopy.postcomp_h, Bimod.Hom.right_act_hom_assoc, CategoryTheory.GrothendieckTopology.Point.presheafFiber_hom_ext_iff, CategoryTheory.CatCenter.localization_one, CategoryTheory.Limits.kernelFactorThruImage_inv_comp_ι_assoc, CategoryTheory.ShrinkHoms.functor_map, AlgebraicGeometry.instMonoObjWalkingSpanCompOverSchemeTopMorphismPropertySpanOverForgetForgetForgetNoneWalkingPairSomeMapInitOfIsOpenImmersionLeftDiscretePUnit, CategoryTheory.ShortComplex.neg_τ₃, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inl_assoc, CategoryTheory.Bicategory.Prod.snd_mapComp_inv, CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_hom_desc, CategoryTheory.Sieve.equalizer_eq_equalizerSieve, CategoryTheory.MonoidalCategory.associator_inv_naturality_left, CategoryTheory.NonPreadditiveAbelian.lift_σ, CategoryTheory.GrpObj.ofIso_mul, CategoryTheory.Limits.pullback.congrHom_inv, FundamentalGroupoid.id_eq_path_refl, CategoryTheory.StrictPseudofunctor.mk''_obj, LightCondensed.comp_val, CategoryTheory.MonoidalClosed.ofEquiv_curry_def, CategoryTheory.Limits.multispanIndexCoend_fst, CategoryTheory.Idempotents.app_idem, CategoryTheory.Presieve.BindStruct.fac, TopCat.Presheaf.toPushforwardOfIso_app, CategoryTheory.OrthogonalReflection.iteration_map_succ_surjectivity, AlgebraicGeometry.Scheme.monObjAsOverPullback_one, CategoryTheory.Limits.snd_opProdIsoCoprod_hom_assoc, CategoryTheory.LaxBraidedFunctor.id_hom, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_obj_map_app, CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_left_assoc, AlgebraicGeometry.IsAffineOpen.ΓSpecIso_hom_fromSpec_app, CategoryTheory.ObjectProperty.IsClosedUnderLimitsOfShape.limitsOfShape_le, AlgebraicGeometry.SpecToEquivOfLocalRing_eq_iff, CategoryTheory.Equivalence.changeInverse_unitIso_hom_app, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso_hom_app_f, CategoryTheory.Bicategory.Pith.comp₂_iso_inv, CategoryTheory.Adjunction.rightAdjointUniq_refl, CategoryTheory.Adjunction.homEquiv_symm_rightAdjointUniq_hom_app, CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv, CategoryTheory.Mat_.id_apply_of_ne, CategoryTheory.Pseudofunctor.map₂_whisker_right_app, CategoryTheory.Abelian.Ext.homEquiv₀_symm_apply, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₁, CategoryTheory.kernelOpOp_hom, HomologicalComplex.truncGE'Map_f_eq, CategoryTheory.IsIso.inv_hom_id_assoc, CategoryTheory.curryingIso_inv_toFunctor_obj_obj_map, CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder_map, CategoryTheory.Oplax.OplaxTrans.Modification.whiskerLeft_naturality, CategoryTheory.RegularEpi.w, CategoryTheory.Bicategory.conjugateEquiv_symm_apply', CategoryTheory.Abelian.PreservesCoimage.iso_inv_π_assoc, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₃, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_r, CategoryTheory.ShortComplex.p_opcyclesMap'_assoc, CategoryTheory.unitOfTensorIsoUnit_hom_app, CategoryTheory.StructuredArrow.mapIso_inverse_map_left, CategoryTheory.Limits.hasPushout_over_zero, CategoryTheory.cones_obj_obj, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_counitIso_inv, Rep.indResHomEquiv_apply_hom, CategoryTheory.NonPreadditiveAbelian.lift_σ_assoc, CategoryTheory.Limits.imageMonoIsoSource_hom_self_assoc, CategoryTheory.Limits.whiskerLeft_ι_colimitCompWhiskeringLeftIsoCompColimit_inv, CategoryTheory.Functor.FullyFaithful.homNatIso_hom_app_down, CategoryTheory.Comma.mapLeft_obj_hom, CategoryTheory.Functor.Final.ι_colimitIso_hom, CategoryTheory.Iso.eq_inv_comp, CategoryTheory.Limits.coprodComparison_natural_assoc, CategoryTheory.NonPreadditiveAbelian.comp_sub, CategoryTheory.GrpObj.lift_comp_inv_right, CategoryTheory.Adjunction.commShiftIso_inv_app_counit_app, ModuleCat.homAddEquiv_apply, SemimoduleCat.MonoidalCategory.rightUnitor_naturality, Quiver.FreeGroupoid.congr_reverse_comp, CategoryTheory.SimplicialObject.augmentedCechNerve_map_left_app, CategoryTheory.Functor.LaxMonoidal.μ_natural_assoc, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₁, CategoryTheory.Functor.PreOneHypercoverDenseData.sieve₁₀_apply, CategoryTheory.Monad.monadMonEquiv_unitIso_hom_app_toNatTrans_app, HomologicalComplex.dFrom_eq, CategoryTheory.MorphismProperty.pullbacks_monotone, Preord.comp_apply, CochainComplex.mappingConeCompTriangle_mor₂, CategoryTheory.PreOneHypercover.cylinder_p₁, SimplexCategoryGenRel.δ_comp_σ_self_assoc, AlgebraicGeometry.Scheme.Hom.SpecMap_residueFieldMap_fromSpecResidueField, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_mul, CategoryTheory.Pseudofunctor.CoGrothendieck.instFaithfulαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor, TopCat.coe_comp, CategoryTheory.preservesLimits_preadditiveCoyonedaObj, CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id_assoc, CategoryTheory.Adjunction.homAddEquiv_symm_sub, AlgebraicTopology.DoldKan.Q_f_idem_assoc, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d_1_0_assoc, CategoryTheory.Endofunctor.Adjunction.Coalgebra.homEquiv_naturality_str_symm, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompYoneda, AlgebraicGeometry.Scheme.comp_app_assoc, CategoryTheory.Bimon.mul_counit_assoc, CategoryTheory.Limits.BinaryFan.assocInv_fst, HomologicalComplex₂.D₁_totalShift₂XIso_hom, CategoryTheory.Functor.mapMatId_inv_app, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_hom_app, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.Functor.obj_d_f, CategoryTheory.CostructuredArrow.initial_map₂_id, CategoryTheory.Limits.Fork.isoForkOfι_inv_hom, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom_assoc, CategoryTheory.Functor.Monoidal.lift_μ, CategoryTheory.MorphismProperty.instIsStableUnderRetractsOppositeOp, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_iso, CategoryTheory.ShortComplex.cyclesOpIso_inv_op_iCycles, CategoryTheory.Sieve.id_mem_iff_eq_top, CategoryTheory.Limits.pushout_inl_inv_inr_of_right_isIso, CategoryTheory.BasedNatTrans.homCategory_comp, CategoryTheory.Adjunction.Triple.leftToRight_app_obj_assoc, CategoryTheory.ShortComplex.SnakeInput.Hom.id_f₂, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_naturality, CategoryTheory.Limits.PreservesPullback.iso_hom_snd, CategoryTheory.Square.category_id_τ₂, CategoryTheory.Limits.map_inl_inv_coprodComparison, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_inv_assoc, CategoryTheory.Limits.opCoproductIsoProduct'_hom_comp_proj_assoc, SSet.Truncated.Path₁.arrow_src, CategoryTheory.shiftFunctorAdd'_assoc_hom_app_assoc, CategoryTheory.Bicategory.Pith.inclusion_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj, CategoryTheory.CommSq.horiz_comp, AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_fac, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp_assoc, CategoryTheory.Equivalence.congrRight_unitIso_hom_app, CategoryTheory.NatTrans.shift_app_comm, CategoryTheory.Join.mapPairRight_hom_app, CategoryTheory.Functor.shiftMap_comp_assoc, CategoryTheory.ObjectProperty.limitsOfShape_le_of_initial, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_whiskerLeft_assoc, SkyscraperPresheafFunctor.map'_app, CategoryTheory.Functor.limitIsoOfIsRightKanExtension_hom_π, CategoryTheory.Subobject.functor_map, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_assoc, CategoryTheory.Bicategory.whiskerLeft_rightUnitor, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_hom_app_hom, AlgebraicGeometry.IsAffineOpen.SpecMap_appLE_fromSpec, CategoryTheory.SemiCartesianMonoidalCategory.fst_def, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_hom_app_one, CategoryTheory.sheafComposeIso_hom_fac_assoc, AlgebraicGeometry.morphismRestrict_app, CategoryTheory.Functor.PullbackObjObj.hom_ext_iff, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, CategoryTheory.Functor.currying_functor_obj_map, CochainComplex.cm5b.degreewiseEpiWithInjectiveKernel_p, CategoryTheory.SimplicialObject.augmentedCechNerve_obj_left_map, AlgebraicGeometry.AffineSpace.comp_homOfVector_assoc, HomotopicalAlgebra.FibrantBrownFactorization.mk'_p, CategoryTheory.Functor.leftOpRightOpEquiv_functor_map_app, CategoryTheory.Limits.Cocone.mapCoconeToOver_hom_hom, CategoryTheory.Limits.prodComparison_inv_natural, CochainComplex.HomComplex.Cochain.rightShift_v, CategoryTheory.Functor.mapConeWhisker_inv_hom, CategoryTheory.yonedaGrp_map_app, CategoryTheory.comp_eqToHom_heq, Bimod.whiskerLeft_comp_bimod, AlgebraicGeometry.Scheme.Hom.appLE_comp_appLE, CategoryTheory.Limits.Sigma.ι_reindex_hom_assoc, CategoryTheory.Preadditive.comp_sub_assoc, groupHomology.cyclesMap_comp_cyclesIso₀_hom_assoc, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_assoc, CategoryTheory.ShortComplex.LeftHomologyMapData.cyclesMap_eq, CategoryTheory.Presieve.ofArrows_bind, CategoryTheory.GradedObject.ι_mapMap, CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id_assoc, CategoryTheory.Limits.π_comp_cokernelIsoOfEq_inv, CochainComplex.mappingConeCompTriangleh_comm₁, CategoryTheory.Functor.ShiftSequence.induced_isoShiftZero_hom_app_obj, AlgebraicTopology.DoldKan.Q_f_naturality, SSet.ι₁_fst_assoc, CategoryTheory.sheafComposeIso_inv_fac, AlgebraicGeometry.tilde.map_neg, CategoryTheory.Equalizer.FirstObj.ext_iff, HomologicalComplex.mapBifunctor₁₂.d₁_eq, AddGrpCat.ofHom_id, AlgebraicGeometry.LocallyRingedSpace.toStalk_stalkMap_toΓSpec, CategoryTheory.Limits.walkingSpanOpEquiv_counitIso_inv_app, AlgebraicTopology.DoldKan.Q_zero, CategoryTheory.Limits.Sigma.ι_isoColimit_inv_assoc, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.functor_map, OrderHom.equivalenceFunctor_unitIso_inv_app, ModuleCat.endRingEquiv_apply, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app_assoc, CategoryTheory.WithInitial.pseudofunctor_mapComp, CategoryTheory.Limits.prod.map_swap, CategoryTheory.IsPullback.isoIsPullback_hom_snd, groupHomology.lsingle_comp_chainsMap_f_assoc, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality, CategoryTheory.Iso.eHomCongr_inv_comp, CategoryTheory.MonObj.one_eq_one, CategoryTheory.InjectiveResolution.homotopyEquiv_inv_ι_assoc, CategoryTheory.ObjectProperty.instIsClosedUnderSubobjectsTop, HomologicalComplex.opcyclesMap_zero, AlgebraicGeometry.Scheme.Hom.toImage_app, HomologicalComplex₂.D₂_totalShift₂XIso_hom, Rep.linearizationTrivialIso_hom_hom, CategoryTheory.MonoidalCategory.inv_hom_whiskerRight'_assoc, SimplexCategoryGenRel.standardσ_comp_standardσ, CategoryTheory.Limits.IsLimit.existsUnique, CategoryTheory.whisker_eq, CategoryTheory.sheafHomSectionsEquiv_symm_apply_coe_apply, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_fst, CategoryTheory.MonoidalClosed.curry_natural_right, HomologicalComplex.d_comp_XIsoOfEq_inv, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_hom_app_app, TopCat.Sheaf.eq_of_locally_eq_iff, ModuleCat.ofHom_id, CategoryTheory.MorphismProperty.universally_mono, AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk, AlgebraicGeometry.LocallyRingedSpace.id_toHom, CategoryTheory.NatTrans.exchange, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp, CategoryTheory.MorphismProperty.presheaf_monomorphisms_le_monomorphisms, CategoryTheory.Localization.homEquiv_map, CategoryTheory.MorphismProperty.pushouts_le_iff, CategoryTheory.Mod_.id_hom, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι_assoc, CategoryTheory.PreOneHypercover.cylinder_p₂, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app_assoc, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_inv_comp_π_assoc, CategoryTheory.FreeBicategory.preinclusion_obj, CategoryTheory.Pseudofunctor.map₂_left_unitor_app_assoc, SimplexCategory.Truncated.δ₂_one_comp_σ₂_zero_assoc, CategoryTheory.Under.inv_right_hom_right_assoc, imageToKernel_epi_of_epi_of_zero, CategoryTheory.CatEnriched.hComp_comp, CategoryTheory.Adjunction.leftAdjointIdIso_inv_app, CategoryTheory.Bifunctor.map_comp_id, MonCat.Colimits.cocone_naturality, AlgebraicGeometry.AffineTargetMorphismProperty.cancel_left_of_respectsIso, AlgebraicTopology.DoldKan.QInfty_f_comp_PInfty_f_assoc, CategoryTheory.Limits.ι_colimitLimitToLimitColimit_π_assoc, CategoryTheory.ShortComplex.rightHomologyMap_smul, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.id_snd_app, CategoryTheory.Functor.map_shiftFunctorCompIsoId_inv_app, PartOrd.hom_comp, CategoryTheory.Adjunction.leftAdjointUniq_trans, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_assoc, CategoryTheory.Equivalence.ε_comp_map_ε_assoc, AlgebraicGeometry.PresheafedSpace.stalkMap.stalkSpecializes_stalkMap_assoc, AlgebraicGeometry.IsImmersion.isImmersion_iff_exists_of_quasiCompact, FinBddDistLat.hom_id, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_η_unmop_app, CategoryTheory.Pseudofunctor.map₂_right_unitor_app_assoc, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_inv, CategoryTheory.Grp_Class.div_comp, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv_def, CategoryTheory.Pseudofunctor.map₂_right_unitor_app, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_obj, AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id, SSet.Truncated.Edge.CompStruct.d₁, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_naturality_app, CategoryTheory.unop_hom_associator, CategoryTheory.Over.mkIdTerminal_from_left, CategoryTheory.regularTopology.EqualizerCondition.bijective_mapToEqualizer_pullback, CategoryTheory.Limits.Sigma.ι_π_eq_id_assoc, CategoryTheory.Limits.Cofork.unop_ι, groupCohomology.isoShortComplexH1_inv, CategoryTheory.NatTrans.unop_whiskerRight_assoc, CategoryTheory.FreeBicategory.lift_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec, CategoryTheory.LaxFunctor.comp_mapComp, CategoryTheory.Limits.Cone.toStructuredArrowCompToUnderCompForget_inv_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_hom_app_app_fst, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_iff_mono₁, CategoryTheory.IsPushout.inr_isoPushout_hom, AlgebraicTopology.DoldKan.identity_N₂_objectwise, CategoryTheory.Iso.hom_inv_id_app_app_app_assoc, CategoryTheory.Join.opEquiv_functor_map_op_inclLeft, CategoryTheory.Abelian.Pseudoelement.eq_zero_iff, CategoryTheory.finallySmall_iff_exists_small_weakly_terminal_set, HomologicalComplex.shortComplexTruncLE_shortExact_δ_eq_zero, CategoryTheory.ComposableArrows.naturality'_assoc, CategoryTheory.conjugateEquiv_comp, CategoryTheory.StructuredArrow.map_id, ModuleCat.image.fac, CategoryTheory.Localization.Monoidal.μ_inv_natural_left, CategoryTheory.additive_coyonedaObj, CategoryTheory.ModObj.mul_smul, CategoryTheory.MonoidalOpposite.tensorRightUnmopIso_hom_app, CategoryTheory.MonoidalCategory.leftUnitor_whiskerRight, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict_assoc, BddOrd.coe_comp, CategoryTheory.Limits.pushout.congrHom_inv, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_invApp, CategoryTheory.map_shrinkYonedaEquiv, CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan_inj_assoc, CategoryTheory.ObjectProperty.small_unop_iff, SemiNormedGrp.ofHom_comp, CategoryTheory.MonoidalCategory.leftUnitor_inv_tensor_id_assoc, CategoryTheory.NatTrans.app_zsmul, CategoryTheory.Quiv.id_eq_id, CategoryTheory.OverPresheafAux.YonedaCollection.map₁_snd, CategoryTheory.Mat_.comp_def, CategoryTheory.cancel_epi, CategoryTheory.GrothendieckTopology.Cover.Arrow.precompRelation_g₁, CategoryTheory.BraidedCategory.braiding_inv_naturality_right, CategoryTheory.WithInitial.opEquiv_inverse_map, AlgebraicGeometry.Scheme.Cover.intersectionOfLocallyDirected_f, CategoryTheory.CostructuredArrow.mapNatIso_functor_map_right, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.hf, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_obj_map_app, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj, CategoryTheory.Limits.prod.functor_obj_map, HomologicalComplex.restrictionToTruncGE'_f_eq_iso_hom_iso_inv, AddCommGrpCat.hom_add_apply, CategoryTheory.Presieve.FamilyOfElements.map_comp, AlgebraicGeometry.PresheafedSpace.comp_c, CategoryTheory.MorphismProperty.isStableUnderBaseChange_iff_pullbacks_le, CategoryTheory.CartesianMonoidalCategory.rightUnitor_inv_fst_assoc, CategoryTheory.Limits.Multicofork.π_comp_hom, CategoryTheory.PrelaxFunctor.map₂_hom_inv_isIso_assoc, CategoryTheory.Functor.HomObj.naturality, CategoryTheory.Biprod.inl_ofComponents, CategoryTheory.Grpd.hom_to_functor, CategoryTheory.Under.opEquivOpOver_functor_map, CategoryTheory.ι_preservesColimitIso_inv, CategoryTheory.Functor.mapCommMon_id_one, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom''_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_ε_unmop_app, CategoryTheory.Triangulated.TStructure.ge_one_le, CoalgCat.toCoalgHom_comp, CategoryTheory.Limits.biproduct.map_lift_mapBiprod, CategoryTheory.MonoidalOpposite.tensorLeftMopIso_inv_app_unmop, CategoryTheory.ObjectProperty.strictColimitsOfShape_le_colimitsOfShape, CategoryTheory.Bimon.equivMonComonCounitIsoAppXAux_hom, CategoryTheory.MonoidalCategory.MonoidalRightAction.action_actionHomRight, CategoryTheory.Limits.biproduct.map_eq, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_inv_app_val_app, CategoryTheory.Preadditive.comp_sub, CategoryTheory.NatTrans.leftDerived_comp, PresheafOfModules.instFullRestrictScalarsIdFunctorOppositeRingCat, CategoryTheory.prod.leftUnitor_map, CategoryTheory.IsPushout.of_coprod_inl_with_id, SimplexCategory.Truncated.δ₂_two_comp_σ₂_one, CategoryTheory.leftDistributor_ext₂_right_iff, SSet.OneTruncation₂.id_edge, CategoryTheory.Adjunction.homEquiv_apply_eq, CategoryTheory.Limits.pullback.congrHom_hom, CategoryTheory.ComposableArrows.Precomp.map_zero_zero, CategoryTheory.yonedaEquiv_symm_map, CategoryTheory.Limits.ι_reflexiveCoequalizerIsoCoequalizer_hom_assoc, CategoryTheory.tensorLeftHomEquiv_whiskerRight_comp_evaluation, groupHomology.cyclesIso₀_inv_comp_iCycles_assoc, CategoryTheory.Factorisation.Hom.comp_h, AlgebraicGeometry.Scheme.Hom.appLE_map, CategoryTheory.Limits.IsLimit.homIso_hom, HomotopicalAlgebra.bifibrantObjects_le_cofibrantObject, CategoryTheory.Limits.CoconeMorphism.inv_hom_id_assoc, CategoryTheory.ShortComplex.SnakeInput.comp_f₁, CategoryTheory.Limits.BinaryBicone.inr_fst, CategoryTheory.NatTrans.whiskerRight_app_tensor_app_assoc, CategoryTheory.Functor.map_nsmul, CategoryTheory.Limits.cokernelZeroIsoTarget_hom, CategoryTheory.obj_ε_app, CochainComplex.cm5b.instInjectiveXIntMappingConeIdI, CategoryTheory.Limits.HasImageMap.comp, ModuleCat.FilteredColimits.ι_colimitDesc_assoc, AddCommGrpCat.ofHom_injective, CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtensionObjIsoColimit_hom_assoc, DerivedCategory.HomologySequence.δ_comp_assoc, AlgebraicGeometry.HasRingHomProperty.iff_of_source_openCover, CategoryTheory.EnrichedCategory.assoc, AlgebraicGeometry.Scheme.Hom.isoImage_hom_ι_assoc, CategoryTheory.ShortComplex.cyclesOpIso_inv_naturality_assoc, CategoryTheory.Square.Hom.id_τ₁, ContinuousCohomology.MultiInd.d_succ, CategoryTheory.ShortComplex.LeftHomologyMapData.commi, CategoryTheory.Subgroupoid.inclusion_faithful, CategoryTheory.GradedObject.Monoidal.triangle, CategoryTheory.CartesianMonoidalCategory.homEquivToProd_apply, CategoryTheory.eHomWhiskerLeft_comp_assoc, CategoryTheory.Limits.coconeEquivalenceOpConeOp_functor_map, CategoryTheory.Adjunction.comp_counit_app_assoc, CategoryTheory.liftedLimitMapsToOriginal_hom_π, ModuleCat.semilinearMapAddEquiv_symm_apply_apply, Bimod.RightUnitorBimod.hom_inv_id, CategoryTheory.Center.forget_δ, HomologicalComplex.stupidTruncMap_stupidTruncXIso_hom, CategoryTheory.kernelCokernelCompSequence.inl_π, CategoryTheory.Limits.CokernelCofork.IsColimit.isZero_of_epi, CategoryTheory.Bicategory.Pith.inclusion_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_snd_assoc, CategoryTheory.NatTrans.leftDerivedToHomotopyCategory_id, SimplexCategoryGenRel.δ_comp_δ, HomotopicalAlgebra.Precylinder.i₁_π, SSet.horn.ι_ι_assoc, CategoryTheory.MorphismProperty.LeftFraction.map_ofInv_hom_id, CategoryTheory.Functor.LaxBraided.braided_assoc, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_assoc, FinPartOrd.hom_comp, CategoryTheory.CostructuredArrow.mapIso_inverse_obj_hom, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.rightUnitor_naturality, CategoryTheory.Mathlib.Tactic.MonTauto.associator_hom_comp_tensorHom_tensorHom_comp, CategoryTheory.Limits.opParallelPairIso_inv_app_zero, HomologicalComplex.biprod_lift_snd_f_assoc, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_inv, CategoryTheory.Join.id_left, CategoryTheory.Iso.hom_comp_eq_id, CategoryTheory.Limits.cokernelCoforkBiproductFromSubtype_cocone, AlgebraicGeometry.Proj.res_apply, CategoryTheory.Comonad.left_counit_assoc, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc, CategoryTheory.NatTrans.leftDerived_id, CategoryTheory.IsIso.out, Rep.coinvariantsAdjunction_homEquiv_apply_hom, CategoryTheory.CostructuredArrow.projectQuotient_factors, CategoryTheory.PreOneHypercover.Hom.comp_h₁, CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_snd_fst, CategoryTheory.Sieve.toFunctor_app_coe, CategoryTheory.NatTrans.naturality_1, HomologicalComplex.mapBifunctor₁₂.d₃_eq, CategoryTheory.Limits.coprod.desc_comp, CategoryTheory.constantPresheafAdj_counit_app_app, DerivedCategory.HomologySequence.δ_comp, CategoryTheory.Equivalence.sheafCongr.unitIso_inv_app_val_app, AlgebraicGeometry.Scheme.inv_base_hom_base_assoc, CategoryTheory.PreOneHypercover.id_h₁, CategoryTheory.ObjectProperty.topEquivalence_inverse, CategoryTheory.Sum.functorEquivFunctorCompSndIso_hom_app_app, AlgebraicGeometry.Scheme.Opens.topIso_hom, CategoryTheory.Join.mapIsoWhiskerLeft_hom_app, HomologicalComplex.biprod_inr_fst_f_assoc, CategoryTheory.PrelaxFunctor.map₂_inv_hom, CategoryTheory.Limits.ι_comp_colimitLeftOpIsoUnopLimit_hom, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv_assoc, CategoryTheory.MonoidalClosed.comp_id, CategoryTheory.GrothendieckTopology.map_yonedaEquiv, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τr, CategoryTheory.Subgroupoid.mem_sInf_arrows, CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_snd_snd_assoc, CategoryTheory.Bicategory.conjugateEquiv_iso, CategoryTheory.Limits.kernelSubobject_arrow_comp, CategoryTheory.CostructuredArrow.mkPrecomp_comp, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_hom_app_fst_app, CategoryTheory.Functor.mapCommGrp_obj_grp_mul, CategoryTheory.effectiveEpi_iff_effectiveEpiFamily, CategoryTheory.Cat.HasLimits.homDiagram_obj, CategoryTheory.rightExactFunctor_le_additiveFunctor, ModuleCat.hom_comp, CategoryTheory.ExactPairing.coevaluation_evaluation_assoc, TopologicalSpace.Opens.overEquivalence_counitIso_hom_app, CategoryTheory.Functor.reprW_hom_app, CategoryTheory.Sheaf.isLocallySurjective_iff_isIso, CategoryTheory.FreeGroupoid.mapCompLift_hom_app, CategoryTheory.ComposableArrows.opEquivalence_counitIso_hom_app_app, CategoryTheory.uliftCoyonedaEquiv_symm_map, groupHomology.H1CoresCoinf_f, CategoryTheory.Over.prodLeftIsoPullback_hom_fst, CategoryTheory.Functor.OplaxMonoidal.comp_δ, CategoryTheory.Iso.inv_hom_id_triangle_hom₃, CategoryTheory.GrothendieckTopology.overMapPullback_assoc, AlgebraicGeometry.StructureSheaf.toOpen_res, SimplexCategory.eq_of_one_to_one, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_fst_snd, CategoryTheory.Limits.Pi.isoLimit_inv_π_assoc, CategoryTheory.Bicategory.Prod.sectR_mapId_hom, CategoryTheory.ShortComplex.comp_homologyMap_comp, CategoryTheory.Over.associator_hom_left_fst_assoc, CategoryTheory.Limits.opParallelPairIso_inv_app_one, CategoryTheory.ExponentiableMorphism.pushforwardId_hom_counit, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_hom_eq_germ_assoc, CategoryTheory.TwoSquare.lanBaseChange_app, MonObj.mopMonObj_mul_unmop, CategoryTheory.Functor.hcongr_hom, Homotopy.extend.hom_eq, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d_assoc, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π, AlgebraicGeometry.Scheme.PartialMap.compHom_hom, CategoryTheory.Sum.functorEquivFunctorCompFstIso_hom_app_app, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.tensorHom_eq, CategoryTheory.GradedObject.ι_mapBifunctorComp₁₂MapObjIso_hom, CategoryTheory.NonPreadditiveAbelian.neg_def, AlgebraicGeometry.Scheme.Pullback.openCoverOfLeft_f, CategoryTheory.MonoidalCategory.whisker_assoc, CategoryTheory.Linear.toCatCenter_apply_app, CategoryTheory.whiskeringLeftCompEvaluation_inv_app, CategoryTheory.OplaxFunctor.mapComp_naturality_right, AlgebraicGeometry.IsSeparated.comp_iff, AlgebraicGeometry.Scheme.ofRestrict_app, CategoryTheory.IsKernelPair.id_of_mono, CategoryTheory.CatCommSq.vId_iso_inv_app, CategoryTheory.Functor.Monoidal.map_rightUnitor, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec_assoc, AlgebraicGeometry.SheafedSpace.congr_app, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_apply_coe, CategoryTheory.MonoidalCategory.associator_naturality_left_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.inv_hom_actionHomLeft_assoc, DistLat.hom_comp, CategoryTheory.Comma.equivProd_unitIso_inv_app_left, HomologicalComplex.mapBifunctor₁₂.ι_D₂, CategoryTheory.ModObj.mul_smul', CategoryTheory.yonedaYonedaColimit_app_inv, CategoryTheory.Limits.Cone.extensions_app, CategoryTheory.Grothendieck.grothendieckTypeToCatInverse_map_base, CategoryTheory.yonedaEquiv_symm_naturality_left, CategoryTheory.Limits.pullbackConeEquivBinaryFan_unitIso, CategoryTheory.Limits.inl_opProdIsoCoprod_inv, CategoryTheory.OplaxFunctor.mapComp_naturality_left_app_assoc, CategoryTheory.Adjunction.left_triangle_components_assoc, CategoryTheory.Functor.RightLinear.δᵣ_comp_μᵣ_assoc, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_symm_apply, CategoryTheory.Comonad.coalgebraPreadditive_homGroup_add_f, CategoryTheory.CosimplicialObject.equivalenceLeftToRight_right, CategoryTheory.Limits.snd_opProdIsoCoprod_hom, CategoryTheory.imageUnopOp_inv_comp_op_factorThruImage, CategoryTheory.Presheaf.comp_isLocallyInjective_iff, CategoryTheory.Bicategory.Prod.swap_mapId_hom, AlgebraicGeometry.UniversallyOpen.instCompScheme, CategoryTheory.ObjectProperty.topEquivalence_functor, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_spec, CategoryTheory.PreGaloisCategory.exists_galois_representative, CategoryTheory.CatCenter.app_neg, FinBddDistLat.ofHom_id, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.IsTerminal.lift_self, SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁_hom_f_f, CategoryTheory.Over.isMonHom_pullbackFst_id_right, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_inv_π, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand', CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_inv_assoc, CategoryTheory.Functor.Monoidal.whiskerRight_δ_μ_assoc, CategoryTheory.PreZeroHypercover.isoMk_inv_h₀, FundamentalGroupoidFunctor.prodToProdTop_map, CategoryTheory.Limits.prod.leftUnitor_inv_naturality, TopModuleCat.kerι_comp, HomologicalComplex.homotopyCofiber.d_sndX_assoc, CategoryTheory.zigzag_prefunctor_obj_of_zigzag, CategoryTheory.ShortComplex.Splitting.unop_s, CategoryTheory.ShortComplex.f'_cyclesMap'_assoc, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransEq_inv_app_f, CategoryTheory.Limits.Pi.map'_id_id, CategoryTheory.Limits.biprod.inr_snd, CategoryTheory.Functor.OplaxMonoidal.lift_δ_assoc, CategoryTheory.ObjectProperty.IsCodetecting.isIso_iff_of_epi, CategoryTheory.Endofunctor.Coalgebra.Terminal.right_inv', ModuleCat.hom_neg, CategoryTheory.Limits.pullbackComparison_comp_fst_assoc, CategoryTheory.EnrichedFunctor.map_id_assoc, FDRep.scalar_product_char_eq_finrank_equivariant, CategoryTheory.Limits.Cotrident.app_one_assoc, CategoryTheory.Limits.isColimitCoconeOfConeUnop_desc, SimplicialObject.Split.id_F, FintypeCat.id_hom, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_left, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_hom_comp_ι, CategoryTheory.δ_μ_app_assoc, CategoryTheory.ShortComplex.HomologyData.comm, CategoryTheory.Over.forgetAdjStar_unit_app_left, CategoryTheory.ShortComplex.Exact.leftHomologyDataOfIsLimitKernelFork_i, CategoryTheory.Bicategory.conjugateEquiv_whiskerLeft, AlgebraicGeometry.pullbackSpecIso_hom_snd, CategoryTheory.ShortComplex.opcyclesMap'_comp, CategoryTheory.Functor.CoreMonoidal.left_unitality_assoc, AlgebraicGeometry.Scheme.Hom.comp_appTop_assoc, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop_assoc, CategoryTheory.GrothendieckTopology.diagramNatTrans_zero, CategoryTheory.Equivalence.leftOp_functor_map, CategoryTheory.Discrete.functorComp_inv_app, CategoryTheory.ObjectProperty.isClosedUnderLimitsOfShape_iff, HomologicalComplex.mapBifunctor₁₂.ι_mapBifunctor₁₂Desc_assoc, SimplexCategory.σ_comp_σ, AlgebraicGeometry.IsAffineOpen.fromSpec_app_of_le, Rep.ihom_obj_ρ, CategoryTheory.IsHomLift.lift_comp_id, CategoryTheory.ShortComplex.p_fromOpcycles_assoc, CondensedSet.epi_iff_locallySurjective_on_compHaus, CategoryTheory.Hom.mulEquivCongrRight_apply, CategoryTheory.Functor.shiftIso_hom_app_comp_shiftMap_of_add_eq_zero, CategoryTheory.Limits.ι_comp_sigmaComparison_assoc, SimplexCategory.hom_zero_zero, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.fromBiprod_δ, CategoryTheory.StrictlyUnitaryLaxFunctor.id_mapId, CategoryTheory.mateEquiv_counit, dNext_nat, CategoryTheory.right_comp_retraction_assoc, SimplexCategoryGenRel.standardσ_cons_assoc, CategoryTheory.GrothendieckTopology.toPlus_plusLift, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₁, CategoryTheory.Limits.HasLimit.isoOfEquivalence_inv_π, CategoryTheory.Comma.unopFunctorCompSnd_hom_app, CategoryTheory.Functor.CommShift.OfComp.map_iso_inv_app, CategoryTheory.Iso.trans_inv, AlgebraicTopology.DoldKan.PInfty_comp_PInftyToNormalizedMooreComplex_assoc, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, CategoryTheory.Square.category_comp_τ₄, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_hom_comp_homologyIso_inv_assoc, CategoryTheory.CatCenter.smul_iso_hom_eq, CategoryTheory.rightAdjointMate_comp, CategoryTheory.LaxFunctor.map₂_associator_app, CategoryTheory.Comonad.coalgebraPreadditive_homGroup_sub_f, CategoryTheory.Limits.coneOfIsSplitMono_pt, CategoryTheory.Presheaf.instIsLocallyInjectiveHomιOpposite, CategoryTheory.Functor.map_dite, CategoryTheory.Pseudofunctor.toLax_mapComp', CategoryTheory.IsHomLift.eqToHom_codomain_lift_id, CategoryTheory.cancel_mono_assoc_iff, CategoryTheory.MonoidalCategory.inv_hom_whiskerRight', CategoryTheory.RelCat.Hom.rel_comp, CategoryTheory.yonedaEquiv_symm_naturality_right, CategoryTheory.OplaxFunctor.mapComp'_comp_mapComp'_whiskerRight_assoc, SheafOfModules.pushforwardSections_unitHomEquiv, CategoryTheory.wideInducedFunctor_map, CategoryTheory.PreGaloisCategory.PointedGaloisObject.cocone_app, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app, CategoryTheory.CartesianMonoidalCategory.tensorμ_fst, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₁₂_assoc, CategoryTheory.Limits.Sigma.map'_id_id, AlgebraicGeometry.Scheme.residueFieldCongr_trans_hom_assoc, HomologicalComplex.extend.mapX_none, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁, CategoryTheory.Functor.compConstIso_inv_app_app, CategoryTheory.Prod.fst_map, CategoryTheory.Functor.mapTriangleInvRotateIso_hom_app_hom₂, CategoryTheory.Limits.limit.pre_pre, CategoryTheory.constantSheafAdj_counit_app, CategoryTheory.MonoidalCategory.tensor_id_comp_id_tensor, CategoryTheory.Grothendieck.congr, CategoryTheory.EffectiveEpiFamily.transitive_of_finite, CategoryTheory.Equalizer.Sieve.SecondObj.ext_iff, CategoryTheory.Functor.leibnizPullback_map_app, CategoryTheory.Limits.prod.leftUnitor_hom_naturality, CategoryTheory.GradedObject.ι_mapBifunctorRightUnitor_hom_apply_assoc, AlgebraicGeometry.IsDominant.comp_iff, HomologicalComplex.neg_f_apply, CategoryTheory.Over.mapCongr_rfl, AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_comp_iff, AlgebraicGeometry.instIsDominantCompScheme, CategoryTheory.MonoidalCategory.prodMonoidal_tensorHom, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₂_app, CategoryTheory.NatTrans.rightOp_id, AlgebraicGeometry.Scheme.Hom.app_appIso_inv, CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id_assoc, Action.resComp_hom_app_hom, CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero_assoc, CategoryTheory.Functor.Monoidal.δ_μ_assoc, CategoryTheory.GrpObj.ofIso_one, groupCohomology.cochainsMap_id_comp_assoc, HomologicalComplex.truncGEMap_comp, CategoryTheory.instNontrivialEndOfSimple, CategoryTheory.MorphismProperty.LeftFraction.map_comp_map_s_assoc, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₄_W, CategoryTheory.eqToHom_naturality, CategoryTheory.Limits.π_comp_cokernelIsoOfEq_hom, CategoryTheory.section_comp_right_assoc, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_inv_app_f, CategoryTheory.isCodetecting_unop_iff, CategoryTheory.Grothendieck.grothendieckTypeToCat_functor_map_coe, CategoryTheory.ShortComplex.opcyclesMap_id, TopCat.Sheaf.interUnionPullbackCone_pt, CategoryTheory.ShortComplex.LeftHomologyMapData.commπ_assoc, CategoryTheory.Localization.SmallShiftedHom.equiv_apply, CategoryTheory.NatTrans.removeRightOp_id, LightCondensed.instSmallHom, HomologicalComplex.pOpcycles_restrictionOpcyclesIso_inv_assoc, CategoryTheory.IsPullback.paste_horiz, HomologicalComplex.unopFunctor_map_f, CategoryTheory.Limits.biproduct.ι_π_ne_assoc, CategoryTheory.StrictPseudofunctor.comp_obj, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_inv, CategoryTheory.ShortComplex.leftHomologyMap_zero, CategoryTheory.Limits.BinaryFan.assoc_fst, CategoryTheory.ShortComplex.LeftHomologyData.τ₁_ofEpiOfIsIsoOfMono_f', CategoryTheory.sheafSectionsNatIsoEvaluation_hom_app, HomologicalComplex.Hom.comm, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_app_assoc, CategoryTheory.Limits.CatCospanTransform.triangle, HomologicalComplex.homologyOp_hom_naturality, Bicategory.Opposite.homCategory_id_unop2, CategoryTheory.Enriched.FunctorCategory.enrichedId_π, CategoryTheory.StructuredArrow.toCostructuredArrow'_map, CategoryTheory.Adjunction.map_η_comp_η, TopCat.Presheaf.stalkSpecializes_stalkPushforward_assoc, CategoryTheory.Square.opFunctor_map_τ₄, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberCompIso_hom_app_assoc, CategoryTheory.Limits.cokernelZeroIsoTarget_inv, CategoryTheory.Grp.Hom.hom_one, CategoryTheory.Limits.coprod.map_swap_assoc, CategoryTheory.Functor.OplaxMonoidal.right_unitality, CategoryTheory.Limits.pullbackSymmetry_hom_comp_fst, AlgebraicGeometry.IsIntegralHom.instCompScheme, HomotopicalAlgebra.Cylinder.symm_i_assoc, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_assoc, CategoryTheory.Equivalence.mkHom_comp_assoc, CategoryTheory.Idempotents.KaroubiKaroubi.p_comm_f_assoc, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.ShortComplex.leftRightHomologyComparison'_compatibility, Mathlib.Tactic.Monoidal.evalComp_nil_cons, CategoryTheory.ShortComplex.fromOpcycles_op_cyclesOpIso_inv, CategoryTheory.Limits.hasEqualizer_comp_mono, AlgebraicTopology.DoldKan.P_idem_assoc, AlgebraicTopology.DoldKan.PInfty_comp_QInfty_assoc, CategoryTheory.StrictPseudofunctor.id_mapComp_inv, CategoryTheory.Limits.colimCompFlipIsoWhiskerColim_inv_app_app, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp_symm, TopCat.Presheaf.stalkPushforward.comp, CategoryTheory.instIsThin, AlgebraicGeometry.LocallyRingedSpace.stalkSpecializes_stalkMap_assoc, MonCat.id_apply, SheafOfModules.instIsRightAdjointPushforwardIdSheafRingCat, inl_coprodIsoPushout_inv_assoc, groupCohomology.map_H0Iso_hom_f_assoc, CategoryTheory.GrothendieckTopology.overMapPullback_id_comp, CategoryTheory.sum.inlCompAssociator_inv_app, CategoryTheory.Bicategory.InducedBicategory.mkHom_eqToHom, CategoryTheory.ObjectProperty.instEssentiallySmallUnopOfOpposite, CategoryTheory.Bicategory.comp_whiskerLeft_symm_assoc, AlgebraicGeometry.Scheme.Hom.normalizationObjIso_hom_val, CategoryTheory.Functor.unopId_hom_app, CategoryTheory.prod.etaIso_inv, CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_comp_assoc, HomologicalComplex.shape, CategoryTheory.Functor.OplaxRightLinear.δᵣ_naturality_right, CommBialgCat.hom_id, CategoryTheory.AsSmall.down_map, CategoryTheory.Functor.essImage.liftFunctor_map, HomologicalComplex₂.flipEquivalenceCounitIso_hom_app_f_f, SSet.stdSimplex.objEquiv_symm_apply, CategoryTheory.Functor.commShift₂_comm_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_inv_app_snd_app, CategoryTheory.ComposableArrows.Mk₁.map_comp, HomologicalComplex.homologyIsoSc'_hom_ι, AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInfty_assoc, CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac, CategoryTheory.FintypeCat.instFiberFunctorActionFintypeCatForget₂HomSubtypeHomCarrierV, AlgebraicGeometry.pointEquivClosedPoint_symm_apply_coe, CategoryTheory.Limits.inr_inl_pushoutAssoc_hom_assoc, CategoryTheory.RetractArrow.i_w_assoc, CategoryTheory.prod.functorProdToProdFunctorAssociator_inv_app, CategoryTheory.Limits.limit.lift_map_assoc, Homotopy.refl_hom, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_aux_mul, CategoryTheory.MorphismProperty.LeftFractionRel.op, CategoryTheory.MorphismProperty.LeftFraction.ofHom_s, CategoryTheory.Localization.HasSmallLocalizedHom.small, CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_right, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv_assoc, CategoryTheory.Limits.MultispanIndex.ι_sndSigmaMap_assoc, CategoryTheory.Localization.Preadditive.map_add, CategoryTheory.ComposableArrows.Precomp.map_id, CochainComplex.HomComplex.Cochain.toSingleEquiv_toSingleMk, CategoryTheory.OverPresheafAux.OverArrows.map_val, GrpCat.id_apply, HomotopicalAlgebra.FibrantObject.HoCat.resolutionMap_fac_assoc, CategoryTheory.RetractArrow.unop_r_left, CategoryTheory.Pretriangulated.TriangleMorphism.comm₂, CommRingCat.moduleCatRestrictScalarsPseudofunctor_obj, CategoryTheory.Pretriangulated.TriangleMorphism.comp_hom₃, CategoryTheory.Functor.sheafAdjunctionCocontinuous_homEquiv_apply_val, CategoryTheory.Functor.whiskerRight_left, CategoryTheory.Limits.biproduct.toSubtype_π, CategoryTheory.ObjectProperty.le_retractClosure, CategoryTheory.Iso.inv_hom_id_app_assoc, CategoryTheory.Functor.limitIsoOfIsRightKanExtension_inv_π, ModuleCat.kernelIsoKer_inv_kernel_ι, CategoryTheory.MorphismProperty.HasLeftCalculusOfFractions.exists_leftFraction, CategoryTheory.PreOneHypercover.forkOfIsColimit_ι_map_inj, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one_assoc, CommAlgCat.ofHom_comp, CategoryTheory.Limits.biproduct.whiskerEquiv_hom_eq_lift, CategoryTheory.IsPushout.inl_isoIsPushout_hom, CommAlgCat.id_apply, CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_nsmul_f, CategoryTheory.MonObj.one_mul, HomologicalComplex.extendHomologyIso_inv_homologyι_assoc, AlgebraicGeometry.Scheme.Cover.pullbackHom_map_assoc, AlgebraicGeometry.Scheme.Cover.gluedCoverT'_fst_fst_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_hom_app_snd_app, CategoryTheory.PreservesFiniteLimitsOfFlat.fac, AlgebraicGeometry.tilde.map_id_assoc, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app_assoc, CategoryTheory.CostructuredArrow.unop_left_comp_underlyingIso_hom_unop, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_yonedaULift_map, HomologicalComplex.pOpcycles_extendOpcyclesIso_inv_assoc, CategoryTheory.Subfunctor.equalizer.condition_assoc, SemimoduleCat.homLinearEquiv_symm_apply, CategoryTheory.Limits.walkingCospanOpEquiv_unitIso_hom_app, CategoryTheory.Functor.FullyFaithful.hasShift.map_zero_inv_app, CategoryTheory.ShortComplex.LeftHomologyData.unop_g', CategoryTheory.Limits.WalkingMultispan.Hom.comp_eq_comp, CategoryTheory.rightAdjointMate_comp_evaluation, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_inverse_map_f, AlgebraicTopology.DoldKan.N₂_map_f_f, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app_assoc, CategoryTheory.Sieve.pullback_id, CategoryTheory.Adjunction.leftAdjointIdIso_hom_app, CategoryTheory.Limits.pullbackAssoc_inv_snd, CategoryTheory.ObjectProperty.isoInv_hom_id_hom_assoc, LinOrd.comp_apply, CategoryTheory.InjectiveResolution.rightDerivedToHomotopyCategory_app_eq, CategoryTheory.coevaluation_comp_rightAdjointMate_assoc, CochainComplex.HomComplex.Cochain.ofHoms_zero, CategoryTheory.CostructuredArrow.mapIso_inverse_map_right, CategoryTheory.GrothendieckTopology.uliftYoneda_obj_val_obj, CategoryTheory.Limits.FormalCoproduct.mapPower_comp_assoc, CategoryTheory.NatTrans.leftOp_comp, HomologicalComplex.dFrom_comp_xNextIso, CategoryTheory.CommSq.fac_left, SSet.KanComplex.hornFilling, CategoryTheory.GradedObject.categoryOfGradedObjects_comp, CategoryTheory.Paths.lift_nil, LinOrd.coe_comp, HomologicalComplex₂.totalAux.ιMapObj_D₁_assoc, HomotopicalAlgebra.PrepathObject.RightHomotopy.h₁, CategoryTheory.Limits.Cocones.precompose_map_hom, CategoryTheory.Idempotents.Karoubi.decompId_i_naturality, CategoryTheory.uliftYonedaEquiv_symm_map_assoc, CategoryTheory.Limits.limitBiconeOfUnique_bicone_ι, CategoryTheory.Limits.constCone_π, CategoryTheory.comp_dite, CategoryTheory.Functor.Monoidal.transport_ε_assoc, HomologicalComplex.mapBifunctor₁₂.d₂_eq, CategoryTheory.StructuredArrow.toCostructuredArrow'_obj, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_comp, CategoryTheory.Abelian.app_hom, commBialgCatEquivComonCommAlgCat_counitIso_hom_app, groupCohomology.eq_d₁₂_comp_inv_assoc, Representation.linHom.invariantsEquivRepHom_apply_hom, AlgebraicGeometry.IsIntegralHom.eq_universallyClosed_inf_isAffineHom, CategoryTheory.MorphismProperty.pullbacks_le, HasFibers.fiber_factorization, CategoryTheory.Functor.Monoidal.transport_δ_assoc, AlgebraicGeometry.PresheafedSpace.map_comp_c_app, CategoryTheory.Iso.map_inv_hom_id_eval_assoc, CategoryTheory.Limits.prod.lift_snd_assoc, TopCat.Presheaf.coveringOfPresieve_apply, groupHomology.cyclesMap_id, SSet.PtSimplex.RelStruct.δ_map_of_gt, CategoryTheory.Limits.WalkingMultispan.instSubsingletonHomLeft, Bicategory.Opposite.op2_id_unbop, CategoryTheory.isIso_prod_iff, CategoryTheory.Functor.curryingEquiv_symm_apply_obj_map, HomologicalComplex.pOpcycles_opcyclesToCycles_assoc, AddGrpCat.hom_id, CategoryTheory.Comonad.ComonadicityInternal.comparisonAdjunction_counit_f_aux, CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inr, CategoryTheory.BraidedCategory.braiding_inv_naturality, HomologicalComplex.opcyclesOpIso_hom_toCycles_op_assoc, CategoryTheory.Limits.opSpan_inv_app, CategoryTheory.Limits.inr_pushoutLeftPushoutInrIso_hom, AlgebraicGeometry.IsPreimmersion.comp, HomologicalComplex.singleObjCyclesSelfIso_hom, CategoryTheory.unop_inv_rightUnitor, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_neg, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_counitIso_hom_app_right_app, CategoryTheory.Functor.HomObj.id_app, CategoryTheory.SingleFunctors.shiftIso_add'_inv_app, CategoryTheory.Sieve.generate_apply, AlgebraicGeometry.AffineSpace.reindex_id, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right_assoc, CategoryTheory.Functor.IsEventuallyConstantTo.isoMap_inv_hom_id_assoc, CategoryTheory.MorphismProperty.ContainsIdentities.id_mem, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_snd', CategoryTheory.Limits.pushoutCoconeOfRightIso_inr, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoColimitUncurryWhiskeringLeft₂_hom, CategoryTheory.RegularEpi.w_assoc, HomotopicalAlgebra.trivialFibrations_op, CategoryTheory.Functor.relativelyRepresentable.pullback₃.snd_fst'_eq_p₁_assoc, CategoryTheory.Functor.LaxMonoidal.μ_natural, PartOrd.ofHom_comp, CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_right, CategoryTheory.Limits.whiskerLeft_ι_colimitCompWhiskeringLeftIsoCompColimit_inv_assoc, CategoryTheory.Limits.colimitCoconeOfUnique_isColimit_desc, CategoryTheory.Limits.prod.diag_map_assoc, CategoryTheory.Pretriangulated.contractible_distinguished₁, CategoryTheory.toOverUnitPullback_hom_app_left, CategoryTheory.Functor.sheafPushforwardContinuousId'_hom_app_val_app, HomologicalComplex.restriction_d_eq_assoc, CategoryTheory.Monad.left_unit_assoc, Bimod.AssociatorBimod.hom_right_act_hom', HomologicalComplex.quasiIsoAt_opFunctor_map_iff, AlgebraicGeometry.LocallyRingedSpace.stalkMap_comp, SSet.Truncated.StrictSegal.spine_δ_vertex_lt, CategoryTheory.Bicategory.leftUnitor_comp, CategoryTheory.Limits.pullbackObjIso_inv_comp_snd, CategoryTheory.ExponentiableMorphism.coev_ev, CategoryTheory.MonObj.mul_rightUnitor, CategoryTheory.Limits.limit.lift_π, CategoryTheory.MonoidalCategory.tensor_hom_inv_id', CategoryTheory.algebraToUnder_map, CategoryTheory.Presheaf.isLocallyInjective_toPlus, SimplexCategory.eq_comp_δ_of_not_surjective, HomologicalComplex.mapBifunctor₂₃.d₁_eq_zero, CategoryTheory.Limits.pullbackAssoc_inv_fst_fst_assoc, CategoryTheory.Limits.IsColimit.fac_assoc, HomologicalComplex₂.d_comm_assoc, CategoryTheory.LocalizerMorphism.RightResolution.Hom.comm_assoc, CommBialgCat.hom_comp, AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_inv_app, CategoryTheory.Bicategory.LeftExtension.w, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isoBot_hom, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso_inv_app_app, CategoryTheory.Mod_.comp_hom, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι, CategoryTheory.compEvaluation_inv_app, CategoryTheory.Lax.OplaxTrans.vComp_naturality_id, CategoryTheory.pathComposition_map, HomotopicalAlgebra.PrepathObject.RightHomotopy.h₁_assoc, CategoryTheory.Comonad.adj_unit, CategoryTheory.MonoidalCategory.tensorδ_tensorμ_assoc, AlgebraicGeometry.StructureSheaf.algebraMap_pushforward_stalk, CategoryTheory.NonPreadditiveAbelian.neg_neg, CategoryTheory.prod.rightInverseUnitor_map, RingCat.id_apply, SimplexCategory.Truncated.Hom.tr_comp'_assoc, CategoryTheory.FinitaryPreExtensive.isPullback_sigmaDesc, CategoryTheory.Limits.Cones.extendComp_hom_hom, CategoryTheory.Adjunction.map_ε_comp_counit_app_unit, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_app, CategoryTheory.SmallObject.πObj_naturality, CategoryTheory.kernelCokernelCompSequence.φ_snd, CategoryTheory.Under.id_right, CategoryTheory.MorphismProperty.IsLocalAtSource.toRespects, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₂, LinearMap.comp_id_moduleCat, CategoryTheory.SingleFunctors.hom_inv_id_hom_app, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id, CategoryTheory.PreOneHypercover.p₂_sigmaOfIsColimit, CategoryTheory.Sum.functorEquiv_unitIso, DerivedCategory.HomologySequence.epi_homologyMap_mor₂_iff, CategoryTheory.PreZeroHypercover.id_s₀, AlgebraicTopology.DoldKan.P_f_naturality, TopModuleCat.hom_neg, CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_right, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_val_app, Mathlib.Tactic.Monoidal.evalHorizontalCompAux_of, CategoryTheory.Limits.coprod.inl_snd_assoc, PartOrdEmb.coe_id, CategoryTheory.toQuotientPaths_map, CategoryTheory.sheafifyMap_sheafifyLift_assoc, FGModuleCat.Iso.conj_hom_eq_conj, CategoryTheory.Iso.prod_hom, Action.FunctorCategoryEquivalence.functor_obj_map, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimIso_aux, CategoryTheory.Limits.FormalCoproduct.coproductIsoSelf_hom_φ, CategoryTheory.ShortComplex.mapToComposableArrows_id, CategoryTheory.ObjectProperty.le_isLocal_W, CategoryTheory.Iso.refl_hom, CategoryTheory.Presheaf.isLocallyInjective_forget, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_invApp, CategoryTheory.unop_sub, CategoryTheory.Localization.Preadditive.zero_add', dNext_eq_zero, CategoryTheory.Limits.Multifork.hom_comp_ι_assoc, CategoryTheory.ActionCategory.hom_as_subtype, AlgebraicGeometry.IsZariskiLocalAtSource.comp, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₃, CategoryTheory.ComonObj.comul_assoc_flip_assoc, SimplicialObject.Split.cofan_inj_naturality_symm, CategoryTheory.MonoidalOpposite.tensorLeftIso_inv_app_unmop, finGaloisGroupMap.map_comp, CategoryTheory.Pseudofunctor.isoMapOfCommSq_eq, CategoryTheory.ShortComplex.rightHomologyι_naturality, CategoryTheory.Limits.LimitPresentation.w_assoc, CommGrpCat.coyoneda_map_app, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃, CategoryTheory.exactFunctor_le_rightExactFunctor, CategoryTheory.Sum.swapCompInr_inv_app, CategoryTheory.cocones_obj_obj, CategoryTheory.Functor.const_obj_map, CategoryTheory.Limits.coprod.map_id_id, commBialgCatEquivComonCommAlgCat_functor_map_unop_hom, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_hom, CategoryTheory.Limits.colimitYonedaHomIsoLimitRightOp_π_apply, CategoryTheory.WithInitial.opEquiv_unitIso_hom_app, CategoryTheory.Localization.Preadditive.neg'_add'_self, HomotopicalAlgebra.Precylinder.trans_i₁, CategoryTheory.MonoidalCategory.MonoidalLeftAction.hom_inv_actionHomLeft, CategoryTheory.CostructuredArrow.map_id, CategoryTheory.LaxFunctor.mapComp_naturality_left, CategoryTheory.obj_η_app, CategoryTheory.LaxFunctor.mapComp_assoc_left_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.hom_inv_actionHomLeft', CategoryTheory.Over.ε_pullback_left, CategoryTheory.Abelian.subobjectIsoSubobjectOp_symm_apply, CategoryTheory.Comon.forget_ε, CategoryTheory.GrothendieckTopology.plusMap_zero, CategoryTheory.ChosenPullbacksAlong.pullbackComp_hom_counit_assoc, CategoryTheory.Functor.RepresentableBy.ofIsoObj_homEquiv, CategoryTheory.Limits.FormalCoproduct.evalCompInclIsoId_hom_app_app, AlgebraicGeometry.Scheme.Opens.eq_presheaf_map_eqToHom, CategoryTheory.unop_hom_leftUnitor, CategoryTheory.LocalizerMorphism.hasRightResolutions_iff_op, inr_coprodIsoPushout_inv_assoc, CategoryTheory.Functor.id_mapMon_one, CochainComplex.mappingCone.lift_f, CategoryTheory.Comma.unopFunctorCompFst_hom_app, TopologicalSpace.OpenNhds.inclusionMapIso_inv_app, CategoryTheory.MorphismProperty.IsMultiplicative.unop, AlgebraicGeometry.Scheme.stalkClosedPointTo_comp, Rep.barComplex.d_comp_diagonalSuccIsoFree_inv_eq, CategoryTheory.NatTrans.Coequifibered.comp, CategoryTheory.ComposableArrows.IsComplex.zero, CategoryTheory.Limits.pullback.lift_fst_snd, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_rightUnitor, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.iSup_P, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_functor, HomologicalComplex.XIsoOfEq_hom_naturality, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_map, CategoryTheory.Limits.cokernelBiproductFromSubtypeIso_inv, CategoryTheory.Over.coprod_map_app, HomologicalComplex.homotopyCofiber.inrX_sndX, CategoryTheory.Functor.CorepresentableBy.coyoneda_homEquiv, ModuleCat.monoidalClosed_pre_app, CategoryTheory.CartesianMonoidalCategory.lift_rightUnitor_hom, BoolAlg.id_apply, CategoryTheory.Adjunction.homEquiv_leftAdjointUniq_hom_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_hom_app_hom_hom, Bimod.LeftUnitorBimod.hom_inv_id, AlgebraicGeometry.pointsPi_surjective, SemimoduleCat.hom_smul, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_hom_assoc, CategoryTheory.instIsSplitEpiComp, CategoryTheory.HopfObj.antipode_right, CategoryTheory.ComposableArrows.IsComplex.cokerToKer_fac, CategoryTheory.Limits.pullback_fst_map_snd_isPullback, HomologicalComplex₂.totalAux.d₁_eq', AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_appLE, CategoryTheory.Functor.LaxRightLinear.μᵣ_unitality_inv, CategoryTheory.ShortComplex.add_τ₁, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ, CategoryTheory.isoCartesianComon_inv_hom, CategoryTheory.Limits.map_π_preserves_coequalizer_inv, CategoryTheory.ShiftMkCore.zero_add_inv_app, CategoryTheory.MonoidalCategory.pentagon_inv_hom_assoc, AlgebraicGeometry.map_injective_of_isIntegral, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.functor_obj, CategoryTheory.Limits.pushout.condition_assoc, CategoryTheory.Limits.colimit.toOver_pt, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π, CategoryTheory.Limits.colimit.isoColimitCocone_ι_hom, Action.ρAut_apply_inv, CategoryTheory.CostructuredArrow.mapIso_inverse_map_left, UniformSpaceCat.extension_comp_hom, CategoryTheory.Limits.hasCokernel_epi_comp, CategoryTheory.Monad.Algebra.comp_f, HomologicalComplex.Hom.comm_to_assoc, CategoryTheory.Subobject.underlying_arrow, CategoryTheory.Limits.Multiequalizer.ιPi_π_assoc, CategoryTheory.MonObj.mul_one_hom, CategoryTheory.ConcreteCategory.injective_le_monomorphisms, CategoryTheory.GrothendieckTopology.uliftYoneda_obj_val_map_down, CategoryTheory.GlueData.t'_comp_eq_pullbackSymmetry, SSet.stdSimplex.nonDegenerateEquiv_symm_apply_coe, CategoryTheory.Limits.inv_prodComparison_map_snd, CategoryTheory.leftDistributor_assoc, CategoryTheory.Functor.ranAdjunction_unit_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraidedObj_map, CategoryTheory.InducedCategory.homLinearEquiv_symm_apply_hom, CategoryTheory.pullbackShiftFunctorAdd'_inv_app, CategoryTheory.Iso.hom_inv_id_triangle_hom₁_assoc, CategoryTheory.ShortComplex.leftRightHomologyComparison_fac_assoc, CategoryTheory.Pseudofunctor.map₂_whisker_right_assoc, CategoryTheory.StructuredArrow.IsUniversal.fac_assoc, CategoryTheory.Limits.kernelCompMono_inv, CategoryTheory.OverPresheafAux.map_mkPrecomp_eqToHom, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_app_π, MagmaCat.ofHom_id, CategoryTheory.Limits.end_.condition_assoc, CategoryTheory.Limits.map_inl_inv_coprodComparison_assoc, CategoryTheory.Arrow.equivSigma_apply_snd_fst, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_limit_map_assoc, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor, CategoryTheory.Functor.shiftIso_hom_naturality, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃'_eq_assoc, HomologicalComplex.cylinder.ι₁_desc, CategoryTheory.WithInitial.ofCommaMorphism_app, SSet.horn.ι_ι, CategoryTheory.Sheaf.ΓRes_naturality, CategoryTheory.Monad.Algebra.unit, CategoryTheory.Functor.coreComp_inv_app_iso_hom, CategoryTheory.CostructuredArrow.map₂_obj_hom, CategoryTheory.Bimon.toMon_Comon_ofMon_Comon_obj_mul, SimplicialObject.Splitting.cofan_inj_comp_app_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_eq, CategoryTheory.Limits.limit.lift_cone, CategoryTheory.Bimon.compatibility, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTrans_map_f, HomologicalComplex.opcyclesToCycles_iCycles, AddCommMonCat.hom_comp, AlgebraicGeometry.Scheme.residueFieldMap_comp, SheafOfModules.pushforwardNatIso_hom, CategoryTheory.GradedObject.Monoidal.leftUnitor_naturality_assoc, CategoryTheory.Functor.Monoidal.ε_η_assoc, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app_assoc, HomologicalComplex.ι_mapBifunctorFlipIso_hom_assoc, CategoryTheory.prodOpEquiv_counitIso_inv_app, CategoryTheory.TwistShiftData.shiftFunctor_map, CategoryTheory.Comonad.beckCoalgebraFork_π_app, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_apply_φ, TopologicalSpace.OpenNhds.apply_mk, CategoryTheory.Paths.of_obj, CategoryTheory.MonoidalOpposite.tensorIso_inv_app_unmop, CategoryTheory.MonoidalOpposite.mopMopEquivalence_counitIso_hom_app, HomologicalComplex.extendSingleIso_hom_f, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_app_assoc, MagmaCat.hom_id, CommGrpCat.ofHom_injective, CategoryTheory.GrothendieckTopology.diagramNatTrans_comp, CochainComplex.HomComplex.CohomologyClass.toHom_mk, CategoryTheory.TwistShiftData.shiftFunctorZero_inv_app, CategoryTheory.ShortComplex.leftHomologyMap'_zero, Action.Hom.comm, ProfiniteAddGrp.hom_comp, CategoryTheory.CartesianMonoidalCategory.whiskerRight_fst_assoc, CategoryTheory.Limits.prod.inr_fst, HomotopicalAlgebra.instFibrationCompOfIsStableUnderCompositionFibrations, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp_hom_app_f, CategoryTheory.Adjunction.homEquiv_naturality_right, HomologicalComplex₂.total.hom_ext_iff, CategoryTheory.Bicategory.InducedBicategory.forget_mapId_hom, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.id_tensorHom, Action.ρ_inv_self_apply, CategoryTheory.Pi.μ_def, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd_assoc, CategoryTheory.Equalizer.Presieve.isSheafFor_singleton_iff_of_hasPullback, CategoryTheory.Functor.lanAdjunction_counit_app, HomologicalComplex.XIsoOfEq_inv_comp_XIsoOfEq_inv_assoc, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst_assoc, CategoryTheory.GradedObject.single_map_singleObjApplyIso_hom_assoc, CategoryTheory.Functor.id_hcomp, CategoryTheory.GrpObj.zpow_comp_assoc, CategoryTheory.Limits.BinaryBiconeMorphism.wsnd_assoc, CategoryTheory.eComp_op_eq, CategoryTheory.Adjunction.unit_comp_map_eq_iff, CategoryTheory.Limits.cokernelOrderHom_coe, AlgebraicGeometry.Scheme.IdealSheafData.subschemeMap_subschemeι, HomotopicalAlgebra.AttachCells.ofArrowIso_g₁, CategoryTheory.Functor.Monoidal.map_rightUnitor_inv_assoc, CategoryTheory.Functor.IsRepresentedBy.iff_exists_representableBy, CategoryTheory.Limits.pushout_inr_inv_inl_of_right_isIso, CategoryTheory.MorphismProperty.pushouts_monotone, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_assoc, AlgebraicGeometry.Scheme.comp_coeBase, AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_eq_id, CategoryTheory.braiding_inv_tensorUnit_left, CategoryTheory.Subfunctor.sieveOfSection_apply, CochainComplex.HomComplex.Cochain.add_v, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_inv_iso_hom, CategoryTheory.ObjectProperty.essentiallySmall_op_iff, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π_assoc, HomologicalComplex.d_eqToHom, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_obj_map_app, CategoryTheory.BraidedCategory.braiding_tensor_right_inv_assoc, CategoryTheory.CosimplicialObject.cechConerveEquiv_apply, CategoryTheory.prod.etaIso_hom, CategoryTheory.Functor.OplaxMonoidal.δ_natural_right_assoc, CategoryTheory.Bicategory.prod_rightUnitor_hom_snd, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_map, CategoryTheory.Functor.rightOp_map_unop, CategoryTheory.MonoidalCategory.pentagon_assoc, CategoryTheory.Functor.isIso_lanAdjunction_counit_app_iff, CategoryTheory.sheafifyLift_id_toSheafify_assoc, CategoryTheory.Discrete.productEquiv_functor_map, CategoryTheory.Bicategory.pentagon_hom_hom_inv_hom_hom, CategoryTheory.Bicategory.conjugateEquiv_symm_apply, CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_snd_assoc, CategoryTheory.Comon.MonOpOpToComonObj_comon_counit, AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalk, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_val_app, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk_assoc, CategoryTheory.MorphismProperty.le_colimitsOfShape_punit, CategoryTheory.Bicategory.prod_associator_hom_snd, AlgebraicGeometry.LocallyRingedSpace.iso_hom_base_inv_base, Action.comp_hom_assoc, groupCohomology.isoShortComplexH2_inv, CochainComplex.πTruncGE_naturality_assoc, CategoryTheory.Bicategory.Adjunction.right_triangle, CategoryTheory.shiftFunctorCompIsoId_zero_zero_inv_app, CategoryTheory.Comon.comp_hom', CategoryTheory.Bicategory.triangle_assoc_comp_left_inv, TopCat.hom_comp, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerRight_naturality, CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_inv_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_inv_app'_assoc, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_inv, CategoryTheory.monoidalUnopUnop_η, CategoryTheory.preadditiveCoyoneda_obj, CategoryTheory.Enriched.FunctorCategory.functorEnriched_assoc, PresheafOfModules.pushforward_id_comp, groupCohomology.map_id_comp_H0Iso_hom_assoc, CategoryTheory.injective_iff_rlp_monomorphisms_zero, CategoryTheory.cosimplicialSimplicialEquiv_functor_obj_map, CategoryTheory.ShortComplex.rightHomologyMap'_zero, HomologicalComplex.biprod_inl_snd_f, CategoryTheory.prod.prodFunctorToFunctorProdAssociator_hom_app_app, CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse_assoc, AlgebraicGeometry.localRingHom_comp_stalkIso, CategoryTheory.GlueData.ι_gluedIso_hom_assoc, CategoryTheory.DinatTrans.dinaturality, AlgebraicGeometry.IsAffineOpen.toSpecΓ_isoSpec_inv_assoc, CochainComplex.toSingle₀Equiv_symm_apply_f_zero, DerivedCategory.left_fac_of_isStrictlyGE, CategoryTheory.Functor.LaxMonoidal.left_unitality_inv, CategoryTheory.Functor.coreComp_inv_app_iso_inv, CategoryTheory.PreOneHypercover.Hom.w₁₁_assoc, AlgebraicGeometry.IsOpenImmersion.isoOfRangeEq_inv_fac, CategoryTheory.Functor.relativelyRepresentable.symmetry_snd, CategoryTheory.Limits.pullbackAssoc_hom_fst_assoc, CategoryTheory.Adjunction.shift_unit_app_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionHom, HomologicalComplex.homologyFunctorIso_inv_app, groupCohomology.isoCocycles₂_hom_comp_i_assoc, CategoryTheory.Functor.mapCoconeMapCocone_inv_hom, CochainComplex.augmentTruncate_hom_f_zero, CategoryTheory.Limits.IsImage.fac_lift_assoc, CategoryTheory.oppositeShiftFunctorAdd_hom_app, CochainComplex.mappingCone.inl_v_fst_v_assoc, AlgebraicGeometry.Scheme.Pullback.openCoverOfLeftRight_X, CategoryTheory.Limits.inl_pushoutRightPushoutInlIso_inv_assoc, CategoryTheory.Bimon.comp_hom', CategoryTheory.ComposableArrows.homMk₀_app, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₂_W, CategoryTheory.Equivalence.counitInv_naturality_assoc, CategoryTheory.Limits.preservesCokernel_zero, AlgebraicGeometry.Scheme.mem_toGrothendieck_smallPretopology, CategoryTheory.Limits.pullbackDiagonalMapIdIso_hom_fst, CategoryTheory.Comma.colimitAuxiliaryCocone_ι_app, CategoryTheory.Arrow.comp_right, HomotopicalAlgebra.CofibrantObject.homMk_id, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_point, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map_assoc, CategoryTheory.monoidalOfHasFiniteProducts.associator_hom_fst, CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLift, CategoryTheory.Localization.Monoidal.associator_naturality₃_assoc, CategoryTheory.Functor.isRightKanExtension_iff_postcomp₁, ModuleCat.semilinearMapAddEquiv_apply, CategoryTheory.Preadditive.comp_add_assoc, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂, CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_fst_assoc, CategoryTheory.curryingIso_hom_toFunctor_map_app, CategoryTheory.quotientPathsTo_map, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_fst, HomologicalComplex.comp_f_assoc, CategoryTheory.Center.forget_μ, CategoryTheory.Oplax.OplaxTrans.Modification.naturality, CategoryTheory.Quotient.comp_mk, CategoryTheory.ShortComplex.HomologyMapData.smul_left, ContAction.resComp_inv, CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatTrans_comp, CategoryTheory.Functor.mapZeroObject_hom, CategoryTheory.Functor.leftOpRightOpIso_inv_app, CategoryTheory.Functor.mapTriangleIdIso_hom_app_hom₁, CategoryTheory.ShortComplex.toCycles_naturality, HomotopicalAlgebra.Precylinder.trans_i₀, Rep.coindIso_hom_hom_hom, CategoryTheory.IsPullback.isoPullback_hom_fst_assoc, ChainComplex.alternatingConst_map_f, CategoryTheory.Meq.condition, MagmaCat.comp_apply, CategoryTheory.Sheaf.sheafifyCocone_ι_app_val, CategoryTheory.MorphismProperty.retracts_monotone, CategoryTheory.Localization.Monoidal.rightUnitor_hom_app, CategoryTheory.SingleFunctors.inv_hom_id_hom, CategoryTheory.MonadHom.id_toNatTrans, CategoryTheory.CartesianMonoidalCategory.braiding_hom_snd, CategoryTheory.Bicategory.Equivalence.right_triangle_hom, CategoryTheory.Functor.ι_colimitIsoColimitGrothendieck_inv, CategoryTheory.ObjectProperty.instSmallISupOfSmall, AddCommMonCat.hom_id, CategoryTheory.Endofunctor.Algebra.Initial.left_inv', ModuleCat.freeHomEquiv_symm_apply, CategoryTheory.Bicategory.Prod.fst_obj, CategoryTheory.SimplicialObject.δ_comp_σ_succ_assoc, AlgebraicGeometry.Scheme.Hom.inv_app, CategoryTheory.Limits.pullbackProdFstIsoProd_hom_snd, CategoryTheory.MonObj.comp_pow_assoc, CategoryTheory.Functor.homologySequenceδ_comp, CategoryTheory.CommSq.LiftStruct.opEquiv_apply, CategoryTheory.StructuredArrow.IsUniversal.fac, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app', AlgebraicGeometry.Scheme.localRingHom_comp_stalkIso, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_hom_app_hom_app, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_app, CategoryTheory.preadditiveCoyonedaObj_obj_isAddCommGroup, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.Functor.mapTriangleIdIso_hom_app_hom₂, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop, AlgebraicGeometry.Scheme.Hom.isoOpensRange_inv_comp, CategoryTheory.ProjectiveResolution.cochainComplex_d_assoc, HomologicalComplex.g_shortComplexTruncLEX₃ToTruncGE_assoc, CategoryTheory.WithTerminal.opEquiv_unitIso_inv_app, CategoryTheory.Functor.ShiftSequence.induced_shiftMap_assoc, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom, CategoryTheory.Limits.map_ι_comp_inv_sigmaComparison, CategoryTheory.Functor.relativelyRepresentable.toPullbackTerminal, CategoryTheory.MonoidalCategory.associator_conjugation, CategoryTheory.CosimplicialObject.comp_left, CategoryTheory.MonoidalCategory.associator_inv_conjugation_assoc, CategoryTheory.Functor.IsLocalization.op, CategoryTheory.Limits.PushoutCocone.unop_snd, CategoryTheory.Limits.diagramIsoParallelPair_inv_app, CategoryTheory.Square.op_f₃₄, CategoryTheory.Limits.pushoutCoconeOfLeftIso_inr, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_inv, CategoryTheory.Limits.pushout.map_id, CategoryTheory.MonoidalCategory.DayConvolution.whiskerRight_comp_unit_app, ChainComplex.fromSingle₀Equiv_symm_apply_f_succ, CategoryTheory.Adjunction.commShiftIso_hom_app_counit_app_shift, CategoryTheory.MorphismProperty.Over.pullbackComp_left_fst_fst, CategoryTheory.GrpObj.inv_comp_inv, CategoryTheory.LaxFunctor.mapComp_assoc_right_app_assoc, CategoryTheory.ShortComplex.opcyclesOpIso_inv_naturality_assoc, CategoryTheory.GlueData.mapGlueData_t', CategoryTheory.Limits.inv_prodComparison_map_fst_assoc, CategoryTheory.Discrete.natIsoFunctor_inv_app, HomologicalComplex.rightUnitor'_inv_comm, CategoryTheory.NatTrans.removeOp_app, CategoryTheory.Iso.conj_apply, SemimoduleCat.hom_sum, Mathlib.Tactic.Monoidal.evalWhiskerRightAux_of, CategoryTheory.instEffectiveEpiFamily, CategoryTheory.MorphismProperty.RightFraction.unop_Y', CategoryTheory.Comma.ext_iff, CategoryTheory.ConcreteCategory.surjective_le_epimorphisms, CategoryTheory.Limits.prod.comp_lift_assoc, CategoryTheory.Limits.lim_μ_π, CategoryTheory.Limits.colimitCoyonedaHomIsoLimitLeftOp_π_apply, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.convolutionUnitApp_eq, CategoryTheory.ObjectProperty.le_strictLimitsClosureIter, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right, CategoryTheory.MonoidalCategory.whiskerRight_tensor_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app, Condensed.id_val, AlgebraicGeometry.Scheme.Cover.pullbackHom_map, CategoryTheory.ExponentiableMorphism.homEquiv_apply_eq, CategoryTheory.Sieve.pushforward_apply_comp, ComplexShape.Embedding.homRestrict_comp_extendMap, CategoryTheory.Groupoid.vertexGroup_mul, CategoryTheory.Limits.kernelSubobjectMap_arrow, CategoryTheory.Center.ofBraided_η_f, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_inv_π_assoc, CategoryTheory.ShortComplex.Homotopy.symm_h₁, CategoryTheory.MorphismProperty.IsLocalAtTarget.inf, CategoryTheory.Over.associator_hom_left_snd_snd, CategoryTheory.Subfunctor.equalizer.ι_ι, SSet.PtSimplex.MulStruct.δ_succ_castSucc_map_assoc, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom_assoc, FinPartOrd.id_apply, CategoryTheory.PreZeroHypercover.shrink_I₀, CategoryTheory.MonoidalCategory.hom_inv_id_tensor_assoc, CategoryTheory.MorphismProperty.Comma.hasLimitsOfShape_of_closedUnderLimitsOfShape, CategoryTheory.Over.associator_inv_left_snd_assoc, FDRep.hom_action_ρ, GrpCat.hom_comp, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₁_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_map, CategoryTheory.Functor.inr_biprodComparison'_assoc, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π_assoc, CategoryTheory.GrpObj.right_inv_assoc, CategoryTheory.PreGaloisCategory.endMulEquivAutGalois_pi, HomotopicalAlgebra.FibrantBrownFactorization.i_r, CategoryTheory.Bimon.toMon_Comon_ofMon_Comon_obj_one, CategoryTheory.Pi.comapComp_hom_app, CategoryTheory.Localization.homEquiv_isoOfHom_inv, CategoryTheory.Bicategory.leftUnitor_comp_inv_assoc, HomologicalComplex.truncGEMap_id, CategoryTheory.Over.coprodObj_map, AlgebraicGeometry.Scheme.Hom.Spec_map_residueFieldMap_fromSpecResidueField, CategoryTheory.Functor.map_braiding, AlgebraicTopology.DoldKan.hσ'_naturality, CategoryTheory.Localization.homEquiv_id, AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_naturality_assoc, CategoryTheory.NatTrans.app_sub, CategoryTheory.Functor.hcomp_id, CategoryTheory.Bicategory.leftUnitor_whiskerRight_assoc, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_two_assoc, AlgebraicTopology.DoldKan.P_add_Q_f, CategoryTheory.Limits.MultispanIndex.inj_fstSigmaMapOfIsColimit, CategoryTheory.Limits.sigmaComparison_map_desc, SemimoduleCat.comp_apply, CategoryTheory.NatTrans.naturality_assoc, CategoryTheory.mono_iff_isPullback, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_left_right, CategoryTheory.ShortComplex.opFunctor_map, CategoryTheory.GlueData.diagramIso_hom_app_right, ModuleCat.homEquiv_extendScalarsId, CategoryTheory.Limits.prod.map_fst, CategoryTheory.yoneda_obj_isGeneratedBy, CategoryTheory.MonoidalCategory.prodCompExternalProduct_hom_app, CategoryTheory.Localization.Monoidal.tensor_comp, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_hom_app_snd_app, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_isoPointwiseLeftKanExtension_hom, CategoryTheory.NatTrans.app_neg, CategoryTheory.Limits.kernelForkBiproductToSubtype_isLimit, CategoryTheory.toOverUnitPullback_inv_app_left, CategoryTheory.NatIso.cancel_natIso_hom_left, CategoryTheory.Comma.mapRightIso_inverse_map_left, CategoryTheory.Functor.sheafPushforwardContinuousComp'_hom_app_val_app, CategoryTheory.IsSplitEqualizer.ι_leftRetraction_assoc, CategoryTheory.ShortComplex.SnakeInput.w₁₃, CategoryTheory.Injective.factors, CategoryTheory.eqToHom_iso_hom_naturality, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app_assoc, groupHomology.d₂₁_comp_d₁₀_assoc, CategoryTheory.Functor.RightLinear.μᵣ_comp_δᵣ_assoc, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.firstMap_app_app_app, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.lift_map, CategoryTheory.Limits.pullbackDiagonalMapIso.inv_snd_snd, CategoryTheory.ShortComplex.HomotopyEquiv.refl_homotopyInvHomId, CpltSepUniformSpace.hom_id, Bimod.whiskerRight_comp_bimod, CategoryTheory.Functor.diag_ε, AddCommGrpCat.hom_neg, CategoryTheory.Limits.hasImage_zero, AlgebraicTopology.DoldKan.hσ'_eq', CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv, HomologicalComplex.opInverse_map, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_inv_app_val_app, CategoryTheory.Limits.constCocone_ι, CategoryTheory.MonoidalClosed.id_comp, CategoryTheory.MorphismProperty.RightFraction.op_s, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_apply, CategoryTheory.FunctorToTypes.eqToHom_map_comp_apply, CategoryTheory.Bicategory.leftUnitor_inv_congr, CategoryTheory.Functor.LaxMonoidal.left_unitality_inv_assoc, SSet.StrictSegal.isRightKanExtension, CategoryTheory.GrothendieckTopology.Plus.toPlus_apply, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.PreOneHypercover.p₂_sigmaOfIsColimit_assoc, CategoryTheory.ComposableArrows.Mk₁.map_id, CategoryTheory.Bicategory.conjugateIsoEquiv_symm_apply_inv, CategoryTheory.Limits.kernelBiproductToSubtypeIso_inv, CategoryTheory.Limits.limitUnopIsoUnopColimit_inv_comp_π, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_assoc, groupCohomology.eq_d₀₁_comp_inv_assoc, CategoryTheory.Subfunctor.Subpresheaf.ofSection_eq_range, AlgebraicGeometry.Scheme.Pullback.Triplet.Spec_map_tensorInl_fromSpecResidueField, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst, CategoryTheory.SingleFunctors.shiftIso_add'_hom_app, CategoryTheory.Under.w_assoc, SemiRingCat.ofHom_comp, CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_hom, CategoryTheory.Limits.image.factor_map, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc, CategoryTheory.Limits.Trident.IsLimit.homIso_natural, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence, CategoryTheory.Comma.mapLeftId_inv_app_right, CategoryTheory.StructuredArrow.w_assoc, HomologicalComplex.dFrom_comp_xNextIsoSelf_assoc, CategoryTheory.Limits.Sigma.ι_comp_map', CategoryTheory.Bicategory.rightUnitor_hom_congr, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_inv_app_op_one, SemiNormedGrp.hom_zsum, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapComp_inv, CategoryTheory.Equivalence.sheafCongr.counitIso_inv_app_val_app, CategoryTheory.Preadditive.sum_comp', CategoryTheory.Arrow.hom_inv_id_left_assoc, CategoryTheory.Functor.mapMatComp_inv_app, HomologicalComplex.singleObjHomologySelfIso_inv_homologyι, GrpCat.comp_apply, groupHomology.coinvariantsMk_comp_H0Iso_inv_assoc, CategoryTheory.unop_whiskerLeft, CategoryTheory.CatEnrichedOrdinary.homEquiv_id, HomologicalComplex.mapBifunctorAssociatorX_hom_D₁_assoc, AlgebraicTopology.DoldKan.HigherFacesVanish.induction, CategoryTheory.Limits.opHomCompWhiskeringLimYonedaIsoCocones_inv_app_app, AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInfty, CategoryTheory.GrothendieckTopology.plusMap_comp, CategoryTheory.StructuredArrow.mapNatIso_functor_map_left, CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp_assoc, CategoryTheory.Limits.Types.binaryCoproductIso_inl_comp_hom, AlgebraicGeometry.LocallyRingedSpace.comp_c_app, CategoryTheory.sheafSectionsNatIsoEvaluation_inv_app, CategoryTheory.WithInitial.down_comp, CategoryTheory.Pseudofunctor.comp_mapId, HomologicalComplex₂.D₁_D₂, CategoryTheory.IsHomLift.isoOfIsoLift_inv_hom_id, CategoryTheory.isGroupoid_iff_isomorphisms_eq_top, FinPartOrd.hom_hom_id, CategoryTheory.Limits.imageSubobject_arrow', HomotopicalAlgebra.Precylinder.inl_i, CategoryTheory.OverPresheafAux.YonedaCollection.map₂_fst, CategoryTheory.ShortComplex.leftHomologyMap_id, CategoryTheory.Limits.Types.Image.lift_fac, CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal_μ_unmop_unmop, CategoryTheory.eqToHom_unop, CategoryTheory.GradedObject.ι_mapBifunctorLeftUnitor_hom_apply_assoc, CategoryTheory.GrothendieckTopology.Cover.Arrow.middle_spec, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitIso_inv_naturality, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd_assoc, TopCat.Presheaf.presheafEquivOfIso_functor_obj_map, CategoryTheory.Bicategory.Prod.swap_mapId_inv, CategoryTheory.NatTrans.unop_app, CategoryTheory.SmallObject.SuccStruct.Iteration.mapObj_trans, CategoryTheory.MorphismProperty.le_multiplicativeClosure, CategoryTheory.BasedNatTrans.homCategory_id, CategoryTheory.Functor.mapDerivedCategoryFactorsh_hom_app, CategoryTheory.Localization.instIsGroupoidLocalizationTopMorphismProperty, CategoryTheory.OplaxFunctor.mapComp_naturality_right_app, CategoryTheory.ShortComplex.Homotopy.compLeft_h₁, CategoryTheory.Limits.colimit.ι_inv_pre_assoc, CochainComplex.HomComplex.Cochain.toSingleMk_sub, CategoryTheory.Limits.HasZeroMorphisms.comp_zero, CategoryTheory.Adjunction.Localization.η_app, CategoryTheory.Subpresheaf.to_sheafifyLift, CategoryTheory.StructuredArrow.map₂_obj_hom, CategoryTheory.sum.inlCompInverseAssociator_hom_app_down_down, CategoryTheory.SimplicialThickening.SimplicialCategory.id_comp, CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id, CategoryTheory.unop_sum, CategoryTheory.Limits.HasBiproductsOfShape.colimIsoLim_inv_app, CategoryTheory.StructuredArrow.mapNatIso_counitIso_inv_app_right, CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal_η_unmop_unmop, CategoryTheory.Limits.Pi.map_π, CategoryTheory.Discrete.productEquiv_inverse_map, CategoryTheory.Bicategory.Prod.sectR_map, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_hom_app_unop, CategoryTheory.Sieve.toUliftFunctor_app_down_coe, CategoryTheory.ShortComplex.leftHomologyMap'_add, CategoryTheory.NatIso.cancel_natIso_inv_left, CategoryTheory.kernelCokernelCompSequence.inr_φ_fst, CategoryTheory.Limits.FormalCoproduct.mapPower_powerMap_assoc, CategoryTheory.Limits.CatCospanTransform.id_whiskerRight, CategoryTheory.StrictPseudofunctor.mk''_map₂, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_zero, AlgebraicGeometry.Scheme.stalkMap_germ, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_assoc, CategoryTheory.Linear.rightComp_apply, CategoryTheory.WithInitial.coconeEquiv_unitIso_inv_app_hom_right, CategoryTheory.ShiftedHom.mk₀_smul, CategoryTheory.Join.mapWhiskerLeft_comp, CategoryTheory.CechNerveTerminalFrom.wideCospan.limitIsoPi_hom_comp_pi, CategoryTheory.OplaxFunctor.mapComp'_comp_whiskerLeft_mapComp'_assoc, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.lift_map_assoc, Semigrp.coe_comp, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberToSpecResidueField_assoc, CategoryTheory.Bimon.Mon_Class.tensorObj.mul_def, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃'_associator_hom_assoc, CategoryTheory.Functor.Monoidal.whiskerLeft_η_ε_assoc, CategoryTheory.IsCofiltered.inf_exists, AlgebraicGeometry.quasiSeparatedSpace_iff_quasiCompact_prod_lift, CategoryTheory.Localization.Monoidal.associator_naturality₁, HomologicalComplex.biprod_inl_desc_f_assoc, CategoryTheory.MonoidalCategory.tensor_dite, CategoryTheory.NonPreadditiveAbelian.sub_self, AlgebraicGeometry.Scheme.Spec.residue_residueFieldIso_hom, CategoryTheory.ProjectiveResolution.fromLeftDerivedZero_eq, CategoryTheory.Pi.ε_def, CategoryTheory.Limits.biprod.hom_ext_iff, CategoryTheory.InjectiveResolution.Hom.ι_comp_hom, HomologicalComplex.extendMap_id, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapId_inv, CategoryTheory.oppositeShiftFunctorAdd'_inv_app, CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit, CategoryTheory.Limits.CatCospanTransform.comp_whiskerLeft, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_ι, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_inv_assoc, CategoryTheory.HopfObj.antipode_counit_assoc, CategoryTheory.LocalizerMorphism.smallShiftedHomMap_mk₀, CategoryTheory.Presieve.isSheafFor_ofArrows_comp_iff, CategoryTheory.left_comp_retraction_assoc, CategoryTheory.Bimon.equivMonComonCounitIsoApp_inv_hom_hom, CategoryTheory.Under.opEquivOpOver_inverse_map, CategoryTheory.Functor.lanUnit_app_app_lanAdjunction_counit_app_app_assoc, CategoryTheory.IsHomLift.instIsHomLiftIdObj, CategoryTheory.ShortComplex.Homotopy.h₀_f, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_right, CategoryTheory.ShortComplex.opcyclesMap'_neg, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.counitIso_hom, AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_toGlued, SimplicialObject.Splitting.cofan_inj_eq_assoc, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_hom, CategoryTheory.Limits.wideEqualizer.hom_ext_iff, CategoryTheory.BraidedCategory.braiding_naturality_right_assoc, groupCohomology.isoCocycles₁_hom_comp_i_assoc, CategoryTheory.Functor.diag_map, FintypeCat.homMk_apply, CategoryTheory.InjectiveResolution.descFOne_zero_comm, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_appTop, CategoryTheory.Cat.FreeRefl.quotientFunctor_map_cons, CategoryTheory.ObjectProperty.isClosedUnderLimitsOfShape_iff_unop, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_germ_assoc, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_map_right, CategoryTheory.IsIso.id, CategoryTheory.GrothendieckTopology.uliftYoneda_map_val_app_down, CategoryTheory.Limits.wideEqualizer.condition, CategoryTheory.PreZeroHypercover.sum_f, CategoryTheory.Limits.FormalCoproduct.evalOpCompInlIsoId_inv_app_app, CategoryTheory.Abelian.DoldKan.comparisonN_inv_app_f, PartOrd.hom_id, CategoryTheory.Abelian.Ext.mk₀_homEquiv₀_apply, CategoryTheory.MonoidalCategory.id_whiskerLeft_symm, SimplexCategory.II_δ, groupHomology.π_comp_H1Iso_inv_assoc, CategoryTheory.Functor.LeftLinear.δₗ_comp_μₗ_assoc, CochainComplex.HomComplex.Cocycle.equivHomShift_apply, CategoryTheory.ObjectProperty.instContainsZeroUnopOfOpposite, CategoryTheory.Limits.Cofork.op_ι, ComplexShape.Embedding.AreComplementary.hom_ext', CategoryTheory.right_unitality_app, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal_basicOpen, CategoryTheory.Abelian.FunctorCategory.imageObjIso_inv, CategoryTheory.MorphismProperty.MapFactorizationData.op_p, CategoryTheory.Adjunction.homEquiv_id, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_inv_app_fst_app, AlgebraicGeometry.IsImmersion.comp_iff, CategoryTheory.Limits.Cones.postcomposeComp_hom_app_hom, CategoryTheory.Enriched.FunctorCategory.functorEnriched_comp_id, CommRingCat.coproductCocone_ι, CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono'_p, SSet.Truncated.HomotopyCategory.homToNerveMk_comp_assoc, CategoryTheory.RelCat.Hom.rel_id, CategoryTheory.CatEnriched.hComp_id, CategoryTheory.instReflectsIsomorphismsForgetTypeHom, CategoryTheory.HasLiftingProperty.of_comp_right, CategoryTheory.Limits.equalizer.hom_ext_iff, CategoryTheory.Equivalence.adjointify_η_ε, TopCat.Presheaf.stalkFunctor_map_germ_assoc, CategoryTheory.Limits.Cocone.extensions_app, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_map_app, CategoryTheory.MonoidalCategory.tensor_right_unitality_assoc, CategoryTheory.Subfunctor.range_id, CategoryTheory.LaxFunctor.mapComp_assoc_left_app_assoc, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₁, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_hom, CategoryTheory.Adjunction.homEquiv_naturality_left, HomologicalComplex.singleObjOpcyclesSelfIso_hom_assoc, CategoryTheory.Comon.monoidal_tensorObj_comon_counit, HomologicalComplex.mapBifunctor.d₁_eq, CategoryTheory.Limits.pushoutCoconeOfRightIso_inl, CategoryTheory.Lax.OplaxTrans.id_app, CategoryTheory.Limits.biprod.inr_map_assoc, AlgebraicGeometry.instHasFiniteCoproductsOverSchemeTopMorphismProperty, CategoryTheory.Limits.ColimitPresentation.bind_ι_app, CategoryTheory.Limits.hasPullbackHorizPaste, TopCat.ofHom_id, CategoryTheory.Oplax.StrongTrans.homCategory_comp_as_app, CategoryTheory.MonoidalCategory.pentagon, CategoryTheory.ShortComplex.Hom.id_τ₂, CategoryTheory.Pretriangulated.binaryProductTriangleIsoBinaryBiproductTriangle_hom_hom₃, HomologicalComplex.homologyMap_comp_assoc, CategoryTheory.LaxFunctor.id_mapComp, CategoryTheory.Equivalence.inverse_counitInv_comp, CategoryTheory.MorphismProperty.LeftFraction.Localization.Q_map_comp_Qinv, CategoryTheory.instEffectiveEpiFamilyComp, CategoryTheory.Functor.PullbackObjObj.ofHasPullback_fst, SemimoduleCat.MonoidalCategory.pentagon, CategoryTheory.Functor.OplaxMonoidal.left_unitality_hom_assoc, CategoryTheory.PreOneHypercover.Homotopy.wr_assoc, CategoryTheory.Functor.IsRepresentedBy.representableBy_homEquiv_apply, CategoryTheory.Preadditive.sub_comp, TopologicalSpace.OpenNhds.inclusionMapIso_hom_app, CategoryTheory.Functor.Monoidal.whiskerLeft_app_snd_assoc, CategoryTheory.flipCompEvaluation_inv_app, CategoryTheory.LocalizerMorphism.LeftResolution.opEquivalence_functor, CategoryTheory.GradedObject.Monoidal.ι_tensorHom, AlgebraicGeometry.IsOpenImmersion.comp_lift, CategoryTheory.Limits.coprod.symmetry', HomotopicalAlgebra.PrepathObject.ι_p₁, CategoryTheory.Functor.FullyFaithful.hasShift.map_zero_hom_app, CategoryTheory.Functor.map_one, CategoryTheory.Limits.MonoFactorisation.isoComp_I, ChainComplex.alternatingConst_obj, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality'_assoc, CategoryTheory.Limits.kernelSubobject_arrow', CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHomLeft, CategoryTheory.Retract.op_r, CategoryTheory.Functor.Fiber.fiberInclusionCompIsoConst_hom_app, CategoryTheory.Cat.leftUnitor_inv_app, CategoryTheory.η_ε_app, CategoryTheory.Functor.leftKanExtensionIsoFiberwiseColimit_inv_app, CategoryTheory.Localization.Construction.morphismProperty_is_top, CategoryTheory.ShortComplex.leftRightHomologyComparison'_fac_assoc, CategoryTheory.Functor.toPseudoFunctor_obj, CategoryTheory.CartesianMonoidalCategory.whiskerLeft_fst_assoc, CategoryTheory.GradedObject.ιMapObjOrZero_eq_zero, MonCat.hom_id, CategoryTheory.Bicategory.associator_inv_naturality_middle_assoc, CategoryTheory.biproduct_ι_comp_leftDistributor_inv_assoc, CategoryTheory.shiftFunctorAdd_assoc_inv_app, AlgebraicGeometry.IsOpenImmersion.lift_fac, HomologicalComplex.singleObjHomologySelfIso_hom_singleObjHomologySelfIso_inv, CategoryTheory.MorphismProperty.Comma.Hom.comp_right, CategoryTheory.LaxFunctor.map₂_leftUnitor_app, CategoryTheory.Limits.Cones.postcompose_map_hom, CategoryTheory.NatTrans.CommShift.id, CategoryTheory.Skeleton.comp_hom_assoc, CategoryTheory.Preadditive.mono_iff_cancel_zero, AlgebraicGeometry.pullbackSpecIso_hom_fst_assoc, CategoryTheory.Adjunction.left_triangle_components, CompHausLike.LocallyConstant.functorToPresheaves_obj_map, CategoryTheory.Bicategory.rightUnitor_comp_inv_assoc, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj, AlgebraicGeometry.ValuativeCriterion.eq, CategoryTheory.Limits.inl_pushoutZeroZeroIso_hom, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₂_assoc, CategoryTheory.Limits.walkingParallelPairOp_right, CategoryTheory.WithTerminal.opEquiv_functor_map, CategoryTheory.PreGaloisCategory.evaluation_aut_injective_of_isConnected, CategoryTheory.Join.InclRightCompRightOpOpEquivFunctor_hom_app, CategoryTheory.Equivalence.unit_app_tensor_comp_inverse_map_δ_functor, PresheafOfModules.zero_app, CategoryTheory.Join.mapPairRight_inv_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τl, CategoryTheory.Lax.OplaxTrans.naturality_naturality_assoc, CategoryTheory.Functor.RightExtension.postcompose₂ObjMkIso_hom_left_app, CategoryTheory.Endofunctor.Coalgebra.comp_f, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂_assoc, CategoryTheory.Limits.opCoproductIsoProduct_inv_comp_ι, CategoryTheory.CostructuredArrow.projectQuotient_mk, CategoryTheory.Limits.Cotrident.IsColimit.homIso_apply_coe, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₁, HomologicalComplex.cylinder.ι₀_desc_assoc, CategoryTheory.CatEnrichedOrdinary.Hom.base_eqToHom, AddCommGrpCat.homAddEquiv_apply, CategoryTheory.ActionCategory.stabilizerIsoEnd_symm_apply, CategoryTheory.Over.coreHomEquivToOverSections_homEquiv, HomologicalComplex₂.totalFlipIsoX_hom_D₁_assoc, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_inv_app_f, CategoryTheory.Functor.PreservesHomology.preservesKernel, CategoryTheory.MorphismProperty.isColocal_iff, UniformSpaceCat.hom_comp, AlgebraicGeometry.Scheme.Hom.fromNormalization_app, CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp_hom_hom₂, groupHomology.π_map, groupHomology.mapCycles₁_comp_i_assoc, Homotopy.nullHomotopy'_hom, CategoryTheory.Limits.cokernelEpiComp_hom, HomotopicalAlgebra.PrepathObject.ι_p₀_assoc, CategoryTheory.Limits.IsInitial.subsingleton_to, CategoryTheory.Limits.Cocones.whiskeringEquivalence_counitIso, CategoryTheory.Iso.map_hom_inv_id_eval_app, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_hom_app, CategoryTheory.Pseudofunctor.Grothendieck.categoryStruct_comp_fiber, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHom_comp, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_assoc, CategoryTheory.GrothendieckTopology.Cover.Arrow.Relation.w, CategoryTheory.Preadditive.neg_comp_assoc, AlgebraicGeometry.Scheme.stalkSpecializes_stalkMap_assoc, CategoryTheory.eqToHom_trans, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right, CategoryTheory.StrictlyUnitaryLaxFunctor.comp_map₂, AlgebraicGeometry.Scheme.Modules.pseudofunctor_associativity, CategoryTheory.Mon.tensor_one, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'_assoc, CategoryTheory.Abelian.Pseudoelement.zero_apply, CategoryTheory.MonoidalCategory.tensor_whiskerLeft_symm, CategoryTheory.NatTrans.CommShiftCore.app_shift_assoc, CategoryTheory.Limits.biprod.lift_desc, AlgebraicGeometry.Scheme.presheaf_map_eqToHom_op, CategoryTheory.Limits.biprod.braid_natural_assoc, PresheafOfModules.map_comp_assoc, CategoryTheory.ShortComplex.homologyIsoImageICyclesCompPOpcycles_ι_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.inv_hom_actionHomLeft, CategoryTheory.mono_comp_iff_of_isIso, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app, CategoryTheory.Arrow.arrow_mk_eqToHom_comp, CategoryTheory.Mat.id_def, CategoryTheory.Functor.Monoidal.μ_δ, CategoryTheory.MorphismProperty.Comma.id_left, CategoryTheory.Preadditive.instEpiNegHom, CategoryTheory.eqToHom_heq_id_dom, CategoryTheory.Limits.biprod.associator_inv, SimplexCategory.δ_comp_σ_succ, CategoryTheory.Functor.homologySequence_mono_shift_map_mor₂_iff, CategoryTheory.Equalizer.Presieve.Arrows.w, CategoryTheory.Comma.mapLeftComp_hom_app_right, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_μ_assoc, CategoryTheory.Endofunctor.Adjunction.Coalgebra.toAlgebraOf_map_f, CategoryTheory.Quiv.forget_obj, AlgebraicGeometry.Scheme.Hom.eqToHom_app, CategoryTheory.Limits.HasZeroObject.zeroIsoInitial_hom, CategoryTheory.Functor.obj.Δ_def, CategoryTheory.MonoidalCategory.tensorHom_id, HomologicalComplex.singleObjOpcyclesSelfIso_hom_naturality, CategoryTheory.Pretriangulated.binaryProductTriangleIsoBinaryBiproductTriangle_hom_hom₁, CategoryTheory.Limits.ι_colimitOfIsReflexivePairIsoCoequalizer_hom_assoc, CategoryTheory.Functor.prod_δ_fst, CategoryTheory.Limits.CategoricalPullback.comp_snd_assoc, CategoryTheory.Functor.whiskeringRight₂_obj_map_app_app, CategoryTheory.Limits.colimit.pre_eq, CategoryTheory.Preadditive.neg_iso_inv, CategoryTheory.shiftFunctorAdd'_assoc_hom_app, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv, SemiNormedGrp.hom_nsum, CategoryTheory.CostructuredArrow.toStructuredArrow_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.iso_hom_naturality, CategoryTheory.Functor.biproductComparison'_comp_biproductComparison_assoc, CategoryTheory.Over.whiskerLeft_left_snd, CategoryTheory.Limits.inr_inr_pushoutAssoc_inv, CategoryTheory.MonoidalCategory.tensor_hom_inv_id, CategoryTheory.Pi.comapId_inv_app, CategoryTheory.Localization.Preadditive.add_comp_assoc, CategoryTheory.Functor.unopComp_hom_app, CategoryTheory.eqToHom_naturality_assoc, PartOrd.id_apply, CategoryTheory.Functor.OplaxMonoidal.right_unitality_hom_assoc, CategoryTheory.Limits.WalkingMulticospan.Hom.id_eq_id, CategoryTheory.Groupoid.comp_inv, CochainComplex.mappingCone.lift_f_snd_v_assoc, CategoryTheory.cokernel_zero_of_nonzero_to_simple, CategoryTheory.ShortComplex.RightHomologyMapData.commι_assoc, CategoryTheory.Functor.rightDerived_fac, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberCompIso_hom_app, CategoryTheory.Limits.Types.coproductIso_ι_comp_hom, CategoryTheory.μ_naturalityₗ_assoc, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_inv_π_π_assoc, CategoryTheory.Precoverage.ZeroHypercover.comp_h₀, AlgebraicTopology.DoldKan.Compatibility.υ_inv_app, HomotopicalAlgebra.PathObject.trans_p₁, CategoryTheory.Functor.compFlipUncurryIso_hom_app, CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_three, CategoryTheory.Grothendieck.transportIso_hom_fiber, CategoryTheory.ShortComplex.zero_τ₂, CategoryTheory.Over.w_assoc, CategoryTheory.Comma.mapRight_map_right, CochainComplex.mappingCone.mapHomologicalComplexXIso'_inv, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHomLeft_unop, CategoryTheory.Functor.IsCoverDense.Types.pushforwardFamily_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_yoneda_map, CategoryTheory.SingleFunctors.postcomp_shiftIso_hom_app, CategoryTheory.Limits.CoconeMorphism.map_w, commBialgCatEquivComonCommAlgCat_counitIso_inv_app, CategoryTheory.Pseudofunctor.CoGrothendieck.compIso_hom_app, HomologicalComplex.extendHomologyIso_hom_homologyι, AlgebraicGeometry.Scheme.id_app, CategoryTheory.whiskeringLeftCompEvaluation_hom_app, CategoryTheory.Limits.prod.lift_fst_comp_snd_comp, CategoryTheory.Functor.IsStronglyCocartesian.map_self, SemimoduleCat.hom_id, SheafOfModules.GeneratingSections.opEpi_id, CochainComplex.cm5b, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_unitIso_inv_app_right_app, CategoryTheory.StructuredArrow.homMk'_mk_id, CategoryTheory.Functor.whiskeringRightObjCompIso_inv_app_app, CategoryTheory.Linear.smul_comp, CategoryTheory.Pretriangulated.Triangle.smul_hom₁, CategoryTheory.ShortComplex.RightHomologyMapData.add_φQ, CategoryTheory.Functor.PreservesZeroMorphisms.map_zero, CategoryTheory.MorphismProperty.cancel_right_of_respectsIso, CategoryTheory.CostructuredArrow.IsUniversal.fac_assoc, TopCat.GlueData.preimage_image_eq_image', CategoryTheory.e_assoc, CategoryTheory.Equivalence.unit_inverse_comp_assoc, CategoryTheory.Pseudofunctor.IsPrestackFor.nonempty_fullyFaithful, CategoryTheory.Join.mkFunctorRight_hom_app, Rep.FiniteCyclicGroup.resolution.π_f, CategoryTheory.Subfunctor.range_comp_le, CategoryTheory.Comma.mapFst_inv_app, CategoryTheory.Limits.Cones.postcomposeId_inv_app_hom, Alexandrov.projSup_map, CategoryTheory.FunctorToTypes.binaryProductIso_hom_comp_fst, SemimoduleCat.MonoidalCategory.braiding_naturality_left, CategoryTheory.Limits.MulticospanIndex.fstPiMap_π, CategoryTheory.LocalizerMorphism.instHasRightResolutionsOppositeOpOpOfHasLeftResolutions, CategoryTheory.MonoidalCategory.associator_inv_naturality_middle, CategoryTheory.Adjunction.Triple.whiskerLeft_leftToRight, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.comp_fst_app, CategoryTheory.leftDistributor_inv_comp_biproduct_π, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_linearCombination, CategoryTheory.SimplicialObject.equivalenceLeftToRight_left_app, CategoryTheory.Limits.inr_comp_pushoutSymmetry_hom, CategoryTheory.Limits.Fork.unop_π, CategoryTheory.Functor.inl_biprodComparison'_assoc, CategoryTheory.ShortComplex.leftHomologyMap_smul, CategoryTheory.Over.liftCocone_pt, CategoryTheory.MorphismProperty.RightFraction.op_Y', AlgebraicGeometry.Scheme.Pullback.Triplet.SpecMap_tensorInl_fromSpecResidueField, HomotopicalAlgebra.CofibrantBrownFactorization.mk'_i, CategoryTheory.GradedObject.mapBifunctorRightUnitor_inv_naturality, CategoryTheory.MonoidalCategory.DayConvolutionUnit.corepresentableByRight_homEquiv, CategoryTheory.Functor.eventualRange_eq_iff, SSet.Truncated.HomotopyCategory.morphismProperty_eq_top, CategoryTheory.Functor.comp_homologySequenceδ_assoc, TopCat.Presheaf.SheafConditionEqualizerProducts.res_π_apply, CategoryTheory.MorphismProperty.transfiniteCompositions_monotone, HomologicalComplex.homotopyCofiber.d_fstX_assoc, AlgebraicGeometry.Scheme.zeroLocus_map_of_eq, AlgebraicGeometry.IsAffineOpen.toSpecΓ_fromSpec, CategoryTheory.WithTerminal.coneEquiv_counitIso_hom_app_hom, CategoryTheory.ShortComplex.RightHomologyMapData.ofEpiOfIsIsoOfMono_φQ, CategoryTheory.Limits.biproduct.ι_map, CategoryTheory.Pseudofunctor.mapComp'_hom_comp_mapComp'_hom_whiskerRight, CategoryTheory.Limits.initial.to_comp, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv, CategoryTheory.ShortComplex.SnakeInput.Hom.comp_f₀, SimplexCategoryGenRel.δ_comp_σ_succ_assoc, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τr, CategoryTheory.Deterministic.copy_natural, CategoryTheory.Functor.OplaxLeftLinear.δₗ_associativity_inv_assoc, CategoryTheory.kernelCokernelCompSequence.snakeInput_L₃_X₂, CategoryTheory.presheafHom_map_app_op_mk_id, CategoryTheory.InjectiveResolution.rightDerived_app_eq, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_app_app_germToPullbackStalk, CategoryTheory.kernelCokernelCompSequence.instMonoι, CategoryTheory.Limits.diagonal_pullback_fst, AlgebraicGeometry.Scheme.PartialMap.fromSpecStalkOfMem_toPartialMap, CategoryTheory.InjectiveResolution.Hom.ι'_comp_hom', CategoryTheory.ShortComplex.opcyclesMap'_smul, CategoryTheory.Limits.coprod.map_inl_inr_codiag_assoc, Lat.ofHom_id, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_comp, CategoryTheory.InducedWideCategory.category_id_coe, CategoryTheory.Bicategory.RightLift.w, CategoryTheory.CartesianMonoidalCategory.homEquivToProd_symm_apply, CategoryTheory.ShortComplex.cyclesMap_comp_assoc, CategoryTheory.Limits.limit.lift_extend, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_inv_app, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_left, CategoryTheory.Pseudofunctor.ObjectProperty.map₂_app_hom, CategoryTheory.ShortComplex.RightHomologyMapData.unop_φH, CategoryTheory.PreservesImage.inv_comp_image_ι_map_assoc, CategoryTheory.CartesianMonoidalCategory.lift_whiskerLeft_assoc, CategoryTheory.ShortComplex.mapLeftHomologyIso_inv_naturality, CategoryTheory.cokernelOpOp_inv, CategoryTheory.ObjectProperty.isoInv_hom_id_hom, HomotopicalAlgebra.weakEquivalence_precomp_iff, CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_hom, CategoryTheory.ShortComplex.p_opcyclesMap, SSet.stdSimplex.face_singleton_compl, CategoryTheory.Functor.partialRightAdjointHomEquiv_map_comp, PresheafOfModules.instIsRightAdjointPushforwardIdFunctorOppositeRingCat, CategoryTheory.Functor.CommShift.isoAdd'_inv_app, CategoryTheory.Adjunction.derivedε_fac_app, CategoryTheory.GrothendieckTopology.OneHypercover.id_h₁, CategoryTheory.LaxMonoidalFunctor.id_hom, CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt', CategoryTheory.Localization.associator_hom_app_app_app, CategoryTheory.Bicategory.triangle_assoc, CategoryTheory.Limits.inr_coprodZeroIso_hom, CategoryTheory.Functor.CommShift.OfComp.map_iso_hom_app, FDRep.endRingEquiv_comp_ρ, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_ι_inv_assoc, CategoryTheory.Functor.CommShift.OfComp.map_iso_inv_app_assoc, CategoryTheory.Functor.CommShift.isoZero'_hom_app, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_inr, CategoryTheory.Equivalence.congrRight_counitIso_inv_app, CategoryTheory.ObjectProperty.FullSubcategory.id_hom, TopologicalSpace.Opens.val_apply, CategoryTheory.Under.w, HomologicalComplex.Hom.fAddMonoidHom_apply, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst_assoc, CategoryTheory.down_comp, CategoryTheory.Equivalence.counit_naturality, CategoryTheory.Pseudofunctor.CoGrothendieck.Hom.ext_iff, CategoryTheory.HomRel.IsStableUnderPostcomp.comp_right, AugmentedSimplexCategory.tensorHom_comp_tensorHom, CategoryTheory.Localization.Monoidal.map_hexagon_forward_assoc, CategoryTheory.HopfObj.one_antipode_assoc, CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_fst, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.unitIso_inv_app_hom_app, CategoryTheory.Limits.colimit.ι_desc_app, CategoryTheory.equiv_punit_iff_unique, SheafOfModules.Presentation.map_π_eq, CategoryTheory.GrothendieckTopology.Cover.coe_pullback, CompHausLike.coe_comp, AlgebraicGeometry.Scheme.homOfLE_rfl, CategoryTheory.Limits.PushoutCocone.unop_fst, CategoryTheory.MonoidalCategory.externalProductBifunctor_obj_map, CategoryTheory.MorphismProperty.LeftFraction.map_eq, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.inverse_map, CategoryTheory.isIso_op_iff, HomologicalComplex.toCycles_i_assoc, AlgebraicGeometry.IsOpenImmersion.lift_app, CategoryTheory.sum.inrCompInverseAssociator_inv_app, CategoryTheory.Functor.comp_mapMon_one, CategoryTheory.SemiCartesianMonoidalCategory.snd_def, CategoryTheory.ShortComplex.RightHomologyMapData.commp, CategoryTheory.ShortComplex.leftHomologyMap_comp_assoc, CategoryTheory.MonObj.one_mul_hom, CategoryTheory.eqToIso.inv, CategoryTheory.sheafComposeNatTrans_fac, CategoryTheory.toSheafify_naturality, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff, CochainComplex.shiftFunctor_obj_d, CategoryTheory.Limits.hasPushout_of_left_factors_epi, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_left_left_as, CategoryTheory.Limits.IsLimit.fac, CategoryTheory.Limits.limitOpIsoOpColimit_hom_comp_ι, HomologicalComplex₂.total.map_id, CategoryTheory.Limits.kernelSubobject_comp_le, CategoryTheory.Mat_.additiveObjIsoBiproduct_hom_π_assoc, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_app_comp_π_assoc, CategoryTheory.Pi.comapEvalIsoEval_inv_app, CategoryTheory.Functor.OplaxMonoidal.associativity_inv_assoc, CategoryTheory.MonoidalCategory.associator_inv_conjugation, CategoryTheory.CostructuredArrow.mapIso_counitIso_inv_app_left, CategoryTheory.Center.whiskerLeft_comm_assoc, CategoryTheory.Comonad.coalgebraPreadditive_homGroup_zero_f, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_inv_fac_assoc, CategoryTheory.Functor.preimage_id, CategoryTheory.BraidedCategory.hexagon_forward_assoc, CategoryTheory.MonoidalCategory.id_tensor_comp, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₁, CategoryTheory.GrothendieckTopology.yonedaEquiv_apply, AlgebraicGeometry.sourceLocalClosure.instRespectsRightScheme, CategoryTheory.PreZeroHypercover.shrink_f, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst_assoc, isoOfQuasiIsoAt_hom_inv_id_assoc, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_ι_assoc, CategoryTheory.Dial.leftUnitorImpl_inv_F, germ_skyscraperPresheafStalkOfSpecializes_hom, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_obj_π_app, groupCohomology.mapCocycles₁_comp_i, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_obj_obj_map, CategoryTheory.OplaxFunctor.map₂_rightUnitor_app_assoc, CategoryTheory.Limits.MonoFactorisation.isoComp_m, CategoryTheory.Limits.equalizer.isoSourceOfSelf_inv, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_inv_fac_assoc, ContinuousMap.Homotopy.hcast_def, Mathlib.Tactic.Bicategory.structuralIsoOfExpr_comp, CategoryTheory.Retract.trans_i, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.toBiprod_apply, CategoryTheory.IsGrothendieckAbelian.instIsRightAdjointModuleCatMulOppositeEndPreadditiveCoyonedaObj, CategoryTheory.shrinkYonedaEquiv_symm_map, CategoryTheory.ComposableArrows.IsComplex.zero', CategoryTheory.Oplax.StrongTrans.vcomp_naturality_inv, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.sup_W, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict_assoc, AlgebraicGeometry.Scheme.IdealSheafData.map_ker, CochainComplex.HomComplex.Cochain.toSingleMk_precomp, CategoryTheory.Sieve.overEquiv_iff, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_snd, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_assoc, Lat.coe_comp, CategoryTheory.ReflQuiver.id_eq_id, CategoryTheory.ShortComplex.leftHomologyMap'_smul, CategoryTheory.Adjunction.map_μ_comp_counit_app_tensor_assoc, CategoryTheory.CartesianMonoidalCategory.tensorδ_fst, HomologicalComplex.ι_mapBifunctorMap, HomotopicalAlgebra.weakEquivalence_postcomp_iff, CategoryTheory.Comma.mapLeftIso_functor_map_right, CategoryTheory.MonoidalCategory.hom_inv_id_tensor, CategoryTheory.MonoidalCategory.DayFunctor.ι_comp_isoPointwiseLeftKanExtension_inv, CategoryTheory.Functor.currying_functor_map_app, CategoryTheory.GradedObject.ι_mapBifunctorComp₂₃MapObjIso_hom_assoc, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv, SimplicialObject.Splitting.cofan_inj_epi_naturality, CategoryTheory.map_coyonedaEquiv, CategoryTheory.toUnit_comp_curryRightUnitorHom, CategoryTheory.Limits.prod.associator_naturality, CategoryTheory.shiftFunctorAdd_zero_add_inv_app, CategoryTheory.Adjunction.homEquiv_symm_apply, CategoryTheory.ShortComplex.comp_τ₁_assoc, CategoryTheory.StructuredArrow.mkPostcomp_id, CategoryTheory.CommSq.HasLift.iff_unop, CategoryTheory.Limits.PushoutCocone.op_fst, CategoryTheory.Limits.limit.w, CategoryTheory.Presieve.FamilyOfElements.map_id, CategoryTheory.Iso.hom_inv_id_app_app_app, CategoryTheory.ShortComplex.cyclesMap_add, CategoryTheory.ShortComplex.LeftHomologyData.op_ι, CategoryTheory.Limits.inv_piComparison_comp_map_π_assoc, CategoryTheory.MorphismProperty.transfiniteCompositions_le_llp_rlp, FintypeCat.instFullForgetHomCarrier, CochainComplex.mappingCone.d_fst_v, CategoryTheory.shiftFunctorComm_hom_app_of_add_eq_zero_assoc, CategoryTheory.DifferentialObject.zero_f, CategoryTheory.Cat.freeMapIdIso_inv_app, CategoryTheory.Limits.combineCones_π_app_app, CategoryTheory.Oplax.OplaxTrans.whiskerRight_as_app, AlgebraicGeometry.Scheme.Pullback.openCoverOfLeft_X, CategoryTheory.Idempotents.toKaroubi_obj_p, CategoryTheory.ShortComplex.opcycles_ext_iff, CategoryTheory.ShortComplex.RightHomologyData.op_π, AddCommGrpCat.coyonedaType_map_app, CategoryTheory.PreOneHypercover.comp_h₁, CategoryTheory.MonObj.mul_eq_mul, CategoryTheory.Over.opEquivOpUnder_functor_obj, CategoryTheory.regularTopology.instEffectiveEpiComp, CategoryTheory.ObjectProperty.small_op_iff, CategoryTheory.Functor.bifunctorComp₂₃Iso_inv_app_app_app, SSet.Truncated.Edge.CompStruct.idCompId_simplex, AlgebraicGeometry.Scheme.stalkMap_congr, CategoryTheory.Bicategory.associator_naturality_middle_assoc, CategoryTheory.ihom.ev_coev, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_snd, AlgebraicGeometry.Spec.homEquiv_symm_apply, ModuleCat.ihom_ev_app, CategoryTheory.ShortComplex.hasHomology_of_hasKernel, CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_snd, HomologicalComplex.mapBifunctor₂₃.d₂_eq_zero, CochainComplex.mappingConeCompHomotopyEquiv_hom_inv_id_assoc, CategoryTheory.Grp.comp_hom, Action.FunctorCategoryEquivalence.functor_η, AlgebraicGeometry.descendsAlong_universallyOpen_surjective_inf_flat_inf_quasicompact, CategoryTheory.HopfObj.hom_antipode, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_hom_app_hom, CategoryTheory.Yoneda.obj_map_id, SimplicialObject.Splitting.IndexSet.eqId_iff_len_le, CategoryTheory.Limits.prod.hom_ext_iff, CategoryTheory.ObjectProperty.smul_mem_trW_iff, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι, CategoryTheory.Mon.id_hom', CategoryTheory.IsSplitCoequalizer.condition_assoc, CategoryTheory.Limits.Multifork.condition_assoc, CategoryTheory.MonoidalClosed.whiskerLeft_curry_ihom_ev_app_assoc, HomologicalComplex.ιOrZero_mapBifunctorAssociatorX_hom_assoc, CategoryTheory.Limits.prodComparison_snd_assoc, CategoryTheory.Pseudofunctor.whiskerRightIso_mapId, CategoryTheory.Limits.limit.pre_π, CategoryTheory.Mathlib.Tactic.MonTauto.eq_one_mul, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.w_app_assoc, CategoryTheory.MonoidalCategory.associator_naturality_right_assoc, CategoryTheory.Pseudofunctor.Grothendieck.map_map_base, HomologicalComplex.homotopyCofiber.inrX_desc_f_assoc, CategoryTheory.Limits.prod_rightUnitor_inv_naturality, CategoryTheory.map_yonedaEquiv', AlgebraicGeometry.IsIntegralHom.comp_iff, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionHom, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_right_right, CategoryTheory.monoidalOfHasFiniteProducts.associator_inv, CategoryTheory.prod.functorProdToProdFunctorAssociator_hom_app, CategoryTheory.StructuredArrow.mapIso_counitIso_hom_app_right, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_associator_inv_as_app, CategoryTheory.Pseudofunctor.toOplax_mapComp', CategoryTheory.Limits.Cowedge.condition, CategoryTheory.GradedObject.ι_mapBifunctorComp₂₃MapObjIso_inv_assoc, CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_inv_assoc, CommMonCat.coyonedaType_map_app, CommRingCat.Under.equalizer_comp, HomologicalComplex.extendMap_id_f, CategoryTheory.CartesianMonoidalCategory.tensorHom_fst_assoc, CategoryTheory.Grp.id_hom_hom, CategoryTheory.Oplax.OplaxTrans.leftUnitor_inv_as_app, CategoryTheory.ObjectProperty.leftOrthogonal_iff, CategoryTheory.Functor.costructuredArrowMapCocone_ι_app, SSet.range_eq_iSup_of_isColimit, CategoryTheory.Adjunction.mapCommGrp_counit, CategoryTheory.Limits.initial.subsingleton_to, CategoryTheory.Over.iteratedSliceForwardIsoPost_hom_app, CategoryTheory.Meq.pullback_apply, CategoryTheory.Functor.map_sum, CategoryTheory.Cokleisli.Adjunction.toCokleisli_map, CategoryTheory.Limits.map_lift_piComparison, Rep.indResHomEquiv_symm_apply_hom, CategoryTheory.FreeBicategory.lift_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj, id_comp, CategoryTheory.Limits.coprod.map_map, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.secondMap_app_app_app, CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_inv_assoc, CategoryTheory.Join.inlCompFromSum_inv_app, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom, CategoryTheory.Limits.FormalCoproduct.pullbackCone_snd_φ, CategoryTheory.kernelCokernelCompSequence.ι_φ_assoc, CategoryTheory.Pretriangulated.id_hom₁, CategoryTheory.CategoryOfElements.toCostructuredArrow_map, CategoryTheory.Functor.mapTriangle_map_hom₂, CategoryTheory.Functor.toOplaxFunctor'_mapId, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom, HomologicalComplex.p_opcyclesMap_assoc, CategoryTheory.Pi.comapEvalIsoEval_hom_app, CategoryTheory.Limits.WidePullbackCone.condition, groupHomology.isoCycles₂_hom_comp_i_assoc, CategoryTheory.GrpObj.lift_inv_comp_right_assoc, CategoryTheory.ObjectProperty.isClosedUnderLimitsOfShape_iff_op, CategoryTheory.Bicategory.RightExtension.w, CategoryTheory.Functor.comp_mapCommMon_one, PresheafOfModules.pushforward_comp_id, CategoryTheory.Bicategory.Prod.fst_mapId_inv, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom, CategoryTheory.Equivalence.congrRight_counitIso_hom_app, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceFunctorProj_inv_app, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop_assoc, CategoryTheory.IsCardinalFiltered.coeq_condition, CategoryTheory.Functor.homEquivOfIsLeftKanExtension_apply_app, CategoryTheory.BasedNatTrans.app_isHomLift, CategoryTheory.Iso.map_inv_hom_id_eval_app_assoc, CategoryTheory.Oplax.OplaxTrans.Modification.id_app, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_hom_whiskerLeft_π, AlgebraicGeometry.Scheme.Pullback.diagonalCover_map, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_right_app, groupHomology.comp_d₃₂_eq, DerivedCategory.left_fac, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.sup_P, groupCohomology.π_comp_H2Iso_hom, CategoryTheory.ExponentiableMorphism.unit_pushforwardComp_hom_assoc, CategoryTheory.Subfunctor.Subpresheaf.lift_ι, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality, CategoryTheory.MorphismProperty.isomorphisms_op, CategoryTheory.MorphismProperty.CostructuredArrow.mk_hom, CategoryTheory.ObjectProperty.le_colimitsCardinalClosure, CategoryTheory.Sum.functorEquiv_counitIso, CategoryTheory.Idempotents.DoldKan.η_hom_app_f, groupHomology.chainsMap_f_0_comp_chainsIso₀, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_right, CategoryTheory.Limits.π_comp_opProductIsoCoproduct_hom, CategoryTheory.StrictlyUnitaryLaxFunctor.comp_obj, HomologicalComplex.restrictionCyclesIso_inv_iCycles, CategoryTheory.simplicialCosimplicialEquiv_functor_obj_map, AlgebraicGeometry.Scheme.inv_base_hom_base, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_left, CategoryTheory.Limits.biproduct.ι_π_self, AlgebraicGeometry.SheafedSpace.Γ_map_op, CategoryTheory.Over.tensorObj_hom, CategoryTheory.ShortComplex.mapLeftHomologyIso_inv_naturality_assoc, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_right, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_hom_iso, CategoryTheory.CartesianMonoidalCategory.tensorμ_snd_assoc, CategoryTheory.GradedObject.ι_mapBifunctorComp₁₂MapObjIso_inv_assoc, CategoryTheory.Pretriangulated.preadditiveCoyoneda_homologySequenceδ_apply, Profinite.exists_hom, CategoryTheory.Bicategory.mateEquiv_apply', CategoryTheory.StructuredArrow.toCostructuredArrow_obj, CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_snd_snd, CategoryTheory.CosimplicialObject.δ_comp_σ_self'_assoc, CategoryTheory.nerve.edgeMk_surjective, SSet.ι₁_comp_assoc, CategoryTheory.Limits.image.compIso_inv_comp_image_ι, CategoryTheory.Mon_Class.mul_mul_mul_comm', CategoryTheory.Bicategory.Equivalence.left_triangle_hom, CategoryTheory.Presheaf.isLocallyInjective_comp, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm_assoc, Action.FintypeCat.toEndHom_trivial_of_mem, CategoryTheory.Monad.Algebra.Hom.h_assoc, CategoryTheory.Adjunction.Triple.leftToRight_app_map_adj₁_unit_app, CategoryTheory.Sigma.inclDesc_hom_app, DistLat.ofHom_comp, CategoryTheory.Over.postAdjunctionLeft_counit_app_left, CategoryTheory.Preadditive.coforkOfCokernelCofork_pt, CategoryTheory.Limits.ι_colimitConstInitial_hom_assoc, CategoryTheory.SimplicialObject.δ_comp_δ_self'_assoc, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_symm_apply, CategoryTheory.Pretriangulated.Triangle.zero_hom₂, CategoryTheory.Comon.id_hom', CategoryTheory.Square.unop_f₃₄, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_left_hom, CategoryTheory.mop_id_unmop, NonemptyFinLinOrd.hom_id, AlgebraicGeometry.PresheafedSpace.stalkMap.congr_point, CategoryTheory.Bicategory.conjugateEquiv_comp, CategoryTheory.OplaxFunctor.mapComp_id_left, CategoryTheory.LaxFunctor.map₂_leftUnitor_app_assoc, CategoryTheory.epi_iff_forall_injective, HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac'_assoc, CategoryTheory.Comma.mapRightComp_inv_app_left, CategoryTheory.GradedNatTrans.naturality, CategoryTheory.Subobject.map_id, CategoryTheory.Cat.eqToHom_app, skyscraperPresheaf_map, CategoryTheory.ShortComplex.HomologyMapData.id_left, CategoryTheory.Presieve.bindOfArrows_ofArrows, CategoryTheory.Arrow.iso_w', HomologicalComplex₂.ιTotal_map_assoc, CategoryTheory.Limits.Sigma.ι_reindex_inv_assoc, CategoryTheory.ShortComplex.rightHomologyι_naturality_assoc, CategoryTheory.Limits.prod.lift_fst_snd, CategoryTheory.StructuredArrow.mapIso_counitIso_inv_app_right, CategoryTheory.Mod_.id_hom', GrpCat.coe_id, CategoryTheory.ShiftMkCore.assoc_hom_app_assoc, CategoryTheory.Equivalence.changeFunctor_counitIso_inv_app, CategoryTheory.MonoidalCategory.leftUnitor_inv_tensor_id, CategoryTheory.GradedObject.ι_mapTrifunctorMapMap, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_symm, CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor, CategoryTheory.Endofunctor.Algebra.Initial.left_inv, AlgebraicGeometry.Scheme.Cover.ι_fromGlued, AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_app, SkyscraperPresheafFunctor.map'_id, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_fst, AlgebraicGeometry.Scheme.Hom.inl_toNormalization_normalizationCoprodIso_inv, HomologicalComplex.ι_mapBifunctorFlipIso_inv, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_three_assoc, StalkSkyscraperPresheafAdjunctionAuxs.toSkyscraperPresheaf_app, AddMagmaCat.hom_comp, AlgebraicGeometry.Scheme.Hom.inr_normalizationCoprodIso_hom_fromNormalization, SSet.PtSimplex.RelStruct.δ_succ_map_assoc, AlgebraicGeometry.Scheme.Hom.appIso_inv_appLE, CategoryTheory.ShortComplex.mapHomologyIso'_inv_naturality_assoc, CategoryTheory.unmop_id_mop, HomologicalComplex.homologyπ_restrictionHomologyIso_hom_assoc, CategoryTheory.IsReflexivePair.common_section', CategoryTheory.BraidedCategory.braiding_tensor_right_inv, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply_assoc, CategoryTheory.BasedNatTrans.isHomLift, CategoryTheory.Adjunction.Triple.rightToLeft_app_adj₂_unit_app_assoc, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_inv, CategoryTheory.Comma.mapRightIso_unitIso_hom_app_right, CategoryTheory.Over.mapComp_inv_app_left, AlgebraicGeometry.Scheme.Modules.map_smul, CategoryTheory.GlueData.diagramIso_hom_app_left, CategoryTheory.PreGaloisCategory.PointedGaloisObject.id_val, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_inv_assoc, HomologicalComplex.homologyι_naturality_assoc, CategoryTheory.MorphismProperty.instIsStableUnderBaseChangeAlongCompOfHasPullbacksAlong, CategoryTheory.IsCardinalFiltered.multicoequalizer, ModuleCat.extendScalars_assoc, CochainComplex.HomComplex.CohomologyClass.homAddEquiv_apply, CategoryTheory.CosimplicialObject.id_left, CategoryTheory.Equivalence.congrRight_unitIso_inv_app, CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_right_assoc, CategoryTheory.Limits.ker_map, CategoryTheory.Adjunction.shift_counit_app_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor, CategoryTheory.GradedObject.Monoidal.tensorObj_ext_iff, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_right, AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom_id, CategoryTheory.shift_neg_shift', CategoryTheory.Limits.hasKernel_iso_comp, TopCat.piIsoPi_inv_π_assoc, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerLeft, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality_assoc, CategoryTheory.Bicategory.triangle_assoc_comp_right_assoc, CategoryTheory.MorphismProperty.Comma.hasLimit_of_closedUnderLimitsOfShape, CategoryTheory.Grothendieck.ι_map, CategoryTheory.ihom.coev_ev_assoc, CategoryTheory.ShortComplex.f_pOpcycles, SheafOfModules.pushforwardNatTrans_comp, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_hom_whiskerRight_π, CategoryTheory.Functor.mapLinearMap_apply, groupCohomology.isoCocycles₂_inv_comp_iCocycles_assoc, CategoryTheory.ShortComplex.leftHomologyMap'_op, CategoryTheory.shrinkYonedaEquiv_shrinkYoneda_map, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_counit, CategoryTheory.Adjunction.mapGrp_counit, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_counitIso_hom, CategoryTheory.ObjectProperty.instSmallUnopOfOpposite, CategoryTheory.Functor.liftOfIsRightKanExtension_fac_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_obj_obj_map, CategoryTheory.Equivalence.functor_unit_comp_assoc, CategoryTheory.Mon_Class.mul_mul_mul_comm, CategoryTheory.Limits.ConeMorphism.inv_hom_id, SimplexCategory.δ_comp_σ_self'_assoc, CategoryTheory.Functor.comp_mapGrp_one, HomotopicalAlgebra.AttachCells.hm, CategoryTheory.enrichedNatTransYoneda_map_app, CategoryTheory.yonedaGrp_naturality, CategoryTheory.Functor.homologySequence_epi_shift_map_mor₂_iff, CategoryTheory.Under.comp_right, CategoryTheory.Pi.comapComp_inv_app, HomologicalComplex.cylinder.πCompι₀Homotopy.inlX_nullHomotopy_f, CategoryTheory.Adjunction.unit_naturality_assoc, CategoryTheory.Functor.FullyFaithful.preimage_id, CategoryTheory.WithTerminal.opEquiv_inverse_map, CategoryTheory.Arrow.squareToSnd_right, CategoryTheory.Functor.PullbackObjObj.isPullback, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_inv_app_fst_app, CategoryTheory.ShiftMkCore.assoc_inv_app, Subobject.presheaf_map, CategoryTheory.constantPresheafAdj_unit_app, AlgebraicGeometry.sourceLocalClosure.le, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app_assoc, CategoryTheory.Subfunctor.toRange_ι, CategoryTheory.leftDistributor_ext_left_iff, AlgebraicGeometry.pointOfClosedPoint_comp, HomologicalComplex₂.totalFlipIso_hom_f_D₂_assoc, CategoryTheory.Limits.limitRightOpIsoOpColimit_inv_comp_π, CategoryTheory.Iso.inv_hom_id_eval, CategoryTheory.SemiCartesianMonoidalCategory.comp_toUnit, HomologicalComplex.pOpcycles_restrictionOpcyclesIso_hom, CategoryTheory.Limits.pullbackAssoc_inv_fst_fst, CategoryTheory.Limits.limit_map_limitObjIsoLimitCompEvaluation_hom, CategoryTheory.Equivalence.symmEquivInverse_map_app, CategoryTheory.prod.associator_map, HomologicalComplex₂.ι_totalShift₁Iso_hom_f, SSet.StrictSegal.spineToSimplex_vertex, AlgebraicGeometry.SheafedSpace.comp_c_app', CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict, Rep.norm_comm, CategoryTheory.ShiftedHom.opEquiv'_add_symm, CategoryTheory.PreOneHypercover.cylinder_Y, CategoryTheory.Sigma.inclDesc_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_hom_app, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_inv_fac, CategoryTheory.Functor.functorHomEquiv_symm_apply_app_app, CategoryTheory.MorphismProperty.Over.map_obj_hom, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_map₂, CategoryTheory.Mon.Hom.hom_one, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_hom, CategoryTheory.CostructuredArrow.IsUniversal.hom_desc, CategoryTheory.Adjunction.Triple.mono_leftToRight_app_iff, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app, CategoryTheory.Idempotents.Karoubi.p_comm, Bimod.LeftUnitorBimod.hom_left_act_hom', CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst_assoc, AddCommGrpCat.hom_zsmul, CategoryTheory.PreGaloisCategory.autMap_id, CategoryTheory.Pi.comapId_hom_app, SSet.Truncated.Edge.tgt_eq, CategoryTheory.Limits.coprodComparison_natural, HomologicalComplex.forgetEval_inv_app, CategoryTheory.colimitYonedaHomEquiv_π_apply, CategoryTheory.Equivalence.induced_counitIso, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_inv_assoc, CategoryTheory.Adjunction.comp_unit_app, CategoryTheory.heq_eqToHom_comp_iff, AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalk_assoc, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_inv_ι, AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ_assoc, CategoryTheory.ObjectProperty.le_shift, CategoryTheory.ParametrizedAdjunction.whiskerLeft_map_counit_assoc, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_apply, CategoryTheory.Functor.Monoidal.μ_δ_assoc, CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_inv_comp_iCycles, AlgebraicGeometry.PresheafedSpace.ofRestrict_c_app, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd_assoc, CategoryTheory.Limits.SequentialProduct.functorMap_commSq, AlgebraicGeometry.descendsAlong_universallyInjective_surjective_inf_flat_inf_quasicompact, CategoryTheory.ShortComplex.Splitting.s_r_assoc, AddSemigrp.ofHom_id, CategoryTheory.mono_iff_forall_injective, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_iff, CategoryTheory.ShortComplex.opcyclesMap'_zero, CategoryTheory.Limits.WidePushout.arrow_ι_assoc, CategoryTheory.MorphismProperty.instFaithfulUnderTopUnderForget, CategoryTheory.Limits.pullbackObjIso_hom_comp_snd, CategoryTheory.ComposableArrows.IsComplex.cokerToKer_fac_assoc, CategoryTheory.dcongr_arg, CategoryTheory.MonoidalCategory.associator_naturality_right, Action.FunctorCategoryEquivalence.functor_ε, CategoryTheory.Square.Hom.comp_τ₃, CategoryTheory.ShortComplex.leftHomologyMap_neg, CategoryTheory.MonoidalCategory.MonoidalLeftAction.inv_hom_actionHomLeft', CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.fac, CategoryTheory.Limits.biprod.ext_from_iff, CategoryTheory.kernelCokernelCompSequence.φ_π_assoc, CategoryTheory.Comon.monoidal_tensorObj_comon_comul, CategoryTheory.Bimon.trivial_X_mon_one, CategoryTheory.uliftCoyonedaEquiv_comp, CategoryTheory.Limits.imageSubobject_factors_comp_self, CategoryTheory.IsHomLift.fac, CategoryTheory.Cat.freeMapCompIso_inv_app, ContinuousMap.Homotopy.eq_diag_path, CategoryTheory.Functor.IsCoverDense.Types.naturality_assoc, CategoryTheory.Abelian.PreservesCoimage.iso_hom_π, CategoryTheory.MorphismProperty.Comma.id_right, CategoryTheory.Arrow.mk_eq_mk_iff, Action.FintypeCat.ofMulAction_apply, AlgebraicGeometry.LocallyRingedSpace.comp_c, CategoryTheory.monoidalOfHasFiniteProducts.associator_inv_fst_fst, MagmaCat.ofHom_comp, AlgebraicGeometry.Scheme.Opens.isoOfLE_inv_ι_assoc, CategoryTheory.Mon.tensor_mul, CategoryTheory.Limits.colimitFlipIsoCompColim_inv_app, CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_hom_hom_assoc, CategoryTheory.LaxFunctor.PseudoCore.mapIdIso_inv, CategoryTheory.CatEnrichedOrdinary.Hom.base_id, CategoryTheory.yonedaEquiv_symm_app_apply, CategoryTheory.MorphismProperty.multiplicativeClosure_le_iff, CategoryTheory.Limits.MonoFactorisation.ofIsoComp_m, CategoryTheory.MonObj.mul_assoc_flip, CategoryTheory.Adjunction.leftAdjointCompNatTrans_app, CategoryTheory.IsSplitEqualizer.condition, CategoryTheory.Functor.map_inv_hom, CategoryTheory.TwoSquare.vId_app, CategoryTheory.MorphismProperty.le_transfiniteCompositions, CategoryTheory.Bicategory.leftUnitor_comp_assoc, SemimoduleCat.homAddEquiv_symm_apply_hom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_hom_app, CategoryTheory.Functor.mapCommMonCompIso_hom_app_hom_hom, CategoryTheory.associator_hom, CategoryTheory.Arrow.equivSigma_symm_apply_right, CategoryTheory.Limits.inr_comp_pushoutComparison, FDRep.finrank_hom_simple_simple, CategoryTheory.Enriched.FunctorCategory.enriched_comp_id, CategoryTheory.WithTerminal.coneEquiv_functor_map_hom, CategoryTheory.Bicategory.LeftLift.w, CategoryTheory.Limits.biproduct.map_desc_assoc, SSet.PtSimplex.MulStruct.δ_castSucc_castSucc_map, HomologicalComplex.mapBifunctor₂₃.ι_D₂_assoc, CategoryTheory.Join.mapIsoWhiskerRight_inv_app, CategoryTheory.Limits.ι_comp_colimitUnopIsoOpLimit_hom, CategoryTheory.Pseudofunctor.mapId'_inv_naturality, CategoryTheory.LaxFunctor.mapComp_naturality_left_assoc, CategoryTheory.tensorLeftHomEquiv_symm_naturality, CategoryTheory.Functor.map_surjective, CategoryTheory.Monad.algebraFunctorOfMonadHom_map_f, AlgebraicGeometry.Scheme.Spec_fromSpecStalk, CategoryTheory.nerve.homEquiv_symm_apply, CategoryTheory.Functor.op_map, CategoryTheory.functorProdFunctorEquivCounitIso_hom_app_app, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_right_assoc, CategoryTheory.Limits.Pi.map_comp_map', CochainComplex.ι_mapBifunctorShift₁Iso_hom_f, CategoryTheory.Limits.pullback_equalizer, groupHomology.chainsMap_f, CategoryTheory.mono_to_simple_zero_of_not_iso, SSet.RelativeMorphism.Homotopy.rel_assoc, CategoryTheory.MorphismProperty.toSet_iSup, CategoryTheory.Functor.Monoidal.η_ε, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left, CategoryTheory.NatTrans.unop_comp, SheafOfModules.unitHomEquiv_apply_coe, CategoryTheory.Monad.right_unit_assoc, AlgebraicTopology.DoldKan.PInfty_add_QInfty, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_app_assoc, CategoryTheory.types_comp_apply, CategoryTheory.preadditiveYonedaObj_map, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInlIso_inv_app_app, AddGrpCat.coe_id, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_app, CategoryTheory.ShortComplex.f_pOpcycles_assoc, CategoryTheory.Limits.pullbackProdSndIsoProd_hom_fst_assoc, CategoryTheory.ShortComplex.ShortExact.comp_δ_assoc, CategoryTheory.MonoidalClosed.id_comp_assoc, CategoryTheory.ShortComplex.π_homologyMap_ι, AlgebraicGeometry.exists_etale_isCompl_of_quasiFiniteAt, CategoryTheory.Limits.Pi.map'_comp_π, AlgebraicTopology.DoldKan.Q_f_idem, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_assoc, CategoryTheory.prod.inverseAssociator_map, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π, CategoryTheory.Limits.CatCospanTransform.rightUnitor_hom_right_app, CategoryTheory.mateEquiv_apply, AlgebraicGeometry.morphismRestrict_id, CategoryTheory.Functor.structuredArrowMapCone_π_app, CategoryTheory.Functor.whiskeringLeftObjCompIso_inv_app_app, CategoryTheory.Limits.biprod.inl_fst_assoc, groupCohomology.map_comp_assoc, CategoryTheory.eHom_whisker_exchange, CategoryTheory.sheafCompose_comp, groupHomology.cyclesMap_comp_isoCycles₁_hom, CategoryTheory.Limits.IsLimit.homEquiv_apply, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd_assoc, CategoryTheory.IsCardinalFiltered.coeq_condition_assoc, CategoryTheory.ShortComplex.mapHomologyIso'_inv_naturality, groupCohomology.cochainsMap_id, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_inv_app_fst_app, CategoryTheory.ShortComplex.mapCyclesIso_hom_naturality, CochainComplex.HomComplex.Cochain.single_v_eq_zero, CategoryTheory.CartesianMonoidalCategory.lift_braiding_inv_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_app, CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_id, CategoryTheory.ShortComplex.cyclesOpIso_hom_naturality_assoc, CategoryTheory.CartesianMonoidalCategory.whiskerRight_snd, CategoryTheory.IsFiltered.wideSpan, CategoryTheory.CartesianMonoidalCategory.whiskerRight_toUnit_comp_leftUnitor_hom_assoc, CategoryTheory.Limits.cokernel.condition_apply, CategoryTheory.Limits.Multifork.pi_condition, HomologicalComplex.Hom.prev_eq, CategoryTheory.InjectiveResolution.cochainComplex_d, CategoryTheory.Quotient.comp_natTransLift, AlgebraicGeometry.tilde.toOpen_map_app, CategoryTheory.Limits.compYonedaSectionsEquiv_symm_apply_coe, CategoryTheory.Limits.KernelFork.map_condition_assoc, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_comp, groupCohomology.d₀₁_eq_zero, CategoryTheory.ComposableArrows.Precomp.map_one_one, CategoryTheory.Limits.biproduct.ι_fromSubtype, CategoryTheory.yonedaEquiv_comp, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app_assoc, CategoryTheory.OverPresheafAux.counitForward_naturality₂, CategoryTheory.Limits.ColimitPresentation.self_ι, CategoryTheory.ObjectProperty.prop_iSup_iff, CategoryTheory.Functor.Monoidal.whiskerLeft_δ_μ_assoc, CochainComplex.mappingCone.map_δ, CategoryTheory.ShortComplex.RightHomologyData.p_g', HomologicalComplex₂.ιTotal_totalFlipIso_f_inv, CategoryTheory.Limits.MonoFactorisation.ofCompIso_e, CategoryTheory.unitCompPartialBijective_symm_apply, CochainComplex.HomComplex.Cochain.ofHom_comp, CategoryTheory.MorphismProperty.transfiniteCompositions_le_iff, CategoryTheory.ihom.coev_ev, AlgebraicGeometry.instIsSchemeTheoreticallyDominantCompScheme, CategoryTheory.eqToHom_comp_homOfLE_assoc, CategoryTheory.Limits.hasKernel_comp_mono, AlgebraicGeometry.Spec.preimage_comp, CategoryTheory.PreGaloisCategory.functorToAction_comp_forget₂_eq, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_εIso_hom, CategoryTheory.Comon.ComonToMonOpOpObj_mon_one, TopologicalSpace.Opens.map_id_eq, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map, CategoryTheory.Bicategory.triangle_assoc_comp_left_inv_assoc, CategoryTheory.Monad.ForgetCreatesColimits.newCocone_ι, CategoryTheory.Functor.currying_inverse_obj_map_app, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right, CategoryTheory.Limits.parallelPairOpIso_hom_app_zero, CategoryTheory.Functor.IsCoverDense.Types.naturality, CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_map, CategoryTheory.Limits.FormalCoproduct.hom_ext_iff', CategoryTheory.Localization.structuredArrowEquiv_apply, CategoryTheory.whiskerLeft_coprod_inr_leftDistrib_inv_assoc, CategoryTheory.LocalizerMorphism.isLeftDerivabilityStructure_iff_op, AlgebraicGeometry.LocallyRingedSpace.stalkMap_germ, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerRight_naturality_assoc, CategoryTheory.Limits.kernelSubobjectMap_id, CategoryTheory.Prefunctor.mapPath_comp', CategoryTheory.CosimplicialObject.δ_comp_σ_of_le_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHom_def'_assoc, AlgebraicGeometry.Scheme.Hom.id_image, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_hom, SimplexCategory.morphismProperty_eq_top, SemimoduleCat.MonoidalCategory.id_tensorHom_id, CategoryTheory.GrothendieckTopology.Cover.Arrow.Relation.w_assoc, CategoryTheory.Limits.kernelSubobject_zero, CategoryTheory.Limits.Bicone.ι_of_isLimit, HomologicalComplex.Hom.sqFrom_id, AlgebraicGeometry.pullbackSpecIso_hom_snd_assoc

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp toCategoryStruct	—	—
assoc' 📖	mathematical	—	CategoryTheory.CategoryStruct.comp toCategoryStruct	—	assoc
comp_id 📖	mathematical	—	CategoryTheory.CategoryStruct.comp toCategoryStruct CategoryTheory.CategoryStruct.id	—	—
id_comp 📖	mathematical	—	CategoryTheory.CategoryStruct.comp toCategoryStruct CategoryTheory.CategoryStruct.id	—	—

CategoryTheory.CategoryStruct

Definitions

Name	Category	Theorems
comp 📖	CompOp	10736 math math: CategoryTheory.Equivalence.adjointify_η_ε_assoc, CategoryTheory.biconeCategoryStruct_comp, CategoryTheory.Limits.MonoFactorisation.fac, CategoryTheory.Functor.inr_biprodComparison', CategoryTheory.Limits.Trident.condition_assoc, CategoryTheory.Limits.limMap_π, CategoryTheory.Localization.Monoidal.leftUnitor_hom_app, CategoryTheory.Iso.inv_hom_id_triangle_hom₃_assoc, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_right, CategoryTheory.shiftFunctorZero_inv_app_obj_of_induced, CategoryTheory.Comon.tensorObj_comul', CategoryTheory.Triangulated.SpectralObject.Hom.comm, CategoryTheory.Bicategory.iterated_mateEquiv_conjugateEquiv, AlgebraicGeometry.Scheme.Hom.resLE_map_assoc, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d, SemimoduleCat.MonoidalCategory.triangle, CategoryTheory.Functor.relativelyRepresentable.pullback₃.snd_fst'_eq_p₁, CategoryTheory.Limits.kernelSubobjectMap_arrow_assoc, CategoryTheory.Limits.IsImage.e_isoExt_inv, CategoryTheory.Over.associator_hom_left_snd_fst_assoc, AlgebraicGeometry.Γ_map_morphismRestrict, SimplexCategoryGenRel.σ_comp_σ, CategoryTheory.MorphismProperty.LeftFraction.map_compatibility, CategoryTheory.Limits.pushoutIsoOpPullback_inr_hom_assoc, CategoryTheory.Limits.Fork.IsLimit.homIso_natural, CategoryTheory.Limits.Cocones.precompose_obj_ι, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyπ_comp_leftHomologyIso_hom, CategoryTheory.Grp.comp', CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_eq, SemiNormedGrp₁.comp_apply, CategoryTheory.CostructuredArrow.homMk'_id, CategoryTheory.InjectiveResolution.Hom.hom'_f, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π, AlgebraicGeometry.AffineSpace.map_Spec_map, CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv_assoc, CategoryTheory.ShortComplex.toCycles_comp_homologyπ, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_fst, SimplicialObject.Splitting.cofan_inj_πSummand_eq_id_assoc, HomologicalComplex.pOpcycles_restrictionOpcyclesIso_hom_assoc, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_assoc, CategoryTheory.MonoidalCategory.tensor_left_unitality, CategoryTheory.Bicategory.prod_whiskerLeft_snd, CategoryTheory.Functor.eventualRange_eq_range_precomp, CategoryTheory.Limits.hasPullbackVertPaste, CategoryTheory.Over.prodLeftIsoPullback_hom_snd_assoc, SSet.Subcomplex.lift_ι, CommRingCat.HomTopology.isEmbedding_precomp_of_surjective, CategoryTheory.Functor.CommShift.isoAdd_hom_app, PresheafOfModules.instIsRightAdjointPushforwardCompFunctorOppositeRingCatWhiskerLeftOp, CategoryTheory.Adjunction.compUliftCoyonedaIso_hom_app_app_down, SimplexCategory.δ_comp_δ', smoothSheafCommRing.ι_forgetStalk_inv, CategoryTheory.ShortComplex.toCycles_comp_homologyπ_assoc, AlgebraicTopology.DoldKan.PInfty_comp_PInftyToNormalizedMooreComplex, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.hπ_assoc, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_map, CategoryTheory.GrpObj.lift_inv_comp_left, CategoryTheory.MonoidalCategory.associator_naturality_middle_assoc, groupHomology.π_comp_H2Iso_hom_assoc, CategoryTheory.PreOneHypercover.forkOfIsColimit_ι_map_inj_assoc, AddCommGrpCat.image.lift_fac, CategoryTheory.BraidedCategory.braiding_naturality_right, CategoryTheory.ShortComplex.Homotopy.h₀_f_assoc, CategoryTheory.Sum.natTransOfWhiskerLeftInlInr_app, SheafOfModules.pushforward_assoc, CategoryTheory.biproduct_ι_comp_leftDistributor_hom_assoc, CategoryTheory.Subobject.map_mk, CommRingCat.HomTopology.isClosedEmbedding_precomp_of_surjective, Bicategory.Opposite.op2_associator, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_inv_fac_app, AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality_assoc, CochainComplex.mappingConeCompTriangleh_comm₁_assoc, HomologicalComplex₂.totalAux.ιMapObj_D₁, CategoryTheory.Mat_.additiveObjIsoBiproduct_hom_π, CategoryTheory.Functor.PushoutObjObj.inr_ι, AlgebraicGeometry.Proj.awayMap_awayToSection_assoc, HomologicalComplex.extendSingleIso_inv_f, LightCondensed.free_internallyProjective_iff_tensor_condition, CategoryTheory.Over.μ_pullback_left_snd', CategoryTheory.Monad.ForgetCreatesColimits.commuting, CategoryTheory.mateEquiv_counit_symm, HomologicalComplex.restrictionToTruncGE'_f_eq_iso_hom_pOpcycles_iso_inv, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst_assoc, CategoryTheory.GrpObj.inv_hom, CategoryTheory.MonoidalCategory.DayConvolution.braidingHomCorepresenting_app, AlgebraicGeometry.Scheme.Hom.toPartialMap_hom, CategoryTheory.Bicategory.RightExtension.w_assoc, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_apply, CategoryTheory.kernelCokernelCompSequence.snakeInput_v₀₁_τ₂, HomotopicalAlgebra.LeftHomotopyRel.postcomp, CategoryTheory.Limits.imageSubobject_arrow_assoc, CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc, CategoryTheory.Subobject.factorThru_right, CommAlgCat.comp_apply, CategoryTheory.Oplax.StrongTrans.Modification.vcomp_app, CategoryTheory.Sieve.pullback_apply, CategoryTheory.StructuredArrow.map_map_right, CategoryTheory.ModObj.one_smul_assoc, CategoryTheory.tensorLeftHomEquiv_symm_coevaluation_comp_whiskerLeft, CategoryTheory.Functor.OplaxMonoidal.δ_comp_tensorHom_η, CategoryTheory.eHom_whisker_cancel, CategoryTheory.Pseudofunctor.map₂_associator_assoc, CategoryTheory.shiftFunctorAdd'_assoc_inv_app, CategoryTheory.instEffectiveEpiFamilyCompOfIsSplitEpi, CategoryTheory.Functor.partialRightAdjointHomEquiv_comp_symm, CategoryTheory.Limits.Multiequalizer.condition_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst_assoc, CategoryTheory.ShortComplex.SnakeInput.w₀₂_assoc, CategoryTheory.Sheaf.ΓHomEquiv_naturality_left_symm, CategoryTheory.preadditiveCoyonedaObj_map, CategoryTheory.Functor.LaxMonoidal.associativity_assoc, CategoryTheory.CosimplicialObject.δ_comp_δ_self_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.unit_actionHomRight_assoc, CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_p, CategoryTheory.Functor.OplaxMonoidal.associativity, AlgebraicTopology.DoldKan.Compatibility.equivalence₀_unitIso_hom_app, CategoryTheory.CommSq.fac_right_assoc, CategoryTheory.Idempotents.app_idem_assoc, CategoryTheory.PreZeroHypercover.inv_hom_h₀, CategoryTheory.Limits.imageSubobjectCompIso_hom_arrow, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_three_assoc, ModuleCat.biproductIsoPi_inv_comp_π, CategoryTheory.CatEnrichedOrdinary.id_hComp_heq, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app', CategoryTheory.SingleFunctors.Hom.comm, CategoryTheory.LaxFunctor.map₂_associator_assoc, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app, CategoryTheory.Functor.OfSequence.congr_f, CategoryTheory.ShortComplex.homologyι_naturality, CategoryTheory.Limits.image.isIso_precomp_iso, CategoryTheory.GrothendieckTopology.toPlus_plusLift_assoc, CategoryTheory.CartesianMonoidalCategory.prodComparison_snd, CategoryTheory.Limits.coprod.inl_snd, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.CartesianMonoidalCategory.tensorδ_snd, groupHomology.mapCycles₂_comp_assoc, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv_assoc, CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux_fac, CategoryTheory.Functor.liftOfIsRightKanExtension_fac, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_appTop, LightProfinite.proj_comp_transitionMap, CategoryTheory.Limits.hasPushout_assoc, HomologicalComplex.dFrom_comp_xNextIsoSelf, AlgebraicGeometry.AffineSpace.map_toSpecMvPoly_assoc, CategoryTheory.Subobject.underlyingIso_hom_comp_eq_mk_assoc, SimplexCategory.Truncated.δ₂_two_comp_σ₂_one_assoc, CategoryTheory.Limits.biproduct.mapBiproduct_inv_map_desc, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp_inv_app_f, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo, CategoryTheory.Preadditive.IsIso.comp_left_eq_zero, CategoryTheory.Presieve.uncurry_bind, CategoryTheory.Localization.Monoidal.whiskerLeft_comp, CategoryTheory.evaluationLeftAdjoint_map_app, CategoryTheory.MonoidalCategory.hom_inv_whiskerRight', CategoryTheory.Bicategory.Adj.rightUnitor_hom_τl, CategoryTheory.DifferentialObject.shiftFunctor_obj_d, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_hom_inv_assoc, CategoryTheory.StructuredArrow.map_comp, CochainComplex.mappingCone.δ_inl, CategoryTheory.Limits.colimitHomIsoLimitYoneda_hom_comp_π, CochainComplex.mappingCone.inl_v_descCochain_v_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_naturality_assoc, HomotopicalAlgebra.PrepathObject.p_fst_assoc, TopCat.pullbackIsoProdSubtype_hom_fst, CategoryTheory.ShortComplex.SnakeInput.naturality_φ₁, CategoryTheory.IsPullback.isoIsPullback_inv_snd_assoc, AlgebraicGeometry.AffineSpace.map_reindex, CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj_map_f, CategoryTheory.IsHomLift.comp_lift_id_right', CategoryTheory.Lax.LaxTrans.comp_naturality, AlgebraicGeometry.IsAffineOpen.map_fromSpec_assoc, CategoryTheory.DinatTrans.dinaturality_assoc, CategoryTheory.Cat.Hom₂.comp_app, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_fst_assoc, AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_fst, CategoryTheory.Functor.rightKanExtensionUniqueOfIso_hom, CategoryTheory.ihom.coev_naturality, CategoryTheory.obj_ε_app_assoc, HomologicalComplex.rightUnitor'_inv, CategoryTheory.ShortComplex.fromOpcycles_naturality, AlgebraicGeometry.LocallyRingedSpace.residueFieldMap_comp, CategoryTheory.SimplicialObject.δ_comp_δ_self_assoc, CategoryTheory.ShortComplex.Homotopy.comm₁, HomologicalComplex.π_homologyIsoSc'_hom, CategoryTheory.MonoidalCategory.tensorμ_natural_assoc, CategoryTheory.ShortComplex.HomologyData.ofIso_right_p, CategoryTheory.Bicategory.Comonad.comul_assoc_flip, HomotopyCategory.quotient_map_out_comp_out, Mathlib.Tactic.Bicategory.evalWhiskerLeft_nil, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_hom_inv', CategoryTheory.ShortComplex.Homotopy.comp_h₃, CategoryTheory.Limits.limitUnopIsoUnopColimit_hom_comp_ι, CategoryTheory.Cat.whiskerRight_toNatTrans, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_associator, AlgebraicGeometry.Scheme.Hom.germ_stalkMap_assoc, AlgebraicGeometry.IsProper.instCompScheme, groupCohomology.toCocycles_comp_isoCocycles₁_hom, HomologicalComplex.mapBifunctor.ι_D₂, CategoryTheory.Functor.OplaxMonoidal.δ_natural_left_assoc, CategoryTheory.Limits.Types.Small.productIso_hom_comp_eval, HomologicalComplex.homologyπ_extendHomologyIso_hom, AlgebraicGeometry.Scheme.Cover.gluedCoverT'_snd_snd_assoc, CategoryTheory.ShortComplex.opcyclesIsoRightHomology_hom_inv_id, CategoryTheory.MonoidalCategory.tensorμ_tensorδ_assoc, CategoryTheory.Limits.biprod.lift_eq, CategoryTheory.ShortComplex.RightHomologyData.ι_g', CategoryTheory.OplaxFunctor.id_mapComp, CategoryTheory.Limits.ConeMorphism.hom_inv_id, HomologicalComplex.mapBifunctor₁₂.ι_D₃_assoc, AlgebraicGeometry.Scheme.Spec_map_stalkMap_fromSpecStalk, DerivedCategory.right_fac, CategoryTheory.Limits.map_ι_comp_inv_sigmaComparison_assoc, CategoryTheory.Bicategory.InducedBicategory.bicategory_whiskerLeft_hom, CategoryTheory.Quiv.comp_eq_comp, CategoryTheory.Limits.wideCoequalizer.condition, CategoryTheory.BraidedCategory.braiding_tensor_right_hom, CategoryTheory.ShortComplex.SnakeInput.comp_f₃_assoc, CategoryTheory.Functor.LaxMonoidal.whiskerLeft_μ_comp_μ_assoc, CategoryTheory.ShortComplex.cyclesOpIso_inv_op_iCycles_assoc, CategoryTheory.CosimplicialObject.comp_app, CategoryTheory.composePath_comp', CategoryTheory.EnrichedOrdinaryCategory.homEquiv_comp, CategoryTheory.Limits.PreservesPushout.inr_iso_inv_assoc, CategoryTheory.Functor.ι_colimitIsoOfIsLeftKanExtension_inv_assoc, CategoryTheory.Functor.shiftIso_add_inv_app, CategoryTheory.Bicategory.Adj.comp_r, CategoryTheory.Comma.mapLeftIso_inverse_map_right, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_snd, CategoryTheory.Subobject.imageFactorisation_F_m, CategoryTheory.MonoidalCategory.DayConvolution.unit_naturality, AlgebraicGeometry.PresheafedSpace.stalkMap_germ, CategoryTheory.Iso.eHomCongr_inv_comp_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_hom_app_eq, CategoryTheory.shiftFunctorComm_zero_hom_app, CategoryTheory.IsPullback.isoIsPullback_inv_snd, CategoryTheory.ShortComplex.cokernel_π_comp_cokernelToAbelianCoimage_assoc, CategoryTheory.NatTrans.rightDerived_comp_assoc, CategoryTheory.ShortComplex.pOpcycles_π_isoOpcyclesOfIsColimit_inv_assoc, HomologicalComplex₂.totalFlipIso_hom_f_D₁, AddCommGrpCat.comp_apply, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_map_left, CategoryTheory.Equivalence.comp_asNatTrans, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_naturality_assoc, CategoryTheory.MonoidalCategory.rightUnitor_monoidal_assoc, HomologicalComplex.singleMapHomologicalComplex_hom_app_self, CategoryTheory.Subobject.underlyingIso_arrow_assoc, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_two, CategoryTheory.Limits.coprod.inl_fst, CategoryTheory.GradedObject.ι_mapBifunctorMapMap, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_hom_app_app_down, HomologicalComplex.πTruncGE_naturality_assoc, CategoryTheory.ShortComplex.homologyOpIso_hom_naturality, CategoryTheory.Abelian.PreservesCoimage.iso_hom_π_assoc, CategoryTheory.ComposableArrows.IsComplex.zero'_assoc, AlgebraicGeometry.Scheme.PartialMap.ext_iff, CategoryTheory.Functor.LeftExtension.precomp₂_obj_hom_app, HomologicalComplex.singleObjHomologySelfIso_hom_singleObjOpcyclesSelfIso_hom_assoc, AddMagmaCat.ofHom_comp, CategoryTheory.CostructuredArrow.map_comp, SSet.PtSimplex.RelStruct.δ_map_of_lt, SSet.Subcomplex.toRange_ι, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.lift_fac, Bimod.TensorBimod.π_tensor_id_actRight, CategoryTheory.Limits.Cotrident.ofCocone_ι, TopCat.GlueData.preimage_image_eq_image, CategoryTheory.ShortComplex.leftHomologyMap_comp, CategoryTheory.Limits.CatCospanTransform.whisker_exchange, CategoryTheory.NatTrans.unop_whiskerLeft, CategoryTheory.Localization.Preadditive.homEquiv_symm_apply, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_hom_inv, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_e, CategoryTheory.Functor.HomObj.comp_app, CategoryTheory.e_comp_id, CategoryTheory.Limits.colimit.isoColimitCocone_ι_inv, CategoryTheory.Functor.CommShift.isoAdd_inv_app, AlgebraicGeometry.Scheme.Hom.app_invApp'_assoc, Bimod.AssociatorBimod.hom_left_act_hom', CategoryTheory.MonoidalCategory.tensor_inv_hom_id_assoc, HomologicalComplex.singleObjCyclesSelfIso_hom_singleObjOpcyclesSelfIso_hom_assoc, AlgebraicGeometry.pointOfClosedPoint_comp_assoc, CategoryTheory.Join.pseudofunctorRight_mapComp_inv_toNatTrans_app, CategoryTheory.Bicategory.eqToHomTransIso_refl_left, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_whiskerRight, CategoryTheory.CommMon.comp_hom, AlgebraicTopology.DoldKan.σ_comp_PInfty_assoc, Bimod.RightUnitorBimod.hom_right_act_hom', Action.inv_hom_hom_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app_assoc, CategoryTheory.SimplicialObject.δ_comp_δ''_assoc, Bicategory.Opposite.op2_associator_inv, HomologicalComplex.XIsoOfEq_hom_comp_XIsoOfEq_hom, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_comp_assoc, CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv'_assoc, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_fst, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv, CategoryTheory.Limits.Trident.app_zero, CategoryTheory.CosimplicialObject.δ_comp_δ_self', AlgebraicGeometry.Scheme.Hom.quasiFiniteLocus_comp, CategoryTheory.ShortComplex.SnakeInput.naturality_δ, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_snd_snd_assoc, CategoryTheory.Pseudofunctor.map₂_associator_app_assoc, CategoryTheory.Bicategory.Pith.inclusion_mapComp, CategoryTheory.Functor.OplaxMonoidal.δ_comp_η_tensorHom_assoc, AlgebraicGeometry.Scheme.Pullback.Triplet.tensorCongr_trans_hom, AlgebraicGeometry.Scheme.app_eq, CochainComplex.mappingCone.inr_f_d_assoc, CategoryTheory.Limits.IsColimit.fac, CategoryTheory.shrinkYonedaEquiv_comp, CategoryTheory.Enriched.FunctorCategory.enriched_id_comp, Bimod.RightUnitorBimod.inv_hom_id, CategoryTheory.Subobject.ofLE_arrow, AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom_ι_assoc, CategoryTheory.NatTrans.naturality_2, CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_snd_assoc, HomotopicalAlgebra.PrepathObject.p_snd, CategoryTheory.GrothendieckTopology.toSheafify_naturality_assoc, Bimod.LeftUnitorBimod.hom_right_act_hom', CategoryTheory.Square.category_comp_τ₂, CategoryTheory.RegularMono.w_assoc, CategoryTheory.SmallObject.SuccStruct.extendToSucc_map_le_succ, ModuleCat.restrictScalarsId'App_inv_naturality_assoc, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberDesc, HomologicalComplex.opcyclesMap_comp, CategoryTheory.Functor.relativelyRepresentable.pullback₃.map_p₃_comp, CategoryTheory.MorphismProperty.RespectsIso.postcomp, AlgebraicTopology.NormalizedMooreComplex.obj_d, CategoryTheory.Limits.biprod.braid_natural, CategoryTheory.CategoryOfElements.fromStructuredArrow_map, CategoryTheory.Category.assoc, ProfiniteGrp.ofHom_comp, CategoryTheory.SimplicialObject.δ_comp_σ_of_gt, CategoryTheory.ShortComplex.homology_π_ι_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_inv_app, CategoryTheory.ShortComplex.SnakeInput.Hom.comm₂₃, CategoryTheory.Limits.coprod.symmetry, CategoryTheory.HasShift.Induced.add_inv_app_obj, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_ι_presheafHom, CategoryTheory.Bicategory.leftAdjointSquare.comp_hvcomp, TopCat.isOpenEmbedding_iff_comp_isIso, CategoryTheory.Limits.pullback_inv_snd_fst_of_left_isIso, SimplexCategoryGenRel.δ_comp_δ_nat, CategoryTheory.Adjunction.Localization.ε_app, CategoryTheory.Mon_Class.mul_comp, CategoryTheory.FunctorToTypes.coprod.desc_inr, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_isLimit_lift, CategoryTheory.biproduct_ι_comp_rightDistributor_inv, CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_inv_comp_iCycles_assoc, HomologicalComplex.pOpcycles_opcyclesToCycles_iCycles_assoc, HomologicalComplex.truncLEMap_comp_assoc, CategoryTheory.Bicategory.conjugateEquiv_whiskerRight, AlgebraicGeometry.Proj.basicOpenIsoSpec_inv_ι_assoc, CategoryTheory.Oplax.OplaxTrans.Modification.whiskerRight_naturality, CategoryTheory.Adjunction.rightAdjointUniq_trans, CategoryTheory.Functor.LaxMonoidal.μ_natural_right, CategoryTheory.Functor.mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app_assoc, CategoryTheory.Iso.comp_inv_eq, CategoryTheory.PullbackShift.adjunction_counit, CategoryTheory.Bicategory.LeftLift.whiskering_map, CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom'_assoc, CategoryTheory.Functor.LaxMonoidal.right_unitality, CategoryTheory.Equivalence.unitIso_hom_app_comp_inverse_map_η_functor_assoc, CochainComplex.HomComplex.Cochain.δ_single, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_app_hom_assoc, CategoryTheory.Adjunction.unit_app_tensor_comp_map_δ_assoc, CategoryTheory.Functor.Monoidal.whiskerLeft_η_ε, CategoryTheory.NonPreadditiveAbelian.diag_σ, CategoryTheory.Limits.colimit.eqToHom_comp_ι_assoc, CategoryTheory.Limits.hasPushout_of_right_factors_epi, CategoryTheory.Functor.Monoidal.whiskerLeft_app_fst_assoc, CategoryTheory.Bicategory.leftUnitor_inv_naturality_assoc, CategoryTheory.ExactPairing.evaluation_coevaluation, CategoryTheory.Bicategory.rightAdjointSquare.comp_vhcomp, HomologicalComplex.pOpcycles_opcyclesIsoSc'_hom, CategoryTheory.Limits.Cone.ofTrident_π, CategoryTheory.Mon_Class.comp_mul, CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse, CategoryTheory.IsPullback.isoPullback_inv_fst, CategoryTheory.ExactPairing.coevaluation_evaluation', CategoryTheory.Limits.biprod.inl_snd_assoc, AddMonCat.comp_apply, CochainComplex.mappingConeCompTriangle_obj₂, CategoryTheory.Limits.BinaryBicone.inl_fst, CategoryTheory.Limits.fiberwiseColimit_map, CategoryTheory.cocones_map_app_app, groupCohomology.π_comp_H0IsoOfIsTrivial_hom_assoc, CategoryTheory.MorphismProperty.FunctorialFactorizationData.i_mapZ_assoc, CategoryTheory.Over.iteratedSliceBackward_map, CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom, CategoryTheory.op_comp, CategoryTheory.Lax.StrongTrans.vComp_naturality_hom, AugmentedSimplexCategory.inr_comp_associator, BddLat.hom_comp, HomologicalComplex.pOpcycles_singleObjOpcyclesSelfIso_inv, AlgebraicGeometry.Scheme.Hom.toNormalization_inl_normalizationCoprodIso_hom_assoc, CategoryTheory.InjectiveResolution.homotopyEquiv_inv_ι, CategoryTheory.Limits.pullbackProdSndIsoProd_hom_snd, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_whiskerRight, quasiIsoAt_iff_comp_right, CategoryTheory.Bicategory.whiskerLeft_inv_hom, CategoryTheory.Over.associator_inv_left_snd, SSet.ι₀_snd_assoc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_π_app, CategoryTheory.Limits.coprod.associator_naturality, CategoryTheory.GradedObject.ι_mapBifunctorMapObjDesc, SSet.Truncated.HomotopyCategory.descOfTruncation_comp, AlgebraicGeometry.Scheme.Hom.toNormalization_normalizationPullback_fst, CategoryTheory.NatIso.cancel_natIso_hom_right, AlgebraicGeometry.instLocallyQuasiFiniteCompSchemeιQuasiFiniteLocus, CategoryTheory.Limits.equalizerComparison_comp_π, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_leftUnitor, CategoryTheory.MonoidalCategory.whisker_exchange, CategoryTheory.SmallObject.ρFunctorObj_π_assoc, HasFibers.inducedMap_comp, CategoryTheory.MonoidalCategory.inv_hom_id_tensor_assoc, AlgebraicTopology.DoldKan.N₁_map_f, CategoryTheory.Bicategory.Adj.associator_inv_τr, CategoryTheory.Bicategory.Prod.sectL_mapId_inv, CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_hom_inv_id, groupCohomology.cocyclesMap_id_comp_assoc, AlgebraicGeometry.IsAffineOpen.map_fromSpec, CategoryTheory.SimplicialThickening.SimplicialCategory.comp_id, CategoryTheory.Grp_Class.comp_inv, CategoryTheory.Pretriangulated.TriangleMorphism.comp_hom₂, CategoryTheory.Functor.leftDerivedNatTrans_fac_assoc, CategoryTheory.Functor.mapCommMon_obj_mon_mul, CategoryTheory.Limits.pullbackDiagonalMapIso.hom_fst, CategoryTheory.CartesianMonoidalCategory.associator_inv_fst_fst, CategoryTheory.eqToHom_comp_homOfLE_op, CategoryTheory.whiskerLeft_coprod_inr_leftDistrib_inv, HomologicalComplex.homologyπ_restrictionHomologyIso_inv_assoc, CategoryTheory.CosimplicialObject.δ_comp_δ''_assoc, AlgebraicGeometry.Spec_Γ_naturality, Frm.coe_comp, CategoryTheory.PreservesImage.factorThruImage_comp_hom, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₃, groupCohomology.d₀₁_comp_d₁₂, CategoryTheory.Limits.CatCospanTransform.comp_whiskerLeft_assoc, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_app_assoc, prevD_comp_left, CategoryTheory.Limits.bicone_ι_π_self_assoc, CategoryTheory.Limits.pushoutIsoOpPullback_inl_hom, CategoryTheory.Equivalence.counitIso_inv_app_comp_functor_map_η_inverse, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_fst_snd_assoc, CategoryTheory.Bicategory.whiskerRight_comp_assoc, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeftLift_snd, CategoryTheory.ShortComplex.π₁Toπ₂_comp_π₂Toπ₃_assoc, AlgebraicGeometry.Scheme.Opens.toSpecΓ_naturality, CategoryTheory.Limits.colimit.ι_pre_assoc, TopCat.Presheaf.germ_stalkPullbackHom, Rep.coindResAdjunction_counit_app, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top, CategoryTheory.HalfBraiding.naturality_assoc, CategoryTheory.BraidedCategory.braiding_tensor_right_hom_assoc, CategoryTheory.Adjunction.map_ε_comp_counit_app_unit_assoc, AddCommGrpCat.ofHom_comp, AlgebraicGeometry.Scheme.Pullback.openCoverOfLeftRight_f, CategoryTheory.CosimplicialObject.δ_comp_δ_assoc, HomologicalComplex.opcyclesIsoSc'_inv_fromOpcycles, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom, CategoryTheory.Cat.Hom.toNatIso_associator, AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_comp_assoc, AlgebraicGeometry.Scheme.comp_toLRSHom_assoc, HomologicalComplex.singleObjOpcyclesSelfIso_hom, CategoryTheory.Limits.Multiequalizer.condition, CategoryTheory.Limits.ConeMorphism.inv_hom_id_assoc, HomologicalComplex.singleObjCyclesSelfIso_inv_iCycles, CategoryTheory.SimplicialObject.σ_naturality_assoc, CategoryTheory.Bicategory.InducedBicategory.bicategory_associator_inv_hom, CategoryTheory.Bicategory.LeftExtension.w_assoc, CategoryTheory.Limits.WidePushout.arrow_ι, TopCat.Presheaf.stalkSpecializes_stalkPushforward, CategoryTheory.Functor.IsEventuallyConstantTo.coneπApp_eq, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_naturality, CategoryTheory.shrinkYonedaEquiv_symm_map_assoc, CategoryTheory.ModObj.mul_smul_assoc, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_specStalkEquiv, CategoryTheory.Functor.OplaxMonoidal.left_unitality, AlgebraicGeometry.Scheme.Hom.inr_toNormalization_normalizationCoprodIso_inv, CategoryTheory.Limits.MultispanIndex.inj_sndSigmaMapOfIsColimit, CategoryTheory.Limits.biprod.hom_ext'_iff, CategoryTheory.Limits.ι_comp_colimitOpIsoOpLimit_hom_assoc, CategoryTheory.Over.inv_left_hom_left_assoc, CategoryTheory.Dial.leftUnitor_naturality, CategoryTheory.IsPullback.isoPullback_inv_snd_assoc, CategoryTheory.Comma.map_obj_hom, HomologicalComplex₂.totalShift₂Iso_hom_naturality_assoc, CategoryTheory.coprod_inr_rightDistrib_hom_assoc, CategoryTheory.CatEnriched.id_hComp, SSet.horn.faceSingletonComplIso_inv_ι_assoc, CategoryTheory.Limits.pullbackSymmetry_inv_comp_snd_assoc, CategoryTheory.Bimon.ofMonComonObjX_mul, CategoryTheory.OplaxFunctor.map₂_associator, CategoryTheory.Bicategory.inv_hom_whiskerRight_whiskerRight_assoc, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_left_assoc, CategoryTheory.CartesianMonoidalCategory.associator_hom_fst_assoc, AlgebraicTopology.DoldKan.MorphComponents.preComp_a, CategoryTheory.Bicategory.mateEquiv_comp_id_right, AlgebraicGeometry.universallyClosedTypeComp, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_hom_eq_germ, CategoryTheory.shift_shift', AlgebraicGeometry.quasiSeparated_comp, CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_hom, CategoryTheory.Limits.HasColimit.isoOfEquivalence_inv_π, groupCohomology.cocyclesIso₀_hom_comp_f, CategoryTheory.InjectiveResolution.ι'_f_zero, CategoryTheory.CartesianMonoidalCategory.prodComparison_fst, CategoryTheory.Pseudofunctor.StrongTrans.homCategory_comp_as_app, CategoryTheory.ShortComplex.abelianImageToKernel_comp_kernel_ι_comp_cokernel_π_assoc, SheafOfModules.pushforwardNatIso_inv, CategoryTheory.Comonad.ComonadicityInternal.unitFork_π_app, prodIsoPullback_inv_fst, CategoryTheory.StructuredArrow.w_prod_fst, CategoryTheory.Limits.Types.coequalizerIso_quot_comp_inv, CategoryTheory.Arrow.mapCechNerve_app, CategoryTheory.Bicategory.inv_hom_whiskerRight_assoc, CategoryTheory.Bicategory.whisker_exchange, CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_left, CategoryTheory.PreOneHypercover.forkOfIsColimit_pt, CategoryTheory.Bicategory.inv_hom_whiskerRight, CochainComplex.mappingCone.liftCochain_v_snd_v_assoc, AlgebraicGeometry.Proj.fromOfGlobalSections_toSpecZero_assoc, CategoryTheory.Limits.ι_colimitCompWhiskeringLeftIsoCompColimit_hom_assoc, CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux_fac_assoc, HomologicalComplex.extend.d_comp_eq_zero_iff, CategoryTheory.Functor.hom_map, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_symm_apply, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_comp, HomotopicalAlgebra.PrepathObject.trans_p₀, CategoryTheory.Functor.mapCommGrp_obj_grp_one, AlgebraicGeometry.morphismRestrict_ι_assoc, CategoryTheory.sum.inlCompInrCompInverseAssociator_hom_app_down_down, CategoryTheory.LaxFunctor.map₂_leftUnitor_assoc, CategoryTheory.GrothendieckTopology.arrow_stable, CategoryTheory.Functor.isLimitConeOfIsRightKanExtension_lift, CategoryTheory.Functor.OplaxRightLinear.δᵣ_unitality_inv, groupCohomology.eq_d₀₁_comp_inv, groupCohomology.H1π_comp_map_assoc, SimplexCategoryGenRel.δ_comp_σ_of_gt_assoc, CategoryTheory.SimplicialObject.comp_right, CategoryTheory.Adjunction.mapMon_unit, CategoryTheory.Functor.Monoidal.tensorHom_app_fst_assoc, CategoryTheory.StructuredArrow.homMk'_comp, CategoryTheory.ObjectProperty.FullSubcategory.comp_hom_assoc, CategoryTheory.MonoidalCategory.leftUnitor_naturality, CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_fst_assoc, CategoryTheory.Cat.associator_hom_app, CategoryTheory.kernelCokernelCompSequence.snakeInput_L₀_X₂, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_point, CochainComplex.mappingCone.inr_f_fst_v, AlgebraicGeometry.Scheme.fromSpecStalk_toSpecΓ_assoc, CategoryTheory.Bicategory.pentagon_inv, HomologicalComplex.biprod_inr_desc_f, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.hf, CategoryTheory.Limits.IsImage.lift_ι_assoc, CategoryTheory.ShortComplex.zero_assoc, CategoryTheory.Limits.equalizerSubobject_arrow'_assoc, CategoryTheory.MonoidalCategory.associator_inv_naturality_right_assoc, SSet.stdSimplex.faceSingletonIso_zero_hom_comp_ι_eq_δ, groupHomology.mapCycles₁_comp_apply, CategoryTheory.ShortComplex.cyclesIsoX₂_hom_inv_id, CategoryTheory.Arrow.hom_inv_id_right_assoc, CategoryTheory.GrothendieckTopology.OneHypercover.comp_h₁, CategoryTheory.GrpObj.lift_inv_right_eq, CategoryTheory.ShortComplex.leftHomologyMap'_comp, CategoryTheory.RetractArrow.retract_left_assoc, CategoryTheory.ShortComplex.HomotopyEquiv.trans_hom, CategoryTheory.CostructuredArrow.w_assoc, AlgebraicGeometry.AffineSpace.SpecIso_hom_appTop, CategoryTheory.Functor.rightDerived_fac_app, CategoryTheory.Limits.HasLimit.isoOfNatIso_inv_π_assoc, CategoryTheory.Limits.Pi.hom_ext_iff, SimplexCategory.δ_comp_δ'', CategoryTheory.MonoidalCategory.pentagon_hom_inv_assoc, groupCohomology.π_comp_H0Iso_hom, CategoryTheory.instHomIsOverComp, CategoryTheory.Comon.tensorObj_comul, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocIso_inv_naturality, CategoryTheory.Limits.coprod.map_inl_inr_codiag, CategoryTheory.NatTrans.CommShiftCore.shift_app_comm, CategoryTheory.Limits.cokernelCompIsIso_hom, CategoryTheory.Functor.map_shiftFunctorComm_hom_app, CategoryTheory.OverPresheafAux.YonedaCollection.map₂_comp, CategoryTheory.ShortComplex.RightHomologyData.wp, Bicategory.Opposite.op2_whiskerLeft, CategoryTheory.Functor.Monoidal.whiskerLeft_μ_δ_assoc, SemiRingCat.comp_apply, HomotopicalAlgebra.Precylinder.i₁_π_assoc, CategoryTheory.Idempotents.functorExtension₂_map_app_f, HomologicalComplex.homotopyCofiber.inlX_fstX, CategoryTheory.IsKernelPair.comp_of_mono, ModuleCat.ofHom_comp, CategoryTheory.Adjunction.derivedε_fac_app_assoc, CategoryTheory.ShortComplex.RightHomologyData.ofAbelian_H, CategoryTheory.ShortComplex.mapOpcyclesIso_hom_naturality_assoc, SimplicialObject.Splitting.IndexSet.fac_pull_assoc, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₁, CategoryTheory.Limits.Fork.π_comp_hom, CategoryTheory.Bicategory.Adjunction.homEquiv₂_symm_apply, CategoryTheory.Monad.Algebra.unit_assoc, groupCohomology.π_comp_H1Iso_hom_assoc, CategoryTheory.PreOneHypercover.comp_s₀, CategoryTheory.Functor.OplaxRightLinear.δᵣ_naturality_right_assoc, CategoryTheory.MorphismProperty.RightFraction.leftFraction_fac, SSet.Subcomplex.fromPreimage_ι_assoc, CategoryTheory.Sieve.pushforward_apply, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_rightHomologyIso_inv, CategoryTheory.BimonObj.one_comul, CategoryTheory.LaxFunctor.comp_mapId, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app, CategoryTheory.Limits.CoconeMorphism.w, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_ι_inv, CategoryTheory.Limits.coprod.associator_inv, CategoryTheory.Limits.Pi.lift_π_assoc, FinBddDistLat.ofHom_comp, CategoryTheory.eHomWhiskerRight_comp, HomologicalComplex.biprod_lift_fst_f_assoc, HomologicalComplex.mapBifunctor.ι_D₂_assoc, CategoryTheory.MonoidalCategory.tensorHom_comp_whiskerRight_assoc, CategoryTheory.Sheaf.toImage_ι_assoc, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_assoc, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_inv_eq_germ_assoc, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.comp, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_right, CategoryTheory.Limits.wideEqualizer.condition_assoc, CategoryTheory.MonadHom.app_μ, FintypeCat.uSwitch_map_uSwitch_map, CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_base, CategoryTheory.down_comp_assoc, CategoryTheory.Limits.image.compIso_hom_comp_image_ι, CategoryTheory.GrothendieckTopology.overMapPullback_comp_id, CategoryTheory.PreOneHypercover.Homotopy.wl, CategoryTheory.GradedObject.Monoidal.associator_naturality, CategoryTheory.MorphismProperty.RespectsIso.precomp, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_naturality, groupHomology.cyclesMap_id_comp, HomotopicalAlgebra.FibrantObject.homMk_homMk, CategoryTheory.Pseudofunctor.map₂_left_unitor_assoc, HomologicalComplex.homotopyCofiber.inrX_fstX_assoc, CategoryTheory.Over.rightUnitor_inv_left_fst_assoc, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_symm_apply_φ, HomologicalComplex.homologyι_singleObjOpcyclesSelfIso_inv_assoc, CategoryTheory.Bicategory.Pith.comp_of, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_fst, LightCondensed.ihomPoints_symm_comp, HomologicalComplex.extendHomologyIso_hom_naturality, CategoryTheory.Limits.prod.lift_map, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id_app, CategoryTheory.ShortComplex.RightHomologyData.p_comp_opcyclesIso_inv, CategoryTheory.yoneda_map_app, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom, CategoryTheory.Functor.LaxLeftLinear.μₗ_naturality_right, CategoryTheory.OplaxFunctor.map₂_associator_app, CategoryTheory.Oplax.LaxTrans.vComp_naturality_id, CategoryTheory.Functor.OplaxMonoidal.δ_snd_assoc, CategoryTheory.ShortComplex.RightHomologyData.wp_assoc, CategoryTheory.Comma.mapLeft_map_left, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_fst, SimplexCategory.Truncated.δ₂_zero_comp_σ₂_zero, CategoryTheory.StrictPseudofunctorCore.map₂_left_unitor, CategoryTheory.SmallObject.πObj_ιIteration_app_right, CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit_proj, groupCohomology.eq_d₁₂_comp_inv, CompHausLike.pullback.condition, CategoryTheory.Limits.PreservesPushout.inr_iso_inv, CategoryTheory.Bicategory.Lan.existsUnique, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_morphismRestrict_assoc, CategoryTheory.CartesianMonoidalCategory.tensorδ_snd_assoc, CategoryTheory.TransportEnrichment.eId_eq, CategoryTheory.MonoidalClosed.ofEquiv_uncurry_def, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_whiskerRight_as_app, CategoryTheory.Oplax.OplaxTrans.Modification.vcomp_app, CategoryTheory.ShortComplex.opcyclesMap'_g', CategoryTheory.Limits.biproduct.fromSubtype_π_subtype, CategoryTheory.Bicategory.eqToHomTransIso_refl_refl, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀', CategoryTheory.Limits.biproduct.ι_π_assoc, CategoryTheory.curryingIso_hom_toFunctor_obj_map, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition', CategoryTheory.CatCommSq.hInv_iso_inv_app, CategoryTheory.FreeBicategory.mk_left_unitor_inv, AlgebraicGeometry.Scheme.SpecToEquivOfField_eq_iff, CategoryTheory.Limits.ColimitPresentation.changeDiag_ι, CategoryTheory.Preregular.exists_fac, CategoryTheory.IsSplitEqualizer.bottom_rightRetraction, Homotopy.nullHomotopicMap_comp, HomologicalComplex.toCycles_i, CategoryTheory.Functor.LaxRightLinear.μᵣ_naturality_right_assoc, CategoryTheory.mop_comp, CategoryTheory.Sieve.ofArrows.fac, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_naturality_assoc, FundamentalGroupoid.conj_eqToHom_assoc, CategoryTheory.Limits.prod.pentagon_assoc, CategoryTheory.Grp_Class.comp_zpow, CategoryTheory.PreZeroHypercover.inv_hom_h₀_comp_f_assoc, CategoryTheory.Localization.isoOfHom_inv_hom_id, CategoryTheory.Functor.descOfIsLeftKanExtension_fac_assoc, CategoryTheory.Limits.colimit.pre_post, ProfiniteGrp.ProfiniteCompletion.lift_eta, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality_assoc, CategoryTheory.Bicategory.RightLift.w_assoc, CategoryTheory.Limits.CategoricalPullback.comp_snd, CategoryTheory.Over.comp_left_assoc, CategoryTheory.MonObj.mul_assoc, groupCohomology.mapCocycles₂_comp_i, CategoryTheory.Limits.MonoFactorisation.compMono_m, CategoryTheory.Bicategory.mateEquiv_vcomp, CategoryTheory.Pseudofunctor.StrongTrans.comp_app, CategoryTheory.ProjectiveResolution.lift_commutes_zero_assoc, CategoryTheory.Limits.BinaryFan.braiding_hom_snd_assoc, HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom_desc_hom_assoc, CategoryTheory.yonedaCommGrpGrpObj_map, TopCat.Presheaf.SheafConditionEqualizerProducts.piOpens.hom_ext_iff, CategoryTheory.GrpObj.lift_inv_comp_left_assoc, CategoryTheory.MonoidalCategory.associator_naturality_assoc, CategoryTheory.ShortComplex.abelianImageToKernel_comp_kernel_ι, HomotopicalAlgebra.instWeakEquivalenceCompOfIsStableUnderCompositionWeakEquivalences, AlgebraicTopology.DoldKan.identity_N₂, groupHomology.eq_d₃₂_comp_inv, CategoryTheory.Dial.rightUnitor_naturality, CategoryTheory.MonObj.ofIso_mul, CategoryTheory.Subobject.map_comp, CategoryTheory.MonoidalClosed.uncurry_natural_right, PresheafOfModules.comp_app, CategoryTheory.Limits.IsImage.lift_fac, CategoryTheory.Functor.shiftIso_hom_app_comp, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.IsTerminal.comm, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_right_symm, CategoryTheory.monoidalComp_refl, CategoryTheory.Bicategory.conjugateEquiv_adjunction_id_symm, AlgebraicTopology.DoldKan.PInfty_comp_QInfty, CategoryTheory.monoidalOfHasFiniteProducts.associator_inv_fst_snd, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom_assoc, TopCat.GlueData.ι_fromOpenSubsetsGlue, CategoryTheory.CartesianMonoidalCategory.lift_leftUnitor_hom_assoc, HomotopicalAlgebra.Precylinder.inr_i, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_assoc, HomotopicalAlgebra.FibrantBrownFactorization.i_r_assoc, CategoryTheory.Pretriangulated.shiftFunctorZero_op_inv_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_ι_app, CategoryTheory.PreOneHypercover.p₁_sigmaOfIsColimit_assoc, CategoryTheory.Iso.inv_hom_id_triangle_hom₂, CategoryTheory.Bicategory.Adj.comp_τl_assoc, CochainComplex.mappingCone.liftCochain_v_snd_v, CategoryTheory.ShortComplex.RightHomologyMapData.homologyMap_eq, CategoryTheory.StructuredArrow.mapIso_inverse_obj_hom, Bimod.whiskerLeft_hom, QuadraticModuleCat.toIsometry_comp, CategoryTheory.Limits.image.compIso_hom_comp_image_ι_assoc, CategoryTheory.Functor.mapMon_obj_mon_mul, CategoryTheory.Functor.isColimitCoconeOfIsLeftKanExtension_desc, CategoryTheory.ShortComplex.exact_iff_iCycles_pOpcycles_zero, CategoryTheory.Oplax.OplaxTrans.StrongCore.naturality_hom, CategoryTheory.NatIso.naturality_1', CategoryTheory.ShortComplex.exact_iff_kernel_ι_comp_cokernel_π_zero, CategoryTheory.Functor.relativelyRepresentable.symmetry_symmetry, CategoryTheory.PreOneHypercover.Hom.w₁₁, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app_assoc, CategoryTheory.Limits.IsLimit.map_π, CategoryTheory.BraidedCategory.braiding_tensor_left_inv, CategoryTheory.Functor.biprodComparison_snd_assoc, CategoryTheory.Subgroupoid.mul_mem_cancel_right, HomologicalComplex.mapBifunctor.ι_D₁_assoc, HomologicalComplex.leftUnitor'_inv_comm, CategoryTheory.Endofunctor.Algebra.Hom.h_assoc, CategoryTheory.Pseudofunctor.CoGrothendieck.map_comp_eq, CategoryTheory.Limits.biproduct.lift_map, CategoryTheory.Limits.end_.map_π, CategoryTheory.MonoidalCategory.triangle_assoc_comp_left_inv, CategoryTheory.Functor.OplaxMonoidal.associativity_assoc, ContinuousMap.Homotopy.apply_zero_path, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.comp_snd_app, CategoryTheory.MonoidalCategory.externalProductBifunctor_map_app, CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_inv_assoc, CategoryTheory.Over.hom_left_inv_left, CategoryTheory.Adjunction.ofCat_counit, CategoryTheory.sum.inrCompInrCompInverseAssociator_hom_app_down, CategoryTheory.Limits.pullback.diagonal_snd_assoc, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id, SimplicialObject.Splitting.PInfty_comp_πSummand_id, CategoryTheory.Deterministic.discard_natural, CategoryTheory.GrothendieckTopology.sheafifyMap_sheafifyLift_assoc, AlgebraicGeometry.Scheme.Cover.glued_cover_cocycle_fst, CategoryTheory.PreGaloisCategory.autMap_comp, CategoryTheory.Limits.opProdIsoCoprod_hom_snd_assoc, CategoryTheory.Limits.ColimitPresentation.comp_base, CategoryTheory.MonoidalCategory.whiskerRight_tensor_symm, AlgebraicGeometry.IsSeparated.instIsClosedImmersionMapDescScheme, CategoryTheory.Presieve.CoverByImageStructure.fac, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_leftUnitor, ComplexShape.Embedding.liftExtend.comm_assoc, CategoryTheory.Limits.biproduct.whiskerEquiv_inv, CategoryTheory.Limits.biproduct.map_desc, AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id_assoc, Mathlib.Tactic.Monoidal.evalWhiskerLeft_of_cons, CategoryTheory.Over.monObjMkPullbackSnd_mul, CategoryTheory.Limits.image.lift_mk_factorThruImage, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerRight, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app, CategoryTheory.IsHomLift.comp_eqToHom_lift_iff, CategoryTheory.CosimplicialObject.δ_comp_δ', AlgebraicGeometry.GeometricallyIrreducible.comp, TopCat.sigmaIsoSigma_hom_ι, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_fst_fst, CategoryTheory.Monad.Algebra.Hom.h, SimplexCategory.const_comp, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp_assoc, CategoryTheory.Adjunction.compCoyonedaIso_inv_app_app, CategoryTheory.MorphismProperty.postcomp_iff, CategoryTheory.Subfunctor.Subpresheaf.equalizer.condition, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app, CategoryTheory.Square.Hom.comm₂₄, CategoryTheory.Grothendieck.map_comp_eq, CategoryTheory.Limits.FormalCoproduct.isoOfComponents_inv_φ, AlgebraicGeometry.Scheme.Hom.iUnion_support_ker_openCover_map_comp, CategoryTheory.Functor.comp_mapGrp_mul, HomologicalComplex₂.comm_f, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app_assoc, CategoryTheory.Abelian.image.fac, CategoryTheory.Grpd.piIsoPi_hom_π, CategoryTheory.CartesianMonoidalCategory.whiskerLeft_toUnit_comp_rightUnitor_hom, HomologicalComplex.extendHomologyIso_hom_naturality_assoc, CategoryTheory.Limits.piComparison_comp_π, CategoryTheory.BicategoricalCoherence.left'_iso, DerivedCategory.HomologySequence.comp_δ, CategoryTheory.eqToHom_iso_hom_naturality_assoc, SSet.PtSimplex.MulStruct.δ_map_of_gt, Bimod.TensorBimod.right_assoc', CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app, CategoryTheory.Limits.π_comp_cokernelIsoOfEq_hom_assoc, CategoryTheory.Functor.PreOneHypercoverDenseData.w_assoc, CategoryTheory.ParametrizedAdjunction.whiskerLeft_map_counit, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_associator, AlgebraicGeometry.diagonal_SpecMap, CategoryTheory.CatCenter.naturality_assoc, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapCompIso_inv, AlgebraicGeometry.Scheme.inv_app, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_map_app_app, CategoryTheory.GrothendieckTopology.ι_plusCompIso_hom_assoc, CategoryTheory.GradedObject.singleObjApplyIso_inv_single_map, CategoryTheory.Functor.mapTriangle_obj, CategoryTheory.Functor.leftDerived_fac_app, CategoryTheory.Iso.eHomCongr_hom, groupCohomology.H0IsoOfIsTrivial_hom, CategoryTheory.rightDistributor_ext₂_right_iff, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_app_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.leftUnitor_inv_one_tensor_mul, CategoryTheory.SplitEpi.id, CategoryTheory.Bicategory.LeftExtension.ofCompId_right, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_hom_inv_id, AlgebraicGeometry.ι_right_coprodIsoSigma_inv, CategoryTheory.LocalizerMorphism.RightResolution.comp_f_assoc, CategoryTheory.Abelian.LeftResolution.chainComplexMap_comp, CategoryTheory.Functor.LeftExtension.postcomp₁_map_right_app, CategoryTheory.CostructuredArrow.IsUniversal.existsUnique, AlgebraicGeometry.ι_sigmaSpec, CategoryTheory.NatTrans.unop_comp_assoc, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_one, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp_app, SimplexCategory.δ_comp_σ_of_gt'_assoc, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_comp_naturality_hom, inl_coprodIsoPushout_hom, HomotopicalAlgebra.Precylinder.inr_i_assoc, CategoryTheory.CostructuredArrow.mkPrecomp_id, CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtension_map_leftKanExtensionObjIsoColimit_hom, CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_π_assoc, CategoryTheory.OplaxFunctor.mapComp_naturality_right_assoc, CategoryTheory.right_comp_retraction, CategoryTheory.ShortComplex.LeftHomologyMapData.commf', AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_hom_app, Action.Hom.comp_hom, CategoryTheory.Functor.Monoidal.η_ε_assoc, CategoryTheory.Oplax.LaxTrans.naturality_naturality_assoc, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left, CategoryTheory.Iso.inv_hom_id, CategoryTheory.DifferentialObject.d_squared_apply, CategoryTheory.GrpObj.left_inv_assoc, CategoryTheory.Functor.mapGrp_id_mul, CategoryTheory.Limits.PushoutCocone.unop_π_app, CategoryTheory.Bicategory.InducedBicategory.categoryStruct_comp_hom, CategoryTheory.eqToHom_map_comp, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_inv_app, CategoryTheory.Functor.relativelyRepresentable.pullback₃.snd_snd_eq_p₃_assoc, CategoryTheory.Functor.homologySequence_comp_assoc, CategoryTheory.Limits.coprod.inl_map_assoc, CategoryTheory.Limits.prod.rightUnitor_hom_naturality, CategoryTheory.Subfunctor.range_le_equalizer_iff, CategoryTheory.CostructuredArrow.w_prod_fst, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app, CategoryTheory.StrictPseudofunctor.id_mapComp_hom, CompHausLike.finiteCoproduct.ι_desc, AlgebraicGeometry.Scheme.Hom.le_ker_comp, HomologicalComplex.restrictionMap_comp, CategoryTheory.MorphismProperty.LeftFraction.rightFraction_fac, CategoryTheory.comp_hom_eq_id, AlgebraicGeometry.coprodSpec_inr, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_postcomp, CategoryTheory.Linear.smulOfRingMorphism_smul_eq', CategoryTheory.Comonad.Coalgebra.comp_f, HomologicalComplex.mapBifunctor₂₃.ι_D₃, CategoryTheory.Limits.biproduct.fromSubtype_π_subtype_assoc, CategoryTheory.Limits.inr_inl_pushoutRightPushoutInlIso_hom_assoc, AlgebraicTopology.DoldKan.PInfty_idem, AlgebraicGeometry.IsOpenImmersion.comp_lift_assoc, CategoryTheory.Join.mapWhiskerRight_leftUnitor_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv, CategoryTheory.ShortComplex.cyclesIsoX₂_hom_inv_id_assoc, SimplicialObject.opFunctor_obj_σ, CategoryTheory.braiding_tensorUnit_left_assoc, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp_symm_assoc, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left, CategoryTheory.Localization.Monoidal.associator_hom_app, TopologicalSpace.OpenNhds.comp_apply, CategoryTheory.Localization.Monoidal.pentagon_aux₁, AlgebraicGeometry.Scheme.stalkSpecializes_stalkMap, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_snd_assoc, CategoryTheory.Adjunction.rightAdjointLaxMonoidal_μ, CategoryTheory.MonoidalCategory.leftUnitor_inv_comp_tensorHom_assoc, CochainComplex.isoHomologyπ₀_inv_naturality_assoc, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_inv_app, CategoryTheory.Center.comp_f, CategoryTheory.Limits.Cocone.ofCotrident_ι, CategoryTheory.Bicategory.InducedBicategory.bicategory_leftUnitor_inv_hom, CategoryTheory.kernelCokernelCompSequence.snakeInput_L₃_g, CochainComplex.mappingCone.homologySequenceδ_triangleh, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_pos_assoc, CategoryTheory.Yoneda.naturality, CategoryTheory.Adjunction.IsMonoidal.leftAdjoint_μ, CategoryTheory.Limits.WalkingReflexivePair.reflexion_comp_left, groupHomology.comap_coinvariantsKer_pOpcycles_range_subtype_pOpcycles_eq_top, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_comp_ι, CategoryTheory.CostructuredArrow.mapIso_functor_obj_hom, CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_self_succ, CategoryTheory.Functor.closedIhom_obj_map, CategoryTheory.ShortComplex.opcyclesMap'_g'_assoc, CategoryTheory.SingleFunctors.Hom.comp_hom, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_inv_naturality_assoc, CategoryTheory.ShortComplex.LeftHomologyData.ofEpiOfIsIsoOfMono'_i, LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition, CategoryTheory.e_id_comp, CategoryTheory.MonoidalCategory.associator_inv_naturality_right, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_app_assoc, CategoryTheory.Limits.LimitPresentation.w, AlgebraicGeometry.Scheme.Spec_map_stalkSpecializes_fromSpecStalk, CategoryTheory.Limits.biproduct.ι_map_assoc, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id_assoc, CategoryTheory.Limits.pullbackProdSndIsoProd_inv_fst_snd, CategoryTheory.Subobject.ofMkLEMk_comp_ofMkLEMk_assoc, CategoryTheory.Over.grpObjMkPullbackSnd_one, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition, groupHomology.cyclesMap_comp_isoCycles₂_hom, HomologicalComplex.mapBifunctor₂₃.d₂_eq, CategoryTheory.Limits.biproduct.map_π_assoc, CategoryTheory.Limits.Multicoequalizer.condition, CategoryTheory.CartesianMonoidalCategory.associator_inv_snd, CategoryTheory.Iso.isoInverseComp_inv_app, AugmentedSimplexCategory.inr_comp_inl_comp_associator, CategoryTheory.ShortComplex.cyclesIsoLeftHomology_hom_inv_id_assoc, CategoryTheory.Functor.Monoidal.coreMonoidalTransport_εIso_inv, CategoryTheory.Abelian.Pseudoelement.comp_apply, AlgebraicGeometry.HasRingHomProperty.comp_of_isOpenImmersion, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₁₂, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.g_app, CategoryTheory.SimplicialThickening.compFunctor_obj, CategoryTheory.Limits.prod.inl_snd, CategoryTheory.Functor.OplaxLeftLinear.δₗ_associativity_inv, HomotopicalAlgebra.LeftHomotopyClass.whitehead, CategoryTheory.Limits.pullbackAssoc_hom_snd_fst_assoc, CategoryTheory.Functor.commShift₂_comm, CategoryTheory.Pseudofunctor.StrongTrans.leftUnitor_inv_as_app, AlgebraicGeometry.Scheme.ideal_ker_le_ker_ΓSpecIso_inv_comp, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_obj, SSet.Subcomplex.toImage_ι, CategoryTheory.δ_naturalityₗ_assoc, CategoryTheory.Comma.mapLeftIso_functor_map_left, CategoryTheory.Iso.map_inv_hom_id_app_assoc, CategoryTheory.MonoidalCategory.inv_hom_id_tensor'_assoc, AlgebraicGeometry.Scheme.stalkMap_congr_assoc, CategoryTheory.MonoidalCategory.leftUnitor_inv_whiskerRight, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_symm_assoc, HomologicalComplex.opcyclesOpIso_inv_naturality_assoc, CategoryTheory.Limits.inl_comp_pushoutComparison_assoc, CategoryTheory.Limits.prod.map_swap_assoc, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_whiskerLeft_as_app, CategoryTheory.Limits.MulticospanIndex.sndPiMap_π_assoc, HomologicalComplex.opcyclesIsoSc'_inv_fromOpcycles_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id_assoc, CategoryTheory.Limits.KernelFork.condition_assoc, groupHomology.comp_d₂₁_eq, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv, HomologicalComplex.inl_biprodXIso_inv_assoc, CategoryTheory.Preadditive.sub_comp_assoc, SemiRingCat.hom_comp, CategoryTheory.GrothendieckTopology.whiskerRight_toSheafify_sheafifyCompIso_hom_assoc, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac, PresheafOfModules.limitPresheafOfModules_map, CategoryTheory.ShortComplex.rightHomologyι_naturality'_assoc, CategoryTheory.Functor.pentagon, CategoryTheory.Limits.Multicofork.π_comp_hom_assoc, CategoryTheory.Subobject.ofLEMk_comp_ofMkLEMk, CategoryTheory.Limits.Sigma.map_comp_map, SimplicialObject.Splitting.cofan_inj_epi_naturality_assoc, HomologicalComplex.cyclesMap_comp_assoc, CategoryTheory.MonObj.ofIso_one, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂_assoc, CategoryTheory.tensorRightHomEquiv_symm_naturality, CategoryTheory.Bicategory.LanLift.CommuteWith.instHasLeftKanLiftComp, CategoryTheory.NatIso.cancel_natIso_inv_right_assoc, groupHomology.mapCycles₁_comp_assoc, CategoryTheory.evaluationRightAdjoint_obj_map, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_map, CategoryTheory.η_naturality_assoc, Semigrp.hom_comp, AlgebraicGeometry.Scheme.isoSpec_inv_toSpecΓ, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_assoc, HomologicalComplex.biprod_inr_snd_f_assoc, CategoryTheory.ShortComplex.Splitting.s_g, CategoryTheory.Functor.cones_map_app, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inr_assoc, CategoryTheory.ShortComplex.LeftHomologyData.f'_π_assoc, CategoryTheory.Over.grpObjMkPullbackSnd_mul, CategoryTheory.Functor.Monoidal.map_associator_inv_assoc, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃_tensorHom, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι_assoc, CategoryTheory.μ_δ_app_assoc, CategoryTheory.Functor.Monoidal.toUnit_ε_assoc, CategoryTheory.IsRegularMono.w, Action.comp_hom, ContinuousMap.Homotopy.evalAt_eq, groupHomology.toCycles_comp_isoCycles₂_hom_assoc, CategoryTheory.Limits.prod.rightUnitor_hom_naturality_assoc, CategoryTheory.Bicategory.pentagon_hom_hom_inv_hom_hom_assoc, CategoryTheory.coprod_inl_leftDistrib_hom, CategoryTheory.Pretriangulated.comp_hom₁_assoc, CategoryTheory.Oplax.OplaxTrans.categoryStruct_id_naturality, HomologicalComplex.biprod_inl_snd_f_assoc, SimplexCategory.Truncated.Hom.tr_comp, CategoryTheory.MonoidalCategory.rightUnitor_tensor_hom, CategoryTheory.Pseudofunctor.mapId'_inv_naturality_assoc, CategoryTheory.Limits.FormalCoproduct.pullbackCone_fst_φ, CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_π, CategoryTheory.coevaluation_comp_leftAdjointMate_assoc, CategoryTheory.TransfiniteCompositionOfShape.fac_assoc, CategoryTheory.η_ε_app_assoc, CategoryTheory.NatTrans.unop_whiskerLeft_assoc, CategoryTheory.conjugateEquiv_symm_comp_assoc, CategoryTheory.Functor.Monoidal.map_associator_assoc, CategoryTheory.Arrow.comp_left, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_inv_τr, Bimod.TensorBimod.whiskerLeft_π_actLeft, CategoryTheory.Limits.Cofork.ofCocone_ι, groupHomology.H0π_comp_map, CategoryTheory.MonoidalClosed.coev_app_comp_pre_app, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_snd_assoc, CategoryTheory.Limits.inl_inr_pushoutAssoc_inv_assoc, TopologicalSpace.Opens.comp_apply, CategoryTheory.Dial.tensorHom_F, CategoryTheory.Localization.SmallHom.equiv_equiv_symm, CategoryTheory.kernelCokernelCompSequence.inl_π_assoc, CategoryTheory.OrthogonalReflection.D₁.ιLeft_comp_l, CategoryTheory.Functor.CommShift.isoZero_hom_app, CategoryTheory.ChosenPullbacksAlong.hom_ext_iff, CategoryTheory.Bicategory.LeftLift.w_assoc, CategoryTheory.Limits.BinaryBicone.inr_snd, HomologicalComplex.eq_liftCycles_homologyπ_up_to_refinements, HomologicalComplex₂.totalAux.d₂_eq, CategoryTheory.LocalizerMorphism.commShift_iso_hom_app, CategoryTheory.IsHomLift.eqToHom_comp_lift, AlgebraicGeometry.ExistsHomHomCompEqCompAux.exists_eq, CategoryTheory.Limits.inl_comp_pushoutObjIso_hom, CategoryTheory.ShortComplex.toCycles_comp_leftHomologyπ_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_hom_app, AlgebraicGeometry.Scheme.ι_toIso_inv, CategoryTheory.section_comp_left_assoc, CategoryTheory.MorphismProperty.RightFraction.map_ofInv_hom_id, CochainComplex.mappingCone.d_snd_v, HomologicalComplex.p_fromOpcycles, CategoryTheory.ShortComplex.mapCyclesIso_hom_iCycles_assoc, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.natTrans_app_uliftYoneda_obj, CategoryTheory.Limits.biprod.lift_snd, CategoryTheory.Bicategory.whiskerRightIso_hom, CategoryTheory.Bicategory.associatorNatIsoLeft_inv_app, CategoryTheory.Equivalence.cancel_unit_right, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_assoc, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_functor_obj, CategoryTheory.Limits.limitConstTerminal_inv_π_assoc, AlgebraicGeometry.Scheme.Hom.stalkSpecializes_stalkMap, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app, CategoryTheory.GradedObject.mapBifunctorObjObjSingle₀Iso_hom, CategoryTheory.IsCofiltered.bowtie, CategoryTheory.Limits.limitOpIsoOpColimit_hom_comp_ι_assoc, CategoryTheory.GradedObject.mapTrifunctorMapObj_ext_iff, AugmentedSimplexCategory.inr_comp_inl_comp_associator_assoc, HomologicalComplex₂.D₂_totalShift₁XIso_hom_assoc, CategoryTheory.Functor.Monoidal.whiskerRight_app_fst_assoc, CochainComplex.HomComplex.Cochain.δ_fromSingleMk, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_inv_assoc, CategoryTheory.Limits.pushoutIsoUnopPullback_inr_hom, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct, CategoryTheory.MonoidalCategory.hom_inv_id_tensor'_assoc, CategoryTheory.Functor.mapHomotopyEquiv_homotopyHomInvId, CategoryTheory.Limits.CatCospanTransform.triangle_assoc, CategoryTheory.Limits.PullbackCone.condition, TopCat.Presheaf.Pushforward.comp_eq, CategoryTheory.Limits.prod.inr_fst_assoc, CategoryTheory.CartesianMonoidalCategory.braiding_hom_snd_assoc, SheafOfModules.unitHomEquiv_symm_comp, CategoryTheory.Presieve.FunctorPushforwardStructure.fac, CategoryTheory.Limits.BinaryFan.braiding_hom_fst_assoc, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_hom, AlgebraicGeometry.Scheme.Hom.preimageIso_hom_ι_assoc, CategoryTheory.Monad.beckCoequalizer_desc, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_hom_iCycles_assoc, CategoryTheory.Limits.isPullback_equalizer_prod, CategoryTheory.Limits.PreservesPushout.inr_iso_hom_assoc, SemiNormedGrp₁.hom_comp, CategoryTheory.ShortComplex.HomotopyEquiv.refl_homotopyHomInvId, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftUnitor_actionHom_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app_assoc, AlgebraicTopology.DoldKan.QInfty_idem, CategoryTheory.ChosenPullbacksAlong.unit_pullbackComp_hom_assoc, SimplexCategory.δ_comp_σ_self', HomologicalComplex.stupidTruncMap_comp, CategoryTheory.ShortComplex.mapHomologyIso_hom_naturality, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ₀_assoc, CategoryTheory.Limits.Sigma.ι_isoColimit_inv, CategoryTheory.ShortComplex.LeftHomologyData.π_comp_homologyIso_inv, CategoryTheory.Limits.PreservesKernel.iso_inv_ι, CategoryTheory.Functor.PullbackObjObj.π_fst, CategoryTheory.Functor.partialRightAdjointHomEquiv_symm_comp, CategoryTheory.RetractArrow.r_w_assoc, CategoryTheory.Functor.FullyFaithful.monObj_mul, CategoryTheory.CommComon.comp_hom, CategoryTheory.CartesianMonoidalCategory.whiskerRight_snd_assoc, CategoryTheory.Bicategory.rightUnitor_inv_naturality, ChainComplex.isoHomologyι₀_inv_naturality_assoc, CategoryTheory.Enriched.FunctorCategory.isLimitConeFunctorEnrichedHom.fac, CategoryTheory.Functor.Monoidal.transport_μ, CategoryTheory.OplaxFunctor.mapComp_assoc_left_app_assoc, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂, SimplicialObject.Split.comp_f, CategoryTheory.MorphismProperty.Comma.comp_right, CategoryTheory.Limits.BinaryBicone.inl_fst_assoc, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_unitIso, HomologicalComplex.biprodXIso_hom_fst, HomologicalComplex₂.D₂_totalShift₂XIso_hom_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_hom_app, CategoryTheory.sum.inlCompInrCompInverseAssociator_inv_app_down_down, CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoCofanPt_assoc, HomologicalComplex₂.d_f_comp_d_f, CategoryTheory.ShortComplex.opcyclesIsoRightHomology_inv_hom_id_assoc, CategoryTheory.BraidedCategory.hexagon_reverse_assoc, CategoryTheory.StructuredArrow.map₂_map_right, CategoryTheory.PreOneHypercover.Hom.comp_h₀, CategoryTheory.Functor.biproductComparison'_comp_biproductComparison, CategoryTheory.Functor.commShiftIso_comp_hom_app, AlgebraicGeometry.Scheme.isoOfEq_inv_ι, CategoryTheory.OverClass.asOverHom_comp_assoc, CategoryTheory.HalfBraiding.naturality, CategoryTheory.Subobject.ofMkLEMk_comp_ofMkLE, CategoryTheory.MonoOver.mapIso_unitIso, CategoryTheory.MonObj.lift_comp_one_right, HomologicalComplex.extend_op_d_assoc, CategoryTheory.CatEnriched.id_hComp_id, CategoryTheory.ComposableArrows.mk₁_eqToHom_comp, CategoryTheory.constantCommuteCompose_hom_app_val, CategoryTheory.CatCenter.smul_iso_inv_eq', HomotopicalAlgebra.Precylinder.LeftHomotopy.h₀_assoc, CategoryTheory.Limits.image.eq_fac, CategoryTheory.MonoidalCategory.MonoidalLeftAction.action_exchange, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.unit_app_ev_app_app_assoc, CategoryTheory.Endofunctor.Adjunction.Algebra.homEquiv_naturality_str, CategoryTheory.Limits.Sigma.ι_desc_assoc, CategoryTheory.Bicategory.Adjunction.homEquiv₁_apply, CategoryTheory.StrictPseudofunctorCore.map₂_associator, CategoryTheory.Limits.desc_op_comp_opCoproductIsoProduct'_hom, CategoryTheory.Functor.Monoidal.map_μ_δ_assoc, CategoryTheory.Equivalence.cancel_counit_right, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict_assoc, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_inv_colimit_map_assoc, CategoryTheory.Limits.pullbackDiagonalMapIso.inv_fst_assoc, SimplicialObject.Splitting.ι_desc_assoc, CategoryTheory.Functor.relativelyRepresentable.hom_ext_iff, AlgebraicGeometry.StructureSheaf.toStalk_stalkSpecializes_assoc, CategoryTheory.Functor.Monoidal.lift_μ_assoc, CategoryTheory.Iso.inv_hom_id_triangle_hom₁, groupCohomology.cochainsMap_comp, AlgebraicGeometry.Scheme.Hom.toNormalization_inr_normalizationCoprodIso_hom, CategoryTheory.MorphismProperty.RightFraction.map_s_comp_map_assoc, CategoryTheory.Limits.colimit.desc_extend, CategoryTheory.InjectiveResolution.toRightDerivedZero'_comp_iCycles, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_associator, CategoryTheory.CosimplicialObject.σ_naturality_assoc, HomologicalComplex.isoHomologyι_inv_hom_id, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃_tensorHom_assoc, CategoryTheory.monoidalOfHasFiniteProducts.associator_hom, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_fac_app_assoc, CategoryTheory.Limits.colimit.homIso_hom, CategoryTheory.MonadHom.comp_toNatTrans, CategoryTheory.LocallyDiscrete.comp_as, CategoryTheory.Limits.prod.associator_naturality_assoc, CategoryTheory.GlueData.ι_gluedIso_inv, CategoryTheory.BraidedCategory.braiding_inv_naturality_assoc, CategoryTheory.tensorRightHomEquiv_whiskerLeft_comp_evaluation, CochainComplex.mappingConeCompTriangle_mor₃, CategoryTheory.Limits.prod.inr_snd_assoc, CategoryTheory.whiskerRight_coprod_inr_rightDistrib_inv_assoc, groupCohomology.comp_d₁₂_eq, CategoryTheory.Idempotents.Karoubi.HomologicalComplex.comp_p_d, CategoryTheory.Join.mapWhiskerLeft_whiskerRight, AlgebraicGeometry.Scheme.Cover.glued_cover_cocycle, CategoryTheory.Sheaf.isLocallySurjective_comp, CommRingCat.toAlgHom_comp, CategoryTheory.BasedCategory.comp_def, CategoryTheory.Center.whiskerLeft_comm, Mathlib.Tactic.Bicategory.naturality_rightUnitor, AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom_ι, CategoryTheory.Localization.Monoidal.μ_inv_natural_right, CategoryTheory.Bicategory.Pith.whiskerRight_iso_inv, AlgebraicGeometry.Scheme.congr_app, SimplicialObject.opFunctor_obj_map, HomologicalComplex₂.D₁_D₁_assoc, CategoryTheory.ShortComplex.Homotopy.compLeft_h₂, CategoryTheory.Cat.Hom₂.comp_app_assoc, CategoryTheory.Limits.PreservesCokernel.π_iso_hom_assoc, CategoryTheory.Functor.homologySequence_comp, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_right_hom, HomologicalComplex₂.total.mapAux.mapMap_D₁_assoc, Bimod.actRight_one, CategoryTheory.Functor.Monoidal.whiskerRight_η_ε, CategoryTheory.Functor.IsCoverDense.isoOver_hom_app, CategoryTheory.CommGrp.comp', CategoryTheory.congrArg_cast_hom_right, CategoryTheory.Limits.limit.w_assoc, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_inv_comp_homologyι, SimplexCategory.δ_comp_δ_self', CategoryTheory.ShortComplex.SnakeInput.Hom.comp_f₁, SemiNormedGrp.coe_comp, CategoryTheory.Limits.ι_colimitPointwiseProductToProductColimit_π, CategoryTheory.ShortComplex.comp_τ₁, CategoryTheory.Limits.image.map_comp, CategoryTheory.InjectiveResolution.of_def, CategoryTheory.Limits.inr_inr_pushoutRightPushoutInlIso_hom, CategoryTheory.Limits.limitIsoLimitCurryCompLim_hom_π_π_assoc, CategoryTheory.Functor.LaxRightLinear.μᵣ_unitality_inv_assoc, Homotopy.extend_hom_eq, CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_fst, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_unit_app, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₁, CategoryTheory.Limits.prod.lift_fst_assoc, groupHomology.π_comp_H1Iso_inv, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_π_app, CategoryTheory.IsSplitEqualizer.ι_leftRetraction, CategoryTheory.toOverPullbackIsoToOver_inv_app_left, HomologicalComplex.isoHomologyι_hom_inv_id, AlgebraicGeometry.Scheme.preimage_comp, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_inv, CategoryTheory.Equivalence.unitInv_naturality, CategoryTheory.CostructuredArrow.w_prod_fst_assoc, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom_assoc, PresheafOfModules.sectionsMap_comp, CategoryTheory.Idempotents.Karoubi.idem_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.lift_fac_assoc, CategoryTheory.CartesianMonoidalCategory.associator_inv_fst_snd, CategoryTheory.MonoidalCategory.tensorμ_natural_right_assoc, CategoryTheory.Bicategory.rightUnitor_inv_congr, CategoryTheory.Functor.LeftExtension.precomp_map_right, CategoryTheory.Functor.LaxBraided.braided, CategoryTheory.Limits.hasPushoutVertPaste, CategoryTheory.Functor.LaxMonoidal.left_unitality_assoc, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_π_app_walkingParallelPair_one, SemimoduleCat.MonoidalCategory.associator_naturality, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_leftUnitor, CategoryTheory.Functor.OplaxMonoidal.δ_snd, HomologicalComplex.homotopyCofiber.inrX_sndX_assoc, CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_fst_snd_assoc, CategoryTheory.Equivalence.functor_unit_comp, AlgebraicGeometry.sourceLocalClosure.iff_forall_exists, CategoryTheory.Limits.cokernelCoforkBiproductFromSubtype_isColimit, CategoryTheory.ProjectiveResolution.cochainComplex_d, CategoryTheory.Endofunctor.Algebra.comp_eq_comp, CategoryTheory.Comonad.right_counit_assoc, HomotopicalAlgebra.CofibrantObject.homMk_homMk, CategoryTheory.Pseudofunctor.map₂_left_unitor, HomologicalComplex.singleObjCyclesSelfIso_inv_homologyπ, CategoryTheory.Limits.pushoutIsoUnopPullback_inl_hom_assoc, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σ, CategoryTheory.Bicategory.unitors_inv_equal, CategoryTheory.Limits.Pi.ι_π_eq_id, CategoryTheory.Bicategory.Pith.leftUnitor_inv_iso_hom, CategoryTheory.Limits.colimitCurrySwapCompColimIsoColimitCurryCompColim_ι_ι_hom, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app', CategoryTheory.MonoidalCategory.whiskerRight_tensor, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap, CategoryTheory.Bicategory.leftZigzagIso_symm, CategoryTheory.GradedObject.Monoidal.pentagon, CategoryTheory.SimplicialObject.Augmented.w₀, CategoryTheory.Functor.RightExtension.coneAt_π_app, CategoryTheory.Preadditive.IsIso.comp_right_eq_zero, CategoryTheory.Bicategory.associator_inv_naturality_middle, CategoryTheory.Comma.mapRightIso_functor_map_left, CategoryTheory.Limits.Sigma.ι_π_assoc, AlgebraicGeometry.Scheme.Pullback.Triplet.isPullback_SpecMap_tensor, CategoryTheory.Regular.frobeniusStrongEpiMonoFactorisation_I, CategoryTheory.μ_naturality₂_assoc, CategoryTheory.Equivalence.inv_fun_map, CochainComplex.HomComplex.Cochain.ofHom_v_comp_d, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₂_assoc, CategoryTheory.Functor.Monoidal.δ_μ, TopCat.Presheaf.pushforwardToOfIso_app, CategoryTheory.Idempotents.Karoubi.Biproducts.bicone_ι_f, CategoryTheory.Bicategory.associator_naturality_right_assoc, CategoryTheory.ShortComplex.Hom.comm₁₂, CategoryTheory.Pseudofunctor.CoGrothendieck.map_map_fiber, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerLeft_naturality_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_hom_inv, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁_assoc, SimplexCategory.Truncated.δ₂_one_comp_σ₂_one, CategoryTheory.Presheaf.freeYonedaHomEquiv_comp, CategoryTheory.SimplicialObject.σ_naturality, CategoryTheory.Limits.coprod.pentagon, CategoryTheory.Bicategory.hom_inv_whiskerRight_whiskerRight_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_comp, CategoryTheory.Limits.hasPushout_of_epi_comp, CategoryTheory.Limits.coprod.map_codiag, HomologicalComplex.Hom.next_eq, CategoryTheory.Comma.map_map_right, CategoryTheory.MonoidalCategory.DayConvolution.whiskerRight_comp_unit_app_assoc, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd_assoc, CochainComplex.shiftShortComplexFunctorIso_add'_hom_app, CategoryTheory.Bicategory.triangle_assoc_comp_left, CategoryTheory.Limits.pullbackProdFstIsoProd_hom_fst_assoc, CategoryTheory.ShortComplex.Hom.comp_τ₃, AlgebraicGeometry.Scheme.Hom.isOver_iff, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_hom_app, CategoryTheory.Limits.pullbackAssoc_inv_fst_snd, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom, CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_inv_hom_id_assoc, CategoryTheory.ShortComplex.RightHomologyData.p_g'_assoc, AlgebraicGeometry.Scheme.PartialMap.fromSpecStalkOfMem_compHom, CategoryTheory.ShortComplex.homologyMap'_comp, CochainComplex.cm5b.fac, CategoryTheory.Quotient.comp_natTransLift_assoc, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₃_assoc, SheafOfModules.instIsRightAdjointPushforwardCompSheafRingCatMapSheafPushforwardContinuous, HomologicalComplex.mapBifunctor₂₃.d₃_eq, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_right, CategoryTheory.Bicategory.associator_inv_naturality_right, CategoryTheory.CostructuredArrow.unop_left_comp_ofMkLEMk_unop, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_point_assoc, PresheafOfModules.ι_fromFreeYonedaCoproduct, CategoryTheory.MonoidalCategory.id_whiskerLeft, CategoryTheory.GrpObj.comp_zpow, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι, CategoryTheory.leftAdjointOfStructuredArrowInitialsAux_apply, CategoryTheory.Limits.colimitIsoSwapCompColim_hom_app, CochainComplex.HomComplex.Cochain.toSingleMk_v, groupCohomology.eq_d₂₃_comp_inv_assoc, CategoryTheory.Limits.BinaryBiconeMorphism.winr, CategoryTheory.Localization.HasProductsOfShapeAux.adj_counit_app, CategoryTheory.Monad.algebraEquivOfIsoMonads_unitIso, CategoryTheory.Functor.Monoidal.whiskerLeft_μ_δ, CategoryTheory.Functor.IsStronglyCocartesian.universal_property', CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIso_hom, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_hom_comp_homologyIso_inv, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₃, HomologicalComplex₂.D₁_D₁, CategoryTheory.Limits.kernelSubobjectIsoComp_hom_arrow, CategoryTheory.Adjunction.compYonedaIso_hom_app_app, RingCat.hom_comp, SSet.Subcomplex.toRange_ι_assoc, AlgebraicGeometry.AffineSpace.map_over_assoc, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapCompIso_hom, AlgebraicGeometry.Scheme.IdealSheafData.inclusion_subschemeι_assoc, CategoryTheory.InjectiveResolution.complex_d_comp, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app_assoc, CategoryTheory.leftDistributor_hom, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.associator_hom_unit_unit, TopCat.Presheaf.germ_res', CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapComp_hom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.w_app, HomologicalComplex.restrictionCyclesIso_hom_iCycles, CategoryTheory.FreeBicategory.mk_right_unitor_inv, CategoryTheory.MonoidalCategory.DayFunctor.ν_comp_unitDesc_assoc, CategoryTheory.Functor.RightExtension.postcomp₁_map_right, AlgebraicGeometry.IsClosedImmersion.comp, CategoryTheory.Limits.PushoutCocone.condition_assoc, CategoryTheory.epi_comp_iff_of_epi, CategoryTheory.Bicategory.whiskerLeft_comp, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompCoyoneda, CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_comp, TopologicalSpace.Opens.map_comp_obj_unop, CategoryTheory.Functor.Monoidal.map_rightUnitor_inv, CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_snd, CategoryTheory.Limits.colimit.ι_map, SSet.RelativeMorphism.Homotopy.h₀_assoc, HomologicalComplex.homotopyCofiber.desc_f', CategoryTheory.Subobject.ofMkLE_arrow, CategoryTheory.Iso.isoInverseComp_hom_app, CategoryTheory.Over.prodLeftIsoPullback_inv_snd, CategoryTheory.tensorLeftHomEquiv_naturality, CategoryTheory.whiskerLeft_coprod_inl_leftDistrib_inv, CategoryTheory.ShortComplex.leftRightHomologyComparison_fac, CategoryTheory.Subgroupoid.mul, HomologicalComplex₂.D₂_D₁_assoc, CategoryTheory.FinCategory.categoryAsType_comp, CategoryTheory.Limits.pushoutIsoUnopPullback_inr_hom_assoc, CategoryTheory.Limits.PreservesPullback.iso_inv_fst_assoc, CategoryTheory.IsPushout.inl_isoIsPushout_inv, CategoryTheory.Limits.piObjIso_hom_comp_π, CategoryTheory.MonoidalClosed.uncurry_natural_left_assoc, CategoryTheory.Iso.inv_comp_eq_id, CategoryTheory.GradedObject.mapMap_comp_assoc, CategoryTheory.kernelCokernelCompSequence.snakeInput_v₂₃_τ₃, Bimod.left_assoc_assoc, CategoryTheory.MonoidalCategory.tensorμ_natural_right, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app, CategoryTheory.ShortComplex.SnakeInput.L₀X₂ToP_comp_pullback_snd, ModuleCat.restrictScalarsId'App_hom_naturality, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map, HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac', CategoryTheory.whiskerRight_coprod_inl_rightDistrib_inv, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.ShortComplex.LeftHomologyData.ofAbelian_H, CategoryTheory.IsSifted.factorization_prodComparison_colim, CategoryTheory.Comma.mapRight_obj_hom, CategoryTheory.NatIso.naturality_1, CategoryTheory.ShortComplex.ShortExact.comp_δ, CategoryTheory.LaxBraidedFunctor.comp_hom, CategoryTheory.Comma.mapRightIso_inverse_map_right, ProfiniteGrp.ProfiniteCompletion.lift_eta_assoc, CategoryTheory.MorphismProperty.RightFraction.map_hom_ofInv_id, AlgebraicGeometry.IsSeparated.instIsClosedImmersionLiftSchemeId, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app, AlgebraicGeometry.Scheme.Pullback.tensorCongr_SpecTensorTo, CategoryTheory.MonoidalClosed.uncurry_pre_app_assoc, CategoryTheory.ShortComplex.RightHomologyData.copy_p, CategoryTheory.Oplax.StrongTrans.Modification.whiskerLeft_naturality, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_hom_assoc, CategoryTheory.Abelian.coimage_image_factorisation, CategoryTheory.Limits.Cocones.whiskeringEquivalence_unitIso, CommSemiRingCat.ofHom_comp, CategoryTheory.LaxFunctor.mapComp_naturality_left_app_assoc, CategoryTheory.Bicategory.conjugateEquiv_apply, CategoryTheory.Bicategory.prod_whiskerRight_fst, AlgebraicGeometry.Scheme.Hom.SpecMap_residueFieldMap_fromSpecResidueField_assoc, CategoryTheory.Iso.inv_hom_id_triangle_hom₂_assoc, CategoryTheory.Sheaf.comp_val, CategoryTheory.Limits.image.lift_fac_assoc, CategoryTheory.InjectiveResolution.desc_commutes_zero_assoc, CategoryTheory.Functor.ShiftSequence.induced.isoZero_hom_app_obj, CategoryTheory.Injective.comp_factorThru_assoc, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoColimitUncurryWhiskeringLeft₂_inv_assoc, CategoryTheory.Limits.colimitCurrySwapCompColimIsoColimitCurryCompColim_ι_ι_inv, CategoryTheory.Pseudofunctor.DescentData.comp_hom, CategoryTheory.Bicategory.whiskerRight_comp_symm, Semigrp.ofHom_comp, CategoryTheory.Functor.LaxRightLinear.μᵣ_associativity_inv_assoc, CategoryTheory.Functor.shiftMap_comp', CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε, CategoryTheory.rightUnitor_inv_braiding, CategoryTheory.ThinSkeleton.fromThinSkeleton_map, CategoryTheory.Limits.MonoFactorisation.compMono_I, CategoryTheory.GradedObject.Monoidal.rightUnitor_naturality_assoc, StalkSkyscraperPresheafAdjunctionAuxs.germ_fromStalk, AlgebraicGeometry.IsImmersion.comp, HomologicalComplex.biprod_lift_fst_f, SSet.Subcomplex.lift_ι_assoc, HomologicalComplex.XIsoOfEq_hom_comp_d_assoc, CategoryTheory.NatTrans.vcomp_app', CategoryTheory.Grothendieck.comp_base, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_inv_τl, CategoryTheory.Adjunction.Triple.rightToLeft_eq_units, HomologicalComplex.pOpcycles_opcyclesIsoSc'_inv_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv, SimplicialObject.Splitting.cofan_inj_eq, CategoryTheory.Bicategory.Pith.comp₂_iso_hom_assoc, CategoryTheory.Limits.inl_pushoutAssoc_inv_assoc, CategoryTheory.Limits.coker_map, Bimod.right_assoc, HomologicalComplex.ιTruncLE_naturality, CategoryTheory.HasShift.Induced.zero_inv_app_obj, CategoryTheory.End.mul_def, SimplexCategoryGenRel.standardσ_simplicialInsert, CategoryTheory.ConcreteCategory.comp_apply, AlgebraicGeometry.Scheme.Hom.toNormalization_fromNormalization_assoc, CategoryTheory.Subobject.ofLE_arrow_assoc, CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_inv, CategoryTheory.GradedObject.Monoidal.symmetry, HomologicalComplex₂.D₂_D₂, CategoryTheory.Cat.leftUnitor_hom_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.hom_inv_actionHomLeft'_assoc, CategoryTheory.Bicategory.associator_eqToHom_hom_assoc, CategoryTheory.Limits.pullback_diagonal_map_snd_snd_fst_assoc, CommGrpCat.coe_comp, ModuleCat.exteriorPower.iso₀_hom_naturality, CategoryTheory.Limits.inr_inl_pushoutLeftPushoutInrIso_hom, CategoryTheory.shift_shift_neg', CategoryTheory.NatTrans.CommShift.shift_comm, CategoryTheory.NatTrans.naturality_2_assoc, CategoryTheory.ShortComplex.Homotopy.g_h₃_assoc, HomologicalComplex.truncLE'_d_eq_toCycles, CategoryTheory.GrpObj.lift_inv_comp_right, CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_snd, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_inv_app, CategoryTheory.Limits.kernelFactorThruImage_hom_comp_ι_assoc, CategoryTheory.Retract.retract, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimIso_aux_assoc, CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inr_assoc, CategoryTheory.LocalizerMorphism.commShift_iso_inv_app, CategoryTheory.MonoidalCategory.id_tensor_comp_tensor_id, CategoryTheory.Bicategory.whiskerRight_id, CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv'_assoc, CategoryTheory.Grothendieck.isoMk_inv_fiber, CategoryTheory.GradedObject.ιMapBifunctor₁₂BifunctorMapObj_eq_assoc, Homotopy.prevD_succ_cochainComplex, CategoryTheory.Limits.prod.symmetry'_assoc, CategoryTheory.Limits.WalkingReflexivePair.leftCompReflexion_eq, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality_assoc, SimplexCategory.Truncated.δ₂_zero_comp_δ₂_two_assoc, CommMonCat.hom_comp, CategoryTheory.MonoOver.mapIso_counitIso, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_hom, CategoryTheory.HasShift.Induced.add_hom_app_obj, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_hom_fac_app, HomotopicalAlgebra.FibrantObject.HoCat.exists_resolution_map, HomologicalComplex.d_toCycles_assoc, CategoryTheory.Abelian.coim_map, CategoryTheory.Limits.coend.condition, CategoryTheory.ExponentiableMorphism.comp_pushforward, CategoryTheory.biproduct_ι_comp_rightDistributor_hom, HomologicalComplex₂.ιTotalOrZero_map_assoc, CategoryTheory.rightDistributor_hom_comp_biproduct_π_assoc, CategoryTheory.MorphismProperty.RespectsLeft.precomp, CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLift_assoc, CategoryTheory.CatCommSq.hComp_iso_hom_app, CategoryTheory.pullbackShiftFunctorZero_inv_app, CategoryTheory.ShortComplex.Splitting.id, CategoryTheory.Subobject.ofMkLE_comp_ofLEMk_assoc, CategoryTheory.Under.liftCone_pt, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f_assoc, HomologicalComplex₂.ιTotal_map, CategoryTheory.Limits.biprod.inr_snd_assoc, CategoryTheory.Iso.homFromEquiv_symm_apply, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app, CategoryTheory.MonObj.comp_mul_assoc, CategoryTheory.NatTrans.rightOp_comp, groupHomology.π_comp_H0Iso_hom_assoc, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans, HomologicalComplex.xPrevIsoSelf_comp_dTo, CategoryTheory.isIso_comp_right_iff, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_hom_fac_app, SheafOfModules.unitHomEquiv_symm_freeHomEquiv_apply, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality, CochainComplex.homotopyUnop_hom_eq, CategoryTheory.CatCommSq.iso_inv_naturality, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_comp, CategoryTheory.Dial.triangle, CategoryTheory.Kleisli.Adjunction.toKleisli_map, CategoryTheory.coyonedaEquiv_comp, HomologicalComplex₂.ι_totalShift₁Iso_hom_f_assoc, groupHomology.d₃₂_comp_d₂₁_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.hom_inv_actionHomLeft_assoc, CategoryTheory.Functor.mapProjectiveResolution_π, CategoryTheory.Limits.Cocones.whiskeringEquivalence_inverse, CategoryTheory.Adjunction.localization_unit_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_def'_assoc, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₂, CategoryTheory.NatTrans.app_naturality, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_left, CategoryTheory.CartesianMonoidalCategory.tensorμ_fst_assoc, CategoryTheory.Limits.inr_opProdIsoCoprod_inv_assoc, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd_assoc, CategoryTheory.ObjectProperty.isoHom_inv_id_hom, SimplexCategory.const_subinterval_eq, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₂, CategoryTheory.IsHomLift.comp_lift_id_right, AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimage, CategoryTheory.Oplax.LaxTrans.naturality_comp_assoc, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_π_assoc, CategoryTheory.Functor.Monoidal.map_leftUnitor_inv, CategoryTheory.Limits.PushoutCocone.isoMk_inv_hom, CategoryTheory.Limits.π_comp_colimitLeftOpIsoUnopLimit_inv, HomologicalComplex.opcyclesOpIso_inv_naturality, CategoryTheory.NatTrans.Equifibered.comp, CategoryTheory.conjugateEquiv_symm_apply_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_id_assoc, AlgebraicGeometry.Scheme.ι_toIso_inv_assoc, HomologicalComplex.ι_mapBifunctorAssociatorX_hom, CategoryTheory.HopfObj.mul_antipode, HomologicalComplex.mapBifunctor₁₂.ι_D₁_assoc, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality, CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_snd_assoc, CochainComplex.mappingCone.inr_f_d, CategoryTheory.Over.tensorObj_ext_iff, CategoryTheory.Join.mapWhiskerLeft_whiskerLeft, CategoryTheory.MonoidalCategory.MonoidalRightAction.inv_hom_actionHomLeft, HomologicalComplex.extend.XOpIso_hom_d_op, CategoryTheory.RetractArrow.i_w, CategoryTheory.IsSplitEqualizer.condition_assoc, CategoryTheory.ε_η_app_assoc, CategoryTheory.Oplax.OplaxTrans.categoryStruct_comp_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_right_unitality_assoc, CategoryTheory.CommGrp.comp_hom, AlgebraicGeometry.Scheme.Hom.toImage_imageι, CategoryTheory.Functor.PreservesRightKanExtension.preserves, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app', CategoryTheory.Limits.FormalCoproduct.category_comp_f, AlgebraicGeometry.Scheme.IdealSheafData.ideal_le_ker_glueDataObjι, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_c_app, CategoryTheory.ReflQuiv.comp_map, CategoryTheory.OppositeShift.adjunction_unit, TopCat.Presheaf.germ_stalkPullbackInv_assoc, CategoryTheory.CostructuredArrow.map_obj_hom, CategoryTheory.ε_naturality_assoc, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_hom_whiskerRight_π_assoc, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_tensorDec, CategoryTheory.Localization.Monoidal.pentagon_aux₂, AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_pullbackHom, CategoryTheory.MonoidalCategory.rightUnitor_inv_comp_tensorHom_assoc, CategoryTheory.MonoidalCategory.id_tensor_rightUnitor_inv_assoc, CategoryTheory.coev_expComparison, CategoryTheory.nerve.homEquiv_apply, CategoryTheory.ShortComplex.leftRightHomologyComparison'_fac, CategoryTheory.Limits.FormalCoproduct.hom_ext_iff, CategoryTheory.MonoidalClosed.uncurry_natural_right_assoc, CategoryTheory.Functor.Monoidal.map_associator, HeytAlg.hom_comp, HomologicalComplex₂.ι_D₁_assoc, CategoryTheory.Limits.IsColimit.ι_map, CategoryTheory.isIso_iff_coyoneda_map_bijective, CategoryTheory.Limits.colimit.ι_post, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π_assoc, CategoryTheory.conjugateEquiv_apply_app, CategoryTheory.Limits.biproductBiproductIso_hom, HomotopicalAlgebra.Cylinder.ofFactorizationData_i₀, CochainComplex.HomComplex.δ_v, CategoryTheory.CatCenter.mul_app, CategoryTheory.Monad.Algebra.assoc_assoc, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_id, CategoryTheory.Limits.biproduct.fromSubtype_toSubtype_assoc, AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_hom_π, CategoryTheory.SmallObject.SuccStruct.ofCocone_map_assoc, CategoryTheory.Functor.partialLeftAdjointHomEquiv_symm_comp, AlgebraicGeometry.PresheafedSpace.componentwiseDiagram_map, groupCohomology.mapShortComplexH2_comp_assoc, AlgebraicGeometry.PresheafedSpace.stalkMap_germ_assoc, CategoryTheory.rightDistributor_ext₂_left_iff, CategoryTheory.Idempotents.app_p_comp, CategoryTheory.MonoidalCategory.whiskerRight_id_symm_assoc, CategoryTheory.ShortComplex.SnakeInput.comp_f₀, CategoryTheory.Limits.kernelCompMono_hom, AlgebraicGeometry.Scheme.Cover.comp_app, CategoryTheory.toSheafify_sheafifyLift_assoc, AlgebraicGeometry.Proj.basicOpenToSpec_app_top, CategoryTheory.exp.coev_ev, HomologicalComplex.d_comp_d_assoc, CategoryTheory.Endofunctor.Algebra.functorOfNatTransComp_hom_app_f, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_naturality, CategoryTheory.Limits.biprod.symmetry, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_naturality, CategoryTheory.ShortComplex.op_pOpcycles_opcyclesOpIso_hom, CategoryTheory.SimplicialObject.δ_comp_σ_succ'_assoc, ContinuousMap.Homotopy.eq_path_of_eq_image, CochainComplex.HomComplex.Cochain.comp_v, CategoryTheory.Limits.WidePushout.hom_eq_desc, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp, HomologicalComplex.homologyι_singleObjOpcyclesSelfIso_inv, CategoryTheory.GradedObject.Monoidal.rightUnitor_inv_apply, CategoryTheory.ShortComplex.π_leftRightHomologyComparison'_ι, HomologicalComplex₂.ιTotal_totalFlipIso_f_inv_assoc, AddCommGrpCat.coe_comp, CategoryTheory.MonoidalCategory.tensorμ_comp_μ_tensorHom_μ_comp_μ_assoc, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.Square.Hom.comm₁₃_assoc, CategoryTheory.Functor.homologySequenceδ_naturality, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_app_assoc, CochainComplex.fromSingle₀Equiv_apply_coe, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app, CategoryTheory.evaluationRightAdjoint_map_app, CategoryTheory.GradedObject.Monoidal.leftUnitor_inv_apply, CategoryTheory.Functor.IsEventuallyConstantTo.isoMap_inv_hom_id, CategoryTheory.eHomWhiskerRight_comp_assoc, CochainComplex.HomComplex.Cochain.comp_zero_cochain_v, HomologicalComplex.dgoToHomologicalComplex_obj_d, CategoryTheory.NatIso.naturality_1'_assoc, CategoryTheory.Bicategory.lanLiftUnit_desc_assoc, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right', CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.liftHom_fac_assoc, CategoryTheory.Endofunctor.Coalgebra.comp_eq_comp, Lat.hom_comp, CategoryTheory.Adjunction.ε_comp_map_ε_assoc, CategoryTheory.Limits.BinaryFan.IsLimit.lift'_coe, CategoryTheory.tensorRightHomEquiv_whiskerRight_comp_evaluation, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_fst, CategoryTheory.toOverIsoToOverUnit_inv_app_left, SimplicialObject.Split.comp_F, CategoryTheory.Subobject.inf_comp_left, CategoryTheory.Bicategory.whiskerLeft_hom_inv, CategoryTheory.Limits.colimit.map_desc, CochainComplex.mappingCone.inr_f_descShortComplex_f_assoc, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app, CommMonCat.coe_comp, CategoryTheory.Limits.Types.binaryProductIso_inv_comp_fst, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.presheafHom_naturality, Bimod.id_whiskerLeft_bimod, CategoryTheory.NatTrans.hcomp_app, CategoryTheory.Limits.Pi.reindex_hom_π_assoc, CategoryTheory.Bicategory.Adj.Bicategory.whiskerRight_τl, AlgebraicGeometry.Scheme.Opens.isoOfLE_hom_ι_assoc, CategoryTheory.Dial.braiding_naturality_right, CategoryTheory.Idempotents.Karoubi.comp_p, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_snd, prodIsoPullback_inv_fst_assoc, CategoryTheory.Functor.FullyFaithful.preimage_comp, CategoryTheory.Linear.units_smul_comp, CategoryTheory.MonoidalCategory.tensor_whiskerLeft_symm_assoc, CategoryTheory.Bicategory.mateEquiv_id_comp_right, CategoryTheory.Limits.Cocone.w_assoc, AlgebraicGeometry.Scheme.toSpecΓ_naturality_assoc, CategoryTheory.Linear.leftComp_apply, CategoryTheory.ShortComplex.cyclesMap'_comp_assoc, CategoryTheory.Functor.OplaxMonoidal.δ_fst_assoc, CategoryTheory.Bicategory.leftUnitor_comp_inv, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_inv_π_assoc, HomologicalComplex.XIsoOfEq_inv_naturality_assoc, CategoryTheory.Limits.Pi.reindex_hom_π, AlgebraicGeometry.Scheme.Modules.pushforwardComp_inv_app_app, CochainComplex.mappingCone.liftCochain_v_descCochain_v, CategoryTheory.GradedObject.CofanMapObjFun.inj_iso_hom, CategoryTheory.Idempotents.app_p_comm, AlgebraicGeometry.LocallyQuasiFinite.comp_iff, CategoryTheory.Presheaf.restrictedULiftYoneda_obj_map, CategoryTheory.Pseudofunctor.mapComp_id_left, CategoryTheory.Limits.inr_comp_pushoutObjIso_hom_assoc, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition_assoc, CategoryTheory.CopyDiscardCategory.copy_tensor, CategoryTheory.Limits.IsBilimit.total, CategoryTheory.IsIso.inv_comp, CategoryTheory.Limits.pushoutIsoUnopPullback_inv_snd, CategoryTheory.BraidedCategory.braiding_tensor_left_hom, CategoryTheory.SemiadditiveOfBinaryBiproducts.comp_add, CategoryTheory.Limits.pushout.condition, AddMonCat.hom_comp, CategoryTheory.Localization.Monoidal.whiskerRight_comp, CochainComplex.mappingCone.lift_f_fst_v, CategoryTheory.obj_zero_map_μ_app_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomLeft_action_assoc, CategoryTheory.braiding_inv_tensorUnit_right_assoc, CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_inv, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_map_app_app, AddGrpCat.hom_comp, GrpWithZero.hom_comp, CategoryTheory.Bicategory.postcomp_obj, CategoryTheory.Functor.isoShift_inv_naturality_assoc, CochainComplex.mappingCone.inl_v_triangle_mor₃_f, CategoryTheory.ShortComplex.Splitting.s_g_assoc, CategoryTheory.Limits.kernelSubobject_arrow_assoc, HomologicalComplex.extend.XOpIso_hom_d_op_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality_app, CategoryTheory.image_ι_op_comp_imageUnopOp_hom, CategoryTheory.Presheaf.comp_isLocallySurjective_iff, CategoryTheory.Limits.HasColimit.isoOfEquivalence_hom_π, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit, CategoryTheory.Idempotents.Karoubi.decompId_p_naturality, CategoryTheory.Functor.partialRightAdjointHomEquiv_comp_symm_assoc, SimplexCategory.δ_comp_σ_self_assoc, CategoryTheory.Mat_.ι_additiveObjIsoBiproduct_inv_assoc, CategoryTheory.Functor.ι_colimitIsoColimitGrothendieck_inv_assoc, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_whisker_right, AlgebraicTopology.DoldKan.PInfty_f_naturality_assoc, HomologicalComplex.mapBifunctorMapHomotopy.comm₁, CategoryTheory.StrictPseudofunctor.comp_mapComp_hom, CategoryTheory.Adjunction.Triple.adj₁_counit_app_rightToLeft_app, HomologicalComplex₂.ι_totalShift₁Iso_inv_f, HomologicalComplex.extendSingleIso_inv_f_assoc, AlgebraicGeometry.IsFinite.comp_iff, CategoryTheory.Limits.WidePullback.π_arrow, CategoryTheory.ComposableArrows.IsComplex.opcyclesToCycles_fac_assoc, CategoryTheory.Monad.FreeCoequalizer.condition, CategoryTheory.Functor.IsCoverDense.Types.appHom_valid_glue, CategoryTheory.Limits.inr_inl_pushoutRightPushoutInlIso_hom, CategoryTheory.Bicategory.leftZigzagIso_hom, CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_mapComp, CategoryTheory.Limits.pullbackAssoc_inv_fst_snd_assoc, CategoryTheory.Functor.obj.ε_def_assoc, CategoryTheory.Functor.Monoidal.ε_η, CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_ext_iff, CategoryTheory.Sieve.equalizer_apply, CategoryTheory.Functor.rightDerived_fac_assoc, AlgebraicGeometry.PresheafedSpace.stalkMap.stalkSpecializes_stalkMap, CategoryTheory.OrthogonalReflection.D₁.ι_comp_t_assoc, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap, HomologicalComplex.XIsoOfEq_inv_comp_XIsoOfEq_inv, CochainComplex.ιTruncLE_naturality_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_hom_inv, AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_fst_assoc, HomologicalComplex₂.ι_totalDesc_assoc, CategoryTheory.IsIso.inv_comp_eq, AlgebraicGeometry.SheafedSpace.comp_hom_c_app, CategoryTheory.MonObj.lift_lift_assoc, CategoryTheory.Limits.image.preComp_epi_of_epi, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd, Bicategory.Opposite.bicategory_associator_hom_unop2, CategoryTheory.Comonad.ForgetCreatesColimits'.newCocone_ι_app, CategoryTheory.SplitEpi.comp_section_, HomotopicalAlgebra.LeftHomotopyClass.postcomp_mk, CategoryTheory.Limits.inl_opProdIsoCoprod_inv_assoc, CategoryTheory.Functor.Monoidal.map_whiskerRight, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app, AlgebraicGeometry.Scheme.isoOfEq_hom_ι, CategoryTheory.Functor.OplaxRightLinear.δᵣ_associativity_inv, CategoryTheory.OplaxFunctor.PseudoCore.mapCompIso_hom, CategoryTheory.StrictPseudofunctor.comp_mapId_hom, CategoryTheory.Limits.inl_comp_pushoutComparison, CategoryTheory.Square.Hom.comp_τ₂, CategoryTheory.CatCenter.smul_iso_inv_eq'_assoc, CategoryTheory.homOfLE_comp_eqToHom, CategoryTheory.Over.rightUnitor_inv_left_fst, HomologicalComplex.truncGEMap_comp_assoc, CategoryTheory.eHomWhiskerLeft_comp, Bimod.TensorBimod.actRight_one', CategoryTheory.CostructuredArrow.homMk'_mk_id, CategoryTheory.epi_comp', CategoryTheory.Oplax.LaxTrans.comp_app, CategoryTheory.Limits.biprod.inr_fst, CategoryTheory.Subobject.ofMkLEMk_comp_ofMkLE_assoc, HomotopicalAlgebra.Cylinder.ofFactorizationData_i₁, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_symm_apply_right, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_def, AlgebraicGeometry.IsAffineHom.comp_iff, CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_comm_f_assoc, CategoryTheory.Limits.IsBilimit.binary_total, CategoryTheory.MonObj.mul_leftUnitor, CategoryTheory.Iso.eq_comp_inv, CategoryTheory.Adjunction.mapCommMon_unit, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality_assoc, HomologicalComplex.extendHomologyIso_hom_homologyι_assoc, CochainComplex.mappingCone.inr_triangleδ, CategoryTheory.Comonad.coassoc, AlgebraicGeometry.Scheme.comp_base, SimplicialObject.opFunctor_map_app, CategoryTheory.Functor.RightExtension.precomp_map_left, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_snd_assoc, CategoryTheory.μ_naturalityᵣ_assoc, CategoryTheory.kernelCokernelCompSequence.ι_φ, CategoryTheory.Pretriangulated.TriangleMorphism.comm₃, AlgebraicGeometry.IsClosedImmersion.lift_fac_assoc, CochainComplex.HomComplex.Cochain.ofHoms_comp, CategoryTheory.LaxFunctor.mapComp_assoc_right_app, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_snd_fst, groupCohomology.cocyclesIso₀_inv_comp_iCocycles, CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_hom_assoc, HomologicalComplex.XIsoOfEq_inv_naturality, CommBialgCat.ofHom_comp, CategoryTheory.Limits.pullbackObjIso_inv_comp_fst_assoc, CategoryTheory.Iso.hom_inv_id_app_app_assoc, CategoryTheory.Limits.coneOfIsSplitMono_ι, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.unit_app_ev_app_app, CategoryTheory.ShortComplex.homologyπ_naturality_assoc, CategoryTheory.Oplax.OplaxTrans.associator_hom_as_app, CategoryTheory.End.smul_left, HomologicalComplex.mapBifunctorFlipIso_hom_naturality_assoc, HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id, CategoryTheory.MonObj.lift_comp_one_right_assoc, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d, CategoryTheory.Iso.hom_inv_id_eval_assoc, CategoryTheory.ShortComplex.cyclesIsoX₂_inv_hom_id_assoc, CategoryTheory.GlueData.t_inv, HomologicalComplex.fromOpcycles_d_assoc, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_hom_inv_assoc, HomologicalComplex.restriction_d_eq, CategoryTheory.Limits.kernelSubobjectMap_comp, CategoryTheory.SimplicialObject.δ_comp_δ_assoc, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality', CategoryTheory.Pseudofunctor.toOplax_mapComp, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app_assoc, groupCohomology.mapCocycles₂_comp_i_assoc, CategoryTheory.Limits.coprod.inl_desc_assoc, SheafOfModules.GeneratingSections.opEpi_comp, HomologicalComplex.dTo_eq, CategoryTheory.eq_whisker, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over_assoc, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.left_triangle_components, CategoryTheory.CartesianMonoidalCategory.lift_braiding_hom, CategoryTheory.Bimon.compatibility_assoc, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_unit_app, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ_ΓToStalk, CategoryTheory.Functor.Monoidal.whiskerRight_μ_δ_assoc, CategoryTheory.Idempotents.Karoubi.eqToHom_f, CategoryTheory.ShortComplex.HomologyMapData.comp_left, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_symm_apply, CategoryTheory.Limits.image.fac_lift, CategoryTheory.Limits.pullback.diagonal_snd, AlgebraicGeometry.IsZariskiLocalAtSource.iff_of_iSup_eq_top, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomLeft_action, CategoryTheory.Under.pushout_map, CategoryTheory.IsPushout.inr_isoPushout_inv_assoc, CategoryTheory.PreZeroHypercover.inv_hom_h₀_comp_f, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_app, AlgebraicTopology.DoldKan.comp_P_eq_self_iff, SimplexCategory.δ_zero_mkOfSucc, CategoryTheory.Functor.ranCounit_app_whiskerLeft_ranAdjunction_unit_app_assoc, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_ι, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_inv, CategoryTheory.Limits.kernelSubobject_comp_mono_isIso, CategoryTheory.BicategoricalCoherence.tensorRight_iso, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom, CategoryTheory.ModObj.mul_smul'_assoc, CategoryTheory.Bicategory.inv_hom_whiskerRight_whiskerRight, CategoryTheory.Limits.Types.binaryCoproductIso_inl_comp_inv, CategoryTheory.ComonadHom.app_ε, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp, CategoryTheory.Limits.pushoutIsoUnopPullback_inv_fst, AlgebraicGeometry.Scheme.Hom.appLE_map', CategoryTheory.Functor.IsStronglyCartesian.map_self, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₃_assoc, CategoryTheory.IsComonHom.hom_comul, CategoryTheory.ComonObj.comul_counit, CategoryTheory.isPullback_of_cofan_isVanKampen, CategoryTheory.Limits.biprod.map_snd, AlgebraicGeometry.Scheme.isoSpec_hom_naturality, CategoryTheory.Bicategory.Prod.sectR_mapComp_inv, CategoryTheory.Bicategory.Prod.fst_mapComp_hom, CategoryTheory.LocalizerMorphism.LeftResolution.Hom.comm, CategoryTheory.Limits.fiberwiseColimitLimitIso_hom_app, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTrans_obj_str, CategoryTheory.Limits.kernelIsoOfEq_hom_comp_ι, CochainComplex.πTruncGE_naturality, CategoryTheory.Limits.inr_pushoutLeftPushoutInrIso_inv, groupHomology.π_comp_H2Iso_inv_assoc, CategoryTheory.FreeMonoidalCategory.normalize_naturality, HomologicalComplex.homologyπ_extendHomologyIso_inv, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHom_def_assoc, HomologicalComplex.homologyπ_restrictionHomologyIso_inv, AlgebraicGeometry.PresheafedSpace.comp_c_app, CategoryTheory.epi_comp, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality', CategoryTheory.Limits.opCoproductIsoProduct'_comp_self, PresheafOfModules.map_comp_apply, CategoryTheory.MonoidalClosed.uncurry_pre_app, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_hom_inv_assoc, AlgebraicGeometry.Scheme.homOfLE_ι, CategoryTheory.IsFiltered.crown₄, CategoryTheory.Limits.biproduct.toSubtype_π_assoc, CategoryTheory.Localization.comp_liftNatTrans, CategoryTheory.Limits.Multicoequalizer.ι_sigmaπ_assoc, CategoryTheory.IsHomLift.lift_comp_eqToHom, AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv_assoc, CategoryTheory.Functor.Final.extendCocone_obj_ι_app, CochainComplex.mappingCone.id_X, AlgebraicGeometry.Scheme.Pullback.residueFieldCongr_inv_residueFieldMap_ofPoint, HomologicalComplex.truncGE'Map_comp, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.ShortComplex.leftHomologyMap_op, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃_associator_inv, CategoryTheory.InjectiveResolution.toRightDerivedZero_eq, CategoryTheory.Bicategory.id_whiskerLeft_symm, CategoryTheory.CartesianMonoidalCategory.braiding_inv_fst_assoc, CategoryTheory.ShortComplex.p_fromOpcycles, HomologicalComplex.iCyclesIso_inv_hom_id, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitIso_hom_naturality_assoc, CommRingCat.HomTopology.continuous_precomp, CategoryTheory.Dial.associator_hom_F, CochainComplex.mappingCone.inr_descShortComplex_assoc, groupHomology.chainsMap_f_3_comp_chainsIso₃, CategoryTheory.PreZeroHypercover.inv_inv_h₀_comp_f, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoColimitUncurryWhiskeringLeft₂_inv, CategoryTheory.ShortComplex.SnakeInput.δ_L₃_f, CategoryTheory.MorphismProperty.Comma.comp_left_assoc, groupHomology.mapCycles₁_id_comp_assoc, CategoryTheory.Limits.image.map_ι, CategoryTheory.Limits.opCoproductIsoProduct'_hom_comp_proj, CategoryTheory.MonoidalCategory.DayConvolution.unit_naturality_assoc, CategoryTheory.ProdPreservesConnectedLimits.forgetCone_π, CategoryTheory.Limits.biprod.symmetry'_assoc, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd, CategoryTheory.Functor.shift_map_op_assoc, CategoryTheory.Limits.coker.condition_assoc, AlgebraicGeometry.Scheme.Hom.resLE_map, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_π_app, CategoryTheory.strongMono_comp, CategoryTheory.Limits.ConeMorphism.w, CategoryTheory.CostructuredArrow.homMk'_right, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_comp_assoc, CategoryTheory.Adjunction.leftAdjointCompNatTrans₀₁₃_eq_conjugateEquiv_symm, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app, CategoryTheory.Functor.IsFibered.comp, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι_assoc, AlgebraicGeometry.Scheme.Hom.comp_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality, HomotopicalAlgebra.PrepathObject.ι_p₁_assoc, groupHomology.eq_d₂₁_comp_inv, CategoryTheory.Preadditive.nsmul_comp, SimplexCategoryGenRel.σ_comp_σ_nat, CategoryTheory.MonoidalCategory.tensor_inv_hom_id', CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitIso_hom_naturality_assoc, CategoryTheory.Limits.equalizerSubobject_arrow_comp, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_inv_assoc, CategoryTheory.Functor.LeftLinear.μₗ_comp_δₗ_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_inv_app, CategoryTheory.Limits.CoconeMorphism.hom_inv_id_assoc, CategoryTheory.GrpObj.one_inv_assoc, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι_ι_eq_support_inter, HomologicalComplex.pOpcycles_opcyclesIsoSc'_inv, HomotopicalAlgebra.RightHomotopyRel.precomp, CategoryTheory.Localization.Monoidal.triangle_aux₃, CategoryTheory.ShortComplex.homologyOpIso_inv_naturality, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app', CategoryTheory.ihom.ev_coev_assoc, CategoryTheory.Limits.limit.lift_post, AlgebraicGeometry.Scheme.Pullback.left_affine_comp_pullback_hasPullback, CategoryTheory.Functor.OplaxRightLinear.δᵣ_unitality_hom_assoc, CategoryTheory.Limits.ι_comp_sigmaObjIso_inv, AlgebraicGeometry.Scheme.hom_base_inv_base, CategoryTheory.CosimplicialObject.δ_comp_σ_self', CategoryTheory.Limits.ι_colimitLimitIso_limit_π, CategoryTheory.Limits.BinaryBicone.inl_snd_assoc, CategoryTheory.Bicategory.LeftLift.IsKan.fac_assoc, CategoryTheory.ShortComplex.mapOpcyclesIso_inv_naturality, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr, HomologicalComplex.cyclesOpIso_inv_naturality_assoc, CategoryTheory.MonoidalCategory.DayConvolution.whiskerLeft_comp_unit_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocIso_inv_naturality_assoc, CategoryTheory.Over.mapComp_hom_app_left, CategoryTheory.Functor.Final.ι_colimitIso_hom_assoc, SSet.Subcomplex.toImage_ι_assoc, CategoryTheory.kernelCokernelCompSequence.inr_π_assoc, CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_fst, CategoryTheory.BimonObj.mul_counit_assoc, CategoryTheory.instIsComonHomComp, AlgebraicGeometry.Scheme.Cover.comp_idx_apply, AlgebraicGeometry.IsLocalAtSource.iff_of_openCover, CategoryTheory.Functor.mapGrp_obj_grp_one, AlgebraicGeometry.StructureSheaf.toStalk_stalkSpecializes, CategoryTheory.MonoidalCategory.triangle_assoc_comp_left_inv_assoc, CategoryTheory.Functor.biprodComparison'_comp_biprodComparison_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_inv_hom, CategoryTheory.Limits.Cotrident.IsColimit.homIso_natural, CategoryTheory.Limits.LimitPresentation.changeDiag_π, CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_fst_fst_assoc, CategoryTheory.MonoidalCategory.rightUnitor_tensor_inv_assoc, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app_assoc, groupHomology.mapCycles₁_comp, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_inv, CategoryTheory.Limits.coequalizer.condition, CategoryTheory.GradedObject.ι_mapBifunctorComp₁₂MapObjIso_hom_assoc, CategoryTheory.Monad.Algebra.comp_eq_comp, CategoryTheory.Limits.prodComparison_natural_of_natTrans_assoc, TopologicalSpace.Opens.mapComp_hom_app, SSet.Subcomplex.topIso_inv_ι, AlgebraicGeometry.Scheme.toSpecΓ_naturality, CategoryTheory.Adjunction.mapCommMon_counit, CategoryTheory.Limits.biprod.mapBiprod_hom_desc, CategoryTheory.Functor.Monoidal.map_ε_η_assoc, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app_assoc, CategoryTheory.Limits.ι_colimitLimitToLimitColimit_π, CategoryTheory.coprod_inl_rightDistrib_hom, CategoryTheory.MonoidalCategory.id_tensor_comp_assoc, CategoryTheory.CatCenter.naturality, CategoryTheory.Bicategory.Adj.rightUnitor_inv_τl, AlgebraicTopology.DoldKan.QInfty_idem_assoc, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_left, SimplexCategory.const_fac_thru_zero, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app, HomologicalComplex.singleObjHomologySelfIso_hom_singleObjOpcyclesSelfIso_hom, HomologicalComplex.mapBifunctor₁₂.hom_ext_iff, CategoryTheory.ShortComplex.iCycles_g, groupHomology.map_comp, CategoryTheory.FreeBicategory.mk_vcomp, HomologicalComplex.mapBifunctor₂₃.ι_mapBifunctor₂₃Desc, CategoryTheory.Subobject.ofLE_comp_ofLEMk_assoc, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_inv, CategoryTheory.LaxFunctor.PseudoCore.mapCompIso_inv, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_map, CategoryTheory.Dial.associatorImpl_inv_F, CategoryTheory.Functor.congr_hom_assoc, CategoryTheory.Limits.π_comp_colimitUnopIsoOpLimit_inv, smoothSheaf.ι_evalHom_assoc, CategoryTheory.Limits.Types.binaryProductFunctor_obj_map, CategoryTheory.Over.whiskerRight_left_fst, HomotopicalAlgebra.AttachCells.ofArrowIso_g₂, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_app_assoc, CategoryTheory.Functor.whiskeringRight₂_obj_obj_obj_map, CochainComplex.mappingConeCompHomotopyEquiv_comm₂_assoc, CategoryTheory.sheafComposeIso_hom_fac, CategoryTheory.Mathlib.Tactic.MonTauto.associator_inv_comp_tensorHom_tensorHom_assoc, AlgebraicGeometry.pointEquivClosedPoint_apply_coe, CategoryTheory.StrictlyUnitaryLaxFunctor.comp_mapId, CategoryTheory.CostructuredArrow.w_prod_snd_assoc, CategoryTheory.Over.postAdjunctionLeft_unit_app_left, CategoryTheory.Limits.fst_opProdIsoCoprod_hom_assoc, CategoryTheory.Limits.BiconeMorphism.wι, CategoryTheory.obj_μ_app, CategoryTheory.PreOneHypercover.Homotopy.wl_assoc, CategoryTheory.Limits.Multicofork.snd_app_right_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality, CategoryTheory.Functor.ι_colimitIsoColimitGrothendieck_hom, SheafOfModules.ιFree_mapFree_inv_assoc, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_naturality, CategoryTheory.Limits.limit.pre_post, CategoryTheory.μ_naturalityₗ, HomologicalComplex.truncGE'.d_comp_d, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_tensorHom_app, SimplexCategory.δ_comp_σ_succ_assoc, HomologicalComplex.Hom.sqFrom_comp, CategoryTheory.Comonad.counit_naturality, HomotopicalAlgebra.PrepathObject.symm_p, CategoryTheory.MonoidalCategory.hom_inv_whiskerRight_assoc, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right_assoc, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_counit_app, CochainComplex.mappingConeCompHomotopyEquiv_hom_inv_id, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp_val_app, CategoryTheory.IsPushout.inr_isoPushout_hom_assoc, CategoryTheory.GrothendieckTopology.sheafifyMap_sheafifyLift, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_inv_app, AlgebraicGeometry.Scheme.Hom.ι_toNormalization, CategoryTheory.Pseudofunctor.map₂_associator_app, CategoryTheory.Functor.leftDerivedNatTrans_comp_assoc, CategoryTheory.Equalizer.Sieve.w, BoolAlg.ofHom_comp, CategoryTheory.Cat.rightUnitor_hom_toNatTrans, CategoryTheory.Limits.Types.equalizerIso_inv_comp_ι, SemimoduleCat.MonoidalCategory.braiding_naturality_right, CategoryTheory.Limits.equalizer.condition, CategoryTheory.Comma.comp_right, AlgebraicGeometry.LocallyRingedSpace.Γ_Spec_left_triangle, SSet.PtSimplex.RelStruct.δ_castSucc_map, CategoryTheory.CosimplicialObject.δ_comp_σ_self_assoc, CategoryTheory.MorphismProperty.IsStableUnderComposition.comp_mem, CategoryTheory.Limits.PullbackCone.condition_assoc, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_fst_assoc, CategoryTheory.PullbackShift.adjunction_unit, CategoryTheory.Limits.kernelComparison_comp_ι, CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id, CategoryTheory.MonoidalCategory.inv_hom_whiskerRight_assoc, groupCohomology.π_map_assoc, CategoryTheory.SmallObject.SuccStruct.extendToSuccObjIso_hom_naturality_assoc, CategoryTheory.Limits.Trident.condition, CategoryTheory.Lax.OplaxTrans.naturality_comp, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_inv_toNatTrans_app_val_app, SimplexCategory.δ_comp_δ_self, isoOfQuasiIsoAt_hom_inv_id, CategoryTheory.ShortComplex.cyclesOpIso_hom_naturality, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_hom_π_π, CategoryTheory.Arrow.square_from_iso_invert, CategoryTheory.IsSplitCoequalizer.leftSection_bottom_assoc, CategoryTheory.Limits.coprodComparison_inl, Lat.comp_apply, HomologicalComplex.extendCyclesIso_inv_iCycles_assoc, CategoryTheory.Localization.Preadditive.add'_comp_assoc, ModuleCat.smul_naturality, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv, CategoryTheory.Limits.inl_inl_pushoutLeftPushoutInrIso_hom_assoc, CategoryTheory.Limits.CatCospanTransform.comp_whiskerRight_assoc, groupCohomology.toCocycles_comp_isoCocycles₂_hom, CategoryTheory.NatTrans.mapHomotopyCategory_comp, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_tensorDesc_app, SheafOfModules.pullback_map_ιFree_comp_pullbackObjFreeIso_hom_assoc, CategoryTheory.Bicategory.leftUnitor_inv_whiskerRight_assoc, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_SpecMap_awayMap_right_assoc, HomologicalComplex.singleObjCyclesSelfIso_hom_naturality, HomologicalComplex.mapBifunctor₁₂.ι_mapBifunctor₁₂Desc, CategoryTheory.Projective.factorThru_comp_assoc, HomologicalComplex.mapBifunctor₁₂.ι_D₂_assoc, CategoryTheory.Limits.prod.lift_fst, CategoryTheory.eHom_whisker_exchange_assoc, CategoryTheory.Functor.RepresentableBy.comp_homEquiv_symm, CategoryTheory.Bicategory.whiskerRight_comp_symm_assoc, CategoryTheory.Limits.PushoutCocone.condition, HomologicalComplex.cylinder.πCompι₀Homotopy.nullHomotopicMap_eq, CategoryTheory.Oplax.StrongTrans.Modification.whiskerRight_naturality, CategoryTheory.Limits.Cofork.condition_assoc, CategoryTheory.Congruence.compRight, CategoryTheory.coprod_inr_rightDistrib_hom, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app_assoc, CochainComplex.HomComplex.Cochain.fromSingleMk_postcomp, HomologicalComplex.singleObjCyclesSelfIso_inv_naturality_assoc, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_naturality_assoc, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv, SimplexCategory.mkOfSucc_subinterval_eq, CochainComplex.ConnectData.d_comp_d, CategoryTheory.IsFiltered.toSup_commutes, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_hom, HomologicalComplex.homotopyCofiber.inrX_d_assoc, CategoryTheory.Enriched.FunctorCategory.enrichedId_π_assoc, CategoryTheory.δ_naturalityᵣ_assoc, CategoryTheory.kernelCokernelCompSequence.ι_fst_assoc, HomologicalComplex.mapBifunctor.hom_ext_iff, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict_assoc, CategoryTheory.Over.prodLeftIsoPullback_inv_fst, groupCohomology.map_comp, CochainComplex.mappingCone.d_snd_v'_assoc, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_comp_assoc, CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inl, CategoryTheory.CatCenter.mul_app', FGModuleCat.hom_comp, CategoryTheory.ι_preservesColimitIso_inv_assoc, CategoryTheory.Limits.MonoFactorisation.isoComp_e, HomologicalComplex.homotopyCofiber.descSigma_ext_iff, CategoryTheory.IsPushout.inr_isoPushout_inv, HomologicalComplex.ι_mapBifunctorDesc, groupHomology.map_id_comp, AlgebraicGeometry.Scheme.comp_coeBase_assoc, CategoryTheory.Limits.Fork.ι_postcompose, CategoryTheory.Abelian.im_map, CategoryTheory.Limits.MonoFactorisation.fac_assoc, ProfiniteAddGrp.ofHom_comp, CategoryTheory.StructuredArrow.map₂_map_left, CategoryTheory.Limits.limitIsoSwapCompLim_hom_app, CategoryTheory.Limits.coprodComparison_inv_natural, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_assoc, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_coproductIsoSelf_inv_assoc, HeytAlg.coe_comp, CategoryTheory.Limits.pullbackProdSndIsoProd_hom_fst, ModuleCat.imageIsoRange_hom_subtype, CategoryTheory.Bicategory.Adj.rightUnitor_hom_τr, HomotopicalAlgebra.PrepathObject.p_fst, GrpWithZero.coe_comp, CategoryTheory.Iso.eHomCongr_comp_assoc, CategoryTheory.Limits.Multiequalizer.hom_ext_iff, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_coproductIsoSelf_inv, AlgebraicTopology.karoubi_alternatingFaceMapComplex_d, CategoryTheory.Adjunction.homEquiv_unit, CategoryTheory.Functor.LaxLeftLinear.μₗ_associativity_inv_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_hom_comp_π_assoc, CategoryTheory.Under.postAdjunctionRight_unit_app_right, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_inv_app, CategoryTheory.NatTrans.shift_comm_assoc, CategoryTheory.ComposableArrows.Precomp.map_zero_succ_succ, groupHomology.mapCycles₁_comp_i, HomologicalComplex.d_pOpcycles, SimplexCategoryGenRel.δ_comp_σ_self, CategoryTheory.Subfunctor.preimage_comp, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality, AlgebraicGeometry.Scheme.Hom.congr_app, CategoryTheory.Functor.CoreMonoidal.left_unitality, CategoryTheory.Functor.IsCartesian.of_iso_comp, CategoryTheory.Pseudofunctor.mapComp_id_right, CategoryTheory.Adjunction.mapCommGrp_unit, CategoryTheory.Bicategory.Adjunction.comp_counit, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app, CategoryTheory.Abelian.LeftResolution.π_naturality_assoc, CategoryTheory.Preadditive.comp_neg, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_inv_colimit_map, CategoryTheory.CartesianMonoidalCategory.comp_lift, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_comp_assoc, CategoryTheory.Functor.map_comp_heq, CategoryTheory.Limits.IsImage.ofIsoI_lift, CategoryTheory.Functor.Final.ι_colimitIso_inv, CategoryTheory.shiftFunctorCompIsoId_add'_inv_app, CategoryTheory.Bicategory.LeftExtension.whiskering_map, CategoryTheory.Bicategory.comp_whiskerRight, CategoryTheory.BicategoricalCoherence.left_iso, CategoryTheory.shiftFunctorAdd_zero_add_hom_app, CategoryTheory.Limits.Pi.ι_π_of_ne, AlgebraicGeometry.Scheme.IdealSheafData.inclusion_subschemeι, CategoryTheory.EnrichedFunctor.forget_map, CategoryTheory.Functor.mapGrp_id_one, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_naturality, PartOrdEmb.comp_apply, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_symm, CategoryTheory.OrthogonalReflection.iteration_map_succ, CategoryTheory.MonoidalClosed.uncurry_eq, SimplexCategory.Truncated.Hom.tr_comp', Bicategory.Opposite.bicategory_leftUnitor_hom_unop2, TopCat.ofHom_comp, CategoryTheory.Limits.ι_comp_colimitRightOpIsoUnopLimit_hom_assoc, AlgebraicGeometry.Scheme.Opens.toSpecΓ_naturality_assoc, CategoryTheory.Adjunction.leftAdjointUniq_hom_app_counit_assoc, CategoryTheory.Monad.ForgetCreatesLimits.newCone_π_app, CategoryTheory.Iso.homCongr_comp, CategoryTheory.Functor.Monoidal.μ_comp_assoc, CategoryTheory.CostructuredArrow.mkPrecomp_left, CategoryTheory.NatTrans.comp_app_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id_app, CategoryTheory.Bicategory.comp_whiskerLeft_symm, CategoryTheory.GrpObj.η_whiskerRight_commutator_assoc, Bicategory.Opposite.op2_whiskerRight, CategoryTheory.Bicategory.inv_whiskerRight, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_assoc, CategoryTheory.SingleFunctors.Hom.comm_assoc, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_app_π_assoc, CategoryTheory.Limits.Types.coproductIso_mk_comp_inv, CategoryTheory.CostructuredArrow.mapIso_functor_map_left, CategoryTheory.MonoidalCategory.rightUnitor_inv_naturality, CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapComp_inv, CategoryTheory.ι_preservesColimitIso_hom_assoc, AlgebraicGeometry.instSmoothOfRelativeDimensionOfNatNatCompScheme, CategoryTheory.Iso.comp_hom_eq_id, CategoryTheory.shiftFunctorComm_hom_app_comp_shift_shiftFunctorAdd_hom_app, CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_comp_d_assoc, CategoryTheory.Localization.Monoidal.μ_natural_right, CategoryTheory.Limits.CatCospanTransform.whiskerRight_id, AlgebraicGeometry.IsAffineOpen.isoSpec_inv, CategoryTheory.GrpObj.lift_comp_inv_right_assoc, CategoryTheory.bijection_natural, AlgebraicTopology.DoldKan.PInfty_f_comp_QInfty_f_assoc, TopCat.Presheaf.comp_app, ChainComplex.toSingle₀Equiv_apply_coe, AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_self_assoc, HomologicalComplex.homologyι_opcyclesToCycles_assoc, CategoryTheory.Limits.Pi.reindex_inv_π_assoc, SSet.horn.faceSingletonComplIso_inv_ι, AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem_ι_assoc, HomologicalComplex.extendMap_f, CategoryTheory.is_coprod_iff_isPushout, CategoryTheory.left_unitality_app_assoc, HomologicalComplex₂.ι_totalShift₂Iso_inv_f_assoc, SimplexCategory.δ_comp_σ_of_gt', CategoryTheory.CartesianMonoidalCategory.lift_lift_associator_inv_assoc, CategoryTheory.GrothendieckTopology.Point.Hom.sheafFiber_comp_assoc, CategoryTheory.μ_naturality₂, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom, CategoryTheory.NormalEpi.w, CategoryTheory.Pretriangulated.TriangleMorphism.comm₁_assoc, CategoryTheory.Limits.limit.post_π, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ, CategoryTheory.Over.prodLeftIsoPullback_inv_snd_assoc, CategoryTheory.Limits.prodComparison_comp, CategoryTheory.Limits.BinaryBiconeMorphism.winl_assoc, CategoryTheory.Over.rightUnitor_inv_left_snd, SimplexCategoryGenRel.δ_comp_σ_of_gt, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHom_comp_assoc, CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_hom, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_map_left, CategoryTheory.GradedObject.ι_mapBifunctor₁₂BifunctorDesc, AlgebraicTopology.DoldKan.P_f_idem_assoc, CategoryTheory.Bicategory.mateEquiv_symm_apply', HomologicalComplex₂.d_comm, CategoryTheory.Subfunctor.image_comp, CategoryTheory.CartesianMonoidalCategory.braiding_hom_fst, CategoryTheory.Oplax.LaxTrans.naturality_naturality, CategoryTheory.rightAdjointMate_comp_evaluation_assoc, CategoryTheory.ShortComplex.HomologyMapData.comp_right, CategoryTheory.MonoidalCategory.whisker_assoc_assoc, CategoryTheory.Limits.PullbackCone.combine_π_app, TopCat.Presheaf.germ_stalkSpecializes_assoc, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone_isColimit_desc, CategoryTheory.Pseudofunctor.mapComp'_comp_id, CategoryTheory.Localization.homEquiv_eq, CategoryTheory.Oplax.StrongTrans.naturality_comp, AlgHom.toUnder_comp, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_hom_assoc, CategoryTheory.GrothendieckTopology.whiskerRight_toPlus_comp_plusCompIso_hom, AlgebraicGeometry.Proj.pullbackAwayιIso_inv_snd_assoc, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberι_assoc, CategoryTheory.OplaxFunctor.map₂_leftUnitor_assoc, CategoryTheory.Bifunctor.map_id_comp, CategoryTheory.ShortComplex.Hom.comp_τ₂, CategoryTheory.leftUnitor_inv_braiding_assoc, CategoryTheory.NatTrans.op_whiskerRight_assoc, CategoryTheory.Subobject.ofLEMk_comp, CategoryTheory.Bicategory.conjugateEquiv_id_comp_right_apply, CategoryTheory.Adjunction.leftAdjointUniq_trans_app_assoc, CategoryTheory.CartesianMonoidalCategory.lift_lift_associator_inv, CategoryTheory.ShortComplex.comp_τ₂, CategoryTheory.Oplax.OplaxTrans.associator_inv_as_app, CategoryTheory.Functor.map_hom_inv, HomologicalComplex.pOpcycles_restrictionOpcyclesIso_inv, CategoryTheory.EnrichedCategory.comp_id, CategoryTheory.mono_comp', HomologicalComplex.extend.mapX_some, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality', CategoryTheory.GradedObject.ιMapBifunctorBifunctor₂₃MapObj_eq_assoc, CategoryTheory.NatTrans.vcomp_app, CategoryTheory.SingleFunctors.comp_hom_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp_app, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.fromBiprod_δ_assoc, CategoryTheory.GradedObject.ιMapObjOrZero_mapMap, CategoryTheory.ShortComplex.π₁Toπ₂_comp_π₂Toπ₃, CategoryTheory.Limits.IsColimit.ι_map_assoc, CategoryTheory.Bicategory.Adjunction.homEquiv₂_apply, CategoryTheory.Over.mapPullbackAdj_counit_app, CategoryTheory.Functor.ι_biproductComparison'_assoc, AlgebraicGeometry.Scheme.IdealSheafData.comapIso_hom_snd_assoc, CategoryTheory.Limits.MultispanIndex.ι_fstSigmaMap_assoc, CategoryTheory.Limits.Pi.ι_π, CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoSelf_hom, Rep.standardComplex.εToSingle₀_comp_eq, CategoryTheory.LocalizerMorphism.LeftResolution.Hom.comp_f, CategoryTheory.Functor.isoShift_inv_naturality, CategoryTheory.ShortComplex.RightHomologyMapData.commg'_assoc, HomologicalComplex.inr_biprodXIso_inv, CategoryTheory.Limits.Cofan.IsColimit.inj_desc, CategoryTheory.Equivalence.cancel_counitInv_right, CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_inv_hom, PartOrdEmb.hom_comp, CategoryTheory.Idempotents.Karoubi.HomologicalComplex.comp_p_d_assoc, CategoryTheory.braiding_rightUnitor_aux₁, CategoryTheory.ShortComplex.RightHomologyMapData.homologyMap_comm, AlgebraicGeometry.Scheme.Hom.app_appIso_inv_assoc, CompHausLike.sigmaComparison_eq_comp_isos, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict, CategoryTheory.Limits.Fork.hom_comp_ι, CategoryTheory.ShortComplex.SnakeInput.Hom.comm₁₂, CategoryTheory.rightDistributor_inv_comp_biproduct_π, CategoryTheory.Functor.CoreMonoidal.μIso_hom_natural_left, CategoryTheory.Localization.Monoidal.triangle_aux₁_assoc, CategoryTheory.μ_naturalityᵣ, CategoryTheory.Oplax.StrongTrans.naturality_id_assoc, CategoryTheory.Functor.Monoidal.map_associator'_assoc, CategoryTheory.StrictlyUnitaryLaxFunctorCore.mapComp_naturality_right, CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.liftHom_fac, CategoryTheory.Join.mapWhiskerRight_comp, CochainComplex.HomComplex.Cochain.zero_cochain_comp_v, CochainComplex.MappingConeCompHomotopyEquiv.hom_inv_id_assoc, CategoryTheory.MonoidalCategory.DayConvolution.hexagon_forward, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_inv_app_unop, CategoryTheory.MorphismProperty.Over.map_comp, CategoryTheory.MonoidalCategory.associator_inv_naturality_left_assoc, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_comp, CategoryTheory.ShortComplex.mapLeftHomologyIso_hom_naturality, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_app, CategoryTheory.leftDistributor_hom_comp_biproduct_π, CategoryTheory.Adjunction.Triple.whiskerRight_rightToLeft_assoc, CategoryTheory.Equivalence.changeFunctor_unitIso_hom_app, CategoryTheory.Limits.colimit.ι_inv_pre, CategoryTheory.Oplax.LaxTrans.naturality_id, CategoryTheory.HopfObj.one_antipode, TopCat.Presheaf.stalkPushforward_germ_assoc, CategoryTheory.Limits.pullback.comp_diagonal_assoc, TopCat.pullbackIsoProdSubtype_inv_fst_assoc, CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_inv_assoc, HomotopicalAlgebra.FibrantObject.HoCat.resolutionMap_fac, CategoryTheory.IsFiltered.coeq₃_condition₃, AlgebraicGeometry.Scheme.Pullback.range_fst_comp, CategoryTheory.ShortComplex.leftHomologyMap'_comp_assoc, CategoryTheory.Square.Hom.comm₁₃, CategoryTheory.ComposableArrows.opEquivalence_unitIso_inv_app, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_left_unitor, CategoryTheory.ShortComplex.SnakeInput.naturality_φ₁_assoc, HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom_desc_hom, CategoryTheory.instIsMonHomComp, CategoryTheory.Limits.prod.diag_map_fst_snd, CochainComplex.g_shortComplexTruncLEX₃ToTruncGE, AlgCat.ofHom_comp, HomologicalComplex₂.d_f_comp_d_f_assoc, CategoryTheory.Pseudofunctor.toLax_mapComp, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_restriction_assoc, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.associator_naturality, CategoryTheory.Dial.rightUnitorImpl_inv_F, CategoryTheory.Mathlib.Tactic.MonTauto.associator_hom_comp_tensorHom_tensorHom_assoc, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_ihom_ev_app_assoc, AlgebraicGeometry.Proj.SpecMap_awayMap_awayι_assoc, CategoryTheory.nerve.nonempty_compStruct_iff, AlgebraicGeometry.Scheme.isoSpec_hom_naturality_assoc, CategoryTheory.Limits.braid_natural_assoc, TopCat.prodIsoProd_hom_snd_assoc, CategoryTheory.isCommMonObj_iff_commutator_eq_toUnit_η, AlgebraicGeometry.pullbackSpecIso_inv_snd, AlgebraicGeometry.IsImmersion.instMapDescScheme, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₃, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι_ι, HomologicalComplex.homotopyCofiber.inlX_sndX_assoc, CategoryTheory.ShortComplex.Homotopy.compRight_h₀, CategoryTheory.Pseudofunctor.isoMapOfCommSq_horiz_id, CategoryTheory.Functor.Monoidal.μ_fst_assoc, CategoryTheory.Oplax.OplaxTrans.naturality_comp, CategoryTheory.Limits.PreservesKernel.iso_inv_ι_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.leftUnitor_inv_one_tensor_mul_assoc, CategoryTheory.Equivalence.map_η_comp_η, CategoryTheory.CatEnriched.id_hComp_heq, CategoryTheory.MonObj.comp_one, CategoryTheory.CosimplicialObject.δ_comp_δ, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app_assoc, CategoryTheory.CartesianMonoidalCategory.tensorHom_fst, AlgebraicGeometry.quasiCompact_comp, CategoryTheory.Limits.pullbackConeEquivBinaryFan_functor_map_hom, CategoryTheory.MonoidalCategory.DayConvolution.associator_inv_unit_unit, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_hom, HomologicalComplex.mapBifunctorAssociatorX_hom_D₂, CategoryTheory.ShortComplex.leftRightHomologyComparison'_eq_descH, CategoryTheory.Join.pseudofunctorLeft_mapComp_hom_toNatTrans_app, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural, CategoryTheory.Sheaf.toImage_ι, CategoryTheory.Equivalence.counit_naturality_assoc, CategoryTheory.StructuredArrow.mapNatIso_functor_obj_hom, CategoryTheory.Limits.Types.Small.productIso_inv_comp_π, ModuleCat.restrictScalarsId'App_inv_naturality, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_inv_hom_assoc, CategoryTheory.Limits.biproduct.map_π, MonCat.ofHom_comp, CategoryTheory.MorphismProperty.RightFraction.map_hom_ofInv_id_assoc, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_inv_naturality, CategoryTheory.MonoidalCategory.DayConvolution.hexagon_reverse, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left, CategoryTheory.uliftYonedaEquiv_symm_map, CategoryTheory.Limits.ConeMorphism.map_w_assoc, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_hom_app, CategoryTheory.Enriched.FunctorCategory.homEquiv_apply_π, HomologicalComplex.homologyι_comp_fromOpcycles, CategoryTheory.MorphismProperty.RightFraction.map_s_comp_map, groupCohomology.comp_d₂₃_eq, CategoryTheory.IsSplitCoequalizer.leftSection_top, CategoryTheory.homOfLE_op_comp_eqToHom_assoc, CategoryTheory.Lax.LaxTrans.naturality_comp, CategoryTheory.NonPreadditiveAbelian.σ_comp, CategoryTheory.Mon.tensorObj_one, SSet.comp_app_assoc, CategoryTheory.PreservesImage.factorThruImage_comp_hom_assoc, FintypeCat.comp_apply, CategoryTheory.Adjunction.unit_app_shift_commShiftIso_inv_app, AlgebraicGeometry.Proj.pullbackAwayιIso_inv_fst, CategoryTheory.Comma.mapRightComp_inv_app_right, CategoryTheory.Subobject.ofLEMk_comp_ofMkLE, CategoryTheory.Bicategory.InducedBicategory.bicategory_whiskerRight_hom, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_naturality_assoc, CategoryTheory.Limits.biprod.symmetry', CategoryTheory.IsMod_Hom.smul_hom, CategoryTheory.Limits.biproduct.matrix_desc_assoc, CategoryTheory.Limits.Multicofork.condition_assoc, quasiIsoAt_comp, CategoryTheory.Limits.BinaryFan.braiding_hom_snd, ProfiniteGrp.comp_apply, CategoryTheory.SemiCartesianMonoidalCategory.comp_toUnit_assoc, AlgebraicGeometry.Scheme.hom_base_inv_base_assoc, CategoryTheory.Iso.inv_comp_eq, CategoryTheory.Monad.left_unit, AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex_homotopyHomInvId, HomologicalComplex₂.ι_D₂, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom, CategoryTheory.GlueData.ι_gluedIso_inv_assoc, CategoryTheory.ShortComplex.RightHomologyData.wι_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π, CategoryTheory.Iso.map_hom_inv_id_assoc, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_right, CategoryTheory.ReflQuiv.comp_eq_comp, CategoryTheory.Functor.CommShift.ofIso_commShiftIso_hom_app, CategoryTheory.Limits.limit.isoLimitCone_hom_π_assoc, CategoryTheory.Quotient.LiftCommShift.iso_hom_app, CategoryTheory.Oplax.StrongTrans.id_naturality_inv, CategoryTheory.CosimplicialObject.comp_right_app, CategoryTheory.Functor.relativelyRepresentable.pullback₃.map_p₁_comp, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_comp, CategoryTheory.InjectiveResolution.Hom.ι_comp_hom_assoc, CategoryTheory.OplaxFunctor.mapComp_assoc_left_app, CategoryTheory.ShortComplex.homology_π_ι, CategoryTheory.preservesColimitIso_inv_comp_desc, Action.hom_inv_hom, FintypeCat.comp_hom, CategoryTheory.ShortComplex.homologyι_naturality_assoc, CategoryTheory.Functor.Monoidal.coreMonoidalTransport_μIso_hom, CategoryTheory.Limits.Cocone.category_comp_hom, CategoryTheory.NatTrans.IsMonoidal.unit, AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ, CategoryTheory.Functor.lanUnit_app_app_lanAdjunction_counit_app_app, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_snd, CategoryTheory.Adjunction.compUliftCoyonedaIso_inv_app_app_down, CategoryTheory.Lax.OplaxTrans.vComp_naturality_comp, CategoryTheory.MonoidalCategory.id_tensor_associator_inv_naturality, AlgebraicGeometry.AffineSpace.map_comp, CategoryTheory.MonObj.one_comp_assoc, CategoryTheory.GradedObject.mapObj_ext_iff, prevD_eq_toPrev_dTo, ModuleCat.cokernel_π_cokernelIsoRangeQuotient_hom, ModuleCat.extendScalars_assoc_assoc, CategoryTheory.ShortComplex.cokernel_π_comp_cokernelToAbelianCoimage, CategoryTheory.Limits.comp_zero, CategoryTheory.Endofunctor.Coalgebra.Hom.h_assoc, AlgebraicTopology.DoldKan.MorphComponents.preComp_b, CategoryTheory.CosimplicialObject.σ_naturality, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst, CategoryTheory.Limits.biprod.lift_mapBiprod, CategoryTheory.Limits.BinaryBiconeMorphism.winl, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_assoc, CategoryTheory.MonoidalCategory.id_tensor_rightUnitor_inv, CategoryTheory.e_comp_id_assoc, CategoryTheory.EnrichedCategory.id_comp, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_leftUnitor_inv_as_app, AlgebraicTopology.DoldKan.Γ₂_obj_p_app, SimplexCategory.eq_σ_comp_of_not_injective, CategoryTheory.Limits.ι_colimMap, prodIsoPullback_hom_fst_assoc, CategoryTheory.Over.prodLeftIsoPullback_hom_snd, CategoryTheory.Functor.lanUnit_app_whiskerLeft_lanAdjunction_counit_app, CategoryTheory.Cat.HasLimits.homDiagram_map, AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_comp_iff_of_isOpenImmersion, Homotopy.nullHomotopicMap'_comp, CategoryTheory.Pseudofunctor.map₂_right_unitor_assoc, CategoryTheory.monoidalOfHasFiniteProducts.associator_hom_snd_fst, CategoryTheory.GrpObj.inv_comp_assoc, CategoryTheory.Bicategory.Prod.sectL_mapComp_hom, CategoryTheory.Comon.comp_hom, CategoryTheory.PreZeroHypercover.Hom.w₀, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc_assoc, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_assoc, CategoryTheory.Limits.biprod.braiding_map_braiding_assoc, CategoryTheory.rightDistributor_ext_right_iff, CategoryTheory.CostructuredArrow.mkPrecomp_right, HomotopicalAlgebra.AttachCells.cell_def, CategoryTheory.Bicategory.associator_inv_naturality_left, CategoryTheory.Functor.ι_colimitIsoOfIsLeftKanExtension_inv, AlgebraicGeometry.Proj.basicOpenToSpec_SpecMap_awayMap, CategoryTheory.IsUniversalColimit.isPullback_prod_of_isColimit, CategoryTheory.GradedObject.Monoidal.tensorHom_comp_tensorHom, CategoryTheory.Limits.PreservesPullback.iso_inv_snd, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc, HomotopicalAlgebra.PrepathObject.trans_p₁, CategoryTheory.Limits.limit.pre_π_assoc, CategoryTheory.Limits.PullbackCone.op_ι_app, CategoryTheory.ShortComplex.opcyclesOpIso_hom_naturality_assoc, AlgebraicGeometry.Scheme.Cover.ι_fromGlued_assoc, CategoryTheory.Functor.Monoidal.coreMonoidalTransport_εIso_hom, CategoryTheory.Iso.hom_inv_id_triangle_hom₂, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_hom_app, CategoryTheory.Functor.Monoidal.map_δ_μ_assoc, CategoryTheory.coprodComparison_tensorRight_braiding_hom, AddMonCat.coe_comp, CategoryTheory.Limits.biprod.inl_desc_assoc, groupHomology.mapCycles₂_id_comp, CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_eq, CategoryTheory.Limits.hasImage_iso_comp, CategoryTheory.Limits.π_reflexiveCoequalizerIsoCoequalizer_inv_assoc, ProfiniteAddGrp.comp_apply, CategoryTheory.MonoidalCategory.whiskerRight_id_symm, CategoryTheory.GradedObject.mapBifunctorRightUnitorCofan_inj, CategoryTheory.Limits.biprod.inl_map, SSet.PtSimplex.RelStruct.δ_castSucc_map_assoc, CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc, smoothSheafCommRing.forgetStalk_inv_comp_eval_assoc, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality_app, CategoryTheory.Iso.hom_inv_id_triangle_hom₂_assoc, SimplexCategoryGenRel.standardσ_comp_standardσ_assoc, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero_assoc, AlgebraicGeometry.Scheme.fromSpecStalk_appTop, AlgebraicTopology.AlternatingFaceMapComplex.d_squared, CategoryTheory.Limits.inr_pushoutZeroZeroIso_hom, CategoryTheory.Limits.pushoutCoconeOfLeftIso_inl, CategoryTheory.Bicategory.leftUnitor_inv_naturality, CategoryTheory.Comonad.delta_naturality_assoc, CategoryTheory.Endofunctor.Algebra.Initial.right_inv, CategoryTheory.Join.mapWhiskerRight_whiskerRight, CategoryTheory.Presheaf.isLocallySurjective_comp_iff, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturality_assoc, CategoryTheory.ShiftMkCore.add_zero_hom_app, AlgebraicGeometry.Scheme.GlueData.glue_condition, CategoryTheory.ShortComplex.mapHomologyIso_hom_naturality_assoc, CategoryTheory.GradedObject.singleObjApplyIsoOfEq_inv_single_map, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_def', UniformSpaceCat.extension_comp_coe, CategoryTheory.StructuredArrow.IsUniversal.existsUnique, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_inv_hom, CategoryTheory.Limits.biprod.decomp_hom_to, CategoryTheory.Biprod.inr_ofComponents, CategoryTheory.Functor.liftOfIsRightKanExtension_fac_app, CategoryTheory.Limits.opCoproductIsoProduct_hom_comp_π, CategoryTheory.Limits.pullbackConeEquivBinaryFan_counitIso, CategoryTheory.Limits.PreservesPullback.iso_inv_fst, AlgebraicGeometry.pullbackRestrictIsoRestrict_inv_fst, CategoryTheory.Functor.congr_hom, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_map_left, SSet.PtSimplex.MulStruct.δ_succ_succ_map_assoc, CategoryTheory.Functor.OplaxMonoidal.oplax_right_unitality, CategoryTheory.Functor.Monoidal.map_whiskerLeft_assoc, CategoryTheory.Bicategory.unitors_equal, CategoryTheory.ShiftedHom.comp_mk₀, CategoryTheory.StructuredArrow.mapNatIso_functor_map_right, CategoryTheory.GradedObject.Monoidal.symmetry_assoc, CategoryTheory.Oplax.OplaxTrans.Modification.whiskerLeft_naturality_assoc, CategoryTheory.Biprod.ofComponents_snd, CategoryTheory.Functor.LaxLeftLinear.μₗ_naturality_right_assoc, CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono'_g'_τ₃, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc, ModuleCat.exteriorPower.iso₁_hom_naturality, Bimod.TensorBimod.middle_assoc', HomologicalComplex₂.total.mapAux.d₁_mapMap, CategoryTheory.Cat.associator_inv_app, CategoryTheory.Limits.pullback_diagonal_map_snd_fst_fst, CategoryTheory.Bicategory.associator_naturality_right, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counitIso_hom_app_tensor_assoc, CategoryTheory.MonoidalCategory.DayConvolution.pentagon, CategoryTheory.Limits.inr_pushoutLeftPushoutInrIso_inv_assoc, CategoryTheory.Bicategory.whiskerRightIso_inv, CategoryTheory.SmallObject.FunctorObjIndex.comm, CategoryTheory.IsSplitCoequalizer.leftSection_bottom, HomologicalComplex.singleObjHomologySelfIso_hom_singleObjHomologySelfIso_inv_assoc, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.ι_toBase, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_apply, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc_assoc, groupHomology.cyclesMap_comp_assoc, CochainComplex.mappingCone.lift_f_fst_v_assoc, CategoryTheory.Limits.biproduct.lift_matrix_assoc, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_snd, CategoryTheory.ShortComplex.LeftHomologyMapData.homologyMap_comm, CategoryTheory.Cat.Hom.comp_toFunctor, CategoryTheory.Limits.biproduct.lift_desc_assoc, CategoryTheory.NatTrans.leftDerivedToHomotopyCategory_comp_assoc, HomologicalComplex.cyclesIsoSc'_inv_iCycles_assoc, CategoryTheory.Limits.prod.leftUnitor_inv_naturality_assoc, CategoryTheory.InducedCategory.comp_hom_assoc, AlgebraicGeometry.Scheme.Pullback.Triplet.Spec_map_tensor_isPullback, CategoryTheory.kernelCokernelCompSequence.ι_fst, CategoryTheory.Subgroupoid.coe_comp_coe, CategoryTheory.OverPresheafAux.YonedaCollection.map₂_snd, AlgebraicGeometry.IsOpenImmersion.isoOfRangeEq_inv_fac_assoc, CategoryTheory.Dial.comp_le_lemma, CategoryTheory.Limits.biprod.braiding_map_braiding, CategoryTheory.Sieve.comp_mem_iff, CategoryTheory.tensorRightHomEquiv_symm_coevaluation_comp_whiskerRight, CategoryTheory.Over.whiskerRight_left_snd_assoc, CategoryTheory.Sheaf.ΓHomEquiv_naturality_left, Mathlib.Tactic.Bicategory.structuralIsoOfExpr_whiskerLeft, CategoryTheory.Arrow.w_mk_right, CategoryTheory.ShortComplex.Homotopy.compRight_h₁, CategoryTheory.NatTrans.mapHomologicalComplex_comp, CategoryTheory.Monad.algebraFunctorOfMonadHomComp_hom_app_f, CategoryTheory.InjectiveResolution.ι_f_zero_comp_complex_d_assoc, CategoryTheory.Cat.rightUnitor_hom_app, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_snd_snd, CategoryTheory.Functor.whiskerLeft_comp_whiskerRight_assoc, CategoryTheory.Functor.Monoidal.whiskerLeft_ε_η_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π_assoc, AlgebraicGeometry.Scheme.Cover.gluedCoverT'_fst_fst, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.g'_eq, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerLeft_assoc, AlgebraicGeometry.pullbackSpecIso_hom_base, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_apply_f, CategoryTheory.Linear.smulOfRingMorphism_smul_eq, CategoryTheory.shiftComm_hom_comp_assoc, CategoryTheory.Limits.biproduct.ι_matrix, CategoryTheory.yonedaMon_naturality_assoc, CategoryTheory.Preadditive.comp_sum_assoc, HomologicalComplex₂.d₁_eq, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocIso_hom_naturality_assoc, CategoryTheory.SmallObject.SuccStruct.extendToSuccObjIso_hom_naturality, Bimod.LeftUnitorBimod.inv_hom_id, DerivedCategory.right_fac_of_isStrictlyLE_of_isStrictlyGE, CategoryTheory.Oplax.LaxTrans.id_naturality, CategoryTheory.Limits.hasPushout_assoc_symm, AlgebraicGeometry.IsOpenImmersion.comp, CategoryTheory.Functor.OplaxMonoidal.δ_comp_whiskerLeft_δ_assoc, groupCohomology.π_comp_H0IsoOfIsTrivial_hom, CategoryTheory.kernelCokernelCompSequence.snakeInput_L₃_f, CategoryTheory.Limits.coprodComparison_inl_assoc, CategoryTheory.TwistShiftData.shiftFunctorZero_hom_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomLeft_tensor, CategoryTheory.Limits.inl_inl_pushoutLeftPushoutInrIso_hom, CategoryTheory.ProjectiveResolution.Hom.hom_comp_π_assoc, SheafOfModules.pushforwardComp_inv_app_val_app, CategoryTheory.Enriched.FunctorCategory.enriched_id_comp_assoc, CategoryTheory.CartesianMonoidalCategory.lift_braiding_inv, GrpCat.SurjectiveOfEpiAuxs.comp_eq, CommRingCat.Colimits.cocone_naturality, CategoryTheory.Pseudofunctor.ObjectProperty.ι_naturality, CategoryTheory.Limits.prodComparison_fst, CategoryTheory.Functor.Monoidal.transport_ε, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_id, LightCondensed.internallyProjective_iff_tensor_condition, CategoryTheory.Limits.isPushout_coequalizer_coprod, CategoryTheory.CartesianClosed.curry_natural_right_assoc, CategoryTheory.Functor.leftDerived_fac_assoc, HomologicalComplex.cyclesMap_comp, CategoryTheory.CartesianMonoidalCategory.tensorHom_snd_assoc, CategoryTheory.Limits.IsLimit.pullbackConeEquivBinaryFanFunctor_lift_left, AlgebraicGeometry.Scheme.Opens.toSpecΓ_appTop_assoc, AlgebraicGeometry.smooth_comp, CategoryTheory.NatTrans.app_homology, CategoryTheory.Pseudofunctor.mapComp_id_right_hom, CategoryTheory.Functor.OplaxLeftLinear.δₗ_naturality_left_assoc, HomologicalComplex.opcyclesToCycles_iCycles_assoc, CategoryTheory.yonedaMonObj_map, Homotopy.prevD_chainComplex, CategoryTheory.CartesianMonoidalCategory.map_toUnit_comp_terminalComparison_assoc, CategoryTheory.MonoidalCategory.whiskerLeft_id_assoc, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_point_assoc, CategoryTheory.ShortComplex.homologyMap'_op, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_unit_app, CategoryTheory.Oplax.StrongTrans.Modification.naturality_assoc, CategoryTheory.eComp_eHomWhiskerRight, groupCohomology.comp_d₀₁_eq, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality_assoc, CategoryTheory.Limits.FormalCoproduct.eval_map_app, CategoryTheory.LaxFunctor.mapComp_naturality_right_app_assoc, CategoryTheory.Grothendieck.comp_fiber, CategoryTheory.instIsSplitMonoComp, CategoryTheory.Limits.kernelBiproductToSubtypeIso_hom, CategoryTheory.ShortComplex.HomologyData.ofIso_left_i, CategoryTheory.Adjunction.mapGrp_unit, CategoryTheory.Limits.imageMonoIsoSource_hom_self, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_hom_fac_assoc, CategoryTheory.uliftYonedaEquiv_naturality, CategoryTheory.SimplicialObject.δ_comp_σ_self'_assoc, CategoryTheory.MonoidalCategory.hom_inv_whiskerRight, CategoryTheory.MonoidalCategory.comp_tensor_id_assoc, CategoryTheory.Over.associator_inv_left_fst_fst_assoc, CategoryTheory.IsFiltered.coeq₃_condition₁, CategoryTheory.MonoidalCategory.triangle_assoc, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_associator_hom_as_app, HomologicalComplex.homologyπ_singleObjHomologySelfIso_hom_assoc, CategoryTheory.Grothendieck.map_map, CategoryTheory.IsIso.inv_hom_id, CategoryTheory.Lax.LaxTrans.vComp_naturality_naturality, CategoryTheory.Bicategory.prod_whiskerRight_snd, CategoryTheory.OrthogonalReflection.toSucc_surjectivity, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocIso_hom_naturality, CategoryTheory.Functor.isoShift_hom_naturality, CategoryTheory.Adjunction.map_restrictFullyFaithful_unit_app_assoc, CategoryTheory.Limits.image.factorThruImage_preComp, CategoryTheory.CatEnrichedOrdinary.hComp_id, CategoryTheory.Limits.pullbackSymmetry_inv_comp_fst_assoc, CategoryTheory.MonoidalClosed.curry'_ihom_map, CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_inv, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.functorMap_comp, CategoryTheory.Limits.CokernelCofork.condition, CategoryTheory.GradedObject.ι_mapTrifunctorMapMap_assoc, CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_inv_desc_assoc, CategoryTheory.conjugateEquiv_counit_symm, AlgebraicGeometry.Scheme.stalkMap_congr_point_assoc, HomotopicalAlgebra.PrepathObject.RightHomotopy.refl_h, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.ev_naturality_app, smoothSheafCommRing.forgetStalk_inv_comp_eval, CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoSelf_hom_assoc, CategoryTheory.CartesianMonoidalCategory.prodComparison_snd_assoc, CategoryTheory.Limits.cokernel.condition, CategoryTheory.Functor.CommShift.isoZero'_inv_app, CategoryTheory.Limits.IsLimit.ofIsoLimit_lift, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_hom_τr, CategoryTheory.StrictPseudofunctor.comp_mapId_inv, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_assoc, CategoryTheory.GradedObject.Monoidal.tensorHom_comp_tensorHom_assoc, CategoryTheory.MonObj.mul_mul_mul_comm'_assoc, CategoryTheory.CatEnrichedOrdinary.hComp_comp, CategoryTheory.conj_eqToHom_iff_heq', HomologicalComplex.biprod_inr_snd_f, CategoryTheory.Functor.map_hom_inv_assoc, CategoryTheory.PreZeroHypercover.inj_sigmaOfIsColimit_f_assoc, ContinuousMap.Homotopy.apply_one_path, CategoryTheory.Functor.Monoidal.whiskerRight_η_ε_assoc, ModuleCat.restrictScalarsId'App_hom_naturality_assoc, CategoryTheory.Localization.Monoidal.associator_naturality₃, CategoryTheory.Over.associator_hom_left_fst, SimplexCategory.Truncated.δ₂_zero_comp_σ₂_zero_assoc, CategoryTheory.Limits.BinaryBiconeMorphism.wsnd, CategoryTheory.ShortComplex.cyclesMap'_comp, CategoryTheory.Bicategory.Adj.comp_τl, HomologicalComplex.singleMapHomologicalComplex_inv_app_self, AlgebraicGeometry.Scheme.fromSpecStalk_toSpecΓ, SimplexCategoryGenRel.δ_comp_σ_succ, CategoryTheory.MonObj.one_mul_assoc, CategoryTheory.Functor.Initial.extendCone_obj_π_app', CategoryTheory.Subfunctor.equalizer.ι_ι_assoc, TopCat.Presheaf.map_germ_eq_Γgerm, CategoryTheory.Limits.WidePullback.hom_ext_iff, SimplexCategoryGenRel.δ_comp_σ_of_le_assoc, groupHomology.coinvariantsMk_comp_H0Iso_inv, CategoryTheory.GradedObject.ιMapObjOrZero_mapMap_assoc, CategoryTheory.Limits.ColimitPresentation.map_ι, CategoryTheory.Limits.PreservesLimitPair.iso_inv_fst_assoc, CategoryTheory.Limits.inr_zeroCoprodIso_hom, CategoryTheory.Limits.PreservesPushout.inl_iso_inv, ModuleCat.image.lift_fac, CategoryTheory.Bimon.ofMon_Comon_ObjX_one, CategoryTheory.Bicategory.Comonad.comul_assoc_flip_assoc, AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTrans, CategoryTheory.EnrichedFunctor.comp_map, CategoryTheory.BraidedCategory.braiding_tensor_left_inv_assoc, HomologicalComplex.restrictionMap_f'_assoc, CategoryTheory.Limits.Fork.IsLimit.homIso_symm_apply, CategoryTheory.Adjunction.leftAdjointUniq_hom_counit, HomologicalComplex.opcyclesToCycles_naturality, RingCat.Colimits.cocone_naturality, CategoryTheory.Functor.CoreMonoidal.associativity_assoc, CategoryTheory.Limits.Cowedge.condition_assoc, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_left, AddCommMonCat.comp_apply, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_1, CategoryTheory.Bicategory.Adj.Bicategory.whiskerLeft_τr, CategoryTheory.DifferentialObject.comp_f, SSet.PtSimplex.MulStruct.δ_succ_succ_map, CategoryTheory.MonoidalCategory.associator_naturality_middle, CategoryTheory.Limits.map_inr_inv_coprodComparison_assoc, CategoryTheory.isIso_comp_left_iff, CategoryTheory.δ_μ_app, AlgebraicGeometry.IsAffineOpen.algebraMap_Spec_obj, CategoryTheory.OplaxFunctor.map₂_associator_app_assoc, CategoryTheory.StrictPseudofunctor.mk'_mapComp, CategoryTheory.Adjunction.unit_app_unit_comp_map_η, CategoryTheory.Localization.Monoidal.map_hexagon_forward, CategoryTheory.Limits.limCompFlipIsoWhiskerLim_inv_app_app, CategoryTheory.Monad.adj_counit, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp, CommRingCat.HomTopology.precompHomeomorph_apply, HomologicalComplex₂.XXIsoOfEq_hom_ιTotal_assoc, CategoryTheory.MonoidalClosed.assoc, AlgebraicGeometry.SheafedSpace.comp_base, CategoryTheory.Limits.prod_rightUnitor_inv_naturality_assoc, SheafOfModules.pushforwardNatTrans_id, CategoryTheory.LaxFunctor.map₂_associator_app_assoc, HomologicalComplex.extendSingleIso_hom_f_assoc, CategoryTheory.Presheaf.functorEnrichedHomCoyonedaObjEquiv_naturality, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_unit, CategoryTheory.SingleObj.comp_as_mul, CategoryTheory.Bicategory.conjugateEquiv_comp_id_right_apply, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_assoc, CategoryTheory.Functor.commShiftOfLocalization_iso_inv_app, CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id_app, CategoryTheory.Limits.ι_colimMap_assoc, SSet.Subcomplex.homOfLE_comp_assoc, HomologicalComplex.restrictionToTruncGE'.comm_assoc, CategoryTheory.Functor.uncurry_map_app, CategoryTheory.Adjunction.map_restrictFullyFaithful_counit_app, CategoryTheory.e_assoc_assoc, CategoryTheory.Comma.comp_left, groupHomology.mapCycles₂_comp_i, AlgebraicGeometry.Scheme.Spec_map_stalkMap_fromSpecStalk_assoc, AugmentedSimplexCategory.inl_comp_inl_comp_associator_assoc, CommMonCat.ofHom_comp, AlgebraicGeometry.Scheme.PartialMap.equiv_toPartialMap_iff_of_isSeparated, CategoryTheory.Functor.CoreMonoidal.right_unitality_assoc, CategoryTheory.HopfObj.antipode_left, CategoryTheory.ShortComplex.RightHomologyMapData.opcyclesMap_comm, HomotopicalAlgebra.AttachCells.hm_assoc, CategoryTheory.Lax.LaxTrans.id_naturality, CategoryTheory.Limits.colimit.ι_pre, groupCohomology.map_H0Iso_hom_f, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_inv_hom_id_assoc, AlgebraicGeometry.AffineSpace.reindex_over, AlgebraicGeometry.Scheme.IdealSheafData.subschemeCover_map_subschemeι, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_comp_assoc, CategoryTheory.hom_comp_eq_id, HomologicalComplex.iCycles_d, CategoryTheory.Functor.commShiftOfLocalization.iso_inv_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.whiskerLeft_actionHomLeft_assoc, AlgebraicGeometry.Scheme.Cover.gluedCoverT'_snd_fst, AlgebraicGeometry.SheafedSpace.comp_c_app, CategoryTheory.GrpObj.tensorHom_inv_inv_mul_assoc, CategoryTheory.Functor.obj.Δ_def_assoc, HomologicalComplex₂.totalAux.ιMapObj_D₂_assoc, CategoryTheory.ShortComplex.Homotopy.comm₃, CategoryTheory.NonPreadditiveAbelian.sub_comp, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_assoc, prevD_nat, CategoryTheory.Limits.pullbackZeroZeroIso_inv_fst, CategoryTheory.Bicategory.leftUnitor_inv_whiskerRight, AlgebraicGeometry.AffineSpace.map_over, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd, TopCat.Presheaf.SheafConditionEqualizerProducts.w, CategoryTheory.Functor.OplaxRightLinear.δᵣ_naturality_left, CategoryTheory.CartesianClosed.curry_natural_left_assoc, CategoryTheory.Limits.coend.map_comp_assoc, CategoryTheory.ShortComplex.op_pOpcycles_opcyclesOpIso_hom_assoc, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_inv_assoc, CategoryTheory.MonoidalCategory.tensorμ_tensorδ, ChainComplex.mk_congr_succ_X₃, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality_assoc, CategoryTheory.IsIso.eq_inv_comp, CochainComplex.isoHomologyπ₀_inv_naturality, CategoryTheory.ShortComplex.RightHomologyData.copy_ι, CategoryTheory.GradedObject.Monoidal.pentagon_inv, CategoryTheory.Limits.IsImage.isoExt_inv_m, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_comp, CategoryTheory.coev_app_comp_pre_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.action_exchange_assoc, CategoryTheory.ShortComplex.RightHomologyData.p_comp_opcyclesIso_inv_assoc, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_associator, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top_assoc, CategoryTheory.Limits.kernelIsIsoComp_hom, AlgebraicGeometry.ExistsHomHomCompEqCompAux.exists_index, CategoryTheory.Abelian.Pseudoelement.pseudoApply_mk', CategoryTheory.MonoidalCategory.leftUnitor_inv_whiskerRight_assoc, CategoryTheory.Localization.Monoidal.μ_natural_left_assoc, CategoryTheory.PreGaloisCategory.comp_autMap, CategoryTheory.Functor.RightLinear.μᵣ_comp_δᵣ, CategoryTheory.StructuredArrow.homMk'_mk_comp, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₂_assoc, AlgebraicGeometry.liftCoborder_app, CategoryTheory.ShortComplex.leftHomologyIso_hom_naturality, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_whiskerLeft_app, CategoryTheory.IsPullback.isoPullback_inv_snd, CategoryTheory.nerve.homEquiv_comp, CompHaus.lift_lifts, CategoryTheory.Adjunction.leftAdjointUniq_hom_app_counit, CategoryTheory.Limits.pullbackZeroZeroIso_hom_snd, CategoryTheory.Triangulated.SpectralObject.triangle_obj₂, CategoryTheory.Functor.LeftExtension.postcompose₂ObjMkIso_inv_right_app, CategoryTheory.Limits.MulticospanIndex.sndPiMap_π, CategoryTheory.ShortComplex.homologyι_comp_fromOpcycles_assoc, CategoryTheory.Functor.CommShift.comp_commShiftIso_inv_app, isoOfQuasiIsoAt_inv_hom_id, CategoryTheory.Over.prodLeftIsoPullback_hom_fst_assoc, CategoryTheory.Limits.pullbackIsoOpPushout_inv_fst_assoc, HomologicalComplex.dTo_comp_dFrom, CategoryTheory.Abelian.Ext.singleFunctor_map_comp_hom, AlgebraicTopology.DoldKan.QInfty_f_comp_PInfty_f, SSet.OneTruncation₂.HoRel₂.mk, SimplexCategory.mkOfSucc_δ_lt, CategoryTheory.CartesianClosed.curry_natural_right, CategoryTheory.Equivalence.counitInv_functor_comp, CategoryTheory.MonoidalCategory.whiskerRight_comp_tensorHom_assoc, CochainComplex.mappingConeCompHomotopyEquiv_comm₁, AlgebraicGeometry.sourceLocalClosure.property_coverMap_comp, CategoryTheory.yonedaMon_naturality, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_snd_assoc, CategoryTheory.Mon.limit_mon_mul, CategoryTheory.Preadditive.neg_comp_neg_assoc, CategoryTheory.MonoidalCategory.tensorμ_comp_μ_tensorHom_μ_comp_μ, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_left, CategoryTheory.ComposableArrows.mk₁_comp_eqToHom, CategoryTheory.GlueData.t'_iji, groupCohomology.π_comp_H1Iso_hom, CategoryTheory.Bicategory.instIsIsoHomLeftZigzagHom, CategoryTheory.NatTrans.rightOpWhiskerRight, CategoryTheory.Limits.Cotrident.condition_assoc, CategoryTheory.instIsCartesianCompOfIsFibered, CategoryTheory.Limits.BinaryFan.braiding_inv_snd, CategoryTheory.Functor.Monoidal.transport_δ, CategoryTheory.precoherentEffectiveEpiFamilyCompEffectiveEpis, CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_inv_π_π, CategoryTheory.MonoidalCategory.associator_monoidal, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_hom, CategoryTheory.heq_comp_eqToHom_iff, groupHomology.map_comp_assoc, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w, CategoryTheory.SmallObject.objMap_comp_assoc, CategoryTheory.ExponentiableMorphism.pushforwardId_hom_counit_assoc, CategoryTheory.GradedObject.ι_mapBifunctorRightUnitor_hom_apply, CategoryTheory.Functor.OplaxLeftLinear.δₗ_unitality_hom_assoc, CategoryTheory.Limits.pullback_lift_diagonal_isPullback, CategoryTheory.Bicategory.Equivalence.right_triangle, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_hom, AlgebraicGeometry.Scheme.Hom.toImage_imageι_assoc, CategoryTheory.Functor.toPseudoFunctor_mapComp, CategoryTheory.Preadditive.neg_comp_neg, CategoryTheory.Abelian.Ext.mk₀_comp_mk₀_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst, BddDistLat.coe_comp, CategoryTheory.ShortComplex.mapRightHomologyIso_inv_naturality, CategoryTheory.Idempotents.Karoubi.decomp_p, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_assoc, CategoryTheory.Bicategory.associator_eqToHom_inv, CategoryTheory.Limits.CoconeMorphism.w_assoc, CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan_inj, CategoryTheory.Bicategory.Equivalence.left_triangle, CategoryTheory.comp_toNatTrans, HomologicalComplex.d_comp_eqToHom, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₂, CategoryTheory.Limits.Pi.lift_π, CategoryTheory.MonoOver.image_map, CategoryTheory.Localization.Preadditive.homEquiv_apply, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app, CategoryTheory.MorphismProperty.iff_of_zeroHypercover_source, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_associator_assoc, CategoryTheory.Limits.inr_pushoutAssoc_hom_assoc, CategoryTheory.Functor.CoreMonoidal.μIso_hom_natural_left_assoc, CategoryTheory.ComonadHom.app_ε_assoc, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app_assoc, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj_condition_assoc, AlgebraicGeometry.StructureSheaf.algebraMap_self_map, TopCat.prodIsoProd_inv_snd_assoc, CategoryTheory.GradedObject.Monoidal.ι_tensorObjDesc_assoc, FinPartOrd.hom_hom_comp, AlgebraicGeometry.Scheme.Hom.preimage_smoothLocus_eq, AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInfty_assoc, CategoryTheory.Adjunction.IsMonoidal.leftAdjoint_ε, CategoryTheory.kernelCokernelCompSequence.φ_snd_assoc, CategoryTheory.Under.mapPushoutAdj_unit_app, HomologicalComplex.homologyIsoSc'_hom_ι_assoc, CategoryTheory.Limits.inl_pushoutRightPushoutInlIso_inv, HomologicalComplex.ιTruncLE_naturality_assoc, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₂, CategoryTheory.Limits.SequentialProduct.functorMap_commSq_aux, CategoryTheory.DifferentialObject.d_squared, CategoryTheory.preservesLimitIso_inv_π_assoc, AlgebraicGeometry.Scheme.stalkMap_hom_inv_assoc, CategoryTheory.Limits.ι_comp_sigmaComparison, CategoryTheory.ShortComplex.SnakeInput.Hom.comm₂₃_assoc, ProfiniteGrp.hom_comp, CategoryTheory.GradedObject.ι_mapBifunctorBifunctor₂₃Desc, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_inv_fac_assoc, CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_snd, ModuleCat.Tilde.toOpen_res, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.tensor_actionHomRight, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom, CategoryTheory.Comma.mapLeftComp_inv_app_left, SSet.stdSimplex.faceSingletonIso_zero_hom_comp_ι_eq_δ_assoc, CategoryTheory.ShiftedHom.mk₀_comp, CategoryTheory.MonoidalClosed.assoc_assoc, NonemptyFinLinOrd.hom_comp, CategoryTheory.shiftFunctorComm_hom_app_comp_shift_shiftFunctorAdd_hom_app_assoc, HomotopicalAlgebra.Precylinder.symm_i_assoc, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv_assoc, CategoryTheory.CartesianMonoidalCategory.lift_rightUnitor_hom_assoc, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj_assoc, HomologicalComplex.restrictionToTruncGE'.comm, CategoryTheory.Limits.ImageMap.factor_map_assoc, Mathlib.Tactic.Bicategory.naturality_associator, AlgebraicGeometry.germ_comp_stalkToFiberRingHom, TopCat.prodIsoProd_inv_fst_assoc, AlgebraicGeometry.Proj.basicOpenIsoSpec_inv_ι, CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIso_inv, CategoryTheory.coreCategory_comp_iso_inv, CategoryTheory.SmallObject.SuccStruct.Iteration.subsingleton.MapEq.w, CategoryTheory.MonoidalCategory.whiskerLeft_comp, CategoryTheory.MorphismProperty.IsLocalAtSource.comp, CategoryTheory.NatTrans.rightDerived_comp, CategoryTheory.StructuredArrow.mkPostcomp_left, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_neg_assoc, AlgebraicGeometry.Scheme.Opens.toSpecΓ_appTop, CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_fst_assoc, CochainComplex.HomComplex.Cochain.fromSingleMk_v, AlgebraicGeometry.Scheme.Hom.isoOpensRange_hom_ι_assoc, CategoryTheory.Limits.pullbackProdFstIsoProd_inv_fst, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_whiskerLeft, CategoryTheory.Bicategory.LanLift.existsUnique, CategoryTheory.IsComonHom.hom_comul_assoc, CategoryTheory.Functor.shiftIso_add_hom_app, CategoryTheory.ChosenPullbacksAlong.condition_assoc, CategoryTheory.ComposableArrows.map'_comp, CategoryTheory.MonoidalCategory.whiskerRight_comp_tensorHom, CategoryTheory.shiftFunctorAdd_inv_app_obj_of_induced, CategoryTheory.ComposableArrows.IsComplex.zero_assoc, CategoryTheory.Oplax.OplaxTrans.categoryStruct_comp_naturality, CategoryTheory.Join.mapWhiskerLeft_whiskerRight_assoc, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_rightHomologyIso_inv_assoc, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_hom_assoc, CategoryTheory.Limits.Cofork.IsColimit.homIso_apply_coe, CategoryTheory.Over.leftUnitor_inv_left_fst, HomologicalComplex.restrictionHomologyIso_inv_homologyι_assoc, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.exists_d_comp_eq_d, Bicategory.Opposite.bicategory_leftUnitor_inv_unop2, CategoryTheory.CatEnriched.hComp_id_heq, CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_fst, AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_snd, AugmentedSimplexCategory.tensorObj_hom_ext_iff, CategoryTheory.Bicategory.Prod.sectR_mapId_inv, CategoryTheory.Limits.instHasImageCompOfIsIso, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃_associator_inv_assoc, CategoryTheory.Functor.partialRightAdjointHomEquiv_comp, AlgebraicGeometry.PresheafedSpace.stalkMap.congr, CategoryTheory.Iso.hom_inv_id, CategoryTheory.Sieve.downward_closed, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_unit_app_left, CategoryTheory.Over.inv_left_hom_left, CategoryTheory.Over.starPullbackIsoStar_hom_app_left, CategoryTheory.Limits.PushoutCocone.ofCocone_ι, CategoryTheory.eComp_eHomWhiskerLeft_assoc, CategoryTheory.Limits.coend.condition_assoc, CategoryTheory.ShortComplex.SnakeInput.snd_δ, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec_assoc, CategoryTheory.Functor.rightDerivedNatTrans_comp, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_naturality, CategoryTheory.Abelian.Ext.mapExactFunctor_hom, CategoryTheory.MonObj.mul_mul_mul_comm, ModuleCat.lof_coprodIsoDirectSum_inv, HomologicalComplex₂.totalFlipIsoX_hom_D₂_assoc, CategoryTheory.ShortComplex.RightHomologyMapData.rightHomologyMap_eq, CategoryTheory.IsMonHom.one_hom_assoc, CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id, AlgebraicGeometry.Scheme.residue_descResidueField, smoothSheafCommRing.ι_evalHom, CategoryTheory.Monad.adj_unit, CategoryTheory.MonObj.mul_comp, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_presheafMap, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zero, CategoryTheory.Adjunction.toCat_counit_toNatTrans, CategoryTheory.Comon.tensorObj_counit, HopfAlgCat.toBialgHom_comp, CategoryTheory.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCocone_π_app_eq_sum, CategoryTheory.PrelaxFunctor.map₂_hom_inv, CategoryTheory.MonoidalCategory.id_tensor_associator_naturality, CategoryTheory.Limits.ι_colimitCompWhiskeringLeftIsoCompColimit_hom, Rep.coindResAdjunction_unit_app, CategoryTheory.Limits.coneOfIsSplitMono_π_app, HomologicalComplex.XIsoOfEq_hom_comp_d, CategoryTheory.Limits.ι_comp_sigmaObjIso_hom, AlgebraicGeometry.Scheme.Hom.isoOpensRange_hom_ι, CategoryTheory.Localization.Monoidal.map_hexagon_reverse, CategoryTheory.Limits.biprod.associator_hom, CategoryTheory.GradedObject.mapBifunctorObjSingle₀ObjIso_hom, AugmentedSimplexCategory.inr_comp_associator_assoc, CategoryTheory.ShortComplex.SnakeInput.snd_δ_inr, CategoryTheory.Functor.partialRightAdjointHomEquiv_map, CategoryTheory.Functor.IsStronglyCartesian.comp, CategoryTheory.StrictlyUnitaryLaxFunctor.id_mapComp, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone_cocone_ι_app, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.ι_toBase_assoc, CategoryTheory.OplaxFunctor.mapComp_assoc_right_app, CategoryTheory.NatTrans.CommShift.comp, AlgebraicGeometry.Scheme.Hom.app_eq, CategoryTheory.Abelian.LeftResolution.chainComplexMap_comp_assoc, HomotopicalAlgebra.PathObject.symm_p_assoc, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_hom_eq_germ, CategoryTheory.Pseudofunctor.StrongTrans.Modification.naturality, CategoryTheory.SimplicialObject.δ_naturality, AlgebraicGeometry.morphismRestrict_ι, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_μ, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_hom_app_app, CategoryTheory.Enriched.FunctorCategory.enriched_comp_id_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp_app, AlgebraicGeometry.Scheme.Hom.preimageIso_inv_ι, CategoryTheory.Lax.OplaxTrans.comp_app, CategoryTheory.IsSplitEpi.id, CategoryTheory.Limits.end_.condition, CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_comp_assoc, AlgebraicGeometry.Scheme.SpecMap_stalkSpecializes_fromSpecStalk, AlgebraicGeometry.Scheme.descResidueField_fromSpecResidueField, TopCat.Presheaf.germ_res_assoc, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec, CategoryTheory.Limits.Multicofork.ofSigmaCofork_π, CategoryTheory.SmallObject.SuccStruct.ofCoconeObjIso_hom_naturality, CategoryTheory.MonoidalCategory.associator_inv_naturality, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_right, CategoryTheory.ShortComplex.Splitting.g_s, HomologicalComplex.opcyclesOpIso_hom_naturality_assoc, CategoryTheory.ProjectiveResolution.Hom.hom'_f_assoc, AlgebraicGeometry.Scheme.Cover.Hom.w, CategoryTheory.Functor.shiftMap_comp, CategoryTheory.ShortComplex.HomologyData.comm_assoc, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i, CategoryTheory.Hom.mul_def, CategoryTheory.Limits.opCoproductIsoProduct'_inv_comp_inj, CategoryTheory.Functor.shiftIso_add'_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app, CategoryTheory.Functor.Monoidal.transport_μ_assoc, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app, AlgebraicGeometry.Scheme.IdealSheafData.map_comp, CategoryTheory.MonoidalCategory.MonoidalRightAction.hom_inv_actionHomLeft', CochainComplex.mappingCone.ext_from_iff, CategoryTheory.section_comp_right, CategoryTheory.Limits.pushout.hom_ext_iff, TopCat.Presheaf.germToPullbackStalk_stalkPullbackHom, CategoryTheory.Limits.Pi.isoLimit_inv_π, CategoryTheory.comp_inv_eq_id, CategoryTheory.ObjectProperty.FullSubcategory.comp_def, CategoryTheory.Bicategory.InducedBicategory.bicategory_comp_hom, HomologicalComplex.opcyclesToCycles_homologyπ, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_obj_obj_map, HomotopicalAlgebra.Precylinder.i₀_π, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app, CategoryTheory.ShortComplex.LeftHomologyData.π_comp_leftHomologyIso_inv_assoc, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_inv_app_app, CommRingCat.HomTopology.isEmbedding_pushout, AlgebraicGeometry.ΓSpecIso_obj_hom, CategoryTheory.MonoidalCategory.rightUnitor_inv_naturality_assoc, groupHomology.mapCycles₁_id_comp_apply, CategoryTheory.ShortComplex.leftHomologyIso_hom_naturality_assoc, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom_assoc, CategoryTheory.Functor.LaxMonoidal.left_unitality, CategoryTheory.MonoidalCategory.MonoidalRightAction.id_actionHomLeft_assoc, CategoryTheory.Subfunctor.homOfLe_ι_assoc, CategoryTheory.Bicategory.pentagon_inv_inv_hom_hom_inv, CategoryTheory.Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor, CategoryTheory.Subfunctor.homOfLe_ι, CategoryTheory.Subgroupoid.mem_map_iff, CategoryTheory.NatTrans.naturality_app_app_assoc, TopologicalSpace.Opens.map_comp_map, Bimod.right_assoc_assoc, CategoryTheory.Adjunction.Triple.leftToRight_app_obj, SSet.ι₀_fst_assoc, SSet.ι₁_comp, CategoryTheory.Limits.Pi.map'_comp_map', CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit_proj, CategoryTheory.Pi.comp_apply, AlgebraicGeometry.Proj.pullbackAwayιIso_inv_snd, CategoryTheory.Square.Hom.comm₃₄, AlgebraicGeometry.Proj.pullbackAwayιIso_inv_fst_assoc, CategoryTheory.tensorLeftHomEquiv_tensor, CategoryTheory.Presheaf.restrictedULiftYoneda_map_app, HomologicalComplex.extendMap_comp_assoc, groupCohomology.cochainsMap_id_comp, SSet.Subcomplex.yonedaEquiv_coe, AlgebraicGeometry.Scheme.IdealSheafData.inclusion_comp_assoc, CategoryTheory.ShortComplex.Hom.comm₁₂_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_naturality_assoc, AlgebraicGeometry.pullbackSpecIso_inv_fst'_assoc, CategoryTheory.ModObj.one_smul'_assoc, CategoryTheory.Functor.OplaxMonoidal.δ_comp_δ_whiskerRight_assoc, HomologicalComplex.cyclesIsoSc'_hom_iCycles_assoc, AlgebraicGeometry.Spec.germ_stalkMapIso_hom_assoc, HomologicalComplex₂.ι_D₂_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_assoc, CategoryTheory.Functor.LaxMonoidal.μ_natural_right_assoc, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac, CategoryTheory.Biprod.ofComponents_eq, CategoryTheory.eqToHom_iso_inv_naturality, CategoryTheory.BraidedCategory.braiding_naturality, CategoryTheory.MonObj.tensorObj.mul_def, TopCat.sigmaIsoSigma_hom_ι_assoc, Mathlib.Tactic.Coherence.assoc_liftHom, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom, CategoryTheory.right_unitality_app_assoc, CategoryTheory.FreeBicategory.mk_left_unitor_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app_assoc, CategoryTheory.GrothendieckTopology.toSheafify_comp_sheafifyCompIso_inv_assoc, HomologicalComplex.homologyπ_naturality, CategoryTheory.Functor.inl_biprodComparison', CategoryTheory.Join.pseudofunctorLeft_mapComp_inv_toNatTrans_app, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv_assoc, CategoryTheory.eqToHom_comp_heq_iff, SSet.Subcomplex.homOfLE_ι_assoc, CategoryTheory.IsIso.inv_comp_assoc, CategoryTheory.Functor.obj.η_def_assoc, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv, inr_coprodIsoPushout_hom_assoc, CategoryTheory.RanIsSheafOfIsCocontinuous.fac_assoc, CategoryTheory.DifferentialObject.Hom.comm_assoc, groupCohomology.mapShortComplexH2_comp, CategoryTheory.Functor.shiftIso_inv_naturality, CategoryTheory.Limits.coprod.map_id_comp, HomologicalComplex.p_opcyclesMap, CategoryTheory.Preadditive.sum_comp, CategoryTheory.MonoidalCategory.MonoidalLeftAction.rightUnitor_actionHom, CategoryTheory.η_app_obj, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_assoc, AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zero, CategoryTheory.CatEnrichedOrdinary.Hom.mk_comp, CategoryTheory.GradedObject.mapMap_comp, ModuleCat.ExtendScalars.map'_comp, CategoryTheory.ProjectiveResolution.pOpcycles_comp_fromLeftDerivedZero'_assoc, CategoryTheory.Functor.partialLeftAdjointHomEquiv_map, CategoryTheory.ExactPairing.evaluation_coevaluation', CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_whiskerRight_app, CategoryTheory.Limits.ker.condition, CategoryTheory.CartesianMonoidalCategory.tensorμ_snd, HomologicalComplex.homotopyCofiber.inrX_fstX, CochainComplex.HomComplex.Cochain.leftUnshift_v, CategoryTheory.Limits.kernelIsIsoComp_inv, CategoryTheory.ShortComplex.SnakeInput.L₁_f_φ₁_assoc, CategoryTheory.Limits.colimitLimitToLimitColimitCone_hom, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_awayι, CategoryTheory.GrothendieckTopology.plusMap_plusLift, AlgebraicGeometry.Scheme.IsLocallyDirected.homOfLE_tAux, CategoryTheory.Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor_assoc, CategoryTheory.Over.mapComp_eq, CategoryTheory.Limits.BinaryBicone.inr_fst_assoc, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_three, CategoryTheory.Limits.image.fac_lift_assoc, CategoryTheory.Limits.wideCoequalizer.condition_assoc, CategoryTheory.Bicategory.Adjunction.ofCat_comp, SimplexCategoryGenRel.exists_P_σ_P_δ_factorization, AlgebraicGeometry.LocallyRingedSpace.residue_comp_residueFieldMap_eq_stalkMap_comp_residue, DerivedCategory.HomologySequence.comp_δ_assoc, ModuleCat.restrictScalarsComp'App_hom_naturality_assoc, CategoryTheory.BraidedCategory.hexagon_reverse_inv, CategoryTheory.Presieve.ofArrows_surj, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_map_assoc, CategoryTheory.Limits.map_inr_inv_coprodComparison, SheafOfModules.freeHomEquiv_symm_comp, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyπ_comp_leftHomologyIso_hom_assoc, CategoryTheory.MonoidalClosed.uncurry_pre, CategoryTheory.cokernel.π_unop, CochainComplex.mappingConeCompHomotopyEquiv_comm₁_assoc, CategoryTheory.Over.tensorHom_left_snd_assoc, CategoryTheory.Limits.Bicone.category_comp_hom, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_whiskerRight_assoc, HomotopicalAlgebra.PathObject.symm_p, HomologicalComplex.homologyπ_naturality_assoc, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality', CategoryTheory.Pseudofunctor.whiskerLeftIso_mapId, CategoryTheory.Limits.biprod.decomp_hom_from, CategoryTheory.MonObj.lift_comp_one_left, CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIsoWhisker_hom_right, Pointed.Hom.comp_toFun', CategoryTheory.Limits.prod.leftUnitor_hom_naturality_assoc, CategoryTheory.Functor.preimage_comp, CategoryTheory.FreeMonoidalCategory.mk_comp, CategoryTheory.Bicategory.Adj.Bicategory.whiskerLeft_τl, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.secondMap_app_app_app, SimplexCategory.δ_comp_σ_of_le, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap_assoc, CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_hom_app, CategoryTheory.Functor.IsCartesian.of_comp_iso, CategoryTheory.Limits.ι_colimitFiberwiseColimitIso_hom_assoc, CategoryTheory.Adjunction.shift_counit_app, CategoryTheory.Limits.Cone.ofPullbackCone_π, CategoryTheory.Bicategory.Pith.rightUnitor_hom_iso, CategoryTheory.FunctorToTypes.coprod.desc_inl, CategoryTheory.Functor.Monoidal.map_rightUnitor_assoc, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_id_assoc, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom, CategoryTheory.Functor.map_shift_unop, CategoryTheory.ShortComplex.LeftHomologyData.copy_i, CategoryTheory.GradedObject.ι_mapBifunctorComp₂₃MapObjIso_hom, CategoryTheory.CosimplicialObject.δ_naturality_assoc, CategoryTheory.Functor.OplaxMonoidal.lift_δ, CategoryTheory.Limits.hasCokernel_comp_iso, isoOfQuasiIsoAt_inv_hom_id_assoc, CategoryTheory.TwoSquare.whiskerVertical_app, CategoryTheory.Limits.ConeMorphism.map_w, CommAlgCat.hom_comp, SSet.Truncated.Edge.CompStruct.nonempty_iff, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_counitIso, CategoryTheory.HopfObj.antipode_comul, CategoryTheory.sheafifyMap_sheafifyLift, HomologicalComplex.singleObjCyclesSelfIso_hom_singleObjOpcyclesSelfIso_hom, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv, CategoryTheory.Limits.prod.map_comp_id, TopologicalSpace.Opens.map_comp_obj', CategoryTheory.Bicategory.Comonad.counit_comul_assoc, CategoryTheory.ShortComplex.SnakeInput.φ₁_L₂_f_assoc, CategoryTheory.OplaxFunctor.mapComp_assoc_left, CategoryTheory.Adjunction.leftAdjointUniq_trans_assoc, groupCohomology.H2π_comp_map, CategoryTheory.ShortComplex.SnakeInput.L₀X₂ToP_comp_φ₁, CategoryTheory.Monad.assoc, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd_assoc, HomologicalComplex.mapBifunctor₂₃.ι_D₁, Bicategory.Opposite.op2_rightUnitor_inv, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_app, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_app, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp_assoc, HomologicalComplex.leftUnitor'_inv_comm_assoc, CategoryTheory.ShortComplex.Homotopy.compRight_h₂, groupCohomology.cochainsMap_comp_assoc, CategoryTheory.Limits.Pi.map'_comp_π_assoc, CategoryTheory.Adjunction.map_restrictFullyFaithful_counit_app_assoc, CategoryTheory.Iso.inv_hom_id_app_app, CategoryTheory.Subobject.factorThru_arrow_assoc, CategoryTheory.endofunctorMonoidalCategory_tensorMap_app, CategoryTheory.Functor.obj.η_def, SimplicialObject.Splitting.cofan_inj_comp_PInfty_eq_zero, groupHomology.π_comp_H2Iso_hom, CategoryTheory.Functor.LaxRightLinear.μᵣ_associativity_inv, CategoryTheory.Limits.limit.isoLimitCone_hom_π, CategoryTheory.Limits.LimitPresentation.ofIso_π, CategoryTheory.Functor.LeftExtension.postcompose₂_map_right_app, HomologicalComplex.opcyclesOpIso_hom_toCycles_op, CategoryTheory.GradedObject.singleObjApplyIso_inv_single_map_assoc, CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_snd, AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_snd_assoc, HomologicalComplex.mapBifunctor₂₃.ι_mapBifunctor₂₃Desc_assoc, CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_fst, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_comp_map, SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zero, CategoryTheory.BicategoricalCoherence.right'_iso, CategoryTheory.Limits.pullbackConeOfRightIso_π_app_right, CategoryTheory.Idempotents.Karoubi.p_comm_assoc, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map, CategoryTheory.ComposableArrows.Exact.opcyclesIsoCycles_hom_fac_assoc, CategoryTheory.Lax.LaxTrans.naturality_comp_assoc, HomologicalComplex.extendCyclesIso_hom_naturality_assoc, CategoryTheory.ExponentiableMorphism.ev_coev, CategoryTheory.Under.map_obj_hom, CategoryTheory.CommaMorphism.w_assoc, CategoryTheory.Limits.FormalCoproduct.inj_comp_cofanPtIsoSelf_hom_assoc, SimplexCategory.σ_comp_σ_assoc, CategoryTheory.Idempotents.app_p_comp_assoc, CategoryTheory.Adjunction.counit_naturality, CategoryTheory.Limits.Types.coequalizerIso_π_comp_hom, CategoryTheory.Bicategory.pentagon_assoc, CategoryTheory.Functor.OplaxLeftLinear.δₗ_unitality_inv, Bimod.Hom.left_act_hom, CategoryTheory.Functor.biproductComparison_π_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.comp, CategoryTheory.MorphismProperty.map_eq_iff_postcomp, CategoryTheory.Limits.biprod.lift_fst, CategoryTheory.Limits.instHasPushoutComp, CategoryTheory.Functor.Monoidal.map_leftUnitor_inv_assoc, CategoryTheory.Localization.Monoidal.triangle_aux₁, CategoryTheory.Functor.op_commShiftIso_hom_app_assoc, CategoryTheory.CartesianMonoidalCategory.whiskerLeft_snd_assoc, CategoryTheory.IsSplitMono.id_assoc, CategoryTheory.CartesianClosed.curry_eq, CategoryTheory.NatTrans.IsMonoidal.tensor, CategoryTheory.pullbackShiftFunctorZero'_hom_app, CategoryTheory.Functor.OplaxMonoidal.oplax_associativity, AlgebraicGeometry.Scheme.Pullback.ofPointTensor_SpecTensorTo_assoc, CategoryTheory.Limits.Types.binaryCoproductIso_inr_comp_hom, HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac, CategoryTheory.Limits.pullback_factors_iff, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_inv_app, CategoryTheory.uliftYonedaEquiv_comp, CategoryTheory.Limits.biprod.desc_eq, CategoryTheory.CostructuredArrow.map_map_right, Bimod.comp_hom, CategoryTheory.MonoidalCategory.rightUnitor_tensor_hom_assoc, MagmaCat.coe_comp, CategoryTheory.Functor.Monoidal.whiskerRight_ε_η_assoc, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app_assoc, CategoryTheory.Limits.IsLimit.hom_lift, CategoryTheory.Over.leftUnitor_inv_left_snd, CategoryTheory.e_assoc', CategoryTheory.μ_naturality, CategoryTheory.CartesianMonoidalCategory.associator_inv_snd_assoc, CategoryTheory.SmallObject.SuccStruct.ofCoconeObjIso_hom_naturality_assoc, CategoryTheory.Functor.sectionsEquivHom_naturality, Homotopy.nullHomotopicMap_f, CategoryTheory.sheafifyLift_id_toSheafify, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_leftUnitor, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₃₁, groupHomology.mapCycles₂_comp, ModuleCat.comp_apply, AlgebraicGeometry.IsFinite.instCompScheme, CategoryTheory.Comonad.left_counit, CategoryTheory.Bicategory.prod_rightUnitor_inv_fst, AlgebraicGeometry.Scheme.Γevaluation_naturality_assoc, HomologicalComplex.pOpcyclesIso_inv_hom_id, CategoryTheory.Bimon.ofMon_Comon_ObjX_mul, CategoryTheory.Limits.MonoFactorisation.compMono_e, CategoryTheory.IsCofiltered.wideCospan, CategoryTheory.pullbackShiftFunctorZero_hom_app, CategoryTheory.ShortComplex.RightHomologyMapData.comp_φQ, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerLeft_assoc, CategoryTheory.Functor.shiftMap_comp'_assoc, PresheafOfModules.pullback_assoc, CategoryTheory.Monad.unit_naturality, CategoryTheory.Arrow.w, CategoryTheory.Square.Hom.comm₂₄_assoc, CategoryTheory.StructuredArrow.homMk'_left, CategoryTheory.Limits.π_comp_colimitLeftOpIsoUnopLimit_inv_assoc, groupHomology.isoShortComplexH1_hom, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_comp_assoc, SimplexCategory.factor_δ_spec, CategoryTheory.MonoidalClosed.pre_comm_ihom_map, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃'_obj_map_app, CategoryTheory.obj_zero_map_μ_app, AlgebraicGeometry.IsClosedImmersion.comp_iff, CategoryTheory.Iso.compInverseIso_inv_app, CategoryTheory.Adjunction.restrictFullyFaithful_homEquiv_apply, CategoryTheory.Limits.pushout_inr_inv_inl_of_right_isIso_assoc, CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_hom, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_SpecMap_awayMap_right, CategoryTheory.ShortComplex.Homotopy.compRight_h₃, CategoryTheory.Limits.Cofork.IsColimit.π_desc_assoc, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac, CategoryTheory.Limits.biproduct.lift_desc, SSet.stdSimplex.map_apply, HomologicalComplex.d_toCycles, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_snd', AlgebraicGeometry.instIsOpenImmersionCompSchemeιQuasiFiniteLocusToNormalization, CategoryTheory.CatCenter.smul_iso_hom_eq'_assoc, FundamentalGroupoid.comp_eq, CategoryTheory.Limits.piObjIso_inv_comp_π, CategoryTheory.GrothendieckTopology.overMapPullback_assoc_assoc, CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id_app, CategoryTheory.LaxFunctor.mapComp'_eq_mapComp, CategoryTheory.MonoidalCategory.triangle_assoc_comp_right_inv, CategoryTheory.Limits.ColimitPresentation.Total.Hom.w, HomologicalComplex.mapBifunctorAssociatorX_hom_D₃_assoc, CategoryTheory.PreZeroHypercover.Hom.ext'_iff, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app_assoc, CategoryTheory.ShortComplex.homologyπ_comp_leftHomologyIso_inv, CategoryTheory.Limits.prod.lift_map_assoc, CategoryTheory.Limits.limMap_π_assoc, CategoryTheory.IsHomLift.fac', CategoryTheory.Limits.MultispanIndex.ι_sndSigmaMap, CategoryTheory.MonoidalClosed.id_tensor_pre_app_comp_ev, CategoryTheory.Limits.biprod.inl_fst, CategoryTheory.PreOneHypercover.p₁_sigmaOfIsColimit, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom, CategoryTheory.Equivalence.unitInv_naturality_assoc, CategoryTheory.Bimon.one_comul, CategoryTheory.IsPushout.inr_isoIsPushout_hom_assoc, CategoryTheory.NatTrans.op_whiskerRight, CategoryTheory.Limits.pullback.diagonal_fst, CategoryTheory.ComposableArrows.Exact.opcyclesIsoCycles_hom_fac, CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_π, CategoryTheory.Functor.mapTriangle_map_hom₁, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι, CategoryTheory.MonoidalCategory.tensor_associativity_assoc, CategoryTheory.ShortComplex.leftHomologyIso_inv_naturality_assoc, CategoryTheory.Oplax.LaxTrans.naturality_comp, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.inverse_map_app, groupCohomology.isoCocycles₂_hom_comp_i, CategoryTheory.ShortComplex.p_opcyclesMap', CategoryTheory.MonoidalClosed.curry_pre_app, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_hom_τl, CategoryTheory.FunctorToTypes.rightAdj_map_app, HomologicalComplex.cyclesIsoSc'_inv_iCycles, CategoryTheory.Comonad.Coalgebra.Hom.h, CategoryTheory.ShortComplex.fromOpcycles_naturality_assoc, CategoryTheory.MonoidalCategory.comp_whiskerRight, CategoryTheory.Limits.ι_colimitFiberwiseColimitIso_inv_assoc, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_inv_π_π, AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app, CategoryTheory.Functor.rightDerivedNatTrans_app_assoc, SheafOfModules.pullbackObjFreeIso_hom_naturality_assoc, CategoryTheory.types_comp, CategoryTheory.Free.single_comp_single, CategoryTheory.PreservesImage.hom_comp_map_image_ι, CategoryTheory.NatTrans.CommShiftCore.shift_app, CategoryTheory.Limits.pullbackDiagonalMapIso.hom_snd_assoc, CategoryTheory.Over.μ_pullback_left_fst_snd', CategoryTheory.Limits.PreservesPushout.inl_iso_inv_assoc, SSet.ι₀_snd, CategoryTheory.NatTrans.whiskerLeft_app_tensor_app_assoc, CategoryTheory.Over.comp_left, CategoryTheory.CartesianMonoidalCategory.rightUnitor_inv_fst, CategoryTheory.Precoverage.IsStableUnderComposition.comp_mem_coverings, CategoryTheory.CatCommSq.vInv_iso_hom_app, CategoryTheory.Over.mapPullbackAdj_unit_app, CategoryTheory.Functor.ShiftSequence.induced_shiftIso_hom_app_obj, CategoryTheory.eqToHom_map_comp_assoc, CategoryTheory.Limits.lim_ε_π_assoc, CategoryTheory.Limits.coprod.inr_snd, AlgebraicGeometry.Scheme.Opens.toSpecΓ_top, Rep.resIndAdjunction_homEquiv_symm_apply, Rep.coinvariantsFunctor_hom_ext_iff, AlgebraicGeometry.LocallyRingedSpace.comp_base, CategoryTheory.ShortComplex.fromOpcycles_op_cyclesOpIso_inv_assoc, CochainComplex.mappingCone.inr_f_snd_v, CategoryTheory.Functor.Monoidal.map_associator_inv, CategoryTheory.Localization.homEquiv_comp, CategoryTheory.ShortComplex.leftHomologyπ_naturality_assoc, CategoryTheory.NatTrans.shift_comm, CategoryTheory.rightDistributor_inv, SSet.PtSimplex.MulStruct.δ_succ_castSucc_map, CategoryTheory.lift_comp_preservesLimitIso_hom_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_hom_inv'_assoc, CategoryTheory.Limits.limitUnopIsoUnopColimit_inv_comp_π_assoc, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.hπ, CategoryTheory.ShortComplex.rightHomologyMap_comp, CategoryTheory.Limits.PushoutCocone.condition_zero, CategoryTheory.preservesLimitIso_inv_π, CategoryTheory.Abelian.PreservesImage.iso_hom_ι, CategoryTheory.Subobject.factors_comp_arrow, CategoryTheory.ShortComplex.toCycles_i_assoc, CategoryTheory.Bicategory.whiskerLeft_isIso, CategoryTheory.Localization.Preadditive.comp_add, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_fst, CategoryTheory.Enriched.FunctorCategory.homEquiv_comp, CochainComplex.mappingConeCompTriangle_mor₃_naturality, AlgebraicGeometry.Scheme.Pullback.openCoverOfRight_f, CategoryTheory.ShortComplex.mapHomologyIso'_hom_naturality, CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp, CategoryTheory.Functor.homologySequenceδ_comp_assoc, CategoryTheory.ComposableArrows.IsComplex.opcyclesToCycles_fac, CategoryTheory.LocalizerMorphism.homMap_apply, CategoryTheory.CostructuredArrow.mapNatIso_functor_obj_hom, CategoryTheory.NatTrans.unop_whiskerRight, CategoryTheory.Limits.limit.π_comp_eqToHom_assoc, CategoryTheory.Subfunctor.lift_ι, groupHomology.comp_d₁₀_eq, HomologicalComplex.d_pOpcycles_assoc, CategoryTheory.Comma.map_map_left, CategoryTheory.ShortComplex.LeftHomologyData.copy_π, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app'_assoc, CategoryTheory.Limits.biprod.inr_desc, CategoryTheory.NatTrans.op_comp_assoc, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left_assoc, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id_app, CategoryTheory.CommSq.LiftStruct.fac_left, CategoryTheory.BraidedCategory.yang_baxter, CategoryTheory.Limits.BinaryBicone.category_comp_hom, CategoryTheory.CostructuredArrow.w_prod_snd, CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_left, AlgebraicGeometry.instSurjectiveCompScheme, CategoryTheory.Functor.relativelyRepresentable.symmetry_symmetry_assoc, AlgebraicGeometry.germ_stalkClosedPointIso_hom_assoc, CategoryTheory.Idempotents.Karoubi.comp_f, CategoryTheory.ShortComplex.RightHomologyMapData.commg', CategoryTheory.Comma.mapRightIso_functor_obj_hom, CategoryTheory.shift_equiv_triangle, CategoryTheory.CosimplicialObject.δ_comp_σ_succ_assoc, CommMonCat.comp_apply, CategoryTheory.Limits.imageSubobjectIso_comp_image_map, AlgebraicGeometry.Scheme.Hom.iInf_ker_openCover_map_comp, CategoryTheory.BraidedCategory.braiding_naturality_left, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₁_assoc, CategoryTheory.Functor.leftDerivedNatTrans_comp, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_app_comp_π, CategoryTheory.ShortComplex.opcyclesOpIso_hom_toCycles_op_assoc, CategoryTheory.PrelaxFunctor.map₂_inv_hom_isIso, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_hom_assoc, CategoryTheory.ProjectiveResolution.of_def, CategoryTheory.Limits.kernelComparison_comp_ι_assoc, CategoryTheory.associator_inv, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_inv_app_app, AddMagmaCat.coe_comp, CategoryTheory.Limits.PreservesPullback.iso_hom_fst, LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition', HomologicalComplex₂.totalAux.d₂_eq', CategoryTheory.Bicategory.eqToHomTransIso_refl_right, CategoryTheory.shiftFunctorZero_hom_app_obj_of_induced, HomotopicalAlgebra.CofibrantObject.exists_bifibrant_map, CategoryTheory.Dial.hexagon_reverse, CategoryTheory.CommaMorphism.w, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_assoc, CategoryTheory.factorThruImage_comp_imageUnopOp_inv, smoothSheafCommRing.forgetStalk_hom_comp_evalHom_assoc, AlgebraicGeometry.specTargetImageFactorization_comp_assoc, CategoryTheory.Limits.Fork.hom_comp_ι_assoc, AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_naturality_app, CategoryTheory.ProjectiveResolution.π'_f_zero_assoc, CategoryTheory.HomRel.IsStableUnderPrecomp.comp_left, CategoryTheory.composePath_comp, CategoryTheory.TransfiniteCompositionOfShape.fac, HomologicalComplex.truncLE'Map_f_eq_cyclesMap, CategoryTheory.ShortComplex.SnakeInput.Hom.comm₁₂_assoc, CategoryTheory.PreGaloisCategory.exists_lift_of_mono_of_isConnected, CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_fst_snd, CategoryTheory.Limits.colimit.pre_pre, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst, CategoryTheory.Functor.PreOneHypercoverDenseData.w, HomotopicalAlgebra.PrepathObject.RightHomotopy.precomp_h, AlgebraicGeometry.AffineSpace.map_reindex_assoc, CategoryTheory.Functor.OplaxLeftLinear.δₗ_associativity, CategoryTheory.ShortComplex.rightHomologyι_comp_fromOpcycles_assoc, CategoryTheory.Adjunction.comp_counit, CategoryTheory.GradedObject.Monoidal.tensorHom_def, HomologicalComplex₂.totalAux.d₁_eq, CategoryTheory.Limits.limitRightOpIsoOpColimit_hom_comp_ι, ComplexShape.Embedding.homRestrict_precomp, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans, groupHomology.H0π_comp_map_assoc, CategoryTheory.CatEnriched.hComp_assoc, CategoryTheory.ShortComplex.opcyclesOpIso_hom_naturality, CategoryTheory.CatCommSq.iso_hom_naturality, CategoryTheory.Limits.opProdIsoCoprod_inv_inl, CategoryTheory.Limits.limit.π_comp_eqToHom, CategoryTheory.Bicategory.pentagon_inv_inv_hom_inv_inv, CategoryTheory.Limits.FormalCoproduct.eval_obj_map, CategoryTheory.Equivalence.changeFunctor_counitIso_hom_app, CategoryTheory.PrelaxFunctor.map₂_inv_hom_isIso_assoc, AlgebraicGeometry.IsLocalAtSource.comp, CategoryTheory.Over.leftUnitor_inv_left_snd_assoc, CategoryTheory.Localization.Monoidal.map_hexagon_reverse_assoc, CategoryTheory.kernelCokernelCompSequence.inr_φ_fst_assoc, CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt_assoc, CategoryTheory.RetractArrow.r_w, CategoryTheory.CatCenter.mul_app_assoc, CategoryTheory.unop_comp, CategoryTheory.Limits.biproduct.ι_matrix_assoc, CategoryTheory.Limits.CatCospanTransform.category_comp_left, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s₀_comp_δ₁_assoc, HomologicalComplex₂.D₁_totalShift₂XIso_hom_assoc, AlgebraicGeometry.Scheme.stalkMap_germ_assoc, CategoryTheory.Pseudofunctor.CoGrothendieck.Hom.congr, HomologicalComplex.homotopyCofiber.sndX_inrX_assoc, CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc, TopCat.Presheaf.SheafConditionEqualizerProducts.piInters.hom_ext_iff, CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom, CategoryTheory.Iso.map_inv_hom_id_app, CategoryTheory.Limits.biproduct.matrix_map_assoc, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app_assoc, CategoryTheory.Subfunctor.Subpresheaf.image_comp, CategoryTheory.LaxBraidedFunctor.comp_hom_assoc, CategoryTheory.Functor.OplaxRightLinear.δᵣ_associativity, CategoryTheory.Functor.LeftLinear.δₗ_comp_μₗ, CategoryTheory.Iso.hom_inv_id_app, CategoryTheory.MonoidalCategory.associator_inv_naturality_middle_assoc, CategoryTheory.ShortComplex.homologyπ_naturality, AddSemigrp.comp_apply, CategoryTheory.Limits.HasLimit.isoOfEquivalence_hom_π, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π, CategoryTheory.Limits.limitConstTerminal_inv_π, CategoryTheory.ComonObj.counit_comul_assoc, CategoryTheory.NatIso.naturality_1_assoc, CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_hom, CategoryTheory.CartesianMonoidalCategory.rightUnitor_inv_snd_assoc, HomologicalComplex.xPrevIso_comp_dTo, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_invApp, CategoryTheory.Limits.pullbackProdSndIsoProd_inv_fst_snd_assoc, CategoryTheory.Bicategory.Adj.whiskerRight_τr, CategoryTheory.unit_conjugateEquiv_symm, CategoryTheory.Adjunction.mapMon_counit, CategoryTheory.CategoryOfElements.comp_val, CategoryTheory.Localization.Preadditive.comp_add'_assoc, CategoryTheory.GrothendieckTopology.Point.Hom.sheafFiber_comp, CategoryTheory.ComonObj.counit_comul_hom, CategoryTheory.Localization.Monoidal.μ_natural_left, CategoryTheory.ShortComplex.quasiIso_iff_comp_right, CommRingCat.hom_comp, Mathlib.Tactic.Monoidal.structuralIsoOfExpr_comp, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom'_assoc, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app_assoc, CategoryTheory.Pretriangulated.preadditiveYoneda_homologySequenceδ_apply, CategoryTheory.ShortComplex.LeftHomologyMapData.homologyMap_eq, CategoryTheory.Functor.NatTrans.hcomp_eq_whiskerLeft_comp_whiskerRight, CategoryTheory.Lax.LaxTrans.naturality_id_assoc, CategoryTheory.comp_leftAdjointMate_assoc, CategoryTheory.Iso.map_hom_inv_id, CategoryTheory.PreservesImage.inv_comp_image_ι_map, CategoryTheory.Limits.pullbackProdFstIsoProd_inv_snd_snd, CategoryTheory.Functor.RightLinear.δᵣ_comp_μᵣ, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_naturality_assoc, CategoryTheory.IsSplitCoequalizer.leftSection_top_assoc, AlgebraicGeometry.SurjectiveOnStalks.comp, CategoryTheory.LaxFunctor.mapComp_naturality_right_assoc, CategoryTheory.ChosenPullbacksAlong.iso_pullback_obj, CategoryTheory.MonoidalCategory.leftUnitor_monoidal, CategoryTheory.kernelCokernelCompSequence.snakeInput_v₂₃_τ₂, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp_assoc, CategoryTheory.Functor.ι_colimitIsoColimitGrothendieck_hom_assoc, AlgebraicGeometry.Scheme.Hom.appIso_inv_app, CategoryTheory.kernelCokernelCompSequence.ι_snd, CategoryTheory.Subfunctor.Subpresheaf.range_comp, prevD_eq, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_inv, CategoryTheory.WideSubcategory.comp_def, SSet.Subcomplex.image_comp, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app_assoc, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom, CategoryTheory.MorphismProperty.MapFactorizationData.fac, CategoryTheory.Preadditive.comp_neg_assoc, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_inv_iso_inv, HomologicalComplex.mapBifunctor.d₂_eq, CategoryTheory.Bicategory.prod_whiskerLeft_fst, CategoryTheory.Limits.MulticospanIndex.fstPiMapOfIsLimit_proj_assoc, groupHomology.toCycles_comp_isoCycles₁_hom_assoc, CategoryTheory.Oplax.OplaxTrans.rightUnitor_hom_as_app, CategoryTheory.Limits.kernelSubobjectIsoComp_inv_arrow, CommRingCat.HomTopology.precompHomeomorph_symm_apply, TopCat.Presheaf.map_germ_eq_Γgerm_assoc, AlgebraicGeometry.Scheme.stalkMap_congr_hom_assoc, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom, CategoryTheory.Limits.pushoutIsoOpPullback_inv_fst, CategoryTheory.unit_conjugateEquiv, CategoryTheory.Limits.pullbackAssoc_hom_snd_snd, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_ι_inv_assoc, PartOrd.coe_comp, CategoryTheory.OplaxFunctor.map₂_associator_assoc, CategoryTheory.Dial.braiding_inv_F, AlgebraicTopology.DoldKan.P_f_idem, CategoryTheory.Bicategory.precomp_obj, DerivedCategory.left_fac_of_isStrictlyLE_of_isStrictlyGE, CategoryTheory.Bicategory.rightAdjointSquare.comp_hvcomp, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct_assoc, CategoryTheory.GradedObject.mapBifunctorObjSingle₀ObjIso_inv, CategoryTheory.GlueData.t_fac, CategoryTheory.unmop_comp, CategoryTheory.SimplicialObject.δ_comp_σ_of_gt'_assoc, AlgebraicTopology.AlternatingCofaceMapComplex.d_squared, CategoryTheory.SmallObject.ιObj_naturality, CategoryTheory.NatTrans.rightDerivedToHomotopyCategory_comp_assoc, CategoryTheory.Limits.biprod.total, CategoryTheory.SmallObject.ιFunctorObj_naturality, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone_ι_app, CategoryTheory.Pseudofunctor.map₂_whisker_left, CategoryTheory.Sieve.uliftNatTransOfLe_comm, HomologicalComplex₂.ι_totalDesc, CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_inv, CategoryTheory.TransfiniteCompositionOfShape.map_isColimit, CategoryTheory.Join.mapWhiskerLeft_associator_hom, CochainComplex.mappingCone.ext_to_iff, CategoryTheory.uliftYoneda_obj_map, TopCat.Sheaf.interUnionPullbackConeLift_right, CategoryTheory.Limits.coprod.map_map_assoc, AlgebraicTopology.DoldKan.PInfty_idem_assoc, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_ι_assoc, HomologicalComplex₂.total.mapAux.d₂_mapMap_assoc, CategoryTheory.regularTopology.mapToEqualizer_eq_comp, CategoryTheory.MonoidalClosed.curry_eq, CategoryTheory.Endofunctor.Coalgebra.Terminal.left_inv, HomologicalComplex.ι_mapBifunctorFlipIso_inv_assoc, Quiver.Hom.comp_toLoc, CategoryTheory.Equivalence.counitInv_app_comp_functor_map_η_inverse_assoc, CategoryTheory.SmallObject.ιFunctorObj_πFunctorObj_assoc, AlgebraicGeometry.Scheme.Hom.map_appLE_assoc, CategoryTheory.MonoidalCategory.inv_hom_id_tensor, Rep.applyAsHom_comm_assoc, CategoryTheory.FunctorToTypes.binaryProductIso_hom_comp_snd, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_comp_base, CategoryTheory.Limits.colimit_obj_ext_iff, CategoryTheory.MonoidalCategory.MonoidalRightAction.action_exchange_assoc, CategoryTheory.Adjunction.Triple.rightToLeft_eq_counits, CategoryTheory.Bicategory.adjointifyCounit_left_triangle, HomologicalComplex.singleObjHomologySelfIso_inv_homologyι_assoc, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_assoc, CategoryTheory.Functor.comp_mapMon_mul, AlgebraicGeometry.Scheme.Modules.pseudofunctor_right_unitality, CategoryTheory.ProjectiveResolution.Hom.hom'_comp_π', CategoryTheory.Limits.image.lift_fac, CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id_app_assoc, CategoryTheory.Sieve.natTransOfLe_comm, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τl, CategoryTheory.Limits.Sigma.ι_isoColimit_hom_assoc, CategoryTheory.Limits.prod.map_map, CategoryTheory.IsPushout.paste_vert, CategoryTheory.ShortComplex.LeftHomologyData.f'_i, CategoryTheory.Lax.StrongTrans.toLax_naturality, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.ShortComplex.LeftHomologyMapData.commπ, CategoryTheory.LocalizerMorphism.commShift_iso_hom_app_assoc, CategoryTheory.NatTrans.op_whiskerLeft_assoc, HomologicalComplex.cyclesMap_i_assoc, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_right, CategoryTheory.BraidedCategory.hexagon_forward_inv_assoc, CategoryTheory.Arrow.comp_right_assoc, CategoryTheory.CosimplicialObject.δ_comp_σ_succ'_assoc, CategoryTheory.EnrichedCat.comp_whiskerRight, CategoryTheory.CosimplicialObject.δ_comp_δ_self'_assoc, CategoryTheory.Functor.liftOfIsRightKanExtension_fac_app_assoc, CategoryTheory.Functor.Monoidal.map_associator_inv', AlgebraicGeometry.IsAffineOpen.isoSpec_inv_toSpecΓ, SemimoduleCat.MonoidalCategory.tensorHom_comp_tensorHom, CategoryTheory.ProjectiveResolution.Hom.hom'_f, CategoryTheory.unitCompPartialBijective_natural, CategoryTheory.IsHomLift.id_comp_lift, AddSemigrp.hom_comp, CategoryTheory.MonoidalCategory.tensorHom_def, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id, CategoryTheory.ShortComplex.homologyOpIso_hom_naturality_assoc, AlgebraicGeometry.Scheme.comp_base_assoc, CategoryTheory.CosimplicialObject.δ_comp_σ_of_le, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, CategoryTheory.Functor.LeftExtension.postcomp₁_obj_hom_app, CategoryTheory.IsHomLift.comp, CategoryTheory.dite_comp, groupCohomology.cocyclesMap_comp, CategoryTheory.ShortComplex.LeftHomologyData.f'_π, CategoryTheory.MonoidalCategory.MonoidalLeftAction.hom_inv_actionHomLeft'_assoc, CategoryTheory.SmallObject.functorMapSrc_functorObjTop, HomologicalComplex.biprod_lift_snd_f, AlgebraicGeometry.LocallyRingedSpace.comp_toShHom, AlgebraicGeometry.Scheme.Hom.map_appLE'_assoc, CategoryTheory.Functor.whiskerLeft_comp, CategoryTheory.ShortComplex.cyclesMap_comp, SimplexCategory.eq_comp_δ_of_not_surjective', CategoryTheory.MorphismProperty.LeftFraction.map_hom_ofInv_id_assoc, Mathlib.Tactic.Reassoc.eq_whisker', AlgebraicGeometry.Scheme.Spec.residue_residueFieldIso_hom_assoc, CategoryTheory.Iso.inv_hom_id_app_app_app, groupHomology.H2π_comp_map_assoc, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app', AlgebraicGeometry.IsAffineOpen.toSpecΓ_isoSpec_inv, CategoryTheory.IsIso.comp_isIso, CategoryTheory.Limits.pullbackConeOfLeftIso_fst, AlgebraicGeometry.Scheme.Hom.appIso_inv_naturality, CompHausLike.ofHom_comp, AlgebraicGeometry.Scheme.IsLocallyDirected.fst_inv_eq_snd_inv, AlgebraicGeometry.tilde.map_comp_assoc, CategoryTheory.Limits.Fork.ofCone_π, CategoryTheory.InducedCategory.comp_hom, HomotopicalAlgebra.Precylinder.LeftHomotopy.refl_h, CategoryTheory.MonoOver.map_obj_arrow, CategoryTheory.kernelCokernelCompSequence.ι_snd_assoc, CategoryTheory.SimplicialObject.δ_comp_δ'_assoc, CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_left, CategoryTheory.ProjectiveResolution.pOpcycles_comp_fromLeftDerivedZero', CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_fst_assoc, CategoryTheory.GrpObj.one_inv, CategoryTheory.SmallObject.functorObj_comm, CategoryTheory.Equivalence.cancel_unitInv_right, CategoryTheory.eqToHom_comp_heq, HomologicalComplex.mapBifunctor₂₃.ι_D₂, AlgebraicTopology.DoldKan.N₂Γ₂_inv_app_f_f, CategoryTheory.Bicategory.prod_associator_inv_fst, CategoryTheory.Limits.opProductIsoCoproduct'_comp_self, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_inv, SSet.stdSimplex.faceSingletonIso_one_hom_comp_ι_eq_δ, CategoryTheory.MonoidalClosed.curry_natural_left, CategoryTheory.PrelaxFunctor.map₂_hom_inv_assoc, Mathlib.Tactic.Bicategory.evalWhiskerLeft_of_cons, CategoryTheory.tensorRightHomEquiv_symm_coevaluation_comp_whiskerLeft, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map, CategoryTheory.SimplicialObject.δ_comp_σ_self', CategoryTheory.Lax.StrongTrans.categoryStruct_comp_app, CategoryTheory.Functor.LaxMonoidal.right_unitality_inv, CategoryTheory.Limits.π_comp_colimitOpIsoOpLimit_inv_assoc, CategoryTheory.ShortComplex.homologyMap_mapNatTrans, CategoryTheory.comp_rightAdjointMate, CategoryTheory.Functor.rightKanExtension_hom_ext_iff, CategoryTheory.EnrichedFunctor.map_id, CategoryTheory.Limits.DiagramOfCocones.comp, CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom_assoc, CategoryTheory.Arrow.inv_hom_id_right, AlgebraicGeometry.Scheme.Hom.comp_app_assoc, CategoryTheory.Arrow.w_mk_right_assoc, CategoryTheory.SmallObject.SuccStruct.iterationFunctor_map_succ_assoc, CategoryTheory.MorphismProperty.FunctorialFactorizationData.i_mapZ, SheafOfModules.freeHomEquiv_comp_apply, AlgebraicGeometry.Scheme.comp_app, ContinuousCohomology.MultiInd.d_comp_d_assoc, CategoryTheory.yonedaMon_map_app, HomologicalComplex.cylinder.ι₁_π, ModuleCat.biprodIsoProd_inv_comp_snd, CategoryTheory.shrinkYonedaEquiv_naturality, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_unit_app, CategoryTheory.BraidedCategory.hexagon_reverse, CategoryTheory.ComonadHom.app_δ_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_rightUnitor, CategoryTheory.Functor.OfSequence.map_comp_assoc, CategoryTheory.Endofunctor.Coalgebra.Terminal.right_inv, TopCat.Presheaf.stalk_hom_ext_iff, CategoryTheory.Equivalence.unitIso_hom_app_comp_inverse_map_η_functor, CategoryTheory.OplaxFunctor.mapComp_naturality_left_app, CategoryTheory.MonoidalCategory.associator_naturality_left, CochainComplex.HomComplex.Cochain.rightUnshift_v, CategoryTheory.Limits.pullbackConeEquivBinaryFan_functor_obj, HomologicalComplex.singleObjCyclesSelfIso_inv_homologyπ_assoc, AlgebraicGeometry.AffineSpace.homOfVector_toSpecMvPoly_assoc, AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInfty, HomologicalComplex.biprod_inl_fst_f_assoc, AlgebraicGeometry.Scheme.evaluation_naturality, AlgebraicGeometry.Spec.sheafedSpaceMap_comp, CategoryTheory.Presieve.ofArrows.eq_eqToHom_comp_hom_idx, CategoryTheory.SmallObject.functorMap_π_assoc, AlgebraicGeometry.Scheme.Cover.glued_cover_cocycle_snd, CategoryTheory.ShortComplex.rightHomologyIso_inv_naturality_assoc, CategoryTheory.GrothendieckTopology.toPlus_comp_plusCompIso_inv, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.right_triangle_components, CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_snd_assoc, CategoryTheory.Enriched.FunctorCategory.functorEnriched_id_comp, CategoryTheory.Iso.compInverseIso_hom_app, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_hom_assoc, CategoryTheory.yonedaEquiv_naturality', AlgebraicGeometry.Scheme.Hom.normalizationPullback_snd_assoc, Condensed.comp_val, CategoryTheory.Localization.Monoidal.rightUnitor_naturality, AlgebraicGeometry.Scheme.Cover.trans_map, AlgebraicGeometry.ΓSpec.left_triangle, CategoryTheory.CartesianMonoidalCategory.inv_prodComparison_map_fst_assoc, CategoryTheory.FunctorToTypes.prod.lift_fst, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerLeft_naturality, CategoryTheory.ProjectiveResolution.Hom.hom_f_zero_comp_π_f_zero_assoc, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app_assoc, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac, AlgebraicGeometry.AffineSpace.comp_homOfVector, CategoryTheory.Limits.colimitIsoSwapCompColim_inv_app, CategoryTheory.CartesianMonoidalCategory.prodComparison_comp, CategoryTheory.Limits.FormalCoproduct.category_comp_φ, CategoryTheory.HopfObj.antipode_comul₂, CategoryTheory.BicategoricalCoherence.tensorRight'_iso, CategoryTheory.Over.map_obj_hom, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app, AlgebraicGeometry.ι_left_coprodIsoSigma_inv, SSet.ι₁_snd_assoc, SimplicialObject.Splitting.ofIso_isColimit', CategoryTheory.Functor.LaxLeftLinear.μₗ_unitality_assoc, CategoryTheory.Limits.WidePushout.hom_ext_iff, CategoryTheory.GrothendieckTopology.plusMap_comp_assoc, CategoryTheory.Limits.Cofork.π_precompose, CategoryTheory.Bicategory.Pith.whiskerRight_iso_hom, CategoryTheory.Bicategory.comp_whiskerRight_assoc, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_one, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero, CategoryTheory.Limits.ReflexiveCofork.condition, CategoryTheory.Over.associator_hom_left_snd_fst, CategoryTheory.CommSq.fac_right, CategoryTheory.Limits.PreservesLimitPair.iso_inv_snd, CategoryTheory.Dial.associator_inv_f, CategoryTheory.tensorHom_def, CategoryTheory.Limits.coker.condition, CategoryTheory.cokernel.π_op, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply', CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app_assoc, CategoryTheory.Limits.colimit.hom_ext_iff, SimplexCategory.diag_subinterval_eq, HomologicalComplex.g_shortComplexTruncLEX₃ToTruncGE, Frm.hom_comp, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv, CategoryTheory.Limits.imageMonoIsoSource_inv_ι, CategoryTheory.Limits.WalkingReflexivePair.reflexion_comp_right, CategoryTheory.TwoSquare.whiskerBottom_app, CategoryTheory.Limits.biprod.lift_fst_assoc, CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_hom, CategoryTheory.Pretriangulated.comp_hom₃_assoc, CategoryTheory.Limits.FormalCoproduct.inj_comp_cofanPtIsoSelf_hom, HomologicalComplex.homotopyCofiber.inr_desc, CategoryTheory.comp_eqToHom_heq_iff, CategoryTheory.Bicategory.hom_inv_whiskerRight_whiskerRight, CategoryTheory.Limits.biproduct.matrix_map, CategoryTheory.Limits.Sigma.map_comp_map', CategoryTheory.monoidalOfHasFiniteProducts.associator_inv_snd, CategoryTheory.Bicategory.Pith.rightUnitor_inv_iso_inv, CategoryTheory.Bicategory.LeftExtension.whiskerIdCancel_right, CategoryTheory.Bicategory.prod_rightUnitor_inv_snd, CategoryTheory.IsMonHom.mul_hom, CategoryTheory.Limits.π_comp_cokernelIsoOfEq_inv_assoc, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counit_app_assoc, CategoryTheory.ReflQuiv.comp_obj, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_app, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_cofanPtIsoSelf_inv_assoc, CategoryTheory.BraidedCategory.braiding_tensor_left_hom_assoc, HomotopicalAlgebra.PathObject.ofFactorizationData_p₁, CategoryTheory.Limits.Cocones.extendComp_hom_hom, HomologicalComplex.truncGE'_d_eq, CategoryTheory.Linear.comp_units_smul, CategoryTheory.Limits.prod.triangle, CategoryTheory.kernelCokernelCompSequence.snakeInput_L₀_g, CategoryTheory.Mathlib.Tactic.MonTauto.rightUnitor_inv_tensor_one_mul_assoc, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_functor_obj_d_f, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_fst, CategoryTheory.ShiftedHom.mk₀_comp_mk₀, CategoryTheory.Functor.ShiftSequence.induced.shiftIso_hom_app_obj, CategoryTheory.IsHomLift.lift_id_comp, AlgebraicGeometry.Scheme.isoSpec_inv_naturality_assoc, CategoryTheory.Abelian.Ext.hom_comp_singleFunctor_map_shift, CategoryTheory.Monad.mu_naturality, AlgebraicGeometry.Spec.map_comp_assoc, CategoryTheory.comp_rightAdjointMate_assoc, CategoryTheory.lift_comp_preservesLimitIso_hom, CategoryTheory.RanIsSheafOfIsCocontinuous.fac', AlgebraicGeometry.IsImmersion.isImmersion_iff_exists, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self, CategoryTheory.Limits.image.fac, CategoryTheory.GradedObject.mapBifunctorRightUnitor_inv_naturality_assoc, CategoryTheory.Equivalence.changeInverse_counitIso_inv_app, CategoryTheory.Functor.Monoidal.coreMonoidalTransport_μIso_inv, CategoryTheory.kernelCokernelCompSequence.inl_φ, CategoryTheory.ShortComplex.Exact.shortExact, ModuleCat.range_mkQ_cokernelIsoRangeQuotient_inv, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_0, CategoryTheory.Functor.commShiftIso_hom_naturality_assoc, CategoryTheory.Bicategory.Pith.associator_hom_iso, ModuleCat.exteriorPower.iso₀_hom_naturality_assoc, AlgebraicGeometry.Scheme.homOfLE_homOfLE_assoc, CategoryTheory.Iso.inv_hom_id_app_app_assoc, CategoryTheory.BimonObj.mul_comul_assoc, CategoryTheory.ShortComplex.opcyclesIsoRightHomology_inv_hom_id, CategoryTheory.monoidalOfHasFiniteProducts.associator_hom_snd_snd, CategoryTheory.Limits.coprod.map_swap, CategoryTheory.Limits.biprod.map_fst, CategoryTheory.Limits.KernelFork.condition, CategoryTheory.Bicategory.Strict.id_comp, HomotopicalAlgebra.CofibrantBrownFactorization.s_p, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_def_assoc, CategoryTheory.Functor.comp_mapCommMon_mul, CategoryTheory.Comonad.Coalgebra.coassoc, CategoryTheory.MorphismProperty.Comma.comp_right_assoc, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict, CategoryTheory.Adjunction.comp_counit_app, CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_hom_comp_i_assoc, CategoryTheory.cancel_mono, AlgebraicGeometry.isLocalIso_iff, CategoryTheory.Limits.biproduct.fromSubtype_π, CategoryTheory.ShortComplex.quasiIso_iff_comp_left, AlgebraicGeometry.Spec.preimage_comp_assoc, CategoryTheory.Cat.Hom.comp_map, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_assoc, CategoryTheory.OrthogonalReflection.D₁.ιLeft_comp_t, CategoryTheory.SingleFunctors.shiftIso_add_inv_app, AlgebraicGeometry.IsClosedImmersion.lift_fac, Bimod.middle_assoc_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app'_assoc, CategoryTheory.whiskerLeft_coprod_inl_leftDistrib_inv_assoc, CategoryTheory.Functor.ShiftSequence.induced_shiftIso_hom_app_obj_assoc, CategoryTheory.Localization.SmallShiftedHom.equiv_shift', AlgebraicGeometry.AffineSpace.hom_ext_iff, CategoryTheory.ShortComplex.rightHomologyIso_hom_comp_homologyι, UniformSpaceCat.coe_comp, CategoryTheory.BraidedCategory.braiding_inv_naturality_right_assoc, CategoryTheory.ShortComplex.mapRightHomologyIso_hom_naturality, CategoryTheory.MonObj.one_comp, groupCohomology.π_comp_H0Iso_hom_assoc, CategoryTheory.yoneda_obj_map, CategoryTheory.MonObj.tensorObj.one_def, CategoryTheory.kernelCokernelCompSequence.inr_π, AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk_assoc, CategoryTheory.CosimplicialObject.δ_comp_δ_self, CategoryTheory.Iso.cancel_iso_inv_left, CategoryTheory.GradedObject.Monoidal.hexagon_reverse, CategoryTheory.Functor.OplaxMonoidal.δ_natural_left, CategoryTheory.Lax.LaxTrans.naturality_id, CategoryTheory.CartesianClosed.uncurry_natural_right, CategoryTheory.ForgetEnrichment.homOf_comp, groupCohomology.π_map, CategoryTheory.Limits.Sigma.ι_map, AlgebraicGeometry.LocallyRingedSpace.stalkMap_germ_assoc, CategoryTheory.Limits.PreservesPullback.iso_inv_snd_assoc, AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_pullbackHom_assoc, CategoryTheory.Functor.IsCartesian.universal_property, CategoryTheory.Monad.mu_naturality_assoc, CategoryTheory.Functor.ι_colimitIsoOfIsLeftKanExtension_hom, CategoryTheory.ShortComplex.opcyclesMap'_comp_assoc, CategoryTheory.SmallObject.ιFunctorObj_eq, CategoryTheory.Functor.commShiftIso_comp_inv_app, CategoryTheory.MonoidalClosed.curry_pre_app_assoc, CategoryTheory.Limits.IsImage.isoExt_hom_m, CategoryTheory.StructuredArrow.mkPostcomp_comp, CategoryTheory.Lax.StrongTrans.naturality_comp_assoc, CategoryTheory.Bicategory.associator_naturality_left_assoc, Semigrp.comp_apply, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_map_right, HomologicalComplex.inl_biprodXIso_inv, CategoryTheory.Limits.biproduct.ι_desc, ModuleCat.imageIsoRange_hom_subtype_assoc, SemiNormedGrp.explicitCokernel_hom_ext_iff, CategoryTheory.Functor.Monoidal.toUnit_ε, CategoryTheory.StrictPseudofunctorCore.map₂_right_unitor, CategoryTheory.Functor.Monoidal.whiskerRight_app_fst, AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjMap_glueDataObjι_assoc, CategoryTheory.Groupoid.inv_comp, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_rightUnitor_inv_as_app, CategoryTheory.CartesianMonoidalCategory.inv_prodComparison_map_snd_assoc, AlgebraicGeometry.stalkMap_toStalk, CategoryTheory.Bicategory.prod_leftUnitor_inv_fst, AlgebraicTopology.DoldKan.QInfty_f_naturality_assoc, CategoryTheory.Functor.mapComon_obj_comon_comul, CategoryTheory.ShortComplex.RightHomologyMapData.rightHomologyMap_comm, AlgebraicTopology.DoldKan.MorphComponents.postComp_a, CategoryTheory.ShiftedHom.mk₀_comp_mk₀_assoc, CategoryTheory.Limits.BiconeMorphism.wι_assoc, CategoryTheory.Bicategory.triangle_assoc_comp_right_inv_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_app_assoc, CategoryTheory.Limits.limit.conePointUniqueUpToIso_hom_comp_assoc, CategoryTheory.MonoidalCategory.whiskerLeft_comp_tensorHom, AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv, HomologicalComplex.fromOpcycles_op_cyclesOpIso_inv_assoc, CategoryTheory.Limits.MonoFactorisation.ofCompIso_m, CategoryTheory.Category.comp_id, CategoryTheory.Pretriangulated.TriangleMorphism.comp_hom₁, CategoryTheory.RetractArrow.retract_left, CategoryTheory.Limits.Fork.IsLimit.homIso_apply_coe, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₂, CategoryTheory.Bicategory.hom_inv_whiskerRight, CategoryTheory.PreZeroHypercover.inter_f, SSet.stdSimplex.faceSingletonComplIso_hom_ι, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app, CategoryTheory.Bicategory.prod_rightUnitor_hom_fst, CategoryTheory.HopfObj.antipode_left_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.associator_hom_comp_tensorHom_tensorHom, CategoryTheory.Limits.HasLimit.isoOfNatIso_inv_π, CategoryTheory.Adjunction.leftAdjointCompIso_inv_app, CategoryTheory.Bicategory.Adjunction.left_triangle, CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_comp, CochainComplex.mappingCone.map_inr, CategoryTheory.CatCommSq.vComp_iso_hom_app, HomologicalComplex.homotopyCofiber.inr_desc_assoc, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_fst, CategoryTheory.LocalizerMorphism.commShift_iso_inv_app_assoc, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_ε, CategoryTheory.GlueData.t'_comp_eq_pullbackSymmetry_assoc, Quiver.FreeGroupoid.congr_comp_reverse, CategoryTheory.LocalizerMorphism.equiv_smallHomMap', CategoryTheory.Functor.map_shiftFunctorCompIsoId_inv_app_assoc, Rep.resIndAdjunction_homEquiv_apply, CategoryTheory.Limits.image.preComp_ι, HomologicalComplex.mapBifunctorFlipIso_hom_naturality, AlgebraicGeometry.Scheme.Pullback.tensorCongr_SpecTensorTo_assoc, CategoryTheory.coyonedaEquiv_naturality, CategoryTheory.Limits.Sigma.eqToHom_comp_ι_assoc, CategoryTheory.SimplicialObject.δ_comp_δ', CategoryTheory.CartesianMonoidalCategory.map_toUnit_comp_terminalComparison, CategoryTheory.PreZeroHypercover.inv_hom_h₀_assoc, CategoryTheory.SingleFunctors.inv_hom_id_hom_assoc, CategoryTheory.Sieve.pushforward_comp, CategoryTheory.Functor.leftDerivedNatTrans_app_assoc, CategoryTheory.Limits.prod.map_snd, AlgebraicGeometry.Scheme.IdealSheafData.comapIso_inv_subschemeι_assoc, CategoryTheory.GrothendieckTopology.yonedaEquiv_comp, HomologicalComplex₂.D₁_totalShift₁XIso_hom_assoc, HomologicalComplex.truncLEMap_comp, CategoryTheory.IsMod_Hom.smul_hom_assoc, CategoryTheory.SemiadditiveOfBinaryBiproducts.add_comp, Homotopy.extend.homAux_eq, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom_assoc, CochainComplex.mappingCone.liftCochain_v_fst_v, CategoryTheory.MonoidalCategory.triangle_assoc_comp_right, CategoryTheory.Lax.OplaxTrans.naturality_naturality, CategoryTheory.InjectiveResolution.ι_f_zero_comp_complex_d, CategoryTheory.Arrow.squareToSnd_left, AugmentedSimplexCategory.inl_comp_tensorHom, AlgebraicGeometry.AffineSpace.map_toSpecMvPoly, CategoryTheory.CostructuredArrow.mapIso_functor_map_right, HomologicalComplex.cylinder.inrX_π_assoc, CategoryTheory.Equivalence.changeInverse_unitIso_inv_app, groupCohomology.H2π_comp_map_assoc, SSet.ι₁_snd, CategoryTheory.Functor.IsStronglyCocartesian.comp, CategoryTheory.Limits.Fork.IsLimit.lift_ι, CategoryTheory.op_comp_assoc, CategoryTheory.Idempotents.Karoubi.p_comp, CategoryTheory.ShortComplex.SnakeInput.comp_f₂, CategoryTheory.IsCoreflexivePair.common_retraction, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_SpecMap_awayMap_left, CategoryTheory.Functor.biprodComparison_fst_assoc, AlgebraicGeometry.Scheme.Hom.app_invApp', CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_hom_app, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right, CategoryTheory.Limits.hasPullback_of_right_factors_mono, CategoryTheory.ShortComplex.leftHomologyπ_naturality', groupHomology.d₁₀_comp_coinvariantsMk, CategoryTheory.Over.rightUnitor_inv_left_snd_assoc, CategoryTheory.Subfunctor.Subpresheaf.toRange_ι, CategoryTheory.MonoidalCategory.MonoidalLeftAction.id_actionHomLeft_assoc, CategoryTheory.Limits.biproduct.toSubtype_fromSubtype, CategoryTheory.Bicategory.triangle_assoc_comp_right_inv, CategoryTheory.Functor.mapMon_obj_mon_one, CategoryTheory.Enriched.FunctorCategory.enrichedComp_π_assoc, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂, CategoryTheory.Bicategory.associator_naturality_middle, CategoryTheory.Functor.IsStronglyCartesian.universal_property', CategoryTheory.Functor.relativelyRepresentable.symmetry_fst, CategoryTheory.DinatTrans.compNatTrans_app, AlgebraicGeometry.Scheme.Hom.inl_normalizationCoprodIso_hom_fromNormalization_assoc, CategoryTheory.MonObj.comp_pow, HomologicalComplex.homologyOp_hom_naturality_assoc, CategoryTheory.Functor.comp_homologySequenceδ, HomologicalComplex.homologyMap_comp, CategoryTheory.Limits.ImageMap.factor_map, CategoryTheory.Limits.kernelIsoOfEq_hom_comp_ι_assoc, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_snd, CategoryTheory.Limits.Types.equalizerIso_hom_comp_subtype, CategoryTheory.MonoidalCategory.triangle_assoc_comp_right_inv_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app, groupHomology.mapCycles₂_comp_apply, HomologicalComplex.mapBifunctor₁₂.ι_D₁, CategoryTheory.Limits.Types.pullbackIsoPullback_inv_snd, CategoryTheory.Center.Hom.comm, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocIso_hom_naturality, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_inv_naturality_assoc, AlgebraicGeometry.Scheme.Hom.stalkSpecializes_stalkMap_assoc, CategoryTheory.Limits.kernel.condition, AddCommMonCat.coe_comp, CategoryTheory.ShortComplex.cyclesOpIso_inv_naturality, CategoryTheory.CartesianClosed.uncurry_eq, CategoryTheory.MonoOver.w, HomologicalComplex.homotopyCofiber.inlX_desc_f_assoc, CategoryTheory.Functor.map_shiftFunctorComm_assoc, HomologicalComplex.biprod_inl_fst_f, CategoryTheory.IsPushout.inl_isoIsPushout_hom_assoc, CategoryTheory.ShortComplex.LeftHomologyData.wπ_assoc, CategoryTheory.GradedObject.CofanMapObjFun.ιMapObj_iso_inv, Bimod.one_actLeft_assoc, SimplicialObject.Splitting.πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty, CategoryTheory.kernel.ι_unop, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_right_assoc, CategoryTheory.Comma.left_hom_inv_right, CategoryTheory.HasClassifier.comm, CategoryTheory.Functor.ShiftSequence.induced_isoShiftZero_hom_app_obj_assoc, CategoryTheory.Oplax.LaxTrans.vComp_naturality_comp, CategoryTheory.MorphismProperty.FunctorsInverting.comp_hom_assoc, CategoryTheory.IsSplitCoequalizer.rightSection_π, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompYoneda, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp_assoc, CategoryTheory.MonObj.mul_one, CategoryTheory.IsComonHom.hom_counit, CategoryTheory.Functor.OplaxMonoidal.right_unitality_hom, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp_assoc, CategoryTheory.Functor.Monoidal.map_associator_inv'_assoc, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp, CochainComplex.mappingCone.decomp_from, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp, CategoryTheory.IsSplitCoequalizer.rightSection_π_assoc, CochainComplex.mappingCone.inl_v_triangle_mor₃_f_assoc, AlgebraicGeometry.pullbackSpecIso_inv_fst, CategoryTheory.Limits.pushout_inr_iso_of_right_factors_epi, AlgebraicTopology.DoldKan.P_succ, FinBddDistLat.comp_apply, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd, CategoryTheory.Limits.colimitHomIsoLimitYoneda_hom_comp_π_assoc, CategoryTheory.Limits.Types.binaryProductFunctor_map_app, CategoryTheory.Mathlib.Tactic.MonTauto.associator_inv_comp_tensorHom_tensorHom_comp, CategoryTheory.Bicategory.prod_leftUnitor_inv_snd, CategoryTheory.Presheaf.w, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_app_assoc, SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁_hom_app_f_f, HomologicalComplex.homotopyCofiber.d_fstX, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_map, CategoryTheory.Limits.inr_comp_pushoutSymmetry_inv_assoc, CategoryTheory.Limits.initial.to_comp_assoc, CategoryTheory.Functor.map_shiftFunctorCompIsoId_hom_app_assoc, CategoryTheory.ShiftMkCore.assoc_inv_app_assoc, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_hom_τl, CategoryTheory.Functor.IsCartesian.fac_assoc, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₁, CategoryTheory.Bicategory.LeftExtension.IsKan.fac_assoc, SimplicialObject.Splitting.cofan_inj_πSummand_eq_id, CategoryTheory.Comma.mapLeftComp_inv_app_right, CategoryTheory.Idempotents.Karoubi.comp_proof, CategoryTheory.CostructuredArrow.map₂_map_right, CategoryTheory.GlueData.glue_condition, CategoryTheory.Limits.terminal.comp_from, CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono_g', CategoryTheory.Limits.biprod.inl_snd, AlgebraicGeometry.Spec.locallyRingedSpaceMap_comp, CategoryTheory.Limits.Wedge.condition, CategoryTheory.Bicategory.leftUnitorNatIso_hom_app, PartOrd.comp_apply, CategoryTheory.Limits.IsInitial.to_comp, CategoryTheory.Functor.Braided.braided, CochainComplex.mappingConeCompTriangle_mor₁, CategoryTheory.RetractArrow.retract_right_assoc, AddMonCat.FilteredColimits.cocone_naturality, CategoryTheory.Bicategory.Strict.assoc, CochainComplex.mappingCone.inr_triangleδ_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_map_app_app, CategoryTheory.ShortComplex.LeftHomologyMapData.comp_φH, CategoryTheory.SmallCategoryOfSet.comp_def, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counitIso_hom_app, groupHomology.chainsMap_id_comp, CategoryTheory.Iso.unop_hom_inv_id_app, CategoryTheory.Coyoneda.naturality, CategoryTheory.Biprod.ofComponents_comp, CategoryTheory.StrictPseudofunctorPreCore.map_comp, HomologicalComplex.homologyπ_restrictionHomologyIso_hom, CategoryTheory.heq_comp, HomologicalComplex.comp_f, CategoryTheory.Localization.Preadditive.add_comp, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_inv_τl, CochainComplex.mappingCone.inl_v_snd_v_assoc, AlgebraicGeometry.AffineSpace.homOfVector_over_assoc, CategoryTheory.Iso.inv_hom_id_assoc, CategoryTheory.NatTrans.IsMonoidal.comp, CategoryTheory.regularTopology.parallelPair_pullback_initial, CategoryTheory.Limits.Cones.extendComp_inv_hom, MonCat.comp_apply, HomologicalComplex.cylinder.inlX_π, HomologicalComplex.cylinder.ι₀_π, CategoryTheory.MorphismProperty.RightFraction.map_ofInv_hom_id_assoc, CategoryTheory.Grp_Class.zpow_comp, SimplexCategoryGenRel.standardσ_cons, CategoryTheory.Functor.commShiftIso_hom_naturality, CategoryTheory.Oplax.StrongTrans.naturality_naturality_assoc, CategoryTheory.Comonad.adj_counit, CategoryTheory.Functor.CommShift.comp_commShiftIso_hom_app, CategoryTheory.Limits.biprod.associator_natural_assoc, CategoryTheory.BraidedCategory.yang_baxter_assoc, CategoryTheory.ShortComplex.SnakeInput.w₁₃_assoc, CategoryTheory.Limits.biprod.associator_inv_natural_assoc, CategoryTheory.MonoidalCategory.leftUnitor_naturality_assoc, CategoryTheory.GlueData.diagram_snd, AlgebraicGeometry.morphismRestrict_comp, HomologicalComplex.XIsoOfEq_hom_comp_XIsoOfEq_inv_assoc, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatTrans_comp, HomologicalComplex.ι_mapBifunctorAssociatorX_hom_assoc, CategoryTheory.Limits.pushoutIsoUnopPullback_inl_hom, CategoryTheory.Localization.Monoidal.whisker_exchange, CategoryTheory.Bicategory.Prod.sectL_mapId_hom, CategoryTheory.MonoidalCategory.associator_monoidal_assoc, CategoryTheory.ComposableArrows.opEquivalence_unitIso_hom_app, AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_comp, AlgebraicGeometry.Scheme.SpecMap_stalkSpecializes_fromSpecStalk_assoc, CategoryTheory.ProjectiveResolution.Hom.hom'_comp_π'_assoc, CategoryTheory.PreZeroHypercover.bind_f, CategoryTheory.Limits.Sigma.ι_π, CategoryTheory.cancel_epi_assoc_iff, CategoryTheory.Limits.equalizer.condition_assoc, CategoryTheory.StructuredArrow.IsUniversal.hom_desc, HomologicalComplex.singleObjOpcyclesSelfIso_inv_naturality, HomologicalComplex.ιOrZero_mapBifunctorAssociatorX_hom, CategoryTheory.eHom_whisker_cancel_assoc, CategoryTheory.TwoSquare.hComp_app, CategoryTheory.MonoidalCategory.id_whiskerLeft_assoc, CategoryTheory.eq_conj_eqToHom, CategoryTheory.ShortComplex.mapToComposableArrows_comp, CategoryTheory.Mon.tensorObj_mul, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right_assoc, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_id_naturality_hom, CategoryTheory.CatCenter.smul_eq', CategoryTheory.MonoidalCategory.MonoidalLeftAction.unit_actionHomRight_assoc, CategoryTheory.Bicategory.InducedBicategory.bicategory_rightUnitor_hom_hom, SkyscraperPresheafFunctor.map'_comp, CategoryTheory.NatTrans.whiskerRight_app_tensor_app, CategoryTheory.Pseudofunctor.isoMapOfCommSq_vert_id, CategoryTheory.Limits.hasPullback_assoc, CategoryTheory.Limits.Multifork.condition, CategoryTheory.η_naturality, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_app_app_germToPullbackStalk_assoc, CategoryTheory.MonoidalClosed.curry'_comp, HomologicalComplex.extend.rightHomologyData.d_comp_desc_eq_zero_iff, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.leftUnitor_naturality, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerRight, HomologicalComplex.cyclesOpIso_inv_naturality, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.lift_fac_assoc, CategoryTheory.yonedaGrp_naturality_assoc, CategoryTheory.Limits.WalkingReflexivePair.reflexion_comp_left_assoc, CategoryTheory.Limits.CategoricalPullback.Hom.w_assoc, CategoryTheory.Sheaf.ΓRes_map_assoc, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_snd_assoc, AlgebraicGeometry.Scheme.Cover.LocallyDirected.trans_comp, AlgebraicTopology.DoldKan.N₂Γ₂_compatible_with_N₁Γ₀, CategoryTheory.CartesianMonoidalCategory.lift_lift_associator_hom, AlgebraicGeometry.Scheme.ΓSpecIso_naturality, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv, CategoryTheory.Bimon.ofMonComon_toMonComon_obj_counit, CategoryTheory.Center.Hom.comm_assoc, CategoryTheory.surjective_up_to_refinements_of_epi, CategoryTheory.GrpObj.whiskerLeft_η_commutator, quasiIso_iff_comp_left, HomologicalComplex.biprod_inr_fst_f, CategoryTheory.Limits.piObjIso_hom_comp_π_assoc, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_fst_assoc, CategoryTheory.Bicategory.Pith.whiskerLeft_iso_hom, CategoryTheory.MonoidalCategory.whisker_exchange_assoc, CategoryTheory.Limits.inv_prodComparison_map_fst, AlgebraicGeometry.Scheme.stalkMap_congr_hom, CategoryTheory.ShortComplex.LeftHomologyMapData.leftHomologyMap_comm, CategoryTheory.Limits.limit.conePointUniqueUpToIso_inv_comp_assoc, CategoryTheory.Limits.CatCospanTransform.triangle_inv, CategoryTheory.Limits.pullbackAssoc_hom_snd_fst, CategoryTheory.MonoidalCategory.tensorHom_comp_whiskerLeft_assoc, CategoryTheory.Bicategory.mateEquiv_symm_apply, CategoryTheory.MonoidalCategory.id_whiskerLeft_symm_assoc, CategoryTheory.Pseudofunctor.map₂_whisker_left_assoc, CategoryTheory.IsPullback.isoIsPullback_hom_fst_assoc, CategoryTheory.Limits.cokernel.condition_assoc, CategoryTheory.CatCommSq.iso_inv_naturality_assoc, CategoryTheory.Under.liftCone_π_app, CategoryTheory.GrpObj.lift_commutator_eq_mul_mul_inv_inv, CategoryTheory.Limits.Cocone.ofCofork_ι, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τr, AlgebraicGeometry.Scheme.Pullback.range_snd_comp, HomologicalComplex.opcyclesOpIso_hom_naturality, CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_hom_assoc, PresheafOfModules.homEquivOfIsLocallyBijective_apply, TopModuleCat.comp_cokerπ, HomologicalComplex₂.total.mapAux.mapMap_D₁, CategoryTheory.Bicategory.Strict.rightUnitor_eqToIso, CategoryTheory.Limits.WalkingMulticospan.Hom.comp_eq_comp, CategoryTheory.Limits.pullbackProdFstIsoProd_inv_snd_fst, Bicategory.Opposite.bicategory_whiskerRight_unop2, CategoryTheory.Bicategory.leftUnitor_whiskerRight, CategoryTheory.Localization.Monoidal.whisker_exchange_assoc, CategoryTheory.MonoidalCategory.tensorHom_def', HomotopicalAlgebra.PathObject.trans_p₀, CategoryTheory.Over.pullback_map_left, CategoryTheory.Limits.MonoFactorisation.ofIsoComp_e, Bicategory.Opposite.homCategory_comp_unop2, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id, groupHomology.mapShortComplexH1_id_comp, TopCat.Presheaf.stalkSpecializes_stalkFunctor_map_assoc, TopCat.Sheaf.comp_app, CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_inv_assoc, CategoryTheory.Functor.rightDerivedNatTrans_fac, CategoryTheory.Localization.liftNatTrans_app, CategoryTheory.NatTrans.naturality_app_assoc, groupHomology.mapShortComplexH1_comp, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_left, CategoryTheory.ShortComplex.leftHomologyπ_naturality'_assoc, HomologicalComplex.homotopyCofiber.eq_desc, CategoryTheory.ShortComplex.Splitting.ofIso_s, CategoryTheory.Limits.biproduct.lift_π_assoc, CategoryTheory.Iso.cancel_iso_hom_right_assoc, AlgebraicGeometry.Scheme.Opens.isoOfLE_hom_ι, CategoryTheory.Limits.pullback.condition_assoc, CochainComplex.HomComplex.Cochain.ofHoms_v_comp_d, CategoryTheory.Limits.FormalCoproduct.cochainComplexFunctor_obj_d, Rep.coindResAdjunction_homEquiv_apply, CochainComplex.mappingCone.inr_f_triangle_mor₃_f, CategoryTheory.Functor.triangle, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_map_fiber, PartOrdEmb.coe_comp, groupCohomology.inhomogeneousCochains.d_comp_d, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftUnitor_actionHom, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp_assoc, CategoryTheory.sum.inrCompInrCompInverseAssociator_inv_app_down, HomologicalComplex.π_homologyIsoSc'_hom_assoc, CategoryTheory.PreGaloisCategory.exists_autMap, HeytAlg.comp_apply, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_hom_π, AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem_ι, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_pt, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_fst_assoc, CategoryTheory.Limits.Multicoequalizer.ι_sigmaπ, CategoryTheory.LocalizerMorphism.LeftResolution.comp_f_assoc, CategoryTheory.Limits.colimCompFlipIsoWhiskerColim_hom_app_app, AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id, CategoryTheory.conjugateEquiv_symm_comp, CategoryTheory.Category.assoc', CategoryTheory.PreZeroHypercover.comp_s₀, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_functor_map_hom, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_fst, CategoryTheory.Comma.mapRightIso_functor_map_right, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.GradedObject.mapBifunctor₁₂BifunctorMapObj_ext_iff, SheafOfModules.ιFree_freeMap, HomologicalComplex.homotopyCofiber.inrX_desc_f, CategoryTheory.Pretriangulated.shiftFunctorZero_op_hom_app, SSet.comp_app, AlgebraicGeometry.Scheme.Modules.pushforwardComp_hom_app_app, CategoryTheory.Oplax.StrongTrans.naturality_id, CategoryTheory.Equivalence.cancel_counitInv_right_assoc, Homotopy.compRight_hom, CategoryTheory.Abelian.factorThruImage_comp_coimageIsoImage'_inv, CategoryTheory.instIsMod_HomComp, CategoryTheory.Comma.limitAuxiliaryCone_π_app, CategoryTheory.MonoidalCategory.associator_conjugation_assoc, CochainComplex.cm5b.fac_assoc, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_inv_hom'_assoc, CategoryTheory.Bicategory.associator_eqToHom_inv_assoc, CochainComplex.ConnectData.d₀_comp, CategoryTheory.Subobject.underlyingIso_arrow, MonCat.coe_comp, CategoryTheory.StrictPseudofunctor.map_comp, CategoryTheory.Limits.Trident.IsLimit.homIso_apply_coe, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι_assoc, CategoryTheory.SimplicialObject.δ_comp_σ_succ', CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_fst, CategoryTheory.MonoidalCategory.pentagon_hom_inv, CategoryTheory.Limits.limit.post_π_assoc, CategoryTheory.Localization.comp_liftNatTrans_assoc, ComplexShape.Embedding.homRestrict_comp_extendMap_assoc, AlgebraicGeometry.Scheme.iso_inv_base_hom_base, CategoryTheory.Sheaf.ΓObjEquivHom_naturality_symm, AlgebraicGeometry.Scheme.Hom.inl_normalizationCoprodIso_hom_fromNormalization, AlgebraicGeometry.germ_stalkClosedPointIso_hom, CategoryTheory.Functor.relativelyRepresentable.pullback₃.map_p₁_comp_assoc, CategoryTheory.Bicategory.prod_leftUnitor_hom_snd, CategoryTheory.GradedObject.mapBifunctorRightUnitor_inv_apply, CategoryTheory.GradedObject.ι_mapBifunctorComp₁₂MapObjIso_inv, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply, CategoryTheory.Idempotents.Karoubi.Hom.comm, CategoryTheory.Limits.WidePullback.π_arrow_assoc, CategoryTheory.ChosenPullbacksAlong.pullbackId_hom_counit, GrpCat.coe_comp, CategoryTheory.Bicategory.Lan.CommuteWith.instHasLeftKanExtensionComp, AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv, CategoryTheory.ι_colimitCompWhiskeringRightIsoColimitComp_hom, CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_inv_hom_id, ChainComplex.mk'_congr_succ'_d, CategoryTheory.Subobject.ofLE_comp_ofLE_assoc, CategoryTheory.tensorRightHomEquiv_naturality, CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor, CategoryTheory.SplitEpi.id_assoc, CategoryTheory.IsReflexivePair.common_section, CategoryTheory.Functor.ranObjObjIsoLimit_inv_π_assoc, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_assoc, AlgebraicGeometry.Scheme.Hom.comp_apply, CategoryTheory.Limits.pullbackConeOfRightIso_snd, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_hom_app_app, CategoryTheory.OplaxFunctor.mapComp_assoc_right_app_assoc, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π_assoc, CategoryTheory.Limits.piPiIso_hom, CategoryTheory.GradedObject.ι_mapBifunctorMapObjDesc_assoc, groupCohomology.toCocycles_comp_isoCocycles₁_hom_assoc, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_inv, CategoryTheory.Subgroupoid.Map.arrows_iff, SimplicialObject.Splitting.IndexSet.fac_pull, CategoryTheory.Groupoid.vertexGroupIsomOfMap_apply, CategoryTheory.rightDistributor_ext_left_iff, AlgebraicGeometry.Scheme.homOfLE_homOfLE, HomologicalComplex.biprodXIso_hom_fst_assoc, CategoryTheory.HalfBraiding.monoidal_assoc, Rep.resIndAdjunction_counit_app, CategoryTheory.GrpObj.lift_inv_left_eq, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_assoc, CategoryTheory.Functor.comp_mapCommGrp_mul, CategoryTheory.Center.whiskerRight_comm, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_inv_π_assoc, SimplicialObject.Split.cofan_inj_naturality_symm_assoc, CategoryTheory.Limits.fiberwiseColimitLimitIso_inv_app, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv_desc_assoc, CategoryTheory.e_id_comp_assoc, AlgebraicGeometry.Proj.awayι_toSpecZero, CategoryTheory.Subobject.ofMkLEMk_comp, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_id_assoc, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_assoc, CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom', CategoryTheory.ProjectiveResolution.lift_commutes_zero, SimplicialObject.Splitting.ofIso_ι, CategoryTheory.ShortComplex.HomotopyEquiv.ext_iff, TopCat.pullbackIsoProdSubtype_inv_fst, CategoryTheory.Limits.biprod.ext_to_iff, CategoryTheory.Limits.pullbackIsoOpPushout_inv_fst, CategoryTheory.Square.fac, CategoryTheory.MonadHom.app_η_assoc, CategoryTheory.Bicategory.whiskerLeft_inv_hom_whiskerRight_assoc, CategoryTheory.Idempotents.whiskeringLeft_obj_preimage_app, AlgebraicGeometry.PresheafedSpace.GlueData.f_invApp_f_app_assoc, groupCohomology.isoCocycles₁_inv_comp_iCocycles, CategoryTheory.Bicategory.whisker_exchange_assoc, CategoryTheory.Limits.inr_pushoutAssoc_hom, CategoryTheory.CartesianMonoidalCategory.tensorδ_fst_assoc, CategoryTheory.tensorRightHomEquiv_tensor, CategoryTheory.biproduct_ι_comp_leftDistributor_hom, groupHomology.π_comp_H0IsoOfIsTrivial_hom, CategoryTheory.Hom.mulEquivCongrRight_symm_apply, CategoryTheory.ShortComplex.LeftHomologyMapData.leftHomologyMap_eq, CategoryTheory.MonObj.mul_comp_assoc, CategoryTheory.BimonObj.one_counit_assoc, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_rightUnitor_hom_as_app, CategoryTheory.Functor.relativelyRepresentable.pullback₃.snd_snd_eq_p₃, CategoryTheory.Iso.map_hom_inv_id_app, CategoryTheory.Functor.op_commShiftIso_inv_app_assoc, HomologicalComplex.mapBifunctorAssociatorX_hom_D₂_assoc, CategoryTheory.HasLiftingProperty.of_comp_left, CategoryTheory.MonoidalCategory.MonoidalRightAction.action_actionHomRight_assoc, CategoryTheory.ShortComplex.mapRightHomologyIso_inv_naturality_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_id, CategoryTheory.Dial.associatorImpl_hom_F, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_symm_apply_f_coe, SSet.comp_const, HomologicalComplex.homologyι_comp_fromOpcycles_assoc, CategoryTheory.Functor.map_shiftFunctorCompIsoId_hom_app, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom_assoc, AlgebraicTopology.DoldKan.QInfty_comp_PInfty, SimplicialObject.opFunctor_obj_δ, AlgebraicTopology.DoldKan.Q_idem, CategoryTheory.Bicategory.InducedBicategory.bicategory_rightUnitor_inv_hom, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃'_tensorHom_assoc, CategoryTheory.IsSplitEqualizer.bottom_rightRetraction_assoc, groupHomology.eq_d₂₁_comp_inv_assoc, CategoryTheory.Square.category_comp_τ₃, HomologicalComplex.opcyclesMap_comp_assoc, CategoryTheory.GlueData.t_fac_assoc, HomologicalComplex.restrictionHomologyIso_hom_homologyι, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv, ModuleCat.imageIsoRange_inv_image_ι, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom, CategoryTheory.Bicategory.pentagon, CategoryTheory.CatEnrichedOrdinary.Hom.base_comp, CategoryTheory.ShortComplex.Homotopy.comp_h₁, CategoryTheory.Oplax.OplaxTrans.homCategory_comp_as_app, CategoryTheory.MonoidalCategory.pentagon_inv_hom, CategoryTheory.Functor.Initial.extendCone_map_hom, HomologicalComplex.cylinder.inlX_π_assoc, CategoryTheory.SimplicialObject.σ_comp_σ, CategoryTheory.Limits.pullbackIsoOpPushout_inv_snd, SheafOfModules.conjugateEquiv_pullbackComp_inv, CategoryTheory.NatTrans.CommShiftCore.shift_app_assoc, CategoryTheory.MonoidalCategory.tensor_hom_inv_id_assoc, AlgebraicTopology.DoldKan.whiskerLeft_toKaroubi_N₂Γ₂_hom, CategoryTheory.kernelCokernelCompSequence.instEpiπ, PresheafOfModules.ι_fromFreeYonedaCoproduct_assoc, TopCat.Presheaf.Pushforward.comp_inv_app, AlgebraicGeometry.Scheme.toIso_inv_ι_assoc, CategoryTheory.braiding_rightUnitor_assoc, CommSemiRingCat.hom_comp, CategoryTheory.Functor.relativelyRepresentable.pullback₃.hom_ext_iff, CategoryTheory.ShortComplex.SnakeInput.L₀_g_δ, CategoryTheory.Functor.LaxMonoidal.tensorHom_ε_comp_μ_assoc, CategoryTheory.Limits.colimit.map_post, CategoryTheory.ForgetEnrichment.homTo_comp, CategoryTheory.IsHomLift.lift_eqToHom_comp_iff, CategoryTheory.shiftFunctorCompIsoId_add'_hom_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_inv_hom', CategoryTheory.Bicategory.rightUnitor_naturality_assoc, CategoryTheory.MonoidalCategory.DayConvolution.triangle, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_comp, CategoryTheory.ProjectiveResolution.leftDerived_app_eq, CategoryTheory.MonadHom.app_μ_assoc, groupHomology.cyclesMap_comp_isoCycles₂_hom_assoc, CategoryTheory.CostructuredArrow.w, CategoryTheory.Limits.colimitFlipIsoCompColim_hom_app, HomologicalComplex.homologyπ_extendHomologyIso_inv_assoc, HomologicalComplex₂.ι_totalShift₁Iso_inv_f_assoc, CategoryTheory.monoidalOfHasFiniteCoproducts.associator_hom, HomologicalComplex₂.ιTotal_totalFlipIso_f_hom_assoc, CategoryTheory.IsPushout.paste_horiz, CategoryTheory.Limits.pullbackLeftPullbackSndIso_hom_snd_assoc, CategoryTheory.Limits.colimit.isoColimitCocone_ι_inv_assoc, CategoryTheory.Monad.Algebra.assoc, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.leftUnitor_hom_unit_app, CategoryTheory.RetractArrow.retract_right, CategoryTheory.Cokleisli.Adjunction.fromCokleisli_map, CategoryTheory.Lax.OplaxTrans.vComp_naturality_naturality, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom, AlgebraicGeometry.Scheme.Hom.appIso_inv_naturality_assoc, CategoryTheory.Limits.prod.inl_snd_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.associator_actionHom_assoc, AlgebraicGeometry.Scheme.Hom.appLE_map_assoc, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_two, CategoryTheory.SimplicialObject.δ_comp_δ'', CategoryTheory.Idempotents.app_p_comm_assoc, CategoryTheory.toOverIteratedSliceForwardIsoPullback_hom_app_left, HomologicalComplex.d_comp_d', CategoryTheory.Limits.bicone_ι_π_ne_assoc, CategoryTheory.Limits.inl_comp_pushoutSymmetry_inv, CategoryTheory.StructuredArrow.homMk'_id, CategoryTheory.Functor.CommShift₂.comm, CategoryTheory.Triangulated.SpectralObject.triangle_mor₂, CategoryTheory.Limits.Fork.π_comp_hom_assoc, CategoryTheory.pullbackShiftFunctorAdd'_hom_app, CategoryTheory.Limits.IsColimit.homEquiv_symm_naturality, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeftLift_fst, BoolAlg.hom_comp, CategoryTheory.Under.mapComp_hom, CategoryTheory.Limits.HasZeroMorphisms.zero_comp, CategoryTheory.Functor.limitIsoOfIsRightKanExtension_hom_π_assoc, CategoryTheory.EnrichedCat.whisker_exchange, CategoryTheory.BraidedCategory.braiding_naturality_assoc, CategoryTheory.ShortComplex.SnakeInput.snd_δ_assoc, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_ι_assoc, CategoryTheory.Dial.whiskerRight_F, CategoryTheory.CatEnrichedOrdinary.id_hComp, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₂₃, CategoryTheory.OplaxFunctor.map₂_rightUnitor_assoc, CategoryTheory.Equivalence.induced_inverse_map, CategoryTheory.ε_naturality, HomologicalComplex₂.total.mapAux.mapMap_D₂, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom, groupHomology.cyclesIso₀_inv_comp_iCycles, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_rightUnitor_assoc, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv_assoc, CategoryTheory.ComonObj.comul_assoc_flip, CategoryTheory.ProjectiveResolution.lift_commutes, AlgebraicGeometry.Scheme.stalkMap_comp, CategoryTheory.CartesianMonoidalCategory.associator_hom_fst, HomologicalComplex₂.XXIsoOfEq_inv_ιTotal_assoc, CochainComplex.MappingConeCompHomotopyEquiv.hom_inv_id, CategoryTheory.MonoidalCategory.inv_hom_id_tensor', CategoryTheory.StructuredArrow.w_prod_snd, CategoryTheory.MorphismProperty.IsLocalAtSource.iff_of_zeroHypercover, CategoryTheory.Localization.Monoidal.μ_inv_natural_left_assoc, HomologicalComplex.cylinder.ι₀_π_assoc, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_inv_app, CategoryTheory.MonoidalCategory.tensor_inv_hom_id'_assoc, CategoryTheory.MorphismProperty.RespectsRight.postcomp, HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom_eq_zero, CategoryTheory.Prod.fac'_assoc, CategoryTheory.Bimon.ofMon_Comon_toMon_Comon_obj_comul, AlgebraicTopology.DoldKan.Q_idem_assoc, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_snd_fst_assoc, AlgebraicGeometry.Scheme.IdealSheafData.comapIso_inv_subschemeι, CategoryTheory.Limits.MultispanIndex.inj_fstSigmaMapOfIsColimit_assoc, AlgebraicGeometry.PresheafedSpace.comp_c_app_assoc, CategoryTheory.ExponentiableMorphism.ev_coev_assoc, CategoryTheory.OrthogonalReflection.D₁.ιLeft_comp_l_assoc, CompHausLike.finiteCoproduct.ι_desc_assoc, CochainComplex.mappingCone.d_snd_v_assoc, CategoryTheory.Lax.LaxTrans.vComp_naturality_id, CategoryTheory.Limits.bicone_ι_π_self, CategoryTheory.shiftFunctorZero_inv_app_shift, CategoryTheory.FreeBicategory.mk_whisker_left, CategoryTheory.ShortComplex.LeftHomologyData.ofEpiOfIsIsoOfMono'_f', CategoryTheory.ShortComplex.opcyclesIsoX₂_inv_hom_id_assoc, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.map_f', CategoryTheory.CechNerveTerminalFrom.wideCospan.limitIsoPi_inv_comp_pi, CategoryTheory.HomOrthogonal.matrixDecomposition_comp, CategoryTheory.Limits.coprod.map_comp_id, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_hom_c_app, Representation.coind'_apply_apply, CategoryTheory.Monoidal.InducingFunctorData.tensorHom_eq, CategoryTheory.ComposableArrows.naturality', CategoryTheory.Functor.map_comp_heq', AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjMap_glueDataObjι, groupCohomology.d₁₂_comp_d₂₃_assoc, AlgebraicGeometry.Scheme.Hom.comp_appIso, ChainComplex.isoHomologyι₀_inv_naturality, CategoryTheory.eComp_op_eq_assoc, HomologicalComplex.cylinder.ι₁_π_assoc, CategoryTheory.MonObj.Mon_tensor_mul_one, CategoryTheory.Adjunction.commShiftIso_inv_app_counit_app_assoc, CategoryTheory.Oplax.OplaxTrans.Modification.naturality_assoc, CategoryTheory.Limits.Multicofork.map_ι_app, CategoryTheory.Functor.leftKanExtension_hom_ext_iff, CategoryTheory.Limits.Pi.ι_π_eq_id_assoc, CategoryTheory.Lax.OplaxTrans.id_naturality, CategoryTheory.Limits.inl_pushoutLeftPushoutInrIso_inv, CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIsoWhisker_inv_right, CategoryTheory.Functor.LaxMonoidal.ε_tensorHom_comp_μ_assoc, CategoryTheory.Limits.WalkingReflexivePair.reflexion_comp_right_assoc, CategoryTheory.Limits.Sigma.map'_comp_map', CategoryTheory.Limits.limit.post_post, CochainComplex.mappingCone.d_snd_v', CategoryTheory.StructuredArrow.mapNatIso_inverse_obj_hom, CategoryTheory.Over.associator_inv_left_fst_snd, AlgebraicGeometry.IsOpenImmersion.range_pullback_to_base_of_left, CategoryTheory.Functor.commShiftIso_inv_naturality_assoc, HomologicalComplex.extend_op_d, CategoryTheory.Limits.Fan.IsLimit.fac_assoc, CategoryTheory.Limits.biproduct.ι_π_ne, CategoryTheory.Limits.CatCospanTransform.whiskerRight_comp, CategoryTheory.Functor.whiskerLeft_twice, CategoryTheory.Functor.OneHypercoverDenseData.SieveStruct.fac, AlgebraicTopology.DoldKan.Γ₀_map_app, CategoryTheory.uliftYoneda_obj_map_down, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence, CategoryTheory.braiding_leftUnitor_aux₂, CategoryTheory.Functor.obj.ε_def, CategoryTheory.braiding_tensorUnit_left, CategoryTheory.BimonObj.mul_counit, CategoryTheory.SimplicialObject.comp_left_app, CategoryTheory.BimonObj.one_comul_assoc, CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv', CategoryTheory.Limits.PushoutCocone.op_π_app, HomologicalComplex.extend.rightHomologyData_p, CategoryTheory.Bicategory.whiskerRight_congr, CategoryTheory.Limits.biproduct.fromSubtype_π_assoc, AlgebraicGeometry.Scheme.Hom.appIso_inv_appLE_assoc, CategoryTheory.Oplax.StrongTrans.categoryStruct_comp_naturality, CategoryTheory.NatTrans.op_comp, CategoryTheory.shiftFunctorAdd'_assoc_inv_app_assoc, CategoryTheory.Functor.LeftExtension.postcompose₂ObjMkIso_hom_right_app, AlgebraicGeometry.Proj.homOfLE_toBasicOpenOfGlobalSections_ι_assoc, CategoryTheory.MonoidalCategory.tensorHom_def'_assoc, CategoryTheory.CartesianMonoidalCategory.lift_whiskerLeft, CategoryTheory.CechNerveTerminalFrom.wideCospan.limitIsoPi_hom_comp_pi_assoc, LightCondensed.free_internallyProjective_iff_tensor_condition', AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp, Bicategory.Opposite.op2_rightUnitor, SimplexCategory.Truncated.δ₂_zero_comp_δ₂_two, CategoryTheory.IsHomLift.comp_of_lift_id, CategoryTheory.coprod_inl_leftDistrib_hom_assoc, CategoryTheory.Comonad.ForgetCreatesLimits'.newCone_π, CategoryTheory.mateEquiv_symm_apply, CategoryTheory.Iso.map_inv_hom_id, SemiNormedGrp₁.coe_comp, HomologicalComplex.Hom.comm_to, CategoryTheory.exp.ev_coev, CategoryTheory.section_comp_left, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap_assoc, CategoryTheory.comp_apply', CategoryTheory.Limits.limit.lift_π_app, CategoryTheory.MonObj.Mon_tensor_one_mul, CategoryTheory.Limits.limit_obj_ext_iff, ProfiniteGrp.profiniteCompletion_map, SSet.RelativeMorphism.comm_assoc, CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_π_assoc, SimplexCategoryGenRel.σ_comp_σ_assoc, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_assoc, CategoryTheory.ShortComplex.leftRightHomologyComparison_eq, CategoryTheory.ShortComplex.kernel_ι_comp_cokernel_π_comp_cokernelToAbelianCoimage, CategoryTheory.CartesianMonoidalCategory.associator_inv_fst_snd_assoc, CategoryTheory.Limits.BinaryBiconeMorphism.wfst_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_assoc, CategoryTheory.Functor.rightDerivedNatTrans_comp_assoc, CategoryTheory.Equivalence.cancel_unit_right_assoc, CategoryTheory.Bicategory.LeftLift.whisker_unit, CategoryTheory.Limits.CategoricalPullback.Hom.w', CompHausLike.LocallyConstant.adjunction_left_triangle, CategoryTheory.Functor.ranCounit_app_app_ranAdjunction_unit_app_app_assoc, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app, CategoryTheory.Limits.image.factorThruImage_preComp_assoc, CategoryTheory.Adjunction.ε_comp_map_ε, smoothSheafCommRing.forgetStalk_hom_comp_evalHom, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_assoc, CategoryTheory.IsFiltered.coeq_condition_assoc, CategoryTheory.ShortComplex.RightHomologyData.wι, CategoryTheory.Functor.LaxRightLinear.μᵣ_naturality_right, CategoryTheory.coreCategory_comp_iso, CategoryTheory.Oplax.OplaxTrans.naturality_id_assoc, CategoryTheory.Limits.coprodComparison_inr_assoc, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map_assoc, CategoryTheory.Limits.pullbackProdFstIsoProd_inv_snd_snd_assoc, CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero, Mathlib.Tactic.CategoryTheory.CancelIso.hom_inv_id_of_eq_assoc, CategoryTheory.IsIso.hom_inv_id_assoc, CategoryTheory.Limits.π_comp_colimitOpIsoOpLimit_inv, CategoryTheory.Limits.hasPullback_assoc_symm, CategoryTheory.Limits.IsImage.e_isoExt_hom, HomologicalComplex.cylinder.ι₀_desc, CategoryTheory.Iso.isoFunctorOfIsoInverse_inv_app, CategoryTheory.prod_comp_fst, CategoryTheory.IsMonHom.one_hom, CategoryTheory.ProjectiveResolution.Hom.hom_comp_π, CategoryTheory.CostructuredArrow.mapNatIso_inverse_obj_hom, CategoryTheory.Dial.hexagon_forward, CategoryTheory.Precoverage.ZeroHypercover.comp_s₀, CategoryTheory.MorphismProperty.MapFactorizationData.fac_assoc, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_comp_π_assoc, CategoryTheory.Functor.Final.extendCocone_obj_ι_app', CategoryTheory.Presheaf.uliftYonedaAdjunction_homEquiv_app, CategoryTheory.ShortComplex.iCycles_g_assoc, CategoryTheory.MonoidalCategory.DayConvolution.symmetry, CategoryTheory.Adjunction.leftAdjointUniq_trans_app, CategoryTheory.Equivalence.counitInv_app_comp_functor_map_η_inverse, CategoryTheory.rightUnitor_inv_braiding_assoc, groupHomology.map_id_comp_H0Iso_hom_assoc, HomologicalComplex.biprodXIso_hom_snd, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w, CategoryTheory.OplaxFunctor.map₂_leftUnitor, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₁_assoc, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_appLE_assoc, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id_assoc, HomologicalComplex.stupidTruncMap_stupidTruncXIso_hom_assoc, SimplexCategory.δ_comp_δ_self'_assoc, CategoryTheory.Conv.one_eq, CategoryTheory.Bicategory.conjugateEquiv_symm_comp, CategoryTheory.Limits.MulticospanIndex.fstPiMap_π_assoc, AlgebraicGeometry.Scheme.IdealSheafData.inclusion_comp, HomologicalComplex.XIsoOfEq_inv_comp_XIsoOfEq_hom_assoc, SimplicialObject.Split.Hom.comm, CategoryTheory.Limits.Types.binaryCoproductIso_inr_comp_inv, CategoryTheory.PreOneHypercover.comp_s₁, CategoryTheory.ShortComplex.LeftHomologyData.homologyπ_comp_homologyIso_hom_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.action_exchange, CategoryTheory.Limits.WidePullbackCone.condition_assoc, CategoryTheory.Limits.lim_ε_π, CategoryTheory.Localization.Monoidal.associator_naturality₂, CategoryTheory.ShortComplex.SnakeInput.w₀₂, CategoryTheory.BraidedCategory.hexagon_forward, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerRight_assoc, CategoryTheory.Join.mapWhiskerRight_associator_hom, CategoryTheory.Limits.Sigma.hom_ext_iff, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, CategoryTheory.Functor.CoreMonoidal.associativity, CategoryTheory.ShortComplex.exact_iff_i_p_zero, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_assoc, CategoryTheory.MorphismProperty.Over.w_assoc, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst_assoc, CategoryTheory.Bicategory.pentagon_hom_hom_inv_inv_hom_assoc, Homotopy.nullHomotopicMap_f_of_not_rel_right, CategoryTheory.toOverPullbackIsoToOver_hom_app_left, CategoryTheory.Limits.biprod.map_eq, TopCat.prodIsoProd_hom_snd, ModuleCat.restrictScalarsComp'App_hom_naturality, CochainComplex.homotopyOp_hom_eq, CategoryTheory.Abelian.PreservesImage.iso_inv_ι_assoc, CategoryTheory.Functor.RightExtension.postcomp₁_map_left_app, CochainComplex.mappingCone.inr_f_descCochain_v_assoc, CategoryTheory.cones_obj_map_app, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π_assoc, AlgebraicTopology.DoldKan.QInfty_f_naturality, CategoryTheory.ShortComplex.RightHomologyData.pOpcycles_comp_opcyclesIso_hom, CategoryTheory.shiftComm', CategoryTheory.SmallObject.πObj_ιIteration_app_right_assoc, CategoryTheory.Limits.pullbackProdSndIsoProd_inv_fst_fst, CategoryTheory.Bicategory.mateEquiv_hcomp, CategoryTheory.LocalizerMorphism.homMap_apply_assoc, HomologicalComplex₂.totalAux.ιMapObj_D₂, CategoryTheory.Iso.homCongr_apply, TopCat.Presheaf.stalkSpecializes_comp, CategoryTheory.toSheafify_plusPlusIsoSheafify_hom, CategoryTheory.Subobject.ofMkLE_comp_ofLEMk, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_right_assoc, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.Lax.LaxTrans.naturality_naturality, CategoryTheory.Bicategory.Adj.leftUnitor_inv_τl, CategoryTheory.Functor.LaxMonoidal.associativity_inv, CategoryTheory.ShortComplex.SnakeInput.L₁_f_φ₁, AlgebraicGeometry.Scheme.LocalRepresentability.yoneda_toGlued_yonedaGluedToSheaf_assoc, CategoryTheory.Limits.coprodComparison_inr, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc, CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_idem, CategoryTheory.ShortComplex.rightHomologyι_naturality', Bicategory.Opposite.op2_rightUnitor_hom, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀'_assoc, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_hom, CategoryTheory.coalgebraToOver_obj, CategoryTheory.Limits.Types.isPullback_iff, CategoryTheory.Over.associator_hom_left_snd_snd_assoc, CategoryTheory.preservesColimitIso_inv_comp_desc_assoc, CategoryTheory.Bicategory.whiskerLeft_eqToHom, CategoryTheory.Comma.mapRightComp_hom_app_left, CategoryTheory.IsCofiltered.infTo_commutes, CategoryTheory.ShortComplex.HomotopyEquiv.trans_homotopyHomInvId, CategoryTheory.Limits.limitRightOpIsoOpColimit_hom_comp_ι_assoc, CategoryTheory.ExponentiableMorphism.pushforwardComp_hom_counit_assoc, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_app, CategoryTheory.MonoidalClosed.id_tensor_pre_app_comp_ev_assoc, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_comp, AlgebraicGeometry.Scheme.Pullback.Triplet.tensorCongr_trans_hom_assoc, AlgebraicGeometry.Proj.awayι_toSpecZero_assoc, groupCohomology.mapShortComplexH2_id_comp_assoc, SSet.Subcomplex.homOfLE_ι, CategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSet_comp, CategoryTheory.Limits.biprod.map_lift_mapBiprod, CategoryTheory.ShortComplex.π_leftRightHomologyComparison_ι_assoc, groupHomology.mapCycles₂_id_comp_assoc, CategoryTheory.braiding_tensorUnit_right_assoc, CategoryTheory.Adjunction.homEquiv_naturality_right_square_iff, CategoryTheory.conjugateEquiv_counit, CategoryTheory.NatTrans.CommShiftCore.shift_app_comm_assoc, CategoryTheory.Bicategory.associator_hom_congr, AlgebraicGeometry.Scheme.Hom.inr_normalizationCoprodIso_hom_fromNormalization_assoc, CategoryTheory.whiskerRight_ι_colimitCompWhiskeringRightIsoColimitComp_inv_assoc, Mathlib.Tactic.Bicategory.naturality_leftUnitor, CategoryTheory.LocalizerMorphism.smallHomMap'_mk, CochainComplex.mappingCone.d_fst_v_assoc, CategoryTheory.EnrichedFunctor.category_comp_out, CategoryTheory.Functor.Initial.limit_cone_comp_aux, HomologicalComplex₂.total.mapAux.mapMap_D₂_assoc, AlgebraicGeometry.Scheme.Hom.residueFieldMap_congr, CategoryTheory.Functor.mapCommMon_id_mul, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.triangle, CategoryTheory.ShortComplex.LeftHomologyData.wi, CategoryTheory.Functor.FullyFaithful.monObj_one, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂'_map_app_app, CategoryTheory.Limits.CatCospanTransform.comp_whiskerRight, HomologicalComplex.π_homologyIsoSc'_inv_assoc, CategoryTheory.Hom.inv_def, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_whiskerLeft, CategoryTheory.Bicategory.Adj.whiskerLeft_τr, CategoryTheory.Limits.prod.symmetry_assoc, CategoryTheory.MonoidalCategory.whiskerRight_tensor_symm_assoc, CategoryTheory.Prod.fac_assoc, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_comp, CategoryTheory.Limits.inr_comp_pushoutSymmetry_hom_assoc, TopCat.pullbackIsoProdSubtype_hom_snd, CategoryTheory.Mathlib.Tactic.MonTauto.eq_mul_one, CategoryTheory.MorphismProperty.comp_mem, CategoryTheory.Adjunction.rightAdjointUniq_trans_app_assoc, AlgebraicGeometry.Scheme.Modules.Hom.comp_app, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_inv_comp_homologyι_assoc, CategoryTheory.Bicategory.pentagon_inv_inv_hom_inv_inv_assoc, groupHomology.mapShortComplexH2_comp, AlgebraicGeometry.IsOpenImmersion.lift_fac_assoc, CategoryTheory.Functor.ranObjObjIsoLimit_hom_π_assoc, HomologicalComplex.cyclesOpIso_hom_naturality_assoc, CategoryTheory.Functor.toOplaxFunctor_mapComp, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_assoc, CategoryTheory.Limits.ι_colimitLimitIso_limit_π_assoc, CategoryTheory.Arrow.mapCechConerve_app, CategoryTheory.leftAdjointMate_comp_evaluation, CategoryTheory.uncurry_pre, SimplexCategoryGenRel.δ_comp_σ_of_le, CategoryTheory.Functor.LaxMonoidal.tensorUnit_whiskerLeft_comp_leftUnitor_hom, Bimod.comp_hom', CategoryTheory.Functor.Monoidal.whiskerRight_app_snd_assoc, HomotopicalAlgebra.Precylinder.LeftHomotopy.h₁_assoc, CategoryTheory.IsHomLift.comp_lift_id_left', CategoryTheory.Bicategory.Comonad.comul_assoc, CategoryTheory.GradedObject.mapBifunctorRightUnitor_naturality, CategoryTheory.SimplicialObject.δ_comp_δ_self, groupCohomology.subtype_comp_d₀₁_assoc, CategoryTheory.sum.inrCompInlCompAssociator_inv_app_down_down, CategoryTheory.CartesianMonoidalCategory.braiding_inv_snd, Bimod.AssociatorBimod.hom_inv_id, CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_hom_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom, CategoryTheory.Limits.Cofork.condition, CategoryTheory.Square.category_comp_τ₁, CategoryTheory.Functor.OplaxRightLinear.δᵣ_unitality_hom, CategoryTheory.shiftFunctorAdd_assoc_hom_app_assoc, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_right, HomologicalComplex₂.ι_totalShift₂Iso_hom_f_assoc, SheafOfModules.ιFree_freeMap_assoc, CategoryTheory.Limits.BinaryFan.braiding_inv_fst_assoc, SimplexCategory.δ_comp_σ_of_gt, CategoryTheory.nerve.δ₁_mk₂_eq, CategoryTheory.Limits.pullback_map_diagonal_isPullback, CategoryTheory.Functor.partialLeftAdjointHomEquiv_map_comp, CategoryTheory.NatTrans.mapHomologicalComplex_naturality, AlgebraicGeometry.Scheme.residueFieldCongr_fromSpecResidueField, CategoryTheory.Limits.PreservesPushout.inl_iso_hom_assoc, CategoryTheory.SmallObject.πObj_naturality_assoc, CategoryTheory.Bicategory.comp_whiskerLeft, CategoryTheory.Lax.LaxTrans.comp_app, CategoryTheory.NatTrans.CommShiftCore.shift_comm, CategoryTheory.Subobject.ofMkLEMk_comp_ofMkLEMk, SimplexCategory.Truncated.δ₂_zero_comp_σ₂_one_assoc, HomologicalComplex.XIsoOfEq_hom_naturality_assoc, CategoryTheory.ConcreteCategory.forget₂_comp_apply, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app, CategoryTheory.ihom.coev_naturality_assoc, CategoryTheory.Limits.end_.hom_ext_iff, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd, CategoryTheory.coprod_inr_leftDistrib_hom, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst, CategoryTheory.Functor.RepresentableBy.homEquiv_comp, HomologicalComplex.HomologySequence.δ_naturality_assoc, CategoryTheory.Limits.ConeMorphism.w_assoc, MonCat.FilteredColimits.cocone_naturality, CategoryTheory.OplaxFunctor.mapComp_naturality_left, HomologicalComplex.biprodXIso_hom_snd_assoc, CategoryTheory.Limits.prod.symmetry', groupHomology.toCycles_comp_isoCycles₂_hom, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_inv_π, SemiNormedGrp.hom_comp, CategoryTheory.LocalizerMorphism.equiv_smallShiftedHomMap, CategoryTheory.Lax.StrongTrans.naturality_id, CategoryTheory.Adjunction.unit_app_shift_commShiftIso_inv_app_assoc, CategoryTheory.Bicategory.LeftLift.whiskerHom_right, groupCohomology.map_id_comp_H0Iso_hom, CategoryTheory.Functor.commShiftOfLocalization.iso_inv_app_assoc, CategoryTheory.OrthogonalReflection.iteration_map_succ_assoc, CategoryTheory.Limits.PullbackCone.unop_ι_app, CategoryTheory.Triangulated.SpectralObject.Hom.comm_assoc, quasiIso_comp, CategoryTheory.Limits.pullbackDiagonalMapIso.hom_snd, ComplexShape.Embedding.liftExtend.comm, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality_assoc, CategoryTheory.Bicategory.prod_associator_hom_fst, CategoryTheory.Grp_Class.inv_comp, CategoryTheory.SymmetricCategory.symmetry_assoc, CategoryTheory.MorphismProperty.precomp_iff, CategoryTheory.exp.ev_coev_assoc, CategoryTheory.Localization.Monoidal.μ_inv_natural_right_assoc, CategoryTheory.Limits.FormalCoproduct.evalOp_map_app, CategoryTheory.Bicategory.LeftExtension.ofCompId_hom, CategoryTheory.Limits.Multifork.toPiFork_π_app_one, CategoryTheory.Idempotents.Karoubi.decompId, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_leftUnitor_hom_as_app, CategoryTheory.CartesianMonoidalCategory.tensorHom_snd, CategoryTheory.SingleFunctors.hom_inv_id_hom, GrpCat.ofHom_comp, CategoryTheory.SmallObject.SuccStruct.Iteration.mapObj_trans_assoc, CategoryTheory.Functor.IsCocartesian.of_iso_comp, AlgebraicGeometry.Scheme.Hom.preimageIso_hom_ι, CategoryTheory.ShortComplex.leftHomologyπ_naturality, CategoryTheory.Limits.Pi.π_comp_eqToHom_assoc, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_hom_naturality_assoc, CategoryTheory.Functor.relativelyRepresentable.w'_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv, AugmentedSimplexCategory.inl_comp_inl_comp_associator, CategoryTheory.Bicategory.prod_homCategory_comp_fst, groupHomology.mapCycles₁_id_comp, StalkSkyscraperPresheafAdjunctionAuxs.germ_fromStalk_assoc, SimplicialObject.Splitting.cofan_inj_πSummand_eq_zero, CategoryTheory.MonoidalCategory.leftUnitor_whiskerRight_assoc, CategoryTheory.Over.μ_pullback_left_fst_fst', HomologicalComplex.homotopyCofiber.inlX_sndX, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₂, AlgebraicGeometry.Scheme.isoOfEq_hom_ι_assoc, CategoryTheory.Functor.LaxMonoidal.μ_natural_left_assoc, CategoryTheory.Limits.pullbackObjIso_hom_comp_fst, CategoryTheory.ProjectiveResolution.π'_f_zero, CategoryTheory.CosimplicialObject.δ_comp_σ_succ', CategoryTheory.Linear.homCongr_apply, CategoryTheory.Lax.StrongTrans.categoryStruct_id_naturality, CategoryTheory.Limits.π_comp_cokernelComparison_assoc, CategoryTheory.CartesianClosed.uncurry_natural_left_assoc, AlgebraicGeometry.Scheme.isoSpec_inv_naturality, CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_snd_snd_assoc, Homotopy.ofExtend_hom, CategoryTheory.Precoverage.comp_mem_coverings, CategoryTheory.shiftFunctorZero_hom_app_shift, HomologicalComplex.truncGE'.d_comp_d_assoc, AlgebraicGeometry.IsAffineOpen.toSpecΓ_fromSpec_assoc, AlgebraicGeometry.Scheme.Hom.ker_comp_of_isIso, CategoryTheory.ShortComplex.SnakeInput.comp_f₀_assoc, HomologicalComplex.leftUnitor'_inv, HomologicalComplex₂.totalFlipIso_hom_f_D₂, CategoryTheory.MonadHom.app_η, AlgebraicGeometry.Scheme.Pullback.openCoverOfRight_X, CategoryTheory.Over.μ_pullback_left_fst_snd, CategoryTheory.Subobject.eq_of_comp_arrow_eq_iff, ModuleCat.homEquiv_extendScalarsComp, CategoryTheory.Equivalence.changeFunctor_unitIso_inv_app, CategoryTheory.ShortComplex.leftRightHomologyComparison'_eq_leftHomologpMap'_comp_iso_hom_comp_rightHomologyMap', CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_hom_inv_id_assoc, CategoryTheory.IsPushout.inr_isoIsPushout_inv, dNext_comp_left, CategoryTheory.Limits.biproduct.hom_ext'_iff, CategoryTheory.Pseudofunctor.mapComp_id_left_inv, CategoryTheory.CostructuredArrow.homMk'_left, CategoryTheory.Over.monObjMkPullbackSnd_one, AlgebraicTopology.DoldKan.P_f_naturality_assoc, CategoryTheory.Limits.Pi.reindex_inv_π, CategoryTheory.unitOfTensorIsoUnit_inv_app, CategoryTheory.Limits.imageSubobjectCompIso_inv_arrow_assoc, CochainComplex.mappingCone.inl_v_fst_v, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_hom_naturality, CategoryTheory.ShortComplex.comp_homologyMap_comp_assoc, CategoryTheory.StructuredArrow.homMk'_right, CategoryTheory.Functor.LaxMonoidal.associativity_inv_assoc, CategoryTheory.SplitMono.id_assoc, Profinite.lift_lifts_assoc, CategoryTheory.Limits.CatCospanTransform.pentagon_assoc, TopCat.pullbackIsoProdSubtype_inv_snd, CategoryTheory.epi_comp_iff_of_isIso, CategoryTheory.NatTrans.naturality_app, CategoryTheory.biproduct_ι_comp_rightDistributor_hom_assoc, CategoryTheory.Functor.relativelyRepresentable.pullback₃.fst_snd_eq_p₂_assoc, CategoryTheory.sum.inlCompInlCompAssociator_inv_app_down, AlgebraicGeometry.Scheme.isoOfEq_inv_ι_assoc, CategoryTheory.InjectiveResolution.desc_commutes, CategoryTheory.Subfunctor.Subpresheaf.range_le_equalizer_iff, CategoryTheory.Functor.biprodComparison'_comp_biprodComparison, smoothSheafCommRing.ι_forgetStalk_inv_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.inv_hom_actionHomLeft_assoc, CategoryTheory.Adjunction.CommShift.compatibilityCounit_left, AlgebraicGeometry.Scheme.Hom.preimageIso_inv_ι_assoc, CategoryTheory.PreZeroHypercover.hom_inv_h₀_assoc, CategoryTheory.Limits.coconeOfIsSplitEpi_pt, HomotopicalAlgebra.RightHomotopyClass.precomp_mk, HomologicalComplex.xPrevIso_comp_dTo_assoc, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_comp_homologyIso_inv_assoc, CategoryTheory.Functor.op_commShiftIso_inv_app, AlgebraicGeometry.Scheme.Cover.gluedCoverT'_snd_fst_assoc, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_whisker_left, CategoryTheory.Limits.Fan.IsLimit.fac, PresheafOfModules.map_comp, CategoryTheory.ShortComplex.LeftHomologyMapData.cyclesMap_comm, CategoryTheory.cocones_obj_map_app, CategoryTheory.Functor.LaxRightLinear.μᵣ_associativity_assoc, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberι, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_tensorDesc_app_assoc, SSet.Subcomplex.image_eq_range, CategoryTheory.Functor.Monoidal.map_associator', CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_iso, CategoryTheory.obj_η_app_assoc, HomologicalComplex.homotopyCofiber.inlX_d, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃'_map_app_app, CategoryTheory.Sieve.mem_functorPushforward_inverse, CategoryTheory.Sieve.pullback_comp, CategoryTheory.Comma.inv_left_hom_right, HomologicalComplex.mapBifunctor₂₃.d₁_eq, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right, CategoryTheory.Functor.map_braiding_assoc, SSet.RelativeMorphism.comm, CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_inv_desc, CategoryTheory.ShortComplex.SnakeInput.naturality_δ_assoc, CategoryTheory.coevaluation_comp_rightAdjointMate, CategoryTheory.ShiftedHom.opEquiv'_symm_apply, CategoryTheory.Limits.imageSubobjectMap_arrow, CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom_assoc, CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_fst_assoc, CategoryTheory.Comonad.coassoc_assoc, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_ihom_ev_app, AlgebraicGeometry.PresheafedSpace.map_id_c_app, CategoryTheory.Conv.mul_eq, CategoryTheory.GrpObj.div_comp_assoc, CategoryTheory.SemiadditiveOfBinaryBiproducts.add_eq_right_addition, AlgebraicGeometry.specTargetImageFactorization_comp, CategoryTheory.ExponentiableMorphism.ev_naturality_assoc, CategoryTheory.Limits.inv_piComparison_comp_map_π, CategoryTheory.Limits.colimitPointwiseProductToProductColimit_app, CategoryTheory.Idempotents.DoldKan.η_inv_app_f, AlgebraicGeometry.Scheme.comp_appTop_assoc, CategoryTheory.Limits.imageSubobjectMap_arrow_assoc, CategoryTheory.Limits.inr_pushoutRightPushoutInlIso_inv, Homotopy.comp_nullHomotopicMap, AddCommGrpCat.kernelIsoKer_inv_comp_ι, CategoryTheory.MonoidalCategory.MonoidalLeftAction.hom_inv_actionHomLeft_assoc, CategoryTheory.LaxFunctor.map₂_associator, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, CategoryTheory.Adjunction.Triple.adj₁_counit_app_rightToLeft_app_assoc, CategoryTheory.Limits.limit.map_post, CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id_app_assoc, CategoryTheory.IsFinitelyPresentable.exists_hom_of_isColimit, AlgebraicGeometry.SheafedSpace.GlueData.ι_isoPresheafedSpace_inv, AddCommGrpCat.image.fac, CategoryTheory.Bicategory.associator_inv_naturality_left_assoc, TopCat.Presheaf.SheafConditionEqualizerProducts.res_π, SSet.PtSimplex.MulStruct.δ_map_of_lt, CategoryTheory.Grp_Class.comp_div, HomologicalComplex.extend.rightHomologyData_g', CategoryTheory.OplaxFunctor.mapComp_id_right_assoc, TopCat.Presheaf.germ_res, CommGrpCat.hom_comp, CategoryTheory.IsFiltered.tulip, CategoryTheory.Bicategory.whiskerLeftIso_inv, CategoryTheory.Limits.pullback_snd_iso_of_left_factors_mono, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_SpecMap_awayMap_left_assoc, CategoryTheory.SmallObject.SuccStruct.iterationFunctor_map_succ, ModuleCat.restrictScalarsComp'App_inv_naturality, CategoryTheory.Oplax.StrongTrans.naturality_comp_assoc, AlgebraicGeometry.PresheafedSpace.GlueData.f_invApp_f_app, TopCat.prodIsoProd_inv_fst, CategoryTheory.Functor.OplaxMonoidal.δ_comp_whiskerLeft_δ, AlgebraicGeometry.Scheme.Hom.resLE_comp_resLE_assoc, CategoryTheory.GrpObj.whiskerLeft_η_commutator_assoc, CategoryTheory.Pretriangulated.comp_hom₂_assoc, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_left, CategoryTheory.Dial.associator_naturality, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapComp_hom, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_σ, CategoryTheory.InjectiveResolution.desc_commutes_assoc, HomologicalComplex.single_map_f_self_assoc, CategoryTheory.tensorObj_def, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocIso_inv_naturality_assoc, CategoryTheory.Localization.SmallHom.mk_comp_mk, CategoryTheory.Limits.IsTerminal.comp_from, CategoryTheory.Square.Hom.comp_τ₁, CategoryTheory.NatTrans.CommShiftCore.shift_comm_assoc, CategoryTheory.Limits.coprod.map_comp_id_assoc, groupHomology.eq_d₁₀_comp_inv, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_symm_apply, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_comp_π, CategoryTheory.OplaxFunctor.mapComp_assoc_right, CategoryTheory.GrpObj.isPullback, CategoryTheory.Bicategory.mateEquiv_eq_iff, HomologicalComplex.ι_mapBifunctorMap_assoc, CategoryTheory.ModObj.one_smul', CategoryTheory.uncurry_expComparison, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_obj_hom_app, CategoryTheory.RegularMono.w, CategoryTheory.Preadditive.comp_sum, CategoryTheory.MonoidalCategory.hom_inv_whiskerRight'_assoc, CategoryTheory.Limits.prod.associator_hom, AlgebraicGeometry.AffineSpace.reindex_comp, CategoryTheory.cancel_epi_id, CategoryTheory.Limits.pullback_diagonal_map_snd_fst_fst_assoc, CategoryTheory.forget₂_comp_apply, CategoryTheory.Limits.limit.isoLimitCone_inv_π_assoc, AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_self, CategoryTheory.CartesianClosed.uncurry_natural_left, CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_inv_apply, CategoryTheory.Limits.BinaryFan.braiding_hom_fst, CategoryTheory.CatCenter.smul_iso_inv_eq_assoc, CategoryTheory.Bicategory.LeftLift.ofIdComp_right, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_inv_naturality_assoc, Preord.hom_comp, groupHomology.isoShortComplexH1_inv, CategoryTheory.FunctorToTypes.map_comp_apply, AlgebraicGeometry.AffineSpace.map_SpecMap, CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_p_assoc, CategoryTheory.OplaxFunctor.mapComp_assoc_left_assoc, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_whiskerLeft, SSet.horn.faceι_ι, HomologicalComplex.extend.homologyData'_right_p, HomologicalComplex.extendCyclesIso_hom_iCycles, CategoryTheory.Adjunction.commShiftIso_hom_app_counit_app_shift_assoc, CategoryTheory.SingleFunctors.hom_inv_id_hom_app_assoc, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_ε_assoc, AlgebraicTopology.DoldKan.degeneracy_comp_PInfty_assoc, CategoryTheory.GrothendieckTopology.dense_covering, CategoryTheory.SmallObject.FunctorObjIndex.w_assoc, CategoryTheory.LocalizerMorphism.homMap_comp, CategoryTheory.Functor.Monoidal.transport_η_assoc, CategoryTheory.Limits.Cotrident.IsColimit.homIso_symm_apply, CategoryTheory.Limits.ColimitPresentation.w_assoc, SheafOfModules.pushforwardComp_hom_app_val_app, CategoryTheory.Projective.factorThru_comp, CategoryTheory.Limits.kernelSubobject_arrow, CategoryTheory.Limits.Cones.postcompose_obj_π, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_inv_app, Bicategory.Opposite.op2_comp, CategoryTheory.Limits.colimit.ι_post_assoc, CategoryTheory.Paths.lift_cons, groupHomology.eq_d₁₀_comp_inv_assoc, CategoryTheory.Functor.OplaxMonoidal.comp_η, CategoryTheory.Bicategory.pentagon_inv_assoc, SimplexCategory.δ_comp_δ, groupCohomology.d₁₂_comp_d₂₃, CategoryTheory.GlueData.t'_inv, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app, CategoryTheory.StructuredArrow.map_map_left, CategoryTheory.GradedObject.CofanMapObjFun.inj_iso_hom_assoc, CategoryTheory.GradedObject.mapBifunctorObjObjSingle₀Iso_inv, CategoryTheory.Iso.map_hom_inv_id_eval_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitIso_inv_naturality_assoc, CategoryTheory.Limits.coprod.inl_desc, CategoryTheory.MonoidalClosed.uncurry_ihom_map, Bimod.comp_whiskerRight_bimod, CategoryTheory.Adjunction.rightAdjointUniq_hom_counit_assoc, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_id_assoc, CategoryTheory.Presheaf.isLocallySurjective_comp, CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_comp_d, CategoryTheory.Limits.ColimitPresentation.Total.Hom.comp_base, TopCat.Presheaf.pullback_obj_obj_ext_iff, CategoryTheory.Limits.biprod.map_snd_assoc, CategoryTheory.Bicategory.whiskerRight_comp, CategoryTheory.ObjectProperty.isLocal.homEquiv_apply, CategoryTheory.ShortComplex.π_leftRightHomologyComparison'_ι_assoc, CategoryTheory.Limits.pullbackProdSndIsoProd_inv_fst_fst_assoc, AlgebraicGeometry.Scheme.GlueData.oneHypercover_p₂, CategoryTheory.CatCenter.smul_eq, CategoryTheory.Endofunctor.Algebra.functorOfNatTrans_map_f, CategoryTheory.Limits.PreservesPushout.inr_iso_hom, CategoryTheory.Bicategory.rightUnitorNatIso_inv_app, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd, CategoryTheory.Functor.RepresentableBy.homEquiv_unop_comp, CategoryTheory.Pseudofunctor.StrongTrans.associator_inv_as_app, groupHomology.chainsMap_f_1_comp_chainsIso₁_assoc, CategoryTheory.SingleFunctors.postcomp_shiftIso_inv_app, CategoryTheory.shiftFunctorAdd_assoc_inv_app_assoc, CpltSepUniformSpace.hom_comp, Bicategory.Opposite.op2_leftUnitor_hom, CategoryTheory.Dial.tensorHomImpl_F, CategoryTheory.Functor.mapCone₂_π_app, CategoryTheory.Limits.PreservesLimitPair.iso_inv_snd_assoc, CategoryTheory.Regular.frobeniusStrongEpiMonoFactorisation_e, CategoryTheory.GradedObject.Monoidal.braiding_naturality_left, CategoryTheory.IsPullback.isoPullback_hom_fst, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc, CategoryTheory.Limits.pullbackDiagonalMapIso.inv_snd_fst, CategoryTheory.Limits.MonoFactorisation.ofCompIso_I, CategoryTheory.StructuredArrow.mkPostcomp_right, CategoryTheory.Linear.comp_smul, ModuleCat.restrictScalarsComp'App_inv_naturality_assoc, CategoryTheory.LocalizerMorphism.RightResolution.comp_f, CategoryTheory.Bicategory.Comonad.comul_counit_assoc, HomologicalComplex.extend.homologyData'_left_i, CategoryTheory.Functor.OplaxMonoidal.δ_comp_η_tensorHom, CategoryTheory.Subfunctor.lift_ι_assoc, CategoryTheory.CartesianMonoidalCategory.whiskerLeft_toUnit_comp_rightUnitor_hom_assoc, CategoryTheory.Limits.pullbackProdFstIsoProd_inv_fst_assoc, HomologicalComplex.truncGE'_d_eq_fromOpcycles, CategoryTheory.ShortComplex.cyclesIsoLeftHomology_hom_inv_id, CategoryTheory.Functor.obj.μ_def, CategoryTheory.Limits.limitFlipIsoCompLim_inv_app, CategoryTheory.MonObj.one_leftUnitor, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_app_hom, CategoryTheory.GlueData.t_inv_assoc, CochainComplex.mappingCone.inr_f_descCochain_v, CategoryTheory.Limits.CatCospanTransform.whisker_exchange_assoc, CategoryTheory.toOverIsoToOverUnit_hom_app_left, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃'_associator_hom, CategoryTheory.Functor.IsCocartesian.universal_property, CategoryTheory.Bicategory.congr_whiskerLeft, CategoryTheory.Adjunction.compYonedaIso_inv_app_app, CategoryTheory.GlueData.t'_jii, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f, CategoryTheory.PreOneHypercover.w, CategoryTheory.MarkovCategory.discard_natural, CategoryTheory.SmallObject.ρFunctorObj_π, AlgebraicGeometry.Surjective.comp_iff, CategoryTheory.ShortComplex.RightHomologyData.ofAbelian_ι, CategoryTheory.eqToHom_comp_homOfLE, CategoryTheory.ComposableArrows.isComplex₂_iff, SimplexCategory.Truncated.δ₂_one_comp_σ₂_zero, CategoryTheory.ShortComplex.RightHomologyMapData.comp_φH, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_inv_hom, prodIsoPullback_hom_snd, CategoryTheory.Preadditive.comp_zsmul, CategoryTheory.Equivalence.changeInverse_counitIso_hom_app, CategoryTheory.Limits.colimit.pre_desc_assoc, CategoryTheory.Over.w, SemimoduleCat.MonoidalCategory.hexagon_forward, CategoryTheory.Limits.HasLimit.isoOfNatIso_hom_π_assoc, CategoryTheory.CartesianMonoidalCategory.whiskerLeft_snd, HomologicalComplex.XIsoOfEq_hom_comp_XIsoOfEq_hom_assoc, HomologicalComplex.restrictionHomologyIso_hom_homologyι_assoc, CategoryTheory.Limits.pushout_inl_iso_of_left_factors_epi, SheafOfModules.Presentation.map_relations_I, HomologicalComplex₂.D₁_totalShift₁XIso_hom, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv, CategoryTheory.Localization.Monoidal.associator_naturality₁_assoc, groupCohomology.cocyclesIso₀_hom_comp_f_assoc, CategoryTheory.Sheaf.adjunction_unit_app_val, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.sq, CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_assoc, CategoryTheory.Limits.sigmaComparison_map_desc_assoc, HomologicalComplex.πTruncGE_naturality, groupHomology.lsingle_comp_chainsMap_f, CategoryTheory.Functor.ι_biproductComparison', AlgebraicGeometry.Proj.fromOfGlobalSections_toSpecZero, HomologicalComplex₂.D₂_totalShift₁XIso_hom, CategoryTheory.ShortComplex.asIsoHomologyπ_inv_comp_homologyπ, AlgebraicTopology.DoldKan.P_idem, CategoryTheory.Cat.comp_eq_comp, CategoryTheory.mono_comp, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_pos, CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_hom_desc_assoc, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_comp_assoc, CategoryTheory.GradedObject.ι_mapBifunctorMapMap_assoc, CategoryTheory.Limits.colimit.pre_desc, CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono_p, CategoryTheory.Subfunctor.toRange_ι_assoc, BoolAlg.coe_comp, CategoryTheory.DifferentialObject.objEqToHom_d, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv, CategoryTheory.Equivalence.fun_inv_map, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_m, CategoryTheory.Cat.leftUnitor_hom_toNatTrans, HomotopicalAlgebra.Precylinder.LeftHomotopy.h₀, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_hom_assoc, CategoryTheory.ShortComplex.homologyι_comp_asIsoHomologyι_inv, AlgebraicGeometry.Scheme.iso_hom_base_inv_base, CategoryTheory.Bicategory.whiskerLeft_inv_hom_whiskerRight, AlgebraicGeometry.Scheme.stalkMap_congr_point, ComplexShape.Embedding.homRestrict.comm_assoc, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π_assoc, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app_assoc, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_π_app, CategoryTheory.Bicategory.Adj.comp_τr_assoc, CategoryTheory.MonoidalCategory.DayConvolution.braidingInvCorepresenting_app, ModuleCat.imageIsoRange_inv_image_ι_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitIso_inv_naturality, CategoryTheory.CartesianMonoidalCategory.associator_inv_fst_fst_assoc, CategoryTheory.ShortComplex.toCycles_comp_leftHomologyπ, HomologicalComplex₂.comm_f_assoc, HomologicalComplex.cylinder.inrX_π, CategoryTheory.MonoidalCategory.MonoidalLeftAction.tensor_actionHomRight_assoc, CategoryTheory.Bicategory.whisker_assoc_assoc, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.δ_toBiprod_assoc, CategoryTheory.GradedObject.ι_mapBifunctor₁₂BifunctorDesc_assoc, HomologicalComplex.d_comp_XIsoOfEq_inv_assoc, CategoryTheory.Preadditive.add_comp, CategoryTheory.Limits.PreservesPullback.iso_hom_snd_assoc, CategoryTheory.Abelian.PreservesCoimage.iso_inv_π, CategoryTheory.Subfunctor.Subpresheaf.homOfLe_ι, CategoryTheory.CommSq.LiftStruct.fac_right, SimplicialObject.Splitting.cofan_inj_comp_app, AlgebraicGeometry.AffineSpace.SpecIso_inv_over_assoc, CategoryTheory.Functor.lanUnit_app_whiskerLeft_lanAdjunction_counit_app_assoc, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_three, TopCat.range_pullback_to_prod, HomologicalComplex.mapBifunctor₂₃.ι_eq, CategoryTheory.NatTrans.whiskerLeft_app_tensor_app, CategoryTheory.Limits.prodComparison_snd, CategoryTheory.Limits.limitOpIsoOpColimit_inv_comp_π_assoc, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₂_assoc, CategoryTheory.DifferentialObject.eqToHom_f', CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_hom_π_π_assoc, CategoryTheory.MorphismProperty.Comma.Hom.comp_left, CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_inv_assoc, CategoryTheory.Subobject.ofLEMk_comp_ofMkLEMk_assoc, CategoryTheory.comp_app, CategoryTheory.Limits.imageSubobject_comp_le, CategoryTheory.GrpObj.comp_div, TopCat.Sheaf.interUnionPullbackConeLift_left, AlgebraicTopology.NormalizedMooreComplex.d_squared, CategoryTheory.Limits.Sigma.map'_comp_map, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality_assoc, CategoryTheory.PreZeroHypercover.inv_inv_h₀_comp_f_assoc, groupHomology.cyclesMap_comp_cyclesIso₀_hom, CategoryTheory.Functor.relativelyRepresentable.w_assoc, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_counitIso, HomologicalComplex₂.totalFlipIso_hom_f_D₁_assoc, CategoryTheory.Limits.kernelSubobject_factors_iff, Homotopy.comp_nullHomotopicMap', CategoryTheory.Preadditive.add_comp_assoc, CategoryTheory.CostructuredArrow.comp_left, AlgebraicGeometry.Scheme.stalkMap_hom_inv, CategoryTheory.DifferentialObject.Hom.comp_f, CategoryTheory.MonObj.one_braiding, CategoryTheory.CartesianMonoidalCategory.whiskerRight_toUnit_comp_leftUnitor_hom, CategoryTheory.Functor.rightDerivedNatTrans_app, CategoryTheory.GradedObject.single_map_singleObjApplyIsoOfEq_hom, CategoryTheory.NatTrans.tensor_naturality_assoc, CategoryTheory.Functor.mapCommGrp_id_one, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_fst_assoc, PresheafOfModules.colimitPresheafOfModules_map, CategoryTheory.ShortComplex.opcyclesOpIso_inv_naturality, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_assoc, groupCohomology.cochainsMap_f, CategoryTheory.MonoidalCategory.pentagon_inv_assoc, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s₀_comp_δ₁, AlgebraicGeometry.Scheme.monObjAsOverPullback_mul, HomologicalComplex.XIsoOfEq_inv_comp_d, CategoryTheory.Iso.map_inv_hom_id_assoc, CategoryTheory.ProjectiveResolution.complex_d_succ_comp, CategoryTheory.Prod.fac, CategoryTheory.MorphismProperty.isLocal_iff, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app_assoc, CategoryTheory.CartesianMonoidalCategory.lift_braiding_hom_assoc, CategoryTheory.Bicategory.associator_eqToHom_hom, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality, CategoryTheory.Mon_Class.comp_pow, Alexandrov.lowerCone_π_app, CategoryTheory.ShortComplex.SnakeInput.φ₁_L₂_f, CategoryTheory.ObjectProperty.isoHom_inv_id_hom_assoc, CategoryTheory.SimplicialObject.δ_comp_σ_of_le, AlgebraicTopology.DoldKan.Γ₀.map_app, CategoryTheory.Limits.Cofan.IsColimit.inj_desc_assoc, CategoryTheory.Bicategory.whisker_assoc_symm, CategoryTheory.extendCofan_ι_app, CategoryTheory.Join.mapWhisker_exchange, CategoryTheory.Limits.ι_comp_colimitRightOpIsoUnopLimit_hom, CategoryTheory.IsComonHom.hom_counit_assoc, CategoryTheory.Mod_.comp_hom', CategoryTheory.Localization.Monoidal.associator_naturality_assoc, Homotopy.dNext_succ_chainComplex, CategoryTheory.Lax.StrongTrans.naturality_naturality_assoc, CategoryTheory.ShortComplex.homologyMap_comp, HomologicalComplex.XIsoOfEq_inv_comp_d_assoc, CategoryTheory.MonObj.Mon_tensor_mul_assoc, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π, CategoryTheory.Localization.SmallShiftedHom.equiv_shift, CategoryTheory.Functor.OplaxMonoidal.left_unitality_hom, CategoryTheory.Functor.LaxLeftLinear.μₗ_associativity, CategoryTheory.TransportEnrichment.eComp_eq, CategoryTheory.Functor.shiftIso_hom_naturality_assoc, TopologicalSpace.Opens.map_comp_eq, CategoryTheory.GlueData.cocycle_assoc, CategoryTheory.Bicategory.Prod.sectL_mapComp_inv, HomotopicalAlgebra.Cylinder.symm_i, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac', CategoryTheory.ShiftMkCore.add_zero_inv_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_obj, HomotopicalAlgebra.Cylinder.trans_i₀, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_comp, CategoryTheory.Limits.equalizerSubobject_factors_iff, CategoryTheory.Limits.Fork.condition, CategoryTheory.Functor.sectionsEquivHom_naturality_symm, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id_assoc, CategoryTheory.IsHomLift.lift_eqToHom_comp, CategoryTheory.HasShift.Induced.zero_hom_app_obj, groupHomology.chainsMap_comp, TopCat.Presheaf.stalkSpecializes_stalkFunctor_map, CategoryTheory.Functor.IsEventuallyConstantFrom.coconeιApp_eq, AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv_assoc, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_two_assoc, CategoryTheory.IsPushout.inl_isoPushout_inv, CategoryTheory.Equalizer.Presieve.w, CategoryTheory.Limits.imageSubobject_arrow, CategoryTheory.Functor.Monoidal.tensorHom_app_fst, CategoryTheory.MorphismProperty.Under.w, HomologicalComplex₂.XXIsoOfEq_inv_ιTotal, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_assoc, groupHomology.d₂₁_comp_d₁₀, CategoryTheory.InjectiveResolution.Hom.ι_f_zero_comp_hom_f_zero, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.δ_toBiprod, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_comp_assoc, CategoryTheory.StructuredArrow.mapIso_functor_map_left, CategoryTheory.Limits.imageSubobject_comp_le_epi_of_epi, CategoryTheory.Limits.Types.productIso_hom_comp_eval, CategoryTheory.eComp_eHomWhiskerRight_assoc, CategoryTheory.Bicategory.id_whiskerLeft_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.rightUnitor_actionHom_assoc, CategoryTheory.ShortComplex.exact_iff_exact_up_to_refinements, CategoryTheory.ShortComplex.LeftHomologyData.wπ, CategoryTheory.Abelian.coimage.fac, CategoryTheory.ShortComplex.LeftHomologyData.π_comp_homologyIso_inv_assoc, HomologicalComplex.cylinder.πCompι₀Homotopy.inrX_nullHomotopy_f, HomologicalComplex.homologyπ_singleObjHomologySelfIso_hom, SSet.Truncated.comp_app_assoc, SSet.Subcomplex.homOfLE_comp, AlgebraicGeometry.Scheme.Hom.comp_preimage, CategoryTheory.CatEnriched.hComp_assoc_heq, CategoryTheory.Bicategory.LeftLift.IsKan.fac, HomologicalComplex.iCyclesIso_hom_inv_id, CategoryTheory.liftedLimitMapsToOriginal_inv_map_π, SheafOfModules.ιFree_mapFree_inv, CategoryTheory.Bimon.ofMon_Comon_toMon_Comon_obj_counit, CategoryTheory.Projective.factors, CategoryTheory.Adjunction.CoreUnitCounit.right_triangle, CategoryTheory.Iso.hom_inv_id_triangle_hom₁, CategoryTheory.EnrichedFunctor.map_comp_assoc, CategoryTheory.Comonad.Coalgebra.Hom.h_assoc, CategoryTheory.Adjunction.shift_unit_app, CategoryTheory.Limits.inl_inl_pushoutAssoc_hom, CategoryTheory.IsCofiltered.cospan, CategoryTheory.Limits.biprod.inr_map, CategoryTheory.Abelian.OfCoimageImageComparisonIsIso.imageMonoFactorisation_e', ModuleCat.kernelIsoKer_hom_ker_subtype, CategoryTheory.Functor.mapHomotopyEquiv_homotopyInvHomId, CategoryTheory.Adjunction.map_η_comp_η_assoc, AlgebraicGeometry.Scheme.Hom.naturality_assoc, CategoryTheory.Functor.PushoutObjObj.inl_ι_assoc, CategoryTheory.Limits.coconeOfIsSplitEpi_π, CategoryTheory.Bicategory.Lan.CommuteWith.commute, SheafOfModules.Presentation.mapRelations_mapGenerators, AlgebraicGeometry.IsZariskiLocalAtSource.iff_of_openCover, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app_assoc, HomologicalComplex₂.total.map_comp, CategoryTheory.ChosenPullbacksAlong.pullbackId_hom_counit_assoc, HomologicalComplex.cyclesOpIso_hom_naturality, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_hom_inv'_assoc, CategoryTheory.Comonad.Coalgebra.coassoc_assoc, groupHomology.chainsMap_f_3_comp_chainsIso₃_assoc, CategoryTheory.SmallObject.SuccStruct.prop.fac_assoc, CategoryTheory.Bicategory.InducedBicategory.forget_mapComp_inv, CategoryTheory.Adjunction.unit_app_commShiftIso_hom_app_assoc, AlgebraicGeometry.AffineSpace.reindex_comp_assoc, CochainComplex.mappingConeCompHomotopyEquiv_comm₂, AlgebraicGeometry.Scheme.Hom.iInf_ker_openCover_map_comp_apply, HomotopicalAlgebra.CofibrantObject.HoCat.exists_resolution_map, CategoryTheory.Abelian.PreservesImage.iso_hom_ι_assoc, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_hom_assoc, CategoryTheory.Functor.OplaxLeftLinear.δₗ_unitality_hom, CategoryTheory.Endofunctor.Algebra.comp_f, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₂₃_assoc, HomotopicalAlgebra.PrepathObject.symm_p_assoc, CategoryTheory.Monad.algebraEquivOfIsoMonads_counitIso, CategoryTheory.Subobject.imageFactorisation_F_I, CategoryTheory.Limits.pullbackDiagonalMapIdIso_hom_fst_assoc, HomotopicalAlgebra.CofibrantObject.HoCat.resolutionMap_fac, SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero_assoc, CategoryTheory.GrpObj.comp_zpow_assoc, CategoryTheory.Subobject.factors_of_factors_right, CategoryTheory.Bicategory.toNatTrans_mateEquiv, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac'_assoc, CategoryTheory.CartesianMonoidalCategory.lift_snd, CategoryTheory.SimplicialObject.δ_comp_σ_self, CategoryTheory.CostructuredArrow.homMk'_mk_comp, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_hom_fac, CategoryTheory.IsHomLift.isoOfIsoLift_hom_inv_id, CategoryTheory.OplaxFunctor.map₂_rightUnitor, prodIsoPullback_hom_snd_assoc, FGModuleCat.hom_hom_comp, CategoryTheory.Over.associator_inv_left_fst_fst, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app_assoc, CategoryTheory.Functor.Final.exists_coeq, CategoryTheory.uliftYoneda_map_app, AlgebraicGeometry.Scheme.Hom.normalizationCoprodIso_inv_coprodDesc_fromNormalization, CategoryTheory.Limits.Cones.postcomposeComp_inv_app_hom, CategoryTheory.MonoidalCategory.comp_whiskerRight_assoc, CategoryTheory.Functor.IsEventuallyConstantTo.isoMap_hom_inv_id, CategoryTheory.ShortComplex.RightHomologyData.ι_g'_assoc, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_obj_hom_app, CategoryTheory.Comma.mapLeftIso_inverse_obj_hom, AlgebraicGeometry.pullbackSpecIso_inv_snd_assoc, CategoryTheory.ShortComplex.abelianImageToKernel_comp_kernel_ι_assoc, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop, CategoryTheory.tensorHom_eComp_op_eq_assoc, AlgebraicGeometry.Scheme.Cover.pushforwardIso_f, CategoryTheory.SimplicialThickening.SimplicialCategory.assoc, CategoryTheory.Functor.Monoidal.whiskerLeft_app_snd, CategoryTheory.Limits.prod.map_fst_assoc, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_assoc, CategoryTheory.OrthogonalReflection.D₁.ιLeft_comp_t_assoc, CategoryTheory.Limits.Sigma.ι_isoColimit_hom, CategoryTheory.Limits.opProdIsoCoprod_hom_fst, SSet.Subcomplex.topIso_inv_ι_assoc, CategoryTheory.Limits.map_π_preserves_coequalizer_inv_assoc, CategoryTheory.StructuredArrow.comp_right, CategoryTheory.NatTrans.naturality_1_assoc, HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac_assoc, HomologicalComplex.mapBifunctor₁₂.ι_D₃, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_leftUnitor_assoc, CategoryTheory.Pretriangulated.TriangleMorphism.comm₃_assoc, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_hom_fac, CategoryTheory.IsCommMonObj.mul_comm'_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app, HomotopicalAlgebra.Precylinder.inl_i_assoc, CochainComplex.HomComplex.δ_zero_cochain_v, CommSemiRingCat.comp_apply, CommGrpCat.comp_apply, CategoryTheory.Limits.ColimitPresentation.Total.Hom.comp_hom, CategoryTheory.Functor.Monoidal.μ_comp, CochainComplex.HomComplex.Cochain.δ_toSingleMk, CategoryTheory.Limits.Pi.whiskerEquiv_hom, CompHausLike.pullback.condition_assoc, groupCohomology.map_id_comp_assoc, ModuleCat.ι_coprodIsoDirectSum_hom, CategoryTheory.Limits.coend.map_comp, CategoryTheory.StrictlyUnitaryLaxFunctorCore.mapComp_naturality_left, CategoryTheory.unit_mateEquiv_symm, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_comp_ι_assoc, CategoryTheory.Limits.inr_inr_pushoutRightPushoutInlIso_hom_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁'_obj_map_app, CategoryTheory.Cat.associator_inv_toNatTrans, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_left_assoc, CategoryTheory.Abelian.coimage_image_factorisation_assoc, SemiNormedGrp.explicitCokernelIso_hom_π, AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff, AlgebraicGeometry.IsProper.comp_iff, CategoryTheory.Iso.homToEquiv_apply, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd, CategoryTheory.SimplicialObject.δ_comp_σ_of_gt_assoc, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp, CategoryTheory.Functor.Monoidal.whiskerRight_μ_δ, CategoryTheory.ShortComplex.opcyclesIsoX₂_inv_hom_id, CategoryTheory.IsCofiltered.eq_condition_assoc, CategoryTheory.Limits.Trident.ofCone_π, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop_assoc, CategoryTheory.Limits.ImageMap.map_ι, CategoryTheory.SmallObject.functorMap_comm, CategoryTheory.Functor.curryingEquiv_apply_map, CategoryTheory.Presieve.FamilyOfElements.compPresheafMap_comp, CategoryTheory.Bifunctor.diagonal, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₂, CompHausLike.pullback.cone_π, CategoryTheory.Bicategory.Adj.whiskerRight_τl, CategoryTheory.Limits.Cocone.w, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv, Mathlib.Tactic.Bicategory.naturality_id, CategoryTheory.Limits.pushoutIsoOpPullback_inr_hom, CategoryTheory.Cat.leftUnitor_inv_toNatTrans, CategoryTheory.GradedObject.Monoidal.ι_tensorObjDesc, CategoryTheory.Limits.PreservesEqualizer.iso_inv_ι, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_fst_assoc, CategoryTheory.Functor.initial_iff_of_isCofiltered, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_naturality_assoc, CategoryTheory.Grp.comp_hom_hom, CategoryTheory.Adjunction.Triple.epi_rightToLeft_app_iff, CategoryTheory.Pseudofunctor.map₂_left_unitor_app, CategoryTheory.ShortComplex.f'_cyclesMap', CategoryTheory.LocalizerMorphism.RightResolution.Hom.comm, HomologicalComplex.mapBifunctorAssociatorX_hom_D₁, CategoryTheory.Functor.LaxMonoidal.tensorUnit_whiskerLeft_comp_leftUnitor_hom_assoc, CategoryTheory.Limits.biproduct.matrix_π, CategoryTheory.Presheaf.isLocallyInjective_comp_iff, CategoryTheory.Limits.biproduct.total, CategoryTheory.Limits.prodComparison_natural_of_natTrans, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ_assoc, CategoryTheory.Bicategory.associator_inv_naturality_right_assoc, CategoryTheory.Adjunction.rightAdjointUniq_hom_counit, CategoryTheory.ShortComplex.LeftHomologyData.homologyIso_hom_comp_leftHomologyIso_inv_assoc, CategoryTheory.Functor.map_comp_assoc, groupHomology.chainsMap_f_0_comp_chainsIso₀_assoc, AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap, CategoryTheory.ShortComplex.SnakeInput.L₀X₂ToP_comp_φ₁_assoc, CategoryTheory.Limits.cokernelEpiComp_inv, AlgebraicGeometry.Scheme.Spec_map_stalkSpecializes_fromSpecStalk_assoc, CategoryTheory.Equivalence.cancel_unit_right_assoc', CategoryTheory.Iso.hom_inv_id_triangle_hom₃, AlgebraicTopology.DoldKan.MorphComponents.preComp_φ, CategoryTheory.GrpObj.zpow_comp, AlgebraicGeometry.morphismRestrict_appTop, CategoryTheory.Functor.commShiftOfLocalization.iso_hom_app, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_self_assoc, CategoryTheory.Comonad.delta_naturality, AlgebraicGeometry.AffineTargetMorphismProperty.cancel_right_of_respectsIso, CategoryTheory.MonObj.mul_mul_mul_comm', CategoryTheory.CartesianMonoidalCategory.lift_snd_assoc, CategoryTheory.Functor.fun_inv_map, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π, Bimod.one_actLeft, CategoryTheory.GlueData'.cocycle_assoc, CategoryTheory.Iso.isoCompInverse_inv_app, CategoryTheory.LocalizerMorphism.LeftResolution.comp_f, CategoryTheory.NatTrans.app_shift_assoc, CochainComplex.HomComplex.Cochain.fromSingleMk_precomp, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality, CategoryTheory.Bicategory.hom_inv_whiskerRight_assoc, CategoryTheory.MonObj.pow_comp_assoc, CategoryTheory.Presieve.IsSheafFor.functorInclusion_comp_extend, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_app_assoc, CategoryTheory.Bicategory.triangle, CategoryTheory.HopfObj.mul_antipode₁, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_unitIso, CompHausLike.const_comp, CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_inv, CategoryTheory.Pseudofunctor.StrongTrans.leftUnitor_hom_as_app, CategoryTheory.MonoidalCategory.associator_naturality, CategoryTheory.Limits.limit.conePointUniqueUpToIso_hom_comp, AlgebraicTopology.DoldKan.Q_f_naturality_assoc, HomologicalComplex.mapBifunctor₂₃.ι_D₁_assoc, CategoryTheory.Limits.pullbackObjIso_hom_comp_fst_assoc, CategoryTheory.Limits.Pi.ι_π_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_inv_hom', CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_limit_map, CategoryTheory.Triangulated.SpectralObject.triangle_mor₁, CategoryTheory.Limits.ι_comp_coequalizerComparison_assoc, TopCat.Presheaf.stalkPushforward_germ, CategoryTheory.Arrow.inv_hom_id_left_assoc, CategoryTheory.Limits.prod.associator_inv, CategoryTheory.ε_app_obj, CategoryTheory.ShortComplex.ShortExact.δ_comp_assoc, CategoryTheory.Functor.toSheafify_pullbackSheafificationCompatibility, HomologicalComplex.singleObjCyclesSelfIso_inv_iCycles_assoc, groupHomology.inhomogeneousChains.ext_iff, CategoryTheory.Over.tensorHom_left_fst, CategoryTheory.Sheaf.ΓHomEquiv_naturality_right_symm, AlgebraicGeometry.SheafedSpace.comp_hom_c_app', CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_right_assoc, CategoryTheory.MonoidalCategory.whisker_assoc_symm_assoc, CategoryTheory.Limits.biprod.inr_desc_assoc, Homotopy.compLeftId_hom, CategoryTheory.Iso.hom_inv_id_app_assoc, SimplicialObject.opFunctorCompOpFunctorIso_hom_app_app, CategoryTheory.Equivalence.induced_unitIso, CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_snd, Bimod.TensorBimod.left_assoc', CategoryTheory.Limits.limit_map_limitObjIsoLimitCompEvaluation_hom_assoc, CategoryTheory.CatEnrichedOrdinary.Hom.comp_eq, SSet.range_eq_iSup_sigma_ι, CategoryTheory.GlueData'.cocycle, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapId_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.whiskerLeft_actionHomLeft, HomologicalComplex.singleObjOpcyclesSelfIso_hom_naturality_assoc, CategoryTheory.CosimplicialObject.δ_comp_σ_succ, AlgebraicGeometry.ΓSpecIso_hom_stalkClosedPointIso_inv, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_assoc, CategoryTheory.IsPullback.paste_vert, CategoryTheory.Over.whiskerRight_left_snd, germ_skyscraperPresheafStalkOfSpecializes_hom_assoc, CategoryTheory.NatTrans.rightOpWhiskerRight_assoc, CategoryTheory.CartesianMonoidalCategory.braiding_hom_fst_assoc, CategoryTheory.Iso.isoInverseOfIsoFunctor_inv_app, CategoryTheory.SmallObject.SuccStruct.ofCocone_map_to_top, CategoryTheory.Limits.CatCospanTransform.id_whiskerLeft_assoc, SSet.Subcomplex.range_comp, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃_eq, CategoryTheory.DifferentialObject.shiftFunctor_map_f, CategoryTheory.Dial.comp_F, CategoryTheory.Square.Hom.comp_τ₄, CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id_app, CategoryTheory.congrArg_mpr_hom_left, AlgebraicGeometry.Scheme.descResidueField_stalkClosedPointTo_fromSpecResidueField, CategoryTheory.GrpObj.eq_lift_inv_right, CategoryTheory.Functor.shiftIso_hom_app_comp_assoc, CategoryTheory.Limits.biprod.add_eq_lift_desc_id, CategoryTheory.strongEpi_comp, CategoryTheory.ShortComplex.Splitting.g_s_assoc, CategoryTheory.Functor.LaxLeftLinear.μₗ_naturality_left, CategoryTheory.Limits.biprod.inl_desc, CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_hom_π_π, SSet.stdSimplex.objEquiv_symm_comp, CategoryTheory.SimplicialObject.Augmented.w₀_assoc, CategoryTheory.Limits.Multiequalizer.ιPi_π, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃_assoc, CategoryTheory.StrictPseudofunctorPreCore.map₂_whisker_right, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj_condition, AlgebraicGeometry.IsOpenImmersion.isoOfRangeEq_hom_fac, CategoryTheory.Adjunction.Triple.leftToRight_app_map_adj₁_unit_app_assoc, CategoryTheory.Limits.coprod.map_codiag_assoc, CategoryTheory.ChosenPullbacksAlong.pullbackComp_hom_counit, TopCat.Presheaf.germ_stalkPullbackHom_assoc, CategoryTheory.Equivalence.inv_fun_map_assoc, CategoryTheory.Limits.inl_inr_pushoutAssoc_inv, CategoryTheory.PresheafOfGroups.OneCochain.ev_precomp, CategoryTheory.ShortComplex.Splitting.f_r_assoc, CategoryTheory.ShortComplex.homologyπ_comp_leftHomologyIso_inv_assoc, CategoryTheory.Limits.pullbackComparison_comp_snd_assoc, CategoryTheory.Functor.biprodComparison_snd, CategoryTheory.Limits.CatCospanTransform.pentagon, CategoryTheory.comp_apply, CategoryTheory.Subobject.factorThru_ofLE, AlgebraicGeometry.coprodSpec_inr_assoc, CategoryTheory.Equivalence.inverse_counitInv_comp_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd_assoc, ModuleCat.ihom_map_apply, CategoryTheory.MonObj.mul_mul_mul_comm_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd, CategoryTheory.FreeBicategory.normalize_naturality, HomologicalComplex.d_comp_XIsoOfEq_hom_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom, FintypeCat.comp_hom_assoc, CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_inv, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocIso_hom_naturality_assoc, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_hom, CategoryTheory.Limits.biproduct.lift_map_assoc, CategoryTheory.Limits.pullbackDiagonalMapIso.inv_fst, SheafOfModules.sectionsMap_comp, CategoryTheory.Sheaf.ΓObjEquivHom_naturality, CategoryTheory.obj_μ_inv_app, AlgebraicGeometry.IsClosedImmersion.Spec_iff, CategoryTheory.Limits.Cocones.extendComp_inv_hom, CategoryTheory.Limits.sigmaSigmaIso_inv, CategoryTheory.HomOrthogonal.matrixDecomposition_apply, HomologicalComplex.pOpcycles_extendOpcyclesIso_hom_assoc, CategoryTheory.Limits.colimit.ι_desc, CategoryTheory.End.smul_right, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_left_symm, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app, AlgebraicGeometry.Scheme.Hom.comp_toLRSHom, CategoryTheory.Limits.end_.map_comp, CategoryTheory.Functor.OplaxMonoidal.associativity_inv, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_σ_assoc, CategoryTheory.Sheaf.ΓRes_map, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_self, CategoryTheory.Bicategory.id_whiskerRight, CategoryTheory.NatTrans.leftDerived_comp_assoc, SimplexCategory.δ_comp_δ_self_assoc, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv, CategoryTheory.Functor.mapCommMon_obj_mon_one, CategoryTheory.Functor.Monoidal.μ_fst, CategoryTheory.Limits.biproduct.whiskerEquiv_hom, CategoryTheory.NatTrans.CommShift₂.instCompFunctor, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_inv_fac, HomologicalComplex.homotopyCofiber.inlX_d'_assoc, CochainComplex.mappingCone.inr_f_fst_v_assoc, CategoryTheory.NatTrans.tensor_naturality, CategoryTheory.Limits.biproduct.matrix_desc, CategoryTheory.Functor.CommShift.ofIso_commShiftIso_inv_app, groupHomology.π_map_assoc, CategoryTheory.Limits.Cofork.IsColimit.homIso_natural, CategoryTheory.LocalizerMorphism.homMap_comp_assoc, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_π_assoc, CategoryTheory.Lax.StrongTrans.naturality_id_assoc, groupCohomology.mapCocycles₁_comp_i_assoc, CategoryTheory.Limits.prod.inl_fst_assoc, CategoryTheory.InjectiveResolution.ι'_f_zero_assoc, CategoryTheory.ShortComplex.homologyOpIso_inv_naturality_assoc, CategoryTheory.Limits.pullbackAssoc_hom_snd_snd_assoc, CategoryTheory.CatCenter.mul_app'_assoc, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit_assoc, HomologicalComplex₂.totalFlipIsoX_hom_D₁, Rep.applyAsHom_comm, CategoryTheory.Functor.Fiber.homMk_comp, CategoryTheory.CatCommSq.vInv_iso_inv_app, CategoryTheory.CartesianMonoidalCategory.braiding_inv_fst, CochainComplex.mappingCone.inl_v_d_assoc, CategoryTheory.regularTopology.equalizerCondition_w', CategoryTheory.MarkovCategory.discard_natural_assoc, AlgebraicGeometry.Scheme.Pullback.openCoverOfBase'_f, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_naturality₂, Bimod.whisker_assoc_bimod, CategoryTheory.Limits.ι_colimitOfIsReflexivePairIsoCoequalizer_hom, CategoryTheory.Limits.Multicofork.fst_app_right, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse_assoc, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_cofanPtIsoSelf_inv, SSet.ι₀_comp_assoc, AlgebraicGeometry.pullbackSpecIso_inv_fst_assoc, CategoryTheory.ShortComplex.LeftHomologyData.ofAbelian_π, AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_naturality_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_comp, SimplicialObject.Splitting.PInfty_comp_πSummand_id_assoc, CategoryTheory.IsIso.eq_comp_inv, HomologicalComplex.inr_biprodXIso_inv_assoc, AlgebraicGeometry.Scheme.Pullback.ofPointTensor_SpecTensorTo, HomologicalComplex.truncLE'_d_eq, ChainComplex.mk'_d, PresheafOfModules.Hom.naturality_assoc, CategoryTheory.Localization.Monoidal.whiskerRight_comp_assoc, CategoryTheory.Functor.LaxRightLinear.μᵣ_unitality, CategoryTheory.Limits.Fork.op_ι_app, CategoryTheory.Limits.biproduct.matrix_π_assoc, HomologicalComplex.pOpcycles_extendOpcyclesIso_inv, CategoryTheory.Functor.LaxMonoidal.μ_whiskerRight_comp_μ_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.associator_inv_comp_tensorHom_tensorHom_comp_assoc, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counitIso_hom_app_assoc, CategoryTheory.IsFiltered.crown₃, CategoryTheory.ShortComplex.mapCyclesIso_hom_naturality_assoc, CategoryTheory.ι_preservesColimitIso_hom, CategoryTheory.ShortComplex.rightHomologyMap_op, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id_assoc, HomologicalComplex.truncLE'ToRestriction_naturality_assoc, AlgebraicGeometry.Scheme.LocalRepresentability.yoneda_toGlued_yonedaGluedToSheaf, CategoryTheory.Limits.pullbackLeftPullbackSndIso_hom_snd, CategoryTheory.Functor.Monoidal.tensorHom_app_snd, CategoryTheory.Bicategory.iterated_mateEquiv_conjugateEquiv_symm, CategoryTheory.conjugateEquiv_comp_assoc, HomologicalComplex.dgoToHomologicalComplex_map_f, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.iso_hom_naturality_assoc, CompHaus.lift_lifts_assoc, groupHomology.eq_d₃₂_comp_inv_assoc, CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_hom_assoc, CategoryTheory.algebraToUnder_obj, CategoryTheory.Limits.biproduct.π_comp_eqToHom_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.inv_hom_actionHomLeft'_assoc, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_incl, CategoryTheory.Limits.Types.binaryProductIso_inv_comp_snd, CategoryTheory.MonoidalClosed.curry_natural_left_assoc, CategoryTheory.associativity_app_assoc, CategoryTheory.Bicategory.Adj.rightUnitor_inv_τr, CategoryTheory.Oplax.OplaxTrans.naturality_id, CategoryTheory.Limits.equalizerSubobject_arrow, CategoryTheory.Limits.coprod.inr_map_assoc, CategoryTheory.Limits.ColimitPresentation.Total.Hom.w_assoc, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv_desc, CategoryTheory.TwoSquare.whiskerLeft_app, CategoryTheory.CatCenter.smul_iso_hom_eq_assoc, CategoryTheory.Limits.pullbackZeroZeroIso_hom_fst, CategoryTheory.Limits.Types.binaryProductIso_hom_comp_fst, CategoryTheory.Idempotents.KaroubiKaroubi.idem_f, CategoryTheory.IsUniversalColimit.isPullback_of_isColimit_right, CategoryTheory.Bicategory.rightUnitor_comp, CategoryTheory.Bicategory.whiskerRight_id_symm, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_naturality, CategoryTheory.CatEnriched.comp_eq, CategoryTheory.Iso.cancel_iso_hom_left, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_fst, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_app, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_assoc, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_hom_inv, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_inv_comp_π, CategoryTheory.sheafifyMap_comp, CategoryTheory.Groupoid.vertexGroupIsomOfMap_symm_apply, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f, AlgebraicGeometry.SheafedSpace.comp_hom_base, CategoryTheory.CartesianClosed.uncurry_natural_right_assoc, HomologicalComplex.ι_mapBifunctorDesc_assoc, CategoryTheory.Limits.map_lift_piComparison_assoc, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_assoc, CategoryTheory.GrpObj.left_inv, HomologicalComplex.homology_π_ι_assoc, CategoryTheory.OplaxFunctor.mapComp_id_right, CategoryTheory.CosimplicialObject.σ_comp_σ, CategoryTheory.Equivalence.map_η_comp_η_assoc, CategoryTheory.Limits.pullback.comp_diagonal, CategoryTheory.Functor.OplaxMonoidal.δ_fst, AddGrpCat.ofHom_comp, CategoryTheory.Limits.hasEqualizer_precomp_of_equalizer, CategoryTheory.eComp_eHomWhiskerLeft, CategoryTheory.Limits.imageSubobject_arrow_comp_assoc, CategoryTheory.braiding_rightUnitor_aux₂, CategoryTheory.SymmetricCategory.symmetry, CategoryTheory.shiftZero', CategoryTheory.Limits.coend.ι_map, CategoryTheory.ShortComplex.LeftHomologyData.f'_i_assoc, CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_hom, AlgebraicGeometry.Scheme.Opens.isoOfLE_inv_ι, CategoryTheory.SmallObject.functorMapSrc_functorObjTop_assoc, CategoryTheory.Bicategory.triangle_assoc_comp_right, CategoryTheory.Limits.prod.map_map_assoc, CategoryTheory.GrothendieckTopology.sheafifyMap_comp, AlgebraicGeometry.Scheme.Hom.ι_toNormalization_assoc, CategoryTheory.Monoidal.InducingFunctorData.whiskerRight_eq, HomotopicalAlgebra.RightHomotopyRel.postcomp, CategoryTheory.Limits.FormalCoproduct.mapPower_comp, CategoryTheory.Limits.Pi.map_eq_prod_map, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.fac_assoc, CategoryTheory.Limits.ι_comp_sigmaObjIso_hom_assoc, CategoryTheory.Cat.Hom.toNatIso_leftUnitor, CategoryTheory.Mat_.ι_additiveObjIsoBiproduct_inv, CategoryTheory.Bicategory.comp_whiskerLeft_assoc, CategoryTheory.ShortComplex.rightHomologyMap'_comp, AlgebraicGeometry.Scheme.Hom.Spec_map_residueFieldMap_fromSpecResidueField_assoc, CategoryTheory.Bicategory.InducedBicategory.forget_mapComp_hom, CategoryTheory.Bimon.mul_counit, CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_hom, CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ, CategoryTheory.ParametrizedAdjunction.unit_whiskerRight_map_assoc, CategoryTheory.MonoidalCategory.tensor_whiskerLeft_assoc, CategoryTheory.Presieve.bind_comp, CategoryTheory.SimplicialObject.δ_naturality_assoc, CategoryTheory.MonoidalCategory.rightUnitor_naturality_assoc, CategoryTheory.Pseudofunctor.mapComp_id_right_inv, SimplexCategory.Truncated.δ₂_two_comp_σ₂_zero, groupCohomology.π_comp_H2Iso_hom_assoc, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inl, CategoryTheory.Bicategory.LeftLift.whisker_lift, SSet.ι₀_comp, CategoryTheory.ModObj.assoc_flip, CategoryTheory.Limits.colimit.post_post, CategoryTheory.Bicategory.whiskerLeft_inv_hom_assoc, CategoryTheory.Over.tensorHom_left_fst_assoc, CategoryTheory.MonoidalCategory.DayFunctor.comp_natTrans, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd_assoc, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_app_assoc, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc, TopCat.Presheaf.germ_stalkPullbackInv, CategoryTheory.Limits.Sigma.ι_map_assoc, CategoryTheory.Monad.algebraFunctorOfMonadHom_obj_a, CategoryTheory.CartesianMonoidalCategory.rightUnitor_inv_snd, HomotopicalAlgebra.FibrantObject.homMk_homMk_assoc, Action.Hom.comm_assoc, CategoryTheory.Join.mapWhiskerRight_whiskerLeft, AlgebraicTopology.DoldKan.Q_succ, CategoryTheory.forgetAdjToOver.homEquiv_symm, CategoryTheory.Functor.map_inv_hom_assoc, CategoryTheory.Bicategory.associatorNatIsoMiddle_hom_app, CategoryTheory.Limits.MultispanIndex.inj_sndSigmaMapOfIsColimit_assoc, CategoryTheory.Localization.Monoidal.associator_naturality₂_assoc, CategoryTheory.tensorHom_eComp_op_eq, CategoryTheory.preservesLimitIso_hom_π_assoc, CategoryTheory.Limits.Types.binaryProductIso_hom_comp_snd, CategoryTheory.ShortComplex.leftRightHomologyComparison'_eq_liftH, AlgebraicGeometry.Flat.comp, AlgebraicGeometry.Scheme.Cover.Hom.sigma_h₀, Rep.standardComplex.d_comp_ε, CategoryTheory.Limits.CatCospanTransform.category_comp_base, groupCohomology.toCocycles_comp_isoCocycles₂_hom_assoc, prodIsoPullback_hom_fst, HomologicalComplex.single_map_f_self, AlgebraicGeometry.Scheme.Hom.fromNormalization_app_assoc, CategoryTheory.IsHomLift.comp_lift_id_left, CategoryTheory.Dial.isoMk_inv_F, AlgebraicGeometry.Scheme.isoSpec_inv_toSpecΓ_assoc, CategoryTheory.IsCardinalFiltered.wideSpan, CategoryTheory.ShortComplex.toCycles_naturality_assoc, AlgebraicGeometry.Proj.fromOfGlobalSections_morphismRestrict, CategoryTheory.MorphismProperty.LeftFraction.map_ofInv_hom_id_assoc, CategoryTheory.ChosenPullbacksAlong.condition, HomologicalComplex.homologyπ_extendHomologyIso_hom_assoc, CategoryTheory.CatCommSq.hComp_iso_inv_app, CategoryTheory.Pseudofunctor.map₂_whisker_right_app_assoc, ContinuousMap.piComparison_fac, CategoryTheory.Functor.isLeftKanExtension_iff_postcomp₁, CategoryTheory.InjectiveResolution.Hom.ι'_comp_hom'_assoc, AlgebraicGeometry.Scheme.Hom.isoImage_inv_ι, CategoryTheory.ShortComplex.Hom.comm₂₃, CategoryTheory.HopfObj.antipode_right_assoc, CategoryTheory.Subfunctor.equalizer.condition, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_π_app, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp, CategoryTheory.ShortComplex.SnakeInput.comp_f₁_assoc, AlgebraicGeometry.AffineSpace.map_comp_assoc, CategoryTheory.shiftFunctorAdd_add_zero_inv_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_hom_inv', CategoryTheory.Bicategory.mateEquiv_square, CategoryTheory.Dial.associator_inv_F, CategoryTheory.Idempotents.Karoubi.p_comp_assoc, HomotopicalAlgebra.BifibrantObject.homMk_homMk, CategoryTheory.SimplicialObject.δ_comp_σ_succ, CategoryTheory.Presieve.BindStruct.fac_assoc, CategoryTheory.Adjunction.leftAdjointUniq_hom_counit_assoc, PresheafOfModules.comp_toPresheaf_map_sheafifyHomEquiv'_symm_hom, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃_assoc, CategoryTheory.extendFan_π_app, AlgebraicGeometry.PresheafedSpace.comp_base, AlgebraicGeometry.Scheme.GlueData.ι_isoCarrier_inv, AlgebraicGeometry.Scheme.IsLocallyDirected.glueDataι_naturality, CategoryTheory.Over.prodLeftIsoPullback_inv_fst_assoc, CategoryTheory.Pseudofunctor.StrongTrans.Modification.naturality_assoc, CategoryTheory.PreZeroHypercover.comp_h₀, CategoryTheory.Limits.lim_μ_π_assoc, CategoryTheory.Lax.LaxTrans.naturality_naturality_assoc, CategoryTheory.Limits.CatCospanTransform.category_comp_right, CategoryTheory.Bicategory.rightUnitor_naturality, CategoryTheory.MonoidalClosed.curry_natural_right_assoc, CategoryTheory.MonoidalCategory.inv_hom_whiskerRight, AddCommMonCat.ofHom_comp, CategoryTheory.Localization.Monoidal.tensor_comp_assoc, CategoryTheory.ShortComplex.opcyclesMap_comp, CategoryTheory.GrpObj.mul_inv_rev_assoc, CategoryTheory.Bicategory.whiskerLeft_comp_assoc, AlgebraicGeometry.Scheme.Hom.isoImage_inv_ι_assoc, AlgebraicTopology.NormalizedMooreComplex.map_f, CategoryTheory.Functor.Monoidal.map_μ_δ, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_obj_obj_map, CategoryTheory.kernelCokernelCompSequence.δ_fac, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_iso, CategoryTheory.evaluationUncurried_map, CategoryTheory.Bicategory.Pith.whiskerLeft_iso_inv, CategoryTheory.Equivalence.counitIso_inv_app_comp_functor_map_η_inverse_assoc, CategoryTheory.ShortComplex.HomologyData.exact_iff_i_p_zero, CategoryTheory.Bicategory.rightZigzagIso_symm, CategoryTheory.left_comp_retraction, CategoryTheory.Join.pseudofunctorRight_mapComp_hom_toNatTrans_app, HomologicalComplex.toCycles_comp_homologyπ, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_whiskerRight_assoc, CategoryTheory.Iso.unop_hom_inv_id_app_assoc, CochainComplex.ConnectData.d_comp_d_assoc, CategoryTheory.CosimplicialObject.δ_comp_δ'', CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_assoc, CategoryTheory.Adjunction.Triple.leftToRight_eq_counits, CategoryTheory.MonObj.comp_mul, CategoryTheory.MonoidalCategory.triangle, CategoryTheory.Limits.colimit.pre_map', Homotopy.compRightId_hom, HomotopicalAlgebra.instCofibrationCompOfIsStableUnderCompositionCofibrations, CategoryTheory.CartesianMonoidalCategory.comp_lift_assoc, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_ι, CategoryTheory.Sigma.SigmaHom.id_comp, CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id_app, CategoryTheory.GradedObject.Monoidal.braiding_naturality_right, CategoryTheory.Limits.coprodComparison_inv_natural_assoc, AlgebraicGeometry.Scheme.Hom.germ_stalkMap, CategoryTheory.SmallObject.SuccStruct.ofCocone.map_comp, HeytAlg.ofHom_comp, CategoryTheory.LaxFunctor.map₂_rightUnitor_assoc, CategoryTheory.Lax.StrongTrans.naturality_comp, CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt'_assoc, AlgebraicGeometry.Scheme.Hom.ker_comp, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_inv_assoc, CategoryTheory.Bicategory.whiskerLeftIso_hom, CategoryTheory.ShiftedHom.opEquiv_symm_apply_comp, CategoryTheory.Limits.pullback.diagonal_fst_assoc, CategoryTheory.braiding_rightUnitor, CategoryTheory.IsHomLift.lift_comp_eqToHom_iff, CategoryTheory.yonedaPairing_map, CategoryTheory.Monad.MonadicityInternal.comparisonAdjunction_counit, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst, CategoryTheory.Localization.isoOfHom_hom_inv_id, CategoryTheory.Lax.OplaxTrans.naturality_id_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.MorphismProperty.Comma.comp_left, CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt, AlgebraicGeometry.ExistsHomHomCompEqCompAux.ha, HomologicalComplex₂.D₂_D₂_assoc, AlgebraicGeometry.Scheme.toOpen_eq, groupCohomology.mapShortComplexH1_id_comp, CategoryTheory.GradedObject.mapBifunctorMapObj_ext_iff, AlgebraicGeometry.IsOpenImmersion.range_pullback_to_base_of_right, HomologicalComplex.homotopyCofiber.d_sndX, CategoryTheory.Presieve.CoverByImageStructure.fac_assoc, CategoryTheory.GrothendieckTopology.toSheafify_comp_sheafifyCompIso_inv, CategoryTheory.Limits.pullbackProdFstIsoProd_inv_snd_fst_assoc, CategoryTheory.Pseudofunctor.map₂_whisker_right, CategoryTheory.Functor.relativelyRepresentable.w', CategoryTheory.Join.mapWhiskerRight_whiskerLeft_assoc, CategoryTheory.MonoidalClosed.comp_id_assoc, TopCat.isOpenEmbedding_iff_isIso_comp, CategoryTheory.Bicategory.whiskerRight_id_assoc, CategoryTheory.GrothendieckTopology.overMapPullback_comp_id_assoc, AlgebraicGeometry.Scheme.IdealSheafData.comapIso_hom_snd, CategoryTheory.Limits.CategoricalPullback.Hom.w, CategoryTheory.Mon_Class.pow_comp, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_apply, CategoryTheory.MonoidalCategory.tensorδ_tensorμ, CategoryTheory.IsCommComonObj.comul_comm_assoc, CategoryTheory.ExponentiableMorphism.coev_ev_assoc, CategoryTheory.InjectiveResolution.Hom.hom'_f_assoc, Mathlib.Tactic.Monoidal.eval_of, CategoryTheory.Functor.FullyFaithful.hasShift.map_add_hom_app, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₂_assoc, SSet.horn.faceι_ι_assoc, CategoryTheory.Bicategory.whisker_assoc_symm_assoc, HomologicalComplex.xPrevIsoSelf_comp_dTo_assoc, CategoryTheory.Cat.Hom.toNatIso_rightUnitor, CategoryTheory.BimonObj.one_counit, groupCohomology.cocyclesMap_comp_assoc, CategoryTheory.GrothendieckTopology.Point.comp_hom, CategoryTheory.Under.hom_right_inv_right, CategoryTheory.uliftYoneda_map_app_down, CategoryTheory.Preadditive.sum_comp_assoc, CategoryTheory.Iso.inv_hom_id_eval_assoc, CategoryTheory.ShortComplex.HomologyMapData.comm, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_assoc, HomotopicalAlgebra.CofibrantBrownFactorization.mk'_s, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom.w_assoc, CategoryTheory.HomOrthogonal.matrixDecompositionAddEquiv_symm_apply, CategoryTheory.unit_mateEquiv, Bimod.comp_whiskerLeft_bimod, SimplicialObject.Splitting.decomposition_id, CategoryTheory.Functor.OplaxRightLinear.δᵣ_associativity_inv_assoc, CategoryTheory.ComonObj.comul_counit_hom_assoc, CategoryTheory.Sigma.SigmaHom.comp_def, CategoryTheory.Functor.mapTriangle_map_hom₃, SemiNormedGrp₁.mkHom_comp, CategoryTheory.GrpObj.inv_comp, CategoryTheory.IsSplitEqualizer.top_rightRetraction, CategoryTheory.Functor.mapDifferentialObject_obj_d, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app, CategoryTheory.Localization.Monoidal.pentagon_aux₃, CategoryTheory.Bicategory.conjugateEquiv_apply', CategoryTheory.Square.Hom.comm₁₂_assoc, Bimod.left_assoc, CategoryTheory.sum.inrCompInlCompAssociator_hom_app_down_down, LinOrd.ofHom_comp, CategoryTheory.ShortComplex.HomologyMapData.comm_assoc, CategoryTheory.Arrow.iso_w, CategoryTheory.Limits.BinaryBiconeMorphism.wfst, groupHomology.isoCycles₂_inv_comp_iCycles_assoc, CategoryTheory.Enriched.FunctorCategory.enriched_assoc_assoc, CategoryTheory.Presieve.ofArrows.hom_idx, CategoryTheory.Limits.BiconeMorphism.wπ_assoc, CategoryTheory.Functor.leftKanExtensionUniqueOfIso_inv, CategoryTheory.Iso.cancel_iso_inv_right, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom, CategoryTheory.Limits.pullback.hom_ext_iff, CategoryTheory.Bicategory.mateEquiv_conjugateEquiv_vcomp, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturality, CategoryTheory.Arrow.comp_left_assoc, AlgebraicGeometry.smoothOfRelativeDimension_comp, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_hom_assoc, CategoryTheory.OplaxFunctor.mapComp_assoc_right_assoc, CategoryTheory.Abelian.PreservesImage.iso_inv_ι, CategoryTheory.Limits.imageSubobject_iso_comp, CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_π_0, CategoryTheory.Limits.coprod.map_comp_inl_inr_codiag, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_hom_τr, BoolAlg.comp_apply, CochainComplex.mappingCone.inl_v_descShortComplex_f_assoc, CategoryTheory.MonObj.comp_one_assoc, groupHomology.isoShortComplexH2_hom, SSet.RelativeMorphism.Homotopy.h₁_assoc, Rep.coindResAdjunction_homEquiv_symm_apply, CategoryTheory.MonoidalCategory.triangle_assoc_comp_right_assoc, CategoryTheory.MonoidalCategory.tensor_id_comp_id_tensor_assoc, CategoryTheory.Mat.comp_apply, HomologicalComplex.toCycles_cyclesIsoSc'_hom_assoc, CategoryTheory.Functor.Monoidal.map_tensor_assoc, Profinite.lift_lifts, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom'', CategoryTheory.Subfunctor.fromPreimage_ι, CategoryTheory.Functor.Monoidal.whiskerLeft_app_fst, CategoryTheory.Limits.limit.lift_pre, CategoryTheory.Functor.OplaxMonoidal.oplax_left_unitality, CategoryTheory.Pseudofunctor.StrongTrans.rightUnitor_inv_as_app, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_app_assoc, CategoryTheory.Over.whiskerLeft_left_fst, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply, CategoryTheory.Idempotents.app_comp_p, CategoryTheory.Iso.trans_hom, CategoryTheory.Functor.mapComon_obj_comon_counit, CategoryTheory.FreeBicategory.mk_associator_hom, CategoryTheory.ProjectiveResolution.lift_commutes_assoc, CategoryTheory.Limits.CoconeMorphism.hom_inv_id, CategoryTheory.Limits.WidePullback.hom_eq_lift, AddCommGrpCat.biprodIsoProd_inv_comp_desc, CategoryTheory.Endofunctor.Coalgebra.Hom.h, CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtensionObjIsoColimit_hom, AlgebraicTopology.DoldKan.MorphComponents.postComp_b, HomologicalComplex₂.ιTotalOrZero_map, HomologicalComplex.truncGE'Map_f_eq_opcyclesMap, CategoryTheory.SmallObject.πFunctorObj_eq, CategoryTheory.μ_δ_app, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality_assoc, HomologicalComplex.restrictionMap_comp_assoc, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerRight_assoc, CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIso_hom, CategoryTheory.Limits.Multicoequalizer.hom_ext_iff, CategoryTheory.LaxFunctor.map₂_leftUnitor, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.functorMap_comp_assoc, HasFibers.inducedMap_comp_assoc, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_id_naturality_inv, ModuleCat.exteriorPower.iso₁_hom_naturality_assoc, CategoryTheory.Limits.biproduct.map_matrix_assoc, CategoryTheory.expComparison_ev, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality, CategoryTheory.Mathlib.Tactic.MonTauto.rightUnitor_inv_tensor_one_mul, CategoryTheory.Limits.biprod.associator_natural, CategoryTheory.MonoOver.inf_map_app, CategoryTheory.Biprod.ofComponents_fst, Bimod.Hom.left_act_hom_assoc, CategoryTheory.MorphismProperty.LeftFraction.map_hom_ofInv_id, CategoryTheory.Limits.CategoricalPullback.comp_fst_assoc, CategoryTheory.Limits.Pi.map_comp_map, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_aux_one, SheafOfModules.unitHomEquiv_comp_apply, CategoryTheory.MorphismProperty.instHasPullbacksAlongCompOfIsStableUnderBaseChangeAlong, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_inv_inv, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitIso_hom_naturality, CategoryTheory.ShortComplex.mapCyclesIso_inv_naturality_assoc, CategoryTheory.LaxFunctor.mapComp_assoc_left_app, SemiNormedGrp.completion.lift_comp_incl, CategoryTheory.Functor.IsCocartesian.fac_assoc, CategoryTheory.Adjunction.unit_naturality, CategoryTheory.Limits.Cone.w, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_comp_map_assoc, CategoryTheory.leftDistributor_ext₂_left_iff, CategoryTheory.Limits.kernelFactorThruImage_inv_comp_ι, CategoryTheory.Presheaf.uliftYonedaAdjunction_unit_app_app, AlgebraicGeometry.ΓSpecIso_inv_ΓSpec_adjunction_homEquiv, AddMonCat.ofHom_comp, CategoryTheory.Mathlib.Tactic.MonTauto.associator_inv_comp_tensorHom_tensorHom, CategoryTheory.PreGaloisCategory.PointedGaloisObject.comp_val, CategoryTheory.Mon_Class.comp_one, CategoryTheory.Bicategory.conjugateEquiv_adjunction_id, HomologicalComplex.restrictionToTruncGE'.f_eq_iso_hom_pOpcycles_iso_inv, CategoryTheory.GradedObject.single_map_singleObjApplyIso_hom, CategoryTheory.MonoidalCategory.tensorμ_natural, CategoryTheory.PreZeroHypercover.inj_sigmaOfIsColimit_f, CategoryTheory.MonoidalCategory.whiskerLeft_comp_assoc, CategoryTheory.SmallObject.objMap_comp, CategoryTheory.left_unitality_app, CategoryTheory.braiding_inv_tensorUnit_left_assoc, CategoryTheory.Limits.image.preComp_mono, CategoryTheory.Cat.rightUnitor_inv_app, CategoryTheory.Limits.coprod.inr_map, CategoryTheory.BraidedCategory.braiding_inv_naturality_left_assoc, CategoryTheory.Limits.PullbackCone.ofCone_π, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app_assoc, AlgebraicGeometry.StructureSheaf.algebraMap_germ_assoc, CategoryTheory.Functor.Monoidal.whiskerLeft_δ_μ, CategoryTheory.ShortComplex.Homotopy.compLeft_h₃, CategoryTheory.ExactPairing.evaluation_coevaluation_assoc, groupHomology.chainsMap_f_1_comp_chainsIso₁, groupCohomology.mapShortComplexH1_comp, SimplexCategory.eq_σ_comp_of_not_injective', CategoryTheory.Functor.Final.ι_colimitIso_inv_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.unit_actionHomRight, CategoryTheory.Pseudofunctor.Grothendieck.Hom.ext_iff, CategoryTheory.Limits.coprod.inl_fst_assoc, CategoryTheory.Limits.inl_comp_pushoutObjIso_inv, CategoryTheory.Equivalence.counitInv_functor_comp_assoc, CategoryTheory.Functor.LeftExtension.postcompose₂_map_left, CategoryTheory.Limits.pullbackObjIso_inv_comp_fst, CategoryTheory.Functor.OplaxLeftLinear.δₗ_naturality_right, CategoryTheory.Functor.uncurry_obj_map, CategoryTheory.CartesianMonoidalCategory.inv_prodComparison_map_snd, CategoryTheory.Limits.CategoricalPullback.comp_fst, CategoryTheory.Iso.comp_inv_eq_id, CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc_assoc, CategoryTheory.Limits.LimitPresentation.map_π, CategoryTheory.Functor.Monoidal.whiskerLeft_ε_η, CategoryTheory.Limits.pullbackAssoc_inv_snd_assoc, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_counit_app_left, CategoryTheory.Presheaf.coconeOfRepresentable_naturality, CategoryTheory.Abelian.Ext.mk₀_comp_mk₀, CategoryTheory.Functor.OplaxLeftLinear.δₗ_associativity_assoc, CategoryTheory.IsSplitEqualizer.top_rightRetraction_assoc, CategoryTheory.Subobject.ofLE_comp_ofLEMk, AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_naturality, CommBialgCat.comp_apply, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.kernel_ι_d_comp_d, Preord.coe_comp, CategoryTheory.EnrichedFunctor.map_comp, CategoryTheory.CatEnrichedOrdinary.homEquiv_comp, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_naturality, CategoryTheory.NatTrans.app_naturality_assoc, CategoryTheory.Limits.Pi.map'_comp_map, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_assoc, CategoryTheory.Adjunction.map_μ_comp_counit_app_tensor, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_as_app, CategoryTheory.Bicategory.InducedBicategory.bicategory_homCategory_comp_hom, CategoryTheory.GradedNatTrans.naturality_assoc, SSet.RelativeMorphism.Homotopy.ofEq_h, CategoryTheory.Arrow.inv_left_hom_right, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counit_app, CategoryTheory.Adjunction.compCoyonedaIso_hom_app_app, CategoryTheory.Kleisli.Adjunction.fromKleisli_map, CategoryTheory.ComposableArrows.Exact.cokerIsoKer_hom_fac_assoc, CategoryTheory.Limits.prodZeroIso_iso_inv_snd, AddCommGrpCat.biprodIsoProd_inv_comp_snd, CategoryTheory.Equivalence.fun_inv_map_assoc, groupHomology.isoCycles₁_inv_comp_iCycles_assoc, CategoryTheory.ShortComplex.pOpcycles_π_isoOpcyclesOfIsColimit_inv, AlgebraicTopology.DoldKan.hσ'_eq, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_hom_fac_assoc, HomologicalComplex₂.d₂_eq, groupHomology.π_comp_H1Iso_hom_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_inv_app_app, CategoryTheory.comp_over_assoc, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac, AlgebraicGeometry.ExistsHomHomCompEqCompAux.hab, CategoryTheory.Functor.Monoidal.transport_η, CategoryTheory.ShortComplex.p_opcyclesMap_assoc, CategoryTheory.Iso.hom_inv_id_eval, CategoryTheory.unop_comp_assoc, AlgebraicGeometry.Proj.basicOpenToSpec_SpecMap_awayMap_assoc, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_as_app, CategoryTheory.Equivalence.ε_comp_map_ε, CategoryTheory.Functor.mapCocone₂_ι_app, AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_comp_assoc, groupHomology.chainsMap_f_2_comp_chainsIso₂, CategoryTheory.Limits.pullback_inv_snd_fst_of_left_isIso_assoc, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv, CategoryTheory.NatTrans.leftOpWhiskerRight, CategoryTheory.Lax.StrongTrans.naturality_naturality, CategoryTheory.ShortComplex.rightHomologyIso_hom_naturality_assoc, AlgebraicGeometry.AffineSpace.homOfVector_over, CategoryTheory.CanonicallyOverClass.over_def, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_inv_ι_assoc, CategoryTheory.biproduct_ι_comp_rightDistributor_inv_assoc, CategoryTheory.NonPreadditiveAbelian.lift_map_assoc, CategoryTheory.Cat.rightUnitor_inv_toNatTrans, CategoryTheory.Localization.lift₃NatTrans_app_app_app, CategoryTheory.ShiftedHom.opEquiv'_zero_add_symm, CategoryTheory.Functor.whiskerLeft_comp_assoc, CategoryTheory.MonoidalClosed.uncurry_natural_left, CategoryTheory.GrpObj.tensorHom_inv_inv_mul, groupHomology.pOpcycles_comp_opcyclesIso_hom, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_hom_assoc, SheafOfModules.pullback_assoc, AlgebraicGeometry.Scheme.Hom.map_appLE', AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv_assoc, CategoryTheory.Functor.ranCounit_app_app_ranAdjunction_unit_app_app, CategoryTheory.ShortComplex.asIsoHomologyπ_inv_comp_homologyπ_assoc, CategoryTheory.Oplax.OplaxTrans.naturality_naturality, CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inl_assoc, CategoryTheory.ShortComplex.zero, Bimod.whiskerRight_id_bimod, groupHomology.H2π_comp_map, Homotopy.nullHomotopicMap'_f_of_not_rel_left, CategoryTheory.ShortComplex.Hom.comp_τ₁, CategoryTheory.Limits.IsColimit.hom_desc, CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_fst_assoc, CategoryTheory.Functor.Final.colimit_cocone_comp_aux, CategoryTheory.SmallObject.SuccStruct.prop.fac, CategoryTheory.ShiftedHom.opEquiv'_symm_op_opShiftFunctorEquivalence_counitIso_inv_app_op_shift, CategoryTheory.LaxMonoidalFunctor.comp_hom, CategoryTheory.Functor.relativelyRepresentable.symmetry_snd_assoc, CategoryTheory.GlueData'.t_inv, CategoryTheory.Functor.RightExtension.precomp_map_right, CategoryTheory.CosimplicialObject.δ_comp_δ'_assoc, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_assoc, SimplexCategory.δ_one_mkOfSucc, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.exists_pushouts, CategoryTheory.ProjectiveResolution.leftDerivedToHomotopyCategory_app_eq, CategoryTheory.composePath_cons, CategoryTheory.Subgroupoid.IsNormal.conjugation_bij, CategoryTheory.Equivalence.comp_asNatTrans_assoc, CategoryTheory.StructuredArrow.map_mk, CategoryTheory.GrpObj.lift_commutator_eq_mul_mul_inv_inv_assoc, CategoryTheory.bicategoricalComp_refl, AlgebraicGeometry.Scheme.PartialMap.restrict_hom, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_hom_app_unop_assoc, CategoryTheory.NatTrans.naturality, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_hom_π_π_assoc, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv, groupHomology.cyclesIso₀_inv_comp_cyclesMap_assoc, CategoryTheory.MonoidalCategory.tensorHom_comp_whiskerLeft, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp_assoc, CategoryTheory.Iso.eHomCongr_comp, groupHomology.π_comp_H2Iso_inv, CategoryTheory.Limits.prod.inr_snd, CategoryTheory.NatTrans.rightDerivedToHomotopyCategory_comp, HomologicalComplex.homotopyCofiber.inlX_d', CategoryTheory.Limits.imageSubobject_arrow'_assoc, CategoryTheory.Bicategory.LeftLift.ofIdComp_hom, CategoryTheory.CartesianMonoidalCategory.lift_whiskerRight_assoc, CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id_assoc, Homotopy.nullHomotopicMap_f_of_not_rel_left, CategoryTheory.Limits.biprod.isIso_inl_iff_id_eq_fst_comp_inl, CategoryTheory.Subobject.factorThru_arrow, AlgebraicGeometry.Scheme.Hom.toNormalization_inr_normalizationCoprodIso_hom_assoc, CategoryTheory.Limits.biproduct.map_matrix, CategoryTheory.PreGaloisCategory.endEquivAutGalois_mul, CategoryTheory.Bicategory.rightZigzagIso_inv, SheafOfModules.Presentation.of_isIso_relations, CategoryTheory.Bicategory.prod_comp_fst, CategoryTheory.braiding_leftUnitor_assoc, groupCohomology.eq_d₂₃_comp_inv, CategoryTheory.Limits.Cotrident.app_one, CategoryTheory.MonoOver.w_assoc, CategoryTheory.CostructuredArrow.map_map_left, Frm.ofHom_comp, CategoryTheory.Limits.FormalCoproduct.mapPower_powerMap, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_hom_app_app_down, CategoryTheory.Pseudofunctor.StrongTrans.associator_hom_as_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom.w, AlgebraicGeometry.pullbackSpecIso_hom_fst, HomologicalComplex.toCycles_comp_homologyπ_assoc, CategoryTheory.Endofunctor.Algebra.Hom.h, CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_hom_assoc, CategoryTheory.MonoidalCategory.tensorHom_comp_whiskerRight, CategoryTheory.Pretriangulated.comp_hom₂, CategoryTheory.CostructuredArrow.map₂_map_left, CategoryTheory.Limits.image.preComp_comp, CategoryTheory.Limits.prod.diag_map_fst_snd_comp_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomLeft_tensor_assoc, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε_assoc, CategoryTheory.Functor.OfSequence.map_comp, CategoryTheory.Pseudofunctor.map₂_right_unitor, CategoryTheory.Bimon.ofMonComonObjX_one, CategoryTheory.Functor.shift_map_op, CategoryTheory.Lax.LaxTrans.StrongCore.naturality_hom, CategoryTheory.Limits.limitIsoSwapCompLim_inv_app, CategoryTheory.Limits.coprod.map_comp_inl_inr_codiag_assoc, HomologicalComplex₂.D₂_D₁, CategoryTheory.Functor.LaxRightLinear.μᵣ_naturality_left_assoc, CategoryTheory.Functor.LaxLeftLinear.μₗ_associativity_inv, AlgebraicGeometry.locallyOfFinitePresentation_comp, CategoryTheory.ε_η_app, CategoryTheory.MonoidalCategory.whiskerRight_id, CategoryTheory.Bicategory.Pith.associator_inv_iso_inv, CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_fst_snd, CategoryTheory.Bicategory.rightUnitor_comp_inv, CategoryTheory.Limits.colimit.pre_map, CategoryTheory.MonoidalCategory.MonoidalLeftAction.unit_actionHomRight, CategoryTheory.GrothendieckTopology.OneHypercover.comp_s₁, CategoryTheory.GlueData'.t_inv_assoc, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv, CategoryTheory.CommSq.fac_left_assoc, CategoryTheory.Localization.Monoidal.leftUnitor_naturality, AddCommGrpCat.hom_comp, CategoryTheory.MonoidalCategory.MonoidalRightAction.comp_actionHomLeft_assoc, CategoryTheory.Functor.LaxLeftLinear.μₗ_unitality_inv, CategoryTheory.Adjunction.comp_unit_app_assoc, CategoryTheory.CartesianMonoidalCategory.hom_ext_iff, CategoryTheory.ShortComplex.SnakeInput.comp_f₃, CategoryTheory.Limits.ι_comp_colimitOpIsoOpLimit_hom, CategoryTheory.NatTrans.id_comm, CategoryTheory.homOfLE_comp, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp_assoc, CategoryTheory.Limits.biproduct.hom_ext_iff, AlgebraicGeometry.AffineSpace.reindex_over_assoc, CategoryTheory.Limits.inr_comp_pushoutObjIso_inv, AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality, CategoryTheory.Localization.isoOfHom_hom_inv_id_assoc, CategoryTheory.Limits.IsLimit.fac_assoc, groupCohomology.isoShortComplexH1_hom, AlgebraicGeometry.Scheme.IdealSheafData.comapIso_hom_fst_assoc, TopCat.GlueData.image_inter, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app, CategoryTheory.Limits.Types.pullbackIsoPullback_inv_fst, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy_homEquiv_apply_app, CategoryTheory.Adjunction.toCat_unit_toNatTrans, CategoryTheory.Limits.prod.diag_map, CategoryTheory.Pretriangulated.shiftFunctor_op_map, CategoryTheory.BicategoricalCoherence.whiskerRight_iso, CategoryTheory.Limits.CokernelCofork.condition_assoc, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_inv_comp_π, AlgebraicTopology.DoldKan.PInfty_f_naturality, HomologicalComplex₂.total.map_comp_assoc, CategoryTheory.Functor.Monoidal.whiskerRight_δ_μ, CategoryTheory.InjectiveResolution.cochainComplex_d_assoc, groupHomology.H1π_comp_map_assoc, CategoryTheory.Limits.BinaryFan.braiding_inv_fst, SemimoduleCat.MonoidalCategory.leftUnitor_naturality, AlgebraicGeometry.Spec.topMap_comp, CategoryTheory.Bicategory.whiskerLeft_hom_inv_assoc, CategoryTheory.CatCenter.smul_iso_inv_eq, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_whiskerRight, CategoryTheory.Localization.Monoidal.triangle, CategoryTheory.Limits.Sigma.ι_reindex_hom, SimplexCategory.mkOfSucc_δ_gt, AlgebraicGeometry.Spec.map_comp, groupCohomology.map_id_comp, CategoryTheory.Limits.BinaryFan.assoc_snd, Action.hom_inv_hom_assoc, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_unitIso, CategoryTheory.Adjunction.rightAdjointUniq_trans_app, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_comp_naturality_inv, CategoryTheory.NormalMono.w, CategoryTheory.SimplicialObject.equivalenceRightToLeft_left, CategoryTheory.ShortComplex.rightHomologyMap'_comp_assoc, CategoryTheory.Bicategory.LeftLift.whiskerOfIdCompIsoSelf_hom_right, SimplexCategory.δ_comp_σ_of_gt_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_hom_inv_assoc, CategoryTheory.uliftCoyonedaEquiv_naturality, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_assoc, AlgebraicTopology.DoldKan.HigherFacesVanish.of_comp, CategoryTheory.exp.coev_ev_assoc, CategoryTheory.MonObj.mul_associator, CategoryTheory.Over.whiskerLeft_left_fst_assoc, CategoryTheory.IsFiltered.bowtie, CategoryTheory.Functor.RightExtension.postcompose₂ObjMkIso_inv_left_app, SimplicialObject.opFunctorCompOpFunctorIso_inv_app_app, CategoryTheory.prod_map_pre_app_comp_ev, CategoryTheory.Limits.opProdIsoCoprod_hom_fst_assoc, BddOrd.hom_comp, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app_assoc, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π_assoc, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app, CategoryTheory.Equivalence.unit_naturality_assoc, CategoryTheory.GrpObj.mul_inv, CategoryTheory.Limits.inr_comp_pushoutSymmetry_inv, CategoryTheory.shiftComm_hom_comp, CategoryTheory.OverPresheafAux.YonedaCollection.map₁_comp, CategoryTheory.Pseudofunctor.mapComp'_eq_mapComp, CategoryTheory.Join.mapWhiskerLeft_associator_hom_assoc, AlgebraicTopology.DoldKan.PInfty_f_idem_assoc, CategoryTheory.Cat.Hom.comp_obj, ComplexShape.Embedding.liftExtend_f, CategoryTheory.Equivalence.unit_app_tensor_comp_inverse_map_δ_functor_assoc, CategoryTheory.NatTrans.shift_app_assoc, Action.inv_hom_hom, AlgebraicTopology.DoldKan.Compatibility.υ_hom_app, Mathlib.Tactic.BicategoryLike.mk_eq_of_cons, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict_assoc, CategoryTheory.NatIso.cancel_natIso_inv_right, CategoryTheory.GradedObject.ι_mapBifunctorLeftUnitor_hom_apply, FinPartOrd.comp_apply, groupCohomology.isoCocycles₂_inv_comp_iCocycles, CategoryTheory.Limits.biproduct.ι_fromSubtype_assoc, CategoryTheory.IsCommMonObj.mul_comm, CategoryTheory.sheafComposeIso_inv_fac_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_inv_app_eq, AlgebraicGeometry.Scheme.Cover.gluedCoverT'_fst_snd_assoc, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp_app, CategoryTheory.Localization.SmallHom.equiv_comp, CategoryTheory.NatIso.naturality_2'_assoc, CategoryTheory.ShortComplex.comp_τ₂_assoc, CategoryTheory.CartesianMonoidalCategory.inv_prodComparison_map_fst, CategoryTheory.Limits.biproduct.eqToHom_comp_ι_assoc, HomologicalComplex.homotopyCofiber.inlX_fstX_assoc, CategoryTheory.MorphismProperty.Over.w, CategoryTheory.Adjunction.derivedη_fac_app, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_left, CategoryTheory.Localization.Monoidal.associator_naturality, CategoryTheory.IsPushout.inl_isoPushout_hom, CategoryTheory.NonPreadditiveAbelian.add_comp, CategoryTheory.Pseudofunctor.Grothendieck.Hom.congr, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom_assoc, CategoryTheory.Limits.biproduct.π_comp_eqToHom, CategoryTheory.Limits.coprod.diag_comp, CategoryTheory.Limits.coprod.inr_fst_assoc, HomologicalComplex.isoHomologyπ_hom_inv_id, CategoryTheory.DinatTrans.precompNatTrans_app, CategoryTheory.ShortComplex.cyclesIsoLeftHomology_inv_hom_id, CategoryTheory.RelCat.Hom.rel_comp_apply₂, CategoryTheory.Functor.obj.μ_def_assoc, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ₀, AlgebraicGeometry.Scheme.Hom.stalkMap_comp, CategoryTheory.Limits.FormalCoproduct.powerMap_comp_assoc, CategoryTheory.Pretriangulated.productTriangle_mor₃, SSet.ι₁_fst, SSet.const_comp, CategoryTheory.PrelaxFunctor.map₂_comp, CategoryTheory.SmallObject.SuccStruct.extendToSucc_map, CategoryTheory.Adjunction.rightAdjointUniq_hom_app_counit, Bicategory.Opposite.unop2_comp, CategoryTheory.OplaxFunctor.mapComp_naturality_left_assoc, CategoryTheory.Limits.imageSubobjectCompIso_hom_arrow_assoc, CategoryTheory.Pseudofunctor.Grothendieck.map_comp_eq, CategoryTheory.Adjunction.derivedη_fac_app_assoc, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_inv_comp_π_assoc, CategoryTheory.Limits.inr_pushoutZeroZeroIso_inv, CategoryTheory.Regular.frobeniusMorphism_isPullback, CategoryTheory.NatTrans.toCatHom₂_comp, CategoryTheory.ShortComplex.leftHomology_ext_iff, CategoryTheory.Functor.RightExtension.postcompose₂_map_left_app, CategoryTheory.CosimplicialObject.σ_comp_σ_assoc, CategoryTheory.Equivalence.unit_naturality, HomologicalComplex.homologyι_naturality, CategoryTheory.Limits.Bicone.ι_π, CategoryTheory.Limits.prod.diag_map_fst_snd_assoc, CategoryTheory.GradedObject.CofanMapObjFun.ιMapObj_iso_inv_assoc, CategoryTheory.IsHomLift.comp_id_lift, CategoryTheory.GrpObj.div_comp, CategoryTheory.Limits.coprod.map_id_comp_assoc, CategoryTheory.Limits.limit.homIso_hom, CategoryTheory.Limits.Cone.category_comp_hom, HomotopicalAlgebra.CofibrantBrownFactorization.s_p_assoc, CategoryTheory.Limits.biprod.inr_fst_assoc, CategoryTheory.Iso.hom_inv_id_app_app, CategoryTheory.Sieve.mem_functorPushforward_functor, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_hom_app_app, AlgebraicGeometry.StructureSheaf.algebraMap_germ, CochainComplex.cm5b.i_f_comp, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom, ModuleCat.FilteredColimits.ι_colimitDesc, CategoryTheory.Functor.LaxMonoidal.right_unitality_assoc, CategoryTheory.Equivalence.functor_unitIso_comp, CategoryTheory.Factorisation.Hom.ι_h, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.pentagon, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_apply, CategoryTheory.Limits.pullbackDiagonalMapIso.inv_snd_fst_assoc, CategoryTheory.Limits.wideCoequalizer.hom_ext_iff, CategoryTheory.ComonObj.counit_comul_hom_assoc, CategoryTheory.Limits.inl_pushoutLeftPushoutInrIso_inv_assoc, CategoryTheory.GrothendieckTopology.overMapPullbackComp_inv_app_val_app, CategoryTheory.Limits.Cocone.ofPushoutCocone_ι, CategoryTheory.Pseudofunctor.Grothendieck.map_map_fiber, ComplexShape.Embedding.homRestrict.comm, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.comp, CategoryTheory.MonObj.one_associator, CategoryTheory.eHom_whisker_cancel_inv_assoc, CommRingCat.comp_apply, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv_assoc, CategoryTheory.MonoidalClosed.curry'_whiskerRight_comp_assoc, CategoryTheory.Limits.limit.map_pre', CategoryTheory.Functor.Monoidal.map_whiskerRight_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app, CategoryTheory.NatTrans.CommShiftCore.app_shift, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullback_cone_of_left_condition, CategoryTheory.Pseudofunctor.StrongTrans.rightUnitor_hom_as_app, CategoryTheory.Pseudofunctor.map₂_whisker_left_app_assoc, CategoryTheory.Join.mapWhiskerLeft_rightUnitor_hom, CategoryTheory.Functor.LaxRightLinear.μᵣ_associativity, AlgebraicGeometry.IsSeparated.instCompScheme, CategoryTheory.Functor.Monoidal.map_leftUnitor, CategoryTheory.Limits.WalkingReflexivePair.rightCompReflexion_eq, CochainComplex.mappingCone.decomp_to, CategoryTheory.Bicategory.lanUnit_desc, CategoryTheory.Functor.leftDerived_fac, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst, CategoryTheory.Limits.inr_pushoutRightPushoutInlIso_inv_assoc, CategoryTheory.Functor.relativelyRepresentable.symmetry_fst_assoc, CategoryTheory.uliftCoyonedaEquiv_symm_map_assoc, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_obj, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.lift_fac, CategoryTheory.StructuredArrow.preEquivalenceInverse_map_right_right, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app, SimplexCategoryGenRel.δ_comp_δ_assoc, CategoryTheory.Iso.map_hom_inv_id_eval_app_assoc, HomologicalComplex.extendCyclesIso_hom_naturality, CategoryTheory.Triangulated.SpectralObject.comp_hom, CategoryTheory.Comma.mapLeft_map_right, CategoryTheory.ShortComplex.comp_τ₃, CategoryTheory.Limits.ι_colimitFiberwiseColimitIso_hom, HomologicalComplex.extend.leftHomologyData_i, CategoryTheory.Skeleton.comp_hom, CategoryTheory.StrictPseudofunctor.comp_mapComp_inv, CategoryTheory.Bicategory.whiskerLeft_id, inhomogeneousCochains.d_eq, CategoryTheory.Limits.pullbackSymmetry_inv_comp_fst, CategoryTheory.Limits.pullback.diagonal_comp, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_symm_apply_f, HomologicalComplex.extend.comp_d_eq_zero_iff, AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex_homotopyInvHomId, CategoryTheory.Functor.relativelyRepresentable.pullback₃.map_p₂_comp_assoc, ProfiniteAddGrp.coe_comp, HomologicalComplex.restrictionCyclesIso_inv_iCycles_assoc, CategoryTheory.CostructuredArrow.IsUniversal.fac, CategoryTheory.Mon.mul_def, CategoryTheory.Limits.biproduct.whiskerEquiv_inv_eq_lift, CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_snd_fst_assoc, CategoryTheory.Pseudofunctor.Grothendieck.categoryStruct_comp_base, CategoryTheory.GradedObject.mapBifunctorRightUnitor_naturality_assoc, CategoryTheory.Functor.Monoidal.map_ε_η, CategoryTheory.GradedObject.Monoidal.hexagon_forward, CategoryTheory.ShortComplex.homologyIsoImageICyclesCompPOpcycles_ι, CategoryTheory.Limits.Trident.IsLimit.homIso_symm_apply, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_inv_assoc, CategoryTheory.ActionCategory.comp_val, CategoryTheory.Adjunction.localization_counit_app, AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom_appTop, CategoryTheory.Lax.StrongTrans.vComp_naturality_inv, CategoryTheory.Limits.inl_comp_pushoutObjIso_inv_assoc, Mathlib.Tactic.Bicategory.eval_of, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_fst_assoc, CategoryTheory.ShortComplex.HomotopyEquiv.trans_inv, CategoryTheory.Over.prodComparisonIso_pullback_Spec_inv_left_fst_fst', CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_restriction, CategoryTheory.Presieve.FamilyOfElements.comp_of_compatible, CategoryTheory.LaxFunctor.mapComp_assoc_right_assoc, AlgebraicGeometry.coprodSpec_inl_assoc, AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem_toSpecΓ, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_awayι_assoc, CategoryTheory.ShortComplex.eq_liftCycles_homologyπ_up_to_refinements, SSet.PtSimplex.MulStruct.δ_castSucc_castSucc_map_assoc, CategoryTheory.Iso.inv_hom_id_triangle_hom₁_assoc, CategoryTheory.CostructuredArrow.map_mk, CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit_proj_assoc, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.isCardinalFiltered_aux, CategoryTheory.Limits.ConeMorphism.hom_inv_id_assoc, ModuleCat.piIsoPi_hom_ker_subtype, CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id_app_assoc, CategoryTheory.Limits.opProdIsoCoprod_inv_inr, HomologicalComplex.singleObjHomologySelfIso_hom_naturality, CategoryTheory.Limits.prod.map_id_comp_assoc, PartOrdEmb.ofHom_comp, CategoryTheory.Oplax.StrongTrans.vcomp_naturality_hom, CategoryTheory.Limits.pullbackObjIso_hom_comp_snd_assoc, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_apply, CategoryTheory.Functor.PreservesLeftKanExtension.preserves, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_inv_app_app, CategoryTheory.toSkeletonFunctor_map_hom, CategoryTheory.Monad.algebraFunctorOfMonadHomComp_inv_app_f, CategoryTheory.Functor.CorepresentableBy.homEquiv_comp, CategoryTheory.Limits.BinaryFan.braiding_inv_snd_assoc, CategoryTheory.Abelian.imageIsoImage_hom_comp_image_ι, CategoryTheory.PreZeroHypercover.hom_inv_h₀, CategoryTheory.ComonObj.comul_counit_assoc, CategoryTheory.CatEnrichedOrdinary.hComp_id_heq, HomologicalComplex₂.D₁_D₂_assoc, CategoryTheory.IsSplitEpi.id_assoc, CategoryTheory.ModObj.one_smul, CategoryTheory.Sum.natTransOfWhiskerLeftInlInr_comp, CategoryTheory.MonoidalCategory.leftUnitor_inv_naturality, CategoryTheory.Limits.PreservesLimitPair.iso_inv_fst, ComplexShape.Embedding.liftExtend.f_eq, CategoryTheory.Lax.StrongTrans.id_naturality_inv, CategoryTheory.Limits.ι_comp_sigmaObjIso_inv_assoc, CategoryTheory.ShortComplex.LeftHomologyMapData.commi_assoc, CategoryTheory.Limits.pushoutIsoOpPullback_inl_hom_assoc, ModuleCat.extendScalars_id_comp_assoc, SimplexCategory.δ_comp_σ_succ', CategoryTheory.Limits.colimit.ι_coconeMorphism, CategoryTheory.Over.whiskerLeft_left_snd_assoc, CategoryTheory.LocalizerMorphism.equiv_smallHomMap, CategoryTheory.Limits.BiconeMorphism.wπ, CategoryTheory.ShortComplex.π_homologyMap_ι_assoc, CategoryTheory.Monad.beckAlgebraCofork_ι_app, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_comp, CategoryTheory.Functor.Monoidal.tensorHom_app_snd_assoc, CategoryTheory.ite_comp, CategoryTheory.Adjunction.CommShift.compatibilityUnit_right, CategoryTheory.Limits.biprod.lift_snd_assoc, CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_inv_hom_assoc, SemiNormedGrp.comp_explicitCokernelπ, CategoryTheory.Functor.CommShift.isoAdd'_hom_app, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_app, CategoryTheory.Limits.Fan.IsLimit.lift_proj, CategoryTheory.Limits.hasPullback_of_left_factors_mono, SimplexCategory.Truncated.δ₂_two_comp_σ₂_zero_assoc, CategoryTheory.Oplax.OplaxTrans.naturality_naturality_assoc, CategoryTheory.Limits.IsColimit.pushoutCoconeEquivBinaryCofanFunctor_desc_right, CategoryTheory.braiding_inv_tensorUnit_right, CategoryTheory.Functor.IsCoverDense.homOver_app, CategoryTheory.FreeBicategory.comp_def, CategoryTheory.NatIso.naturality_2', CategoryTheory.Iso.cancel_iso_hom_right, CategoryTheory.Limits.Sigma.ι_π_of_ne_assoc, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_inv_app_app, SimplexCategory.δ_comp_σ_self, CategoryTheory.CartesianMonoidalCategory.lift_comp_fst_snd, CategoryTheory.Limits.kernelSubobject_comp_mono, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w_assoc, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app, CategoryTheory.Join.mapWhiskerRight_rightUnitor_hom, CategoryTheory.Limits.equalizerSubobject_arrow', CategoryTheory.Limits.FormalCoproduct.powerMap_comp, CochainComplex.mappingCone.liftCochain_v_fst_v_assoc, HomologicalComplex.cylinder.ι₁_desc_assoc, CategoryTheory.Limits.prod.pentagon, CategoryTheory.Limits.hasImage_comp_iso, CategoryTheory.IsIso.comp_inv_eq, CategoryTheory.Limits.Cone.ofFork_π, CategoryTheory.Limits.colimit.ι_map_assoc, CategoryTheory.ShortComplex.cyclesMap'_i_assoc, CategoryTheory.Limits.CatCospanTransform.whiskerLeft_comp, AlgebraicGeometry.Scheme.Hom.comp_toLRSHom_assoc, CategoryTheory.ComonadHom.app_δ, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom, CategoryTheory.Retract.trans_r, HomotopicalAlgebra.Precylinder.LeftHomotopy.h₁, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left_assoc, CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_idem_assoc, CategoryTheory.FunctorToTypes.rightAdj_obj_map_app, CategoryTheory.CosimplicialObject.δ_comp_σ_self, CategoryTheory.imageUnopOp_hom_comp_image_ι, CategoryTheory.ShortComplex.SnakeInput.Hom.comm₀₁, CategoryTheory.SimplicialObject.δ_comp_σ_of_gt', CategoryTheory.Adjunction.Triple.map_rightToLeft_app, CategoryTheory.Localization.Preadditive.add'_comp, CategoryTheory.IsFiltered.crown, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_associator, CategoryTheory.CartesianMonoidalCategory.lift_whiskerRight, CategoryTheory.Limits.limitUnopIsoUnopColimit_hom_comp_ι_assoc, CategoryTheory.Bicategory.Adj.Bicategory.associator_inv_τl, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app_assoc, CategoryTheory.Subobject.underlying_arrow_assoc, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_comp, groupHomology.H1π_comp_map, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_app, CategoryTheory.Limits.desc_op_comp_opCoproductIsoProduct_hom, HomologicalComplex.homologyIsoSc'_inv_ι, CategoryTheory.Localization.lift₂NatTrans_app_app, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles, HomologicalComplex.restrictionHomologyIso_inv_homologyι, CategoryTheory.Limits.CokernelCofork.map_condition, CategoryTheory.Bicategory.Adj.whiskerLeft_τl, CategoryTheory.Limits.biproduct.lift_matrix, CategoryTheory.Adjunction.eq_unit_comp_map_iff, ModuleCat.extendScalars_assoc', CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₃₁_assoc, HomologicalComplex.restrictionToTruncGE'_naturality_assoc, HomologicalComplex.singleObjHomologySelfIso_hom_naturality_assoc, FinBddDistLat.hom_comp, AddSemigrp.coe_comp, CategoryTheory.IsPullback.isoIsPullback_inv_fst_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_id, ModuleCat.piIsoPi_inv_kernel_ι, CategoryTheory.Limits.Types.Pushout.condition, CategoryTheory.NatTrans.mapHomologicalComplex_naturality_assoc, HomologicalComplex.singleObjHomologySelfIso_inv_naturality_assoc, HomologicalComplex.pOpcyclesIso_hom_inv_id_assoc, CategoryTheory.Limits.pullback_snd_iso_of_right_factors_mono, NonemptyFinLinOrd.comp_apply, CategoryTheory.MonObj.pow_comp, CategoryTheory.Pretriangulated.triangleCategory_comp, CategoryTheory.Functor.leftKanExtensionIsoFiberwiseColimit_hom_app, CategoryTheory.Limits.biprod.symmetry_assoc, CategoryTheory.MonoidalCategory.tensor_inv_hom_id, CategoryTheory.ShortComplex.RightHomologyMapData.commι, smoothSheafCommRing.ι_forgetStalk_hom_assoc, CategoryTheory.Pseudofunctor.map₂_associator, CategoryTheory.CosimplicialObject.equivalenceRightToLeft_right_app, CategoryTheory.ShortComplex.toCycles_i, CategoryTheory.Functor.LaxMonoidal.comp_ε, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_assoc, CategoryTheory.IsSplitMono.id, CategoryTheory.shiftFunctorAdd_add_zero_hom_app, AlgebraicGeometry.Proj.awayMap_awayToSection, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, CategoryTheory.Limits.MonoFactorisation.ofIsoI_m, CategoryTheory.LocalizerMorphism.RightResolution.Hom.comp_f, CategoryTheory.Limits.π_comp_cokernelComparison, CategoryTheory.ShortComplex.homologyι_comp_fromOpcycles, CategoryTheory.Bicategory.conjugateEquiv_associator_hom, CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ', AlgebraicGeometry.Scheme.Hom.map_resLE, CategoryTheory.Limits.Sigma.ι_reindex_inv, CategoryTheory.Equivalence.cancel_counitInv_right_assoc', CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_fst, CategoryTheory.MonoidalCategory.tensor_associativity, CategoryTheory.Limits.MultispanIndex.ι_fstSigmaMap, DerivedCategory.right_fac_of_isStrictlyLE, CategoryTheory.Presheaf.map_comp_uliftYonedaEquiv_down_assoc, CategoryTheory.homOfLE_op_comp_eqToHom, HomologicalComplex₂.ι_totalShift₂Iso_inv_f, CategoryTheory.Abelian.coimage.comp_π_eq_zero, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_hom, CategoryTheory.Idempotents.Karoubi.idem, CategoryTheory.Functor.id_mapMon_mul, CategoryTheory.StructuredArrow.w, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_inv_hom'_assoc, groupHomology.pOpcycles_comp_opcyclesIso_hom_assoc, CategoryTheory.MonObj.mul_braiding, CategoryTheory.IsPushout.inl_isoPushout_hom_assoc, CategoryTheory.PrelaxFunctor.map₂_hom_inv_isIso, CategoryTheory.Functor.curryingFlipEquiv_apply_map, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_assoc, Bimod.triangle_bimod, CategoryTheory.Limits.π_comp_colimitRightOpIsoUnopLimit_inv, CategoryTheory.Limits.ι_comp_colimitUnopIsoOpLimit_hom_assoc, AlgebraicTopology.DoldKan.PInfty_f_idem, CategoryTheory.Functor.CoreMonoidal.μIso_hom_natural_right, CategoryTheory.inv_comp_eq_id, AlgebraicGeometry.Proj.SpecMap_awayMap_awayι, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_fac_app, CategoryTheory.Dial.pentagon, CategoryTheory.Functor.RightExtension.postcompose₂_map_right, AlgebraicGeometry.basicOpenIsoSpecAway_inv_homOfLE_assoc, CategoryTheory.Subgroupoid.IsNormal.conj', AlgebraicTopology.DoldKan.N₂_obj_p_f, inr_coprodIsoPushout_hom, CategoryTheory.NatTrans.leftOpWhiskerRight_assoc, CategoryTheory.ShortComplex.Splitting.r_f, ModuleCat.extendScalars_id_comp, SheafOfModules.GeneratingSections.ofEpi_π, CategoryTheory.Oplax.OplaxTrans.Modification.whiskerRight_naturality_assoc, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_inv_inv_assoc, CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit_assoc, CategoryTheory.Square.Hom.comm₃₄_assoc, SSet.Truncated.HomotopyCategory.BinaryProduct.square, CategoryTheory.Over.leftUnitor_inv_left_fst_assoc, CategoryTheory.Limits.ι_comp_coequalizerComparison, CategoryTheory.ShortComplex.opcyclesIsoX₂_hom_inv_id_assoc, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv, HomologicalComplex.pOpcycles_opcyclesIsoSc'_hom_assoc, CategoryTheory.Functor.OneHypercoverDenseData.SieveStruct.fac_assoc, CategoryTheory.Functorial.map_comp, CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero, CategoryTheory.Limits.inr_inl_pushoutAssoc_hom, CategoryTheory.Idempotents.app_comp_p_assoc, CategoryTheory.Subobject.ofLE_comp_ofLE, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_hom_comp_map_π, CategoryTheory.whiskerRight_coprod_inl_rightDistrib_inv_assoc, CategoryTheory.Functor.Initial.exists_eq, CategoryTheory.Functor.CommShift.isoZero_inv_app, CategoryTheory.Limits.IsImage.lift_fac_assoc, CategoryTheory.TwoSquare.whiskerTop_app, HomologicalComplex.eqToHom_comp_d, CochainComplex.HomComplex.Cochain.leftShift_v, CategoryTheory.Limits.coend.hom_ext_iff, CategoryTheory.Bicategory.Strict.comp_id, CochainComplex.mappingCone.d_fst_v'_assoc, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitIso_inv_naturality_assoc, AlgebraicGeometry.Scheme.residue_residueFieldMap_assoc, CategoryTheory.Limits.equalizerSubobject_arrow_comp_assoc, Bicategory.Opposite.op2_leftUnitor_inv, CategoryTheory.kernelCokernelCompSequence.snakeInput_v₀₁_τ₁, CategoryTheory.Bicategory.InducedBicategory.Hom.category_comp_hom, CategoryTheory.Subobject.ofMkLE_comp_ofLE, CategoryTheory.ExactPairing.coevaluation_evaluation, CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_hom_comp_i, CategoryTheory.Functor.commShiftIso_inv_naturality, CategoryTheory.Limits.pullback_diagonal_map_snd_snd_fst, CategoryTheory.Limits.kernelSubobject_arrow'_assoc, CategoryTheory.Limits.limitIsoLimitCurryCompLim_inv_π, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_app, CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_comp, AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit_map, CategoryTheory.Limits.colimit.ι_desc_assoc, CategoryTheory.Adjunction.left_triangle, SheafOfModules.comp_val_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app_assoc, groupHomology.cyclesIso₀_comp_H0π_assoc, CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_inv, CategoryTheory.Idempotents.Karoubi.decompId_assoc, AlgebraicTopology.DoldKan.σ_comp_PInfty, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapCompIso_inv, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_mul, CategoryTheory.Bicategory.eqToHom_whiskerRight, CategoryTheory.GrothendieckTopology.Point.comp_hom_assoc, CategoryTheory.Functor.relativelyRepresentable.pullback₃.map_p₂_comp, CategoryTheory.Bicategory.Adj.associator_inv_τl, AlgebraicTopology.DoldKan.Compatibility.τ₁_hom_app, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj, CategoryTheory.Bicategory.prod_comp_snd, CategoryTheory.Functor.LeftExtension.precomp_map_left, CategoryTheory.Limits.prod.map_snd_assoc, CategoryTheory.IsFiltered.span, CategoryTheory.Comma.mapLeftIso_functor_obj_hom, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_inv_fac, CategoryTheory.Equivalence.unit_app_comp_inverse_map_η_functor, CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_hom_assoc, CategoryTheory.Preadditive.comp_add, LightCondensed.ihom_map_val_app, CategoryTheory.Dial.comp_f, AlgebraicGeometry.Scheme.comp_toLRSHom, prodIsoPullback_inv_snd, CategoryTheory.Oplax.OplaxTrans.rightUnitor_inv_as_app, CategoryTheory.PreOneHypercover.Hom.w₁₂_assoc, groupHomology.mapCycles₂_comp_i_assoc, CategoryTheory.Limits.Multicoequalizer.condition_assoc, CategoryTheory.PreZeroHypercover.Hom.w₀_assoc, CategoryTheory.Functor.mapGrp_obj_grp_mul, CategoryTheory.LaxFunctor.map₂_rightUnitor_app_assoc, CategoryTheory.Functor.LaxLeftLinear.μₗ_unitality, CategoryTheory.MorphismProperty.RightFraction.leftFraction_fac_assoc, CategoryTheory.Functor.mapCommpGrp_id_mul, SheafOfModules.map_ιFree_mapFree_hom, CategoryTheory.rightDistributor_inv_comp_biproduct_π_assoc, CategoryTheory.Enriched.FunctorCategory.enriched_assoc, CategoryTheory.GradedObject.mapBifunctorRightUnitorCofan_inj_assoc, groupCohomology.isoCocycles₁_hom_comp_i, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk, CategoryTheory.Iso.map_hom_inv_id_app_assoc, HomotopyCategory.homologyFunctor_shiftMap_assoc, AlgebraicGeometry.PresheafedSpace.stalkMap.congr_hom, dNext_eq_dFrom_fromNext, AddCommGrpCat.biproductIsoPi_inv_comp_π, CategoryTheory.Functor.whiskerRight_comp_assoc, AlgebraicGeometry.ι_sigmaSpec_assoc, CategoryTheory.Subobject.underlyingIso_inv_top_arrow_assoc, HomologicalComplex.double_d, CategoryTheory.rightDistributor_hom_comp_biproduct_π, CategoryTheory.Bicategory.leftAdjointSquare.comp_vhcomp, CategoryTheory.Preadditive.sum_comp'_assoc, CategoryTheory.ι_colimitCompWhiskeringRightIsoColimitComp_hom_assoc, HomologicalComplex₂.totalShift₂Iso_hom_naturality, CochainComplex.mappingCone.inl_v_d, Bimod.RightUnitorBimod.hom_left_act_hom', CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_app_assoc, CategoryTheory.Linear.homCongr_symm_apply, CategoryTheory.DifferentialObject.Hom.comm, CategoryTheory.Iso.hom_inv_id_assoc, AlgebraicGeometry.Scheme.IdealSheafData.subSchemeCover_map_inclusion_assoc, CategoryTheory.ShortComplex.Homotopy.comp_h₀, CategoryTheory.Bicategory.Pith.comp₂_iso_hom, CategoryTheory.Limits.biproduct.desc_eq, CategoryTheory.Bicategory.lanLiftUnit_desc, CategoryTheory.Bicategory.leftUnitor_naturality_assoc, CategoryTheory.Limits.inl_comp_pushoutSymmetry_inv_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.whiskerRight_actionHomLeft, CategoryTheory.Lax.StrongTrans.id_naturality_hom, AlgebraicGeometry.ΓSpec.right_triangle, CategoryTheory.Limits.Pi.π_comp_eqToHom, AddGrpCat.comp_apply, CategoryTheory.Enriched.FunctorCategory.functorEnriched_id_comp_assoc, CategoryTheory.Limits.colimit.ι_desc_app_assoc, CategoryTheory.TwoSquare.whiskerRight_app, CategoryTheory.Functor.CoreMonoidal.right_unitality, TopologicalSpace.Opens.op_map_comp_obj, CategoryTheory.isIso_iff_yoneda_map_bijective, CategoryTheory.Limits.π_colimitOfIsReflexivePairIsoCoequalizer_inv, CategoryTheory.TwistShiftData.shiftFunctorAdd'_inv_app, CategoryTheory.Limits.PullbackCone.combine_pt_map, CategoryTheory.Bicategory.whisker_assoc, CategoryTheory.Limits.equalizerSubobject_arrow_assoc, CategoryTheory.Lax.OplaxTrans.naturality_id, CategoryTheory.Functor.OplaxRightLinear.δᵣ_naturality_left_assoc, CategoryTheory.comp_ite, CategoryTheory.Limits.Fork.IsLimit.lift_ι_assoc, CategoryTheory.MorphismProperty.RightFraction.exists_leftFraction, CategoryTheory.MorphismProperty.LeftFraction.exists_rightFraction, AlgebraicGeometry.Scheme.residue_residueFieldCongr, CategoryTheory.ShortComplex.ShortExact.δ_comp, CochainComplex.HomComplex.Cochain.shift_v, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom, CategoryTheory.MonoidalCategory.tensor_right_unitality, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₃, CategoryTheory.CartesianMonoidalCategory.prodComparison_fst_assoc, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counit_app_tensor_assoc, CategoryTheory.Arrow.hom_inv_id_left, CategoryTheory.StructuredArrow.w_prod_fst_assoc, AlgebraicGeometry.Scheme.Hom.appIso_hom, CategoryTheory.MonoidalCategory.MonoidalRightAction.inv_hom_actionHomLeft', CategoryTheory.Limits.colimit.eqToHom_comp_ι, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_inv_comp_rightHomologyι_assoc, CategoryTheory.Limits.opProdIsoCoprod_hom_snd, CategoryTheory.Limits.biprod.lift_desc_assoc, CategoryTheory.Limits.coprod.inr_snd_assoc, CategoryTheory.Functor.isMittagLeffler_iff_subset_range_comp, CategoryTheory.toSheafify_sheafifyLift, CategoryTheory.Functor.Monoidal.map_whiskerLeft, CategoryTheory.Functor.limitIsoOfIsRightKanExtension_inv_π_assoc, CategoryTheory.ProjectiveResolution.Hom.hom_f_zero_comp_π_f_zero, CategoryTheory.ShortComplex.leftRightHomologyComparison'_naturality_assoc, CategoryTheory.Comonad.counit_naturality_assoc, HomologicalComplex.pOpcycles_singleObjOpcyclesSelfIso_inv_assoc, CategoryTheory.SimplicialObject.δ_comp_σ_self_assoc, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.IsTerminal.comm_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_inv_assoc, CategoryTheory.ShiftedHom.opEquiv'_symm_comp, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀, CategoryTheory.PreOneHypercover.sieve₁_apply, CategoryTheory.leftDistributor_ext_right_iff, CategoryTheory.δ_naturality_assoc, CategoryTheory.CatCommSq.vComp_iso_inv_app, AlgebraicGeometry.instIsAffineHomCompScheme, SimplicialObject.Splitting.IndexSet.epiComp_snd_coe, CategoryTheory.Bicategory.Adj.comp_τr, CategoryTheory.Limits.limit.hom_ext_iff, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd_assoc, SimplicialObject.Split.Hom.comm_assoc, CochainComplex.mappingCone.inr_f_snd_v_assoc, CategoryTheory.Over.liftCocone_ι_app, CategoryTheory.Adjunction.homEquiv_naturality_left_square_iff, CategoryTheory.Pretriangulated.TriangleMorphism.comm₁, CategoryTheory.Limits.image.fac_assoc, CategoryTheory.IsPushout.inl_isoPushout_inv_assoc, CategoryTheory.comp_eqToHom_iff, CategoryTheory.cancel_mono_id, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm, CategoryTheory.Limits.inr_comp_pushoutComparison_assoc, HomologicalComplex.truncGE'Map_comp_assoc, CategoryTheory.Limits.ι_colimitFiberwiseColimitIso_inv, CategoryTheory.Sieve.ofArrows.exists, TopCat.comp_app, CategoryTheory.eHom_whisker_cancel_inv, CategoryTheory.Iso.map_inv_hom_id_eval, CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_π_succ, AlgebraicTopology.DoldKan.N₁Γ₀_hom_app, CategoryTheory.GrpObj.mul_inv_rev, HomotopicalAlgebra.FibrantBrownFactorization.mk'_r, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_εIso_inv, CategoryTheory.NatTrans.IsMonoidal.unit_assoc, CategoryTheory.coprod_inr_leftDistrib_hom_assoc, CategoryTheory.SplitMono.comp_retraction, CategoryTheory.GrpObj.mulRight_hom, HomologicalComplex.mapBifunctorMapHomotopy.comm₁_aux, CategoryTheory.MorphismProperty.FunctorsInverting.comp_hom, CategoryTheory.Functor.PullbackObjObj.π_snd_assoc, CategoryTheory.Limits.biprod.inl_map_assoc, CategoryTheory.Adjunction.homEquiv_naturality_right_symm, CategoryTheory.Functor.LaxMonoidal.μ_natural_left, CategoryTheory.SmallObject.functorMap_π, groupHomology.mapCycles₂_id_comp_apply, CategoryTheory.NatIso.naturality_2, AlgebraicGeometry.Scheme.residue_residueFieldMap, CategoryTheory.ExponentiableMorphism.coev_naturality_assoc, CategoryTheory.Functor.rightDerived_fac_app_assoc, SimplicialObject.Splitting.ι_desc, HomologicalComplex.Hom.comm_assoc, AlgCat.comp_apply, CategoryTheory.Mon_Class.one_comp, CategoryTheory.StructuredArrow.mapIso_functor_obj_hom, CategoryTheory.Preadditive.neg_comp, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_fst, CategoryTheory.GradedObject.Monoidal.pentagon_inv_assoc, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_left, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc, HomotopicalAlgebra.PrepathObject.RightHomotopy.h₀, CategoryTheory.Subfunctor.Subpresheaf.preimage_comp, CategoryTheory.Limits.coprod.map_desc_assoc, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_functor_obj_d_f, CategoryTheory.ShortComplex.mapCyclesIso_hom_iCycles, CategoryTheory.Congruence.compLeft, CategoryTheory.Limits.limit.lift_π_assoc, CategoryTheory.Functor.ranObjObjIsoLimit_hom_π, AlgebraicGeometry.Scheme.evaluation_naturality_assoc, CategoryTheory.Dial.isoMk_hom_F, AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.toBiprod_fromBiprod_assoc, CategoryTheory.Functor.LaxLeftLinear.μₗ_unitality_inv_assoc, HomotopicalAlgebra.RightHomotopyClass.whitehead, CategoryTheory.Functor.OplaxLeftLinear.δₗ_unitality_inv_assoc, CategoryTheory.Bicategory.Prod.sectR_mapComp_hom, SSet.Quasicategory.hornFilling, CategoryTheory.Limits.MonoFactorisation.kernel_ι_comp, CategoryTheory.Limits.pullback_inv_fst_snd_of_right_isIso, CategoryTheory.StrictPseudofunctor.mapComp_eq_eqToIso, AlgebraicGeometry.Scheme.Hom.resLE_comp_ι_assoc, AlgebraicGeometry.tilde.toOpen_res, CategoryTheory.MonoidalCategory.leftUnitor_inv_comp_tensorHom, AlgebraicGeometry.tilde.toOpen_res_assoc, CategoryTheory.PreservesImage.hom_comp_map_image_ι_assoc, AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap_assoc, AlgebraicGeometry.PresheafedSpace.stalkMap.comp, CategoryTheory.PrelaxFunctor.map₂_comp_assoc, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv_assoc, CategoryTheory.Functor.rightKanExtensionUniqueOfIso_inv, CategoryTheory.kernelCokernelCompSequence.snakeInput_v₀₁_τ₃, CategoryTheory.Dial.symmetry, CategoryTheory.Adjunction.Triple.whiskerRight_rightToLeft, CategoryTheory.LaxFunctor.mapComp_naturality_right, AlgebraicGeometry.Scheme.Hom.ι_fromNormalization_assoc, SimplexCategory.δ_comp_σ_of_le_assoc, CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_two_symm, CategoryTheory.Idempotents.natTrans_eq, HomologicalComplex.mapBifunctor.ι_D₁, CategoryTheory.Functor.isoShift_hom_naturality_assoc, CategoryTheory.Functor.Monoidal.map_δ_μ, AlgebraicGeometry.LocallyRingedSpace.iso_inv_base_hom_base, RingCat.ofHom_comp, CategoryTheory.SplitMono.id, CategoryTheory.GrothendieckTopology.whiskerRight_toPlus_comp_plusCompIso_hom_assoc, CategoryTheory.Limits.CategoricalPullback.Hom.w'_assoc, HomologicalComplex₂.total.mapAux.d₂_mapMap, CategoryTheory.NatTrans.leftDerivedToHomotopyCategory_comp, FinBddDistLat.coe_comp, AlgebraicGeometry.Scheme.Cover.trans_comp, TopCat.pullbackIsoProdSubtype_inv_snd_assoc, CategoryTheory.congrArg_cast_hom_left, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_fst_fst_assoc, CategoryTheory.SingleFunctors.inv_hom_id_hom_app_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_as_app, CategoryTheory.StrictPseudofunctorPreCore.map₂_whisker_left, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃, CategoryTheory.MonoidalClosed.whiskerLeft_curry_ihom_ev_app, CategoryTheory.Limits.Sigma.ι_comp_map'_assoc, CategoryTheory.SemiadditiveOfBinaryBiproducts.add_eq_left_addition, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_snd, HomologicalComplex.restrictionMap_f', CategoryTheory.Limits.pullbackSymmetry_hom_comp_snd_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_hom_comp_π, HomologicalComplex.homotopyCofiber.inrX_d, CategoryTheory.kernel.ι_op, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj_hom_ext_iff, CategoryTheory.Bicategory.associatorNatIsoRight_hom_app, CategoryTheory.GrothendieckTopology.diagramNatTrans_app, AlgebraicGeometry.basicOpenIsoSpecAway_inv_homOfLE, CategoryTheory.Limits.prodComparison_natural, AlgebraicGeometry.Scheme.Hom.map_resLE_assoc, TopCat.Presheaf.stalkSpecializes_comp_assoc, AlgebraicGeometry.IsLocalIso.exists_isOpenImmersion, CategoryTheory.Bicategory.instIsIsoHomRightZigzagHom, AlgebraicGeometry.Scheme.Hom.comp_base_assoc, AlgebraicTopology.DoldKan.MorphComponents.postComp_φ, CategoryTheory.Limits.Sigma.eqToHom_comp_ι, CategoryTheory.NatTrans.naturality', AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_map, CategoryTheory.yonedaEquiv_naturality, CategoryTheory.ComonObj.comul_assoc, TopCat.prodIsoProd_hom_fst, SimplicialObject.Splitting.πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty_assoc, CategoryTheory.ShortComplex.SnakeInput.comp_f₂_assoc, CategoryTheory.Adjunction.homEquiv_apply, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_symm_apply, CategoryTheory.Limits.limit.pre_eq, CategoryTheory.ShortComplex.rightHomologyIso_hom_comp_homologyι_assoc, RingCat.comp_apply, CategoryTheory.coalgebraToOver_map, AlgebraicGeometry.coprodSpec_inl, CategoryTheory.Limits.limit.lift_map, SimplexCategory.Truncated.δ₂_one_comp_σ₂_one_assoc, SheafOfModules.pushforwardNatTrans_app_val_app, HomotopicalAlgebra.PrepathObject.p_snd_assoc, CategoryTheory.Mat_.comp_apply, CategoryTheory.Functor.relativelyRepresentable.pullback₃.fst_fst'_eq_p₁_assoc, CategoryTheory.Functor.relativelyRepresentable.hom_ext'_iff, CategoryTheory.Limits.pullbackSymmetry_hom_comp_snd, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_assoc, CategoryTheory.kernelCokernelCompSequence.φ_π, HomologicalComplex₂.ιTotal_totalFlipIso_f_hom, CategoryTheory.Limits.hasEqualizer_precomp_of_hasEqualizer, AlgebraicGeometry.Scheme.IdealSheafData.subSchemeCover_map_inclusion, CategoryTheory.Endofunctor.Algebra.functorOfNatTransComp_inv_app_f, CategoryTheory.Bicategory.associator_inv_congr, CategoryTheory.Bicategory.inv_whiskerLeft, BddLat.comp_apply, CochainComplex.ConnectData.d₀_comp_assoc, CategoryTheory.Limits.Fan.IsLimit.lift_proj_assoc, CategoryTheory.ExponentiableMorphism.pushforwardComp_hom_counit, CategoryTheory.Iso.isoCompInverse_hom_app, CategoryTheory.Functor.IsCartesian.fac, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app_assoc, CategoryTheory.Limits.FormalCoproduct.cosimplicialObjectFunctor_obj_map, CategoryTheory.Comonad.Coalgebra.counit_assoc, CategoryTheory.braiding_leftUnitor, CategoryTheory.Iso.isoInverseOfIsoFunctor_hom_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app_assoc, CategoryTheory.Limits.ColimitPresentation.ofIso_ι, CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app, CochainComplex.mappingCone.d_fst_v', CategoryTheory.MonoidalCategory.comp_tensor_id, CategoryTheory.Bimon.one_comul_assoc, CategoryTheory.Endofunctor.Algebra.functorOfNatTrans_obj_str, CategoryTheory.Limits.coequalizer.hom_ext_iff, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv_assoc, CategoryTheory.Limits.colimit.map_desc_assoc, CategoryTheory.Limits.prod.symmetry, CategoryTheory.InjectiveResolution.desc_commutes_zero, CategoryTheory.δ_naturality, CategoryTheory.MonoidalCategory.DayConvolution.associator_naturality, HomotopicalAlgebra.CofibrantObject.homMk_homMk_assoc, CategoryTheory.Pseudofunctor.id_mapComp, CategoryTheory.ComposableArrows.Exact.cokerIsoKer_hom_fac, HomologicalComplex.singleObjCyclesSelfIso_hom_assoc, CategoryTheory.Comonad.right_counit, CategoryTheory.Bicategory.Adj.comp_adj, CategoryTheory.Bimon.ofMonComon_toMonComon_obj_comul, CategoryTheory.GrpObj.lift_comp_inv_left_assoc, CategoryTheory.Functor.comp_mapCommGrp_one, CategoryTheory.Limits.π_reflexiveCoequalizerIsoCoequalizer_inv, AddCommGrpCat.biprodIsoProd_inv_comp_fst, CategoryTheory.Subobject.underlyingIso_inv_top_arrow, CategoryTheory.SimplicialObject.δ_comp_δ_self', CategoryTheory.Limits.pushout.mapLift_comp, CategoryTheory.CatCenter.smul_iso_hom_eq', SimplexCategory.Truncated.Hom.tr_comp_assoc, CategoryTheory.BraidedCategory.braiding_naturality_left_assoc, CategoryTheory.Over.associator_inv_left_fst_snd_assoc, CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id, CategoryTheory.IsPullback.isoPullback_hom_snd_assoc, CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_hom_inv_id_assoc, CategoryTheory.Comma.mapRight_map_left, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_inv, CategoryTheory.Limits.Multifork.ofPiFork_π_app_right, CochainComplex.mappingCone.inl_v_descCochain_v, SSet.RelativeMorphism.Homotopy.h₀, CategoryTheory.Monoidal.InducingFunctorData.whiskerLeft_eq, Bicategory.Opposite.op2_leftUnitor, CategoryTheory.Limits.kernel.condition_assoc, ComplexShape.Embedding.homRestrict_precomp_assoc, CategoryTheory.Arrow.inv_hom_id_left, CategoryTheory.Iso.map_inv_hom_id_eval_app, CategoryTheory.DifferentialObject.eqToHom_f'_assoc, CategoryTheory.GrpObj.comp_inv_assoc, CategoryTheory.GrothendieckTopology.toPlus_naturality_assoc, AlgebraicGeometry.Spec_Γ_naturality_assoc, CategoryTheory.Abelian.PreservesCoimage.hom_coimageImageComparison, AlgebraicGeometry.Scheme.Hom.appLE_map'_assoc, CategoryTheory.IsKernelPair.pullback, CategoryTheory.Limits.Multicofork.snd_app_right, HomologicalComplex.d_comp_XIsoOfEq_hom, CategoryTheory.SmallObject.SuccStruct.Iteration.congr_map, CategoryTheory.Functor.LeftExtension.postcomp₁_map_left, CategoryTheory.Bicategory.mateEquiv_leftUnitor_hom_rightUnitor_inv, TopCat.Presheaf.germ_res'_assoc, CategoryTheory.Adjunction.rightAdjointUniq_trans_assoc, CategoryTheory.Bicategory.LeftExtension.whisker_unit, CategoryTheory.Bicategory.conjugateEquiv_mateEquiv_vcomp, CategoryTheory.ShortComplex.mapCyclesIso_inv_naturality, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_π_app_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_app, CategoryTheory.mono_comp_iff_of_mono, CategoryTheory.Adjunction.CoreUnitCounit.left_triangle, CategoryTheory.Iso.map_hom_inv_id_eval, CategoryTheory.Limits.ι_reflexiveCoequalizerIsoCoequalizer_hom, TopologicalSpace.Opens.mapComp_inv_app, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_symm_apply, CategoryTheory.Limits.Cotrident.condition, HomologicalComplex.singleObjCyclesSelfIso_inv_naturality, HomotopicalAlgebra.AttachCells.cell_def_assoc, quasiIsoAt_iff_comp_left, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_inv, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackComp_inv, CategoryTheory.Functor.map_shift_unop_assoc, CategoryTheory.NatTrans.naturality_app_app, CategoryTheory.Limits.Types.productIso_inv_comp_π, HomotopicalAlgebra.LeftHomotopyRel.precomp, CategoryTheory.ShiftMkCore.zero_add_hom_app, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_comp, CategoryTheory.Pseudofunctor.mapComp'_id_comp, HomotopicalAlgebra.BifibrantObject.homMk_homMk_assoc, AlgebraicGeometry.StructureSheaf.toOpen_germ, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_assoc, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality, HomologicalComplex.mapBifunctor.d₁_eq', AlgebraicGeometry.PresheafedSpace.comp_base_assoc, CategoryTheory.Limits.FormalCoproduct.pullbackCone_condition, Bimod.actRight_one_assoc, HomologicalComplex.Hom.comm_from, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₃_assoc, CategoryTheory.Functor.Monoidal.whiskerRight_ε_η, CategoryTheory.Limits.biproduct.ι_π_self_assoc, AlgebraicGeometry.Scheme.Hom.naturality, CategoryTheory.MorphismProperty.Over.pullback_map_left, CategoryTheory.MonoidalCategory.MonoidalLeftAction.comp_actionHomLeft, CategoryTheory.Limits.pullbackProdSndIsoProd_hom_snd_assoc, CategoryTheory.Comma.mapRightComp_hom_app_right, CategoryTheory.Iso.homCongr_symm_apply, NonemptyFinLinOrd.hom_hom_comp, CategoryTheory.IsCofilteredOrEmpty.cone_maps, CategoryTheory.whiskerRight_coprod_inr_rightDistrib_inv, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app, CategoryTheory.ShortComplex.mapLeftHomologyIso_hom_naturality_assoc, CategoryTheory.yonedaCommGrpGrp_map_app, CategoryTheory.Limits.kernelIsoOfEq_inv_comp_ι, CategoryTheory.Limits.Multifork.ofPiFork_π_app_left, CategoryTheory.regularTopology.equalizerCondition_w, CategoryTheory.Functor.inv_fun_map, CategoryTheory.Limits.pullbackComparison_comp_fst, CategoryTheory.MonoidalCategory.tensorμ_natural_left, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_hom_iCycles, CategoryTheory.ShortComplex.Homotopy.comm₂, CategoryTheory.leftAdjointMate_comp_evaluation_assoc, CategoryTheory.Injective.comp_factorThru, CategoryTheory.Limits.biproduct.ι_π, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_assoc, HomologicalComplex.d_comp_d, CategoryTheory.Functor.partialRightAdjointHomEquiv_symm_comp_assoc, CategoryTheory.ihom.ev_naturality, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_naturality_assoc, AlgebraicGeometry.Scheme.Hom.resLE_comp_ι, ChainComplex.mk_congr_succ_d₂, Bimod.middle_assoc, CommRingCat.HomTopology.isHomeomorph_precomp, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_hom_comp_map_π_assoc, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃, CategoryTheory.Bicategory.Adj.Bicategory.associator_hom_τr, CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_inv, CategoryTheory.Limits.zeroProdIso_inv_snd, CategoryTheory.Abelian.image.ι_comp_eq_zero, CategoryTheory.Functor.LaxMonoidal.associativity, CategoryTheory.MonoidalCategory.tensor_left_unitality_assoc, CategoryTheory.MonoidalCategory.whisker_assoc_symm, AlgebraicGeometry.Scheme.Hom.liftCoborder_ι_assoc, CategoryTheory.GrpObj.comp_div_assoc, CategoryTheory.OrthogonalReflection.D₁.ι_comp_t, CategoryTheory.Mat.comp_def, CategoryTheory.Functor.isRightKanExtension_iff_precomp, CategoryTheory.Limits.MonoFactorisation.ofIsoComp_I, CategoryTheory.Functor.relativelyRepresentable.pullback₃.fst_snd_eq_p₂, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_assoc, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_cone_π_app, AlgebraicGeometry.Scheme.Pullback.Triplet.Spec_ofPointTensor_SpecTensorTo, CategoryTheory.Bicategory.associatorNatIsoLeft_hom_app, CategoryTheory.MorphismProperty.HasRightCalculusOfFractions.exists_rightFraction, HomologicalComplex.XIsoOfEq_inv_comp_XIsoOfEq_hom, CategoryTheory.ShortComplex.Splitting.s_r, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π_assoc, CategoryTheory.ShortComplex.π_leftRightHomologyComparison_ι, CategoryTheory.Limits.colimit.isoColimitCocone_ι_hom_assoc, CochainComplex.HomComplex.Cocycle.equivHomShift_comp, groupHomology.inhomogeneousChains.d_comp_d, CategoryTheory.ShortComplex.SnakeInput.naturality_φ₂, AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_naturality, CategoryTheory.Limits.pullbackComparison_comp_snd, CategoryTheory.Adjunction.rightAdjointUniq_hom_app_counit_assoc, CategoryTheory.Functor.relativelyRepresentable.pullback₃.fst_fst'_eq_p₁, CochainComplex.cm5b.i_f_comp_assoc, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_inv_assoc, CategoryTheory.CartesianMonoidalCategory.lift_fst, HomologicalComplex.singleObjOpcyclesSelfIso_inv_naturality_assoc, CategoryTheory.Bicategory.LeftLift.whiskerIdCancel_right, CategoryTheory.Comma.mapRightIso_inverse_obj_hom, SSet.stdSimplex.faceSingletonComplIso_hom_ι_assoc, CategoryTheory.TwistShiftData.shiftFunctorAdd'_hom_app, CategoryTheory.Cat.HasLimits.comp_def, AlgebraicGeometry.Scheme.IdealSheafData.inclusion_id_assoc, CategoryTheory.Sheaf.ΓHomEquiv_naturality_right, HomologicalComplex.d_eqToHom_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.hom_inv_actionHomLeft, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_inv_assoc, CategoryTheory.Subobject.ofMkLE_comp_ofLE_assoc, CategoryTheory.MonoidalCategory.hom_inv_id_tensor', CategoryTheory.Limits.Pi.map_π_assoc, PresheafOfModules.pushforward_assoc, CategoryTheory.PrelaxFunctor.map₂_inv_hom_assoc, CategoryTheory.Limits.Pi.ι_π_of_ne_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_hom_app_app, CategoryTheory.ExponentiableMorphism.coev_naturality, groupHomology.π_comp_H0Iso_hom, Homotopy.comp_hom, CategoryTheory.CatEnrichedOrdinary.hComp_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict, CategoryTheory.Bicategory.Prod.fst_mapComp_inv, CategoryTheory.ShortComplex.abelianImageToKernel_comp_kernel_ι_comp_cokernel_π, dNext_eq, CategoryTheory.Limits.IsImage.lift_ι, CategoryTheory.Oplax.StrongTrans.Modification.naturality, CategoryTheory.Limits.prod.comp_lift, CategoryTheory.rightAdjointOfCostructuredArrowTerminalsAux_symm_apply, CategoryTheory.Limits.inl_comp_pushoutObjIso_hom_assoc, TopologicalSpace.Opens.map_comp_obj, CategoryTheory.tensorLeftHomEquiv_symm_coevaluation_comp_whiskerRight, CategoryTheory.StructuredArrow.mapIso_inverse_map_right, CategoryTheory.eHomEquiv_comp, CategoryTheory.BraidedCategory.hexagon_reverse_inv_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom, CategoryTheory.Square.Hom.comm₁₂, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app_assoc, CategoryTheory.MonoidalCategory.pentagon_inv, CategoryTheory.Limits.kernelIsoOfEq_inv_comp_ι_assoc, CategoryTheory.Limits.coprod.inl_map, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoColimitUncurryWhiskeringLeft₂_hom_assoc, CategoryTheory.Functor.shiftIso_hom_app_comp_shiftMap, Mathlib.Tactic.CategoryTheory.CancelIso.hom_inv_id_of_eq, HomotopicalAlgebra.PrepathObject.RightHomotopy.h₀_assoc, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_comp, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_hom, CategoryTheory.Hom.one_def, CategoryTheory.Mon.comp_hom', CategoryTheory.Over.μ_pullback_left_snd, groupCohomology.mapShortComplexH1_id_comp_assoc, CategoryTheory.Functor.partialLeftAdjointHomEquiv_symm_comp_assoc, CategoryTheory.Subfunctor.Subpresheaf.fromPreimage_ι, Preord.ofHom_comp, CategoryTheory.ShortComplex.homologyMap_op, CategoryTheory.Limits.BinaryCofan.IsColimit.desc'_coe, CategoryTheory.Adjunction.Triple.whiskerLeft_leftToRight_assoc, CategoryTheory.Functor.shiftIso_add'_inv_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_naturality₂, CategoryTheory.Limits.opProdIsoCoprod_inv_inr_assoc, CategoryTheory.Functor.biprodComparison_fst, CategoryTheory.Under.mapPushoutAdj_counit_app, CategoryTheory.WithTerminal.pseudofunctor_mapComp, CategoryTheory.Limits.combineCocones_ι_app_app, CategoryTheory.Over.iteratedSliceBackward_obj, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right, CategoryTheory.Comonad.beckEqualizer_lift, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.tensorHom_comp_tensorHom, CategoryTheory.Limits.CatCospanTransform.triangle_inv_assoc, SSet.ι₀_fst, CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_fst, HomologicalComplex.biprod_inl_desc_f, CategoryTheory.PreGaloisCategory.autEmbedding_range, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom_assoc, HomologicalComplex.π_homologyIsoSc'_inv, HomologicalComplex.singleObjHomologySelfIso_inv_naturality, CategoryTheory.CostructuredArrow.homMk'_comp, CochainComplex.ιTruncLE_naturality, AlgebraicGeometry.Scheme.Modules.pseudofunctor_left_unitality, CategoryTheory.Adjunction.Triple.map_adj₂_counit_app_leftToRight_app, CategoryTheory.NonPreadditiveAbelian.comp_add, CategoryTheory.Adjunction.Triple.map_rightToLeft_app_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.comp_actionHomLeft_assoc, CategoryTheory.Regular.frobeniusStrongEpiMonoFactorisation_m, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_hom_app_app, TopCat.prodIsoProd_inv_snd, HomologicalComplex.cyclesIsoSc'_hom_iCycles, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_assoc, CategoryTheory.GrpObj.inv_hom_assoc, Bimod.AssociatorBimod.inv_hom_id, CategoryTheory.Under.mapComp_eq, CategoryTheory.Limits.pullbackLeftPullbackSndIso_hom_fst_assoc, CategoryTheory.Limits.coprod.inr_desc_assoc, CategoryTheory.GradedObject.ι_mapBifunctorBifunctor₂₃Desc_assoc, AlgebraicGeometry.Scheme.Hom.isoOpensRange_inv_comp_assoc, CategoryTheory.Functor.leftDerived_fac_app_assoc, CategoryTheory.Bicategory.Adj.associator_hom_τr, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom, HomotopicalAlgebra.Cylinder.trans_i₁, CategoryTheory.HopfObj.antipode_comul₁, AlgebraicTopology.DoldKan.N₂_obj_X_d, CategoryTheory.Limits.FormalCoproduct.evalOp_obj_map, AlgebraicGeometry.Scheme.Modules.pseudofunctor_associativity_assoc, CategoryTheory.Limits.Multicofork.sigma_condition, CategoryTheory.MonoidalCategory.DayConvolution.whiskerLeft_comp_unit_app_assoc, CategoryTheory.Adjunction.unit_app_tensor_comp_map_δ, LinOrd.hom_comp, groupCohomology.mapShortComplexH1_comp_assoc, CategoryTheory.Limits.MonoFactorisation.ofIsoI_e, CategoryTheory.Subgroupoid.mul_mem_cancel_left, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃_eq_assoc, CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf_hom_right, groupHomology.cyclesIso₀_inv_comp_cyclesMap, CategoryTheory.Limits.Sigma.ι_desc, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_π, CategoryTheory.GradedObject.mapBifunctorBifunctor₂₃MapObj_ext_iff, AlgebraicGeometry.ProjectiveSpectrum.Proj.stalkMap_toSpec, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_app, AlgebraicGeometry.pullbackSpecIso_hom_base_assoc, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_toSpecΓ_assoc, CategoryTheory.Limits.CatCospanTransform.id_whiskerLeft, AlgebraicGeometry.Scheme.Cover.gluedCoverT'_snd_snd, CategoryTheory.Dial.braiding_hom_F, CategoryTheory.Limits.coprod.hom_ext_iff, BddDistLat.ofHom_comp, CategoryTheory.Limits.Sigma.whiskerEquiv_inv, CategoryTheory.Functor.OplaxLeftLinear.δₗ_naturality_left, CategoryTheory.RanIsSheafOfIsCocontinuous.fac, CategoryTheory.GrpObj.ofIso_inv, AlgebraicGeometry.Scheme.Hom.normalizationCoprodIso_inv_coprodDesc_fromNormalization_assoc, TopCat.piIsoPi_inv_π, AlgebraicGeometry.Scheme.IdealSheafData.comapIso_hom_fst, CategoryTheory.Limits.limit.isoLimitCone_inv_π, CategoryTheory.GrothendieckTopology.toPlus_naturality, CategoryTheory.coevaluation_comp_leftAdjointMate, CategoryTheory.Functor.FullyFaithful.hasShift.map_add_inv_app, CategoryTheory.IsSplitCoequalizer.condition, CategoryTheory.Sieve.pullback_ofArrows_of_iso, CategoryTheory.IsFiltered.coeq_condition, CategoryTheory.Bicategory.prod_leftUnitor_hom_fst, CategoryTheory.Functor.Monoidal.μ_snd, SimplicialObject.Splitting.cofan_inj_πSummand_eq_zero_assoc, AlgebraicGeometry.pullbackRestrictIsoRestrict_inv_fst_assoc, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberDesc_assoc, CategoryTheory.Limits.pullbackZeroZeroIso_inv_snd, CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_fst_snd_assoc, CategoryTheory.Functor.IsCoverDense.isoOver_inv_app, CategoryTheory.Limits.inl_pushoutAssoc_inv, CategoryTheory.Limits.pullbackLeftPullbackSndIso_hom_fst, HomologicalComplex.restrictionToTruncGE'_naturality, HomotopicalAlgebra.PathObject.ofFactorizationData_p₀, CategoryTheory.ShortComplex.LeftHomologyData.homologyIso_hom_comp_leftHomologyIso_inv, CategoryTheory.Functor.OplaxMonoidal.δ_comp_tensorHom_η_assoc, groupHomology.H0π_comp_H0Iso_hom, CategoryTheory.ExponentiableMorphism.unit_pushforwardId_hom, CategoryTheory.Functor.FullyFaithful.grpObj_mul, CategoryTheory.Iso.cancel_iso_inv_right_assoc, CategoryTheory.Limits.IsImage.fac_lift, AlgebraicGeometry.Scheme.GlueData.ι_isoLocallyRingedSpace_inv, CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app_assoc, CategoryTheory.Lax.OplaxTrans.comp_naturality, groupHomology.isoCycles₁_hom_comp_i_assoc, CategoryTheory.MonoidalCategory.DayConvolution.associator_inv_unit_unit_assoc, CategoryTheory.Limits.limitOpIsoOpColimit_inv_comp_π, CategoryTheory.Limits.biproduct.lift_eq, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_fst, CategoryTheory.Localization.Monoidal.triangle_aux₂, CategoryTheory.Limits.coprod.triangle, AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem_toSpecΓ_assoc, AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp, CategoryTheory.Subobject.arrow_congr, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberToSpecResidueField, CategoryTheory.MorphismProperty.LeftFraction.rightFraction_fac_assoc, CategoryTheory.Limits.equalizerComparison_comp_π_assoc, smoothSheaf.ι_evalHom, CategoryTheory.ShortComplex.LeftHomologyMapData.comp_φK, CategoryTheory.Dial.leftUnitor_inv_F, CategoryTheory.Limits.inl_inl_pushoutAssoc_hom_assoc, CategoryTheory.GlueData.ι_gluedIso_hom, CategoryTheory.Localization.Preadditive.comp_add', CategoryTheory.Limits.CoconeMorphism.inv_hom_id, CategoryTheory.ShortComplex.cyclesMap_i_assoc, HomologicalComplex.HomologySequence.δ_naturality, CategoryTheory.Grpd.comp_eq_comp, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τl, AlgebraicGeometry.locallyOfFiniteType_comp, ProfiniteGrp.coe_comp, CochainComplex.mappingCone.inr_descShortComplex, CategoryTheory.Functor.whiskerLeft_comp_whiskerRight, AlgebraicGeometry.Scheme.comp_appTop, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π, smoothSheafCommRing.ι_evalHom_assoc, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_inv_assoc, CategoryTheory.Oplax.OplaxTrans.naturality_comp_assoc, CategoryTheory.MonoidalCategory.whiskerLeft_comp_tensorHom_assoc, CategoryTheory.Equivalence.counitInv_naturality, groupHomology.map_id_comp_H0Iso_hom, CategoryTheory.Bicategory.Adjunction.comp_left_triangle_aux, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom_assoc, CategoryTheory.Functor.CommShift.OfComp.map_iso_hom_app_assoc, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_hom_assoc, CategoryTheory.SimplicialObject.σ_comp_σ_assoc, CategoryTheory.Bicategory.whiskerLeft_hom_inv_whiskerRight, AddSemigrp.ofHom_comp, CategoryTheory.CartesianMonoidalCategory.lift_leftUnitor_hom, CategoryTheory.Limits.DiagramOfCones.comp, CategoryTheory.GrpObj.mulRight_inv, CategoryTheory.Functor.rightDerivedNatTrans_fac_assoc, CommRingCat.HomTopology.mvPolynomialHomeomorph_apply_fst, CategoryTheory.Limits.biproduct.eqToHom_comp_ι, CochainComplex.ι_mapBifunctorShift₁Iso_hom_f_assoc, groupCohomology.isoShortComplexH2_hom, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity, CategoryTheory.GlueData'.t_fac, CategoryTheory.Functor.Monoidal.map_η_ε_assoc, TopCat.Presheaf.Pushforward.comp_hom_app, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w_assoc, CategoryTheory.Functor.LaxMonoidal.whiskerRight_tensorUnit_comp_rightUnitor_hom, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_comp_assoc, CategoryTheory.Iso.homToEquiv_symm_apply, CategoryTheory.Mod_.scalarRestriction_smul, CategoryTheory.Limits.prod.lift_snd, CategoryTheory.preservesLimitIso_hom_π, CategoryTheory.Limits.PullbackCone.condition_one, CategoryTheory.unitCompPartialBijective_symm_natural, CategoryTheory.Limits.piComparison_comp_π_assoc, CategoryTheory.ShortComplex.rightHomologyIso_inv_naturality, CategoryTheory.GrothendieckTopology.coneCompEvaluationOfConeCompDiagramFunctorCompEvaluation_π_app, CategoryTheory.ObjectProperty.FullSubcategory.comp_hom, CategoryTheory.Subfunctor.range_comp, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inr, CategoryTheory.Functor.toPseudoFunctor'_mapComp, CategoryTheory.Limits.inl_pushoutRightPushoutInlIso_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocIso_inv_naturality, CategoryTheory.Limits.inr_inr_pushoutAssoc_inv_assoc, CategoryTheory.Limits.limitIsoLimitCurryCompLim_inv_π_assoc, CategoryTheory.Subobject.inf_comp_left_assoc, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_germ, CategoryTheory.Iso.homFromEquiv_apply, CategoryTheory.GrothendieckTopology.Cover.Arrow.precomp_f, CategoryTheory.Dial.associatorImpl_inv_f, CategoryTheory.Presieve.piComparison_fac, CategoryTheory.Equivalence.unit_inverse_comp, CochainComplex.mappingCone.mapHomologicalComplexXIso'_hom, AlgebraicGeometry.Scheme.stalkMap_inv_hom, AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp_assoc, CategoryTheory.Functor.map_comp, CategoryTheory.SmallObject.ιObj_πObj, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst, inl_coprodIsoPushout_inv, CategoryTheory.NatTrans.op_whiskerLeft, AlgebraicGeometry.Etale.etale_comp, CategoryTheory.Localization.Monoidal.β_hom_app, CategoryTheory.GrpObj.mul_inv_assoc, AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_map_assoc, CategoryTheory.Adjunction.right_triangle_components, CategoryTheory.Limits.pullbackObjIso_inv_comp_snd_assoc, Bicategory.Opposite.bicategory_homCategory_comp_unop2, CategoryTheory.ihom.ev_naturality_assoc, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_hom_whiskerLeft_π_assoc, HomotopicalAlgebra.CofibrantObject.HoCat.resolutionMap_fac_assoc, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc, CategoryTheory.GrpObj.comp_inv, AlgebraicGeometry.Scheme.comp_base_apply, AlgebraicGeometry.Scheme.fromSpecStalk_app, CategoryTheory.IsIso.hom_inv_id, HomologicalComplex.homotopyCofiber.inlX_d_assoc, HomologicalComplex.pOpcycles_extendOpcyclesIso_hom, AlgebraicGeometry.SpecMap_residueFieldIsoBase_inv, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id_app, CochainComplex.HomComplex.Cochain.d_comp_ofHom_v, groupCohomology.d₀₁_comp_d₁₂_assoc, CategoryTheory.CartesianMonoidalCategory.whiskerLeft_fst, AlgebraicTopology.DoldKan.karoubi_PInfty_f, CategoryTheory.ParametrizedAdjunction.unit_whiskerRight_map, CategoryTheory.Adjunction.unit_app_commShiftIso_hom_app, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counitIso_hom_app_tensor, CategoryTheory.Under.inv_right_hom_right, CategoryTheory.Functor.whiskerRight_comp, CategoryTheory.Limits.biproduct.ι_toSubtype_subtype_assoc, CategoryTheory.IsCommMonObj.mul_comm_assoc, AlgebraicGeometry.Scheme.PartialMap.isOver_iff, CategoryTheory.ShortComplex.mapOpcyclesIso_inv_naturality_assoc, CategoryTheory.Limits.inl_pushoutZeroZeroIso_inv, CategoryTheory.Limits.inl_pushoutRightPushoutInlIso_hom_assoc, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isColimit, CategoryTheory.CechNerveTerminalFrom.wideCospan.limitIsoPi_inv_comp_pi_assoc, HomologicalComplex.mapBifunctorAssociatorX_hom_D₃, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_comp, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac, HomotopicalAlgebra.PrepathObject.ι_p₀, HomologicalComplex.stupidTruncMap_comp_assoc, CategoryTheory.Arrow.arrow_mk_comp_eqToHom, AlgebraicGeometry.SpecMap_residueFieldIsoBase_inv_assoc, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp_assoc, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_hom_π_assoc, CategoryTheory.Limits.pushout_inl_inv_inr_of_right_isIso_assoc, CategoryTheory.Functor.Monoidal.μ_snd_assoc, CategoryTheory.Subfunctor.fromPreimage_ι_assoc, HomologicalComplex.homotopyCofiber.desc_f, CategoryTheory.Limits.pullbackDiagonalMapIso.inv_snd_snd_assoc, FundamentalGroupoid.conj_eqToHom, CategoryTheory.Functor.Monoidal.map_η_ε, AlgebraicGeometry.Scheme.Hom.toNormalization_normalizationPullback_fst_assoc, SimplexCategory.Truncated.δ₂_zero_comp_σ₂_one, CategoryTheory.CostructuredArrow.mapNatIso_functor_map_left, CategoryTheory.Limits.Multicofork.condition, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_comp, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app_assoc, CategoryTheory.Functor.HomObj.naturality_assoc, HomologicalComplex.extendCyclesIso_inv_iCycles, CategoryTheory.Limits.IsColimit.ofIsoColimit_desc, CategoryTheory.Limits.CoconeMorphism.map_w_assoc, CategoryTheory.Functor.Monoidal.map_tensor, CategoryTheory.IsCardinalPresentable.exists_hom_of_isColimit, CochainComplex.ConnectData.comp_d₀, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom, CategoryTheory.Limits.coprod.desc_comp_assoc, CategoryTheory.MorphismProperty.LeftFraction.map_comp_map_s, CategoryTheory.Presieve.IsSheafFor.functorInclusion_comp_extend_assoc, HomotopyCategory.homologyShiftIso_hom_app, CategoryTheory.Presheaf.map_comp_uliftYonedaEquiv_down, CategoryTheory.Limits.limCompFlipIsoWhiskerLim_hom_app_app, CategoryTheory.Limits.limitIsoLimitCurryCompLim_hom_π_π, CategoryTheory.Limits.prodComparison_natural_assoc, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_assoc, AlgebraicGeometry.AffineSpace.homOfVector_toSpecMvPoly, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app, HomologicalComplex.restrictionCyclesIso_hom_iCycles_assoc, AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_comp, CategoryTheory.Lax.LaxTrans.vComp_naturality_comp, CategoryTheory.ShortComplex.homologyπ_comp_asIsoHomologyπ_inv_assoc, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_apply, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_obj_hom, Rep.norm_comm_assoc, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv_assoc, CategoryTheory.obj_μ_app_assoc, HomologicalComplex.ι_mapBifunctorFlipIso_hom, groupCohomology.mapShortComplexH2_id_comp, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_left, Bimod.whisker_exchange_bimod, CategoryTheory.Bicategory.id_whiskerLeft, SSet.RelativeMorphism.Homotopy.h₁, groupHomology.π_comp_H0IsoOfIsTrivial_hom_assoc, CategoryTheory.GrothendieckTopology.whiskerRight_toSheafify_sheafifyCompIso_hom, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_counit_app, CategoryTheory.Limits.inr_opProdIsoCoprod_inv, CategoryTheory.Functor.Monoidal.whiskerRight_app_snd, smoothSheafCommRing.ι_forgetStalk_hom, CategoryTheory.GrothendieckTopology.overMapPullbackComp_hom_app_val_app, SimplicialObject.Splitting.comp_PInfty_eq_zero_iff, CategoryTheory.GrpObj.η_whiskerRight_commutator, CategoryTheory.ShortComplex.SnakeInput.L₀X₂ToP_comp_pullback_snd_assoc, CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_snd_assoc, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_germ, CategoryTheory.Limits.hasPullback_of_comp_mono, CategoryTheory.ComonObj.comul_assoc_assoc, CategoryTheory.Bicategory.LeftExtension.whisker_extension, ModuleCat.biprodIsoProd_inv_comp_fst, CategoryTheory.MonoidalCategory.tensor_hom_inv_id'_assoc, CategoryTheory.Iso.inverseCompIso_inv_app, CategoryTheory.Limits.fst_opProdIsoCoprod_hom, HomologicalComplex.homology_π_ι, CategoryTheory.comp_leftAdjointMate, CategoryTheory.MonoidalCategory.MonoidalLeftAction.inv_hom_actionHomLeft'_assoc, AlgebraicGeometry.pullbackSpecIso_hom_fst'_assoc, CategoryTheory.Bicategory.Pith.associator_inv_iso_hom, CategoryTheory.Bicategory.whiskerLeft_hom_inv_whiskerRight_assoc, CategoryTheory.StructuredArrow.projectSubobject_factors, HomologicalComplex.truncLE'Map_comp, CategoryTheory.Pseudofunctor.mapComp_id_left_hom, CategoryTheory.Limits.Sigma.ι_π_eq_id, ContinuousCohomology.MultiInd.d_comp_d, AlgebraicGeometry.Scheme.GlueData.glue_condition_assoc, CategoryTheory.Functor.OplaxMonoidal.δ_natural, CategoryTheory.Functor.LaxLeftLinear.μₗ_naturality_left_assoc, AlgebraicGeometry.PresheafedSpace.congr_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict_assoc, CategoryTheory.Bicategory.prod_associator_inv_snd, CategoryTheory.Dial.whiskerLeft_F, CategoryTheory.pullbackShiftFunctorZero'_inv_app, CategoryTheory.ShortComplex.leftHomologyIso_inv_naturality, CategoryTheory.Limits.limit.coneMorphism_π, CategoryTheory.CartesianMonoidalCategory.lift_fst_assoc, CategoryTheory.Limits.end_.map_comp_assoc, CategoryTheory.Abelian.FunctorCategory.imageObjIso_hom, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv, CategoryTheory.Limits.coprod.inr_desc, HomologicalComplex.biprod_inr_desc_f_assoc, CategoryTheory.Idempotents.DoldKan.Γ_map_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitIso_hom_naturality, AlgebraicGeometry.IsAffineOpen.SpecMap_appLE_fromSpec_assoc, CategoryTheory.Subobject.underlyingIso_hom_comp_eq_mk, CategoryTheory.Limits.ι_colimitPointwiseProductToProductColimit_π_assoc, CategoryTheory.Functor.OplaxMonoidal.δ_natural_right, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_snd, CategoryTheory.Oplax.LaxTrans.naturality_id_assoc, Rep.resIndAdjunction_unit_app, CategoryTheory.Subobject.pullback_comp, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd, HomologicalComplex.isoHomologyπ_inv_hom_id_assoc, CategoryTheory.Limits.KernelFork.map_condition, groupHomology.d₃₂_comp_d₂₁, CategoryTheory.Limits.pullbackAssoc_hom_fst, CategoryTheory.Under.mapComp_inv, HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_apply, CategoryTheory.Pseudofunctor.map₂_whisker_left_app, DistLat.coe_comp, CategoryTheory.Limits.coend.ι_map_assoc, CategoryTheory.MonoidalCategory.rightUnitor_inv_comp_tensorHom, CategoryTheory.Limits.PreservesPullback.iso_hom_fst_assoc, CategoryTheory.Adjunction.homEquiv_naturality_left_symm, HomologicalComplex.opcyclesToCycles_homologyπ_assoc, CategoryTheory.Enriched.FunctorCategory.homEquiv_apply_π_assoc, Bimod.TensorBimod.one_act_left', CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_rightUnitor, CategoryTheory.Idempotents.KaroubiKaroubi.idem_f_assoc, HomologicalComplex₂.totalShift₁Iso_hom_naturality_assoc, CategoryTheory.Limits.imageSubobjectCompIso_inv_arrow, CategoryTheory.NatTrans.congr, ModuleCat.extendScalars_comp_id_assoc, CategoryTheory.GrpObj.inv_comp_inv_assoc, AlgebraicTopology.DoldKan.Γ₂N₁.natTrans_app_f_app, CategoryTheory.CartesianMonoidalCategory.lift_lift_associator_hom_assoc, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_inv_π, CategoryTheory.braiding_tensorUnit_right, CategoryTheory.Functor.OplaxRightLinear.δᵣ_associativity_assoc, CategoryTheory.BraidedCategory.braiding_inv_naturality_left, CategoryTheory.NatIso.naturality_2_assoc, CategoryTheory.Limits.inl_comp_pushoutSymmetry_hom_assoc, CategoryTheory.shiftFunctorComm_hom_app_of_add_eq_zero, CategoryTheory.Pretriangulated.comp_hom₃, CategoryTheory.Limits.PushoutCocone.isoMk_hom_hom, CategoryTheory.Over.μ_pullback_left_fst_fst, CategoryTheory.MonoidalClosed.compTranspose_eq, CategoryTheory.Limits.biprod.add_eq_lift_id_desc, CategoryTheory.Limits.CatCospanTransform.whiskerRight_comp_assoc, CategoryTheory.Bicategory.LanLift.CommuteWith.commute, CategoryTheory.IsCommComonObj.comul_comm, CategoryTheory.Bicategory.Prod.snd_mapComp_hom, CategoryTheory.Iso.isoFunctorOfIsoInverse_hom_app, CochainComplex.mappingCone.inl_v_descShortComplex_f, AlgebraicGeometry.SpecToEquivOfLocalRing_symm_apply, SimplexCategory.comp_toOrderHom, CategoryTheory.Under.hom_right_inv_right_assoc, CategoryTheory.ShiftedHom.opEquiv_symm_apply, CategoryTheory.Limits.pullback_inv_fst_snd_of_right_isIso_assoc, CategoryTheory.Over.starPullbackIsoStar_inv_app_left, CategoryTheory.Bicategory.leftUnitor_hom_congr, HomologicalComplex.truncLE'Map_comp_assoc, BddOrd.comp_apply, CategoryTheory.Join.mapWhiskerLeft_whiskerLeft_assoc, CategoryTheory.Oplax.StrongTrans.Modification.whiskerLeft_naturality_assoc, CategoryTheory.Limits.Sigma.ι_π_of_ne, AddCommGrpCat.kernelIsoKer_hom_comp_subtype, CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero_assoc, CategoryTheory.Center.whiskerRight_comm_assoc, CategoryTheory.Functor.descOfIsLeftKanExtension_fac_app_assoc, CategoryTheory.ComonObj.comul_counit_hom, AlgebraicGeometry.Scheme.Hom.stalkMap_congr, HomologicalComplex.homotopyCofiber.sndX_inrX, CategoryTheory.Comonad.CofreeEqualizer.condition, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_snd, HomologicalComplex₂.ι_D₁, CategoryTheory.Limits.end_.map_π_assoc, CategoryTheory.Limits.coprod.map_desc, CategoryTheory.ShortComplex.Splitting.r_f_assoc, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left, CategoryTheory.Limits.imageMonoIsoSource_inv_ι_assoc, CategoryTheory.Sieve.functor_map_coe, AlgebraicTopology.DoldKan.degeneracy_comp_PInfty, CategoryTheory.Limits.kernelSubobject_arrow_comp_assoc, CategoryTheory.Mon.comp_hom, CategoryTheory.Functor.FullyFaithful.preimage_comp_assoc, CochainComplex.HomComplex.Cochain.d_comp_ofHoms_v, TopCat.prodIsoProd_hom_fst_assoc, CochainComplex.HomComplex.Cochain.toSingleMk_postcomp, CategoryTheory.Presheaf.freeYonedaHomEquiv_comp_assoc, CategoryTheory.GrothendieckTopology.overMapPullback_id_comp_assoc, CategoryTheory.coreCategory_comp_iso_hom, CategoryTheory.Quotient.comp_left, CategoryTheory.Functor.Final.exists_coeq_of_locally_small, CategoryTheory.SmallObject.ιObj_πObj_assoc, CategoryTheory.Subgroupoid.mem_im_iff, CategoryTheory.ShortComplex.mapRightHomologyIso_hom_naturality_assoc, CategoryTheory.coyonedaPairing_map, CategoryTheory.Bicategory.Adj.leftUnitor_inv_τr, CategoryTheory.Adjunction.homEquiv_counit, CategoryTheory.leftDistributor_inv, CategoryTheory.Bicategory.whiskerRight_isIso, CategoryTheory.Localization.Monoidal.μ_natural_right_assoc, CategoryTheory.kernelCokernelCompSequence.snakeInput_L₀_f, CategoryTheory.Limits.ker.condition_assoc, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_hom_app, AlgebraicGeometry.pullbackSpecIso_inv_fst', CategoryTheory.Limits.pullbackDiagonalMapIdIso_hom_snd_assoc, SemiNormedGrp.comp_apply, CategoryTheory.WithTerminal.down_comp, CategoryTheory.GrpObj.right_inv, CategoryTheory.Functor.IsCocartesian.of_comp_iso, SemiNormedGrp.comp_explicitCokernelπ_assoc, CategoryTheory.Functor.mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app, CategoryTheory.Limits.hasCoequalizer_epi_comp, CategoryTheory.Functor.LaxRightLinear.μᵣ_unitality_assoc, CategoryTheory.CommSq.vert_comp, CategoryTheory.Bicategory.rightUnitor_inv_naturality_assoc, CategoryTheory.HomIsOver.comp_over, CategoryTheory.Equivalence.unit_app_comp_inverse_map_η_functor_assoc, CategoryTheory.Functor.LaxMonoidal.ε_tensorHom_comp_μ, CategoryTheory.Limits.coprod.inr_fst, CategoryTheory.Limits.pullbackSymmetry_hom_comp_fst_assoc, CategoryTheory.Dial.associator_hom_f, HomologicalComplex.extendCyclesIso_hom_iCycles_assoc, CategoryTheory.Limits.opProdIsoCoprod_inv_inl_assoc, AlgebraicGeometry.Scheme.Hom.comp_appTop, CochainComplex.mappingCone.inr_f_descShortComplex_f, CategoryTheory.StrictPseudofunctor.mk''_mapComp, HomologicalComplex.Hom.comm_from_assoc, CategoryTheory.ShiftedHom.opEquiv'_apply, CategoryTheory.Limits.biproduct.fromSubtype_toSubtype, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₁_assoc, CategoryTheory.MonoidalCategory.rightUnitor_tensor_inv, CategoryTheory.Limits.colimit.post_desc, CategoryTheory.SmallObject.ιFunctorObj_naturality_assoc, CategoryTheory.ShortComplex.LeftHomologyMapData.commf'_assoc, CategoryTheory.Functor.LaxMonoidal.whiskerLeft_μ_comp_μ, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app_assoc, AlgebraicGeometry.IsAffineOpen.Spec_map_appLE_fromSpec, CategoryTheory.Cat.HasLimits.limitConeLift_toFunctor, CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_fst_fst, CategoryTheory.Limits.braid_natural, CategoryTheory.Adjunction.leftAdjointCompNatTrans₀₂₃_eq_conjugateEquiv_symm, CategoryTheory.CatCommSq.iso_hom_naturality_assoc, CategoryTheory.Prod.fac', CategoryTheory.Adjunction.counit_naturality_assoc, CategoryTheory.Functor.obj.ι_def_assoc, CategoryTheory.Limits.Trident.app_zero_assoc, CategoryTheory.GrpObj.lift_comp_inv_left, CategoryTheory.MorphismProperty.Under.w_assoc, CategoryTheory.braiding_leftUnitor_aux₁, CategoryTheory.Arrow.square_to_iso_invert, CategoryTheory.CommSq.w, CategoryTheory.constantSheafAdj_counit_w, CategoryTheory.Limits.colimit_map_colimitObjIsoColimitCompEvaluation_hom, ComplexShape.Embedding.homRestrict_f, HomologicalComplex.opcyclesToCycles_naturality_assoc, CategoryTheory.Limits.pullbackDiagonalMapIso.hom_fst_assoc, HomologicalComplex.singleObjCyclesSelfIso_hom_naturality_assoc, CategoryTheory.GradedObject.ι_descMapObj, CommGrpCat.ofHom_comp, AlgebraicGeometry.Scheme.Cover.gluedCoverT'_fst_snd, SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero, CategoryTheory.Limits.terminal.comp_from_assoc, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.presheafHom_naturality_assoc, CategoryTheory.GrpObj.eq_lift_inv_left, CategoryTheory.sum.inlCompInlCompAssociator_hom_app_down, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_comp_assoc, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec, CategoryTheory.SingleFunctors.hom_inv_id_hom_assoc, groupHomology.isoCycles₁_inv_comp_iCycles, CategoryTheory.IsPushout.hom_eq_add_up_to_refinements, AlgebraicGeometry.LocallyRingedSpace.stalkSpecializes_stalkMap, CategoryTheory.BicategoricalCoherence.assoc_iso, CategoryTheory.HalfBraiding.monoidal, CategoryTheory.toOverIteratedSliceForwardIsoPullback_inv_app_left, CategoryTheory.Limits.CatCospanTransform.whiskerRight_id_assoc, CategoryTheory.Over.hom_left_inv_left_assoc, CategoryTheory.Join.mapWhiskerRight_whiskerRight_assoc, CategoryTheory.Bicategory.Comonad.comul_assoc_assoc, CategoryTheory.tensorLeftHomEquiv_whiskerLeft_comp_evaluation, CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_comm_f, CategoryTheory.Functor.PullbackObjObj.π_snd, CategoryTheory.Preadditive.comp_nsmul, HomologicalComplex.homologyι_opcyclesToCycles, CompHausLike.LocallyConstant.sigmaComparison_comp_sigmaIso, CategoryTheory.Limits.coconeOfCoconeFiberwiseColimit_ι_app, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂'_obj_obj_map, CategoryTheory.Limits.pushoutIsoOpPullback_inv_snd, CategoryTheory.Limits.combineCones_pt_map, CategoryTheory.LocalizerMorphism.LeftResolution.Hom.comm_assoc, HomologicalComplex.extend.d_eq, CategoryTheory.SmallObject.functorObj_comm_assoc, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counit_app_tensor, CategoryTheory.Adjunction.Triple.leftToRight_app, AlgebraicGeometry.Scheme.residue_residueFieldCongr_assoc, CategoryTheory.Limits.PreservesPushout.inl_iso_hom, CategoryTheory.Limits.prod.map_id_comp, CategoryTheory.Mon.limit_mon_one, CategoryTheory.PreGaloisCategory.exists_lift_of_mono, CategoryTheory.Pretriangulated.exists_iso_binaryBiproduct_of_distTriang, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_assoc, CategoryTheory.Limits.PreservesCokernel.π_iso_hom, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_assoc, CategoryTheory.ShortComplex.cyclesIsoX₂_inv_hom_id, CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm_assoc, AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom_comp_assoc, CategoryTheory.Bicategory.Pith.leftUnitor_hom_iso, CategoryTheory.Quotient.LiftCommShift.iso_inv_app, CategoryTheory.ShortComplex.cycles_ext_iff, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_hom_right, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app, CategoryTheory.pre_map, HomotopicalAlgebra.Precylinder.i₀_π_assoc, CategoryTheory.CartesianMonoidalCategory.lift_snd_comp_fst_comp_assoc, CategoryTheory.Limits.limit.conePointUniqueUpToIso_inv_comp, CategoryTheory.Join.mapWhiskerLeft_leftUnitor_hom, AlgebraicGeometry.Scheme.Hom.appLE_comp_appLE_assoc, CategoryTheory.Functor.descOfIsLeftKanExtension_fac, AlgebraicGeometry.Scheme.Hom.liftCoborder_ι, AlgebraicGeometry.Scheme.IsLocallyDirected.exists_of_pullback_V_V, groupHomology.cyclesMap_comp_isoCycles₁_hom_assoc, HomologicalComplex.mapBifunctor.d₂_eq', CochainComplex.g_shortComplexTruncLEX₃ToTruncGE_assoc, CategoryTheory.Limits.IsLimit.map_π_assoc, HomologicalComplex.iCyclesIso_inv_hom_id_assoc, AlgebraicGeometry.Scheme.Modules.pseudofunctor_left_unitality_assoc, CategoryTheory.ShortComplex.Homotopy.compLeft_h₀, CochainComplex.mappingCone.inr_f_triangle_mor₃_f_assoc, PresheafOfModules.Hom.naturality, CategoryTheory.ChosenPullbacksAlong.iso_pullback_map, CategoryTheory.Comonad.Coalgebra.counit, CategoryTheory.conjugateEquiv_adjunction_id_symm, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_morphismRestrict, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_symm_apply, CategoryTheory.Monad.right_unit, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_naturality_assoc, groupHomology.mapShortComplexH2_id_comp, CategoryTheory.CartesianMonoidalCategory.lift_map, Homotopy.compLeft_hom, AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom_comp, CategoryTheory.Functor.OplaxMonoidal.δ_natural_assoc, CategoryTheory.ShortComplex.mapHomologyIso_inv_naturality, Mathlib.Tactic.BicategoryCoherence.assoc_liftHom₂, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom', CategoryTheory.Bicategory.lanUnit_desc_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_assoc, CategoryTheory.Limits.ColimitPresentation.w, AddGrpCat.coe_comp, CategoryTheory.Functor.LaxMonoidal.right_unitality_inv_assoc, CategoryTheory.GradedObject.ι_descMapObj_assoc, CategoryTheory.Oplax.LaxTrans.vComp_naturality_naturality, CategoryTheory.Bicategory.associator_naturality_left, CategoryTheory.Limits.Cofork.IsColimit.π_desc, CategoryTheory.MonObj.lift_comp_one_left_assoc, CategoryTheory.Limits.image_map_comp_imageSubobjectIso_inv, groupHomology.isoShortComplexH2_inv, CategoryTheory.Grothendieck.map_map_fiber, CategoryTheory.Sheaf.comp_val_assoc, CategoryTheory.Limits.opProductIsoCoproduct'_inv_comp_lift, CategoryTheory.HopfObj.mul_antipode₂, CategoryTheory.PresheafHom.IsSheafFor.exists_app, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompCoyoneda, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_inv_hom_assoc, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃'_tensorHom, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_app, CategoryTheory.ShrinkHoms.comp_def, HomologicalComplex.truncLE'Map_f_eq, groupHomology.toCycles_comp_isoCycles₁_hom, CategoryTheory.Limits.pullbackIsoOpPushout_inv_snd_assoc, CategoryTheory.SingleFunctors.inv_hom_id_hom_app, CategoryTheory.Limits.FormalCoproduct.coproductIsoSelf_inv_φ, AlgebraicGeometry.LocallyRingedSpace.comp_toHom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHom_def, CategoryTheory.Limits.piObjIso_inv_comp_π_assoc, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_hom_eq_germ_assoc, CategoryTheory.Iso.unop_inv_hom_id_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_hom_toNatTrans_app_val_app, prevD_comp_right, CategoryTheory.Functor.isLeftKanExtension_iff_precomp, CategoryTheory.Bicategory.Pith.rightUnitor_inv_iso_hom, HomologicalComplex.Hom.comm', HomologicalComplex₂.ι_totalShift₂Iso_hom_f, AlgebraicTopology.DoldKan.N₁Γ₀_inv_app, CategoryTheory.Bicategory.Pith.comp₂_iso_inv_assoc, CategoryTheory.OverClass.asOverHom_comp, CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_snd_snd, AlgebraicGeometry.Scheme.Hom.inl_toNormalization_normalizationCoprodIso_inv_assoc, CategoryTheory.ShortComplex.Homotopy.g_h₃, SheafOfModules.pullbackObjFreeIso_hom_naturality, CategoryTheory.Functor.ranObjObjIsoLimit_inv_π, SSet.yonedaEquiv_comp, LightDiagram.comp_hom_hom_hom_apply, CategoryTheory.Iso.eHomCongr_inv, AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_inv_ι_app, CategoryTheory.MorphismProperty.RightFraction₂.exists_leftFraction₂, CategoryTheory.MonoidalCategory.rightUnitor_monoidal, CategoryTheory.Iso.hom_inv_id_triangle_hom₃_assoc, CategoryTheory.IsCofiltered.eq_condition, HomologicalComplex.dFrom_comp_xNextIso_assoc, CategoryTheory.Limits.colimit_map_colimitObjIsoColimitCompEvaluation_hom_assoc, CategoryTheory.Iso.inverseCompIso_hom_app, CategoryTheory.Comonad.Coalgebra.comp_eq_comp, HomologicalComplex.toCycles_cyclesIsoSc'_hom, CategoryTheory.Sieve.ofArrows.fac_assoc, CategoryTheory.MonObj.mul_assoc_assoc, CategoryTheory.GrothendieckTopology.toSheafify_naturality, CategoryTheory.ObjectProperty.isColocal.homEquiv_apply, CategoryTheory.Adjunction.right_triangle, CategoryTheory.leftUnitor_inv_braiding, CategoryTheory.Functor.OplaxMonoidal.left_unitality_assoc, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.inverse_obj, CategoryTheory.MonoidalCategory.tensor_whiskerLeft, CategoryTheory.Limits.biproduct.ι_desc_assoc, Frm.comp_apply, CategoryTheory.Limits.coequalizer.condition_assoc, CategoryTheory.ShortComplex.opcyclesIsoRightHomology_hom_inv_id_assoc, HomologicalComplex.fromOpcycles_op_cyclesOpIso_inv, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_hom_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHom_def', CategoryTheory.Limits.Types.Pushout.cocone_ι_app, CategoryTheory.leftDistributor_inv_comp_biproduct_π_assoc, CategoryTheory.EnrichedCat.whiskerRight_out_app, Bimod.whiskerRight_hom, CategoryTheory.MonoidalCategory.leftUnitor_monoidal_assoc, CategoryTheory.Bicategory.prod_homCategory_comp_snd, CategoryTheory.GradedObject.ι_mapMap_assoc, AlgebraicGeometry.Scheme.germ_residue_assoc, Lat.ofHom_comp, CategoryTheory.ShortComplex.comp_τ₃_assoc, CategoryTheory.Limits.colimit.w_assoc, CategoryTheory.Idempotents.Karoubi.Biproducts.bicone_π_f, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq, CategoryTheory.Functor.IsEventuallyConstantTo.isoMap_hom_inv_id_assoc, CategoryTheory.InjectiveResolution.Hom.ι_f_zero_comp_hom_f_zero_assoc, SSet.Quasicategory.hornFilling', SemimoduleCat.MonoidalCategory.braiding_naturality, CategoryTheory.IsPushout.inl_isoIsPushout_inv_assoc, CategoryTheory.GrothendieckTopology.ι_plusCompIso_hom, AlgebraicGeometry.IsAffineOpen.Spec_map_appLE_fromSpec_assoc, groupHomology.chainsMap_f_2_comp_chainsIso₂_assoc, CategoryTheory.Functor.leftDerivedNatTrans_app, CategoryTheory.Oplax.StrongTrans.id_naturality_hom, CategoryTheory.Bicategory.leftUnitor_naturality, CategoryTheory.Limits.zero_comp, CategoryTheory.obj_μ_zero_app, CategoryTheory.Limits.inl_comp_pushoutSymmetry_hom, CategoryTheory.Limits.coprod.associator_hom, CategoryTheory.ExponentiableMorphism.unit_pushforwardId_hom_assoc, CategoryTheory.CatEnrichedOrdinary.id_hComp_id, CategoryTheory.IsCommMonObj.mul_comm', CategoryTheory.IsPushout.inr_isoIsPushout_hom, Bimod.pentagon_bimod, CategoryTheory.IsPullback.isoIsPullback_hom_fst, CategoryTheory.MonoidalCategory.MonoidalRightAction.whiskerRight_actionHomLeft, CategoryTheory.Bicategory.Adj.Bicategory.associator_inv_τr, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst_assoc, HomologicalComplex.pOpcycles_opcyclesToCycles_iCycles, CategoryTheory.ExponentiableMorphism.ev_naturality, HomologicalComplex.extend_d_eq, AlgebraicGeometry.diagonal_Spec_map, SSet.OneTruncation₂.nerveHomEquiv_apply, CategoryTheory.Limits.Pi.isoLimit_hom_π, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_ι_inv, CategoryTheory.Functor.commShiftOfLocalization_iso_hom_app, AlgebraicTopology.DoldKan.QInfty_f_idem_assoc, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict, CategoryTheory.eqToHom_iso_inv_naturality_assoc, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv, FintypeCat.homMk_eq_comp_iff, CategoryTheory.Functor.OplaxRightLinear.δᵣ_unitality_inv_assoc, CategoryTheory.Functor.OplaxLeftLinear.δₗ_naturality_right_assoc, CategoryTheory.ShortComplex.Hom.comm₂₃_assoc, CategoryTheory.ShortComplex.Homotopy.comp_h₂, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_map_app_assoc, CategoryTheory.StructuredArrow.mapIso_functor_map_right, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_hom_assoc, CategoryTheory.Limits.ι_colimitConstInitial_hom, CategoryTheory.Bifunctor.diagonal', CategoryTheory.BraidedCategory.hexagon_forward_inv, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_assoc, CategoryTheory.Limits.π_comp_colimitRightOpIsoUnopLimit_inv_assoc, CategoryTheory.SingleFunctors.comp_hom, CategoryTheory.LaxFunctor.mapComp_assoc_left, CategoryTheory.Adjunction.map_restrictFullyFaithful_unit_app, CategoryTheory.Sheaf.sheafifyCocone_ι_app_val_assoc, CategoryTheory.Bicategory.Comonad.counit_comul, HomologicalComplex.extendMap_comp, CategoryTheory.IsPushout.inr_isoIsPushout_inv_assoc, CategoryTheory.MonoidalCategory.rightUnitor_naturality, CategoryTheory.GrothendieckTopology.OneHypercover.comp_h₀, CategoryTheory.MonoidalCategory.tensorHom_def_assoc, CategoryTheory.PreZeroHypercover.Hom.comp_h₀, CategoryTheory.Dial.braiding_naturality_left, CategoryTheory.Under.costar_map_left, CategoryTheory.Dial.associatorImpl_hom_f, CategoryTheory.CatEnriched.eqToHom_hComp_eqToHom, CategoryTheory.Monad.unit_naturality_assoc, CategoryTheory.Adjunction.ofCat_unit, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.firstMap_app_app_app, CategoryTheory.Limits.CatCospanTransform.whiskerLeft_comp_assoc, CategoryTheory.Presieve.extension_iff_amalgamation, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_whiskerRight, groupCohomology.subtype_comp_d₀₁, BialgCat.toBialgHom_comp, CategoryTheory.OplaxFunctor.map₂_rightUnitor_app, CategoryTheory.ShortComplex.mapHomologyIso'_hom_naturality_assoc, CategoryTheory.prod_comp, CategoryTheory.MonoidalCategory.tensorμ_natural_left_assoc, CategoryTheory.CatEnrichedOrdinary.eqToHom_hComp_eqToHom, CategoryTheory.MonoidalClosed.pre_map, BddOrd.ofHom_comp, CategoryTheory.NonPreadditiveAbelian.diag_σ_assoc, CategoryTheory.Over.whiskerRight_left_fst_assoc, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_right_unitor, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_assoc, ComplexShape.Embedding.homRestrict.f_eq, CategoryTheory.CartesianClosed.curry_natural_left, CategoryTheory.PreOneHypercover.Hom.w₁₂, CategoryTheory.Functor.LaxMonoidal.tensorHom_ε_comp_μ, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_app, CategoryTheory.Cat.Hom.toNatTrans_comp, CategoryTheory.Limits.Multifork.hom_comp_ι, CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv_assoc, AlgebraicTopology.DoldKan.QInfty_f_idem, CategoryTheory.LaxFunctor.mapComp_naturality_right_app, groupHomology.isoCycles₂_hom_comp_i, HomologicalComplex.restrictionToTruncGE'.f_eq_iso_hom_iso_inv, CategoryTheory.TwoSquare.vComp_app, CategoryTheory.Functor.LaxMonoidal.comp_μ, CategoryTheory.ComonObj.counit_comul, SSet.RelativeMorphism.Homotopy.rel, CategoryTheory.SmallObject.FunctorObjIndex.comm_assoc, AlgebraicGeometry.Scheme.stalkMap_inv_hom_assoc, CategoryTheory.LaxFunctor.mapComp_assoc_right, CategoryTheory.Functor.leftKanExtensionUniqueOfIso_hom, AlgebraicGeometry.tilde.toOpen_map_app_assoc, CategoryTheory.Limits.biproduct.ι_toSubtype, CategoryTheory.CartesianMonoidalCategory.lift_map_assoc, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d_1_0, CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIsoWhisker_inv_right, CategoryTheory.Limits.limitFlipIsoCompLim_hom_app, CategoryTheory.shiftFunctorAdd_assoc_hom_app, groupHomology.π_comp_H1Iso_hom, CochainComplex.mappingCone.inl_v_snd_v, CategoryTheory.Bicategory.mateEquiv_apply, CategoryTheory.Limits.prod.comp_diag, CategoryTheory.Bicategory.Adj.associator_hom_τl, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_hom_π_π, CategoryTheory.Bicategory.Adj.Bicategory.whiskerRight_τr, CategoryTheory.SmallObject.ιFunctorObj_πFunctorObj, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_right, CategoryTheory.GradedObject.Monoidal.rightUnitor_naturality, CategoryTheory.Limits.image.lift_mk_factorThruImage_assoc, CategoryTheory.HasClassifier.comm_assoc, CategoryTheory.Over.tensorHom_left_snd, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_rightUnitor, CategoryTheory.Bicategory.LeftExtension.whiskerHom_right, CategoryTheory.Limits.pullback.mapDesc_comp, HomologicalComplex.p_fromOpcycles_assoc, CategoryTheory.StrictlyUnitaryLaxFunctor.comp_mapComp, CategoryTheory.Bicategory.InducedBicategory.bicategory_associator_hom_hom, CategoryTheory.Abelian.DoldKan.comparisonN_hom_app_f, CategoryTheory.eHomEquiv_comp_assoc, CategoryTheory.ShortComplex.RightHomologyMapData.commp_assoc, CategoryTheory.Oplax.StrongTrans.naturality_naturality, CategoryTheory.Subobject.inf_comp_right, groupHomology.isoCycles₂_inv_comp_iCycles, CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv', CategoryTheory.HopfObj.antipode_counit, AddMagmaCat.comp_apply, CategoryTheory.Functor.LaxMonoidal.whiskerRight_tensorUnit_comp_rightUnitor_hom_assoc, HomologicalComplex.extendHomologyIso_inv_homologyι, CategoryTheory.StructuredArrow.w_prod_snd_assoc, HomologicalComplex₂.XXIsoOfEq_hom_ιTotal, CategoryTheory.kernelCokernelCompSequence.inl_φ_assoc, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_hom_left, SheafOfModules.pullback_map_ιFree_comp_pullbackObjFreeIso_hom, AugmentedSimplexCategory.inr_comp_tensorHom, CategoryTheory.Subfunctor.Subpresheaf.range_comp_le, CategoryTheory.Bicategory.pentagon_hom_hom_inv_inv_hom, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerLeft, CategoryTheory.Triangulated.SpectralObject.comp_hom_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_inv_app_app, CategoryTheory.MonObj.mul_one_assoc, CategoryTheory.IsFiltered.sup_exists, CategoryTheory.MonoidalCategory.MonoidalRightAction.comp_actionHomLeft, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition'_assoc, CategoryTheory.NonPreadditiveAbelian.sub_def, CategoryTheory.ShortComplex.Splitting.ofIso_r, CategoryTheory.DifferentialObject.d_squared_assoc, CategoryTheory.conjugateEquiv_adjunction_id, CategoryTheory.Limits.prodComparison_fst_assoc, CategoryTheory.ShortComplex.SnakeInput.Hom.comm₀₁_assoc, inr_coprodIsoPushout_inv, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_π, CategoryTheory.Limits.prod.inl_fst, SSet.stdSimplex.faceSingletonIso_one_hom_comp_ι_eq_δ_assoc, CategoryTheory.Subobject.ofLEMk_comp_ofMkLE_assoc, AlgebraicGeometry.Scheme.ΓSpecIso_naturality_assoc, CategoryTheory.Oplax.OplaxTrans.leftUnitor_hom_as_app, CategoryTheory.GradedObject.Monoidal.leftUnitor_naturality, CategoryTheory.MonObj.mul_assoc_flip_assoc, CategoryTheory.Limits.biproduct.ι_toSubtype_assoc, CategoryTheory.Functor.final_iff_of_isFiltered, AlgebraicGeometry.ExistsHomHomCompEqCompAux.hb, CategoryTheory.coyonedaEquiv_symm_map, HomologicalComplex₂.totalShift₁Iso_hom_naturality, CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id_app_assoc, groupCohomology.cocyclesMap_id_comp, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ_assoc, groupCohomology.isoCocycles₁_inv_comp_iCocycles_assoc, CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_hom_assoc, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom, CategoryTheory.Limits.opCoproductIsoProduct_hom_comp_π_assoc, AlgebraicGeometry.Scheme.Hom.comp_image, CategoryTheory.SmallObject.SuccStruct.ofCocone_map, CategoryTheory.Limits.proj_comp_opProductIsoCoproduct'_hom, CategoryTheory.GradedObject.Monoidal.ιTensorObj₄_eq, CategoryTheory.Functor.cocones_map_app, AlgebraicGeometry.Scheme.appLE_comp_appLE, CategoryTheory.Enriched.FunctorCategory.functorEnriched_comp_id_assoc, CategoryTheory.CommSq.w_assoc, CategoryTheory.ShiftMkCore.assoc_hom_app, CategoryTheory.rightDistributor_hom, ModuleCat.ofHom₂_compr₂, CategoryTheory.Functor.Monoidal.map_leftUnitor_assoc, CochainComplex.mappingConeCompTriangle_mor₃_naturality_assoc, SSet.Truncated.HomotopyCategory.homMk_comp_homMk_assoc, CategoryTheory.Functor.RightExtension.postcomp₁_obj_hom_app, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_map, CategoryTheory.leftAdjointMate_comp, CategoryTheory.eqToHom_trans_assoc, CategoryTheory.Limits.Multicofork.sigma_condition_assoc, ModuleCat.extendScalars_comp_id, CategoryTheory.Limits.colimit.w, CategoryTheory.Functor.OplaxMonoidal.right_unitality_assoc, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app, BddDistLat.comp_apply, HomologicalComplex₂.total.mapAux.d₁_mapMap_assoc, CategoryTheory.SmallObject.ιObj_naturality_assoc, CategoryTheory.Limits.pullbackProdFstIsoProd_hom_snd_assoc, CategoryTheory.Pretriangulated.comp_hom₁, CategoryTheory.Precoherent.pullback, AlgebraicGeometry.Scheme.Hom.resLE_comp_resLE, TopCat.Presheaf.germ_stalkSpecializes, AlgebraicGeometry.Scheme.residue_descResidueField_assoc, CategoryTheory.ProjectiveResolution.liftFOne_zero_comm, CategoryTheory.Functor.FullyFaithful.grpObj_one, CategoryTheory.Enriched.FunctorCategory.functorEnriched_assoc_assoc, CategoryTheory.Functor.commShiftOfLocalization.iso_hom_app_assoc, AlgebraicGeometry.IsLocalAtSource.iff_of_iSup_eq_top, CategoryTheory.Limits.Multifork.pi_condition_assoc, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_hom, CategoryTheory.Limits.SequentialProduct.cone_π_app, CategoryTheory.Functor.biproductComparison_π, PresheafOfModules.freeYonedaEquiv_comp, AlgebraicGeometry.ΓSpec_adjunction_homEquiv_eq, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_assoc, CategoryTheory.ShortComplex.leftRightHomologyComparison'_naturality, CochainComplex.ConnectData.comp_d₀_assoc, AlgebraicGeometry.Scheme.Cover.LocallyDirected.w, Bicategory.Opposite.bicategory_associator_inv_unop2, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_assoc, CategoryTheory.toSheafify_naturality_assoc, AlgebraicTopology.DoldKan.PInfty_f_comp_QInfty_f, CategoryTheory.PreOneHypercover.comp_h₀, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₃, BddDistLat.hom_comp, CategoryTheory.Limits.limit.lift_π_app_assoc, CategoryTheory.Limits.ImageMap.map_ι_assoc, CategoryTheory.NatTrans.app_shift, CategoryTheory.Lax.OplaxTrans.naturality_comp_assoc, CategoryTheory.ShortComplex.LeftHomologyData.homologyπ_comp_homologyIso_hom, CategoryTheory.Functor.leftDerivedNatTrans_fac, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv_assoc, HomologicalComplex₂.d₂_eq', CategoryTheory.Limits.limitRightOpIsoOpColimit_inv_comp_π_assoc, CategoryTheory.Functor.ι_colimitIsoOfIsLeftKanExtension_hom_assoc, CategoryTheory.Functor.homologySequenceδ_naturality_assoc, CategoryTheory.eqToHom_comp_iff, CategoryTheory.Factorisation.Hom.h_π, CategoryTheory.NatTrans.comp_app, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id, CategoryTheory.Limits.Cone.w_assoc, CategoryTheory.LaxFunctor.mapComp_naturality_left_app, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right_assoc, AlgebraicGeometry.Scheme.Hom.isoImage_hom_ι, CategoryTheory.Bicategory.pentagon_inv_inv_hom_hom_inv_assoc, CategoryTheory.cones_map_app_app, CategoryTheory.IsPullback.isoPullback_inv_fst_assoc, AlgebraicGeometry.AffineSpace.SpecIso_inv_over, CategoryTheory.Limits.BinaryBiconeMorphism.winr_assoc, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_hom_assoc, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_hom_comp_ι_assoc, CategoryTheory.MonoidalCategory.associator_inv_naturality_assoc, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp, CategoryTheory.Limits.image.compIso_inv_comp_image_ι_assoc, CategoryTheory.OplaxFunctor.mapComp_id_left_assoc, CategoryTheory.comp_over, CategoryTheory.CartesianMonoidalCategory.lift_fst_comp_snd_comp, CategoryTheory.ShortComplex.Splitting.f_r, CategoryTheory.MorphismProperty.Comma.comp_hom, CompHausLike.LocallyConstant.incl_comap, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality, CategoryTheory.MonoidalClosed.coev_app_comp_pre_app_assoc, CategoryTheory.whiskerRight_ι_colimitCompWhiskeringRightIsoColimitComp_inv, AlgebraicGeometry.Scheme.Hom.toNormalization_fromNormalization, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapCompIso_hom, CategoryTheory.Functor.relativelyRepresentable.w, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₂, AlgCat.hom_comp, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_inv_comp_rightHomologyι, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.toBiprod_fromBiprod, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃'_eq, CategoryTheory.GradedObject.ιMapBifunctor₁₂BifunctorMapObj_eq, SSet.Truncated.comp_app, CategoryTheory.ChosenPullbacksAlong.unit_pullbackComp_hom, SemimoduleCat.ofHom_comp, CategoryTheory.Limits.π_colimitOfIsReflexivePairIsoCoequalizer_inv_assoc, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app_assoc, AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id_assoc, Homotopy.dNext_cochainComplex, CategoryTheory.MonoidalCategory.leftUnitor_inv_naturality_assoc, CategoryTheory.associativity_app, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_precomp, DistLat.comp_apply, CategoryTheory.PreOneHypercover.Homotopy.wr, Homotopy.nullHomotopicMap'_f, CategoryTheory.Bicategory.Prod.swap_mapComp_hom, AlgebraicGeometry.Scheme.toIso_inv_ι, SemimoduleCat.MonoidalCategory.hexagon_reverse, AlgebraicGeometry.SheafedSpace.congr_hom_app, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_right, CategoryTheory.Enriched.FunctorCategory.homEquiv_comp_assoc, CategoryTheory.Dial.rightUnitor_inv_F, quasiIso_iff_comp_right, CategoryTheory.Limits.pullbackSymmetry_inv_comp_snd, CategoryTheory.Pseudofunctor.StrongTrans.Modification.vcomp_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformPrecomposeObjSquare_iso_hom_comp, CategoryTheory.Mathlib.Tactic.MonTauto.associator_hom_comp_tensorHom_tensorHom_comp_assoc, CategoryTheory.Limits.limit.map_pre, AlgebraicGeometry.Scheme.residueFieldCongr_trans_hom, CategoryTheory.CatEnrichedOrdinary.hComp_assoc_heq, CategoryTheory.Iso.inv_hom_id_app_app_app_assoc, CategoryTheory.Functor.LaxMonoidal.μ_whiskerRight_comp_μ, CategoryTheory.NatTrans.IsMonoidal.tensor_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_assoc, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_inv_app_unop_assoc, CategoryTheory.Functor.OplaxMonoidal.δ_comp_δ_whiskerRight, CategoryTheory.Iso.inv_hom_id_app, HomologicalComplex₂.totalFlipIsoX_hom_D₂, CategoryTheory.SingleFunctors.shiftIso_add_hom_app, AlgebraicGeometry.Scheme.Hom.toNormalization_inl_normalizationCoprodIso_hom, CategoryTheory.Arrow.left_hom_inv_right, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_apply_app, SSet.Subcomplex.fromPreimage_ι, AlgebraicGeometry.Scheme.Hom.opensRange_comp_of_isIso, CategoryTheory.ShortComplex.exact_iff_of_forks, CategoryTheory.Sieve.mem_ofArrows_iff, CategoryTheory.OppositeShift.adjunction_counit, CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf_inv_right, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_inv_naturality, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_inv_app, CategoryTheory.shiftFunctorCompIsoId_zero_zero_hom_app, CategoryTheory.Functor.LeftLinear.μₗ_comp_δₗ, CategoryTheory.GradedObject.ι_mapBifunctorComp₂₃MapObjIso_inv, CategoryTheory.ShortComplex.HomotopyEquiv.trans_homotopyInvHomId, CategoryTheory.Functor.PushoutObjObj.inr_ι_assoc, CategoryTheory.epi_iff_surjective_up_to_refinements, CategoryTheory.Limits.image.preComp_ι_assoc, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one, CategoryTheory.MorphismProperty.cancel_left_of_respectsIso, CategoryTheory.Arrow.hom_inv_id_right, CategoryTheory.SimplicialObject.δ_comp_σ_of_le_assoc, CategoryTheory.SimplicialObject.δ_comp_δ, CategoryTheory.obj_μ_inv_app_assoc, AlgebraicGeometry.Scheme.homOfLE_ι_assoc, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.f'_eq, CategoryTheory.MonObj.one_rightUnitor, CategoryTheory.IsCoreflexivePair.common_retraction', CategoryTheory.Limits.imageSubobject_arrow_comp, HomologicalComplex.extend.leftHomologyData.lift_d_comp_eq_zero_iff, CategoryTheory.e_assoc'_assoc, CategoryTheory.Limits.BinaryBicone.inl_snd, CategoryTheory.GrothendieckTopology.Cover.Arrow.base_f, CategoryTheory.Functor.CorepresentableBy.homEquiv_symm_comp, prodIsoPullback_inv_snd_assoc, AlgebraicGeometry.Scheme.residueFieldCongr_fromSpecResidueField_assoc, CategoryTheory.δ_naturalityₗ, AlgebraicGeometry.Scheme.Hom.inr_toNormalization_normalizationCoprodIso_inv_assoc, HomologicalComplex.mapBifunctor₂₃.ι_D₃_assoc, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_assoc, AlgebraicGeometry.Scheme.germ_residue, CategoryTheory.InjectiveResolution.toRightDerivedZero'_comp_iCycles_assoc, CategoryTheory.Limits.ColimitPresentation.comp_hom, CategoryTheory.Mod_.assoc_flip, CategoryTheory.FreeBicategory.mk_associator_inv, CategoryTheory.Functor.PushoutObjObj.hom_ext_iff, CategoryTheory.Limits.Cofan.IsColimit.fac_assoc, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_comp, AlgebraicGeometry.Scheme.Hom.normalizationPullback_snd, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁, CategoryTheory.SmallObject.FunctorObjIndex.w, CategoryTheory.GradedObject.Monoidal.ι_tensorHom_assoc, CategoryTheory.TwoSquare.vComp'_app, SSet.Truncated.HomotopyCategory.homMk_comp_homMk, CommRingCat.isLocalHom_comp, CategoryTheory.Functor.relativelyRepresentable.pullback₃.map_p₃_comp_assoc, CategoryTheory.Bicategory.Adj.comp_l, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_inv_app', CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app_assoc, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_left, AlgebraicGeometry.PresheafedSpace.GlueData.ιInvApp_π, HomologicalComplex.pOpcycles_opcyclesToCycles, CategoryTheory.MonoidalCategory.id_tensor_associator_inv_naturality_assoc, CategoryTheory.ShortComplex.quasiIso_comp, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_left, CategoryTheory.Enriched.FunctorCategory.enrichedComp_π, groupHomology.cyclesIso₀_comp_H0π, HomologicalComplex.homologyIsoSc'_inv_ι_assoc, CategoryTheory.Limits.prod.map_comp_id_assoc, SemimoduleCat.hom_comp, CategoryTheory.ShortComplex.RightHomologyData.pOpcycles_comp_opcyclesIso_hom_assoc, AlgebraicGeometry.Scheme.Hom.opensRange_comp, CategoryTheory.eqToHom_comp_homOfLE_op_assoc, MonCat.hom_comp, AugmentedSimplexCategory.inl_comp_tensorHom_assoc, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_comp_assoc, CategoryTheory.coprod_inl_rightDistrib_hom_assoc, CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ι_assoc, CategoryTheory.Idempotents.Karoubi.comp_p_assoc, SSet.RelativeMorphism.Homotopy.refl_h, AlgebraicGeometry.Scheme.Hom.ι_fromNormalization, CategoryTheory.ConcreteCategory.coe_comp, SimplexCategory.mkOfSucc_δ_eq, CategoryTheory.Bicategory.rightUnitor_comp_assoc, CategoryTheory.HomOrthogonal.matrixDecomposition_symm_apply, CategoryTheory.NonPreadditiveAbelian.lift_map, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_inv, Bimod.Hom.right_act_hom, CategoryTheory.Localization.Preadditive.comp_add_assoc, CategoryTheory.CartesianMonoidalCategory.braiding_inv_snd_assoc, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_inv_eq_germ, CategoryTheory.GrothendieckTopology.liftToPlusObjLimitObj_fac, AlgebraicGeometry.Scheme.Hom.comp_base, CategoryTheory.LaxMonoidalFunctor.comp_hom_assoc, AlgebraicGeometry.exists_finite_imageι_comp_morphismRestrict_of_finite_image_preimage, CategoryTheory.Adjunction.right_triangle_components_assoc, CategoryTheory.Arrow.inv_hom_id_right_assoc, CategoryTheory.ComposableArrows.Precomp.map_comp, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom, CategoryTheory.TransfiniteCompositionOfShape.map_incl, SheafOfModules.map_ιFree_mapFree_hom_assoc, CategoryTheory.Functor.homEquivOfIsRightKanExtension_apply_app, Mathlib.Tactic.Bicategory.evalComp_nil_cons, CategoryTheory.ShortComplex.rightHomology_ext_iff, CategoryTheory.Mon.one_def, CategoryTheory.Limits.combineCocones_pt_map, CategoryTheory.Adjunction.comp_unit, CategoryTheory.ExponentiableMorphism.unit_pushforwardComp_hom, CategoryTheory.Limits.IsLimit.homEquiv_symm_naturality, Homotopy.nullHomotopicMap'_f_of_not_rel_right, CategoryTheory.Bicategory.Adj.leftUnitor_hom_τr, CategoryTheory.Limits.inr_inl_pushoutLeftPushoutInrIso_hom_assoc, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₁, CategoryTheory.Pseudofunctor.mapId'_hom_naturality, CategoryTheory.Retract.retract_assoc, CategoryTheory.toSheafify_plusPlusIsoSheafify_hom_assoc, AlgebraicGeometry.Scheme.IdealSheafData.comap_comp, CategoryTheory.HomOrthogonal.matrixDecompositionAddEquiv_apply, Mathlib.Tactic.Bicategory.evalWhiskerRightAux_of, CategoryTheory.coprodComparison_tensorLeft_braiding_hom, dNext_comp_right, CategoryTheory.Oplax.StrongTrans.categoryStruct_comp_app, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_hom, HomologicalComplex.homotopyCofiber.inlX_desc_f, CategoryTheory.Pseudofunctor.DescentData.comp_hom_assoc, CategoryTheory.Functor.ranCounit_app_whiskerLeft_ranAdjunction_unit_app, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_app, AlgebraicTopology.DoldKan.QInfty_comp_PInfty_assoc, AlgebraicGeometry.instLocallyQuasiFiniteCompScheme, AlgebraicGeometry.Scheme.Hom.map_appLE, AlgebraicGeometry.tilde.map_comp, CategoryTheory.Bicategory.LeftExtension.IsKan.fac, CategoryTheory.ShortComplex.SnakeInput.Hom.comp_f₃, HomologicalComplex.fromOpcycles_d, CategoryTheory.Functor.shiftIso_inv_naturality_assoc, CategoryTheory.conj_eqToHom_iff_heq, SSet.PtSimplex.RelStruct.δ_succ_map, CategoryTheory.Oplax.StrongTrans.categoryStruct_id_naturality, CategoryTheory.DifferentialObject.objEqToHom_d_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_inv_hom_assoc, CategoryTheory.biproduct_ι_comp_leftDistributor_inv, HomologicalComplex.iCycles_d_assoc, CategoryTheory.Iso.conj_comp, CategoryTheory.Iso.unop_inv_hom_id_app_assoc, CategoryTheory.ShortComplex.opcyclesOpIso_hom_toCycles_op, inl_coprodIsoPushout_hom_assoc, CategoryTheory.ShortComplex.rightHomologyι_comp_fromOpcycles, CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ι, MagmaCat.hom_comp, CategoryTheory.kernelCokernelCompSequence.snakeInput_v₂₃_τ₁, CategoryTheory.Functor.LeftExtension.coconeAt_ι_app, CategoryTheory.ShortComplex.RightHomologyMapData.opcyclesMap_eq, AlgebraicGeometry.Scheme.Γevaluation_naturality, CategoryTheory.Limits.coconeOfIsSplitEpi_ι_app, CategoryTheory.CosimplicialObject.δ_naturality, CategoryTheory.Adjunction.unit_app_unit_comp_map_η_assoc, CategoryTheory.ShortComplex.rightHomologyIso_hom_naturality, LightProfinite.proj_comp_transitionMapLE, CategoryTheory.FreeBicategory.lift_mapComp, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₃, CategoryTheory.hom_comp, HomologicalComplex₂.d₁_eq', CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst_assoc, CategoryTheory.Limits.π_comp_colimitUnopIsoOpLimit_inv_assoc, CategoryTheory.Localization.isoOfHom_inv_hom_id_assoc, CategoryTheory.Bicategory.Comonad.comul_counit, CategoryTheory.Limits.kernelFactorThruImage_hom_comp_ι, CategoryTheory.ShortComplex.LeftHomologyData.ofEpiOfIsIsoOfMono_i, CategoryTheory.Adjunction.leftAdjointCompIso_hom_app, groupHomology.inhomogeneousChains.d_eq, CategoryTheory.NatTrans.shift_app_comm_assoc, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse, HomologicalComplex.cyclesMap_i, CategoryTheory.Limits.pullback.condition, CategoryTheory.Over.lift_left, CategoryTheory.Functor.whiskerRight_twice, CategoryTheory.Bicategory.leftZigzagIso_inv, CategoryTheory.Functor.toOplaxFunctor'_mapComp, CategoryTheory.homOfLE_comp_eqToHom_assoc, SheafOfModules.pushforwardNatTrans_app_val_app_apply, HomologicalComplex.truncLE'ToRestriction_naturality, CategoryTheory.IsRegularEpi.w, AlgebraicGeometry.Spec.germ_stalkMapIso_hom, AlgebraicTopology.DoldKan.Γ₂_map_f_app, CategoryTheory.Bicategory.Adjunction.comp_right_triangle_aux, CategoryTheory.Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone_ι_app_eq_sum, AlgebraicGeometry.Proj.homOfLE_toBasicOpenOfGlobalSections_ι, CategoryTheory.MonoidalCategory.MonoidalLeftAction.associator_actionHom, CategoryTheory.NatTrans.shift_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app, CategoryTheory.Limits.pullbackProdSndIsoProd_inv_snd_assoc, CategoryTheory.DifferentialObject.d_squared_apply_assoc, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_naturality_app, CategoryTheory.Limits.prod.diag_map_fst_snd_comp, CategoryTheory.Limits.biproduct.toSubtype_fromSubtype_assoc, CategoryTheory.Limits.biproduct.lift_π, SSet.Truncated.HomotopyCategory.homToNerveMk_comp, CategoryTheory.MorphismProperty.map_eq_iff_precomp, CategoryTheory.MonoidalCategory.id_tensor_comp_tensor_id_assoc, CategoryTheory.Abelian.LeftResolution.π_naturality, CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoCofanPt, CategoryTheory.Under.postAdjunctionRight_counit_app_right, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_counitIso, CategoryTheory.Limits.inr_comp_pushoutObjIso_inv_assoc, CategoryTheory.Functor.ShiftSequence.induced_shiftMap, CategoryTheory.monoidalOfHasFiniteCoproducts.associator_inv, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_app_assoc, CategoryTheory.Limits.biprod.associator_inv_natural, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_comp_fiber, CategoryTheory.Sigma.SigmaHom.assoc, groupHomology.d₁₀_comp_coinvariantsMk_assoc, CategoryTheory.IsHomLift.comp_eqToHom_lift, CategoryTheory.Limits.cokernelCompIsIso_inv, CategoryTheory.Limits.CokernelCofork.map_condition_assoc, CategoryTheory.unitCompPartialBijectiveAux_symm_apply, CategoryTheory.Pretriangulated.TriangleMorphism.comm₂_assoc, CategoryTheory.Limits.inr_comp_pushoutObjIso_hom, AugmentedSimplexCategory.inr_comp_tensorHom_assoc, AlgebraicTopology.DoldKan.decomposition_Q, CategoryTheory.MonoidalCategory.id_whiskerRight_assoc, CategoryTheory.IsPullback.isoPullback_hom_snd, CategoryTheory.MonoidalCategory.id_tensor_associator_naturality_assoc, CategoryTheory.Cat.whiskerLeft_toNatTrans, CategoryTheory.Idempotents.KaroubiKaroubi.p_comm_f, CategoryTheory.Subfunctor.Subpresheaf.equalizer.ι_ι, CategoryTheory.isCardinalFiltered_iff, CategoryTheory.μ_naturality_assoc, CategoryTheory.IsPullback.isoIsPullback_hom_snd_assoc, CategoryTheory.Oplax.StrongTrans.toOplax_naturality, CategoryTheory.Pseudofunctor.mapId'_hom_naturality_assoc, CategoryTheory.CopyDiscardCategory.discard_tensor, CategoryTheory.Limits.Pi.isoLimit_hom_π_assoc, CategoryTheory.Limits.BinaryFan.assocInv_snd, CategoryTheory.shiftFunctorAdd_hom_app_obj_of_induced, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_succ_succ, CategoryTheory.ShortComplex.cyclesMap_i, CategoryTheory.Comma.mapLeftIso_inverse_map_left, CategoryTheory.Dial.tensorHom_comp_tensorHom, CategoryTheory.Limits.biprod.mapBiprod_inv_map_desc, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left_assoc, HomotopicalAlgebra.Precylinder.symm_i, CategoryTheory.Functor.map_shiftFunctorComm, CategoryTheory.OplaxFunctor.mapComp_naturality_right_app_assoc, CategoryTheory.Functor.LaxRightLinear.μᵣ_naturality_left, CategoryTheory.IsPullback.isoIsPullback_inv_fst, CategoryTheory.ShortComplex.SnakeInput.naturality_φ₂_assoc, CategoryTheory.IsUniversalColimit.isPullback_of_isColimit_left, CategoryTheory.Arrow.w_assoc, CategoryTheory.IsFiltered.coeq₃_condition₂, CategoryTheory.Functor.op_commShiftIso_hom_app, CategoryTheory.SmallObject.ιFunctorObj_extension, CategoryTheory.Limits.biproduct.mapBiproduct_hom_desc, AlgebraicGeometry.Scheme.IdealSheafData.subschemeMap_subschemeι_assoc, groupHomology.isoCycles₁_hom_comp_i, SheafOfModules.comp_val, CategoryTheory.StructuredArrow.map_obj_hom, CategoryTheory.leftDistributor_hom_comp_biproduct_π_assoc, CategoryTheory.CostructuredArrow.preEquivalence.inverse_map_left_left, CategoryTheory.CartesianMonoidalCategory.whiskerRight_fst, AlgebraicTopology.DoldKan.σ_comp_P_eq_zero, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_inv_naturality, AlgebraicGeometry.Spec.fromSpecStalk_eq, HomologicalComplex.mapBifunctor₁₂.ι_eq, CategoryTheory.GlueData.cocycle, CategoryTheory.Limits.biprod.map_fst_assoc, CategoryTheory.Functor.PushoutObjObj.inl_ι, CategoryTheory.Limits.pullbackProdFstIsoProd_hom_fst, CategoryTheory.Abelian.Pseudoelement.comp_comp, CategoryTheory.Limits.coprod.symmetry'_assoc, CategoryTheory.Idempotents.FunctorExtension₁.map_app_f, CategoryTheory.Bicategory.Adjunction.homEquiv₁_symm_apply, CochainComplex.HomComplex.Cocycle.equivHomShift_comp_shift, CategoryTheory.Oplax.StrongTrans.Modification.whiskerRight_naturality_assoc, HomologicalComplex.isoHomologyι_hom_inv_id_assoc, HomotopyCategory.homologyFunctor_shiftMap, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over, CategoryTheory.NatTrans.vcomp_eq_comp, CategoryTheory.GradedObject.ιMapBifunctorBifunctor₂₃MapObj_eq, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_inv_hom_id, CategoryTheory.BimonObj.mul_comul, CategoryTheory.Lax.StrongTrans.categoryStruct_comp_naturality, CategoryTheory.Equivalence.mkHom_comp, CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm, CategoryTheory.Bicategory.Adjunction.comp_unit, CategoryTheory.Limits.prodComparison_inv_natural_assoc, CategoryTheory.Subfunctor.to_sheafifyLift, CategoryTheory.Limits.PullbackCone.isoMk_hom_hom, CategoryTheory.MonoidalCategory.whiskerRight_id_assoc, CategoryTheory.Localization.Monoidal.whiskerLeft_comp_assoc, CategoryTheory.Functor.descOfIsLeftKanExtension_fac_app, CategoryTheory.CatCommSq.hInv_iso_hom_app, CategoryTheory.IsMonHom.mul_hom_assoc, CategoryTheory.Comma.mapLeftComp_hom_app_left, CategoryTheory.Comonad.ForgetCreatesLimits'.commuting, CategoryTheory.Limits.coprod.desc_comp_inl_comp_inr, CategoryTheory.Pseudofunctor.comp_mapComp, AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_π, CategoryTheory.MonoidalCategory.DayFunctor.ν_comp_unitDesc, CategoryTheory.δ_naturalityᵣ, TopCat.Presheaf.stalkFunctor_map_germ, CategoryTheory.Limits.SequentialProduct.functorMap_commSq_succ, CategoryTheory.ComposableArrows.mkOfObjOfMapSucc_exists, CategoryTheory.ShortComplex.mapHomologyIso_inv_naturality_assoc, CategoryTheory.Limits.Cofan.IsColimit.fac, CategoryTheory.Bicategory.Prod.swap_mapComp_inv, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_comp_homologyIso_inv, CategoryTheory.Functor.CoreMonoidal.μIso_hom_natural_right_assoc, CategoryTheory.Limits.pullbackProdSndIsoProd_inv_snd, CategoryTheory.Monad.MonadicityInternal.counitCofork_ι_app, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app, CategoryTheory.Limits.Multifork.ofPiFork_ι, CategoryTheory.IsFilteredOrEmpty.cocone_maps, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp, CategoryTheory.Limits.Cofork.IsColimit.homIso_symm_apply, CategoryTheory.Adjunction.Triple.rightToLeft_app_adj₂_unit_app, CategoryTheory.Limits.inr_pushoutLeftPushoutInrIso_hom_assoc, CategoryTheory.ShortComplex.LeftHomologyData.wi_assoc, CategoryTheory.ShortComplex.mapOpcyclesIso_hom_naturality, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality, CategoryTheory.Functor.PullbackObjObj.π_fst_assoc, CategoryTheory.Limits.BinaryBicone.inr_snd_assoc, CategoryTheory.ShortComplex.SnakeInput.Hom.comp_f₂, HomologicalComplex.pOpcyclesIso_inv_hom_id_assoc, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_assoc, CochainComplex.mappingCone.lift_f_snd_v, CategoryTheory.Functor.Initial.extendCone_obj_π_app, CategoryTheory.PreGaloisCategory.PointedGaloisObject.comp_val_assoc, CategoryTheory.CartesianMonoidalCategory.lift_snd_comp_fst_comp, CategoryTheory.NatIso.cancel_natIso_hom_right_assoc, CategoryTheory.Localization.SmallHom.equiv_shift, CategoryTheory.FunctorToTypes.prod.lift_snd, CategoryTheory.Subobject.inf_comp_right_assoc, CategoryTheory.Limits.Fork.condition_assoc, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp, TopCat.Presheaf.germToPullbackStalk_stalkPullbackHom_assoc, CategoryTheory.Limits.opProductIsoCoproduct_inv_comp_lift, CategoryTheory.Functor.IsCocartesian.fac, CommRingCat.ofHom_comp, CategoryTheory.FunctorToTypes.comp, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₁, groupHomology.H0π_comp_H0Iso_hom_assoc, CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_mapComp, groupCohomology.H1π_comp_map, CategoryTheory.Limits.ι_comp_colimitLeftOpIsoUnopLimit_hom_assoc, AlgebraicGeometry.IsAffineOpen.app_basicOpen_eq_away_map, CategoryTheory.ShortComplex.cyclesMap'_i, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv_assoc, HomologicalComplex.XIsoOfEq_hom_comp_XIsoOfEq_inv, AlgebraicGeometry.IsPreimmersion.comp_iff, CategoryTheory.IsIso.comp_isIso', CategoryTheory.Limits.biproduct.ι_toSubtype_subtype, TopModuleCat.hom_comp, CategoryTheory.GrothendieckTopology.OneHypercover.comp_s₀, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.rightUnitor_hom_unit_app, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_inv_app_assoc, CategoryTheory.Limits.HasLimit.isoOfNatIso_hom_π, CategoryTheory.Preadditive.zsmul_comp, HomologicalComplex.truncGE'.homologyι_truncGE'XIsoOpcycles_inv_d, CategoryTheory.MonoidalClosed.curry'_whiskerRight_comp, CategoryTheory.IsHomLift.eqToHom_comp_lift_iff, AlgebraicGeometry.pullbackSpecIso_hom_fst', CategoryTheory.Quotient.comp_right, CategoryTheory.Limits.HasBiproductsOfShape.colimIsoLim_hom_app, AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjι_ι, CategoryTheory.Limits.Wedge.condition_assoc, CategoryTheory.Bicategory.LeftLift.whiskering_obj, groupHomology.cyclesMap_comp, CategoryTheory.Limits.inv_prodComparison_map_snd_assoc, LightCondensed.internallyProjective_iff_tensor_condition', CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_symm_assoc, CategoryTheory.Functor.LaxLeftLinear.μₗ_associativity_assoc, CategoryTheory.Limits.bicone_ι_π_ne, CategoryTheory.Limits.pullbackDiagonalMapIdIso_hom_snd, CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac_assoc, AlgebraicGeometry.IsOpenImmersion.isoOfRangeEq_hom_fac_assoc, CategoryTheory.Factorisation.ι_π, CategoryTheory.ShortComplex.LeftHomologyData.π_comp_leftHomologyIso_inv, CategoryTheory.InducedWideCategory.category_comp_coe, CategoryTheory.Functor.Final.extendCocone_map_hom, SemiNormedGrp.explicitCokernelIso_inv_π, SimplexCategory.δ_comp_σ_succ'_assoc, CategoryTheory.congrArg_mpr_hom_right, HomotopicalAlgebra.Precylinder.LeftHomotopy.postcomp_h, Bimod.Hom.right_act_hom_assoc, CategoryTheory.GrothendieckTopology.Point.presheafFiber_hom_ext_iff, CategoryTheory.Limits.kernelFactorThruImage_inv_comp_ι_assoc, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inl_assoc, CategoryTheory.Bicategory.Prod.snd_mapComp_inv, CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_hom_desc, CategoryTheory.Bicategory.Adj.Bicategory.associator_hom_τl, CategoryTheory.MonoidalCategory.associator_inv_naturality_left, CategoryTheory.NonPreadditiveAbelian.lift_σ, CategoryTheory.GrpObj.ofIso_mul, LightCondensed.comp_val, CategoryTheory.MonoidalClosed.ofEquiv_curry_def, CategoryTheory.Idempotents.app_idem, CategoryTheory.Presieve.BindStruct.fac, TopCat.Presheaf.toPushforwardOfIso_app, CategoryTheory.OrthogonalReflection.iteration_map_succ_surjectivity, AlgebraicGeometry.Scheme.monObjAsOverPullback_one, CategoryTheory.Limits.snd_opProdIsoCoprod_hom_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_obj_map_app, CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_left_assoc, AlgebraicGeometry.IsAffineOpen.ΓSpecIso_hom_fromSpec_app, AlgebraicGeometry.SpecToEquivOfLocalRing_eq_iff, CategoryTheory.Equivalence.changeInverse_unitIso_hom_app, CategoryTheory.Bicategory.Pith.comp₂_iso_inv, CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv, CategoryTheory.Pseudofunctor.map₂_whisker_right_app, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₁, HomologicalComplex.truncGE'Map_f_eq, CategoryTheory.IsIso.inv_hom_id_assoc, CategoryTheory.Oplax.OplaxTrans.Modification.whiskerLeft_naturality, CategoryTheory.RegularEpi.w, CategoryTheory.Bicategory.conjugateEquiv_symm_apply', CategoryTheory.Abelian.PreservesCoimage.iso_inv_π_assoc, CategoryTheory.ShortComplex.p_opcyclesMap'_assoc, CategoryTheory.unitOfTensorIsoUnit_hom_app, CategoryTheory.StructuredArrow.mapIso_inverse_map_left, CategoryTheory.NonPreadditiveAbelian.lift_σ_assoc, CategoryTheory.Limits.imageMonoIsoSource_hom_self_assoc, CategoryTheory.Limits.whiskerLeft_ι_colimitCompWhiskeringLeftIsoCompColimit_inv, CategoryTheory.Comma.mapLeft_obj_hom, CategoryTheory.Functor.Final.ι_colimitIso_hom, CategoryTheory.Iso.eq_inv_comp, CategoryTheory.Limits.coprodComparison_natural_assoc, CategoryTheory.NonPreadditiveAbelian.comp_sub, CategoryTheory.GrpObj.lift_comp_inv_right, CategoryTheory.Adjunction.commShiftIso_inv_app_counit_app, SemimoduleCat.MonoidalCategory.rightUnitor_naturality, Quiver.FreeGroupoid.congr_reverse_comp, CategoryTheory.SimplicialObject.augmentedCechNerve_map_left_app, CategoryTheory.Functor.LaxMonoidal.μ_natural_assoc, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₁, CategoryTheory.Functor.PreOneHypercoverDenseData.sieve₁₀_apply, HomologicalComplex.dFrom_eq, Preord.comp_apply, CochainComplex.mappingConeCompTriangle_mor₂, CategoryTheory.PreOneHypercover.cylinder_p₁, SimplexCategoryGenRel.δ_comp_σ_self_assoc, AlgebraicGeometry.Scheme.Hom.SpecMap_residueFieldMap_fromSpecResidueField, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_mul, TopCat.coe_comp, CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id_assoc, AlgebraicTopology.DoldKan.Q_f_idem_assoc, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d_1_0_assoc, CategoryTheory.Endofunctor.Adjunction.Coalgebra.homEquiv_naturality_str_symm, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompYoneda, AlgebraicGeometry.Scheme.comp_app_assoc, CategoryTheory.Bimon.mul_counit_assoc, CategoryTheory.Limits.BinaryFan.assocInv_fst, HomologicalComplex₂.D₁_totalShift₂XIso_hom, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.Functor.obj_d_f, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom_assoc, CategoryTheory.Functor.Monoidal.lift_μ, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_iso, CategoryTheory.ShortComplex.cyclesOpIso_inv_op_iCycles, CategoryTheory.Limits.pushout_inl_inv_inr_of_right_isIso, CategoryTheory.BasedNatTrans.homCategory_comp, CategoryTheory.Adjunction.Triple.leftToRight_app_obj_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_naturality, CategoryTheory.Limits.PreservesPullback.iso_hom_snd, CategoryTheory.Limits.map_inl_inv_coprodComparison, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_inv_assoc, CategoryTheory.Limits.opCoproductIsoProduct'_hom_comp_proj_assoc, CategoryTheory.shiftFunctorAdd'_assoc_hom_app_assoc, CategoryTheory.CommSq.horiz_comp, AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_fac, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp_assoc, CategoryTheory.Equivalence.congrRight_unitIso_hom_app, CategoryTheory.NatTrans.shift_app_comm, CategoryTheory.Functor.shiftMap_comp_assoc, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_whiskerLeft_assoc, SkyscraperPresheafFunctor.map'_app, CategoryTheory.Functor.limitIsoOfIsRightKanExtension_hom_π, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_assoc, CategoryTheory.Bicategory.whiskerLeft_rightUnitor, AlgebraicGeometry.IsAffineOpen.SpecMap_appLE_fromSpec, CategoryTheory.SemiCartesianMonoidalCategory.fst_def, CategoryTheory.sheafComposeIso_hom_fac_assoc, AlgebraicGeometry.morphismRestrict_app, CategoryTheory.Functor.PullbackObjObj.hom_ext_iff, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, CategoryTheory.Functor.currying_functor_obj_map, AlgebraicGeometry.AffineSpace.comp_homOfVector_assoc, HomotopicalAlgebra.FibrantBrownFactorization.mk'_p, CategoryTheory.Limits.prodComparison_inv_natural, CochainComplex.HomComplex.Cochain.rightShift_v, CategoryTheory.comp_eqToHom_heq, Bimod.whiskerLeft_comp_bimod, AlgebraicGeometry.Scheme.Hom.appLE_comp_appLE, CategoryTheory.Limits.Sigma.ι_reindex_hom_assoc, CategoryTheory.Preadditive.comp_sub_assoc, groupHomology.cyclesMap_comp_cyclesIso₀_hom_assoc, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_assoc, CategoryTheory.ShortComplex.LeftHomologyMapData.cyclesMap_eq, CategoryTheory.Presieve.ofArrows_bind, CategoryTheory.GradedObject.ι_mapMap, CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id_assoc, CategoryTheory.Limits.π_comp_cokernelIsoOfEq_inv, CochainComplex.mappingConeCompTriangleh_comm₁, CategoryTheory.Functor.ShiftSequence.induced_isoShiftZero_hom_app_obj, AlgebraicTopology.DoldKan.Q_f_naturality, SSet.ι₁_fst_assoc, CategoryTheory.sheafComposeIso_inv_fac, HomologicalComplex.mapBifunctor₁₂.d₁_eq, AlgebraicGeometry.LocallyRingedSpace.toStalk_stalkMap_toΓSpec, CategoryTheory.Limits.Sigma.ι_isoColimit_inv_assoc, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app_assoc, CategoryTheory.WithInitial.pseudofunctor_mapComp, CategoryTheory.Limits.prod.map_swap, CategoryTheory.IsPullback.isoIsPullback_hom_snd, groupHomology.lsingle_comp_chainsMap_f_assoc, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality, CategoryTheory.Iso.eHomCongr_inv_comp, CategoryTheory.InjectiveResolution.homotopyEquiv_inv_ι_assoc, AlgebraicGeometry.Scheme.Hom.toImage_app, HomologicalComplex₂.D₂_totalShift₂XIso_hom, CategoryTheory.MonoidalCategory.inv_hom_whiskerRight'_assoc, SimplexCategoryGenRel.standardσ_comp_standardσ, CategoryTheory.whisker_eq, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_fst, CategoryTheory.MonoidalClosed.curry_natural_right, HomologicalComplex.d_comp_XIsoOfEq_inv, AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk, CategoryTheory.NatTrans.exchange, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι_assoc, CategoryTheory.PreOneHypercover.cylinder_p₂, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app_assoc, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_inv_comp_π_assoc, CategoryTheory.Pseudofunctor.map₂_left_unitor_app_assoc, SimplexCategory.Truncated.δ₂_one_comp_σ₂_zero_assoc, CategoryTheory.Under.inv_right_hom_right_assoc, CategoryTheory.CatEnriched.hComp_comp, CategoryTheory.Adjunction.leftAdjointIdIso_inv_app, CategoryTheory.Bifunctor.map_comp_id, MonCat.Colimits.cocone_naturality, AlgebraicGeometry.AffineTargetMorphismProperty.cancel_left_of_respectsIso, AlgebraicTopology.DoldKan.QInfty_f_comp_PInfty_f_assoc, CategoryTheory.Limits.ι_colimitLimitToLimitColimit_π_assoc, CategoryTheory.Functor.map_shiftFunctorCompIsoId_inv_app, PartOrd.hom_comp, CategoryTheory.Adjunction.leftAdjointUniq_trans, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_assoc, CategoryTheory.Equivalence.ε_comp_map_ε_assoc, AlgebraicGeometry.PresheafedSpace.stalkMap.stalkSpecializes_stalkMap_assoc, AlgebraicGeometry.IsImmersion.isImmersion_iff_exists_of_quasiCompact, CategoryTheory.Pseudofunctor.map₂_right_unitor_app_assoc, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_inv, CategoryTheory.Grp_Class.div_comp, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv_def, CategoryTheory.Pseudofunctor.map₂_right_unitor_app, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_obj, AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_naturality_app, CategoryTheory.Limits.Sigma.ι_π_eq_id_assoc, groupCohomology.isoShortComplexH1_inv, CategoryTheory.NatTrans.unop_whiskerRight_assoc, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec, CategoryTheory.LaxFunctor.comp_mapComp, CategoryTheory.IsPushout.inr_isoPushout_hom, AlgebraicTopology.DoldKan.identity_N₂_objectwise, CategoryTheory.Iso.hom_inv_id_app_app_app_assoc, CategoryTheory.ObjectProperty.ind_iff_exists, CategoryTheory.ComposableArrows.naturality'_assoc, CategoryTheory.conjugateEquiv_comp, ModuleCat.image.fac, CategoryTheory.Localization.Monoidal.μ_inv_natural_left, CategoryTheory.ModObj.mul_smul, CategoryTheory.MonoidalCategory.leftUnitor_whiskerRight, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict_assoc, BddOrd.coe_comp, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_invApp, CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan_inj_assoc, SemiNormedGrp.ofHom_comp, CategoryTheory.MonoidalCategory.leftUnitor_inv_tensor_id_assoc, CategoryTheory.Mat_.comp_def, CategoryTheory.cancel_epi, CategoryTheory.BraidedCategory.braiding_inv_naturality_right, CategoryTheory.CostructuredArrow.mapNatIso_functor_map_right, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.hf, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_obj_map_app, HomologicalComplex.restrictionToTruncGE'_f_eq_iso_hom_iso_inv, CategoryTheory.Presieve.FamilyOfElements.map_comp, AlgebraicGeometry.PresheafedSpace.comp_c, CategoryTheory.CartesianMonoidalCategory.rightUnitor_inv_fst_assoc, CategoryTheory.Limits.Multicofork.π_comp_hom, CategoryTheory.PrelaxFunctor.map₂_hom_inv_isIso_assoc, CategoryTheory.Functor.HomObj.naturality, CategoryTheory.Biprod.inl_ofComponents, CategoryTheory.Grpd.hom_to_functor, CategoryTheory.ι_preservesColimitIso_inv, CategoryTheory.Functor.mapCommMon_id_one, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom''_assoc, CoalgCat.toCoalgHom_comp, CategoryTheory.Limits.biproduct.map_lift_mapBiprod, CategoryTheory.MonoidalCategory.MonoidalRightAction.action_actionHomRight, CategoryTheory.Limits.biproduct.map_eq, CategoryTheory.Preadditive.comp_sub, CategoryTheory.NatTrans.leftDerived_comp, SimplexCategory.Truncated.δ₂_two_comp_σ₂_one, CategoryTheory.leftDistributor_ext₂_right_iff, CategoryTheory.yonedaEquiv_symm_map, CategoryTheory.Limits.ι_reflexiveCoequalizerIsoCoequalizer_hom_assoc, CategoryTheory.tensorLeftHomEquiv_whiskerRight_comp_evaluation, groupHomology.cyclesIso₀_inv_comp_iCycles_assoc, CategoryTheory.Factorisation.Hom.comp_h, AlgebraicGeometry.Scheme.Hom.appLE_map, CategoryTheory.Limits.CoconeMorphism.inv_hom_id_assoc, CategoryTheory.ShortComplex.SnakeInput.comp_f₁, CategoryTheory.Limits.BinaryBicone.inr_fst, CategoryTheory.NatTrans.whiskerRight_app_tensor_app_assoc, CategoryTheory.obj_ε_app, CategoryTheory.Limits.HasImageMap.comp, ModuleCat.FilteredColimits.ι_colimitDesc_assoc, CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtensionObjIsoColimit_hom_assoc, DerivedCategory.HomologySequence.δ_comp_assoc, AlgebraicGeometry.HasRingHomProperty.iff_of_source_openCover, CategoryTheory.EnrichedCategory.assoc, AlgebraicGeometry.Scheme.Hom.isoImage_hom_ι_assoc, CategoryTheory.ShortComplex.cyclesOpIso_inv_naturality_assoc, CategoryTheory.ShortComplex.LeftHomologyMapData.commi, CategoryTheory.GradedObject.Monoidal.triangle, CategoryTheory.CartesianMonoidalCategory.homEquivToProd_apply, CategoryTheory.eHomWhiskerLeft_comp_assoc, CategoryTheory.Adjunction.comp_counit_app_assoc, CategoryTheory.liftedLimitMapsToOriginal_hom_π, Bimod.RightUnitorBimod.hom_inv_id, HomologicalComplex.stupidTruncMap_stupidTruncXIso_hom, CategoryTheory.kernelCokernelCompSequence.inl_π, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_snd_assoc, SimplexCategoryGenRel.δ_comp_δ, HomotopicalAlgebra.Precylinder.i₁_π, SSet.horn.ι_ι_assoc, CategoryTheory.MorphismProperty.LeftFraction.map_ofInv_hom_id, CategoryTheory.Functor.LaxBraided.braided_assoc, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_assoc, FinPartOrd.hom_comp, CategoryTheory.CostructuredArrow.mapIso_inverse_obj_hom, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.rightUnitor_naturality, CategoryTheory.Mathlib.Tactic.MonTauto.associator_hom_comp_tensorHom_tensorHom_comp, HomologicalComplex.biprod_lift_snd_f_assoc, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_inv, CategoryTheory.Iso.hom_comp_eq_id, CategoryTheory.Comonad.left_counit_assoc, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc, CategoryTheory.IsIso.out, Rep.coinvariantsAdjunction_homEquiv_apply_hom, CategoryTheory.CostructuredArrow.projectQuotient_factors, CategoryTheory.PreOneHypercover.Hom.comp_h₁, CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_snd_fst, CategoryTheory.Sieve.toFunctor_app_coe, CategoryTheory.NatTrans.naturality_1, HomologicalComplex.mapBifunctor₁₂.d₃_eq, CategoryTheory.Limits.coprod.desc_comp, DerivedCategory.HomologySequence.δ_comp, AlgebraicGeometry.Scheme.inv_base_hom_base_assoc, HomologicalComplex.biprod_inr_fst_f_assoc, CategoryTheory.PrelaxFunctor.map₂_inv_hom, CategoryTheory.Limits.ι_comp_colimitLeftOpIsoUnopLimit_hom, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv_assoc, CategoryTheory.MonoidalClosed.comp_id, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τr, CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_snd_snd_assoc, CategoryTheory.Limits.kernelSubobject_arrow_comp, CategoryTheory.CostructuredArrow.mkPrecomp_comp, CategoryTheory.Functor.mapCommGrp_obj_grp_mul, ModuleCat.hom_comp, CategoryTheory.ExactPairing.coevaluation_evaluation_assoc, CategoryTheory.uliftCoyonedaEquiv_symm_map, CategoryTheory.Over.prodLeftIsoPullback_hom_fst, CategoryTheory.Functor.OplaxMonoidal.comp_δ, CategoryTheory.Iso.inv_hom_id_triangle_hom₃, CategoryTheory.GrothendieckTopology.overMapPullback_assoc, AlgebraicGeometry.StructureSheaf.toOpen_res, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_fst_snd, CategoryTheory.Limits.Pi.isoLimit_inv_π_assoc, CategoryTheory.Bicategory.Prod.sectR_mapId_hom, CategoryTheory.ShortComplex.comp_homologyMap_comp, CategoryTheory.Over.associator_hom_left_fst_assoc, CategoryTheory.ExponentiableMorphism.pushforwardId_hom_counit, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_hom_eq_germ_assoc, Homotopy.extend.hom_eq, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d_assoc, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π, AlgebraicGeometry.Scheme.PartialMap.compHom_hom, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.tensorHom_eq, CategoryTheory.GradedObject.ι_mapBifunctorComp₁₂MapObjIso_hom, AlgebraicGeometry.Scheme.Pullback.openCoverOfLeft_f, CategoryTheory.MonoidalCategory.whisker_assoc, HomologicalComplex.isoHomologyπ_hom_inv_id_assoc, CategoryTheory.OplaxFunctor.mapComp_naturality_right, AlgebraicGeometry.IsSeparated.comp_iff, CategoryTheory.Bicategory.Strict.leftUnitor_eqToIso, CategoryTheory.Functor.Monoidal.map_rightUnitor, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec_assoc, AlgebraicGeometry.Scheme.IsLocallyDirected.homOfLE_tAux_assoc, AlgebraicGeometry.SheafedSpace.congr_app, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_apply_coe, CategoryTheory.MonoidalCategory.associator_naturality_left_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.inv_hom_actionHomLeft_assoc, DistLat.hom_comp, HomologicalComplex.mapBifunctor₁₂.ι_D₂, CategoryTheory.ModObj.mul_smul', CategoryTheory.yonedaYonedaColimit_app_inv, CategoryTheory.Limits.Cone.extensions_app, CategoryTheory.yonedaEquiv_symm_naturality_left, CategoryTheory.Limits.pullbackConeEquivBinaryFan_unitIso, CategoryTheory.Limits.inl_opProdIsoCoprod_inv, CategoryTheory.OplaxFunctor.mapComp_naturality_left_app_assoc, CategoryTheory.Adjunction.left_triangle_components_assoc, CategoryTheory.Functor.RightLinear.δᵣ_comp_μᵣ_assoc, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_symm_apply, CategoryTheory.CosimplicialObject.equivalenceLeftToRight_right, CategoryTheory.Limits.snd_opProdIsoCoprod_hom, CategoryTheory.imageUnopOp_inv_comp_op_factorThruImage, CategoryTheory.Presheaf.comp_isLocallyInjective_iff, AlgebraicGeometry.UniversallyOpen.instCompScheme, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_spec, SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁_hom_f_f, CategoryTheory.Over.isMonHom_pullbackFst_id_right, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_inv_π, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand', CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_inv_assoc, CategoryTheory.Functor.Monoidal.whiskerRight_δ_μ_assoc, CategoryTheory.PreZeroHypercover.isoMk_inv_h₀, CategoryTheory.Limits.prod.leftUnitor_inv_naturality, TopModuleCat.kerι_comp, HomologicalComplex.homotopyCofiber.d_sndX_assoc, CategoryTheory.ShortComplex.f'_cyclesMap'_assoc, CategoryTheory.MorphismProperty.ind_iff_exists, CategoryTheory.Limits.biprod.inr_snd, CategoryTheory.Functor.OplaxMonoidal.lift_δ_assoc, CategoryTheory.Endofunctor.Coalgebra.Terminal.right_inv', CategoryTheory.Cat.whiskerRight_app, CategoryTheory.Limits.pullbackComparison_comp_fst_assoc, CategoryTheory.EnrichedFunctor.map_id_assoc, CategoryTheory.Limits.Cotrident.app_one_assoc, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_left, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_hom_comp_ι, CategoryTheory.δ_μ_app_assoc, CategoryTheory.ShortComplex.HomologyData.comm, CategoryTheory.Bicategory.conjugateEquiv_whiskerLeft, AlgebraicGeometry.pullbackSpecIso_hom_snd, CategoryTheory.ShortComplex.opcyclesMap'_comp, CategoryTheory.Functor.CoreMonoidal.left_unitality_assoc, AlgebraicGeometry.Scheme.Hom.comp_appTop_assoc, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop_assoc, HomologicalComplex.mapBifunctor₁₂.ι_mapBifunctor₁₂Desc_assoc, SimplexCategory.σ_comp_σ, AlgebraicGeometry.IsAffineOpen.fromSpec_app_of_le, CategoryTheory.IsHomLift.lift_comp_id, CategoryTheory.ShortComplex.p_fromOpcycles_assoc, CategoryTheory.Hom.mulEquivCongrRight_apply, CategoryTheory.Functor.shiftIso_hom_app_comp_shiftMap_of_add_eq_zero, CategoryTheory.Limits.ι_comp_sigmaComparison_assoc, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.fromBiprod_δ, CategoryTheory.mateEquiv_counit, dNext_nat, CategoryTheory.right_comp_retraction_assoc, SimplexCategoryGenRel.standardσ_cons_assoc, CategoryTheory.GrothendieckTopology.toPlus_plusLift, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₁, CategoryTheory.Limits.HasLimit.isoOfEquivalence_inv_π, CategoryTheory.Functor.CommShift.OfComp.map_iso_inv_app, CategoryTheory.Iso.trans_inv, AlgebraicTopology.DoldKan.PInfty_comp_PInftyToNormalizedMooreComplex_assoc, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, CategoryTheory.Square.category_comp_τ₄, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_hom_comp_homologyIso_inv_assoc, CategoryTheory.CatCenter.smul_iso_hom_eq, CategoryTheory.rightAdjointMate_comp, CategoryTheory.LaxFunctor.map₂_associator_app, CategoryTheory.Limits.coneOfIsSplitMono_pt, CategoryTheory.FreeBicategory.mk_right_unitor_hom, CategoryTheory.Bicategory.LeftExtension.whiskering_obj, CategoryTheory.cancel_mono_assoc_iff, CategoryTheory.MonoidalCategory.inv_hom_whiskerRight', CategoryTheory.RelCat.Hom.rel_comp, CategoryTheory.yonedaEquiv_symm_naturality_right, SheafOfModules.pushforwardSections_unitHomEquiv, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app, CategoryTheory.CartesianMonoidalCategory.tensorμ_fst, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₁₂_assoc, AlgebraicGeometry.Scheme.residueFieldCongr_trans_hom_assoc, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁, CategoryTheory.Limits.limit.pre_pre, CategoryTheory.constantSheafAdj_counit_app, CategoryTheory.MonoidalCategory.tensor_id_comp_id_tensor, CategoryTheory.Grothendieck.congr, CategoryTheory.EffectiveEpiFamily.transitive_of_finite, CategoryTheory.Limits.prod.leftUnitor_hom_naturality, CategoryTheory.GradedObject.ι_mapBifunctorRightUnitor_hom_apply_assoc, AlgebraicGeometry.IsDominant.comp_iff, AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_comp_iff, AlgebraicGeometry.instIsDominantCompScheme, AlgebraicGeometry.Scheme.Hom.app_appIso_inv, CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id_assoc, CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero_assoc, CategoryTheory.Functor.Monoidal.δ_μ_assoc, CategoryTheory.GrpObj.ofIso_one, groupCohomology.cochainsMap_id_comp_assoc, HomologicalComplex.truncGEMap_comp, Mathlib.Tactic.Bicategory.structuralIsoOfExpr_whiskerRight, CategoryTheory.MorphismProperty.LeftFraction.map_comp_map_s_assoc, CategoryTheory.eqToHom_naturality, CategoryTheory.Limits.π_comp_cokernelIsoOfEq_hom, CategoryTheory.section_comp_right_assoc, CategoryTheory.ShortComplex.LeftHomologyMapData.commπ_assoc, CategoryTheory.Localization.SmallShiftedHom.equiv_apply, CategoryTheory.Sigma.SigmaHom.comp_id, HomologicalComplex.pOpcycles_restrictionOpcyclesIso_inv_assoc, CategoryTheory.IsPullback.paste_horiz, CategoryTheory.Limits.biproduct.ι_π_ne_assoc, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_inv, CategoryTheory.Limits.BinaryFan.assoc_fst, CategoryTheory.ShortComplex.LeftHomologyData.τ₁_ofEpiOfIsIsoOfMono_f', HomologicalComplex.Hom.comm, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_app_assoc, CategoryTheory.Limits.CatCospanTransform.triangle, HomologicalComplex.homologyOp_hom_naturality, CategoryTheory.Enriched.FunctorCategory.enrichedId_π, CategoryTheory.Adjunction.map_η_comp_η, TopCat.Presheaf.stalkSpecializes_stalkPushforward_assoc, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberCompIso_hom_app_assoc, CategoryTheory.Limits.coprod.map_swap_assoc, CategoryTheory.Functor.OplaxMonoidal.right_unitality, CategoryTheory.Limits.pullbackSymmetry_hom_comp_fst, AlgebraicGeometry.IsIntegralHom.instCompScheme, HomotopicalAlgebra.Cylinder.symm_i_assoc, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_assoc, CategoryTheory.Equivalence.mkHom_comp_assoc, CategoryTheory.Idempotents.KaroubiKaroubi.p_comm_f_assoc, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.ShortComplex.leftRightHomologyComparison'_compatibility, Mathlib.Tactic.Monoidal.evalComp_nil_cons, CategoryTheory.ShortComplex.fromOpcycles_op_cyclesOpIso_inv, CategoryTheory.Limits.hasEqualizer_comp_mono, AlgebraicTopology.DoldKan.P_idem_assoc, AlgebraicTopology.DoldKan.PInfty_comp_QInfty_assoc, CategoryTheory.StrictPseudofunctor.id_mapComp_inv, CategoryTheory.Limits.colimCompFlipIsoWhiskerColim_inv_app_app, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp_symm, TopCat.Presheaf.stalkPushforward.comp, AlgebraicGeometry.LocallyRingedSpace.stalkSpecializes_stalkMap_assoc, inl_coprodIsoPushout_inv_assoc, groupCohomology.map_H0Iso_hom_f_assoc, CategoryTheory.GrothendieckTopology.overMapPullback_id_comp, CategoryTheory.Bicategory.comp_whiskerLeft_symm_assoc, AlgebraicGeometry.Scheme.Hom.normalizationObjIso_hom_val, CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_comp_assoc, CategoryTheory.Functor.OplaxRightLinear.δᵣ_naturality_right, CategoryTheory.Functor.essImage.liftFunctor_map, CategoryTheory.Functor.commShift₂_comm_assoc, CategoryTheory.ComposableArrows.Mk₁.map_comp, HomologicalComplex.homologyIsoSc'_hom_ι, AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInfty_assoc, CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac, AlgebraicGeometry.pointEquivClosedPoint_symm_apply_coe, CategoryTheory.Limits.inr_inl_pushoutAssoc_hom_assoc, CategoryTheory.RetractArrow.i_w_assoc, CategoryTheory.Limits.limit.lift_map_assoc, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_aux_mul, CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_right, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv_assoc, CategoryTheory.Limits.MultispanIndex.ι_sndSigmaMap_assoc, CategoryTheory.OverPresheafAux.OverArrows.map_val, HomotopicalAlgebra.FibrantObject.HoCat.resolutionMap_fac_assoc, CategoryTheory.Pretriangulated.TriangleMorphism.comm₂, CategoryTheory.Pretriangulated.TriangleMorphism.comp_hom₃, CategoryTheory.Functor.whiskerRight_left, CategoryTheory.Limits.biproduct.toSubtype_π, CategoryTheory.Iso.inv_hom_id_app_assoc, CategoryTheory.Functor.limitIsoOfIsRightKanExtension_inv_π, ModuleCat.kernelIsoKer_inv_kernel_ι, CategoryTheory.MorphismProperty.HasLeftCalculusOfFractions.exists_leftFraction, CategoryTheory.PreOneHypercover.forkOfIsColimit_ι_map_inj, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one_assoc, CommAlgCat.ofHom_comp, CategoryTheory.Limits.biproduct.whiskerEquiv_hom_eq_lift, CategoryTheory.IsPushout.inl_isoIsPushout_hom, CategoryTheory.MonObj.one_mul, HomologicalComplex.extendHomologyIso_inv_homologyι_assoc, AlgebraicGeometry.Scheme.Cover.pullbackHom_map_assoc, AlgebraicGeometry.Scheme.Cover.gluedCoverT'_fst_fst_assoc, CategoryTheory.PreservesFiniteLimitsOfFlat.fac, AlgebraicGeometry.tilde.map_id_assoc, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app_assoc, CategoryTheory.CostructuredArrow.unop_left_comp_underlyingIso_hom_unop, HomologicalComplex.pOpcycles_extendOpcyclesIso_inv_assoc, CategoryTheory.Subfunctor.equalizer.condition_assoc, CategoryTheory.Functor.FullyFaithful.hasShift.map_zero_inv_app, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_snd, CategoryTheory.Limits.WalkingMultispan.Hom.comp_eq_comp, CategoryTheory.rightAdjointMate_comp_evaluation, AlgebraicTopology.DoldKan.N₂_map_f_f, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app_assoc, CategoryTheory.Adjunction.leftAdjointIdIso_hom_app, CategoryTheory.Limits.pullbackAssoc_inv_snd, CategoryTheory.ObjectProperty.isoInv_hom_id_hom_assoc, LinOrd.comp_apply, CategoryTheory.InjectiveResolution.rightDerivedToHomotopyCategory_app_eq, CategoryTheory.coevaluation_comp_rightAdjointMate_assoc, CategoryTheory.CostructuredArrow.mapIso_inverse_map_right, CategoryTheory.Limits.FormalCoproduct.mapPower_comp_assoc, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_fst, CategoryTheory.NatTrans.leftOp_comp, HomologicalComplex.dFrom_comp_xNextIso, CategoryTheory.CommSq.fac_left, SSet.KanComplex.hornFilling, CategoryTheory.GradedObject.categoryOfGradedObjects_comp, LinOrd.coe_comp, HomologicalComplex₂.totalAux.ιMapObj_D₁_assoc, HomotopicalAlgebra.PrepathObject.RightHomotopy.h₁, CategoryTheory.Limits.Cocones.precompose_map_hom, CategoryTheory.Idempotents.Karoubi.decompId_i_naturality, CategoryTheory.uliftYonedaEquiv_symm_map_assoc, CategoryTheory.comp_dite, CategoryTheory.Functor.Monoidal.transport_ε_assoc, HomologicalComplex.mapBifunctor₁₂.d₂_eq, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_comp, CategoryTheory.Abelian.app_hom, groupCohomology.eq_d₁₂_comp_inv_assoc, HasFibers.fiber_factorization, CategoryTheory.Functor.Monoidal.transport_δ_assoc, AlgebraicGeometry.PresheafedSpace.map_comp_c_app, CategoryTheory.Iso.map_inv_hom_id_eval_assoc, CategoryTheory.Limits.prod.lift_snd_assoc, SSet.PtSimplex.RelStruct.δ_map_of_gt, HomologicalComplex.pOpcycles_opcyclesToCycles_assoc, CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inr, CategoryTheory.BraidedCategory.braiding_inv_naturality, HomologicalComplex.opcyclesOpIso_hom_toCycles_op_assoc, CategoryTheory.Limits.inr_pushoutLeftPushoutInrIso_hom, AlgebraicGeometry.IsPreimmersion.comp, HomologicalComplex.singleObjCyclesSelfIso_hom, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_neg, CategoryTheory.SingleFunctors.shiftIso_add'_inv_app, CategoryTheory.Sieve.generate_apply, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right_assoc, CategoryTheory.Functor.IsEventuallyConstantTo.isoMap_inv_hom_id_assoc, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_snd', CategoryTheory.Limits.pushoutCoconeOfRightIso_inr, HomologicalComplex.iCyclesIso_hom_inv_id_assoc, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoColimitUncurryWhiskeringLeft₂_hom, CategoryTheory.RegularEpi.w_assoc, CategoryTheory.Functor.relativelyRepresentable.pullback₃.snd_fst'_eq_p₁_assoc, CategoryTheory.Functor.LaxMonoidal.μ_natural, PartOrd.ofHom_comp, CategoryTheory.Limits.whiskerLeft_ι_colimitCompWhiskeringLeftIsoCompColimit_inv_assoc, CategoryTheory.Limits.prod.diag_map_assoc, HomologicalComplex.restriction_d_eq_assoc, CategoryTheory.Monad.left_unit_assoc, HomologicalComplex.pOpcyclesIso_hom_inv_id, Bimod.AssociatorBimod.hom_right_act_hom', AlgebraicGeometry.LocallyRingedSpace.stalkMap_comp, CategoryTheory.Bicategory.leftUnitor_comp, CategoryTheory.Limits.pullbackObjIso_inv_comp_snd, CategoryTheory.ExponentiableMorphism.coev_ev, CategoryTheory.MonObj.mul_rightUnitor, CategoryTheory.Limits.limit.lift_π, CategoryTheory.MonoidalCategory.tensor_hom_inv_id', CategoryTheory.algebraToUnder_map, SimplexCategory.eq_comp_δ_of_not_surjective, CategoryTheory.BicategoricalCoherence.assoc'_iso, CategoryTheory.Limits.pullbackAssoc_inv_fst_fst_assoc, CategoryTheory.Limits.IsColimit.fac_assoc, HomologicalComplex₂.d_comm_assoc, CategoryTheory.LocalizerMorphism.RightResolution.Hom.comm_assoc, CommBialgCat.hom_comp, AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_inv_app, CategoryTheory.Bicategory.LeftExtension.w, CategoryTheory.Mod_.comp_hom, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι, CategoryTheory.Lax.OplaxTrans.vComp_naturality_id, HomotopicalAlgebra.PrepathObject.RightHomotopy.h₁_assoc, CategoryTheory.Comonad.adj_unit, CategoryTheory.MonoidalCategory.tensorδ_tensorμ_assoc, AlgebraicGeometry.StructureSheaf.algebraMap_pushforward_stalk, SimplexCategory.Truncated.Hom.tr_comp'_assoc, CategoryTheory.FinitaryPreExtensive.isPullback_sigmaDesc, CategoryTheory.Limits.Cones.extendComp_hom_hom, CategoryTheory.Adjunction.map_ε_comp_counit_app_unit, CategoryTheory.SmallObject.πObj_naturality, CategoryTheory.kernelCokernelCompSequence.φ_snd, CategoryTheory.SingleFunctors.hom_inv_id_hom_app, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id, CategoryTheory.PreOneHypercover.p₂_sigmaOfIsColimit, AlgebraicTopology.DoldKan.P_f_naturality, CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_right, Mathlib.Tactic.Monoidal.evalHorizontalCompAux_of, CategoryTheory.Limits.coprod.inl_snd_assoc, CategoryTheory.sheafifyMap_sheafifyLift_assoc, CategoryTheory.Cat.associator_hom_toNatTrans, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimIso_aux, CategoryTheory.Limits.FormalCoproduct.coproductIsoSelf_hom_φ, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_invApp, CategoryTheory.Limits.Multifork.hom_comp_ι_assoc, AlgebraicGeometry.IsZariskiLocalAtSource.comp, CategoryTheory.ComonObj.comul_assoc_flip_assoc, SimplicialObject.Split.cofan_inj_naturality_symm, finGaloisGroupMap.map_comp, CategoryTheory.ShortComplex.rightHomologyι_naturality, CategoryTheory.Limits.LimitPresentation.w_assoc, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_hom, HomotopicalAlgebra.Precylinder.trans_i₁, CategoryTheory.MonoidalCategory.MonoidalLeftAction.hom_inv_actionHomLeft, CategoryTheory.LaxFunctor.mapComp_naturality_left, CategoryTheory.obj_η_app, CategoryTheory.LaxFunctor.mapComp_assoc_left_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.hom_inv_actionHomLeft', CategoryTheory.Bicategory.LeftLift.whiskerOfIdCompIsoSelf_inv_right, CategoryTheory.ChosenPullbacksAlong.pullbackComp_hom_counit_assoc, inr_coprodIsoPushout_inv_assoc, CategoryTheory.Functor.id_mapMon_one, CochainComplex.mappingCone.lift_f, AlgebraicGeometry.Scheme.stalkClosedPointTo_comp, Rep.barComplex.d_comp_diagonalSuccIsoFree_inv_eq, CategoryTheory.NatTrans.Coequifibered.comp, CategoryTheory.ComposableArrows.IsComplex.zero, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_rightUnitor, HomologicalComplex.XIsoOfEq_hom_naturality, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_map, CategoryTheory.Limits.cokernelBiproductFromSubtypeIso_inv, HomologicalComplex.homotopyCofiber.inrX_sndX, CategoryTheory.CartesianMonoidalCategory.lift_rightUnitor_hom, Bimod.LeftUnitorBimod.hom_inv_id, CategoryTheory.Bicategory.associatorNatIsoMiddle_inv_app, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_hom_assoc, CategoryTheory.instIsSplitEpiComp, CategoryTheory.HopfObj.antipode_right, CategoryTheory.ComposableArrows.IsComplex.cokerToKer_fac, CategoryTheory.Limits.pullback_fst_map_snd_isPullback, HomologicalComplex₂.totalAux.d₁_eq', AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_appLE, CategoryTheory.Functor.LaxRightLinear.μᵣ_unitality_inv, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ, CategoryTheory.Limits.map_π_preserves_coequalizer_inv, CategoryTheory.ShiftMkCore.zero_add_inv_app, CategoryTheory.MonoidalCategory.pentagon_inv_hom_assoc, CategoryTheory.Limits.pushout.condition_assoc, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π, CategoryTheory.Limits.colimit.isoColimitCocone_ι_hom, CategoryTheory.CostructuredArrow.mapIso_inverse_map_left, UniformSpaceCat.extension_comp_hom, CategoryTheory.Limits.hasCokernel_epi_comp, CategoryTheory.Monad.Algebra.comp_f, HomologicalComplex.Hom.comm_to_assoc, CategoryTheory.Subobject.underlying_arrow, CategoryTheory.Limits.Multiequalizer.ιPi_π_assoc, CategoryTheory.MonObj.mul_one_hom, CategoryTheory.GrothendieckTopology.uliftYoneda_obj_val_map_down, CategoryTheory.GlueData.t'_comp_eq_pullbackSymmetry, CategoryTheory.Limits.inv_prodComparison_map_snd, CategoryTheory.pullbackShiftFunctorAdd'_inv_app, CategoryTheory.Iso.hom_inv_id_triangle_hom₁_assoc, CategoryTheory.ShortComplex.leftRightHomologyComparison_fac_assoc, CategoryTheory.Pseudofunctor.map₂_whisker_right_assoc, CategoryTheory.StructuredArrow.IsUniversal.fac_assoc, CategoryTheory.Limits.kernelCompMono_inv, CategoryTheory.OverPresheafAux.map_mkPrecomp_eqToHom, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_app_π, CategoryTheory.Limits.end_.condition_assoc, CategoryTheory.Limits.map_inl_inv_coprodComparison_assoc, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_limit_map_assoc, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.Functor.shiftIso_hom_naturality, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃'_eq_assoc, CategoryTheory.KleisliCat.comp_def, HomologicalComplex.cylinder.ι₁_desc, SSet.horn.ι_ι, CategoryTheory.Sheaf.ΓRes_naturality, CategoryTheory.Monad.Algebra.unit, CategoryTheory.CostructuredArrow.map₂_obj_hom, CategoryTheory.Bimon.toMon_Comon_ofMon_Comon_obj_mul, SimplicialObject.Splitting.cofan_inj_comp_app_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_eq, CategoryTheory.Bimon.compatibility, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTrans_map_f, HomologicalComplex.opcyclesToCycles_iCycles, AddCommMonCat.hom_comp, AlgebraicGeometry.Scheme.residueFieldMap_comp, SheafOfModules.pushforwardNatIso_hom, CategoryTheory.GradedObject.Monoidal.leftUnitor_naturality_assoc, CategoryTheory.Functor.Monoidal.ε_η_assoc, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app_assoc, HomologicalComplex.ι_mapBifunctorFlipIso_hom_assoc, CategoryTheory.TwistShiftData.shiftFunctor_map, CategoryTheory.Comonad.beckCoalgebraFork_π_app, HomologicalComplex.extendSingleIso_hom_f, CategoryTheory.ShortComplex.homologyπ_comp_asIsoHomologyπ_inv, CategoryTheory.GrothendieckTopology.diagramNatTrans_comp, CategoryTheory.TwistShiftData.shiftFunctorZero_inv_app, Action.Hom.comm, ProfiniteAddGrp.hom_comp, CategoryTheory.CartesianMonoidalCategory.whiskerRight_fst_assoc, CategoryTheory.Limits.prod.inr_fst, HomotopicalAlgebra.instFibrationCompOfIsStableUnderCompositionFibrations, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp_hom_app_f, CategoryTheory.Adjunction.homEquiv_naturality_right, HomologicalComplex₂.total.hom_ext_iff, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd_assoc, HomologicalComplex.XIsoOfEq_inv_comp_XIsoOfEq_inv_assoc, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst_assoc, CategoryTheory.GradedObject.single_map_singleObjApplyIso_hom_assoc, CategoryTheory.GrpObj.zpow_comp_assoc, CategoryTheory.Limits.BinaryBiconeMorphism.wsnd_assoc, CategoryTheory.eComp_op_eq, CategoryTheory.Adjunction.unit_comp_map_eq_iff, AlgebraicGeometry.Scheme.IdealSheafData.subschemeMap_subschemeι, HomotopicalAlgebra.AttachCells.ofArrowIso_g₁, CategoryTheory.Functor.Monoidal.map_rightUnitor_inv_assoc, CategoryTheory.Limits.pushout_inr_inv_inl_of_right_isIso, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_assoc, AlgebraicGeometry.Scheme.comp_coeBase, AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_eq_id, CategoryTheory.braiding_inv_tensorUnit_left, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_inv_iso_hom, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π_assoc, HomologicalComplex.d_eqToHom, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_obj_map_app, CategoryTheory.BraidedCategory.braiding_tensor_right_inv_assoc, CategoryTheory.Functor.OplaxMonoidal.δ_natural_right_assoc, CategoryTheory.Bicategory.prod_rightUnitor_hom_snd, CategoryTheory.MonoidalCategory.pentagon_assoc, CategoryTheory.sheafifyLift_id_toSheafify_assoc, CategoryTheory.Bicategory.pentagon_hom_hom_inv_hom_hom, CategoryTheory.Bicategory.conjugateEquiv_symm_apply, CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_snd_assoc, AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalk, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk_assoc, CategoryTheory.Bicategory.prod_associator_hom_snd, AlgebraicGeometry.LocallyRingedSpace.iso_hom_base_inv_base, Action.comp_hom_assoc, groupCohomology.isoShortComplexH2_inv, CochainComplex.πTruncGE_naturality_assoc, CategoryTheory.Bicategory.Adjunction.right_triangle, CategoryTheory.shiftFunctorCompIsoId_zero_zero_inv_app, CategoryTheory.Comon.comp_hom', CategoryTheory.Bicategory.triangle_assoc_comp_left_inv, TopCat.hom_comp, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerRight_naturality, CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_inv_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_inv_app'_assoc, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_inv, CategoryTheory.Enriched.FunctorCategory.functorEnriched_assoc, groupCohomology.map_id_comp_H0Iso_hom_assoc, HomologicalComplex.biprod_inl_snd_f, CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse_assoc, AlgebraicGeometry.localRingHom_comp_stalkIso, CategoryTheory.GlueData.ι_gluedIso_hom_assoc, CategoryTheory.DinatTrans.dinaturality, AlgebraicGeometry.IsAffineOpen.toSpecΓ_isoSpec_inv_assoc, DerivedCategory.left_fac_of_isStrictlyGE, CategoryTheory.Functor.LaxMonoidal.left_unitality_inv, CategoryTheory.PreOneHypercover.Hom.w₁₁_assoc, AlgebraicGeometry.IsOpenImmersion.isoOfRangeEq_inv_fac, CategoryTheory.Functor.relativelyRepresentable.symmetry_snd, CategoryTheory.Limits.pullbackAssoc_hom_fst_assoc, CategoryTheory.Adjunction.shift_unit_app_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionHom, groupCohomology.isoCocycles₂_hom_comp_i_assoc, CategoryTheory.Limits.IsImage.fac_lift_assoc, CochainComplex.mappingCone.inl_v_fst_v_assoc, AlgebraicGeometry.Scheme.Pullback.openCoverOfLeftRight_X, CategoryTheory.Limits.inl_pushoutRightPushoutInlIso_inv_assoc, CategoryTheory.Bimon.comp_hom', CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₂_W, CategoryTheory.Equivalence.counitInv_naturality_assoc, CategoryTheory.Limits.pullbackDiagonalMapIdIso_hom_fst, CategoryTheory.Comma.colimitAuxiliaryCocone_ι_app, CategoryTheory.Arrow.comp_right, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_point, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map_assoc, CategoryTheory.monoidalOfHasFiniteProducts.associator_hom_fst, CategoryTheory.Oplax.LaxTrans.comp_naturality, CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLift, CategoryTheory.Localization.Monoidal.associator_naturality₃_assoc, CategoryTheory.Functor.isRightKanExtension_iff_postcomp₁, CategoryTheory.Preadditive.comp_add_assoc, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂, CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_fst_assoc, CategoryTheory.curryingIso_hom_toFunctor_map_app, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_fst, HomologicalComplex.comp_f_assoc, CategoryTheory.Oplax.OplaxTrans.Modification.naturality, CategoryTheory.Quotient.comp_mk, CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatTrans_comp, CategoryTheory.ShortComplex.toCycles_naturality, HomotopicalAlgebra.Precylinder.trans_i₀, CategoryTheory.IsPullback.isoPullback_hom_fst_assoc, CategoryTheory.BicategoricalCoherence.right_iso, MagmaCat.comp_apply, CategoryTheory.Sheaf.sheafifyCocone_ι_app_val, CategoryTheory.Localization.Monoidal.rightUnitor_hom_app, CategoryTheory.SingleFunctors.inv_hom_id_hom, CategoryTheory.CartesianMonoidalCategory.braiding_hom_snd, CategoryTheory.Bicategory.Equivalence.right_triangle_hom, CategoryTheory.Functor.ι_colimitIsoColimitGrothendieck_inv, CategoryTheory.Endofunctor.Algebra.Initial.left_inv', CategoryTheory.SimplicialObject.δ_comp_σ_succ_assoc, AlgebraicGeometry.Scheme.Hom.inv_app, CategoryTheory.Limits.pullbackProdFstIsoProd_hom_snd, CategoryTheory.MonObj.comp_pow_assoc, CategoryTheory.Functor.homologySequenceδ_comp, CategoryTheory.StructuredArrow.IsUniversal.fac, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app', AlgebraicGeometry.Scheme.localRingHom_comp_stalkIso, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_app, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop, AlgebraicGeometry.Scheme.Hom.isoOpensRange_inv_comp, CategoryTheory.ProjectiveResolution.cochainComplex_d_assoc, HomologicalComplex.g_shortComplexTruncLEX₃ToTruncGE_assoc, CategoryTheory.Functor.ShiftSequence.induced_shiftMap_assoc, CategoryTheory.Limits.map_ι_comp_inv_sigmaComparison, CategoryTheory.Functor.relativelyRepresentable.toPullbackTerminal, CategoryTheory.MonoidalCategory.associator_conjugation, CategoryTheory.CosimplicialObject.comp_left, CategoryTheory.MonoidalCategory.associator_inv_conjugation_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_inv, CategoryTheory.MonoidalCategory.DayConvolution.whiskerRight_comp_unit_app, CategoryTheory.Adjunction.commShiftIso_hom_app_counit_app_shift, CategoryTheory.MorphismProperty.Over.pullbackComp_left_fst_fst, CategoryTheory.GrpObj.inv_comp_inv, CategoryTheory.LaxFunctor.mapComp_assoc_right_app_assoc, CategoryTheory.ShortComplex.opcyclesOpIso_inv_naturality_assoc, CategoryTheory.GlueData.mapGlueData_t', CategoryTheory.Limits.inv_prodComparison_map_fst_assoc, HomologicalComplex.rightUnitor'_inv_comm, CategoryTheory.Iso.conj_apply, Mathlib.Tactic.Monoidal.evalWhiskerRightAux_of, CategoryTheory.Bicategory.associatorNatIsoRight_inv_app, CategoryTheory.Limits.prod.comp_lift_assoc, CategoryTheory.Limits.lim_μ_π, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.convolutionUnitApp_eq, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right, CategoryTheory.MonoidalCategory.whiskerRight_tensor_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app, AlgebraicGeometry.Scheme.Cover.pullbackHom_map, CategoryTheory.Sieve.pushforward_apply_comp, ComplexShape.Embedding.homRestrict_comp_extendMap, CategoryTheory.Groupoid.vertexGroup_mul, CategoryTheory.ShortComplex.homologyι_comp_asIsoHomologyι_inv_assoc, CategoryTheory.BicategoricalCoherence.whiskerLeft_iso, CategoryTheory.Limits.kernelSubobjectMap_arrow, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_inv_π_assoc, CategoryTheory.Over.associator_hom_left_snd_snd, CategoryTheory.Subfunctor.equalizer.ι_ι, SSet.PtSimplex.MulStruct.δ_succ_castSucc_map_assoc, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom_assoc, CategoryTheory.MonoidalCategory.hom_inv_id_tensor_assoc, CategoryTheory.Over.associator_inv_left_snd_assoc, GrpCat.hom_comp, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₁_assoc, CategoryTheory.Functor.inr_biprodComparison'_assoc, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π_assoc, CategoryTheory.GrpObj.right_inv_assoc, HomotopicalAlgebra.FibrantBrownFactorization.i_r, CategoryTheory.Bimon.toMon_Comon_ofMon_Comon_obj_one, CategoryTheory.Bicategory.leftUnitor_comp_inv_assoc, AlgebraicGeometry.Scheme.Hom.Spec_map_residueFieldMap_fromSpecResidueField, CategoryTheory.Functor.map_braiding, AlgebraicTopology.DoldKan.hσ'_naturality, AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_naturality_assoc, CategoryTheory.Bicategory.leftUnitor_whiskerRight_assoc, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_two_assoc, CategoryTheory.Limits.MultispanIndex.inj_fstSigmaMapOfIsColimit, CategoryTheory.Limits.sigmaComparison_map_desc, SemimoduleCat.comp_apply, CategoryTheory.NatTrans.naturality_assoc, CategoryTheory.Limits.prod.map_fst, CategoryTheory.Localization.Monoidal.tensor_comp, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_isoPointwiseLeftKanExtension_hom, CategoryTheory.Limits.kernelForkBiproductToSubtype_isLimit, CategoryTheory.NatIso.cancel_natIso_hom_left, CategoryTheory.Comma.mapRightIso_inverse_map_left, CategoryTheory.IsSplitEqualizer.ι_leftRetraction_assoc, CategoryTheory.ShortComplex.SnakeInput.w₁₃, CategoryTheory.Injective.factors, CategoryTheory.eqToHom_iso_hom_naturality, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app_assoc, groupHomology.d₂₁_comp_d₁₀_assoc, CategoryTheory.Functor.RightLinear.μᵣ_comp_δᵣ_assoc, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.firstMap_app_app_app, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.lift_map, CategoryTheory.Limits.pullbackDiagonalMapIso.inv_snd_snd, CategoryTheory.ShortComplex.HomotopyEquiv.refl_homotopyInvHomId, Bimod.whiskerRight_comp_bimod, CategoryTheory.MonoidalClosed.id_comp, CategoryTheory.Bicategory.leftUnitor_inv_congr, CategoryTheory.Functor.LaxMonoidal.left_unitality_inv_assoc, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.PreOneHypercover.p₂_sigmaOfIsColimit_assoc, CategoryTheory.Limits.limitUnopIsoUnopColimit_inv_comp_π, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_assoc, groupCohomology.eq_d₀₁_comp_inv_assoc, AlgebraicGeometry.Scheme.Pullback.Triplet.Spec_map_tensorInl_fromSpecResidueField, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst, CategoryTheory.Bicategory.Adj.forget₁_mapComp, CategoryTheory.SingleFunctors.shiftIso_add'_hom_app, CategoryTheory.Under.w_assoc, SemiRingCat.ofHom_comp, CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_hom, CategoryTheory.Limits.image.factor_map, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc, CategoryTheory.Limits.Trident.IsLimit.homIso_natural, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence, CategoryTheory.StructuredArrow.w_assoc, HomologicalComplex.dFrom_comp_xNextIsoSelf_assoc, CategoryTheory.Limits.Sigma.ι_comp_map', CategoryTheory.Bicategory.rightUnitor_hom_congr, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapComp_inv, CategoryTheory.Preadditive.sum_comp', CategoryTheory.Arrow.hom_inv_id_left_assoc, HomologicalComplex.singleObjHomologySelfIso_inv_homologyι, GrpCat.comp_apply, groupHomology.coinvariantsMk_comp_H0Iso_inv_assoc, HomologicalComplex.mapBifunctorAssociatorX_hom_D₁_assoc, AlgebraicTopology.DoldKan.HigherFacesVanish.induction, AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInfty, CategoryTheory.GrothendieckTopology.plusMap_comp, CategoryTheory.StructuredArrow.mapNatIso_functor_map_left, CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp_assoc, CategoryTheory.Limits.Types.binaryCoproductIso_inl_comp_hom, AlgebraicGeometry.LocallyRingedSpace.comp_c_app, CategoryTheory.WithInitial.down_comp, HomologicalComplex₂.D₁_D₂, CategoryTheory.IsHomLift.isoOfIsoLift_inv_hom_id, CategoryTheory.Limits.imageSubobject_arrow', HomotopicalAlgebra.Precylinder.inl_i, CategoryTheory.OverPresheafAux.YonedaCollection.map₂_fst, CategoryTheory.Limits.Types.Image.lift_fac, CategoryTheory.GradedObject.ι_mapBifunctorLeftUnitor_hom_apply_assoc, CategoryTheory.GrothendieckTopology.Cover.Arrow.middle_spec, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitIso_inv_naturality, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd_assoc, CategoryTheory.SmallObject.SuccStruct.Iteration.mapObj_trans, CategoryTheory.Functor.mapDerivedCategoryFactorsh_hom_app, CategoryTheory.OplaxFunctor.mapComp_naturality_right_app, CategoryTheory.ShortComplex.Homotopy.compLeft_h₁, CategoryTheory.Limits.colimit.ι_inv_pre_assoc, CategoryTheory.Limits.HasZeroMorphisms.comp_zero, CategoryTheory.Adjunction.Localization.η_app, CategoryTheory.Subpresheaf.to_sheafifyLift, CategoryTheory.StructuredArrow.map₂_obj_hom, CategoryTheory.SimplicialThickening.SimplicialCategory.id_comp, CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id, CategoryTheory.Limits.HasBiproductsOfShape.colimIsoLim_inv_app, CategoryTheory.ShortComplex.opcyclesIsoX₂_hom_inv_id, CategoryTheory.Limits.Pi.map_π, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_hom_app_unop, CategoryTheory.Sieve.toUliftFunctor_app_down_coe, CategoryTheory.NatIso.cancel_natIso_inv_left, CategoryTheory.kernelCokernelCompSequence.inr_φ_fst, CategoryTheory.Limits.FormalCoproduct.mapPower_powerMap_assoc, AlgebraicGeometry.Scheme.stalkMap_germ, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_assoc, CategoryTheory.Linear.rightComp_apply, CategoryTheory.Join.mapWhiskerLeft_comp, CategoryTheory.CechNerveTerminalFrom.wideCospan.limitIsoPi_hom_comp_pi, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.lift_map_assoc, Semigrp.coe_comp, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberToSpecResidueField_assoc, CategoryTheory.Bimon.Mon_Class.tensorObj.mul_def, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃'_associator_hom_assoc, CategoryTheory.Functor.Monoidal.whiskerLeft_η_ε_assoc, CategoryTheory.IsCofiltered.inf_exists, CategoryTheory.Localization.Monoidal.associator_naturality₁, HomologicalComplex.biprod_inl_desc_f_assoc, CategoryTheory.Functor.mapDifferentialObject_map_f, AlgebraicGeometry.Scheme.Spec.residue_residueFieldIso_hom, CategoryTheory.ProjectiveResolution.fromLeftDerivedZero_eq, CategoryTheory.Limits.biprod.hom_ext_iff, CategoryTheory.InjectiveResolution.Hom.ι_comp_hom, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapId_inv, CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit, CategoryTheory.Limits.CatCospanTransform.comp_whiskerLeft, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_ι, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_inv_assoc, CategoryTheory.HopfObj.antipode_counit_assoc, CategoryTheory.LocalizerMorphism.smallShiftedHomMap_mk₀, CategoryTheory.Presieve.isSheafFor_ofArrows_comp_iff, CategoryTheory.left_comp_retraction_assoc, CategoryTheory.Functor.lanUnit_app_app_lanAdjunction_counit_app_app_assoc, CategoryTheory.ShortComplex.Homotopy.h₀_f, Bicategory.Opposite.op2_associator_hom, SimplicialObject.Splitting.cofan_inj_eq_assoc, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_hom, CategoryTheory.Limits.wideEqualizer.hom_ext_iff, CategoryTheory.BraidedCategory.braiding_naturality_right_assoc, groupCohomology.isoCocycles₁_hom_comp_i_assoc, CategoryTheory.InjectiveResolution.descFOne_zero_comm, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_appTop, CategoryTheory.Cat.FreeRefl.quotientFunctor_map_cons, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_germ_assoc, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_map_right, CategoryTheory.GrothendieckTopology.uliftYoneda_map_val_app_down, CategoryTheory.Limits.wideEqualizer.condition, CategoryTheory.Abelian.DoldKan.comparisonN_inv_app_f, CategoryTheory.MonoidalCategory.id_whiskerLeft_symm, groupHomology.π_comp_H1Iso_inv_assoc, CategoryTheory.Functor.LeftLinear.δₗ_comp_μₗ_assoc, CategoryTheory.right_unitality_app, CategoryTheory.Abelian.FunctorCategory.imageObjIso_inv, AlgebraicGeometry.IsImmersion.comp_iff, CategoryTheory.Limits.Cones.postcomposeComp_hom_app_hom, CategoryTheory.Enriched.FunctorCategory.functorEnriched_comp_id, CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono'_p, SSet.Truncated.HomotopyCategory.homToNerveMk_comp_assoc, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_inv_τr, CategoryTheory.CatEnriched.hComp_id, CategoryTheory.HasLiftingProperty.of_comp_right, CategoryTheory.Limits.equalizer.hom_ext_iff, CategoryTheory.Equivalence.adjointify_η_ε, TopCat.Presheaf.stalkFunctor_map_germ_assoc, CategoryTheory.Limits.Cocone.extensions_app, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_map_app, CategoryTheory.MonoidalCategory.tensor_right_unitality_assoc, CategoryTheory.LaxFunctor.mapComp_assoc_left_app_assoc, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_hom, CategoryTheory.Adjunction.homEquiv_naturality_left, HomologicalComplex.singleObjOpcyclesSelfIso_hom_assoc, HomologicalComplex.mapBifunctor.d₁_eq, CategoryTheory.Limits.biprod.inr_map_assoc, CategoryTheory.Limits.ColimitPresentation.bind_ι_app, CategoryTheory.Limits.hasPullbackHorizPaste, CategoryTheory.Oplax.StrongTrans.homCategory_comp_as_app, CategoryTheory.MonoidalCategory.pentagon, CategoryTheory.Bicategory.rightZigzagIso_hom, HomologicalComplex.homologyMap_comp_assoc, CategoryTheory.LaxFunctor.id_mapComp, CategoryTheory.Equivalence.inverse_counitInv_comp, CategoryTheory.MorphismProperty.LeftFraction.Localization.Q_map_comp_Qinv, CategoryTheory.instEffectiveEpiFamilyComp, SemimoduleCat.MonoidalCategory.pentagon, CategoryTheory.Functor.OplaxMonoidal.left_unitality_hom_assoc, CategoryTheory.PreOneHypercover.Homotopy.wr_assoc, CategoryTheory.Preadditive.sub_comp, CategoryTheory.Functor.Monoidal.whiskerLeft_app_snd_assoc, CategoryTheory.GradedObject.Monoidal.ι_tensorHom, AlgebraicGeometry.IsOpenImmersion.comp_lift, CategoryTheory.Limits.coprod.symmetry', HomotopicalAlgebra.PrepathObject.ι_p₁, CategoryTheory.Functor.FullyFaithful.hasShift.map_zero_hom_app, CategoryTheory.Limits.MonoFactorisation.isoComp_I, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality'_assoc, CategoryTheory.Limits.kernelSubobject_arrow', CategoryTheory.Cat.leftUnitor_inv_app, CategoryTheory.η_ε_app, CategoryTheory.Functor.leftKanExtensionIsoFiberwiseColimit_inv_app, CategoryTheory.ShortComplex.leftRightHomologyComparison'_fac_assoc, CategoryTheory.CartesianMonoidalCategory.whiskerLeft_fst_assoc, CategoryTheory.Bicategory.associator_inv_naturality_middle_assoc, CategoryTheory.biproduct_ι_comp_leftDistributor_inv_assoc, CategoryTheory.shiftFunctorAdd_assoc_inv_app, AlgebraicGeometry.IsOpenImmersion.lift_fac, HomologicalComplex.singleObjHomologySelfIso_hom_singleObjHomologySelfIso_inv, CategoryTheory.MorphismProperty.Comma.Hom.comp_right, CategoryTheory.LaxFunctor.map₂_leftUnitor_app, CategoryTheory.Limits.Cones.postcompose_map_hom, CategoryTheory.Skeleton.comp_hom_assoc, AlgebraicGeometry.pullbackSpecIso_hom_fst_assoc, CategoryTheory.Adjunction.left_triangle_components, CategoryTheory.Bicategory.rightUnitor_comp_inv_assoc, CategoryTheory.op_comp_unop, CategoryTheory.Limits.inl_pushoutZeroZeroIso_hom, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₂_assoc, CategoryTheory.Equivalence.unit_app_tensor_comp_inverse_map_δ_functor, CategoryTheory.Lax.OplaxTrans.naturality_naturality_assoc, CategoryTheory.Functor.RightExtension.postcompose₂ObjMkIso_hom_left_app, CategoryTheory.Endofunctor.Coalgebra.comp_f, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂_assoc, CategoryTheory.Limits.opCoproductIsoProduct_inv_comp_ι, CategoryTheory.Limits.Cotrident.IsColimit.homIso_apply_coe, HomologicalComplex.cylinder.ι₀_desc_assoc, HomologicalComplex₂.totalFlipIsoX_hom_D₁_assoc, CategoryTheory.MorphismProperty.isColocal_iff, UniformSpaceCat.hom_comp, AlgebraicGeometry.Scheme.Hom.fromNormalization_app, groupHomology.π_map, groupHomology.mapCycles₁_comp_i_assoc, CategoryTheory.Limits.cokernelEpiComp_hom, CategoryTheory.Bicategory.InducedBicategory.bicategory_leftUnitor_hom_hom, HomotopicalAlgebra.PrepathObject.ι_p₀_assoc, CategoryTheory.Limits.Cocones.whiskeringEquivalence_counitIso, CategoryTheory.Iso.map_hom_inv_id_eval_app, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_hom_app, CategoryTheory.Pseudofunctor.Grothendieck.categoryStruct_comp_fiber, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHom_comp, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_assoc, CategoryTheory.GrothendieckTopology.Cover.Arrow.Relation.w, CategoryTheory.Preadditive.neg_comp_assoc, AlgebraicGeometry.Scheme.stalkSpecializes_stalkMap_assoc, CategoryTheory.eqToHom_trans, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right, AlgebraicGeometry.Scheme.Modules.pseudofunctor_associativity, CategoryTheory.Mon.tensor_one, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'_assoc, CategoryTheory.MonoidalCategory.tensor_whiskerLeft_symm, CategoryTheory.NatTrans.CommShiftCore.app_shift_assoc, CategoryTheory.Limits.biprod.lift_desc, CategoryTheory.Limits.biprod.braid_natural_assoc, PresheafOfModules.map_comp_assoc, CategoryTheory.ShortComplex.homologyIsoImageICyclesCompPOpcycles_ι_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.inv_hom_actionHomLeft, CategoryTheory.mono_comp_iff_of_isIso, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app, CategoryTheory.Arrow.arrow_mk_eqToHom_comp, CategoryTheory.Functor.Monoidal.μ_δ, CategoryTheory.Limits.biprod.associator_inv, SimplexCategory.δ_comp_σ_succ, CategoryTheory.Equalizer.Presieve.Arrows.w, Bicategory.Opposite.bicategory_rightUnitor_hom_unop2, CategoryTheory.Comma.mapLeftComp_hom_app_right, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_μ_assoc, HomologicalComplex.isoHomologyι_inv_hom_id_assoc, CategoryTheory.Functor.obj.Δ_def, HomologicalComplex.singleObjOpcyclesSelfIso_hom_naturality, CategoryTheory.Limits.ι_colimitOfIsReflexivePairIsoCoequalizer_hom_assoc, CategoryTheory.Limits.CategoricalPullback.comp_snd_assoc, CategoryTheory.Limits.colimit.pre_eq, CategoryTheory.shiftFunctorAdd'_assoc_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.iso_hom_naturality, CategoryTheory.Functor.biproductComparison'_comp_biproductComparison_assoc, CategoryTheory.Over.whiskerLeft_left_snd, CategoryTheory.Limits.inr_inr_pushoutAssoc_inv, CategoryTheory.MonoidalCategory.tensor_hom_inv_id, CategoryTheory.Localization.Preadditive.add_comp_assoc, CategoryTheory.eqToHom_naturality_assoc, CategoryTheory.Functor.OplaxMonoidal.right_unitality_hom_assoc, CategoryTheory.Groupoid.comp_inv, CochainComplex.mappingCone.lift_f_snd_v_assoc, CategoryTheory.ShortComplex.RightHomologyMapData.commι_assoc, CategoryTheory.Functor.rightDerived_fac, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberCompIso_hom_app, CategoryTheory.Limits.Types.coproductIso_ι_comp_hom, CategoryTheory.μ_naturalityₗ_assoc, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_inv_π_π_assoc, CategoryTheory.Precoverage.ZeroHypercover.comp_h₀, AlgebraicTopology.DoldKan.Compatibility.υ_inv_app, HomotopicalAlgebra.PathObject.trans_p₁, CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_three, SSet.Truncated.Edge.CompStruct.homotopyCategory₂_fac, CategoryTheory.Over.w_assoc, CategoryTheory.Comma.mapRight_map_right, CochainComplex.mappingCone.mapHomologicalComplexXIso'_inv, CategoryTheory.SingleFunctors.postcomp_shiftIso_hom_app, CategoryTheory.Limits.CoconeMorphism.map_w, HomologicalComplex.extendHomologyIso_hom_homologyι, CategoryTheory.Limits.prod.lift_fst_comp_snd_comp, CategoryTheory.Functor.IsStronglyCocartesian.map_self, CochainComplex.cm5b, CategoryTheory.Bicategory.Strict.associator_eqToIso, CategoryTheory.StructuredArrow.homMk'_mk_id, CategoryTheory.Linear.smul_comp, CategoryTheory.MorphismProperty.cancel_right_of_respectsIso, CategoryTheory.CostructuredArrow.IsUniversal.fac_assoc, TopCat.GlueData.preimage_image_eq_image', CategoryTheory.e_assoc, CategoryTheory.Equivalence.unit_inverse_comp_assoc, Rep.FiniteCyclicGroup.resolution.π_f, CategoryTheory.Subfunctor.range_comp_le, CategoryTheory.FunctorToTypes.binaryProductIso_hom_comp_fst, SemimoduleCat.MonoidalCategory.braiding_naturality_left, CategoryTheory.Limits.MulticospanIndex.fstPiMap_π, CategoryTheory.MonoidalCategory.associator_inv_naturality_middle, CategoryTheory.Adjunction.Triple.whiskerLeft_leftToRight, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.comp_fst_app, CategoryTheory.leftDistributor_inv_comp_biproduct_π, CategoryTheory.SimplicialObject.equivalenceLeftToRight_left_app, CategoryTheory.Limits.inr_comp_pushoutSymmetry_hom, CategoryTheory.Functor.inl_biprodComparison'_assoc, CategoryTheory.Over.liftCocone_pt, AlgebraicGeometry.Scheme.Pullback.Triplet.SpecMap_tensorInl_fromSpecResidueField, HomotopicalAlgebra.CofibrantBrownFactorization.mk'_i, CategoryTheory.GradedObject.mapBifunctorRightUnitor_inv_naturality, CategoryTheory.Functor.eventualRange_eq_iff, CategoryTheory.Functor.comp_homologySequenceδ_assoc, HomologicalComplex.homotopyCofiber.d_fstX_assoc, AlgebraicGeometry.IsAffineOpen.toSpecΓ_fromSpec, CategoryTheory.Limits.biproduct.ι_map, CategoryTheory.Limits.initial.to_comp, CategoryTheory.ShortComplex.SnakeInput.Hom.comp_f₀, SimplexCategoryGenRel.δ_comp_σ_succ_assoc, CategoryTheory.Deterministic.copy_natural, CategoryTheory.Functor.OplaxLeftLinear.δₗ_associativity_inv_assoc, CategoryTheory.kernelCokernelCompSequence.snakeInput_L₃_X₂, CategoryTheory.InjectiveResolution.rightDerived_app_eq, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_app_app_germToPullbackStalk, CategoryTheory.kernelCokernelCompSequence.instMonoι, CategoryTheory.Limits.diagonal_pullback_fst, CategoryTheory.Cat.whiskerLeft_app, CategoryTheory.OplaxFunctor.mapComp'_eq_mapComp, AlgebraicGeometry.Scheme.PartialMap.fromSpecStalkOfMem_toPartialMap, CategoryTheory.InjectiveResolution.Hom.ι'_comp_hom', CategoryTheory.Limits.coprod.map_inl_inr_codiag_assoc, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_comp, CategoryTheory.Bicategory.RightLift.w, CategoryTheory.ShortComplex.cyclesMap_comp_assoc, CategoryTheory.Limits.limit.lift_extend, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_left, CategoryTheory.PreservesImage.inv_comp_image_ι_map_assoc, CategoryTheory.CartesianMonoidalCategory.lift_whiskerLeft_assoc, CategoryTheory.ShortComplex.mapLeftHomologyIso_inv_naturality, CategoryTheory.ObjectProperty.isoInv_hom_id_hom, HomotopicalAlgebra.weakEquivalence_precomp_iff, CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_hom, CategoryTheory.ShortComplex.p_opcyclesMap, CategoryTheory.Functor.partialRightAdjointHomEquiv_map_comp, CategoryTheory.Functor.CommShift.isoAdd'_inv_app, CategoryTheory.Adjunction.derivedε_fac_app, CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt', CategoryTheory.Localization.associator_hom_app_app_app, CategoryTheory.Bicategory.triangle_assoc, CategoryTheory.Limits.inr_coprodZeroIso_hom, CategoryTheory.Functor.CommShift.OfComp.map_iso_hom_app, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_ι_inv_assoc, CategoryTheory.Functor.CommShift.OfComp.map_iso_inv_app_assoc, CategoryTheory.Functor.CommShift.isoZero'_hom_app, CategoryTheory.Bicategory.leftUnitorNatIso_inv_app, CategoryTheory.Equivalence.congrRight_counitIso_inv_app, CategoryTheory.Under.w, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst_assoc, CategoryTheory.down_comp, CategoryTheory.Equivalence.counit_naturality, CategoryTheory.Pseudofunctor.CoGrothendieck.Hom.ext_iff, CategoryTheory.HomRel.IsStableUnderPostcomp.comp_right, AugmentedSimplexCategory.tensorHom_comp_tensorHom, CategoryTheory.Localization.Monoidal.map_hexagon_forward_assoc, CategoryTheory.HopfObj.one_antipode_assoc, CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_fst, CategoryTheory.Limits.colimit.ι_desc_app, SheafOfModules.Presentation.map_π_eq, CategoryTheory.GrothendieckTopology.Cover.coe_pullback, CompHausLike.coe_comp, CategoryTheory.MonoidalCategory.externalProductBifunctor_obj_map, CategoryTheory.MorphismProperty.LeftFraction.map_eq, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.inverse_map, HomologicalComplex.toCycles_i_assoc, AlgebraicGeometry.IsOpenImmersion.lift_app, CategoryTheory.Functor.comp_mapMon_one, CategoryTheory.SemiCartesianMonoidalCategory.snd_def, CategoryTheory.ShortComplex.RightHomologyMapData.commp, CategoryTheory.ShortComplex.leftHomologyMap_comp_assoc, CategoryTheory.MonObj.one_mul_hom, CategoryTheory.sheafComposeNatTrans_fac, CategoryTheory.toSheafify_naturality, CategoryTheory.Limits.hasPushout_of_left_factors_epi, CategoryTheory.Limits.IsLimit.fac, CategoryTheory.Limits.limitOpIsoOpColimit_hom_comp_ι, CategoryTheory.Limits.kernelSubobject_comp_le, CategoryTheory.Mat_.additiveObjIsoBiproduct_hom_π_assoc, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_app_comp_π_assoc, CategoryTheory.Functor.OplaxMonoidal.associativity_inv_assoc, CategoryTheory.MonoidalCategory.associator_inv_conjugation, CategoryTheory.Center.whiskerLeft_comm_assoc, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_inv_fac_assoc, CategoryTheory.BraidedCategory.hexagon_forward_assoc, CategoryTheory.MonoidalCategory.id_tensor_comp, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst_assoc, isoOfQuasiIsoAt_hom_inv_id_assoc, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_ι_assoc, CategoryTheory.Dial.leftUnitorImpl_inv_F, germ_skyscraperPresheafStalkOfSpecializes_hom, groupCohomology.mapCocycles₁_comp_i, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_obj_obj_map, CategoryTheory.OplaxFunctor.map₂_rightUnitor_app_assoc, CategoryTheory.Limits.MonoFactorisation.isoComp_m, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_inv_fac_assoc, Mathlib.Tactic.Bicategory.structuralIsoOfExpr_comp, CategoryTheory.Retract.trans_i, CategoryTheory.shrinkYonedaEquiv_symm_map, CategoryTheory.ComposableArrows.IsComplex.zero', CategoryTheory.Oplax.StrongTrans.vcomp_naturality_inv, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict_assoc, AlgebraicGeometry.Scheme.IdealSheafData.map_ker, CochainComplex.HomComplex.Cochain.toSingleMk_precomp, Bicategory.Opposite.bicategory_whiskerLeft_unop2, CategoryTheory.Sieve.overEquiv_iff, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_snd, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_assoc, Lat.coe_comp, CategoryTheory.Adjunction.map_μ_comp_counit_app_tensor_assoc, CategoryTheory.CartesianMonoidalCategory.tensorδ_fst, HomologicalComplex.ι_mapBifunctorMap, HomotopicalAlgebra.weakEquivalence_postcomp_iff, CategoryTheory.Comma.mapLeftIso_functor_map_right, CategoryTheory.MonoidalCategory.hom_inv_id_tensor, CategoryTheory.MonoidalCategory.DayFunctor.ι_comp_isoPointwiseLeftKanExtension_inv, CategoryTheory.Functor.currying_functor_map_app, CategoryTheory.GradedObject.ι_mapBifunctorComp₂₃MapObjIso_hom_assoc, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv, SimplicialObject.Splitting.cofan_inj_epi_naturality, CategoryTheory.toUnit_comp_curryRightUnitorHom, CategoryTheory.Limits.prod.associator_naturality, CategoryTheory.shiftFunctorAdd_zero_add_inv_app, CategoryTheory.Adjunction.homEquiv_symm_apply, CategoryTheory.ShortComplex.comp_τ₁_assoc, CategoryTheory.StructuredArrow.mkPostcomp_id, CategoryTheory.Limits.limit.w, CategoryTheory.Iso.hom_inv_id_app_app_app, CategoryTheory.Limits.inv_piComparison_comp_map_π_assoc, CochainComplex.mappingCone.d_fst_v, CategoryTheory.shiftFunctorComm_hom_app_of_add_eq_zero_assoc, CategoryTheory.Limits.combineCones_π_app_app, CategoryTheory.Oplax.OplaxTrans.whiskerRight_as_app, AlgebraicGeometry.Scheme.Pullback.openCoverOfLeft_X, CategoryTheory.ShortComplex.opcycles_ext_iff, CategoryTheory.PreOneHypercover.comp_h₁, CategoryTheory.regularTopology.instEffectiveEpiComp, AlgebraicGeometry.Scheme.stalkMap_congr, CategoryTheory.Bicategory.associator_naturality_middle_assoc, CategoryTheory.ihom.ev_coev, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_snd, Bicategory.Opposite.bicategory_rightUnitor_inv_unop2, CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_snd, CochainComplex.mappingConeCompHomotopyEquiv_hom_inv_id_assoc, CategoryTheory.Grp.comp_hom, CategoryTheory.HopfObj.hom_antipode, CategoryTheory.Limits.prod.hom_ext_iff, CategoryTheory.SimplicialThickening.comp_I, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι, CategoryTheory.IsSplitCoequalizer.condition_assoc, CategoryTheory.Limits.Multifork.condition_assoc, CategoryTheory.MonoidalClosed.whiskerLeft_curry_ihom_ev_app_assoc, HomologicalComplex.ιOrZero_mapBifunctorAssociatorX_hom_assoc, CategoryTheory.Limits.prodComparison_snd_assoc, CategoryTheory.Pseudofunctor.whiskerRightIso_mapId, CategoryTheory.Limits.limit.pre_π, CategoryTheory.Mathlib.Tactic.MonTauto.eq_one_mul, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.w_app_assoc, CategoryTheory.MonoidalCategory.associator_naturality_right_assoc, HomologicalComplex.homotopyCofiber.inrX_desc_f_assoc, CategoryTheory.Subgroupoid.IsNormal.conj, CategoryTheory.Limits.prod_rightUnitor_inv_naturality, AlgebraicGeometry.IsIntegralHom.comp_iff, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionHom, CategoryTheory.monoidalOfHasFiniteProducts.associator_inv, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_associator_inv_as_app, CategoryTheory.Limits.Cowedge.condition, CategoryTheory.GradedObject.ι_mapBifunctorComp₂₃MapObjIso_inv_assoc, CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_inv_assoc, CommRingCat.Under.equalizer_comp, CategoryTheory.CartesianMonoidalCategory.tensorHom_fst_assoc, CategoryTheory.Oplax.OplaxTrans.leftUnitor_inv_as_app, CategoryTheory.Functor.costructuredArrowMapCocone_ι_app, SSet.range_eq_iSup_of_isColimit, CategoryTheory.Adjunction.mapCommGrp_counit, CategoryTheory.Meq.pullback_apply, CategoryTheory.Cokleisli.Adjunction.toCokleisli_map, CategoryTheory.Limits.map_lift_piComparison, CategoryTheory.Category.id_comp, CategoryTheory.Limits.coprod.map_map, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.secondMap_app_app_app, CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_inv_assoc, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom, CategoryTheory.Limits.FormalCoproduct.pullbackCone_snd_φ, CategoryTheory.kernelCokernelCompSequence.ι_φ_assoc, CategoryTheory.Functor.mapTriangle_map_hom₂, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom, HomologicalComplex.p_opcyclesMap_assoc, CategoryTheory.Limits.WidePullbackCone.condition, groupHomology.isoCycles₂_hom_comp_i_assoc, CategoryTheory.GrpObj.lift_inv_comp_right_assoc, CategoryTheory.evaluationLeftAdjoint_obj_map, CategoryTheory.Bicategory.RightExtension.w, CategoryTheory.Functor.comp_mapCommMon_one, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom, CategoryTheory.Equivalence.congrRight_counitIso_hom_app, CategoryTheory.Bicategory.Adj.leftUnitor_hom_τl, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop_assoc, CategoryTheory.IsCardinalFiltered.coeq_condition, CategoryTheory.Functor.homEquivOfIsLeftKanExtension_apply_app, CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIso_inv, CategoryTheory.Iso.map_inv_hom_id_eval_app_assoc, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_hom_whiskerLeft_π, AlgebraicGeometry.Scheme.Pullback.diagonalCover_map, groupHomology.comp_d₃₂_eq, DerivedCategory.left_fac, groupCohomology.π_comp_H2Iso_hom, CategoryTheory.ExponentiableMorphism.unit_pushforwardComp_hom_assoc, CategoryTheory.Subfunctor.Subpresheaf.lift_ι, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality, CategoryTheory.Idempotents.DoldKan.η_hom_app_f, groupHomology.chainsMap_f_0_comp_chainsIso₀, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_right, CategoryTheory.Limits.π_comp_opProductIsoCoproduct_hom, HomologicalComplex.restrictionCyclesIso_inv_iCycles, AlgebraicGeometry.Scheme.inv_base_hom_base, CategoryTheory.Limits.biproduct.ι_π_self, CategoryTheory.Over.tensorObj_hom, CategoryTheory.ShortComplex.mapLeftHomologyIso_inv_naturality_assoc, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_right, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_hom_iso, CategoryTheory.CartesianMonoidalCategory.tensorμ_snd_assoc, CategoryTheory.GradedObject.ι_mapBifunctorComp₁₂MapObjIso_inv_assoc, CategoryTheory.Pretriangulated.preadditiveCoyoneda_homologySequenceδ_apply, Profinite.exists_hom, CategoryTheory.Bicategory.mateEquiv_apply', CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_snd_snd, CategoryTheory.CosimplicialObject.δ_comp_σ_self'_assoc, CategoryTheory.ShortComplex.asIsoHomologyι_inv_comp_homologyι_assoc, SSet.ι₁_comp_assoc, CategoryTheory.Limits.image.compIso_inv_comp_image_ι, CategoryTheory.Mon_Class.mul_mul_mul_comm', CategoryTheory.Bicategory.Equivalence.left_triangle_hom, CategoryTheory.Presheaf.isLocallyInjective_comp, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm_assoc, CategoryTheory.Monad.Algebra.Hom.h_assoc, CategoryTheory.Adjunction.Triple.leftToRight_app_map_adj₁_unit_app, DistLat.ofHom_comp, CategoryTheory.Over.postAdjunctionLeft_counit_app_left, CategoryTheory.Limits.ι_colimitConstInitial_hom_assoc, CategoryTheory.SimplicialObject.δ_comp_δ_self'_assoc, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_symm_apply, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_left_hom, AlgebraicGeometry.PresheafedSpace.stalkMap.congr_point, CategoryTheory.Bicategory.conjugateEquiv_comp, CategoryTheory.OplaxFunctor.mapComp_id_left, CategoryTheory.LaxFunctor.map₂_leftUnitor_app_assoc, CategoryTheory.epi_iff_forall_injective, HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac'_assoc, CategoryTheory.Comma.mapRightComp_inv_app_left, CategoryTheory.GradedNatTrans.naturality, CategoryTheory.Presieve.bindOfArrows_ofArrows, CategoryTheory.Arrow.iso_w', HomologicalComplex₂.ιTotal_map_assoc, CategoryTheory.Limits.Sigma.ι_reindex_inv_assoc, CategoryTheory.ShortComplex.rightHomologyι_naturality_assoc, CategoryTheory.ShiftMkCore.assoc_hom_app_assoc, CategoryTheory.Equivalence.changeFunctor_counitIso_inv_app, CategoryTheory.MonoidalCategory.leftUnitor_inv_tensor_id, CategoryTheory.GradedObject.ι_mapTrifunctorMapMap, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_symm, CategoryTheory.Endofunctor.Algebra.Initial.left_inv, AlgebraicGeometry.Scheme.Cover.ι_fromGlued, AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_app, AlgebraicGeometry.Scheme.Hom.inl_toNormalization_normalizationCoprodIso_inv, HomologicalComplex.ι_mapBifunctorFlipIso_inv, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_three_assoc, StalkSkyscraperPresheafAdjunctionAuxs.toSkyscraperPresheaf_app, AddMagmaCat.hom_comp, AlgebraicGeometry.Scheme.Hom.inr_normalizationCoprodIso_hom_fromNormalization, SSet.PtSimplex.RelStruct.δ_succ_map_assoc, AlgebraicGeometry.Scheme.Hom.appIso_inv_appLE, CategoryTheory.ShortComplex.mapHomologyIso'_inv_naturality_assoc, HomologicalComplex.homologyπ_restrictionHomologyIso_hom_assoc, CategoryTheory.IsReflexivePair.common_section', CategoryTheory.BraidedCategory.braiding_tensor_right_inv, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply_assoc, CategoryTheory.Adjunction.Triple.rightToLeft_app_adj₂_unit_app_assoc, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_inv, CategoryTheory.Over.mapComp_inv_app_left, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_inv_assoc, HomologicalComplex.homologyι_naturality_assoc, CategoryTheory.MorphismProperty.instIsStableUnderBaseChangeAlongCompOfHasPullbacksAlong, CategoryTheory.IsCardinalFiltered.multicoequalizer, ModuleCat.extendScalars_assoc, CategoryTheory.Equivalence.congrRight_unitIso_inv_app, CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_right_assoc, CategoryTheory.Limits.ker_map, CategoryTheory.Adjunction.shift_counit_app_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor, CategoryTheory.GradedObject.Monoidal.tensorObj_ext_iff, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_right, CategoryTheory.shift_neg_shift', CategoryTheory.Limits.hasKernel_iso_comp, TopCat.piIsoPi_inv_π_assoc, CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIsoWhisker_hom_right, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerLeft, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality_assoc, CategoryTheory.Bicategory.triangle_assoc_comp_right_assoc, CategoryTheory.Grothendieck.ι_map, CategoryTheory.ihom.coev_ev_assoc, CategoryTheory.ShortComplex.f_pOpcycles, SheafOfModules.pushforwardNatTrans_comp, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_hom_whiskerRight_π, groupCohomology.isoCocycles₂_inv_comp_iCocycles_assoc, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_counit, CategoryTheory.Adjunction.mapGrp_counit, CategoryTheory.Functor.liftOfIsRightKanExtension_fac_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_obj_obj_map, CategoryTheory.Equivalence.functor_unit_comp_assoc, CategoryTheory.Mon_Class.mul_mul_mul_comm, CategoryTheory.Limits.ConeMorphism.inv_hom_id, SimplexCategory.δ_comp_σ_self'_assoc, CategoryTheory.Functor.comp_mapGrp_one, HomotopicalAlgebra.AttachCells.hm, CategoryTheory.enrichedNatTransYoneda_map_app, CategoryTheory.yonedaGrp_naturality, CategoryTheory.Under.comp_right, HomologicalComplex.cylinder.πCompι₀Homotopy.inlX_nullHomotopy_f, CategoryTheory.Adjunction.unit_naturality_assoc, CategoryTheory.Arrow.squareToSnd_right, CategoryTheory.ShiftMkCore.assoc_inv_app, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app_assoc, CategoryTheory.Subfunctor.toRange_ι, CategoryTheory.leftDistributor_ext_left_iff, AlgebraicGeometry.pointOfClosedPoint_comp, HomologicalComplex₂.totalFlipIso_hom_f_D₂_assoc, CategoryTheory.Limits.limitRightOpIsoOpColimit_inv_comp_π, CategoryTheory.Iso.inv_hom_id_eval, CategoryTheory.SemiCartesianMonoidalCategory.comp_toUnit, HomologicalComplex.pOpcycles_restrictionOpcyclesIso_hom, CategoryTheory.Limits.pullbackAssoc_inv_fst_fst, CategoryTheory.Limits.limit_map_limitObjIsoLimitCompEvaluation_hom, CategoryTheory.Equivalence.symmEquivInverse_map_app, HomologicalComplex₂.ι_totalShift₁Iso_hom_f, AlgebraicGeometry.SheafedSpace.comp_c_app', CategoryTheory.FreeBicategory.liftHom_comp, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict, Rep.norm_comm, CategoryTheory.ShiftedHom.opEquiv'_add_symm, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_hom_app, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_inv_fac, CategoryTheory.MorphismProperty.Over.map_obj_hom, CategoryTheory.Bicategory.rightUnitorNatIso_hom_app, CategoryTheory.CostructuredArrow.IsUniversal.hom_desc, CategoryTheory.Adjunction.Triple.mono_leftToRight_app_iff, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app, CategoryTheory.Idempotents.Karoubi.p_comm, Bimod.LeftUnitorBimod.hom_left_act_hom', CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst_assoc, CategoryTheory.Limits.coprodComparison_natural, CategoryTheory.Equivalence.induced_counitIso, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_inv_assoc, CategoryTheory.Adjunction.comp_unit_app, CategoryTheory.heq_eqToHom_comp_iff, AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalk_assoc, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_inv_ι, AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ_assoc, CategoryTheory.ParametrizedAdjunction.whiskerLeft_map_counit_assoc, CategoryTheory.Functor.Monoidal.μ_δ_assoc, CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_inv_comp_iCycles, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd_assoc, CategoryTheory.Limits.SequentialProduct.functorMap_commSq, CategoryTheory.ShortComplex.Splitting.s_r_assoc, CategoryTheory.mono_iff_forall_injective, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_iff, CategoryTheory.Limits.WidePushout.arrow_ι_assoc, CategoryTheory.Limits.pullbackObjIso_hom_comp_snd, CategoryTheory.ComposableArrows.IsComplex.cokerToKer_fac_assoc, CategoryTheory.dcongr_arg, CategoryTheory.MonoidalCategory.associator_naturality_right, CategoryTheory.Square.Hom.comp_τ₃, CategoryTheory.MonoidalCategory.MonoidalLeftAction.inv_hom_actionHomLeft', CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.fac, CategoryTheory.Limits.biprod.ext_from_iff, CategoryTheory.kernelCokernelCompSequence.φ_π_assoc, CategoryTheory.uliftCoyonedaEquiv_comp, CategoryTheory.Limits.imageSubobject_factors_comp_self, CategoryTheory.IsHomLift.fac, ContinuousMap.Homotopy.eq_diag_path, CategoryTheory.Functor.IsCoverDense.Types.naturality_assoc, CategoryTheory.Abelian.PreservesCoimage.iso_hom_π, CategoryTheory.Arrow.mk_eq_mk_iff, AlgebraicGeometry.LocallyRingedSpace.comp_c, CategoryTheory.monoidalOfHasFiniteProducts.associator_inv_fst_fst, MagmaCat.ofHom_comp, AlgebraicGeometry.Scheme.Opens.isoOfLE_inv_ι_assoc, CategoryTheory.Mon.tensor_mul, CategoryTheory.Limits.colimitFlipIsoCompColim_inv_app, CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_hom_hom_assoc, CategoryTheory.Limits.MonoFactorisation.ofIsoComp_m, CategoryTheory.MonObj.mul_assoc_flip, CategoryTheory.Adjunction.leftAdjointCompNatTrans_app, CategoryTheory.IsSplitEqualizer.condition, CategoryTheory.Functor.map_inv_hom, CategoryTheory.Bicategory.leftUnitor_comp_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_hom_app, CategoryTheory.associator_hom, CategoryTheory.Limits.inr_comp_pushoutComparison, CategoryTheory.Enriched.FunctorCategory.enriched_comp_id, CategoryTheory.Bicategory.LeftLift.w, CategoryTheory.Limits.biproduct.map_desc_assoc, SSet.PtSimplex.MulStruct.δ_castSucc_castSucc_map, HomologicalComplex.mapBifunctor₂₃.ι_D₂_assoc, CategoryTheory.Limits.ι_comp_colimitUnopIsoOpLimit_hom, CategoryTheory.Pseudofunctor.mapId'_inv_naturality, CategoryTheory.LaxFunctor.mapComp_naturality_left_assoc, CategoryTheory.tensorLeftHomEquiv_symm_naturality, CategoryTheory.Monad.algebraFunctorOfMonadHom_map_f, CategoryTheory.ShortComplex.cyclesIsoLeftHomology_inv_hom_id_assoc, AlgebraicGeometry.Scheme.Spec_fromSpecStalk, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_right_assoc, CategoryTheory.Limits.Pi.map_comp_map', CochainComplex.ι_mapBifunctorShift₁Iso_hom_f, CategoryTheory.Limits.pullback_equalizer, groupHomology.chainsMap_f, SSet.RelativeMorphism.Homotopy.rel_assoc, CategoryTheory.Functor.Monoidal.η_ε, CategoryTheory.NatTrans.unop_comp, CategoryTheory.Monad.right_unit_assoc, CategoryTheory.types_comp_apply, CategoryTheory.preadditiveYonedaObj_map, CategoryTheory.ShortComplex.f_pOpcycles_assoc, CategoryTheory.Limits.pullbackProdSndIsoProd_hom_fst_assoc, CategoryTheory.ShortComplex.ShortExact.comp_δ_assoc, CategoryTheory.MonoidalClosed.id_comp_assoc, CategoryTheory.ShortComplex.π_homologyMap_ι, AlgebraicGeometry.exists_etale_isCompl_of_quasiFiniteAt, CategoryTheory.Limits.Pi.map'_comp_π, AlgebraicTopology.DoldKan.Q_f_idem, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_assoc, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π, CategoryTheory.mateEquiv_apply, CategoryTheory.Functor.structuredArrowMapCone_π_app, CategoryTheory.Limits.biprod.inl_fst_assoc, groupCohomology.map_comp_assoc, CategoryTheory.eHom_whisker_exchange, CategoryTheory.sheafCompose_comp, groupHomology.cyclesMap_comp_isoCycles₁_hom, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd_assoc, CategoryTheory.IsCardinalFiltered.coeq_condition_assoc, CategoryTheory.ShortComplex.mapHomologyIso'_inv_naturality, CategoryTheory.ShortComplex.mapCyclesIso_hom_naturality, CategoryTheory.CartesianMonoidalCategory.lift_braiding_inv_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_app, CategoryTheory.ShortComplex.cyclesOpIso_hom_naturality_assoc, CategoryTheory.CartesianMonoidalCategory.whiskerRight_snd, CategoryTheory.IsFiltered.wideSpan, CategoryTheory.CartesianMonoidalCategory.whiskerRight_toUnit_comp_leftUnitor_hom_assoc, CategoryTheory.Limits.Multifork.pi_condition, HomologicalComplex.Hom.prev_eq, CategoryTheory.InjectiveResolution.cochainComplex_d, CategoryTheory.Quotient.comp_natTransLift, AlgebraicGeometry.tilde.toOpen_map_app, CategoryTheory.Limits.KernelFork.map_condition_assoc, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_comp, CategoryTheory.Limits.biproduct.ι_fromSubtype, CategoryTheory.yonedaEquiv_comp, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app_assoc, CategoryTheory.prod_comp_snd, CategoryTheory.Functor.Monoidal.whiskerLeft_δ_μ_assoc, CochainComplex.mappingCone.map_δ, CategoryTheory.ShortComplex.RightHomologyData.p_g', HomologicalComplex₂.ιTotal_totalFlipIso_f_inv, CategoryTheory.Limits.MonoFactorisation.ofCompIso_e, CategoryTheory.unitCompPartialBijective_symm_apply, CochainComplex.HomComplex.Cochain.ofHom_comp, CategoryTheory.ihom.coev_ev, AlgebraicGeometry.instIsSchemeTheoreticallyDominantCompScheme, CategoryTheory.eqToHom_comp_homOfLE_assoc, CategoryTheory.Limits.hasKernel_comp_mono, AlgebraicGeometry.Spec.preimage_comp, HomologicalComplex.isoHomologyπ_inv_hom_id, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_εIso_hom, CategoryTheory.Bicategory.triangle_assoc_comp_left_inv_assoc, CategoryTheory.Monad.ForgetCreatesColimits.newCocone_ι, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right, CategoryTheory.Functor.IsCoverDense.Types.naturality, CategoryTheory.Limits.FormalCoproduct.hom_ext_iff', CategoryTheory.whiskerLeft_coprod_inr_leftDistrib_inv_assoc, AlgebraicGeometry.LocallyRingedSpace.stalkMap_germ, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerRight_naturality_assoc, CategoryTheory.ShortComplex.asIsoHomologyι_inv_comp_homologyι, CategoryTheory.Prefunctor.mapPath_comp', CategoryTheory.CosimplicialObject.δ_comp_σ_of_le_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHom_def'_assoc, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_hom, CategoryTheory.GrothendieckTopology.Cover.Arrow.Relation.w_assoc, AlgebraicGeometry.pullbackSpecIso_hom_snd_assoc
id 📖	CompOp	3792 math math: CategoryTheory.SmallObject.functorMap_id, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₃, CategoryTheory.Limits.Cones.postcomposeId_hom_app_hom, CategoryTheory.Limits.Bicone.category_id_hom, SemimoduleCat.MonoidalCategory.triangle, CategoryTheory.Adjunction.adjToComonadIso_inv_toNatTrans_app, CategoryTheory.GrothendieckTopology.overMapPullbackId_hom_app_val_app, CategoryTheory.Adjunction.adjunctionOfEquivLeft_counit_app, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id, CategoryTheory.CostructuredArrow.homMk'_id, CategoryTheory.Functor.whiskeringRightObjIdIso_hom_app_app, Action.forget_η, CategoryTheory.Join.pseudofunctorLeft_mapId_inv_toNatTrans_app, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₁, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_assoc, CategoryTheory.Functor.functorHomEquiv_apply_app, CategoryTheory.Limits.Cocone.category_id_hom, CategoryTheory.SimplicialObject.id_left_app, CategoryTheory.sum.inrCompInverseAssociator_hom_app, CategoryTheory.ShortComplex.rightHomologyMap_id, CategoryTheory.SingleFunctors.postcompPostcompIso_hom_hom_app, CommBialgCat.ofSelfIso_inv, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_hom_app_zero, CategoryTheory.uliftCoyonedaEquiv_apply, CategoryTheory.Limits.DiagramOfCones.id, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_hom_left, CategoryTheory.Functor.isoSum_inv_app_inl, CategoryTheory.Limits.Cone.toUnder_pt, CategoryTheory.Mon.id_hom, AddMagmaCat.coe_id, CategoryTheory.WithTerminal.coneEquiv_unitIso_hom_app_hom_left, CategoryTheory.Functor.mapTriangleIdIso_inv_app_hom₃, CategoryTheory.Monad.monadMonEquiv_unitIso_inv_app_toNatTrans_app, CategoryTheory.StrictPseudofunctorPreCore.map_id, BoolAlg.coe_id, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_apply, CategoryTheory.Functor.coreComp_hom_app_iso_inv, CategoryTheory.kernelCokernelCompSequence.snakeInput_v₀₁_τ₂, CategoryTheory.ComposableArrows.threeδ₂Toδ₁_app_zero, AlgebraicTopology.DoldKan.P_f_0_eq, CategoryTheory.Functor.natTransEquiv_apply_app, CategoryTheory.Functor.mapComposableArrowsObjMk₂Iso_inv_app, CategoryTheory.Pseudofunctor.DescentData.subtypeCompatibleHomEquiv_toCompatible_presheafHomObjHomEquiv, SimplexCategory.mkOfSucc_eq_id, CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_right, CategoryTheory.NatTrans.hcomp_id_app, CategoryTheory.IsPullback.of_id_fst, CategoryTheory.IsHomLift.eqToHom_domain_lift_id, CategoryTheory.BraidedCategory.yang_baxter', CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair_hom_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_left, CategoryTheory.ShortComplex.HomologyData.canonical_iso_hom, AlgebraicTopology.DoldKan.PInfty_f_add_QInfty_f, CategoryTheory.CatEnrichedOrdinary.id_hComp_heq, CategoryTheory.Limits.inr_of_isLimit, SimplexCategoryGenRel.standardσ_nil, AlgebraicGeometry.Spec.map_eq_id, CategoryTheory.Endofunctor.Coalgebra.id_f, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp_inv_app_f, TopologicalSpace.Opens.map_id_obj_unop, CategoryTheory.MonoidalCategory.hom_inv_whiskerRight', CategoryTheory.Join.inlCompFromSum_hom_app, CategoryTheory.Bicategory.Adj.rightUnitor_hom_τl, AlgebraicGeometry.Scheme.Modules.pushforwardId_inv_app_app, CategoryTheory.Limits.CatCospanTransform.associator_hom_right_app, CategoryTheory.SmallObject.SuccStruct.prop.arrowIso_hom_left, CategoryTheory.Retract.refl_r, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_fst_assoc, CategoryTheory.Monad.id_η_app, CategoryTheory.Functor.mapHomologicalComplexIdIso_hom_app_f, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_hom_inv', CategoryTheory.Join.mapPairId_hom_app, CategoryTheory.ShortComplex.opcyclesIsoRightHomology_hom_inv_id, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_hom_hom, CategoryTheory.OplaxFunctor.id_mapComp, CategoryTheory.Limits.ConeMorphism.hom_inv_id, CategoryTheory.Functor.rightDerivedNatTrans_id, SimplexCategory.eq_id_of_isIso, CategoryTheory.Comma.mapLeftEq_inv_app_right, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceInverseπ_hom_app, CategoryTheory.Square.category_id_τ₃, CategoryTheory.Grothendieck.ιCompMap_hom_app_fiber, CategoryTheory.Join.mapWhiskerLeft_app, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_map_left, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_naturality_assoc, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_hom_app, CategoryTheory.Functor.mapConeMapCone_hom_hom, CategoryTheory.Limits.coprod.inl_fst, AddGrpCat.id_apply, PresheafOfModules.pullback_id_comp, CategoryTheory.SmallObject.SuccStruct.prop.arrowIso_inv_left, CategoryTheory.e_comp_id, CategoryTheory.MonoidalCategory.tensor_inv_hom_id_assoc, groupHomology.mapShortComplexH2_id, CategoryTheory.Bicategory.eqToHomTransIso_refl_left, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_id, CategoryTheory.IsPushout.id_horiz, CategoryTheory.Functor.opUnopIso_hom_app, CategoryTheory.FreeMonoidalCategory.mk_id, CategoryTheory.MonoidalOpposite.tensorLeftMopIso_hom_app_unmop, CategoryTheory.NatTrans.rightDerivedToHomotopyCategory_id, SimplexCategory.const_eq_id, CategoryTheory.Enriched.FunctorCategory.enriched_id_comp, Bimod.RightUnitorBimod.inv_hom_id, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_id_base, CategoryTheory.LocalizerMorphism.LeftResolution.id_f, LinearMap.id_fgModuleCat_comp, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_hom, CategoryTheory.Limits.map_id_right_eq_curry_swap_map, Preord.ofHom_id, CategoryTheory.Limits.coprod.symmetry, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapId_hom_iso, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_ι_presheafHom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_inv_app_hom, CategoryTheory.SmallCategoryOfSet.id_def, CategoryTheory.Functor.Monoidal.whiskerLeft_η_ε, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_left_app, CategoryTheory.Bicategory.leftUnitor_inv_naturality_assoc, CategoryTheory.GradedObject.mapTrifunctorMapFunctorObj_obj_map, CategoryTheory.Functor.mapCommGrpCompIso_inv_app_hom_hom_hom, CategoryTheory.Sum.functorEquivFunctorCompFstIso_inv_app_app, CategoryTheory.OverPresheafAux.unitAux_hom, CategoryTheory.Limits.BinaryBicone.inl_fst, CategoryTheory.CosimplicialObject.id_right_app, CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom, CategoryTheory.Cat.Hom.id_map, CategoryTheory.Retract.refl_i, FGModuleCat.hom_hom_id, CategoryTheory.monoidalOfHasFiniteCoproducts.whiskerLeft, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_app_snd_app, CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp_inv_hom₁, CategoryTheory.Bicategory.whiskerLeft_inv_hom, CategoryTheory.StrictlyUnitaryLaxFunctor.mapIdIso_hom, CategoryTheory.FreeBicategory.lift_mapId, CategoryTheory.MorphismProperty.LeftFraction.ofInv_f, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_leftUnitor, CategoryTheory.MonoidalCategory.inv_hom_id_tensor_assoc, CategoryTheory.Bicategory.Prod.sectL_mapId_inv, CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_hom_inv_id, CategoryTheory.SimplicialThickening.SimplicialCategory.comp_id, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_map, TopCat.Presheaf.Pushforward.id_inv_app, CategoryTheory.Limits.spanCompIso_inv_app_zero, CategoryTheory.Mon.forget_μ, CategoryTheory.WithInitial.opEquiv_unitIso_inv_app, CategoryTheory.Limits.CatCospanTransform.rightUnitor_inv_left_app, CategoryTheory.Limits.Cocone.toOver_ι_app, CochainComplex.mappingCone.id, CategoryTheory.Under.postComp_inv_app_right, AlgebraicGeometry.Scheme.Pullback.openCoverOfLeftRight_f, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom, CategoryTheory.Functor.isoSum_inv_app_inr, CategoryTheory.ShortComplex.LeftHomologyMapData.id_φK, CategoryTheory.Functor.IsEventuallyConstantTo.coneπApp_eq, CategoryTheory.MonoidalCategory.MonoidalRightAction.id_actionHom, CategoryTheory.epi_iff_isPushout, CategoryTheory.Dial.leftUnitor_naturality, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₂, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_apply, CategoryTheory.CatEnriched.id_hComp, CategoryTheory.Bimon.ofMonComonObjX_mul, commBialgCatEquivComonCommAlgCat_unitIso_inv_app, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_left_assoc, CategoryTheory.Bicategory.mateEquiv_comp_id_right, CategoryTheory.Limits.parallelPairOpIso_inv_app_zero, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₁_W, CategoryTheory.SingleFunctors.id_hom, CategoryTheory.Bicategory.inv_hom_whiskerRight, CategoryTheory.sum.inlCompInrCompInverseAssociator_hom_app_down_down, CochainComplex.augmentTruncate_inv_f_zero, CategoryTheory.LaxFunctor.map₂_leftUnitor_assoc, CategoryTheory.NatTrans.removeLeftOp_id, CategoryTheory.eHomEquiv_id, CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_left_app, CategoryTheory.Under.forgetMapInitial_inv_app, CategoryTheory.Grp.id', CategoryTheory.ShortComplex.cyclesIsoX₂_hom_inv_id, SemiNormedGrp₁.coe_id, CategoryTheory.RetractArrow.retract_left_assoc, CategoryTheory.MonoidalCategory.pentagon_hom_inv_assoc, CategoryTheory.Limits.coprod.map_inl_inr_codiag, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_hom_app_snd_app, CategoryTheory.Bicategory.isLeftAdjoint_TFAE, HomologicalComplex.homotopyCofiber.inlX_fstX, CategoryTheory.WithTerminal.liftStar_inv, CategoryTheory.Bicategory.Adjunction.homEquiv₂_symm_apply, CategoryTheory.Bicategory.InducedBicategory.Hom.category_id_hom, CategoryTheory.ShortComplex.LeftHomologyMapData.id_φH, CategoryTheory.LaxFunctor.comp_mapId, TopologicalSpace.OpenNhds.inclusionMapIso_hom, CategoryTheory.Functor.curryObjCompIso_hom_app_app, CategoryTheory.Functor.unopOpIso_inv_app, CategoryTheory.GrothendieckTopology.overMapPullback_comp_id, CategoryTheory.Pseudofunctor.map₂_left_unitor_assoc, CategoryTheory.Over.rightUnitor_inv_left_fst_assoc, CategoryTheory.Functor.uncurryObjFlip_hom_app, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_id, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_map_mkHom_id_homMk, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_id, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id_app, Pointed.Hom.id_toFun', CategoryTheory.Oplax.LaxTrans.vComp_naturality_id, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_fst, SimplexCategory.Truncated.δ₂_zero_comp_σ₂_zero, CategoryTheory.StrictPseudofunctorCore.map₂_left_unitor, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_id_fiber, AlgebraicTopology.DoldKan.Γ₀NondegComplexIso_inv_f, CategoryTheory.Bicategory.eqToHomTransIso_refl_refl, SheafOfModules.sectionsMap_id, CategoryTheory.GrothendieckTopology.overMapPullbackId_inv_app_val_app, CategoryTheory.FreeBicategory.mk_left_unitor_inv, PresheafOfModules.pullback_comp_id, AugmentedSimplexCategory.whiskerLeft_id_star, CategoryTheory.IsSplitEqualizer.bottom_rightRetraction, CategoryTheory.Limits.prod.pentagon_assoc, CategoryTheory.Localization.isoOfHom_inv_hom_id, SSet.OneTruncation₂.nerveHomEquiv_id, CommRingCat.id_apply, CategoryTheory.Functor.mapTriangleRotateIso_inv_app_hom₂, CategoryTheory.FreeBicategory.liftHom_id, CategoryTheory.ShrinkHoms.id_def, AlgebraicTopology.DoldKan.identity_N₂, CategoryTheory.Dial.rightUnitor_naturality, CategoryTheory.EnrichedCat.leftUnitor_hom_out_app, CategoryTheory.ExponentiableMorphism.id_pushforward, CategoryTheory.conjugateEquiv_symm_id, CategoryTheory.Subgroupoid.id_mem_of_tgt, CategoryTheory.Bicategory.conjugateEquiv_adjunction_id_symm, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_assoc, CategoryTheory.Iso.inv_hom_id_triangle_hom₂, CategoryTheory.Join.inclRightCompOpEquivInverse_inv_app_op, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_inv_app_hom, CategoryTheory.Bicategory.Adj.forget₁_mapId, CategoryTheory.Limits.BinaryBicone.ofLimitCone_inl, CategoryTheory.Mon.forget_ε, CategoryTheory.Grp.trivial_grp_inv, CategoryTheory.Functor.relativelyRepresentable.symmetry_symmetry, groupHomology.chainsMap_id, ContinuousMap.Homotopy.apply_zero_path, CategoryTheory.cosimplicialSimplicialEquiv_counitIso_hom_app_app, HomotopicalAlgebra.BifibrantObject.homMk_id, CategoryTheory.Adjunction.adjunctionOfEquivRight_counit_app, CategoryTheory.Over.hom_left_inv_left, CategoryTheory.Adjunction.ofCat_counit, CategoryTheory.sum.inrCompInrCompInverseAssociator_hom_app_down, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id, CategoryTheory.Functor.mapTriangleCompIso_inv_app_hom₂, CategoryTheory.SingleObj.id_as_one, CategoryTheory.InjectiveResolution.self_ι, CategoryTheory.Functor.pi'CompEval_hom_app, CategoryTheory.LocallyDiscrete.id_as, CategoryTheory.GrothendieckTopology.Point.id_hom, CategoryTheory.Oplax.OplaxTrans.homCategory_id_as_app, CategoryTheory.Functor.leftOpRightOpEquiv_counitIso_inv_app_app, CategoryTheory.GradedObject.mapBifunctor_triangle, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_unitIso_hom_app_f, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app, CategoryTheory.Over.whiskerLeft_left, CategoryTheory.Monad.algebraFunctorOfMonadHomId_inv_app_f, CategoryTheory.MonoidalOpposite.mopFunctor_ε, CategoryTheory.Dial.rightUnitorImpl_inv_f, AddCommMonCat.coe_id, CategoryTheory.Over.forgetMapTerminal_hom_app, CategoryTheory.Adjunction.leftAdjointUniq_refl, CategoryTheory.BicategoricalCoherence.left'_iso, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app, CategoryTheory.Limits.image.map_id, ProfiniteAddGrp.ofHom_id, AlgebraicGeometry.LocallyRingedSpace.id_toShHom', AddMonCat.ofHom_id, CategoryTheory.SplitEpi.id, AlgebraicGeometry.Scheme.Hom.id_appTop, CategoryTheory.Functor.RepresentableBy.homEquiv_eq, CategoryTheory.Bicategory.LeftExtension.ofCompId_right, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_hom_inv_id, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_one, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_id, CategoryTheory.CatCommSq.hId_iso_hom_app, CategoryTheory.Limits.coend.map_id, CategoryTheory.Functor.LeftExtension.postcomp₁_map_right_app, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_inv_hom, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_one, CategoryTheory.Functor.mapComposableArrowsObjMk₁Iso_inv_app, CategoryTheory.CostructuredArrow.mkPrecomp_id, CategoryTheory.right_comp_retraction, HomotopyCategory.isZero_quotient_obj_iff, LinOrd.hom_id, CategoryTheory.Join.id_right, CategoryTheory.Functor.mapCoconePrecompose_inv_hom, CategoryTheory.simplicialCosimplicialEquiv_counitIso_inv_app_app, CategoryTheory.Iso.inv_hom_id, CategoryTheory.GrpObj.left_inv_assoc, CategoryTheory.Functor.mapGrp_id_mul, CategoryTheory.EnrichedFunctor.forgetComp_inv_app, CategoryTheory.Biproduct.column_nonzero_of_iso', CompHausLike.coe_id, CategoryTheory.GrothendieckTopology.plusMap_id, CategoryTheory.Limits.prod.rightUnitor_hom_naturality, CategoryTheory.MonoidalCategory.DayFunctor.equiv_unitIso_hom_app, CategoryTheory.Abelian.LeftResolution.chainComplexMap_id, CategoryTheory.StrictPseudofunctor.id_mapComp_hom, CategoryTheory.comp_hom_eq_id, CategoryTheory.Functor.mapGrpIdIso_hom_app_hom_hom, AlgebraicTopology.DoldKan.homotopyPInftyToId_hom, CategoryTheory.Limits.Multifork.isoOfι_hom_hom, CategoryTheory.WithInitial.down_id, CategoryTheory.Localization.Monoidal.associator_hom_app, CategoryTheory.Limits.CatCospanTransform.rightUnitor_hom_left_app, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_snd_assoc, CategoryTheory.Limits.MulticospanIndex.multicospan_map, CategoryTheory.Functor.inlCompSum'_inv_app, CategoryTheory.Bicategory.InducedBicategory.bicategory_leftUnitor_inv_hom, CategoryTheory.kernelCokernelCompSequence.snakeInput_L₃_g, CategoryTheory.Cat.Hom₂.id_app, CategoryTheory.Limits.WalkingReflexivePair.reflexion_comp_left, groupHomology.comap_coinvariantsKer_pOpcycles_range_subtype_pOpcycles_eq_top, CategoryTheory.Grothendieck.ιNatTrans_app_fiber, CategoryTheory.Discrete.natIsoFunctor_hom_app, CategoryTheory.MonoidalCategory.externalProductCompDiagIso_hom_app_app, CategoryTheory.e_id_comp, CategoryTheory.Limits.FormalCoproduct.mapPower_id, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id_assoc, HeytAlg.hom_id, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_left_right, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_hom_app_fst_app, Action.FunctorCategoryEquivalence.counitIso_inv_app_app, CategoryTheory.prod_id_fst, HomotopicalAlgebra.LeftHomotopyClass.whitehead, CategoryTheory.WithTerminal.map₂_app, CategoryTheory.Pseudofunctor.StrongTrans.leftUnitor_inv_as_app, CategoryTheory.MonoidalCategory.inv_hom_id_tensor'_assoc, CategoryTheory.Limits.prod.map_swap_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id_assoc, CategoryTheory.PreOneHypercover.trivial_p₁, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_left, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_inv_app_coe, CategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSet_id, CategoryTheory.Functor.mapCoconeWhisker_hom_hom, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂_assoc, CategoryTheory.sheafificationNatIso_inv_app_val, CategoryTheory.Limits.colimitCoyonedaHomIsoLimit'_π_apply, AlgebraicGeometry.Scheme.isoSpec_inv_toSpecΓ, CategoryTheory.ShortComplex.Splitting.s_g, MonObj.mopEquivCompForgetIso_hom_app_unmop, CategoryTheory.ShortComplex.RightHomologyMapData.compatibilityOfZerosOfIsColimitCokernelCofork_φH, CategoryTheory.Bimon.equivMonComonUnitIsoAppXAux_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_inv_app_app_hom_hom, SemiNormedGrp.hom_id, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_inv_app_snd_app, CategoryTheory.PreOneHypercover.cylinderHom_h₁, ContinuousMap.Homotopy.evalAt_eq, CategoryTheory.Limits.prod.rightUnitor_hom_naturality_assoc, CategoryTheory.Oplax.OplaxTrans.categoryStruct_id_naturality, CategoryTheory.Localization.Construction.natTransExtension_hcomp, CategoryTheory.Join.isoMkFunctor_hom_app, CategoryTheory.Center.forget_η, CategoryTheory.LocalizerMorphism.homMap_id, CategoryTheory.IsPullback.of_prod_fst_with_id, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_inv_τr, CategoryTheory.MorphismProperty.Over.pullbackComp_hom_app_left, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_inv_app_op_zero, CategoryTheory.Limits.BinaryBicone.inr_snd, HomotopicalAlgebra.instWeakEquivalenceIdOfContainsIdentitiesWeakEquivalences, CategoryTheory.Comma.mapRightIso_counitIso_inv_app_left, AlgebraicGeometry.Scheme.ι_toIso_inv, CategoryTheory.MorphismProperty.RightFraction.map_ofInv_hom_id, CategoryTheory.Abelian.LeftResolution.karoubi.F'_map_f, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_right, CategoryTheory.Limits.Fork.isoForkOfι_hom_hom, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app, AlgebraicGeometry.tilde.map_id, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₂, CommSemiRingCat.hom_id, CategoryTheory.Comma.mapRightEq_hom_app_right, CategoryTheory.MonoidalCategory.hom_inv_id_tensor'_assoc, CategoryTheory.Functor.mapHomotopyEquiv_homotopyHomInvId, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_inv_app_snd_app, CategoryTheory.yonedaEquiv_apply, Rep.coinvariantsAdjunction_counit_app, CategoryTheory.Limits.isPullback_equalizer_prod, CategoryTheory.coprodMonad_μ_app, CategoryTheory.ShortComplex.HomotopyEquiv.refl_homotopyHomInvId, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app_assoc, SimplexCategory.δ_comp_σ_self', SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_inv_app, CategoryTheory.Comma.mapRightIso_counitIso_inv_app_right, CategoryTheory.Bicategory.rightUnitor_inv_naturality, ProfiniteGrp.coe_id, CategoryTheory.Abelian.Ext.mk₀_id_comp, CategoryTheory.sum.inlCompInrCompInverseAssociator_inv_app_down_down, CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal_ε_unmop_unmop, CategoryTheory.Functor.biproductComparison'_comp_biproductComparison, TopologicalSpace.OpenNhds.inclusionMapIso_inv, CategoryTheory.IsPushout.of_id_snd, groupHomology.map_id, CategoryTheory.Comma.mapLeftEq_hom_app_left, CategoryTheory.Functor.coreId_hom_app_iso_hom, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₂_app, CategoryTheory.Monad.monadMonEquiv_counitIso_hom_app_hom, CategoryTheory.MonoOver.mapIso_unitIso, LinearMap.comp_id_fgModuleCat, CategoryTheory.CommGrp.id', CategoryTheory.CatEnriched.id_hComp_id, CategoryTheory.Limits.CatCospanTransform.rightUnitor_inv_base_app, CategoryTheory.Bimon.trivial_comon_counit_hom, CategoryTheory.Bicategory.Adjunction.homEquiv₁_apply, CategoryTheory.Iso.inv_hom_id_triangle_hom₁, HomologicalComplex.isoHomologyι_inv_hom_id, CategoryTheory.WithInitial.opEquiv_functor_map, CategoryTheory.Functor.mapConePostcompose_inv_hom, AlgebraicGeometry.Scheme.Cover.glued_cover_cocycle, CategoryTheory.Endofunctor.Algebra.functorOfNatTransId_inv_app_f, Mathlib.Tactic.Bicategory.naturality_rightUnitor, CategoryTheory.Monad.algebraFunctorOfMonadHomId_hom_app_f, CategoryTheory.Functor.Monoidal.whiskerRight_η_ε, CategoryTheory.Functor.currying₃_unitIso_hom_app_app_app_app, CategoryTheory.ShortComplex.LeftHomologyMapData.compatibilityOfZerosOfIsColimitCokernelCofork_φK, SSet.Subcomplex.homOfLE_refl, CategoryTheory.MorphismProperty.RightFraction.ofHom_s, CochainComplex.HomComplex.Cochain.comp_id, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_unit_app, Lat.coe_id, CategoryTheory.IsSplitEqualizer.ι_leftRetraction, CategoryTheory.toOverPullbackIsoToOver_inv_app_left, HomologicalComplex.isoHomologyι_hom_inv_id, CategoryTheory.Functor.opComp_inv_app, CategoryTheory.ProjectiveResolution.self_π, CategoryTheory.Bicategory.rightUnitor_inv_congr, CategoryTheory.Monad.id_μ_app, CategoryTheory.Functor.LeftExtension.precomp_map_right, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_id, CategoryTheory.Functor.IsCartesian.map_self, CategoryTheory.Equivalence.functor_unit_comp, CategoryTheory.IsPushout.zero_top, CategoryTheory.Pseudofunctor.map₂_left_unitor, CategoryTheory.types_id, CategoryTheory.Limits.CatCospanTransform.category_id_left, CategoryTheory.Grpd.id_to_functor, CategoryTheory.Bicategory.unitors_inv_equal, CategoryTheory.Limits.Pi.ι_π_eq_id, CategoryTheory.Bicategory.Pith.leftUnitor_inv_iso_hom, CategoryTheory.types_id_apply, CategoryTheory.FreeGroupoid.mapComp_hom_app, CategoryTheory.Bicategory.leftZigzagIso_symm, CategoryTheory.GradedObject.Monoidal.pentagon, CategoryTheory.Square.Hom.id_τ₂, SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_hom_app, CategoryTheory.StrictPseudofunctor.mk''_mapId, CategoryTheory.Functor.Monoidal.δ_μ, CategoryTheory.TwoSquare.guitartExact_id', CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_right, CategoryTheory.Limits.prod.rightUnitor_inv, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_right, groupHomology.coresNatTrans_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_hom_inv, CategoryTheory.Functor.prod'CompSnd_inv_app, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁_assoc, SimplexCategory.Truncated.δ₂_one_comp_σ₂_one, CategoryTheory.Limits.coprod.pentagon, CategoryTheory.StrictlyUnitaryLaxFunctor.mapId_isIso, CategoryTheory.Pseudofunctor.Grothendieck.map_id_eq, CategoryTheory.Bicategory.prod_id_fst, CategoryTheory.CartesianClosed.curry_id_eq_coev, CategoryTheory.Bicategory.triangle_assoc_comp_left, CommBialgCat.id_apply, CategoryTheory.WithInitial.opEquiv_counitIso_hom_app, CategoryTheory.Adjunction.id_counit, CategoryTheory.prodComonad_δ_app, Preord.coe_id, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.ofRestrict_invApp, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_hom_app_hom, CochainComplex.cm5b.fac, CategoryTheory.WideSubcategory.id_def, CategoryTheory.Quotient.lift.isLift_hom, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_right, HomologicalComplex.natIsoSc'_inv_app_τ₂, DerivedCategory.singleFunctorsPostcompQIso_inv_hom, AlgebraicGeometry.Spec.locallyRingedSpaceMap_id, CategoryTheory.Bimon.equivMonComonUnitIsoApp_hom_hom_hom, CategoryTheory.MonoidalCategory.id_tensorHom, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_hom_app_hom_hom_app, CategoryTheory.Monad.algebraEquivOfIsoMonads_unitIso, CategoryTheory.Functor.Monoidal.whiskerLeft_μ_δ, CategoryTheory.Functor.mapTriangleCompIso_hom_app_hom₂, CategoryTheory.Subfunctor.Subpresheaf.preimage_id, PresheafOfModules.freeYonedaEquiv_symm_app, CategoryTheory.Functor.currying_counitIso_hom_app_app, CategoryTheory.MorphismProperty.Over.mapCongr_inv_app_left, CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapComp_hom, CategoryTheory.Over.mapId_eq, CategoryTheory.Bicategory.whiskerLeft_iff, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_fiber, CategoryTheory.FreeBicategory.mk_right_unitor_inv, CategoryTheory.Functor.RightExtension.postcomp₁_map_right, CategoryTheory.Functor.prod'CompSnd_hom_app, CategoryTheory.ForgetEnrichment.homOf_eId, CategoryTheory.Functor.mapActionComp_hom, CategoryTheory.BasedNatIso.id_hom, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionActionOfMonoidalFunctorToEndofunctorIso_inv_app_app, CategoryTheory.eqToHom_heq_id_cod, CategoryTheory.Limits.Cones.extendId_inv_hom, CategoryTheory.Iso.inv_comp_eq_id, CategoryTheory.kernelCokernelCompSequence.snakeInput_v₂₃_τ₃, CategoryTheory.Bicategory.conjugateEquiv_symm_id, CategoryTheory.Limits.span_map_id, CategoryTheory.Over.iteratedSliceForwardIsoPost_inv_app, CategoryTheory.ShortComplex.SnakeInput.id_f₂, CategoryTheory.Grp.ε_def, CategoryTheory.MorphismProperty.RightFraction.map_hom_ofInv_id, AlgebraicGeometry.IsSeparated.instIsClosedImmersionLiftSchemeId, CategoryTheory.Bicategory.conjugateEquiv_apply, CategoryTheory.ShortComplex.RightHomologyMapData.compatibilityOfZerosOfIsLimitKernelFork_φH, CommRingCat.ofHom_id, CategoryTheory.Limits.Multifork.isoOfι_inv_hom, CategoryTheory.Sum.functorEquiv_unit_app_app_inr, CategoryTheory.Functor.IsCartesian.domainUniqueUpToIso_inv_isHomLift, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε, CategoryTheory.GradedObject.Monoidal.rightUnitor_naturality_assoc, CategoryTheory.MonoidalCategory.DayFunctor.id_natTrans, CategoryTheory.Limits.walkingParallelPairHom_id, SSet.stdSimplex.map_id, CategoryTheory.monoidalOpOp_δ, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_inv_τl, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_inv_app_left, CategoryTheory.ReflQuiv.id_map, CategoryTheory.Limits.Cocones.eta_inv_hom, CategoryTheory.StructuredArrow.eta_hom_right, CategoryTheory.GradedObject.Monoidal.symmetry, CategoryTheory.Cat.leftUnitor_hom_app, CategoryTheory.Functor.curry₃_obj_obj_map_app, CategoryTheory.ComposableArrows.threeδ₃Toδ₂_app_one, CategoryTheory.IsPullback.id_horiz, CategoryTheory.Sum.functorEquiv_unitIso_inv_app_app_inl, CategoryTheory.Retract.retract, CategoryTheory.MonoidalCategory.id_tensor_comp_tensor_id, CategoryTheory.Bicategory.whiskerRight_id, CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv'_assoc, CategoryTheory.MonoOver.mapIso_counitIso, CategoryTheory.sheafToPresheaf_μ, CategoryTheory.NatTrans.mapHomologicalComplex_id, HasFibers.homLift, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₁_app, CategoryTheory.Cat.FreeRefl.homMk_id, CategoryTheory.ShortComplex.Splitting.id, CategoryTheory.Functor.mapTriangleRotateIso_inv_app_hom₁, BddDistLat.hom_id, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompPointIso_hom_app, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans, CategoryTheory.StructuredArrow.eta_inv_right, CategoryTheory.Discrete.compNatIsoDiscrete_hom_app, CategoryTheory.comul_eq_lift, CategoryTheory.CostructuredArrow.mapIso_unitIso_hom_app_left, Rep.resCoindAdjunction_unit_app_hom_hom, CategoryTheory.Dial.triangle, HomologicalComplex.cyclesMap_id, CategoryTheory.ObjectProperty.isoHom_inv_id_hom, CategoryTheory.EnrichedCat.associator_inv_out_app, CategoryTheory.Limits.PushoutCocone.isoMk_inv_hom, CategoryTheory.Limits.colimitYonedaHomIsoLimit'_π_apply, CategoryTheory.Prod.symmetry_hom_app, CategoryTheory.WithInitial.liftFromUnderComp_inv_app, CategoryTheory.MorphismProperty.Over.pullbackMapHomPullback_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_id_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionActionOfMonoidalFunctorToEndofunctorMopIso_hom_app_unmop_app, CategoryTheory.Limits.WalkingParallelPair.inclusionWalkingReflexivePair_map, AlgebraicGeometry.Scheme.Hom.id_preimage, BddOrd.coe_id, CategoryTheory.coreCategory_id_iso_inv, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_right, CategoryTheory.Limits.Cone.toStructuredArrowCompProj_inv_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.inv_hom_actionHomLeft, CategoryTheory.Limits.parallelPairOpIso_inv_app_one, AlgebraicGeometry.Scheme.Modules.pseudofunctor_right_unitality_assoc, CategoryTheory.Join.inrCompFromSum_hom_app, CategoryTheory.ShortComplex.RightHomologyMapData.id_φH, CategoryTheory.CostructuredArrow.toOver_map_right, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_c_app, CategoryTheory.LaxFunctor.id_mapId, CategoryTheory.Comma.toPUnitIdEquiv_counitIso_hom_app, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagram_map, CategoryTheory.MonoidalCategory.id_tensor_rightUnitor_inv_assoc, CategoryTheory.MonoidalCategory.prodCompExternalProduct_inv_app, CategoryTheory.Equivalence.mkHom_id_inverse, CategoryTheory.FreeGroupoid.mapId_hom_app, BddOrd.hom_id, CategoryTheory.Functor.mapMatComp_hom_app, CategoryTheory.Sigma.mapComp_hom_app, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_left, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_id, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_inv_app_app_fst, Rep.FiniteCyclicGroup.chainComplexFunctor_obj, CategoryTheory.Oplax.StrongTrans.homCategory_id_as_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom, CategoryTheory.exp.coev_ev, CategoryTheory.Endofunctor.Algebra.functorOfNatTransComp_hom_app_f, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.ofRestrict_invApp, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, CategoryTheory.Limits.biprod.symmetry, CategoryTheory.Comma.mapSnd_inv_app, CategoryTheory.ShortComplex.opcyclesMap'_id, HomologicalComplex.forgetEval_hom_app, CategoryTheory.Functor.compConstIso_hom_app_app, CategoryTheory.Preadditive.commGrpEquivalence_unitIso_inv_app, commBialgCatEquivComonCommAlgCat_unitIso_hom_app, CategoryTheory.Limits.CategoricalPullback.id_fst, CategoryTheory.Functor.coreComp_hom_app_iso_hom, CategoryTheory.CatCommSq.vId_iso_hom_app, CategoryTheory.ComposableArrows.fourδ₄Toδ₃_app_two, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_inv_app_snd_app, CategoryTheory.WithTerminal.opEquiv_counitIso_inv_app, CategoryTheory.Functor.IsEventuallyConstantTo.isoMap_inv_hom_id, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_inv_app_hom_left, PresheafOfModules.id_app, CategoryTheory.Codiscrete.natIsoFunctor_hom_app, CategoryTheory.Functor.flipping_counitIso_inv_app_app_app, CategoryTheory.Bicategory.whiskerLeft_hom_inv, CategoryTheory.Lax.LaxTrans.id_app, CategoryTheory.ShortComplex.opMap_id, CategoryTheory.Dial.braiding_naturality_right, CategoryTheory.Limits.CatCospanTransform.whiskerleft_id, CategoryTheory.WithTerminal.liftStar_hom, CategoryTheory.SmallObject.SuccStruct.arrowMap_refl, CategoryTheory.Bicategory.mateEquiv_id_comp_right, CategoryTheory.Discrete.id_def, CategoryTheory.Bicategory.leftUnitor_comp_inv, CategoryTheory.Functor.curryObjProdComp_hom_app_app, AlgebraicGeometry.Scheme.Modules.pushforwardComp_inv_app_app, CategoryTheory.Functor.associator_hom_app, CategoryTheory.Pseudofunctor.mapComp_id_left, CategoryTheory.Limits.IsBilimit.total, BddDistLat.coe_id, CategoryTheory.MonoOver.mkArrowIso_hom_hom_left, CategoryTheory.Functor.rightOpComp_hom_app, CategoryTheory.Limits.equalizerPullbackMapIso_inv_ι_snd, CategoryTheory.hom_id, CategoryTheory.EnrichedCat.rightUnitor_hom_out_app, CategoryTheory.Idempotents.Karoubi.decompId_p_naturality, CategoryTheory.Biprod.unipotentLower_inv, CategoryTheory.NatTrans.id_app', CategoryTheory.ShortComplex.RightHomologyData.ofHasKernel_p, CategoryTheory.Functor.mapContActionComp_inv, CategoryTheory.Bicategory.leftZigzagIso_hom, AddSemigrp.coe_id, CategoryTheory.Functor.rightOpLeftOpIso_hom_app, CategoryTheory.Functor.Monoidal.ε_η, CategoryTheory.LocalizerMorphism.LeftResolution.Hom.id_f, BddDistLat.ofHom_id, CategoryTheory.Preadditive.commGrpEquivalence_unitIso_hom_app, CategoryTheory.ObjectProperty.ι_η, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_hom_inv, GrpWithZero.coe_id, CategoryTheory.StrictPseudofunctor.comp_mapId_hom, CategoryTheory.Over.rightUnitor_inv_left_fst, CategoryTheory.Limits.piConst_map_app, GrpCat.hom_id, CategoryTheory.CostructuredArrow.homMk'_mk_id, CategoryTheory.Functor.mapMonCompIso_hom_app_hom, CategoryTheory.MonObj.instIsMonHomId, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_fiber, CategoryTheory.nerve.edgeMk_id, CategoryTheory.Functor.LeftExtension.coconeAtWhiskerRightIso_inv_hom, SSet.Subcomplex.image_id, CategoryTheory.Limits.IsBilimit.binary_total, CategoryTheory.prod_id, CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_right, TopCat.Sheaf.id_app, Bicategory.Opposite.unop2_id_bop, CategoryTheory.Functor.RightExtension.precomp_map_left, CategoryTheory.Limits.Cocone.toCostructuredArrowCompProj_hom_app, CategoryTheory.ShortComplex.rightHomologyMap'_id, CategoryTheory.Limits.coneOfIsSplitMono_ι, CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp_inv_hom₃, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_hom_hom₂, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id, CategoryTheory.GlueData.t_inv, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.ofRestrict_invApp_apply, CategoryTheory.StructuredArrow.id_right, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_right_app, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.const_s', HomotopicalAlgebra.FibrantBrownFactorization.mk'_i, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.left_triangle_components, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_unit_app, CategoryTheory.Limits.equalizerPullbackMapIso_inv_ι_fst, CategoryTheory.Limits.pullback.diagonal_snd, CategoryTheory.Over.mapCongr_inv_app_left, CategoryTheory.BicategoricalCoherence.tensorRight_iso, CategoryTheory.IsPullback.zero_top, CategoryTheory.Bicategory.inv_hom_whiskerRight_whiskerRight, CategoryTheory.Functor.IsStronglyCartesian.map_self, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.id_fst_app, CategoryTheory.Bicategory.Prod.sectR_mapComp_inv, CategoryTheory.Bicategory.Prod.fst_mapComp_hom, CategoryTheory.Cat.freeMapIdIso_hom_app, CategoryTheory.Functor.curryingFlipEquiv_symm_apply_map_app, CategoryTheory.HomOrthogonal.matrixDecomposition_id, CategoryTheory.Limits.pullbackConeOfLeftIso_snd, CochainComplex.mappingCone.id_X, CategoryTheory.Bicategory.id_whiskerLeft_symm, HomologicalComplex.iCyclesIso_inv_hom_id, CategoryTheory.Functor.opId_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_hom_app_fst_app, CategoryTheory.Over.mapCongr_hom_app_left, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd, CategoryTheory.CostructuredArrow.homMk'_right, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app, CategoryTheory.Functor.opUnopIso_inv_app, SemiNormedGrp₁.hom_id, CategoryTheory.MonoidalCategory.tensor_inv_hom_id', CategoryTheory.Limits.LimitPresentation.self_π, CategoryTheory.GrothendieckTopology.sheafifyMap_id, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_inv_app, AlgebraicGeometry.Scheme.hom_base_inv_base, CategoryTheory.CosimplicialObject.δ_comp_σ_self', CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_hom_app_unmop_unmop, CategoryTheory.WithInitial.inclLift_hom_app, CategoryTheory.IsPullback.of_id_snd, CategoryTheory.Localization.Monoidal.id_tensorHom, CategoryTheory.Over.mapComp_hom_app_left, CategoryTheory.Limits.walkingCospanOpEquiv_counitIso_hom_app, TopologicalSpace.Opens.mapId_hom_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_inv_hom, CategoryTheory.Functor.mapTriangleInvRotateIso_inv_app_hom₃, CategoryTheory.Grothendieck.id_fiber, CategoryTheory.Comma.equivProd_unitIso_hom_app_left, SSet.Subcomplex.topIso_inv_ι, CategoryTheory.PreZeroHypercover.restrictIndexHom_h₀, CategoryTheory.SimplicialObject.Truncated.rightExtensionInclusion_hom_app, CategoryTheory.MonoidalCategory.id_tensor_comp_assoc, CategoryTheory.ShortComplex.HomotopyEquiv.refl_hom, CategoryTheory.Bicategory.Adj.rightUnitor_inv_τl, CategoryTheory.GradedObject.mapBifunctorMap_obj_map, PartOrd.coe_id, CategoryTheory.PreZeroHypercover.Hom.id_h₀, CategoryTheory.Functor.unopId_inv_app, CategoryTheory.Square.Hom.id_τ₄, OrderHom.equivalenceFunctor_counitIso_inv_app_app, Action.FunctorCategoryEquivalence.unitIso_inv_app_hom, CategoryTheory.Functor.mapCommGrpCompIso_hom_app_hom_hom_hom, CategoryTheory.Join.pseudofunctorLeft_mapId_hom_toNatTrans_app, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_app_assoc, CategoryTheory.Limits.colimit.toOver_ι_app, AlgebraicGeometry.pointEquivClosedPoint_apply_coe, CategoryTheory.StrictlyUnitaryLaxFunctor.comp_mapId, CategoryTheory.Over.postAdjunctionLeft_unit_app_left, CategoryTheory.Functor.mapActionComp_inv, CategoryTheory.Idempotents.functorExtension₂CompWhiskeringLeftToKaroubiIso_hom_app_app_f, CategoryTheory.Functor.ι_colimitIsoColimitGrothendieck_hom, CategoryTheory.GradedObject.mapTrifunctorMapFunctorObj_map_app, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_counit_app, CochainComplex.mappingConeCompHomotopyEquiv_hom_inv_id, CommSemiRingCat.ofHom_id, CategoryTheory.Cat.rightUnitor_hom_toNatTrans, CategoryTheory.BasedNatTrans.isHomLift', CategoryTheory.Limits.spanCompIso_hom_app_zero, CategoryTheory.Functor.const.opObjUnop_hom_app, AlgebraicGeometry.LocallyRingedSpace.Γ_Spec_left_triangle, CategoryTheory.Adjunction.mkOfHomEquiv_counit_app, CategoryTheory.Functor.prod'CompFst_hom_app, CategoryTheory.Functor.coreId_inv_app_iso_inv, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_inv_app_hom_hom_app, CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id, CategoryTheory.MonoidalOpposite.tensorLeftUnmopIso_inv_app, isoOfQuasiIsoAt_hom_inv_id, CategoryTheory.compEvaluation_hom_app, ProfiniteGrp.hom_id, AlgebraicGeometry.Spec.preimage_id, CategoryTheory.Over.preservesTerminalIso_pullback, CategoryTheory.Bicategory.leftUnitor_inv_whiskerRight_assoc, ProfiniteAddGrp.hom_id, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_hom_hom₁, CategoryTheory.Precoverage.ZeroHypercover.id_h₀, HomologicalComplex.cylinder.πCompι₀Homotopy.nullHomotopicMap_eq, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app_assoc, CommGrpCat.hom_id, CategoryTheory.StrictlyUnitaryPseudofunctor.mk'_mapId, CategoryTheory.EnrichedFunctor.category_id_out, CategoryTheory.NatTrans.op_id, CategoryTheory.FreeGroupoid.mapCompLift_inv_app, CategoryTheory.MorphismProperty.FunctorsInverting.id_hom, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_inv_right, CategoryTheory.StructuredArrow.map₂_map_left, CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapId_inv, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_coproductIsoSelf_inv_assoc, CategoryTheory.Bicategory.Adj.rightUnitor_hom_τr, AlgebraicGeometry.Scheme.Pullback.cocycle, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_coproductIsoSelf_inv, CategoryTheory.Under.postAdjunctionRight_unit_app_right, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapId_inv_iso_inv, SimplexCategoryGenRel.δ_comp_σ_self, CategoryTheory.Pseudofunctor.mapComp_id_right, CategoryTheory.Functor.curry₃ObjProdComp_inv_app_app_app, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.id_tensorHom_id, CategoryTheory.WithTerminal.coneEquiv_counitIso_inv_app_hom, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₃_app, CategoryTheory.BicategoricalCoherence.left_iso, CategoryTheory.Limits.FormalCoproduct.cofan_inj, CategoryTheory.Functor.mapGrp_id_one, CategoryTheory.ComposableArrows.threeδ₂Toδ₁_app_two, CategoryTheory.Monad.Algebra.id_f, Bicategory.Opposite.bicategory_leftUnitor_hom_unop2, TopologicalSpace.Opens.map_id_obj', CategoryTheory.Functor.OplaxMonoidal.id_δ, CategoryTheory.uliftYonedaEquiv_apply, HomologicalComplex₂.flipEquivalenceUnitIso_hom_app_f_f, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_map, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id_app, CategoryTheory.CosimplicialObject.id_app, AlgCat.id_apply, CategoryTheory.CartesianMonoidalCategory.prodComparison_id, CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapComp_inv, CategoryTheory.Bicategory.Pith.id₂_iso_inv, CategoryTheory.Iso.comp_hom_eq_id, AlgebraicGeometry.Scheme.Hom.id_app, CategoryTheory.Functor.currying_inverse_obj_obj_map, HomologicalComplex.opcyclesMap_id, CategoryTheory.Square.Hom.id_τ₃, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_left, CategoryTheory.Sigma.mapComp_inv_app, CategoryTheory.Comon.id_hom, CategoryTheory.Pretriangulated.triangleMorphismId_hom₃, CategoryTheory.Functor.diag_δ, CategoryTheory.Over.rightUnitor_inv_left_snd, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_map_left, CategoryTheory.Limits.Cone.toStructuredArrowCompToUnderCompForget_hom_app, CategoryTheory.Bicategory.mateEquiv_symm_apply', CategoryTheory.Comma.equivProd_counitIso_hom_app, CategoryTheory.Functor.mapCoconeOp_inv_hom, CategoryTheory.Limits.spanCompIso_inv_app_left, Action.FunctorCategoryEquivalence.functor_δ, CategoryTheory.Mat_.id_apply_self, CategoryTheory.Pseudofunctor.mapComp'_comp_id, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_id, CategoryTheory.WithTerminal.down_id, CategoryTheory.OplaxFunctor.map₂_leftUnitor_assoc, CategoryTheory.prodOpEquiv_unitIso_hom_app, CategoryTheory.Bifunctor.map_id_comp, CategoryTheory.Bicategory.conjugateEquiv_id_comp_right_apply, CategoryTheory.Functor.map_hom_inv, CategoryTheory.Functor.rightUnitor_hom_app, CategoryTheory.Comma.mapRightId_inv_app_left, CategoryTheory.EnrichedCategory.comp_id, CategoryTheory.Bicategory.Adjunction.homEquiv₂_apply, CategoryTheory.Functor.leftOpId_hom_app, CategoryTheory.Over.mapPullbackAdj_counit_app, CategoryTheory.WithTerminal.opEquiv_unitIso_hom_app, CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoSelf_hom, CategoryTheory.Limits.CatCospanTransform.category_id_right, CategoryTheory.Limits.equalizerPullbackMapIso_hom_fst_assoc, CategoryTheory.Comma.mapLeftId_hom_app_right, CategoryTheory.Oplax.StrongTrans.naturality_id_assoc, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₃, HomotopicalAlgebra.FibrantBrownFactorization.mk'_Z, CategoryTheory.MonoidalCategory.DayConvolution.hexagon_forward, CategoryTheory.WithTerminal.opEquiv_counitIso_hom_app, CategoryTheory.Oplax.LaxTrans.naturality_id, CategoryTheory.Limits.pullback.comp_diagonal_assoc, AlgebraicGeometry.Scheme.IdealSheafData.comap_id, CategoryTheory.Preadditive.commGrpEquivalence_functor_obj_grp_inv, HomologicalComplex.stupidTruncMap_id, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_left_unitor, CategoryTheory.SimplicialObject.Augmented.const_obj_hom, CategoryTheory.Limits.prod.diag_map_fst_snd, TopologicalSpace.OpenNhds.op_map_id_obj, FinBddDistLat.coe_id, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_inv_app, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_hom_app, CategoryTheory.PreOneHypercover.trivial_toPreZeroHypercover, CategoryTheory.Pseudofunctor.isoMapOfCommSq_horiz_id, CategoryTheory.CatEnriched.id_hComp_heq, CategoryTheory.CostructuredArrow.mapIso_unitIso_inv_app_left, CategoryTheory.MonoidalCategory.DayConvolution.hexagon_reverse, CategoryTheory.PreOneHypercover.id_h₀, CategoryTheory.MonoidalCategory.DayFunctor.equiv_counitIso_inv_app, AlgebraicGeometry.Spec.topMap_id, ChainComplex.truncateAugment_inv_f, CategoryTheory.Comma.mapRightComp_inv_app_right, CategoryTheory.Localization.SmallShiftedHom.comp_mk₀_id, CategoryTheory.Limits.biprod.symmetry', CategoryTheory.SingleFunctors.Hom.id_hom, CategoryTheory.Functor.whiskerRight_id', CategoryTheory.IsIso.inv_id, CategoryTheory.Monad.left_unit, AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex_homotopyHomInvId, CategoryTheory.Endofunctor.Coalgebra.id_eq_id, AddSemigrp.hom_id, CategoryTheory.Functor.compFlipUncurryIso_inv_app, CategoryTheory.NatTrans.leftOp_id, CategoryTheory.Limits.pullback_symmetry_hom_of_epi_eq, CategoryTheory.Pretriangulated.id_hom₃, Action.hom_inv_hom, CategoryTheory.Comonad.Coalgebra.id_eq_id, AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ, CategoryTheory.Functor.lanUnit_app_app_lanAdjunction_counit_app_app, CategoryTheory.MonoidalCategory.id_tensor_associator_inv_naturality, CategoryTheory.FinCategory.categoryAsType_id, CategoryTheory.homOfLE_refl, CategoryTheory.MonoidalCategory.id_tensor_rightUnitor_inv, CategoryTheory.Oplax.LaxTrans.id_app, CategoryTheory.EnrichedCategory.id_comp, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_leftUnitor_inv_as_app, CategoryTheory.EnrichedFunctor.id_map, CategoryTheory.Functor.lanUnit_app_whiskerLeft_lanAdjunction_counit_app, SemiRingCat.hom_id, ModuleCat.id_apply, CategoryTheory.Limits.parallelPairOpIso_hom_app_one, CategoryTheory.Limits.walkingCospanOpEquiv_counitIso_inv_app, CategoryTheory.Pseudofunctor.map₂_right_unitor_assoc, CategoryTheory.Functor.mapTriangleInvRotateIso_hom_app_hom₃, CategoryTheory.Bicategory.Prod.sectL_mapComp_hom, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff, CategoryTheory.Limits.IsColimit.desc_self, CategoryTheory.CostructuredArrow.mkPrecomp_right, CategoryTheory.Limits.coprod.leftUnitor_hom, CategoryTheory.prod_id', CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso_inv_app_f, CategoryTheory.Limits.HasEqualizersOfHasPullbacksAndBinaryProducts.pullbackFst_eq_pullback_snd, CategoryTheory.Iso.hom_inv_id_triangle_hom₂, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_hom_app, CategoryTheory.Functor.constComp_inv_app, BoolAlg.hom_id, CategoryTheory.Comon.forget_η, CategoryTheory.Bimon.equivMonComonCounitIsoAppXAux_inv, CategoryTheory.ComonadHom.id_toNatTrans, CategoryTheory.Discrete.functor_map_id, CategoryTheory.Bicategory.leftUnitor_inv_naturality, CategoryTheory.Endofunctor.Algebra.Initial.right_inv, CategoryTheory.WithTerminal.lift_map, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_inv_hom, CategoryTheory.Sum.swapCompInl_hom_app, CategoryTheory.Bicategory.unitors_equal, CategoryTheory.MonoidalCategory.DayConvolution.pentagon, CategoryTheory.IsSplitCoequalizer.leftSection_bottom, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_hom_app_f, CategoryTheory.Limits.Cocones.extendId_hom_hom, CategoryTheory.Limits.prod.leftUnitor_inv_naturality_assoc, CommAlgCat.ofHom_id, CategoryTheory.Monad.comparisonForget_hom_app, DistLat.hom_id, CategoryTheory.Monoidal.tensorUnit_map, CategoryTheory.Dial.comp_le_lemma, CategoryTheory.MonoidalOpposite.tensorIso_hom_app_unmop, CategoryTheory.Cat.rightUnitor_hom_app, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_right_app, AlgebraicGeometry.Scheme.id_appTop, CategoryTheory.Limits.IsInitial.to_self, Bimod.LeftUnitorBimod.inv_hom_id, CategoryTheory.Oplax.LaxTrans.id_naturality, CategoryTheory.kernelCokernelCompSequence.snakeInput_L₃_f, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_id, CategoryTheory.Limits.isPushout_coequalizer_coprod, CategoryTheory.endofunctorMonoidalCategory_associator_inv_app, SSet.id_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_app_fst_app, CategoryTheory.Pseudofunctor.mapComp_id_right_hom, CategoryTheory.Functor.currying_counitIso_inv_app_app, CategoryTheory.MonoidalCategory.whiskerLeft_id_assoc, CategoryTheory.WithTerminal.inclLift_hom_app, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_unit_app, CategoryTheory.CostructuredArrow.eta_hom_left, CategoryTheory.over_def, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_inv_app_hom, CategoryTheory.MonoidalCategory.hom_inv_whiskerRight, CategoryTheory.MonoidalCategory.comp_tensor_id_assoc, CategoryTheory.Dial.whiskerRight_f, CategoryTheory.Comon.forget_δ, CategoryTheory.MonoidalCategory.tensor_left_iff, CategoryTheory.Functor.curry₃_obj_map_app_app, CategoryTheory.Functor.coreId_inv_app_iso_hom, CategoryTheory.GradedObject.categoryOfGradedObjects_id, CategoryTheory.IsIso.inv_hom_id, CategoryTheory.Under.mapId_inv, CategoryTheory.CatEnrichedOrdinary.hComp_id, CategoryTheory.MonObj.one_def, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_base, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.ev_naturality_app, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_inv_left, CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoSelf_hom_assoc, CategoryTheory.Grothendieck.ιCompMap_inv_app_fiber, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_hom_τr, CategoryTheory.StrictPseudofunctor.comp_mapId_inv, HomologicalComplex.biprod_inr_snd_f, CategoryTheory.Pseudofunctor.Grothendieck.map_id_map, ContinuousMap.Homotopy.apply_one_path, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₁, HomologicalComplex.id_f, CategoryTheory.id_app, CategoryTheory.Localization.SmallShiftedHom.mk₀_id_comp, CategoryTheory.Limits.opParallelPairIso_hom_app_zero, CategoryTheory.Bicategory.Adj.id_τl, CategoryTheory.Limits.map_id_left_eq_curry_map, CategoryTheory.TwoSquare.guitartExact_id, SimplexCategoryGenRel.δ_comp_σ_succ, CategoryTheory.IsPushout.zero_bot, CategoryTheory.Limits.BinaryBicone.ofLimitCone_inr, HeytAlg.id_apply, CategoryTheory.IsPushout.zero_left, CategoryTheory.Pseudofunctor.ObjectProperty.mapId_inv_app, CategoryTheory.Limits.inr_zeroCoprodIso_hom, CategoryTheory.Limits.Cocone.toCostructuredArrowCompToOverCompForget_inv_app, CategoryTheory.Limits.CatCospanTransform.rightUnitor_inv_right_app, CategoryTheory.ShortComplex.Hom.id_τ₁, CategoryTheory.Bimon.ofMon_Comon_ObjX_one, CategoryTheory.Limits.BinaryBicone.category_id_hom, CategoryTheory.Biprod.unipotentUpper_hom, CategoryTheory.CatCommSq.hId_iso_inv_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.id_actionHomLeft, CategoryTheory.δ_μ_app, AlgebraicGeometry.Scheme.isMonHom_fst_id_right, CategoryTheory.Monad.adj_counit, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app_assoc, TopologicalSpace.Opens.map_id_obj, FintypeCat.id_apply, CategoryTheory.Limits.prod_rightUnitor_inv_naturality_assoc, SheafOfModules.pushforwardNatTrans_id, CategoryTheory.Bicategory.conjugateEquiv_comp_id_right_apply, CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id_app, CategoryTheory.Limits.piConst_obj_map, CategoryTheory.FinitaryPreExtensive.isIso_sigmaDesc_map, CategoryTheory.ComposableArrows.twoδ₂Toδ₁_app_zero, CategoryTheory.WithInitial.coconeEquiv_counitIso_inv_app_hom, CategoryTheory.ObjectProperty.ι_ε, CategoryTheory.Lax.LaxTrans.id_naturality, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₃, AlgebraicTopology.DoldKan.Γ₀NondegComplexIso_hom_f, CategoryTheory.hom_comp_eq_id, SemiNormedGrp.id_apply, CategoryTheory.flipCompEvaluation_hom_app, CategoryTheory.NatTrans.removeOp_id, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_assoc, CategoryTheory.Bicategory.leftUnitor_inv_whiskerRight, CategoryTheory.MonoidalOpposite.mopFunctor_η, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd, CategoryTheory.sheafifyMap_id, CategoryTheory.Idempotents.idem_of_id_sub_idem, CategoryTheory.MonoidalCategory.tensorμ_tensorδ, ModuleCat.ExtendScalars.map'_id, CategoryTheory.GradedObject.Monoidal.pentagon_inv, CategoryTheory.Subobject.pullback_id, CategoryTheory.WithInitial.commaFromUnder_map_left, CategoryTheory.Functor.RightLinear.μᵣ_comp_δᵣ, Action.resId_inv_app_hom, CategoryTheory.SimplicialObject.Augmented.const_map_left, Semigrp.id_apply, CategoryTheory.Functor.LeftExtension.postcompose₂ObjMkIso_inv_right_app, isoOfQuasiIsoAt_inv_hom_id, CategoryTheory.ChosenPullbacksAlong.Over.tensorUnit_hom, CategoryTheory.Limits.CategoricalPullback.id_snd, AlgebraicGeometry.Scheme.Cover.trans_id, CategoryTheory.MonoidalCategory.MonoidalLeftAction.id_actionHom, CategoryTheory.FreeBicategory.mk_id, CategoryTheory.Equivalence.counitInv_functor_comp, CochainComplex.mappingConeCompHomotopyEquiv_comm₁, CategoryTheory.Functor.sheafPushforwardContinuousCompSheafToPresheafIso_inv_app_app, CategoryTheory.Bicategory.instIsIsoHomLeftZigzagHom, CategoryTheory.Limits.colimitYonedaHomIsoLimit_π_apply, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_hom, AlgebraicGeometry.SheafedSpace.id_hom_c_app, CategoryTheory.Functor.inlCompSum'_hom_app, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, CategoryTheory.WithTerminal.liftToTerminal_map, CategoryTheory.ExponentiableMorphism.pushforwardId_hom_counit_assoc, CategoryTheory.Quotient.natTransLift_id, CategoryTheory.Limits.pullback_lift_diagonal_isPullback, CategoryTheory.Limits.walkingCospanOpEquiv_unitIso_inv_app, CategoryTheory.Bicategory.Equivalence.right_triangle, CategoryTheory.Join.mapPairComp_hom_app_right, LinOrd.id_apply, CategoryTheory.Oplax.OplaxTrans.categoryStruct_id_app, CategoryTheory.Idempotents.Karoubi.decomp_p, CategoryTheory.ShortComplex.RightHomologyMapData.ofEpiOfIsIsoOfMono'_φH, CategoryTheory.Bicategory.Equivalence.left_triangle, CategoryTheory.Bifunctor.map_id, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map_id, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app_assoc, CategoryTheory.OplaxFunctor.mapId'_eq_mapId, CategoryTheory.Under.mapPushoutAdj_unit_app, AlgebraicGeometry.Spec.map_id, CategoryTheory.Center.ofBraided_ε_f, CategoryTheory.Functor.leftOpRightOpIso_hom_app, CategoryTheory.Comma.mapLeftComp_inv_app_left, CategoryTheory.Pseudofunctor.StrongTrans.id.toOplax, CategoryTheory.Mat_.embeddingLiftIso_hom_app, CategoryTheory.Limits.FormalCoproduct.cofan_inj_φ, CategoryTheory.Join.mapWhiskerRight_app, CategoryTheory.Over.tensorUnit_hom, AlgebraicGeometry.Scheme.id.base, CategoryTheory.instEpiId, CategoryTheory.StructuredArrow.mkPostcomp_left, CategoryTheory.StructuredArrow.left_eq_id, CategoryTheory.MonoidalClosed.curry_id_eq_coev, CategoryTheory.Limits.opParallelPairIso_hom_app_one, CategoryTheory.Over.leftUnitor_inv_left_fst, Bicategory.Opposite.bicategory_leftUnitor_inv_unop2, CategoryTheory.Limits.cospanCompIso_inv_app_left, CategoryTheory.Limits.CatCospanTransform.associator_hom_left_app, CategoryTheory.Functor.mapTriangleCompIso_inv_app_hom₃, CategoryTheory.CatEnriched.hComp_id_heq, CategoryTheory.Functor.rightOpId_inv_app, CategoryTheory.Bicategory.Prod.sectR_mapId_inv, CategoryTheory.Square.category_id_τ₄, CategoryTheory.WithInitial.inclLiftToInitial_inv_app, CategoryTheory.Iso.hom_inv_id, SimplexCategory.eq_id_of_epi, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_unit_app_left, CategoryTheory.Over.inv_left_hom_left, CategoryTheory.Limits.inl_of_isLimit, CategoryTheory.Over.starPullbackIsoStar_hom_app_left, CategoryTheory.StructuredArrow.mapNatIso_unitIso_hom_app_right, FGModuleCat.hom_id, CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id, CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp_hom_hom₁, CategoryTheory.Monad.adj_unit, CategoryTheory.CostructuredArrow.id_left, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left, CategoryTheory.simplicialCosimplicialEquiv_counitIso_hom_app_app, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_presheafMap, CategoryTheory.Adjunction.toCat_counit_toNatTrans, CategoryTheory.PrelaxFunctor.map₂_hom_inv, CategoryTheory.MonoidalCategory.id_tensor_associator_naturality, CategoryTheory.Functor.mapTriangleCompIso_hom_app_hom₃, CategoryTheory.Limits.coneOfIsSplitMono_π_app, CategoryTheory.Functor.partialRightAdjointHomEquiv_map, CategoryTheory.StrictlyUnitaryLaxFunctor.id_mapComp, CategoryTheory.Limits.pullback.map_id, CategoryTheory.Join.isoMkFunctor_inv_app, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_map_base, CategoryTheory.IsHomLift.id, LinOrd.ofHom_id, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransId_inv_app_f, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp_app, CategoryTheory.IsSplitEpi.id, CategoryTheory.WithInitial.coconeEquiv_unitIso_hom_app_hom_right, CategoryTheory.Functor.CorepresentableBy.homEquiv_eq, CategoryTheory.ShortComplex.Splitting.g_s, CategoryTheory.Over.forgetMapTerminal_inv_app, AlgebraicGeometry.LocallyRingedSpace.stalkMap_id, CategoryTheory.Abelian.LeftResolution.karoubi.F'_obj_p, CategoryTheory.MorphismProperty.Over.mapCongr_hom_app_left, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.hom_inv_actionHomLeft', CategoryTheory.section_comp_right, Semigrp.hom_id, CategoryTheory.comp_inv_eq_id, HomotopicalAlgebra.Precylinder.i₀_π, ChainComplex.augmentTruncate_inv_f_succ, ProfiniteAddGrp.id_apply, CategoryTheory.ULift.equivalence_unitIso_inv, CategoryTheory.MonoidalCategory.MonoidalRightAction.id_actionHomLeft_assoc, AlgebraicGeometry.IsOpenImmersion.isPullback_lift_id, CategoryTheory.Preadditive.commGrpEquivalenceAux_hom_app_hom_hom_hom, Action.tensorUnit_ρ, CategoryTheory.Pseudofunctor.StrongTrans.homCategory_id_as_app, CategoryTheory.ShiftedHom.mk₀_id_comp, HomologicalComplex.restrictionMap_id, CategoryTheory.Sum.natTransOfWhiskerLeftInlInr_id, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan_inv_app_app_apply_eq_id, CategoryTheory.Discrete.functorComp_hom_app, CategoryTheory.ShortComplex.id_τ₁, CategoryTheory.OverClass.asOverHom_id, Preord.id_apply, CategoryTheory.Functor.mapCoconeMapCocone_hom_hom, CategoryTheory.FreeBicategory.mk_left_unitor_hom, AddCommGrpCat.hom_id, CategoryTheory.Factorisation.Hom.id_h, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app_assoc, CategoryTheory.Limits.PushoutCocone.eta_inv_hom, CategoryTheory.Bicategory.Adjunction.ofCat_id, CategoryTheory.Over.conePostIso_hom_app_hom, CategoryTheory.EnrichedCat.rightUnitor_inv_out_app, groupCohomology.map_id, CategoryTheory.Limits.coprod.map_id_comp, Preord.hom_id, CategoryTheory.Functor.partialLeftAdjointHomEquiv_map, CategoryTheory.MonoidalCategory.DayFunctor.equiv_counitIso_hom_app, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInrIso_inv_app_app, CategoryTheory.Localization.Monoidal.tensorHom_id, CategoryTheory.ShortComplex.RightHomologyMapData.ofEpiOfIsIsoOfMono'_φQ, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_id, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapIdIso_inv, CategoryTheory.MonoidalOpposite.mopMopEquivalenceFunctorMonoidal_μ, CochainComplex.mappingConeCompHomotopyEquiv_comm₁_assoc, CategoryTheory.Functor.curry₃ObjProdComp_hom_app_app_app, CategoryTheory.Pseudofunctor.whiskerLeftIso_mapId, CategoryTheory.Functor.whiskeringLeftObjIdIso_hom_app_app, CategoryTheory.Limits.prod.leftUnitor_hom_naturality_assoc, CategoryTheory.Idempotents.Karoubi.id_f, CategoryTheory.Grp.μ_def, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_hom_app_hom_hom_app, CategoryTheory.Bicategory.Pith.rightUnitor_hom_iso, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_id_assoc, CategoryTheory.NatTrans.toCatHom₂_id, SheafOfModules.Presentation.quasicoherentData_presentation, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_counitIso, CategoryTheory.mop_id, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_base, CategoryTheory.SmallObject.ε_app, CategoryTheory.Limits.prod.map_comp_id, CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_inv_app, CategoryTheory.Center.forget_ε, CategoryTheory.Bicategory.Comonad.counit_comul_assoc, SSet.Truncated.id_app, CategoryTheory.curryingIso_inv_toFunctor_obj_map_app, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd_assoc, Bicategory.Opposite.op2_rightUnitor_inv, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_app, CategoryTheory.Pseudofunctor.id_mapId, CategoryTheory.Iso.inv_hom_id_app_app, CategoryTheory.Discrete.productEquiv_counitIso_hom_app, CategoryTheory.Functor.LeftExtension.postcompose₂_map_right_app, CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_snd, CategoryTheory.MonoidalCategory.tensor_right_iff, CategoryTheory.Biprod.unipotentLower_hom, CategoryTheory.BicategoricalCoherence.right'_iso, CategoryTheory.Join.mapIsoWhiskerRight_hom_app, CategoryTheory.ExponentiableMorphism.ev_coev, CategoryTheory.Limits.FormalCoproduct.inj_comp_cofanPtIsoSelf_hom_assoc, Rep.indResAdjunction_counit_app_hom_hom, CategoryTheory.MonoidalOpposite.mopMopEquivalenceFunctorMonoidal_ε, CategoryTheory.Functor.Monoidal.whiskeringLeft_ε_app, CategoryTheory.Limits.prod.leftUnitor_inv, CategoryTheory.Limits.Cone.category_id_hom, CategoryTheory.ULift.equivalence_counitIso_hom_app, CategoryTheory.IsPushout.of_id_fst, CategoryTheory.CommGrp.trivial_grp_one, CategoryTheory.CostructuredArrow.map_map_right, CategoryTheory.Over.leftUnitor_inv_left_snd, CategoryTheory.ShortComplex.SnakeInput.Hom.id_f₃, CategoryTheory.Bicategory.Adj.id_τr, CategoryTheory.sheafifyLift_id_toSheafify, CategoryTheory.Subgroupoid.IsWide.wide, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst_assoc, CategoryTheory.Limits.snd_of_isColimit, CategoryTheory.Oplax.StrongTrans.Modification.id_app, CategoryTheory.Comonad.left_counit, TopCat.id_app, CategoryTheory.Bicategory.prod_rightUnitor_inv_fst, AddMonCat.coe_id, HomologicalComplex.pOpcyclesIso_inv_hom_id, CategoryTheory.Bimon.ofMon_Comon_ObjX_mul, CategoryTheory.Presheaf.freeYoneda_map, CategoryTheory.ComposableArrows.fourδ₄Toδ₃_app_one, CategoryTheory.StructuredArrow.homMk'_left, CategoryTheory.unmop_id, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionActionOfMonoidalFunctorToEndofunctorMopIso_inv_app_unmop_app, CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id_app, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app_assoc, CategoryTheory.Functor.Monoidal.whiskeringLeft_μ_app, CategoryTheory.Comma.equivProd_unitIso_hom_app_right, CategoryTheory.Dial.leftUnitor_inv_f, CategoryTheory.Limits.biprod.inl_fst, CategoryTheory.Limits.pullback.diagonal_fst, CategoryTheory.SmallObject.objMap_id, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_hom_τl, CategoryTheory.bijection_symm_apply_id, CategoryTheory.Limits.Sigma.map_id, CategoryTheory.Limits.id_zero, SimplexCategory.id_toOrderHom, CategoryTheory.ShortComplex.HomologyMapData.compatibilityOfZerosOfIsLimitKernelFork_left, CategoryTheory.Pretriangulated.contractible_distinguished₂, CategoryTheory.CartesianMonoidalCategory.rightUnitor_inv_fst, CategoryTheory.Limits.pullbackConeOfRightIso_fst, IsFreeGroupoid.SpanningTree.loopOfHom_eq_id, CategoryTheory.Over.mapPullbackAdj_unit_app, CategoryTheory.sheafToPresheaf_δ, CategoryTheory.prod.leftInverseUnitor_map, CategoryTheory.Limits.coprod.inr_snd, CategoryTheory.monoidalUnopUnop_ε, CochainComplex.mappingCone.inr_f_snd_v, ProfiniteAddGrp.coe_id, TopCat.hom_id, CategoryTheory.whiskeringRightCompEvaluation_inv_app, CategoryTheory.Functor.associator_inv_app, AlgebraicGeometry.Scheme.Pullback.openCoverOfRight_f, DistLat.id_apply, CategoryTheory.Over.mapId_inv_app_left, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id_app, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_functor_map, CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_left, CategoryTheory.MorphismProperty.Over.pullbackComp_inv_app_left, CategoryTheory.shift_equiv_triangle, CategoryTheory.Functor.flipping_counitIso_hom_app_app_app, CommRingCat.toAlgHom_id, CategoryTheory.PrelaxFunctor.map₂_inv_hom_isIso, CategoryTheory.Comma.toIdPUnitEquiv_unitIso_inv_app_right, CategoryTheory.Pseudofunctor.Grothendieck.categoryStruct_id_fiber, CategoryTheory.Bicategory.eqToHomTransIso_refl_right, CategoryTheory.Limits.colimitCoyonedaHomIsoLimitUnop_π_apply, SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_inv_app, CategoryTheory.Dial.hexagon_reverse, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_assoc, CategoryTheory.Comma.toPUnitIdEquiv_unitIso_inv_app_left, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_right, CategoryTheory.Functor.isIso_ranAdjunction_unit_app_iff, CategoryTheory.leftAdjointMate_id, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst, CategoryTheory.Join.mkFunctorLeft_hom_app, CategoryTheory.Triangulated.Octahedron.triangleMorphism₁_hom₁, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_inv_app_unmop, CategoryTheory.Bicategory.whiskerRight_iff, CategoryTheory.Over.leftUnitor_inv_left_snd_assoc, CategoryTheory.kernelCokernelCompSequence.inr_φ_fst_assoc, CategoryTheory.GlueData.diagramIso_inv_app_left, CategoryTheory.Iso.map_inv_hom_id_app, CategoryTheory.LocalizerMorphism.RightResolution.Hom.id_f, CategoryTheory.Functor.LeftLinear.δₗ_comp_μₗ, CategoryTheory.Iso.hom_inv_id_app, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_inv_hom, CategoryTheory.CatEnrichedOrdinary.Hom.id_eq, finGaloisGroupMap.map_id, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom'_assoc, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app_assoc, HomologicalComplex.homologyMap_id, CategoryTheory.Lax.LaxTrans.naturality_id_assoc, CategoryTheory.Groupoid.vertexGroup_one, CategoryTheory.PreZeroHypercover.pullbackCoverOfLeft_f, CategoryTheory.Iso.map_hom_inv_id, CategoryTheory.Functor.RightLinear.δᵣ_comp_μᵣ, CategoryTheory.kernelCokernelCompSequence.snakeInput_v₂₃_τ₂, CategoryTheory.Limits.BinaryFan.rightUnitor_inv, CategoryTheory.Functor.ι_colimitIsoColimitGrothendieck_hom_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_inv, AlgebraicGeometry.Scheme.Cover.id_idx_apply, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id, CategoryTheory.Oplax.OplaxTrans.rightUnitor_hom_as_app, TopologicalSpace.Opens.op_map_id_obj, CategoryTheory.Abelian.Ext.comp_mk₀_id, CategoryTheory.Limits.biprod.total, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionActionOfMonoidalFunctorToEndofunctorIso_hom_app_app, CategoryTheory.Enriched.FunctorCategory.homEquiv_id, CategoryTheory.Endofunctor.Coalgebra.Terminal.left_inv, CompHausLike.ofHom_id, CategoryTheory.RelCat.Hom.rel_id_apply₂, CategoryTheory.Functor.mapTriangleRotateIso_hom_app_hom₂, SheafOfModules.pullback_comp_id, CategoryTheory.GradedObject.mapTrifunctorMap_map_app_app, CategoryTheory.Under.postComp_hom_app_right, CategoryTheory.MonoidalCategory.inv_hom_id_tensor, CategoryTheory.Functor.LaxMonoidal.id_ε, CategoryTheory.Functor.mapCommMonCompIso_inv_app_hom_hom, CategoryTheory.Bicategory.adjointifyCounit_left_triangle, AlgebraicGeometry.Scheme.Modules.pseudofunctor_right_unitality, CategoryTheory.EnrichedOrdinaryCategory.homEquiv_id, CategoryTheory.Pi.η_def, CategoryTheory.Idempotents.toKaroubi_map_f, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app, TopologicalSpace.OpenNhds.map_id_obj_unop, CategoryTheory.Functor.curry₃_obj_obj_obj_map, CategoryTheory.Subfunctor.preimage_id, CategoryTheory.Functor.mapComposableArrowsObjMk₂Iso_hom_app, CategoryTheory.TwoSquare.hId_app, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_right, CategoryTheory.Functor.RightExtension.coneAtWhiskerRightIso_inv_hom, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_inv_hom₁, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_toSpecΓ, CategoryTheory.IsHomLift.id_comp_lift, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_right, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInlIso_hom_app_app, CategoryTheory.ShortComplex.homologyMap'_id, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id, CategoryTheory.Comonad.id_δ_app, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_inv_app_left, CategoryTheory.Pseudofunctor.toOplax_mapId, CategoryTheory.op_id_unop, CategoryTheory.biconeCategoryStruct_id, AlgebraicGeometry.Scheme.stalkMap_id, CategoryTheory.Functor.mapCommMonIdIso_hom_app_hom_hom, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_left, CategoryTheory.Iso.inv_hom_id_app_app_app, AlgebraicGeometry.IsAffineOpen.toSpecΓ_isoSpec_inv, CategoryTheory.Limits.WalkingReflexivePair.Hom.id_eq, AlgebraicGeometry.SheafedSpace.id_hom_base, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_inv, CategoryTheory.SimplicialObject.δ_comp_σ_self', CategoryTheory.Arrow.inv_hom_id_right, Action.forget_δ, CategoryTheory.StrictlyUnitaryLaxFunctor.mapId_eq_eqToHom, HomologicalComplex.cylinder.ι₁_π, CategoryTheory.Functor.pointwiseLeftKanExtensionUnit_app, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_unit_app, CategoryTheory.Endofunctor.Coalgebra.Terminal.right_inv, CategoryTheory.eqToHom_refl, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id, CategoryTheory.CostructuredArrow.mapIso_counitIso_hom_app_left, CategoryTheory.Center.ofBraided_δ_f, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.right_triangle_components, Action.id_hom, CategoryTheory.Enriched.FunctorCategory.functorEnriched_id_comp, CategoryTheory.Limits.coprod.functor_map_app, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_hom_app_app, TopCat.coe_id, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_inv_app_fst_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_hom_app_snd_app, CategoryTheory.StrictlyUnitaryLaxFunctor.map_id, AlgebraicGeometry.ΓSpec.left_triangle, CategoryTheory.BicategoricalCoherence.tensorRight'_iso, SimplexCategory.revCompRevIso_inv_app, CategoryTheory.monoidalUnopUnop_δ, CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj_inv_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_hom_app_fst_app, CategoryTheory.Limits.walkingSpanOpEquiv_counitIso_hom_app, CategoryTheory.Functor.map₂HomologicalComplex_map_app, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_one, CategoryTheory.Functor.IsEventuallyConstantTo.coneπApp_eq_id, CategoryTheory.Functor.constCompWhiskeringLeftIso_hom_app_app, CategoryTheory.ShortComplex.LeftHomologyMapData.ofEpiOfIsIsoOfMono'_φK, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv, CategoryTheory.Limits.WalkingReflexivePair.reflexion_comp_right, CategoryTheory.Over.postComp_inv_app_left, CategoryTheory.CosimplicialObject.Augmented.const_map_right, CategoryTheory.Limits.FormalCoproduct.inj_comp_cofanPtIsoSelf_hom, CategoryTheory.Bicategory.hom_inv_whiskerRight_whiskerRight, Rep.FiniteCyclicGroup.chainComplexFunctor_map_f, CategoryTheory.Bicategory.Pith.rightUnitor_inv_iso_inv, CategoryTheory.Bicategory.LeftExtension.whiskerIdCancel_right, CategoryTheory.Bicategory.prod_rightUnitor_inv_snd, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.functorMap_id, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_cofanPtIsoSelf_inv_assoc, CategoryTheory.Limits.Cocones.extendComp_hom_hom, CategoryTheory.Limits.prod.triangle, CategoryTheory.kernelCokernelCompSequence.snakeInput_L₀_g, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_right, CategoryTheory.IsHomLift.lift_id_comp, CategoryTheory.Equivalence.inverseFunctorObjIso_inv, AlgebraicGeometry.PresheafedSpace.stalkMap.id, CategoryTheory.Functor.coreCompInclusionIso_hom_app, CategoryTheory.Localization.SmallShiftedHom.mk₀Inv_comp_mk₀, CategoryTheory.Over.toOverSectionsAdj_unit_app, CategoryTheory.GradedObject.mapBifunctorRightUnitor_inv_naturality_assoc, CategoryTheory.Functor.diag_μ, CategoryTheory.Limits.IndObjectPresentation.yoneda_isColimit_desc, groupCohomology.resNatTrans_app, CategoryTheory.Comma.mapRightEq_inv_app_left, CategoryTheory.ShortComplex.opcyclesIsoRightHomology_inv_hom_id, CategoryTheory.Limits.coprod.map_swap, CategoryTheory.Bicategory.Strict.id_comp, SSet.OneTruncation₂.nerveEquiv_symm_apply_map, HomotopicalAlgebra.CofibrantBrownFactorization.s_p, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_inv_f_f, CategoryTheory.instMonoId, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_assoc, CategoryTheory.Grothendieck.map_id_eq, PartOrdEmb.hom_id, CategoryTheory.Functor.unopOpIso_hom_app, CategoryTheory.Pretriangulated.triangleCategory_id, CategoryTheory.CostructuredArrow.eta_inv_left, PartOrdEmb.ofHom_id, CategoryTheory.Dial.rightUnitor_inv_f, CategoryTheory.Limits.WidePullbackShape.hom_id, CategoryTheory.Lax.LaxTrans.naturality_id, CategoryTheory.Functor.IsCartesian.universal_property, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_inv_app_hom, CategoryTheory.Adjunction.mkOfHomEquiv_unit_app, CategoryTheory.Localization.SmallHom.comp_mk_id, CategoryTheory.StrictPseudofunctorCore.map₂_right_unitor, CategoryTheory.Groupoid.inv_comp, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_rightUnitor_inv_as_app, CategoryTheory.Bicategory.prod_leftUnitor_inv_fst, CategoryTheory.Limits.spanCompIso_inv_app_right, CategoryTheory.GlueData.diagramIso_inv_app_right, CategoryTheory.Bicategory.triangle_assoc_comp_right_inv_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_app_assoc, CategoryTheory.Category.comp_id, CategoryTheory.EnrichedFunctor.forgetId_inv_app, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagramOfIsLimit_map, SSet.Truncated.HomotopyCategory.homMk_id, CategoryTheory.RetractArrow.retract_left, CategoryTheory.Bicategory.hom_inv_whiskerRight, CategoryTheory.WithTerminal.inclLiftToTerminal_inv_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app, CategoryTheory.Bicategory.prod_rightUnitor_hom_fst, CategoryTheory.Bicategory.Adjunction.left_triangle, CategoryTheory.Functor.mapCochainComplexShiftIso_inv_app_f, CategoryTheory.PreOneHypercover.id_s₁, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_fst, CategoryTheory.GradedObject.Monoidal.id_tensorHom_id, CategoryTheory.Limits.ColimitPresentation.id_base, Quiver.FreeGroupoid.congr_comp_reverse, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id_val_app, HeytAlg.ofHom_id, SheafOfModules.id_val, CategoryTheory.MonoidalCategory.externalProductCompDiagIso_inv_app_app, CategoryTheory.Functor.prod'CompFst_inv_app, CategoryTheory.coyonedaEquiv_apply, CategoryTheory.Idempotents.Karoubi.decompId_i_f, CategoryTheory.CostructuredArrow.mapIso_functor_map_right, CategoryTheory.Comonad.comparisonForget_inv_app, HomologicalComplex.cylinder.inrX_π_assoc, CategoryTheory.Functor.isoSum_hom_app_inl, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_id, CochainComplex.truncateAugment_inv_f, CategoryTheory.IsCoreflexivePair.common_retraction, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_id, CategoryTheory.ShortComplex.LeftHomologyMapData.ofEpiOfIsIsoOfMono'_φH, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompPointIso_inv_app, CategoryTheory.Over.rightUnitor_inv_left_snd_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.id_actionHomLeft_assoc, CategoryTheory.Limits.biproduct.toSubtype_fromSubtype, CategoryTheory.Functor.rightOpLeftOpIso_inv_app, CategoryTheory.Bicategory.Prod.fst_mapId_hom, CategoryTheory.Bicategory.triangle_assoc_comp_right_inv, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso_inv_app_f, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂, CategoryTheory.Over.toOverSectionsAdj_counit_app, CategoryTheory.Functor.mapMonIdIso_hom_app_hom, CategoryTheory.Bicategory.prod_id_snd, CategoryTheory.Join.mapPairComp_inv_app_right, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_inv_naturality_assoc, CategoryTheory.Functor.Fiber.fiberInclusion_homMk, HomologicalComplex.biprod_inl_fst_f, CategoryTheory.Biprod.column_nonzero_of_iso, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_right_assoc, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_hom_app_coe, CategoryTheory.prodComonad_map, CategoryTheory.Localization.Monoidal.whiskerRight_id, CategoryTheory.IsSplitCoequalizer.rightSection_π, CategoryTheory.forgetAdjToOver_unit_app, CategoryTheory.Adjunction.adjToComonadIso_hom_toNatTrans_app, CategoryTheory.Cat.FreeRefl.quotientFunctor_map_id, CategoryTheory.Subgroupoid.IsWide.id_mem, CategoryTheory.EnrichedCat.associator_hom_out_app, AlgebraicTopology.DoldKan.P_succ, CategoryTheory.ShortComplex.RightHomologyMapData.ofEpiOfIsIsoOfMono_φH, CategoryTheory.Mathlib.Tactic.MonTauto.associator_inv_comp_tensorHom_tensorHom_comp, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_inv_left_app, CategoryTheory.Bicategory.prod_leftUnitor_inv_snd, CategoryTheory.Over.iteratedSliceEquivOverMapIso_inv_app_left_left, CategoryTheory.Limits.Cone.mapConeToUnder_inv_hom, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_hom_τl, CategoryTheory.PreOneHypercover.inter_p₂, AddMonCat.hom_id, CategoryTheory.Over.iteratedSliceEquivOverMapIso_hom_app_left_left, TopModuleCat.hom_id, SimplicialObject.Splitting.cofan_inj_πSummand_eq_id, CategoryTheory.Comma.mapLeftComp_inv_app_right, CategoryTheory.Comma.equivProd_counitIso_inv_app, CategoryTheory.Endofunctor.Algebra.id_eq_id, CategoryTheory.CostructuredArrow.map₂_map_right, CategoryTheory.endofunctorMonoidalCategory_rightUnitor_inv_app, CategoryTheory.pre_id, CategoryTheory.Comma.toIdPUnitEquiv_unitIso_hom_app_right, CategoryTheory.Bicategory.leftUnitorNatIso_hom_app, CategoryTheory.Limits.HasCoequalizersOfHasPushoutsAndBinaryCoproducts.pushoutInl_eq_pushout_inr, CategoryTheory.Limits.CatCospanTransform.rightUnitor_hom_base_app, CochainComplex.mappingConeCompTriangle_mor₁, CategoryTheory.RetractArrow.retract_right_assoc, CochainComplex.cm5b.instIsStrictlyGEBiprodIntMappingConeIdIOfHAddOfNat, CategoryTheory.Grothendieck.id_base, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_left, CategoryTheory.Precoverage.ZeroHypercover.id_s₀, CategoryTheory.Iso.unop_hom_inv_id_app, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_inv_τl, AugmentedSimplexCategory.id_star_whiskerRight, CategoryTheory.Limits.Cones.extendComp_inv_hom, CategoryTheory.monoidalOpOp_μ, HomologicalComplex.cylinder.ι₀_π, CategoryTheory.Join.mapPairLeft_inv_app, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_inverse_map, CategoryTheory.cosimplicialSimplicialEquiv_counitIso_inv_app_app, CategoryTheory.Codiscrete.natIsoFunctor_inv_app, CategoryTheory.overToCoalgebra_map_f, CategoryTheory.Comonad.adj_counit, CategoryTheory.composePath_nil, CategoryTheory.endomorphism_simple_eq_smul_id, CategoryTheory.Bicategory.Prod.sectL_mapId_hom, CategoryTheory.Limits.WidePushoutShape.hom_id, CategoryTheory.ObjectProperty.ι_δ, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_id_naturality_hom, CategoryTheory.SimplicialObject.isCoskeletal_iff, CategoryTheory.Bicategory.InducedBicategory.bicategory_rightUnitor_hom_hom, CategoryTheory.Limits.Cocone.toOver_pt, CategoryTheory.Adjunction.adjunctionOfEquivRight_unit_app, CategoryTheory.Functor.mapComposableArrowsObjMk₁Iso_hom_app, CategoryTheory.Pseudofunctor.isoMapOfCommSq_vert_id, CategoryTheory.Pseudofunctor.isPrestackFor_iff_isSheafFor, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_left_app, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.leftUnitor_naturality, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_hom_app_app_hom_hom, groupCohomology.mapShortComplexH1_id, MagmaCat.id_apply, CategoryTheory.ShortComplex.HomotopyEquiv.refl_inv, CategoryTheory.Grp.δ_def, CategoryTheory.Bimon.ofMonComon_toMonComon_obj_counit, CategoryTheory.ShortComplex.HomologyMapData.id_right, Frm.id_apply, CategoryTheory.ShiftedHom.comp_mk₀_id, CategoryTheory.Square.category_id_τ₁, CategoryTheory.LocalizerMorphism.RightResolution.id_f, CategoryTheory.Pseudofunctor.bijective_toDescentData_map_iff, CategoryTheory.Functor.uncurryObjFlip_inv_app, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_inv_app_hom, CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_id, CategoryTheory.Functor.Elements.initialOfCorepresentableBy_snd, CategoryTheory.Limits.CatCospanTransform.leftUnitor_inv_right_app, CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_left, CategoryTheory.Bicategory.Strict.rightUnitor_eqToIso, CategoryTheory.isoCartesianComon_hom_hom, CategoryTheory.Bicategory.leftUnitor_whiskerRight, CategoryTheory.ShortComplex.LeftHomologyData.ofZeros_i, AddCommGrpCat.id_apply, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id, HasFibers.Fib.mkIsoSelfIsHomLift, CategoryTheory.Cat.FreeRefl.quotientFunctor_map_nil, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_inv_app_app, CategoryTheory.ULift.equivalence_unitIso_hom, HomologicalComplex.truncLE'Map_id, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.counitIso_hom_app_app_hom, CategoryTheory.Mat_.embeddingLiftIso_inv_app, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_counitIso_inv_app_f, CategoryTheory.Join.pseudofunctorRight_mapId_hom_toNatTrans_app, CategoryTheory.Under.forgetMapInitial_hom_app, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_map_fiber, CategoryTheory.sum.inrCompInrCompInverseAssociator_inv_app_down, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_fst_assoc, CategoryTheory.Functor.mapHomologicalComplexIdIso_inv_app_f, CategoryTheory.Endofunctor.Algebra.id_f, AlgebraicGeometry.Scheme.Modules.pushforwardComp_hom_app_app, CategoryTheory.Oplax.StrongTrans.naturality_id, CochainComplex.cm5b.fac_assoc, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_assoc, CategoryTheory.SimplicialObject.δ_comp_σ_succ', CategoryTheory.MonoidalCategory.pentagon_hom_inv, CategoryTheory.prodOpEquiv_unitIso_inv_app, AlgebraicGeometry.Scheme.iso_inv_base_hom_base, CategoryTheory.Bicategory.prod_leftUnitor_hom_snd, CategoryTheory.Grothendieck.toTransport_fiber, CategoryTheory.ChosenPullbacksAlong.pullbackId_hom_counit, AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv, CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_inv_hom_id, CommMonCat.coe_id, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_hom_app_hom_left, CategoryTheory.IsReflexivePair.common_section, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_assoc, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_hom_f_f, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_assoc, CategoryTheory.Cat.HasLimits.id_def, Frm.coe_id, ContAction.resComp_hom, CategoryTheory.StrictlyUnitaryPseudofunctor.mapId_eq_eqToIso, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_hom_hom, CategoryTheory.MonoidalOpposite.tensorRightUnmopIso_inv_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_id_assoc, Action.Hom.id_hom, CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom', HomologicalComplex₂.flipEquivalenceUnitIso_inv_app_f_f, CategoryTheory.ShortComplex.HomotopyEquiv.ext_iff, CategoryTheory.Idempotents.whiskeringLeft_obj_preimage_app, CategoryTheory.Limits.cospanCompIso_inv_app_right, CategoryTheory.Cat.freeMapCompIso_hom_app, CategoryTheory.monoidalOpOp_η, CategoryTheory.Grp.id_hom, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.isoAux_hom_app, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_fst, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_rightUnitor_hom_as_app, CategoryTheory.Iso.map_hom_inv_id_app, StalkSkyscraperPresheafAdjunctionAuxs.unit_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₂, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_hom_app_snd_app, CategoryTheory.Pretriangulated.binaryProductTriangle_mor₁, CategoryTheory.prod.prodFunctorToFunctorProdAssociator_inv_app_app, CategoryTheory.Functor.mapGrpCompIso_hom_app_hom_hom, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_map_mkHom_homMk_id, CategoryTheory.Bicategory.InducedBicategory.bicategory_rightUnitor_inv_hom, CategoryTheory.Functor.mapTriangleInvRotateIso_inv_app_hom₂, CategoryTheory.SimplicialObject.Augmented.const_map_right, CategoryTheory.Factorisation.initial_ι, CategoryTheory.Limits.sigmaConst_obj_map, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv, CategoryTheory.Functor.leftOpId_inv_app, CategoryTheory.MonoidalCategory.pentagon_inv_hom, AlgebraicGeometry.Scheme.Pullback.t_id, CategoryTheory.Comonad.comparisonForget_hom_app, CategoryTheory.MonoidalCategory.tensor_hom_inv_id_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_inv_app_snd_app, SimplexCategory.Truncated.Hom.tr_id, CategoryTheory.EnrichedCat.leftUnitor_inv_out_app, TopCat.Presheaf.Pushforward.comp_inv_app, CategoryTheory.WithTerminal.liftFromOverComp_hom_app, CategoryTheory.ShortComplex.LeftHomologyMapData.compatibilityOfZerosOfIsLimitKernelFork_φH, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_inv_hom', CategoryTheory.Bicategory.rightUnitor_naturality_assoc, CategoryTheory.MonoidalCategory.DayConvolution.triangle, CategoryTheory.Over.tensorHom_left, CategoryTheory.Dial.Hom.le, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_inv_app_snd_app, CategoryTheory.ShortComplex.RightHomologyData.ofIsLimitKernelFork_p, CategoryTheory.RetractArrow.retract_right, CategoryTheory.Limits.end_.map_id, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_obj, AlgebraicTopology.DoldKan.MorphComponents.id_φ, CategoryTheory.MorphismProperty.Over.mapComp_hom_app_left, AlgebraicGeometry.Scheme.Cover.id_app, CategoryTheory.Limits.PullbackCone.eta_inv_hom, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_inv_app_zero, AlgebraicGeometry.Scheme.Hom.resLE_id, CategoryTheory.MonoidalCategory.id_whiskerRight, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.unitIso_hom_app_hom_app, CategoryTheory.StructuredArrow.homMk'_id, MonObj.mopEquiv_counitIso_hom_app_hom_unmop, CategoryTheory.CatEnrichedOrdinary.id_hComp, CategoryTheory.OplaxFunctor.map₂_rightUnitor_assoc, CategoryTheory.nerve.homEquiv_id, CochainComplex.MappingConeCompHomotopyEquiv.hom_inv_id, CategoryTheory.MonoidalCategory.inv_hom_id_tensor', TopologicalSpace.Opens.mapId_inv_app, CategoryTheory.id_apply, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_counitIso_inv_app_right_app, CategoryTheory.MonoidalCategory.tensor_inv_hom_id'_assoc, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_id, CategoryTheory.Prod.fac'_assoc, CategoryTheory.Bimon.ofMon_Comon_toMon_Comon_obj_comul, CategoryTheory.Lax.LaxTrans.vComp_naturality_id, CategoryTheory.Limits.bicone_ι_π_self, CategoryTheory.Bimon.equivMonComonUnitIsoAppXAux_inv, CategoryTheory.ShortComplex.RightHomologyMapData.id_φQ, CategoryTheory.Limits.coprod.map_comp_id, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_hom_c_app, CategoryTheory.Limits.Cones.eta_inv_hom, CategoryTheory.Limits.CatCospanTransform.associator_inv_left_app, CategoryTheory.Functor.CommShift.id_commShiftIso_inv_app, CategoryTheory.Lax.OplaxTrans.id_naturality, CategoryTheory.DifferentialObject.id_f, CategoryTheory.Functor.curryingFlipEquiv_symm_apply_obj_map, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₃, CategoryTheory.Endofunctor.Algebra.functorOfNatTransEq_inv_app_f, CategoryTheory.NatTrans.IsMonoidal.id, CategoryTheory.Limits.CatCospanTransform.leftUnitor_hom_left_app, CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv', AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_right, CategoryTheory.Functor.LeftExtension.postcompose₂ObjMkIso_hom_right_app, CategoryTheory.MonoidalOpposite.unmopEquiv_counitIso_hom_app, Bicategory.Opposite.op2_rightUnitor, CategoryTheory.IsHomLift.comp_of_lift_id, CategoryTheory.ShortComplex.RightHomologyData.ofZeros_p, CategoryTheory.Functor.sheafPushforwardContinuousComp_inv_app_val_app, CategoryTheory.Iso.map_inv_hom_id, CategoryTheory.exp.ev_coev, CategoryTheory.section_comp_left, AlgebraicGeometry.Scheme.Modules.Hom.id_app, CategoryTheory.biconeMk_map, CompHausLike.LocallyConstant.adjunction_left_triangle, CategoryTheory.CartesianMonoidalCategory.lift_fst_snd, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_left, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_hom_app_app_snd, CategoryTheory.Oplax.OplaxTrans.naturality_id_assoc, CategoryTheory.Functor.curryingEquiv_symm_apply_map_app, CategoryTheory.WithTerminal.inclLift_inv_app, CategoryTheory.Join.InclLeftCompRightOpOpEquivFunctor_hom_app, SSet.Truncated.HomotopyCategory₂.homMk_id, CategoryTheory.Dial.hexagon_forward, CategoryTheory.IsPullback.zero_left, CategoryTheory.MonoidalCategory.DayConvolution.symmetry, CategoryTheory.Bicategory.prod_homCategory_id_fst, SheafOfModules.pullback_id_comp, CategoryTheory.OplaxFunctor.map₂_leftUnitor, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id_assoc, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIso_inv_app_hom, CategoryTheory.WithInitial.equivComma_inverse_obj_map, CategoryTheory.Limits.lim_ε_π, CategoryTheory.CartesianClosed.uncurry_id_eq_ev, CategoryTheory.IsPushout.id_vert, CategoryTheory.Functor.RightExtension.postcomp₁_map_left_app, CategoryTheory.Limits.sigmaConst_map_app, CategoryTheory.Comma.toIdPUnitEquiv_counitIso_hom_app, AlgCat.ofHom_id, CategoryTheory.Limits.walkingSpanOpEquiv_unitIso_inv_app, CategoryTheory.CopyDiscardCategory.discard_unit, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_right, HomologicalComplex.natIsoSc'_hom_app_τ₂, CategoryTheory.WithTerminal.ofCommaObject_map, CategoryTheory.Bicategory.Adj.leftUnitor_inv_τl, MagmaCat.coe_id, Bicategory.Opposite.op2_rightUnitor_hom, CategoryTheory.Comma.mapRightComp_hom_app_left, CategoryTheory.ShortComplex.HomotopyEquiv.trans_homotopyHomInvId, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_left, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_inv_app_snd_app, CategoryTheory.sum.inlCompAssociator_hom_app, CategoryTheory.Bicategory.Pith.id₂_iso_hom, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₂, Mathlib.Tactic.Bicategory.naturality_leftUnitor, CategoryTheory.Functor.mapCommMon_id_mul, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_left, CategoryTheory.Functor.sheafPushforwardCocontinuousCompSheafToPresheafIso_inv, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.triangle, CategoryTheory.monoidalOfHasFiniteCoproducts.whiskerRight, CategoryTheory.Prod.fac_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.eq_mul_one, AddMonCat.id_apply, SimplicialObject.Splitting.IndexSet.id_snd_coe, CommMonCat.hom_id, CategoryTheory.Functor.sheafPushforwardContinuousComp_hom_app_val_app, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatTrans_id, CategoryTheory.ComonObj.instTensorUnit_counit, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_assoc, CategoryTheory.Limits.IndObjectPresentation.yoneda_ι_app, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidalObj_map, CategoryTheory.GradedObject.mapBifunctorRightUnitor_naturality, CategoryTheory.sum.inrCompInlCompAssociator_inv_app_down_down, Bimod.AssociatorBimod.hom_inv_id, CategoryTheory.KleisliCat.id_def, CategoryTheory.whiskeringRightCompEvaluation_hom_app, SemimoduleCat.id_apply, CategoryTheory.Limits.pullback_map_diagonal_isPullback, ChainComplex.augmentTruncate_hom_f_succ, CochainComplex.mappingCone.map_id, CategoryTheory.eHomWhiskerLeft_id, CategoryTheory.Bicategory.Adj.id_adj, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₁, CategoryTheory.Limits.prod.symmetry', CategoryTheory.Pi.id_apply, CategoryTheory.FreeGroupoid.mapComp_inv_app, CategoryTheory.Lax.StrongTrans.naturality_id, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₁, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_inv_app_hom, CategoryTheory.Functor.Monoidal.whiskeringLeft_η_app, CategoryTheory.Functor.Fiber.instIsHomLiftIdMapFiberInclusion, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_hom_right_app, CategoryTheory.Bicategory.LeftExtension.ofCompId_hom, CategoryTheory.Idempotents.Karoubi.decompId, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_leftUnitor_hom_as_app, CategoryTheory.Bimon.equivMonComonCounitIsoAppX_hom_hom, CategoryTheory.SingleFunctors.hom_inv_id_hom, CategoryTheory.Functor.LaxMonoidal.id_μ, CategoryTheory.ForgetEnrichment.homTo_id, CategoryTheory.CatEnrichedOrdinary.id_eq_eqToHom, CategoryTheory.Join.inclRightCompOpEquivInverse_hom_app_op, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.tensorHom_id, CategoryTheory.Functor.RepresentableBy.isRepresentedBy, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₂, CategoryTheory.CosimplicialObject.δ_comp_σ_succ', CategoryTheory.FreeBicategory.id_def, CategoryTheory.Lax.StrongTrans.categoryStruct_id_naturality, CategoryTheory.Over.whiskerRight_left, CategoryTheory.ShortComplex.leftRightHomologyComparison'_eq_leftHomologpMap'_comp_iso_hom_comp_rightHomologyMap', CategoryTheory.Pseudofunctor.mapComp_id_left_inv, CochainComplex.mappingCone.inl_v_fst_v, CategoryTheory.Arrow.id_left, CategoryTheory.Limits.Cones.eta_hom_hom, CategoryTheory.WithInitial.pseudofunctor_mapId, CategoryTheory.ComposableArrows.twoδ₁Toδ₀_app_one, BoolAlg.ofHom_id, CategoryTheory.sum.inlCompInlCompAssociator_inv_app_down, AlgebraicGeometry.Scheme.Hom.id_appIso, CategoryTheory.Functor.biprodComparison'_comp_biprodComparison, CategoryTheory.OverPresheafAux.YonedaCollection.map₂_id, CategoryTheory.Functor.flipping_unitIso_hom_app_app_app, CategoryTheory.Triangulated.SpectralObject.id_hom, CategoryTheory.Equivalence.inverseFunctorObj'_hom_app, CategoryTheory.Limits.coconeOfIsSplitEpi_pt, CategoryTheory.Limits.pullbackSymmetry_hom_of_mono_eq, CategoryTheory.StructuredArrow.pre_map_left, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τr, CategoryTheory.Join.pseudofunctorRight_mapId_inv_toNatTrans_app, CategoryTheory.Comma.unopFunctorCompSnd_inv_app, PartOrdEmb.id_apply, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_iso, CategoryTheory.GradedObject.mapMap_id, AlgebraicGeometry.PresheafedSpace.map_id_c_app, CategoryTheory.SemiadditiveOfBinaryBiproducts.add_eq_right_addition, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.IsTerminal.prop_id, CategoryTheory.Bicategory.Comonad.counit_def, CategoryTheory.Functor.mapTriangleIdIso_hom_app_hom₃, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, CategoryTheory.OplaxFunctor.mapComp_id_right_assoc, LinearMap.id_moduleCat_comp, CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_mapId, CategoryTheory.Functor.LeftExtension.coconeAtWhiskerRightIso_hom_hom, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_hom_app_left, CategoryTheory.plusPlusAdjunction_counit_app_val, CategoryTheory.Limits.coprod.map_comp_id_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_app, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_inv_app_f, CategoryTheory.coreCategory_id_iso_hom, CategoryTheory.Adjunction.adjToMonadIso_inv_toNatTrans_app, CategoryTheory.Limits.WidePushoutShape.wideSpan_map, CategoryTheory.ShortComplex.SnakeInput.id_f₁, CategoryTheory.Functor.sheafPushforwardCocontinuousCompSheafToPresheafIso_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHom_id, CategoryTheory.cancel_epi_id, CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv, CategoryTheory.Bicategory.LeftLift.ofIdComp_right, CategoryTheory.GrothendieckTopology.OneHypercover.id_s₁, CategoryTheory.Idempotents.KaroubiUniversal₁.counitIso_hom_app_app_f, CategoryTheory.Functor.CommShift.id_commShiftIso_hom_app, CategoryTheory.Limits.CatCospanTransform.associator_inv_base_app, CategoryTheory.Bicategory.InducedBicategory.forget_mapId_inv, CategoryTheory.Pretriangulated.id_hom₂, CategoryTheory.Arrow.id_right, CategoryTheory.Pretriangulated.triangleMorphismId_hom₂, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_inv_app, CategoryTheory.ComposableArrows.threeδ₁Toδ₀_app_two, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_unitIso_inv_app_f, CategoryTheory.Idempotents.KaroubiUniversal₁.counitIso_inv_app_app_f, CategoryTheory.GlueData.t'_inv, CategoryTheory.Subfunctor.Subpresheaf.range_id, CategoryTheory.StructuredArrow.map_map_left, CategoryTheory.PreOneHypercover.id_s₀, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_assoc, TopCat.Presheaf.Pushforward.id_hom_app, CategoryTheory.id_of_comp_left_id, CategoryTheory.Pseudofunctor.StrongTrans.Modification.id_app, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_id_assoc, BddOrd.id_apply, FintypeCat.homMk_eq_id_iff, CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_id, CategoryTheory.Bicategory.rightUnitorNatIso_inv_app, CategoryTheory.Functor.flipIsoCurrySwapUncurry_hom_app_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso_hom_app_app, CategoryTheory.Idempotents.Karoubi.coe_p, CategoryTheory.Limits.Multicofork.isoOfπ_hom_hom, CategoryTheory.MonoidalCategory.MonoidalRightAction.id_actionHomLeft, Bicategory.Opposite.op2_leftUnitor_hom, CategoryTheory.Subobject.ofLE_refl, CategoryTheory.PreZeroHypercover.pullbackCoverOfRight_f, CategoryTheory.Bicategory.Comonad.comul_counit_assoc, CategoryTheory.rightDistributor_assoc, CategoryTheory.FreeGroupoid.mapId_inv_app, CategoryTheory.ShortComplex.cyclesIsoLeftHomology_hom_inv_id, CategoryTheory.Subobject.ofMkLEMk_refl, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_hom_app, CategoryTheory.MonObj.one_leftUnitor, CategoryTheory.Functor.IsCocartesian.universal_property, SimplexCategory.Truncated.δ₂_one_comp_σ₂_zero, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_inv_hom, CategoryTheory.MonoidalClosed.uncurry_id_eq_ev, TopCat.Presheaf.id_pushforward, CategoryTheory.DifferentialObject.Hom.id_f, CochainComplex.cm5b.instQuasiIsoIntP, CategoryTheory.Pseudofunctor.toLax_mapId, CategoryTheory.Limits.MonoCoprod.mono_map'_of_injective, CategoryTheory.Functor.leftUnitor_inv_app, CategoryTheory.Limits.Cones.extendId_hom_hom, CategoryTheory.Functor.mapTriangleRotateIso_hom_app_hom₁, CategoryTheory.Functor.coreCompInclusionIso_inv_app, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv, CategoryTheory.ObjectProperty.FullSubcategory.id_def, TopCat.Presheaf.Pushforward.id_eq, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_inv, CategoryTheory.ShortComplex.asIsoHomologyπ_inv_comp_homologyπ, CategoryTheory.Coyoneda.colimitCoconeIsColimit_desc, CategoryTheory.Comma.mapLeftEq_hom_app_right, CategoryTheory.Functor.const_map_app, CategoryTheory.Endofunctor.Algebra.functorOfNatTransId_hom_app_f, CategoryTheory.StructuredArrow.mapIso_unitIso_inv_app_right, CategoryTheory.Cat.leftUnitor_hom_toNatTrans, CategoryTheory.ShortComplex.homologyι_comp_asIsoHomologyι_inv, AlgebraicGeometry.Scheme.iso_hom_base_inv_base, CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_left, CategoryTheory.Bicategory.whiskerLeft_inv_hom_whiskerRight, SheafOfModules.instIsLeftAdjointOverOverRingCatPushforwardIdSheafOver, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app_assoc, CategoryTheory.MonoidalOpposite.tensorLeftUnmopIso_hom_app, Bimod.id'_hom, HomologicalComplex.cylinder.inrX_π, CategoryTheory.Limits.spanCompIso_hom_app_right, NonemptyFinLinOrd.hom_hom_id, CategoryTheory.Subobject.factorThru_self, CategoryTheory.PreOneHypercover.Hom.id_h₀, CategoryTheory.instIsComonHomId, CategoryTheory.Functor.const.opObjOp_hom_app, MonObj.mopEquivCompForgetIso_inv_app_unmop, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_counitIso, CategoryTheory.Functor.mapCommGrp_id_one, CategoryTheory.Prod.fac, AddMagmaCat.ofHom_id, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_hom_app_fst_app, Alexandrov.lowerCone_π_app, CategoryTheory.Comma.opFunctorCompSnd_hom_app, CategoryTheory.nerve.σ₀_mk₀_eq, CategoryTheory.MonoidalClosed.pre_id, CategoryTheory.Center.id_f, CommGrpCat.coe_id, CategoryTheory.Bicategory.Prod.sectL_mapComp_inv, CategoryTheory.WithInitial.opEquiv_counitIso_inv_app, PartOrd.ofHom_id, CommGrpCat.id_apply, CategoryTheory.Functor.IsEventuallyConstantFrom.coconeιApp_eq, CategoryTheory.NatTrans.unop_id, CategoryTheory.Pretriangulated.contractibleTriangle_mor₁, PresheafOfModules.Elements.fromFreeYoneda_app_apply, CategoryTheory.Iso.refl_inv, CategoryTheory.StructuredArrow.mapIso_functor_map_left, CategoryTheory.Bicategory.id_whiskerLeft_assoc, CategoryTheory.Functor.sheafPushforwardContinuousId_hom_app_val_app, CategoryTheory.Functor.flipping_unitIso_inv_app_app_app, HomologicalComplex.cylinder.πCompι₀Homotopy.inrX_nullHomotopy_f, HomologicalComplex.iCyclesIso_hom_inv_id, CategoryTheory.Bimon.equivMonComonUnitIsoApp_inv_hom_hom, CategoryTheory.Bimon.ofMon_Comon_toMon_Comon_obj_counit, CategoryTheory.Iso.hom_inv_id_triangle_hom₁, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_inv_app_one, CategoryTheory.Bicategory.Pith.id_of, CategoryTheory.Join.inclLeftCompOpEquivInverse_inv_app_op, CategoryTheory.Functor.mapHomotopyEquiv_homotopyInvHomId, CategoryTheory.Limits.coconeOfIsSplitEpi_π, CategoryTheory.ChosenPullbacksAlong.pullbackId_hom_counit_assoc, CategoryTheory.Bicategory.InducedBicategory.forget_mapComp_inv, Bicategory.Opposite.op2_id, CategoryTheory.Monad.algebraEquivOfIsoMonads_counitIso, CategoryTheory.Limits.pullbackDiagonalMapIdIso_hom_fst_assoc, CategoryTheory.Sigma.inclCompMap_hom_app, CategoryTheory.SimplicialObject.δ_comp_σ_self, CategoryTheory.Factorisation.terminal_π, CategoryTheory.IsHomLift.isoOfIsoLift_hom_inv_id, CategoryTheory.OplaxFunctor.map₂_rightUnitor, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso_hom_app_f, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff, CategoryTheory.Limits.Cones.postcomposeComp_inv_app_hom, CategoryTheory.Functor.IsEventuallyConstantTo.isoMap_hom_inv_id, CategoryTheory.Preadditive.commGrpEquivalenceAux_inv_app_hom_hom_hom, CategoryTheory.Limits.CatCospanTransform.category_id_base, CategoryTheory.CostructuredArrow.right_eq_id, CategoryTheory.Functor.mapConePostcomposeEquivalenceFunctor_inv_hom, AddCommGrpCat.coe_id, CategoryTheory.GrpObj.inv_eq_inv, CategoryTheory.NatTrans.mapHomotopyCategory_id, CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp_hom_hom₃, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_right, CategoryTheory.Comma.mapLeftId_hom_app_left, CochainComplex.cm5b.instMonoFIntI, CategoryTheory.Limits.pullbackConeOfRightIso_π_app_left, CategoryTheory.MonoidalOpposite.mopMopEquivalence_counitIso_inv_app, CategoryTheory.ComposableArrows.fourδ₂Toδ₁_app_three, CategoryTheory.Functor.Monoidal.whiskerRight_μ_δ, CategoryTheory.Limits.Cone.toStructuredArrowCompProj_hom_app, CategoryTheory.ShortComplex.opcyclesIsoX₂_inv_hom_id, CategoryTheory.Grpd.id_eq_id, CommSemiRingCat.id_apply, CategoryTheory.Bifunctor.diagonal, CategoryTheory.Cat.leftUnitor_inv_toNatTrans, Rep.linearizationTrivialIso_inv_hom, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_naturality_assoc, CategoryTheory.Join.mapPairId_inv_app, CategoryTheory.Functor.const.opObjOp_inv_app, CategoryTheory.Pseudofunctor.map₂_left_unitor_app, BddDistLat.id_apply, CategoryTheory.Pseudofunctor.mapId'_eq_mapId, CategoryTheory.Limits.biproduct.total, CategoryTheory.FunctorToTypes.functorHomEquiv_apply_app, CategoryTheory.Iso.hom_inv_id_triangle_hom₃, CategoryTheory.Bimon.id_hom', CategoryTheory.Comma.mapLeftId_inv_app_left, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_right, CategoryTheory.Functor.mapMonIdIso_inv_app_hom, CategoryTheory.Bicategory.Prod.snd_mapId_hom, CategoryTheory.Bicategory.triangle, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_unitIso, CategoryTheory.Functor.mapConePostcomposeEquivalenceFunctor_hom_hom, CategoryTheory.Pseudofunctor.StrongTrans.leftUnitor_hom_as_app, CategoryTheory.sum.inrCompAssociator_hom_app_down_down, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_inv_hom', CategoryTheory.FunctorToTypes.map_id_apply, CategoryTheory.Monad.Algebra.id_eq_id, AlgebraicGeometry.PresheafedSpace.id_base, SimplexCategory.revCompRevIso_hom_app, Action.ρ_one, Homotopy.compLeftId_hom, SemimoduleCat.ofHom_id, CategoryTheory.MonoidalOpposite.tensorRightIso_hom_app_unmop, CategoryTheory.GlueData'.cocycle, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapId_hom, CategoryTheory.instIsMod_HomId, CategoryTheory.CosimplicialObject.δ_comp_σ_succ, MonObj.mopEquiv_unitIso_hom_app_hom, CategoryTheory.Pseudofunctor.ObjectProperty.mapId_hom_app, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_assoc, TopCat.Presheaf.stalkPushforward.id, AlgebraicGeometry.Scheme.instIsOverFstOverInferInstanceOverClassId, CategoryTheory.Functor.commShiftIso_id_hom_app, CategoryTheory.Grothendieck.ιCompMap_inv_app_base, CategoryTheory.Dial.comp_F, CategoryTheory.Over.conePostIso_inv_app_hom, CategoryTheory.Bicategory.Prod.sectR_map₂, CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair_inv_app, CategoryTheory.Limits.colimit.desc_cocone, CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id_app, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_mapPullbackAdj_unit_app, CategoryTheory.Limits.biprod.add_eq_lift_desc_id, CategoryTheory.Mon.trivial_mon_one, CategoryTheory.ShortComplex.Splitting.g_s_assoc, CategoryTheory.ShortComplex.SnakeInput.id_f₀, CategoryTheory.Functor.Fiber.inducedFunctorCompIsoSelf_hom_app, HopfAlgCat.toBialgHom_id, CategoryTheory.Functor.curryObjCompIso_inv_app_app, CategoryTheory.leftDistributor_rightDistributor_assoc, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapIdIso_inv, CategoryTheory.GradedObject.mapBifunctorMap_map_app, CategoryTheory.Functor.mapCommGrpIdIso_hom_app_hom_hom_hom, CategoryTheory.Presieve.factorsThruAlong_id, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransEq_hom_app_f, CategoryTheory.rightAdjointMate_id, CategoryTheory.Limits.Cocones.extendComp_inv_hom, CategoryTheory.Bicategory.Prod.sectL_map, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app, CategoryTheory.IsHomLift.id_lift_eqToHom_domain, CategoryTheory.monoidalOfHasFiniteCoproducts.rightUnitor_hom, CategoryTheory.GrothendieckTopology.isoToPlus_inv, AlgebraicGeometry.AffineSpace.map_id, CategoryTheory.Bicategory.id_whiskerRight, CategoryTheory.Functor.const.unop_functor_op_obj_map, CategoryTheory.Functor.leftOpComp_inv_app, CategoryTheory.Comma.opFunctorCompFst_hom_app, CategoryTheory.ComposableArrows.fourδ₂Toδ₁_app_zero, CategoryTheory.CommComon.trivial_comon_counit, CategoryTheory.Lax.StrongTrans.naturality_id_assoc, CategoryTheory.DifferentialObject.objEqToHom_refl, CategoryTheory.monoidalOpOp_ε, CategoryTheory.underToAlgebra_obj_a, CategoryTheory.Comma.toPUnitIdEquiv_unitIso_hom_app_left, CategoryTheory.ChosenPullbacksAlong.pullbackMap_id, CategoryTheory.Limits.WalkingParallelFamily.hom_id, CategoryTheory.Functor.Fiber.homMk_comp, CategoryTheory.ShortComplex.id_τ₂, AlgebraicGeometry.Scheme.Pullback.openCoverOfBase'_f, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_cofanPtIsoSelf_inv, CategoryTheory.Functor.constCompEvaluationObj_inv_app, CategoryTheory.Comma.mapRightIso_unitIso_hom_app_left, CategoryTheory.MonoidalOpposite.tensorRightIso_inv_app_unmop, RingCat.ofHom_id, CategoryTheory.Limits.equalizerPullbackMapIso_hom_snd_assoc, CategoryTheory.Limits.fiberwiseColimCompEvaluationIso_hom_app, AlgebraicGeometry.Scheme.Hom.id_base, CategoryTheory.Idempotents.Karoubi.decompId_i_toKaroubi, CategoryTheory.Mathlib.Tactic.MonTauto.associator_inv_comp_tensorHom_tensorHom_comp_assoc, CategoryTheory.functorProdFunctorEquivCounitIso_inv_app_app, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id_assoc, CategoryTheory.ObjectProperty.ι_μ, CategoryTheory.Bicategory.Adj.rightUnitor_inv_τr, CategoryTheory.Oplax.OplaxTrans.naturality_id, Semigrp.ofHom_id, CategoryTheory.Functor.pointwiseRightKanExtensionCounit_app, ChainComplex.truncateAugment_hom_f, CategoryTheory.endofunctorMonoidalCategory_leftUnitor_hom_app, CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp_inv_hom₂, CategoryTheory.Bicategory.rightUnitor_comp, CategoryTheory.Bicategory.whiskerRight_id_symm, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_naturality, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_hom_inv, CategoryTheory.ConcreteCategory.coe_id, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_assoc, CategoryTheory.GrpObj.left_inv, CategoryTheory.OplaxFunctor.mapComp_id_right, CategoryTheory.Limits.pullback.comp_diagonal, CategoryTheory.Comma.opFunctorCompFst_inv_app, CategoryTheory.SymmetricCategory.symmetry, CategoryTheory.Limits.cospan_map_id, CategoryTheory.Limits.Cocones.eta_hom_hom, CategoryTheory.Bicategory.triangle_assoc_comp_right, CategoryTheory.WithInitial.inclLift_inv_app, CategoryTheory.Cat.Hom.toNatIso_leftUnitor, AlgebraicGeometry.instQuasiCompactLiftSchemeIdOfQuasiSeparatedSpaceCarrierCarrierCommRingCat, CategoryTheory.Functor.coreId_hom_app_iso_inv, CategoryTheory.Bicategory.InducedBicategory.forget_mapComp_hom, AugmentedSimplexCategory.tensor_id, CategoryTheory.Over.star_map_left, CategoryTheory.Functor.mapTriangleCompIso_inv_app_hom₁, CategoryTheory.Pseudofunctor.mapComp_id_right_inv, CategoryTheory.Limits.pushout.desc_inl_inr, CategoryTheory.Functor.pi'CompEval_inv_app, CategoryTheory.Mon.tensorUnit_one, groupCohomology.H1InfRes_g, CommBialgCat.ofSelfIso_hom, CategoryTheory.Functor.leftOpRightOpEquiv_counitIso_hom_app_app, AlgebraicGeometry.Scheme.Cover.LocallyDirected.trans_id, CategoryTheory.ShortComplex.SnakeInput.Hom.id_f₀, CategoryTheory.Limits.WalkingMultispan.Hom.id_eq_id, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_hom_inv', AlgebraicGeometry.Scheme.isSeparated_iff_isClosedImmersion_prod_lift, CategoryTheory.SimplicialObject.δ_comp_σ_succ, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInrIso_hom_app_app, CategoryTheory.Bicategory.rightUnitor_naturality, CategoryTheory.Functor.currying_unitIso_inv_app_app_app, CategoryTheory.MonoidalCategory.inv_hom_whiskerRight, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_hom_left, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_hom_app_hom, CategoryTheory.CommMon.trivial_mon_one, CategoryTheory.Functor.Monoidal.map_μ_δ, CategoryTheory.MonoidalCategory.whiskerLeft_id, CategoryTheory.Functor.currying_unitIso_hom_app_app_app, CategoryTheory.ConcreteCategory.id_apply, CategoryTheory.Limits.PullbackCone.eta_hom_hom, CategoryTheory.Pseudofunctor.Grothendieck.categoryStruct_id_base, CategoryTheory.Discrete.productEquiv_counitIso_inv_app, CategoryTheory.Bicategory.rightZigzagIso_symm, CategoryTheory.left_comp_retraction, CategoryTheory.CosimplicialObject.Augmented.const_map_left, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isoBot_inv, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapIdIso_hom, CategoryTheory.Functor.mapCoconeWhisker_inv_hom, CategoryTheory.Limits.coprod.desc_inl_inr, AlgebraicGeometry.Scheme.Modules.pushforwardId_hom_app_app, AddCommGrpCat.ofHom_id, Homotopy.compRightId_hom, CategoryTheory.Pretriangulated.binaryProductTriangleIsoBinaryBiproductTriangle_inv_hom₃, CategoryTheory.Sigma.SigmaHom.id_comp, CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id_app, AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_fst_assoc, CategoryTheory.WithInitial.inclLiftToInitial_hom_app, CategoryTheory.LaxFunctor.map₂_rightUnitor_assoc, CategoryTheory.Pi.sum_obj_map, CategoryTheory.instIsMonHomId, CategoryTheory.Monad.MonadicityInternal.comparisonAdjunction_counit, CategoryTheory.Localization.isoOfHom_hom_inv_id, CategoryTheory.Lax.OplaxTrans.naturality_id_assoc, CategoryTheory.Over.η_pullback_left, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_hom_hom, CategoryTheory.Functor.IsCocartesian.map_isHomLift, CategoryTheory.Limits.splitEpiOfIdempotentOfIsColimitCofork_section_, CategoryTheory.Sigma.inclCompMap_inv_app, CategoryTheory.Bicategory.whiskerRight_id_assoc, CategoryTheory.GrothendieckTopology.overMapPullback_comp_id_assoc, CategoryTheory.Functor.rightOpComp_inv_app, CategoryTheory.Limits.cospanCompIso_inv_app_one, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_apply, CategoryTheory.MonoidalCategory.tensorδ_tensorμ, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_inv_app_hom_hom_hom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_inv_app_fst_app, CategoryTheory.Cat.Hom.toNatIso_rightUnitor, CategoryTheory.BimonObj.one_counit, CategoryTheory.Under.hom_right_inv_right, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left, CategoryTheory.Over.id_left, CategoryTheory.MorphismProperty.Comma.id_hom, CategoryTheory.Join.mapPairComp_hom_app_left, CategoryTheory.Functor.opId_inv_app, HomotopicalAlgebra.CofibrantBrownFactorization.mk'_s, CategoryTheory.MonoOver.top_arrow, CategoryTheory.MorphismProperty.pullback_map, SimplicialObject.Splitting.decomposition_id, CategoryTheory.Bicategory.conjugateEquiv_apply', CategoryTheory.sum.inrCompInlCompAssociator_hom_app_down_down, CategoryTheory.Limits.spanCompIso_hom_app_left, OrderHom.equivalenceFunctor_counitIso_hom_app_app, Action.forget_ε, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_right, CategoryTheory.endofunctorMonoidalCategory_associator_hom_app, CategoryTheory.Functor.RepresentableBy.ext_iff, CategoryTheory.Under.mapId_hom, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_inv_app_app_snd, CategoryTheory.Functor.const.opObjUnop_inv_app, CategoryTheory.Over.postComp_hom_app_left, CategoryTheory.GrothendieckTopology.OneHypercover.id_h₀, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_hom_τr, CategoryTheory.Cat.Hom.id_obj, CategoryTheory.MonoidalCategory.tensor_id_comp_id_tensor_assoc, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom'', SemiRingCat.ofHom_id, CategoryTheory.Discrete.id_def', CategoryTheory.Pseudofunctor.StrongTrans.rightUnitor_inv_as_app, ChainComplex.augmentTruncate_hom_f_zero, CategoryTheory.InducedCategory.id_hom, CategoryTheory.Limits.CoconeMorphism.hom_inv_id, CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtensionObjIsoColimit_hom, CategoryTheory.μ_δ_app, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_hom_app_unmop, NonemptyFinLinOrd.id_apply, CategoryTheory.LaxFunctor.map₂_leftUnitor, CategoryTheory.StructuredArrow.mapNatIso_counitIso_hom_app_right, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_id_naturality_inv, CategoryTheory.SingleFunctors.postcompPostcompIso_inv_hom_app, CategoryTheory.Sum.functorEquivFunctorCompSndIso_inv_app_app, CategoryTheory.MorphismProperty.LeftFraction.map_hom_ofInv_id, CategoryTheory.Biprod.unipotentUpper_inv, CategoryTheory.Discrete.compNatIsoDiscrete_inv_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_aux_one, CategoryTheory.ShortComplex.leftHomologyMap'_id, CategoryTheory.Comma.mapRightId_hom_app_right, CategoryTheory.ShortComplex.SnakeInput.Hom.id_f₁, CategoryTheory.MonoidalCategory.id_tensorHom_id, CategoryTheory.Functor.IsCocartesian.map_self, CategoryTheory.Limits.Pi.map_id, CategoryTheory.Bicategory.conjugateEquiv_adjunction_id, SSet.Truncated.HomotopyCategory.BinaryProduct.associativity'Iso_hom_app, CategoryTheory.Grothendieck.transportIso_inv_fiber, CategoryTheory.Sum.functorEquiv_unitIso_inv_app_app_inr, CochainComplex.cm5b.instMonoIntI, QuadraticModuleCat.toIsometry_id, CategoryTheory.left_unitality_app, CategoryTheory.Cat.rightUnitor_inv_app, CategoryTheory.Functor.map_id, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app_assoc, CategoryTheory.Functor.Monoidal.whiskerLeft_δ_μ, CategoryTheory.ShortComplex.RightHomologyData.ofZeros_ι, CategoryTheory.Functor.LeftExtension.postcompose₂_map_left, CategoryTheory.CosimplicialObject.Augmented.const_obj_hom, CategoryTheory.Bicategory.Prod.snd_mapId_inv, CategoryTheory.Iso.comp_inv_eq_id, CategoryTheory.Functor.Monoidal.whiskerLeft_ε_η, CategoryTheory.NatTrans.id_hcomp_app, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_counit_app_left, CategoryTheory.Join.inclLeftCompOpEquivInverse_hom_app_op, CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_left, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_naturality, CategoryTheory.eHomWhiskerRight_id, CategoryTheory.MonoOver.mkArrowIso_inv_hom_left, AlgebraicTopology.DoldKan.P_add_Q, CategoryTheory.GrothendieckTopology.Point.Hom.sheafFiber_id, CategoryTheory.Functor.currying₃_unitIso_inv_app_app_app_app, CategoryTheory.ReflQuiv.id_eq_id, CategoryTheory.Functor.mapConeWhisker_hom_hom, CategoryTheory.Limits.prodZeroIso_iso_inv_snd, CategoryTheory.Cat.Hom.toNatTrans_id, CategoryTheory.Functor.whiskeringLeftObjIdIso_inv_app_app, CategoryTheory.Limits.Cocone.toCostructuredArrowCompToOverCompForget_hom_app, OrderHom.equivalenceFunctor_unitIso_hom_app, CategoryTheory.IsPullback.id_vert, CategoryTheory.Iso.hom_inv_id_eval, CategoryTheory.Limits.equalizerPullbackMapIso_hom_snd, Lat.hom_id, AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_left, Action.resComp_inv_app_hom, CategoryTheory.NonPreadditiveAbelian.lift_map_assoc, CategoryTheory.Cat.rightUnitor_inv_toNatTrans, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_right_right, CategoryTheory.GrothendieckTopology.OneHypercover.id_s₀, CategoryTheory.Functor.toPseudoFunctor_mapId, AddMagmaCat.hom_id, CategoryTheory.Functor.ranCounit_app_app_ranAdjunction_unit_app_app, CategoryTheory.Subobject.top_eq_id, CategoryTheory.Comma.mapRightId_hom_app_left, CategoryTheory.CommMon.id_hom, CategoryTheory.GlueData'.t_inv, CategoryTheory.Functor.RightExtension.precomp_map_right, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_assoc, CategoryTheory.Over.mapId_hom_app_left, CategoryTheory.Comma.mapLeftEq_inv_app_left, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_right, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_apply, CategoryTheory.WithInitial.map₂_app, CategoryTheory.NatTrans.CommShift₂.instIdFunctor, CategoryTheory.Limits.prod.inr_snd, CategoryTheory.Center.ofBraided_μ_f, CategoryTheory.Bicategory.LeftLift.ofIdComp_hom, AlgebraicTopology.DoldKan.PInfty_f_0, CategoryTheory.Limits.biprod.isIso_inl_iff_id_eq_fst_comp_inl, CategoryTheory.WithTerminal.commaFromOver_map_right, CategoryTheory.Bicategory.rightZigzagIso_inv, CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_right, HomologicalComplex.truncLEMap_id, CategoryTheory.ShortComplex.Hom.id_τ₃, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_presheafHom_uliftYoneda_obj, CategoryTheory.Pseudofunctor.map₂_right_unitor, CategoryTheory.Bimon.ofMonComonObjX_one, CategoryTheory.tensorUnit_def, CategoryTheory.ε_η_app, CategoryTheory.Bicategory.rightUnitor_comp_inv, Action.FunctorCategoryEquivalence.unitIso_hom_app_hom, CategoryTheory.Sum.swapCompInl_inv_app, HomologicalComplex.truncGE.rightHomologyMapData_φH, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_inv_app_fst_app, CategoryTheory.EnrichedFunctor.forgetId_hom_app, CategoryTheory.Adjunction.leftAdjointOfEquiv_map, CategoryTheory.GlueData.t_id, groupHomology.mapShortComplexH1_id, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app, CategoryTheory.Adjunction.toCat_unit_toNatTrans, CategoryTheory.Idempotents.functorExtension₂CompWhiskeringLeftToKaroubiIso_inv_app_app_f, CategoryTheory.Functor.Monoidal.whiskerRight_δ_μ, SemimoduleCat.MonoidalCategory.leftUnitor_naturality, CategoryTheory.Limits.cospanCompIso_hom_app_left, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_unitIso, CategoryTheory.IsHomLift.lift_id_inv_isIso, CategoryTheory.Pseudofunctor.DescentData.full_pullFunctor, CategoryTheory.Bicategory.LeftLift.whiskerOfIdCompIsoSelf_hom_right, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceFunctorProj_hom_app, CategoryTheory.Limits.equalizerPullbackMapIso_hom_fst, HeytAlg.coe_id, CategoryTheory.ShortComplex.RightHomologyMapData.compatibilityOfZerosOfIsLimitKernelFork_φQ, CategoryTheory.Functor.RightExtension.postcompose₂ObjMkIso_inv_left_app, CategoryTheory.Bicategory.Adj.id_l, Frm.ofHom_id, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app_assoc, CategoryTheory.PreZeroHypercover.sumInr_h₀, CategoryTheory.Endofunctor.Algebra.functorOfNatTransEq_hom_app_f, CategoryTheory.Under.mapId_eq, Action.inv_hom_hom, CategoryTheory.CatCenter.app_neg_one_zpow, CategoryTheory.Limits.CatCospanTransform.leftUnitor_inv_left_app, CategoryTheory.Sheaf.id_val, HomotopicalAlgebra.CofibrantBrownFactorization.mk'_p, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp_app, CategoryTheory.SimplicialObject.IsCoskeletal.isRightKanExtension, CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_inv_app_unmop_unmop, CategoryTheory.Limits.fst_of_isColimit, CategoryTheory.Functor.inrCompSum'_inv_app, CategoryTheory.Functor.constComp_hom_app, Frm.hom_id, GrpCat.ofHom_id, AugmentedSimplexCategory.tensorHom_id, HomologicalComplex.isoHomologyπ_hom_inv_id, CategoryTheory.ShortComplex.cyclesIsoLeftHomology_inv_hom_id, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ₀, SSet.ι₁_fst, CategoryTheory.nerve.σ_zero_nerveEquiv_symm, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.const_s, CategoryTheory.Functor.RightExtension.postcompose₂_map_left_app, CategoryTheory.IsHomLift.comp_id_lift, CategoryTheory.isoSheafify_inv, CategoryTheory.Limits.coprod.map_id_comp_assoc, CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_two, CategoryTheory.sum.inrCompAssociator_inv_app_down_down, CategoryTheory.Iso.hom_inv_id_app_app, CochainComplex.cm5b.i_f_comp, CategoryTheory.Equivalence.functor_unitIso_comp, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.pentagon, CategoryTheory.Bimon.equivMonComonCounitIsoAppX_inv_hom, CategoryTheory.Comma.mapFst_hom_app, CategoryTheory.Functor.curry_obj_obj_map, CommAlgCat.hom_id, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₃_app, CategoryTheory.Limits.equalizerPullbackMapIso_inv_ι_snd_assoc, SemiNormedGrp₁.id_apply, CochainComplex.mappingCone.inr_snd, CategoryTheory.Functor.IsEventuallyConstantFrom.coconeιApp_eq_id, LinOrd.coe_id, CategoryTheory.ReflQuiv.id_obj, CategoryTheory.Pseudofunctor.StrongTrans.rightUnitor_hom_as_app, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.trans_app_left, CategoryTheory.Functor.whiskeringRightObjCompIso_hom_app_app, CategoryTheory.IsHomLift.id_lift_eqToHom_codomain, CategoryTheory.Functor.whiskerLeft_id', AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_right, CategoryTheory.Bicategory.whiskerLeft_id, CategoryTheory.Limits.pullback.diagonal_comp, AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex_homotopyInvHomId, CategoryTheory.GradedObject.mapBifunctorRightUnitor_naturality_assoc, CategoryTheory.Functor.Monoidal.map_ε_η, BialgCat.toBialgHom_id, CategoryTheory.unop_id_op, CategoryTheory.Functor.mapGrpIdIso_inv_app_hom_hom, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₂, CategoryTheory.Comma.unopFunctorCompFst_inv_app, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIso_hom_app_hom, CochainComplex.mappingCone.inl_fst, AlgebraicGeometry.SheafedSpace.id_hom, SemiNormedGrp₁.mkHom_id, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_hom, CategoryTheory.IsPullback.zero_bot, CategoryTheory.Limits.prod.map_id_comp_assoc, LightDiagram.id_hom_hom_hom_apply, CategoryTheory.Limits.coequalizer.isoTargetOfSelf_hom, CategoryTheory.Localization.Monoidal.id_tensorHom_id, CategoryTheory.CatEnrichedOrdinary.hComp_id_heq, ModuleCat.hom_id, CategoryTheory.Join.mapWhiskerRight_id, CategoryTheory.Limits.CatCospanTransform.associator_inv_right_app, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.eq_id_of_D₂_W, SimplexCategory.δ_comp_σ_succ', CategoryTheory.Comma.equivProd_unitIso_inv_app_right, CategoryTheory.Idempotents.Karoubi.complement_p, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_inv_app_fst_app, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_app, CategoryTheory.GrpObj.inv_def, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_norm, CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal_δ_unmop_unmop, SimplexCategory.δ_comp_σ_self, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app, CategoryTheory.Limits.prod.pentagon, CategoryTheory.Limits.MultispanIndex.parallelPairDiagramOfIsColimit_map, CategoryTheory.Functor.mapTriangleCompIso_hom_app_hom₁, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_hom_app_f, CategoryTheory.PreZeroHypercover.id_h₀, CategoryTheory.CosimplicialObject.δ_comp_σ_self, CategoryTheory.End.one_def, SimplicialObject.Split.id_f, CategoryTheory.MonoidalOpposite.tensorRightMopIso_inv_app_unmop, CategoryTheory.Limits.FormalCoproduct.powerMap_id, ModuleCat.extendScalars_assoc', CategoryTheory.Functor.constCompEvaluationObj_hom_app, CategoryTheory.MonoidalCategory.tensor_inv_hom_id, CategoryTheory.Monad.comparisonForget_inv_app, CategoryTheory.IsSplitMono.id, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, CategoryTheory.ShortComplex.SnakeInput.id_f₃, CategoryTheory.StructuredArrow.mapIso_unitIso_hom_app_right, CategoryTheory.MonoidalOpposite.mopMopEquivalenceFunctorMonoidal_δ, CategoryTheory.Functor.id_mapMon_mul, CategoryTheory.Prod.sectL_map, CategoryTheory.PrelaxFunctor.map₂_hom_inv_isIso, CochainComplex.ConnectData.map_id, CategoryTheory.EnrichedFunctor.forgetComp_hom_app, CategoryTheory.Oplax.StrongTrans.categoryStruct_id_app, CategoryTheory.CommGrp.id_hom, CategoryTheory.inv_comp_eq_id, CategoryTheory.conjugateEquiv_id, CategoryTheory.Functor.constCompWhiskeringLeftIso_inv_app_app, CategoryTheory.Dial.pentagon, CategoryTheory.Functor.RightExtension.postcompose₂_map_right, CategoryTheory.Abelian.Ext.smul_eq_comp_mk₀, CategoryTheory.ShortComplex.Splitting.r_f, ModuleCat.extendScalars_id_comp, CategoryTheory.Bicategory.Pith.inclusion_mapId, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.single_W, CategoryTheory.Functor.leftOpComp_hom_app, CategoryTheory.PreOneHypercover.trivial_p₂, CategoryTheory.Limits.cospanCompIso_hom_app_one, RingCat.hom_id, CategoryTheory.Over.leftUnitor_inv_left_fst_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_app_snd_app, CategoryTheory.Limits.CatCospanTransform.associator_hom_base_app, CategoryTheory.IsPullback.zero_right, CategoryTheory.Bicategory.Strict.comp_id, CategoryTheory.WithTerminal.inclLiftToTerminal_hom_app, CategoryTheory.Functor.sheafPushforwardContinuousCompSheafToPresheafIso_hom_app_app, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left, CategoryTheory.StrictPseudofunctor.id_mapId_hom, Bicategory.Opposite.op2_leftUnitor_inv, groupHomology.H1CoresCoinfOfTrivial_f, CategoryTheory.kernelCokernelCompSequence.snakeInput_v₀₁_τ₁, CategoryTheory.Mat.id_apply_of_ne, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_counitIso_hom_app_f, CategoryTheory.Adjunction.left_triangle, CategoryTheory.Bicategory.Adj.id_r, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app_assoc, CategoryTheory.Idempotents.Karoubi.decompId_assoc, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_id, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_mul, CategoryTheory.WithTerminal.liftFromOver_obj_map, CategoryTheory.Functor.LeftExtension.precomp_map_left, UniformSpaceCat.hom_id, CategoryTheory.Oplax.OplaxTrans.rightUnitor_inv_as_app, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_hom_f_f, CategoryTheory.LaxFunctor.map₂_rightUnitor_app_assoc, CategoryTheory.Functor.mapCommpGrp_id_mul, LinearMap.id_semiModuleCat_comp, CategoryTheory.sheafToPresheaf_η, CategoryTheory.Dial.id_f, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_right, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_hom_app_app_hom, GrpWithZero.hom_id, CochainComplex.augmentTruncate_inv_f_succ, CategoryTheory.Subobject.underlyingIso_inv_top_arrow_assoc, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_hom_app_left, AlgebraicGeometry.SheafedSpace.id_hom_c, CategoryTheory.Bicategory.leftUnitor_naturality_assoc, CategoryTheory.Bicategory.conjugateEquiv_id, AlgebraicGeometry.ΓSpec.right_triangle, DistLat.ofHom_id, CategoryTheory.Localization.liftNatTrans_id, CategoryTheory.Adjunction.homEquiv_symm_id, AlgebraicGeometry.SheafedSpace.id_c_app, AlgebraicGeometry.instIsAffineXSchemeCoverOfIsIsoIsOpenImmersionId, CategoryTheory.Limits.pushout.congrHom_hom, CategoryTheory.Lax.OplaxTrans.naturality_id, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom, CategoryTheory.Join.mapPairComp_inv_app_left, CategoryTheory.Arrow.hom_inv_id_left, CategoryTheory.WithInitial.coconeEquiv_inverse_map_hom_right, CategoryTheory.MonoidalCategory.MonoidalRightAction.inv_hom_actionHomLeft', CategoryTheory.Sigma.mapId_hom_app, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_inv_assoc, CategoryTheory.Functor.unopComp_inv_app, FinPartOrd.hom_id, CategoryTheory.OplaxFunctor.PseudoCore.mapIdIso_hom, CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.pullHom_id, SemiNormedGrp.coe_id, SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_hom_app, CategoryTheory.cancel_mono_id, CategoryTheory.Iso.map_inv_hom_id_eval, HomotopicalAlgebra.FibrantBrownFactorization.mk'_r, CategoryTheory.Preadditive.inv_def, CategoryTheory.GrpObj.mulRight_hom, MonCat.ofHom_id, CategoryTheory.Functor.mapMonCompIso_inv_app_hom, CategoryTheory.Functor.opComp_hom_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_left, HomologicalComplex.truncGE'Map_id, CategoryTheory.GradedObject.Monoidal.pentagon_inv_assoc, CategoryTheory.Limits.Cocone.mapCoconeToOver_inv_hom, CategoryTheory.StructuredArrow.mapNatIso_unitIso_inv_app_right, CategoryTheory.BasedNatIso.id_inv, CategoryTheory.Limits.FormalCoproduct.category_id_f, HomotopicalAlgebra.RightHomotopyClass.whitehead, CategoryTheory.Bicategory.Prod.sectR_mapComp_hom, CategoryTheory.kernelCokernelCompSequence.snakeInput_v₀₁_τ₃, CategoryTheory.Dial.symmetry, CategoryTheory.Triangulated.Octahedron.triangleMorphism₂_hom₂, CategoryTheory.Equivalence.id_asNatTrans, CategoryTheory.Idempotents.natTrans_eq, DistLat.coe_id, CategoryTheory.Functor.Monoidal.map_δ_μ, AlgebraicGeometry.LocallyRingedSpace.iso_inv_base_hom_base, CategoryTheory.SplitMono.id, CategoryTheory.ShortComplex.LeftHomologyMapData.ofEpiOfIsIsoOfMono_φK, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_id, CategoryTheory.CommComon.id_hom, CategoryTheory.SemiadditiveOfBinaryBiproducts.add_eq_left_addition, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_snd, CategoryTheory.underToAlgebra_map_f, CategoryTheory.Join.InclLeftCompRightOpOpEquivFunctor_inv_app, CategoryTheory.Functor.OfSequence.map_id, CategoryTheory.ULift.equivalence_counitIso_inv_app, CategoryTheory.Sum.swapCompInr_hom_app, CategoryTheory.ShortComplex.HomologyData.canonical_iso_inv, MonCat.coe_id, CategoryTheory.Bicategory.instIsIsoHomRightZigzagHom, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_symm_apply, CategoryTheory.Grp.trivial_grp_one, CategoryTheory.ComposableArrows.fourδ₃Toδ₂_app_one, CategoryTheory.WithTerminal.pseudofunctor_mapId, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_left, CategoryTheory.Endofunctor.Algebra.functorOfNatTransComp_inv_app_f, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackId_hom, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_id_app, CategoryTheory.Bimon.equivMonComonCounitIsoApp_hom_hom_hom, CategoryTheory.MonoidalCategory.comp_tensor_id, PresheafOfModules.sectionsMap_id, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_inv_hom, CategoryTheory.Limits.prod.symmetry, CategoryTheory.MonoidalOpposite.mopMopEquivalenceFunctorMonoidal_η, CategoryTheory.Comonad.right_counit, CategoryTheory.Bimon.ofMonComon_toMonComon_obj_comul, CategoryTheory.Limits.coprod.rightUnitor_hom, CategoryTheory.Subobject.underlyingIso_inv_top_arrow, CategoryTheory.Functor.toPseudoFunctor'_mapId, CategoryTheory.GrothendieckTopology.isoSheafify_inv, CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id, AugmentedSimplexCategory.id_tensorHom, AlgebraicTopology.DoldKan.P_zero, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_inv, Bicategory.Opposite.op2_leftUnitor, CategoryTheory.Arrow.inv_hom_id_left, CategoryTheory.GrothendieckTopology.covering_iff_covers_id, CategoryTheory.Iso.map_inv_hom_id_eval_app, CategoryTheory.IsKernelPair.pullback, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_inv_right_app, CategoryTheory.Comma.mapRightId_inv_app_right, CategoryTheory.Functor.LeftExtension.postcomp₁_map_left, CategoryTheory.Bicategory.mateEquiv_leftUnitor_hom_rightUnitor_inv, CategoryTheory.LaxFunctor.map₂_rightUnitor_app, CategoryTheory.Idempotents.split_iff_of_iso, CategoryTheory.Iso.map_hom_inv_id_eval, CategoryTheory.Functor.mapConeOp_inv_hom, groupCohomology.H1Map_id, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_hom_app_hom_hom_hom, CategoryTheory.ActionCategory.id_val, CategoryTheory.PreOneHypercover.Hom.id_h₁, CategoryTheory.Pseudofunctor.mapComp'_id_comp, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_assoc, CategoryTheory.Over.rightUnitor_hom_left, CategoryTheory.monoidalUnopUnop_μ, CategoryTheory.Functor.Monoidal.whiskerRight_ε_η, CochainComplex.augmentTruncate_hom_f_succ, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₁_app, CategoryTheory.Comma.mapRightComp_hom_app_right, CategoryTheory.Functor.diag_η, CategoryTheory.Comma.opFunctorCompSnd_inv_app, CategoryTheory.Functor.mapCommGrpIdIso_inv_app_hom_hom_hom, CategoryTheory.NatTrans.id_app, CategoryTheory.Functor.mapConePostcompose_hom_hom, CategoryTheory.Functor.whiskeringRightObjIdIso_inv_app_app, CategoryTheory.Bicategory.prod_homCategory_id_snd, CategoryTheory.IsHomLift.lift_id_inv, CategoryTheory.Pi.δ_def, CategoryTheory.ShortComplex.cyclesMap'_id, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app, CategoryTheory.Limits.zeroProdIso_inv_snd, CategoryTheory.CatEnriched.id_eq, CategoryTheory.Subobject.underlyingIso_top_hom, CategoryTheory.monoidalOfHasFiniteCoproducts.leftUnitor_hom, CategoryTheory.ShortComplex.cyclesMap_id, Bicategory.Opposite.bicategory_homCategory_id_unop2, CategoryTheory.Comonad.Coalgebra.id_f, CategoryTheory.Dial.whiskerLeft_f, CategoryTheory.composePath_id, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, CategoryTheory.Over.sections_map, CommMonCat.id_apply, CategoryTheory.Functor.RightExtension.coneAtWhiskerRightIso_hom_hom, CochainComplex.cm5b.i_f_comp_assoc, CategoryTheory.Bicategory.LeftLift.whiskerIdCancel_right, Action.FunctorCategoryEquivalence.counitIso_hom_app_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.hom_inv_actionHomLeft, CategoryTheory.MonoidalCategory.hom_inv_id_tensor', CategoryTheory.ShortComplex.unopMap_id, SimplexCategory.concreteCategoryHom_id, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.ofRestrict_invApp, CategoryTheory.Bicategory.Prod.fst_mapComp_inv, PresheafOfModules.map_id, CategoryTheory.sum.inlCompInverseAssociator_inv_app_down_down, Mathlib.Tactic.CategoryTheory.CancelIso.hom_inv_id_of_eq, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, CategoryTheory.Under.mapPushoutAdj_counit_app, ProfiniteGrp.ofHom_id, CategoryTheory.Localization.SmallHom.mk_comp_mkInv, CategoryTheory.Comonad.id_ε_app, SSet.ι₀_fst, AlgebraicGeometry.Scheme.Modules.pseudofunctor_left_unitality, Bimod.id_whiskerRight_bimod, Bimod.AssociatorBimod.inv_hom_id, CategoryTheory.Comma.id_left, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom, Bicategory.Opposite.unop2_id, CategoryTheory.evaluationAdjunctionRight_unit_app, CategoryTheory.Idempotents.Karoubi.coe_X, CategoryTheory.WithTerminal.coneEquiv_unitIso_inv_app_hom_left, CategoryTheory.ShortComplex.RightHomologyData.ofIsColimitCokernelCofork_ι, CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf_hom_right, CategoryTheory.PreOneHypercover.sieve₁'_cylinder, CategoryTheory.Pi.sum_map_app, CategoryTheory.BasedFunctor.instIsHomLiftObjPIdObj, CategoryTheory.Functor.mapMatId_hom_app, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_app, CategoryTheory.Triangulated.instNonemptyOctahedron, CategoryTheory.Join.InclRightCompRightOpOpEquivFunctor_inv_app, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_hom_app_f, CategoryTheory.Bicategory.prod_leftUnitor_hom_fst, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_inv_hom₂, CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj_hom_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_left, CategoryTheory.ExponentiableMorphism.unit_pushforwardId_hom, AlgebraicGeometry.Scheme.IdealSheafData.map_id, CategoryTheory.ShortComplex.HomologyMapData.compatibilityOfZerosOfIsLimitKernelFork_right, CategoryTheory.Limits.coprod.triangle, CategoryTheory.Grp_Class.inv_eq_inv, Bimod.id_hom', CategoryTheory.Mon.forget_η, Rep.FiniteCyclicGroup.leftRegular.range_norm_eq_ker_applyAsHom_sub, CategoryTheory.OverPresheafAux.YonedaCollection.map₁_id, CategoryTheory.Functor.isoSum_hom_app_inr, CategoryTheory.ShortComplex.LeftHomologyData.ofIsLimitKernelFork_π, CategoryTheory.Functor.OplaxMonoidal.id_η, HomotopicalAlgebra.CofibrantBrownFactorization.mk'_Z, CategoryTheory.Limits.CoconeMorphism.inv_hom_id, CategoryTheory.Equivalence.mkHom_id_functor, CategoryTheory.Limits.fiberwiseColimCompEvaluationIso_inv_app, CategoryTheory.WithInitial.liftFromUnderComp_hom_app, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_inv_assoc, CategoryTheory.Limits.kernelZeroIsoSource_inv, CategoryTheory.Bicategory.Adjunction.comp_left_triangle_aux, CategoryTheory.Bicategory.whiskerLeft_hom_inv_whiskerRight, CategoryTheory.SemiCartesianMonoidalCategory.toUnit_unit, CategoryTheory.GrpObj.mulRight_inv, CategoryTheory.Mat.id_apply, CategoryTheory.PresheafHom.IsSheafFor.app_cond, CategoryTheory.Monad.monadMonEquiv_counitIso_inv_app_hom, TopCat.Presheaf.Pushforward.comp_hom_app, CategoryTheory.Functor.mapCoconeOp_hom_hom, CategoryTheory.sheafToPresheaf_ε, MonObj.mopEquiv_counitIso_inv_app_hom_unmop, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_inv_app_hom_app, CategoryTheory.Functor.Fiber.homMk_id, CategoryTheory.ComposableArrows.map'_self, CategoryTheory.Limits.prod.map_id_id, CategoryTheory.StrictlyUnitaryPseudofunctor.map_id, CategoryTheory.Equivalence.unit_inverse_comp, CategoryTheory.sheafificationAdjunction_counit_app_val, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_inv_app_app, CategoryTheory.Adjunction.right_triangle_components, CategoryTheory.Pretriangulated.triangleMorphismId_hom₁, CategoryTheory.WithInitial.coconeEquiv_counitIso_hom_app_hom, Action.FunctorCategoryEquivalence.functor_μ, CategoryTheory.Limits.Cone.toUnder_π_app, CategoryTheory.IsIso.hom_inv_id, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id_app, CategoryTheory.Limits.colimitCoyonedaHomIsoLimit_π_apply, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_inv_f_f, CategoryTheory.Comma.id_right, CategoryTheory.Iso.conj_id, groupCohomology.cocyclesMap_id, CategoryTheory.Under.inv_right_hom_right, Lat.id_apply, HomotopicalAlgebra.PrepathObject.ι_p₀, CategoryTheory.Functor.commShiftIso_id_inv_app, CategoryTheory.Limits.DiagramOfCocones.id, BddLat.id_apply, CategoryTheory.Functor.rightOpId_hom_app, CategoryTheory.Localization.Monoidal.whiskerLeft_id, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_inv_app_hom_hom_app, CategoryTheory.Functor.Monoidal.map_η_ε, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app_assoc, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_hom_app_hom, CategoryTheory.coprodMonad_map, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_left, ChainComplex.augmentTruncate_inv_f_zero, CategoryTheory.Idempotents.isIdempotentComplete_iff_hasEqualizer_of_id_and_idempotent, CategoryTheory.WithInitial.liftFromUnder_map_app, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIdIso_inv_app_hom, CategoryTheory.Bicategory.id_whiskerLeft, CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_hom_app, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_counit_app, CochainComplex.truncateAugment_hom_f, AlgebraicTopology.DoldKan.homotopyPToId_eventually_constant, CategoryTheory.Quotient.lift.isLift_inv, CategoryTheory.Sigma.mapId_inv_app, AlgebraicGeometry.Spec.sheafedSpaceMap_id, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_snd, Quiver.Hom.id_toLoc, CategoryTheory.MonoidalCategory.tensor_hom_inv_id'_assoc, SemiNormedGrp.ofHom_id, CategoryTheory.HopfObj.antipode_antipode, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_obj_map, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_right, CategoryTheory.Pseudofunctor.mapComp_id_left_hom, CategoryTheory.Limits.Sigma.ι_π_eq_id, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_unitIso_hom_app_right_app, CategoryTheory.Abelian.FunctorCategory.imageObjIso_hom, CategoryTheory.OplaxFunctor.id_mapId, CategoryTheory.Join.mkFunctorRight_inv_app, CategoryTheory.Oplax.LaxTrans.naturality_id_assoc, CategoryTheory.endofunctorMonoidalCategory_rightUnitor_hom_app, CategoryTheory.MorphismProperty.RightFraction.ofInv_f, SheafOfModules.pushforward_comp_id, CategoryTheory.Functor.mapContActionComp_hom, CategoryTheory.overToCoalgebra_obj_a, CategoryTheory.Functor.map₂HomologicalComplex_obj_map, CategoryTheory.MorphismProperty.Over.mapComp_inv_app_left, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_rightUnitor, CommGrpCat.ofHom_id, CategoryTheory.Limits.colimitYonedaHomIsoLimitOp_π_apply, CategoryTheory.Limits.IsLimit.lift_self, CategoryTheory.SimplicialObject.id_right, CategoryTheory.ObjectProperty.ιOfLE_ε, CategoryTheory.Limits.PushoutCocone.isoMk_hom_hom, CategoryTheory.Limits.biprod.add_eq_lift_id_desc, CategoryTheory.Bicategory.Prod.snd_mapComp_hom, CategoryTheory.prodOpEquiv_counitIso_hom_app, CategoryTheory.Over.starPullbackIsoStar_inv_app_left, CategoryTheory.Bicategory.leftUnitor_hom_congr, CategoryTheory.Comma.mapSnd_hom_app, HomologicalComplex.homotopyCofiber.sndX_inrX, CategoryTheory.ShortComplex.homologyMap_id, CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapId_hom, HomologicalComplex₂.flipEquivalenceCounitIso_inv_app_f_f, CategoryTheory.ShortComplex.Splitting.r_f_assoc, CategoryTheory.Functor.mapTriangleIdIso_inv_app_hom₁, HomologicalComplex.homologyFunctorIso_hom_app, CategoryTheory.Limits.FormalCoproduct.category_id_φ, CategoryTheory.Functor.mapGrpCompIso_inv_app_hom_hom, CategoryTheory.GrothendieckTopology.overMapPullback_id_comp_assoc, CategoryTheory.PreZeroHypercover.sumInl_h₀, CategoryTheory.Bicategory.Adj.leftUnitor_inv_τr, CategoryTheory.IsPushout.zero_right, CategoryTheory.Localization.SmallHom.mk_id_comp, CategoryTheory.kernelCokernelCompSequence.snakeInput_L₀_f, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app, CategoryTheory.Limits.cospanCompIso_hom_app_right, CategoryTheory.Limits.pullbackDiagonalMapIdIso_hom_snd_assoc, CategoryTheory.GrpObj.right_inv, AlgebraicGeometry.PresheafedSpace.id_c_app, CategoryTheory.PreOneHypercover.toPullback_cylinder, CategoryTheory.PrelaxFunctor.map₂_id, CategoryTheory.CostructuredArrow.pre_map_right, CategoryTheory.Bicategory.rightUnitor_inv_naturality_assoc, CategoryTheory.NatTrans.removeUnop_id, CategoryTheory.Pseudofunctor.CoGrothendieck.map_id_eq, CategoryTheory.Pseudofunctor.CoGrothendieck.compIso_inv_app, CategoryTheory.Join.mapWhiskerLeft_id, CategoryTheory.Limits.CatCospanTransform.leftUnitor_inv_base_app, CategoryTheory.Limits.biproduct.fromSubtype_toSubtype, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app_assoc, CategoryTheory.Adjunction.id_unit, CategoryTheory.Functor.toOplaxFunctor_mapId, CategoryTheory.Prod.fac', CategoryTheory.Prod.symmetry_inv_app, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_left, CochainComplex.HomComplex.Cochain.id_comp, AlgCat.hom_id, CategoryTheory.sheafCompose_id, CategoryTheory.Pretriangulated.binaryProductTriangleIsoBinaryBiproductTriangle_inv_hom₁, CategoryTheory.sum.inlCompInlCompAssociator_hom_app_down, CategoryTheory.Functor.curry_obj_map_app, CategoryTheory.Comma.toPUnitIdEquiv_counitIso_inv_app, CategoryTheory.Limits.Cocones.extendId_inv_hom, CategoryTheory.toOverIteratedSliceForwardIsoPullback_inv_app_left, CategoryTheory.Functor.mapCoconePrecompose_hom_hom, CategoryTheory.BasedCategory.id_def, CategoryTheory.ComposableArrows.threeδ₁Toδ₀_app_one, CategoryTheory.Comonad.ComonadicityInternal.comparisonAdjunction_counit, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIdIso_hom_app_hom, CategoryTheory.Limits.prod.map_id_comp, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_right_app, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceInverseπ_inv_app, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_assoc, CategoryTheory.ShortComplex.cyclesIsoX₂_inv_hom_id, CategoryTheory.Mat_.id_apply, CategoryTheory.ComposableArrows.threeδ₃Toδ₂_app_zero, CategoryTheory.Bicategory.Pith.leftUnitor_hom_iso, AlgebraicGeometry.IsImmersion.instLiftSchemeId, CategoryTheory.WithInitial.lift_map, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app, Action.resId_hom_app_hom, UniformSpaceCat.coe_id, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map_id, AlgebraicGeometry.Scheme.Modules.pseudofunctor_left_unitality_assoc, CategoryTheory.Comonad.Coalgebra.counit, CategoryTheory.Limits.Cone.mapConeToUnder_hom_hom, CategoryTheory.Monad.right_unit, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_naturality_assoc, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom', CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_assoc, CategoryTheory.ComposableArrows.fourδ₂Toδ₁_app_two, CategoryTheory.Idempotents.Karoubi.decompId_p_f, CategoryTheory.CategoryOfElements.id_val, CategoryTheory.Functor.IsCartesian.domainUniqueUpToIso_hom_isHomLift, CategoryTheory.NatTrans.rightDerived_id, HomotopicalAlgebra.FibrantObject.homMk_id, CategoryTheory.instHomIsOverId, CategoryTheory.PresheafHom.IsSheafFor.exists_app, SimplexCategory.eq_id_of_mono, CategoryTheory.SingleFunctors.inv_hom_id_hom_app, CategoryTheory.Limits.BinaryFan.leftUnitor_inv, AlgebraicGeometry.SheafedSpace.id_c, CategoryTheory.ShortComplex.LeftHomologyMapData.ofEpiOfIsIsoOfMono_φH, CategoryTheory.Limits.IsTerminal.from_self, Action.forget_μ, CategoryTheory.Iso.unop_inv_hom_id_app, CategoryTheory.Bicategory.Pith.rightUnitor_inv_iso_hom, CategoryTheory.Bicategory.InducedBicategory.bicategory_id_hom, CategoryTheory.Coyoneda.fullyFaithful_preimage, CategoryTheory.MorphismProperty.id_mem, AlgebraicGeometry.Scheme.IdealSheafData.inclusion_id, CategoryTheory.MonoidalOpposite.tensorLeftIso_hom_app_unmop, CategoryTheory.ShortComplex.RightHomologyMapData.compatibilityOfZerosOfIsColimitCokernelCofork_φQ, CategoryTheory.Mat.id_apply_self, CategoryTheory.Comon.trivial_comon_counit, CategoryTheory.Functor.mapConeOp_hom_hom, CategoryTheory.Adjunction.right_triangle, CategoryTheory.Limits.Cocone.toCostructuredArrowCompProj_inv_app, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_hom_assoc, CategoryTheory.Prod.sectR_map, CategoryTheory.Bicategory.leftUnitor_naturality, CategoryTheory.Functor.mapTriangleIdIso_inv_app_hom₂, CategoryTheory.Dial.leftUnitorImpl_inv_f, CategoryTheory.Bicategory.InducedBicategory.bicategory_homCategory_id_hom, CategoryTheory.ExponentiableMorphism.unit_pushforwardId_hom_assoc, CategoryTheory.CatEnrichedOrdinary.id_hComp_id, CategoryTheory.StrictlyUnitaryLaxFunctor.mk'_mapId, CategoryTheory.Mon.forget_δ, AlgebraicGeometry.LocallyRingedSpace.residueFieldMap_id, CategoryTheory.Comma.mapRightEq_hom_app_left, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_left, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₂, CategoryTheory.Join.inrCompFromSum_inv_app, CategoryTheory.WithTerminal.liftFromOverComp_inv_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_right, CategoryTheory.WithInitial.liftToInitial_map, CategoryTheory.Comma.mapRightEq_inv_app_right, CategoryTheory.Bifunctor.diagonal', AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τl, CategoryTheory.Bicategory.Comonad.counit_comul, CategoryTheory.Functor.curryObjProdComp_inv_app_app, SheafOfModules.conjugateEquiv_pullbackId_hom, CategoryTheory.Dial.braiding_naturality_left, CategoryTheory.Under.costar_map_left, CategoryTheory.Adjunction.ofCat_unit, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapId_inv_iso_hom, CategoryTheory.Limits.splitMonoOfIdempotentOfIsLimitFork_retraction, CategoryTheory.OplaxFunctor.map₂_rightUnitor_app, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_right_unitor, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_assoc, CategoryTheory.ShortComplex.id_τ₃, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_left_map, CategoryTheory.GrothendieckTopology.diagramNatTrans_id, CategoryTheory.ShortComplex.LeftHomologyData.ofZeros_π, CategoryTheory.Sum.functorEquiv_unit_app_app_inl, CategoryTheory.Join.mkFunctorLeft_inv_app, SemiRingCat.id_apply, CategoryTheory.MonoidalOpposite.unmopEquiv_counitIso_inv_app, CategoryTheory.ComposableArrows.mk₀_map, CategoryTheory.Discrete.functor_map, CategoryTheory.GradedObject.Monoidal.rightUnitor_naturality, CategoryTheory.WithInitial.ofCommaObject_map, CategoryTheory.MonoidalOpposite.tensorRightMopIso_hom_app_unmop, CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv', FinBddDistLat.id_apply, CategoryTheory.StructuredArrow.toUnder_map_left, CategoryTheory.Localization.SmallHom.mkInv_comp_mk, CategoryTheory.Grp.η_def, CategoryTheory.Cat.id_eq_id, CategoryTheory.WithTerminal.equivComma_inverse_obj_map, SSet.Truncated.HomotopyCategory.BinaryProduct.associativityIso_hom_app, AddCommMonCat.id_apply, CategoryTheory.Functor.toEssImageCompι_inv_app, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapIdIso_hom, TopologicalSpace.OpenNhds.map_id_obj, AlgebraicGeometry.PresheafedSpace.id_c, CategoryTheory.Yoneda.fullyFaithful_preimage, CategoryTheory.Limits.prod.inl_fst, CategoryTheory.Oplax.OplaxTrans.leftUnitor_hom_as_app, AddMagmaCat.id_apply, CategoryTheory.GradedObject.Monoidal.leftUnitor_naturality, CategoryTheory.Comma.toIdPUnitEquiv_counitIso_inv_app, CategoryTheory.PreOneHypercover.inter_p₁, CommRingCat.hom_id, CategoryTheory.MonoidalCategory.DayFunctor.equiv_unitIso_inv_app, CategoryTheory.Limits.coprod.functor_obj_map, ModuleCat.extendScalars_comp_id, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app, CategoryTheory.Adjunction.adjToMonadIso_hom_toNatTrans_app, LightCondensed.id_val, CategoryTheory.Functor.leftDerivedNatTrans_id, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_assoc, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_assoc, CategoryTheory.endofunctorMonoidalCategory_leftUnitor_inv_app, IsFreeGroupoid.SpanningTree.treeHom_root, CategoryTheory.WithInitial.liftFromUnder_obj_map, CategoryTheory.Limits.IsZero.iff_id_eq_zero, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₂, CategoryTheory.Limits.PushoutCocone.eta_hom_hom, CategoryTheory.Pseudofunctor.DescentData.id_hom, BddOrd.ofHom_id, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id, CategoryTheory.Functor.IsCartesian.map_isHomLift, CategoryTheory.ComposableArrows.fourδ₃Toδ₂_app_three, CategoryTheory.Join.mapPairLeft_hom_app, CategoryTheory.Localization.SmallShiftedHom.mk₀_comp_mk₀Inv, Semigrp.coe_id, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransId_hom_app_f, CategoryTheory.Functor.flipIsoCurrySwapUncurry_inv_app_app, CategoryTheory.OplaxFunctor.mapComp_id_left_assoc, AlgebraicGeometry.SheafedSpace.id_base, CategoryTheory.StrictPseudofunctor.mk'_mapId, CategoryTheory.ShortComplex.Splitting.f_r, CategoryTheory.WithTerminal.liftFromOver_map_app, DerivedCategory.singleFunctorsPostcompQIso_hom_hom, CategoryTheory.Presieve.FamilyOfElements.compPresheafMap_id, groupCohomology.mapShortComplexH2_id, CategoryTheory.Functor.sheafPushforwardContinuousId_inv_app_val_app, LinearMap.comp_id_semiModuleCat, CategoryTheory.Bicategory.Prod.swap_mapComp_hom, AlgebraicGeometry.Scheme.toIso_inv_ι, CategoryTheory.Mathlib.Tactic.MonTauto.associator_hom_comp_tensorHom_tensorHom_comp_assoc, AddSemigrp.id_apply, CategoryTheory.WithTerminal.coneEquiv_inverse_map_hom_left, CategoryTheory.Functor.mapCochainComplexShiftIso_hom_app_f, CategoryTheory.StrictPseudofunctor.id_mapId_inv, CategoryTheory.Iso.inv_hom_id_app, CategoryTheory.Idempotents.Karoubi.decompId_p_toKaroubi, CategoryTheory.MonoidalClosed.curry'_id, CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf_inv_right, CategoryTheory.Functor.bifunctorComp₁₂Iso_inv_app_app_app, CategoryTheory.Functor.LeftLinear.μₗ_comp_δₗ, CategoryTheory.ShortComplex.HomotopyEquiv.trans_homotopyInvHomId, CategoryTheory.Functor.Elements.initialOfRepresentableBy_snd, CategoryTheory.Equivalence.inverseFunctorObjIso_hom, CategoryTheory.Arrow.hom_inv_id_right, CategoryTheory.MonObj.one_rightUnitor, CategoryTheory.Limits.prod.functor_map_app, CategoryTheory.Functor.CorepresentableBy.ext_iff, ProfiniteGrp.id_apply, CategoryTheory.IsCoreflexivePair.common_retraction', CategoryTheory.Functor.toEssImageCompι_hom_app, CategoryTheory.StrictlyUnitaryLaxFunctor.mapIdIso_inv, AlgebraicGeometry.Scheme.instIsClosedImmersionLiftIdOfIsSeparated, CommBialgCat.ofHom_id, CategoryTheory.Under.mkIdInitial_to_right, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁, CategoryTheory.Limits.walkingSpanOpEquiv_unitIso_hom_app, CategoryTheory.Join.mapIsoWhiskerLeft_inv_app, CategoryTheory.SmallObject.SuccStruct.ofCocone.map_id, CategoryTheory.MonoidalCategory.id_tensor_associator_inv_naturality_assoc, CategoryTheory.Equivalence.inverseFunctorObj'_inv_app, CategoryTheory.Limits.prod.map_comp_id_assoc, Bimod.whiskerLeft_id_bimod, CategoryTheory.Functor.rightUnitor_inv_app, CategoryTheory.Functor.leftUnitor_hom_app, CategoryTheory.Grothendieck.ιCompMap_hom_app_base, AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_id, CategoryTheory.Bicategory.rightUnitor_comp_assoc, CategoryTheory.Limits.WidePullbackShape.wideCospan_map, CategoryTheory.NonPreadditiveAbelian.lift_map, CategoryTheory.Functor.mapConeMapCone_inv_hom, CategoryTheory.Limits.CatCospanTransform.leftUnitor_hom_base_app, CategoryTheory.Dial.id_F, CategoryTheory.Limits.Multicofork.isoOfπ_inv_hom, CategoryTheory.Dial.id_tensorHom_id, CategoryTheory.Bicategory.Adj.leftUnitor_hom_τr, CategoryTheory.Pseudofunctor.DescentData.hom_self, CategoryTheory.Functor.ranCounit_app_whiskerLeft_ranAdjunction_unit_app, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_app, CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_mapId, CategoryTheory.Oplax.StrongTrans.categoryStruct_id_naturality, CategoryTheory.Functor.linear_iff, CategoryTheory.kernelCokernelCompSequence.snakeInput_v₂₃_τ₁, AddCommMonCat.ofHom_id, CategoryTheory.Limits.coconeOfIsSplitEpi_ι_app, AlgebraicGeometry.Scheme.residueFieldMap_id, CategoryTheory.Bicategory.Comonad.comul_counit, CategoryTheory.Bicategory.leftZigzagIso_inv, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_id, CategoryTheory.Limits.ColimitPresentation.id_hom, CategoryTheory.Mat_.id_def, CategoryTheory.Bicategory.Adjunction.comp_right_triangle_aux, BddLat.hom_id, CategoryTheory.Functor.Monoidal.whiskeringLeft_δ_app, CategoryTheory.MonoidalOpposite.unmopFunctor_η, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_naturality_app, CategoryTheory.Limits.biproduct.toSubtype_fromSubtype_assoc, CategoryTheory.MonoidalCategory.id_tensor_comp_tensor_id_assoc, CategoryTheory.Under.postAdjunctionRight_counit_app_right, CategoryTheory.MonoidalCategory.id_whiskerRight_assoc, CategoryTheory.Functorial.map_id, CategoryTheory.MonoidalCategory.id_tensor_associator_naturality_assoc, CategoryTheory.Bicategory.Prod.sectL_map₂, CategoryTheory.Pseudofunctor.DescentData.pullFunctorEquivalence_counitIso, CategoryTheory.Functor.mapCommMonIdIso_inv_app_hom_hom, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₃_W, CommMonCat.ofHom_id, CategoryTheory.prod_id_snd, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_app_fst_app, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_inv_naturality, CategoryTheory.GlueData.cocycle, CategoryTheory.Bicategory.Adjunction.homEquiv₁_symm_apply, CoalgCat.toCoalgHom_id, CategoryTheory.Functor.bifunctorComp₁₂Iso_hom_app_app_app, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_inv_hom_id, CategoryTheory.Functor.Fiber.inducedFunctorCompIsoSelf_inv_app, CategoryTheory.Limits.PullbackCone.isoMk_hom_hom, CategoryTheory.Presieve.isSheafFor_singleton_iso, HasFibers.inducedFunctor_map_coe, CategoryTheory.Limits.CatCospanTransform.leftUnitor_hom_right_app, TopCat.Presheaf.stalkSpecializes_refl, CategoryTheory.Comma.mapLeftComp_hom_app_left, AlgebraicGeometry.Scheme.Hom.stalkMap_id, CategoryTheory.Presheaf.instIsLeftKanExtensionFunctorOppositeTypeIdCompUliftYonedaOfPreservesColimitsOfSizeOfHasPointwiseLeftKanExtension, CategoryTheory.PresheafHom.isAmalgamation_iff, CategoryTheory.Bicategory.Prod.swap_mapComp_inv, CategoryTheory.Comon.monoidal_tensorUnit_comon_counit, CategoryTheory.Functor.bifunctorComp₂₃Iso_hom_app_app_app, CategoryTheory.Subgroupoid.id_mem_of_nonempty_isotropy, MonObj.mopEquiv_unitIso_inv_app_hom, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₃, CategoryTheory.CommGrp.trivial_grp_inv, SheafOfModules.pushforward_id_comp, CategoryTheory.Functor.inrCompSum'_hom_app, CategoryTheory.Functor.whiskeringLeftObjCompIso_hom_app_app, CategoryTheory.Comon.forget_μ, CategoryTheory.Functor.LeftExtension.precomp₂_map_left, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_inv_app_hom_hom, CategoryTheory.MonoidalOpposite.unmopFunctor_ε, CategoryTheory.Limits.pullbackDiagonalMapIdIso_hom_snd, CategoryTheory.Bicategory.Prod.snd_mapComp_inv, CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_one, CategoryTheory.NonPreadditiveAbelian.lift_σ, CategoryTheory.Limits.pullback.congrHom_inv, FundamentalGroupoid.id_eq_path_refl, CategoryTheory.LaxBraidedFunctor.id_hom, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso_hom_app_f, CategoryTheory.Adjunction.rightAdjointUniq_refl, CategoryTheory.Mat_.id_apply_of_ne, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₁, CategoryTheory.curryingIso_inv_toFunctor_obj_obj_map, CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder_map, CategoryTheory.Bicategory.conjugateEquiv_symm_apply', CategoryTheory.StructuredArrow.mapIso_inverse_map_left, CategoryTheory.NonPreadditiveAbelian.lift_σ_assoc, SemimoduleCat.MonoidalCategory.rightUnitor_naturality, Quiver.FreeGroupoid.congr_reverse_comp, CategoryTheory.Monad.monadMonEquiv_unitIso_hom_app_toNatTrans_app, CochainComplex.mappingConeCompTriangle_mor₂, CategoryTheory.PreOneHypercover.cylinder_p₁, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_mul, CategoryTheory.Functor.mapMatId_inv_app, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_hom_app, CategoryTheory.CostructuredArrow.initial_map₂_id, CategoryTheory.Limits.Fork.isoForkOfι_inv_hom, CategoryTheory.Sieve.id_mem_iff_eq_top, CategoryTheory.ShortComplex.SnakeInput.Hom.id_f₂, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_naturality, CategoryTheory.Square.category_id_τ₂, CategoryTheory.Join.mapPairRight_hom_app, CategoryTheory.Bicategory.whiskerLeft_rightUnitor, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_hom_app_hom, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_hom_app_one, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, CochainComplex.cm5b.degreewiseEpiWithInjectiveKernel_p, HomotopicalAlgebra.FibrantBrownFactorization.mk'_p, CategoryTheory.Limits.Cocone.mapCoconeToOver_hom_hom, CategoryTheory.Functor.mapConeWhisker_inv_hom, AddGrpCat.ofHom_id, CategoryTheory.Limits.walkingSpanOpEquiv_counitIso_inv_app, OrderHom.equivalenceFunctor_unitIso_inv_app, CategoryTheory.Limits.prod.map_swap, Rep.linearizationTrivialIso_hom_hom, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_hom_app_app, ModuleCat.ofHom_id, AlgebraicGeometry.LocallyRingedSpace.id_toHom, CategoryTheory.Mod_.id_hom, CategoryTheory.PreOneHypercover.cylinder_p₂, CategoryTheory.Pseudofunctor.map₂_left_unitor_app_assoc, CategoryTheory.Bifunctor.map_comp_id, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.id_snd_app, FinBddDistLat.hom_id, CategoryTheory.Pseudofunctor.map₂_right_unitor_app_assoc, CategoryTheory.Pseudofunctor.map₂_right_unitor_app, CategoryTheory.Over.mkIdTerminal_from_left, CategoryTheory.Limits.Cone.toStructuredArrowCompToUnderCompForget_inv_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_hom_app_app_fst, AlgebraicTopology.DoldKan.identity_N₂_objectwise, CategoryTheory.StructuredArrow.map_id, CategoryTheory.MonoidalOpposite.tensorRightUnmopIso_hom_app, CategoryTheory.Limits.pushout.congrHom_inv, CategoryTheory.MonoidalCategory.leftUnitor_inv_tensor_id_assoc, CategoryTheory.Quiv.id_eq_id, CategoryTheory.GrothendieckTopology.Cover.Arrow.precompRelation_g₁, CategoryTheory.WithInitial.opEquiv_inverse_map, CategoryTheory.CostructuredArrow.mapNatIso_functor_map_right, CategoryTheory.Limits.prod.functor_obj_map, AlgebraicGeometry.Scheme.IsLocallyDirected.t_id, CategoryTheory.Functor.mapCommMon_id_one, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom''_assoc, CategoryTheory.MonoidalOpposite.tensorLeftMopIso_inv_app_unmop, CategoryTheory.Bimon.equivMonComonCounitIsoAppXAux_hom, PresheafOfModules.instFullRestrictScalarsIdFunctorOppositeRingCat, CategoryTheory.IsPushout.of_coprod_inl_with_id, SimplexCategory.Truncated.δ₂_two_comp_σ₂_one, CategoryTheory.Limits.pullback.congrHom_hom, CategoryTheory.ComposableArrows.Precomp.map_zero_zero, CategoryTheory.Limits.cokernelZeroIsoTarget_hom, CochainComplex.cm5b.instInjectiveXIntMappingConeIdI, CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtensionObjIsoColimit_hom_assoc, CategoryTheory.Square.Hom.id_τ₁, CategoryTheory.GradedObject.Monoidal.triangle, Bimod.RightUnitorBimod.hom_inv_id, CategoryTheory.Center.forget_δ, CategoryTheory.WithInitial.liftStar_hom, CategoryTheory.NatTrans.leftDerivedToHomotopyCategory_id, HomotopicalAlgebra.Precylinder.i₁_π, CategoryTheory.MorphismProperty.LeftFraction.map_ofInv_hom_id, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.rightUnitor_naturality, CategoryTheory.Pseudofunctor.CoGrothendieck.map_id_map, CategoryTheory.Mathlib.Tactic.MonTauto.associator_hom_comp_tensorHom_tensorHom_comp, CategoryTheory.Limits.opParallelPairIso_inv_app_zero, CategoryTheory.Join.id_left, CategoryTheory.Iso.hom_comp_eq_id, CategoryTheory.NatTrans.leftDerived_id, CategoryTheory.IsIso.out, CategoryTheory.PreOneHypercover.id_h₁, CategoryTheory.Sum.functorEquivFunctorCompSndIso_hom_app_app, CategoryTheory.Join.mapIsoWhiskerLeft_hom_app, CategoryTheory.PrelaxFunctor.map₂_inv_hom, CategoryTheory.MonoidalClosed.comp_id, CategoryTheory.ShortComplex.LeftHomologyData.ofIsColimitCokernelCofork_i, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_hom_app_fst_app, CategoryTheory.FreeGroupoid.mapCompLift_hom_app, groupHomology.H1CoresCoinf_f, CategoryTheory.Iso.inv_hom_id_triangle_hom₃, SimplexCategory.eq_of_one_to_one, CategoryTheory.Bicategory.Prod.sectR_mapId_hom, CategoryTheory.Limits.opParallelPairIso_inv_app_one, CategoryTheory.ExponentiableMorphism.pushforwardId_hom_counit, CategoryTheory.Sum.functorEquivFunctorCompFstIso_hom_app_app, AlgebraicGeometry.Scheme.Pullback.openCoverOfLeft_f, CategoryTheory.Linear.toCatCenter_apply_app, CategoryTheory.whiskeringLeftCompEvaluation_inv_app, CategoryTheory.Bicategory.Strict.leftUnitor_eqToIso, CategoryTheory.IsKernelPair.id_of_mono, CategoryTheory.CatCommSq.vId_iso_inv_app, CategoryTheory.ShortComplex.LeftHomologyMapData.compatibilityOfZerosOfIsLimitKernelFork_φK, CategoryTheory.Comma.equivProd_unitIso_inv_app_left, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_symm_apply, CategoryTheory.Lax.StrongTrans.categoryStruct_id_app, CategoryTheory.Bicategory.Prod.swap_mapId_hom, FinBddDistLat.ofHom_id, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.IsTerminal.lift_self, CategoryTheory.Over.isMonHom_pullbackFst_id_right, CategoryTheory.Limits.prod.leftUnitor_inv_naturality, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransEq_inv_app_f, CategoryTheory.Limits.Pi.map'_id_id, CategoryTheory.Limits.biprod.inr_snd, CategoryTheory.Endofunctor.Coalgebra.Terminal.right_inv', SimplicialObject.Split.id_F, FintypeCat.id_hom, CategoryTheory.Over.forgetAdjStar_unit_app_left, CategoryTheory.Discrete.functorComp_inv_app, CategoryTheory.IsHomLift.lift_comp_id, SimplexCategory.hom_zero_zero, CategoryTheory.StrictlyUnitaryLaxFunctor.id_mapId, CategoryTheory.Comma.unopFunctorCompSnd_hom_app, CategoryTheory.Limits.coneOfIsSplitMono_pt, CategoryTheory.FreeBicategory.mk_right_unitor_hom, CategoryTheory.IsHomLift.eqToHom_codomain_lift_id, CategoryTheory.MonoidalCategory.inv_hom_whiskerRight', CategoryTheory.Limits.Sigma.map'_id_id, CategoryTheory.Functor.compConstIso_inv_app_app, CategoryTheory.Functor.mapTriangleInvRotateIso_hom_app_hom₂, CategoryTheory.MonoidalCategory.tensor_id_comp_id_tensor, CategoryTheory.Limits.prod.leftUnitor_hom_naturality, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₂_app, CategoryTheory.NatTrans.rightOp_id, Action.resComp_hom_app_hom, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₄_W, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_inv_app_f, CategoryTheory.ShortComplex.opcyclesMap_id, CategoryTheory.NatTrans.removeRightOp_id, CategoryTheory.Sigma.SigmaHom.comp_id, CategoryTheory.sheafSectionsNatIsoEvaluation_hom_app, Bicategory.Opposite.homCategory_id_unop2, CategoryTheory.Limits.coprod.map_swap_assoc, CategoryTheory.ShortComplex.leftRightHomologyComparison'_compatibility, CategoryTheory.ComposableArrows.fourδ₄Toδ₃_app_zero, CategoryTheory.StrictPseudofunctor.id_mapComp_inv, MonCat.id_apply, SheafOfModules.instIsRightAdjointPushforwardIdSheafRingCat, CategoryTheory.GrothendieckTopology.overMapPullback_id_comp, CategoryTheory.sum.inlCompAssociator_inv_app, CategoryTheory.Functor.unopId_hom_app, CategoryTheory.prod.etaIso_inv, CommBialgCat.hom_id, HomologicalComplex₂.flipEquivalenceCounitIso_hom_app_f_f, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_inv_app_snd_app, AlgebraicGeometry.pointEquivClosedPoint_symm_apply_coe, CategoryTheory.prod.functorProdToProdFunctorAssociator_inv_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_aux_mul, CategoryTheory.MorphismProperty.LeftFraction.ofHom_s, CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_right, CategoryTheory.ComposableArrows.Precomp.map_id, CategoryTheory.Pseudofunctor.DescentData.faithful_pullFunctor, GrpCat.id_apply, CategoryTheory.Limits.equalizerPullbackMapIso_inv_ι_fst_assoc, CommAlgCat.id_apply, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_hom_app_snd_app, AlgebraicGeometry.tilde.map_id_assoc, CategoryTheory.Limits.walkingCospanOpEquiv_unitIso_hom_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app_assoc, CategoryTheory.Sieve.pullback_id, CategoryTheory.Pseudofunctor.DescentData.pullFunctorEquivalence_unitIso, CategoryTheory.CostructuredArrow.mapIso_inverse_map_right, CategoryTheory.Paths.lift_nil, CategoryTheory.Idempotents.Karoubi.decompId_i_naturality, CategoryTheory.Limits.constCone_π, commBialgCatEquivComonCommAlgCat_counitIso_hom_app, groupHomology.cyclesMap_id, Bicategory.Opposite.op2_id_unbop, CategoryTheory.Functor.curryingEquiv_symm_apply_obj_map, AddGrpCat.hom_id, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_counitIso_hom_app_right_app, CategoryTheory.Functor.HomObj.id_app, AlgebraicGeometry.AffineSpace.reindex_id, CategoryTheory.MorphismProperty.ContainsIdentities.id_mem, CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_right, CategoryTheory.Pretriangulated.contractible_distinguished₁, CategoryTheory.toOverUnitPullback_hom_app_left, HomologicalComplex.pOpcyclesIso_hom_inv_id, CategoryTheory.Bicategory.leftUnitor_comp, CategoryTheory.ExponentiableMorphism.coev_ev, CategoryTheory.MonoidalCategory.tensor_hom_inv_id', CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isoBot_hom, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso_inv_app_app, CategoryTheory.compEvaluation_inv_app, CategoryTheory.Lax.OplaxTrans.vComp_naturality_id, CategoryTheory.Comonad.adj_unit, CategoryTheory.prod.rightInverseUnitor_map, RingCat.id_apply, CategoryTheory.Limits.Cones.extendComp_hom_hom, CategoryTheory.Under.id_right, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₂, LinearMap.comp_id_moduleCat, CategoryTheory.SingleFunctors.hom_inv_id_hom_app, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id, CategoryTheory.PreZeroHypercover.id_s₀, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_val_app, CategoryTheory.ObjectProperty.ιOfLE_η, PartOrdEmb.coe_id, CategoryTheory.ShortComplex.mapToComposableArrows_id, CategoryTheory.Iso.refl_hom, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₃, CategoryTheory.MonoidalOpposite.tensorLeftIso_inv_app_unmop, CategoryTheory.Sum.swapCompInr_inv_app, CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_three, CategoryTheory.Functor.const_obj_map, CategoryTheory.Limits.coprod.map_id_id, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_hom, CategoryTheory.Limits.colimitYonedaHomIsoLimitRightOp_π_apply, CategoryTheory.WithInitial.opEquiv_unitIso_hom_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.hom_inv_actionHomLeft, CategoryTheory.CostructuredArrow.map_id, CategoryTheory.MonoidalCategory.MonoidalLeftAction.hom_inv_actionHomLeft', CategoryTheory.Bicategory.LeftLift.whiskerOfIdCompIsoSelf_inv_right, CategoryTheory.Over.ε_pullback_left, CategoryTheory.Comon.forget_ε, CategoryTheory.Limits.FormalCoproduct.evalCompInclIsoId_hom_app_app, CategoryTheory.Functor.id_mapMon_one, CategoryTheory.Comma.unopFunctorCompFst_hom_app, TopologicalSpace.OpenNhds.inclusionMapIso_inv_app, CategoryTheory.Limits.pullback.lift_fst_snd, CategoryTheory.Over.coprod_map_app, HomologicalComplex.homotopyCofiber.inrX_sndX, BoolAlg.id_apply, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_hom_app_hom_hom, Bimod.LeftUnitorBimod.hom_inv_id, CategoryTheory.Limits.pullback_fst_map_snd_isPullback, CategoryTheory.isoCartesianComon_inv_hom, CategoryTheory.MonoidalCategory.pentagon_inv_hom_assoc, CategoryTheory.Limits.colimit.toOver_pt, CategoryTheory.leftDistributor_assoc, CategoryTheory.Functor.ranAdjunction_unit_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraidedObj_map, CategoryTheory.Adjunction.rightAdjointOfEquiv_map, MagmaCat.ofHom_id, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.ShortComplex.LeftHomologyMapData.compatibilityOfZerosOfIsColimitCokernelCofork_φH, CategoryTheory.Monad.Algebra.unit, CategoryTheory.Functor.coreComp_inv_app_iso_hom, CategoryTheory.Bimon.toMon_Comon_ofMon_Comon_obj_mul, CategoryTheory.Limits.limit.lift_cone, CategoryTheory.Cat.Hom.id_toFunctor, CategoryTheory.GradedObject.Monoidal.leftUnitor_naturality_assoc, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app_assoc, CategoryTheory.prodOpEquiv_counitIso_inv_app, CategoryTheory.MonoidalOpposite.tensorIso_inv_app_unmop, CategoryTheory.ObjectProperty.ιOfLE_μ, CategoryTheory.MonoidalOpposite.mopMopEquivalence_counitIso_hom_app, MagmaCat.hom_id, CategoryTheory.ShortComplex.homologyπ_comp_asIsoHomologyπ_inv, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp_hom_app_f, CategoryTheory.Bicategory.InducedBicategory.forget_mapId_hom, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.id_tensorHom, CategoryTheory.Pi.μ_def, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd_assoc, CategoryTheory.Functor.lanAdjunction_counit_app, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst_assoc, CategoryTheory.Functor.id_hcomp, CategoryTheory.Bicategory.InducedBicategory.categoryStruct_id_hom, CategoryTheory.Functor.IsRepresentedBy.iff_exists_representableBy, AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_eq_id, CategoryTheory.prod.etaIso_hom, CategoryTheory.Bicategory.prod_rightUnitor_hom_snd, CategoryTheory.Functor.isIso_lanAdjunction_counit_app_iff, CategoryTheory.sheafifyLift_id_toSheafify_assoc, CategoryTheory.Bicategory.conjugateEquiv_symm_apply, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_val_app, AlgebraicGeometry.LocallyRingedSpace.iso_hom_base_inv_base, CategoryTheory.Bicategory.Adjunction.right_triangle, CategoryTheory.Bicategory.triangle_assoc_comp_left_inv, CategoryTheory.monoidalUnopUnop_η, PresheafOfModules.pushforward_id_comp, CategoryTheory.prod.prodFunctorToFunctorProdAssociator_hom_app_app, CategoryTheory.Functor.coreComp_inv_app_iso_inv, HomologicalComplex.homologyFunctorIso_inv_app, CategoryTheory.Functor.mapCoconeMapCocone_inv_hom, CochainComplex.augmentTruncate_hom_f_zero, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₂_W, CategoryTheory.Limits.pullbackDiagonalMapIdIso_hom_fst, HomotopicalAlgebra.CofibrantObject.homMk_id, CategoryTheory.Center.forget_μ, ContAction.resComp_inv, CategoryTheory.Functor.leftOpRightOpIso_inv_app, CategoryTheory.Functor.mapTriangleIdIso_hom_app_hom₁, ChainComplex.alternatingConst_map_f, CategoryTheory.BicategoricalCoherence.right_iso, CategoryTheory.SingleFunctors.inv_hom_id_hom, CategoryTheory.MonadHom.id_toNatTrans, CategoryTheory.Bicategory.Equivalence.right_triangle_hom, AddCommMonCat.hom_id, CategoryTheory.Endofunctor.Algebra.Initial.left_inv', CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_hom_app_hom_app, CategoryTheory.Functor.mapTriangleIdIso_hom_app_hom₂, CategoryTheory.WithTerminal.opEquiv_unitIso_inv_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom, CategoryTheory.Functor.relativelyRepresentable.toPullbackTerminal, CategoryTheory.Limits.pushoutCoconeOfLeftIso_inr, CategoryTheory.Limits.pushout.map_id, CategoryTheory.GrpObj.inv_comp_inv, CategoryTheory.Discrete.natIsoFunctor_inv_app, CategoryTheory.Limits.colimitCoyonedaHomIsoLimitLeftOp_π_apply, Condensed.id_val, CategoryTheory.Center.ofBraided_η_f, FinPartOrd.id_apply, CategoryTheory.MonoidalCategory.hom_inv_id_tensor_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_map, CategoryTheory.GrpObj.right_inv_assoc, HomotopicalAlgebra.FibrantBrownFactorization.i_r, CategoryTheory.Bimon.toMon_Comon_ofMon_Comon_obj_one, CategoryTheory.Pi.comapComp_hom_app, CategoryTheory.Bicategory.leftUnitor_comp_inv_assoc, HomologicalComplex.truncGEMap_id, CategoryTheory.Over.coprodObj_map, CategoryTheory.Localization.homEquiv_id, CategoryTheory.Functor.hcomp_id, CategoryTheory.Bicategory.leftUnitor_whiskerRight_assoc, AlgebraicTopology.DoldKan.P_add_Q_f, CategoryTheory.mono_iff_isPullback, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_left_right, CategoryTheory.GlueData.diagramIso_hom_app_right, CategoryTheory.yoneda_obj_isGeneratedBy, CategoryTheory.MonoidalCategory.prodCompExternalProduct_hom_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_hom_app_snd_app, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_isoPointwiseLeftKanExtension_hom, CategoryTheory.toOverUnitPullback_inv_app_left, CategoryTheory.ShortComplex.HomotopyEquiv.refl_homotopyInvHomId, CpltSepUniformSpace.hom_id, CategoryTheory.Functor.diag_ε, CategoryTheory.Limits.constCocone_ι, CategoryTheory.MonoidalClosed.id_comp, CategoryTheory.Bicategory.leftUnitor_inv_congr, SSet.StrictSegal.isRightKanExtension, CategoryTheory.ComposableArrows.Mk₁.map_id, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_assoc, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst, CategoryTheory.Comma.mapLeftId_inv_app_right, CategoryTheory.Bicategory.rightUnitor_hom_congr, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_inv_app_op_one, CategoryTheory.Functor.mapMatComp_inv_app, CategoryTheory.CatEnrichedOrdinary.homEquiv_id, AlgebraicTopology.DoldKan.HigherFacesVanish.induction, CategoryTheory.StructuredArrow.mapNatIso_functor_map_left, CategoryTheory.sheafSectionsNatIsoEvaluation_inv_app, CategoryTheory.Pseudofunctor.comp_mapId, CategoryTheory.IsHomLift.isoOfIsoLift_inv_hom_id, FinPartOrd.hom_hom_id, CategoryTheory.ShortComplex.leftHomologyMap_id, CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal_μ_unmop_unmop, CategoryTheory.Bicategory.Prod.swap_mapId_inv, CategoryTheory.BasedNatTrans.homCategory_id, CategoryTheory.sum.inlCompInverseAssociator_hom_app_down_down, CategoryTheory.SimplicialThickening.SimplicialCategory.id_comp, CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id, CategoryTheory.StructuredArrow.mapNatIso_counitIso_inv_app_right, CategoryTheory.ShortComplex.opcyclesIsoX₂_hom_inv_id, CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal_η_unmop_unmop, CategoryTheory.Bicategory.Prod.sectR_map, CategoryTheory.kernelCokernelCompSequence.inr_φ_fst, CategoryTheory.Limits.CatCospanTransform.id_whiskerRight, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_zero, CategoryTheory.WithInitial.coconeEquiv_unitIso_inv_app_hom_right, AlgebraicGeometry.quasiSeparatedSpace_iff_quasiCompact_prod_lift, CategoryTheory.Pi.ε_def, HomologicalComplex.extendMap_id, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapId_inv, CategoryTheory.Bimon.equivMonComonCounitIsoApp_inv_hom_hom, CategoryTheory.IsHomLift.instIsHomLiftIdObj, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_right, CategoryTheory.IsIso.id, CategoryTheory.Limits.FormalCoproduct.evalOpCompInlIsoId_inv_app_app, PartOrd.hom_id, CategoryTheory.right_unitality_app, CategoryTheory.Abelian.FunctorCategory.imageObjIso_inv, CategoryTheory.Adjunction.homEquiv_id, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_inv_app_fst_app, CategoryTheory.Limits.Cones.postcomposeComp_hom_app_hom, CategoryTheory.Enriched.FunctorCategory.functorEnriched_comp_id, CategoryTheory.RelCat.Hom.rel_id, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_inv_τr, CategoryTheory.CatEnriched.hComp_id, CategoryTheory.Equivalence.adjointify_η_ε, CategoryTheory.Subfunctor.range_id, CategoryTheory.Limits.pushoutCoconeOfRightIso_inl, CategoryTheory.Lax.OplaxTrans.id_app, TopCat.ofHom_id, CategoryTheory.ShortComplex.Hom.id_τ₂, CategoryTheory.Pretriangulated.binaryProductTriangleIsoBinaryBiproductTriangle_hom_hom₃, CategoryTheory.Bicategory.rightZigzagIso_hom, CategoryTheory.LaxFunctor.id_mapComp, CategoryTheory.Equivalence.inverse_counitInv_comp, TopologicalSpace.OpenNhds.inclusionMapIso_hom_app, CategoryTheory.flipCompEvaluation_inv_app, CategoryTheory.Limits.coprod.symmetry', HomotopicalAlgebra.PrepathObject.ι_p₁, ChainComplex.alternatingConst_obj, CategoryTheory.Cat.leftUnitor_inv_app, CategoryTheory.η_ε_app, MonCat.hom_id, CategoryTheory.LaxFunctor.map₂_leftUnitor_app, CategoryTheory.NatTrans.CommShift.id, CategoryTheory.Adjunction.left_triangle_components, CategoryTheory.Bicategory.rightUnitor_comp_inv_assoc, CategoryTheory.WithTerminal.opEquiv_functor_map, CategoryTheory.ComposableArrows.fourδ₃Toδ₂_app_zero, CategoryTheory.Join.InclRightCompRightOpOpEquivFunctor_hom_app, CategoryTheory.Join.mapPairRight_inv_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τl, CategoryTheory.Functor.RightExtension.postcompose₂ObjMkIso_hom_left_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₁, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_inv_app_f, CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp_hom_hom₂, CategoryTheory.Bicategory.InducedBicategory.bicategory_leftUnitor_hom_hom, CategoryTheory.Iso.map_hom_inv_id_eval_app, CategoryTheory.ObjectProperty.ιOfLE_δ, CategoryTheory.MonoidalCategory.MonoidalLeftAction.inv_hom_actionHomLeft, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app, CategoryTheory.Mat.id_def, CategoryTheory.Functor.Monoidal.μ_δ, CategoryTheory.MorphismProperty.Comma.id_left, CategoryTheory.eqToHom_heq_id_dom, SimplexCategory.δ_comp_σ_succ, Bicategory.Opposite.bicategory_rightUnitor_hom_unop2, CategoryTheory.Comma.mapLeftComp_hom_app_right, CategoryTheory.MonoidalCategory.tensorHom_id, CategoryTheory.Pretriangulated.binaryProductTriangleIsoBinaryBiproductTriangle_hom_hom₁, CategoryTheory.Functor.whiskeringRight₂_obj_map_app_app, CategoryTheory.MonoidalCategory.tensor_hom_inv_id, CategoryTheory.Pi.comapId_inv_app, CategoryTheory.Functor.unopComp_hom_app, PartOrd.id_apply, CategoryTheory.Limits.WalkingMulticospan.Hom.id_eq_id, CategoryTheory.Groupoid.comp_inv, CategoryTheory.Functor.compFlipUncurryIso_hom_app, commBialgCatEquivComonCommAlgCat_counitIso_inv_app, CategoryTheory.Pseudofunctor.CoGrothendieck.compIso_hom_app, AlgebraicGeometry.Scheme.id_app, CategoryTheory.whiskeringLeftCompEvaluation_hom_app, CategoryTheory.Functor.IsStronglyCocartesian.map_self, SemimoduleCat.hom_id, SheafOfModules.GeneratingSections.opEpi_id, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_unitIso_inv_app_right_app, CategoryTheory.StructuredArrow.homMk'_mk_id, CategoryTheory.Functor.whiskeringRightObjCompIso_inv_app_app, CategoryTheory.Join.mkFunctorRight_hom_app, Rep.FiniteCyclicGroup.resolution.π_f, CategoryTheory.Comma.mapFst_inv_app, CategoryTheory.Limits.Cones.postcomposeId_inv_app_hom, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_linearCombination, HomotopicalAlgebra.CofibrantBrownFactorization.mk'_i, CategoryTheory.GradedObject.mapBifunctorRightUnitor_inv_naturality, CategoryTheory.WithTerminal.coneEquiv_counitIso_hom_app_hom, CategoryTheory.ShortComplex.RightHomologyMapData.ofEpiOfIsIsoOfMono_φQ, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τr, CategoryTheory.presheafHom_map_app_op_mk_id, Lat.ofHom_id, CategoryTheory.Bicategory.isRightAdjoint_TFAE, CategoryTheory.InducedWideCategory.category_id_coe, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_inv_app, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_left, CategoryTheory.ObjectProperty.isoInv_hom_id_hom, PresheafOfModules.instIsRightAdjointPushforwardIdFunctorOppositeRingCat, CategoryTheory.GrothendieckTopology.OneHypercover.id_h₁, CategoryTheory.LaxMonoidalFunctor.id_hom, CategoryTheory.Bicategory.triangle_assoc, CategoryTheory.Limits.inr_coprodZeroIso_hom, CategoryTheory.Bicategory.leftUnitorNatIso_inv_app, CategoryTheory.ObjectProperty.FullSubcategory.id_hom, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.unitIso_inv_app_hom_app, AlgebraicGeometry.Scheme.homOfLE_rfl, CategoryTheory.sum.inrCompInverseAssociator_inv_app, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff, HomologicalComplex₂.total.map_id, CategoryTheory.Pi.comapEvalIsoEval_inv_app, CategoryTheory.CostructuredArrow.mapIso_counitIso_inv_app_left, CategoryTheory.Functor.preimage_id, CategoryTheory.MonoidalCategory.id_tensor_comp, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₁, CategoryTheory.GrothendieckTopology.yonedaEquiv_apply, CategoryTheory.OplaxFunctor.map₂_rightUnitor_app_assoc, CategoryTheory.Limits.equalizer.isoSourceOfSelf_inv, CategoryTheory.id_of_comp_right_id, CategoryTheory.ReflQuiver.id_eq_id, CategoryTheory.MonoidalCategory.hom_inv_id_tensor, CategoryTheory.MonoidalCategory.DayFunctor.ι_comp_isoPointwiseLeftKanExtension_inv, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv, CategoryTheory.StructuredArrow.mkPostcomp_id, CategoryTheory.Presieve.FamilyOfElements.map_id, CategoryTheory.Iso.hom_inv_id_app_app_app, CategoryTheory.unop_id, CategoryTheory.Cat.freeMapIdIso_inv_app, CategoryTheory.Idempotents.toKaroubi_obj_p, CategoryTheory.Functor.bifunctorComp₂₃Iso_inv_app_app_app, CategoryTheory.ihom.ev_coev, Bicategory.Opposite.bicategory_rightUnitor_inv_unop2, Action.FunctorCategoryEquivalence.functor_η, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_hom_app_hom, CategoryTheory.Yoneda.obj_map_id, CategoryTheory.Mon.id_hom', CategoryTheory.Pseudofunctor.whiskerRightIso_mapId, CategoryTheory.Mathlib.Tactic.MonTauto.eq_one_mul, CategoryTheory.Limits.prod_rightUnitor_inv_naturality, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_right_right, CategoryTheory.prod.functorProdToProdFunctorAssociator_hom_app, CategoryTheory.StructuredArrow.mapIso_counitIso_hom_app_right, HomologicalComplex.extendMap_id_f, CategoryTheory.Grp.id_hom_hom, CategoryTheory.Oplax.OplaxTrans.leftUnitor_inv_as_app, CategoryTheory.Over.iteratedSliceForwardIsoPost_hom_app, CategoryTheory.Category.id_comp, CategoryTheory.Join.inlCompFromSum_inv_app, CategoryTheory.op_id, CategoryTheory.Pretriangulated.id_hom₁, CategoryTheory.Functor.toOplaxFunctor'_mapId, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom, CategoryTheory.Pi.comapEvalIsoEval_hom_app, PresheafOfModules.pushforward_comp_id, CategoryTheory.Bicategory.Prod.fst_mapId_inv, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom, CategoryTheory.Bicategory.Adj.leftUnitor_hom_τl, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceFunctorProj_inv_app, CategoryTheory.BasedNatTrans.app_isHomLift, CategoryTheory.Oplax.OplaxTrans.Modification.id_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_right_app, AlgebraicGeometry.Scheme.inv_base_hom_base, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_left, CategoryTheory.Limits.biproduct.ι_π_self, CategoryTheory.Bicategory.mateEquiv_apply', CategoryTheory.Subgroupoid.id_mem_of_src, CategoryTheory.Bicategory.Equivalence.left_triangle_hom, Action.FintypeCat.toEndHom_trivial_of_mem, CategoryTheory.Sigma.inclDesc_hom_app, CategoryTheory.Over.postAdjunctionLeft_counit_app_left, CategoryTheory.Comon.id_hom', CategoryTheory.mop_id_unmop, NonemptyFinLinOrd.hom_id, CategoryTheory.OplaxFunctor.mapComp_id_left, CategoryTheory.LaxFunctor.map₂_leftUnitor_app_assoc, CategoryTheory.Comma.mapRightComp_inv_app_left, CategoryTheory.Subobject.map_id, CategoryTheory.ShortComplex.HomologyMapData.id_left, CategoryTheory.Limits.prod.lift_fst_snd, CategoryTheory.StructuredArrow.mapIso_counitIso_inv_app_right, CategoryTheory.Mod_.id_hom', GrpCat.coe_id, CategoryTheory.MonoidalCategory.leftUnitor_inv_tensor_id, CategoryTheory.Endofunctor.Algebra.Initial.left_inv, AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_app, SkyscraperPresheafFunctor.map'_id, CategoryTheory.unmop_id_mop, CategoryTheory.IsReflexivePair.common_section', CategoryTheory.BasedNatTrans.isHomLift, CategoryTheory.Comma.mapRightIso_unitIso_hom_app_right, CategoryTheory.Over.mapComp_inv_app_left, CategoryTheory.GlueData.diagramIso_hom_app_left, CategoryTheory.PreGaloisCategory.PointedGaloisObject.id_val, CategoryTheory.CosimplicialObject.id_left, CategoryTheory.SimplicialThickening.id_I, CategoryTheory.ShortComplex.LeftHomologyData.ofHasCokernel_i, CategoryTheory.LaxFunctor.map₂_rightUnitor, AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom_id, CategoryTheory.Bicategory.triangle_assoc_comp_right_assoc, CategoryTheory.Grothendieck.ι_map, CategoryTheory.LaxFunctor.mapId'_eq_mapId, CategoryTheory.Limits.ConeMorphism.inv_hom_id, CategoryTheory.Pi.comapComp_inv_app, HomologicalComplex.cylinder.πCompι₀Homotopy.inlX_nullHomotopy_f, CategoryTheory.Functor.FullyFaithful.preimage_id, CategoryTheory.WithTerminal.opEquiv_inverse_map, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_inv_app_fst_app, CategoryTheory.constantPresheafAdj_unit_app, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app_assoc, AlgebraicGeometry.pointOfClosedPoint_comp, CategoryTheory.Iso.inv_hom_id_eval, CategoryTheory.PreOneHypercover.cylinder_Y, CategoryTheory.Sigma.inclDesc_inv_app, CategoryTheory.WithInitial.liftStar_inv, CategoryTheory.Bicategory.rightUnitorNatIso_hom_app, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_hom, CategoryTheory.PreGaloisCategory.autMap_id, CategoryTheory.Pi.comapId_hom_app, CategoryTheory.IsIdempotentComplete.idempotents_split, HomologicalComplex.forgetEval_inv_app, CategoryTheory.colimitYonedaHomEquiv_π_apply, AddSemigrp.ofHom_id, Action.FunctorCategoryEquivalence.functor_ε, CategoryTheory.MonoidalCategory.MonoidalLeftAction.inv_hom_actionHomLeft', CategoryTheory.Bimon.trivial_X_mon_one, CategoryTheory.Cat.freeMapCompIso_inv_app, CategoryTheory.MorphismProperty.Comma.id_right, CategoryTheory.LaxFunctor.PseudoCore.mapIdIso_inv, CategoryTheory.CatEnrichedOrdinary.Hom.base_id, CategoryTheory.Adjunction.adjunctionOfEquivLeft_unit_app, CategoryTheory.Functor.map_inv_hom, CategoryTheory.TwoSquare.vId_app, CategoryTheory.Bicategory.leftUnitor_comp_assoc, CategoryTheory.Functor.mapCommMonCompIso_hom_app_hom_hom, CategoryTheory.evaluationAdjunctionLeft_counit_app, CategoryTheory.Enriched.FunctorCategory.enriched_comp_id, CategoryTheory.Join.mapIsoWhiskerRight_inv_app, AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_fst, CategoryTheory.functorProdFunctorEquivCounitIso_hom_app_app, CategoryTheory.Functor.Monoidal.η_ε, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left, AlgebraicTopology.DoldKan.PInfty_add_QInfty, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInlIso_inv_app_app, AddGrpCat.coe_id, CategoryTheory.Limits.CatCospanTransform.rightUnitor_hom_right_app, AlgebraicGeometry.morphismRestrict_id, CategoryTheory.Functor.whiskeringLeftObjCompIso_inv_app_app, groupCohomology.cochainsMap_id, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_inv_app_fst_app, CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_id, CategoryTheory.ComposableArrows.Precomp.map_one_one, CategoryTheory.Limits.ColimitPresentation.self_ι, CategoryTheory.ihom.coev_ev, HomologicalComplex.isoHomologyπ_inv_hom_id, TopologicalSpace.Opens.map_id_eq, CategoryTheory.Bicategory.triangle_assoc_comp_left_inv_assoc, CategoryTheory.Functor.currying_inverse_obj_map_app, CategoryTheory.Limits.parallelPairOpIso_hom_app_zero, CategoryTheory.ShortComplex.asIsoHomologyι_inv_comp_homologyι, CategoryTheory.Limits.kernelSubobjectMap_id, AlgebraicGeometry.Scheme.Hom.id_image, SemimoduleCat.MonoidalCategory.id_tensorHom_id, HomologicalComplex.Hom.sqFrom_id
toQuiver 📖	CompOp	5856 math math: CategoryTheory.Functor.IsDenseSubsite.mapPreimage_map_of_fac, TopologicalSpace.OpenNhds.coe_id, HomotopicalAlgebra.fibration_op_iff, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_right, CategoryTheory.Comon.tensorObj_comul', CategoryTheory.Bicategory.iterated_mateEquiv_conjugateEquiv, CategoryTheory.LocalizerMorphism.LeftResolution.opFunctor_map_f, CategoryTheory.ShortComplex.opcyclesMap_smul, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d, CategoryTheory.Grp.Hom.hom_div, AlgebraicGeometry.Γ_map_morphismRestrict, CategoryTheory.Limits.pushoutIsoOpPullback_inr_hom_assoc, CategoryTheory.Limits.Fork.IsLimit.homIso_natural, CategoryTheory.CommSq.LiftStruct.op_l, CategoryTheory.GrothendieckTopology.overMapPullbackId_hom_app_val_app, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_eq, CategoryTheory.Pseudofunctor.mapComp'_naturality_1_assoc, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π, AlgebraicGeometry.Scheme.Modules.pushforward_obj_presheaf_map, CategoryTheory.Join.pseudofunctorLeft_mapId_inv_toNatTrans_app, CategoryTheory.ShortComplex.toCycles_comp_homologyπ, Rep.resCoindHomEquiv_symm_apply_hom, SimplicialObject.Splitting.cofan_inj_πSummand_eq_id_assoc, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_assoc, CategoryTheory.Functor.functorHomEquiv_apply_app, CategoryTheory.Pseudofunctor.DescentData.isEquivalence_toDescentData_of_sieve_le, CategoryTheory.Bicategory.prod_whiskerLeft_snd, Rep.resCoindHomEquiv_apply_hom, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_hom_right, CategoryTheory.Functor.FullyFaithful.homNatIsoMaxRight_inv_app, CommRingCat.HomTopology.isEmbedding_precomp_of_surjective, CategoryTheory.Functor.map_homCongr, CategoryTheory.Adjunction.compUliftCoyonedaIso_hom_app_app_down, CategoryTheory.ShortComplex.toCycles_comp_homologyπ_assoc, ModuleCat.hom_zero, CategoryTheory.uliftCoyonedaEquiv_apply, CategoryTheory.Limits.eq_zero_of_mono_cokernel, CategoryTheory.PreOneHypercover.forkOfIsColimit_ι_map_inj_assoc, CategoryTheory.Limits.zero_of_from_zero, CategoryTheory.TwoSquare.equivNatTrans_symm_apply, CategoryTheory.ShortComplex.Homotopy.h₀_f_assoc, CommRingCat.HomTopology.isClosedEmbedding_precomp_of_surjective, Bicategory.Opposite.op2_associator, CategoryTheory.Presieve.ofArrows_eq_ofArrows_uncurry, CategoryTheory.Limits.cokernelBiproductιIso_hom, Rep.invariantsAdjunction_homEquiv_symm_apply_hom, CategoryTheory.Groupoid.reverse_eq_inv, CategoryTheory.ShortComplex.LeftHomologyData.op_g', CategoryTheory.Types.instIsCorepresentableForgetTypeHom, AlgebraicGeometry.Proj.awayMap_awayToSection_assoc, CategoryTheory.Equivalence.leftOp_unitIso_hom_app, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_hom_app_val_app, CategoryTheory.Limits.limitConeOfUnique_cone_π, CategoryTheory.StrictPseudofunctorPreCore.map_id, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, CategoryTheory.ComposableArrows.opEquivalence_counitIso_inv_app_app, CategoryTheory.Pseudofunctor.DescentData.ofObj_hom, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom, TopModuleCat.hom_zero, CategoryTheory.Bicategory.RightExtension.w_assoc, SemimoduleCat.Hom.hom₂_apply, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_apply, CategoryTheory.Functor.natTransEquiv_apply_app, CategoryTheory.Functor.mapComposableArrowsObjMk₂Iso_inv_app, CategoryTheory.uliftCoyonedaIsoCoyoneda_hom_app_app, CategoryTheory.Pseudofunctor.DescentData.subtypeCompatibleHomEquiv_toCompatible_presheafHomObjHomEquiv, CategoryTheory.LaxFunctor.mapComp'_whiskerRight_comp_mapComp', CategoryTheory.coyonedaEquiv_symm_app_apply, CategoryTheory.Presheaf.instIsLocallySurjectiveHomWhiskerRightOppositeForget, CategoryTheory.Oplax.StrongTrans.Modification.vcomp_app, HomologicalComplex.singleMapHomologicalComplex_hom_app_ne, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_adj, CategoryTheory.ObjectProperty.isoModSerre_zero_iff, CategoryTheory.tensorLeftHomEquiv_symm_coevaluation_comp_whiskerLeft, TopCat.PrelocalPredicate.res, CategoryTheory.PreGaloisCategory.mulAction_def, CategoryTheory.Pseudofunctor.map₂_associator_assoc, CategoryTheory.Functor.partialRightAdjointHomEquiv_comp_symm, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionRight_unop, CategoryTheory.ShortComplex.SnakeInput.w₀₂_assoc, CategoryTheory.Sheaf.ΓHomEquiv_naturality_left_symm, TopologicalSpace.Opens.id_apply, CategoryTheory.preadditiveCoyonedaObj_map, CategoryTheory.kernelUnopOp_inv, CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair_hom_app, CategoryTheory.Functor.homObjEquiv_apply_app, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_three_assoc, CategoryTheory.Limits.Bicone.π_of_isColimit, AlgebraicTopology.DoldKan.PInfty_f_add_QInfty_f, CategoryTheory.CatEnrichedOrdinary.id_hComp_heq, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app', CategoryTheory.Limits.inr_of_isLimit, CategoryTheory.sum_whiskerRight, CategoryTheory.LaxFunctor.map₂_associator_assoc, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map, CategoryTheory.Limits.coprod.inl_snd, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.ShortComplex.Homotopy.refl_h₀, CategoryTheory.Equivalence.sheafCongr.counitIso_hom_app_val_app, LightProfinite.proj_comp_transitionMap, HomologicalComplex.dFrom_comp_xNextIsoSelf, CategoryTheory.Preadditive.IsIso.comp_left_eq_zero, CochainComplex.HomComplex.Cochain.fromSingleMk_neg, 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CategoryTheory.Bicategory.Comonad.comul_assoc_flip, HomotopyCategory.quotient_map_out_comp_out, Mathlib.Tactic.Bicategory.evalWhiskerLeft_nil, CategoryTheory.regularTopology.EqualizerCondition.bijective_mapToEqualizer_pullback', CategoryTheory.ShortComplex.Homotopy.comp_h₃, CategoryTheory.Limits.limitUnopIsoUnopColimit_hom_comp_ι, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id_assoc, CategoryTheory.Join.mapPairId_hom_app, CategoryTheory.Sheaf.instIsLocallySurjectiveHomToImage, TopCat.presheafToType_map, CategoryTheory.Functor.leftOpRightOpEquiv_functor_obj_map, TopCat.Sheaf.interUnionPullbackCone_snd, CategoryTheory.linearCoyoneda_map_app, CategoryTheory.linearCoyoneda_obj_obj_carrier, LightCondensed.isoFinYonedaComponents_hom_apply, CategoryTheory.ShortComplex.Splitting.op_r, CategoryTheory.Limits.biprod.lift_eq, CategoryTheory.ShortComplex.RightHomologyData.ι_g', CategoryTheory.ShortComplex.SnakeInput.op_δ, CategoryTheory.Limits.isLimitConeRightOpOfCocone_lift, CategoryTheory.OplaxFunctor.id_mapComp, Rep.MonoidalClosed.linearHomEquiv_symm_hom, CategoryTheory.ShortComplex.cyclesOpIso_inv_op_iCycles_assoc, CategoryTheory.composePath_comp', CategoryTheory.EnrichedOrdinaryCategory.homEquiv_comp, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_snd, CategoryTheory.Iso.eHomCongr_inv_comp_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_hom_app_eq, CategoryTheory.op_hom_leftUnitor, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app, CategoryTheory.ShortComplex.pOpcycles_π_isoOpcyclesOfIsColimit_inv_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_assoc, CategoryTheory.Join.mapWhiskerLeft_app, Bicategory.Opposite.op2_unop2, HomologicalComplex.double_d_eq_zero₀, Action.neg_hom, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_two, CategoryTheory.Limits.coconeEquivalenceOpConeOp_unitIso, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_hom_app_app_down, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.ShortComplex.homologyOpIso_hom_naturality, CategoryTheory.ComposableArrows.IsComplex.zero'_assoc, CategoryTheory.Preadditive.commGrpEquivalence_functor_obj_grp_one, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_inv_app_val_app, CategoryTheory.Abelian.LeftResolution.karoubi.F_obj_p, CategoryTheory.Linear.instMonoHSMulHomOfInvertible, HomologicalComplex.mapBifunctor₁₂.d_eq, CategoryTheory.Localization.Preadditive.homEquiv_symm_apply, CategoryTheory.Comma.opFunctor_obj, AlgebraicGeometry.Scheme.Hom.app_invApp'_assoc, CategoryTheory.Classifier.SubobjectRepresentableBy.pullback_homEquiv_symm_obj_Ω₀, CategoryTheory.ReflQuiv.adj_homEquiv, CategoryTheory.ShortComplex.LeftHomologyMapData.unop_φQ, CategoryTheory.Join.pseudofunctorRight_mapComp_inv_toNatTrans_app, CategoryTheory.Bicategory.eqToHomTransIso_refl_left, AlgebraicTopology.DoldKan.σ_comp_PInfty_assoc, CategoryTheory.StrictlyUnitaryLaxFunctor.id_map₂, SimplicialObject.Splitting.IndexSet.epiComp_fst, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app_assoc, CategoryTheory.MonoidalOpposite.tensorLeftMopIso_hom_app_unmop, Bicategory.Opposite.op2_associator_inv, HomologicalComplex.dFrom_eq_zero, CategoryTheory.Pseudofunctor.map₂_associator_app_assoc, CategoryTheory.Bicategory.Pith.inclusion_mapComp, LightCondensed.ihomPoints_apply, TopCat.Presheaf.isSheaf_iff_isSheafUniqueGluing_types, AlgebraicGeometry.Scheme.app_eq, CategoryTheory.shrinkYonedaEquiv_comp, CategoryTheory.ShortComplex.LeftHomologyData.unop_p, CategoryTheory.Subfunctor.Subpresheaf.range_eq_ofSection', HomotopicalAlgebra.instWeakEquivalenceOppositeOp, CategoryTheory.ShortComplex.homologyMap_add, CategoryTheory.Grp.Hom.hom_hom_zpow, CategoryTheory.Localization.isoOfHom_unop, CategoryTheory.Groupoid.invEquivalence_inverse_map, AlgebraicTopology.NormalizedMooreComplex.obj_d, 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TopCat.Presheaf.coveringOfPresieve.iSup_eq_of_mem_grothendieck, CategoryTheory.Functor.sheafPushforwardContinuousComp'_inv_app_val_app, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_leftUnitor, TopCat.Presheaf.germ_eq_of_isBasis, CategoryTheory.Functor.rightOp_map, SSet.Subcomplex.mem_ofSimplex_obj_iff, CategoryTheory.ShortComplex.homologyMap_zero, CategoryTheory.Bicategory.Adj.associator_inv_τr, CategoryTheory.Bicategory.Prod.sectL_mapId_inv, CondensedMod.IsSolid.isIso_solidification_map, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app, CategoryTheory.ExponentiableMorphism.homEquiv_symm_apply_eq, CategoryTheory.Grp_Class.comp_inv, groupHomology.map₁_one, CochainComplex.HomComplex.Cocycle.equivHom_symm_apply, CategoryTheory.eqToHom_comp_homOfLE_op, CategoryTheory.Functor.coe_mapLinearMap, AlgebraicGeometry.Spec_Γ_naturality, AddCommGrpCat.hom_add, CategoryTheory.FunctorToTypes.functorHomEquiv_symm_apply_app_app, groupCohomology.d₀₁_comp_d₁₂, CategoryTheory.MorphismProperty.LeftFraction.op_map, CategoryTheory.iterated_mateEquiv_conjugateEquiv_symm, CategoryTheory.Functor.map_mul, prevD_comp_left, CategoryTheory.WithInitial.opEquiv_unitIso_inv_app, CategoryTheory.Limits.pushoutIsoOpPullback_inl_hom, CategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy.hg', ModuleCat.freeHomEquiv_apply, CategoryTheory.Idempotents.neg_def, CategoryTheory.Bicategory.whiskerRight_comp_assoc, CategoryTheory.ShortComplex.π₁Toπ₂_comp_π₂Toπ₃_assoc, CategoryTheory.Bicategory.Prod.snd_map, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_assoc, CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_homEquiv_symm, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom, CategoryTheory.Limits.Multicofork.ofπ_ι_app, CategoryTheory.ShortComplex.RightHomologyMapData.neg_φH, CategoryTheory.op_inv_associator, CategoryTheory.Bicategory.InducedBicategory.bicategory_associator_inv_hom, CategoryTheory.Abelian.Pseudoelement.pseudoZero_def, CategoryTheory.Limits.walkingParallelPairOp_left, CategoryTheory.Bicategory.LeftExtension.w_assoc, TopCat.coe_of_of, CategoryTheory.Functor.IsEventuallyConstantTo.coneπApp_eq, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_naturality, CategoryTheory.shrinkYonedaEquiv_symm_map_assoc, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_counit_app_app, CategoryTheory.ShortComplex.op_g, CategoryTheory.Limits.ι_comp_colimitOpIsoOpLimit_hom_assoc, CategoryTheory.instHasFunctorialSurjectiveInjectiveFactorizationTypeHom, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_apply, CategoryTheory.CatEnriched.id_hComp, CategoryTheory.OplaxFunctor.map₂_associator, CategoryTheory.Bicategory.inv_hom_whiskerRight_whiskerRight_assoc, commBialgCatEquivComonCommAlgCat_unitIso_inv_app, CategoryTheory.Bicategory.Adj.rIso_inv, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_app_apply, CategoryTheory.Bicategory.mateEquiv_comp_id_right, CategoryTheory.Limits.parallelPairOpIso_inv_app_zero, CategoryTheory.CatCenter.app_sub, CategoryTheory.HasLiftingProperty.unop, CategoryTheory.Pseudofunctor.StrongTrans.homCategory_comp_as_app, CategoryTheory.ShortComplex.abelianImageToKernel_comp_kernel_ι_comp_cokernel_π_assoc, CategoryTheory.Comonad.ComonadicityInternal.unitFork_π_app, CategoryTheory.StructuredArrow.w_prod_fst, CategoryTheory.Bicategory.inv_hom_whiskerRight_assoc, CategoryTheory.Bicategory.whisker_exchange, CategoryTheory.Functor.CorepresentableBy.uniqueUpToIso_inv, CategoryTheory.PreOneHypercover.forkOfIsColimit_pt, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_eq_iff', CategoryTheory.Bicategory.inv_hom_whiskerRight, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_left_hom, TopModuleCat.hom_zero_apply, HomologicalComplex.extend.d_comp_eq_zero_iff, CategoryTheory.finrank_hom_simple_simple_le_one, CategoryTheory.Functor.hom_map, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_symm_apply, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_comp, CategoryTheory.sum.inlCompInrCompInverseAssociator_hom_app_down_down, CategoryTheory.Functor.uliftCoyonedaCoreprXIso_hom_app, CategoryTheory.LaxFunctor.map₂_leftUnitor_assoc, CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.hg, CategoryTheory.eHomEquiv_id, CategoryTheory.eval_map, Profinite.Extend.functorOp_map, CategoryTheory.Cat.associator_hom_app, CategoryTheory.Limits.kernelBiprodSndIso_hom, CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_obj, CochainComplex.mappingCone.inr_f_fst_v, CategoryTheory.ShortComplex.Homotopy.smul_h₁, CategoryTheory.Bicategory.pentagon_inv, CategoryTheory.ShortComplex.zero_assoc, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_hom_app_app, AddMonCat.zeroHom_apply, CategoryTheory.MorphismProperty.LeftFraction₂.map_add, groupHomology.mapShortComplexH1_zero, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHomRight, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_map_app, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_app_assoc, CategoryTheory.op_tensorHom, CategoryTheory.ShortComplex.RightHomologyData.wp, Bicategory.Opposite.op2_whiskerLeft, SimplicialObject.Splitting.IndexSet.fac_pull_assoc, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₁, CategoryTheory.Bicategory.Adjunction.homEquiv₂_symm_apply, CategoryTheory.PreGaloisCategory.endEquivSectionsFibers_π, CategoryTheory.Sieve.pushforward_apply, CategoryTheory.Bicategory.InducedBicategory.Hom.category_id_hom, CategoryTheory.LaxFunctor.comp_mapId, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app, CategoryTheory.ShiftedHom.mk₀_zero, CategoryTheory.Equivalence.rightOp_counitIso_inv_app, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_right, CategoryTheory.Quiv.pathsOf_pathComposition_toPrefunctor, HomologicalComplex.op_d, CategoryTheory.down_comp_assoc, CategoryTheory.Pseudofunctor.map₂_left_unitor_assoc, HomologicalComplex.homotopyCofiber.inrX_fstX_assoc, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_symm_apply_φ, CategoryTheory.GrothendieckTopology.Cover.Arrow.ext_iff, CategoryTheory.ShortComplex.leftHomologyMap_sub, CategoryTheory.Bicategory.Pith.comp_of, CochainComplex.HomComplex.Cochain.fromSingleEquiv_fromSingleMk, CategoryTheory.Adjunction.homEquiv_naturality_left_square, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_fst, LightCondensed.ihomPoints_symm_comp, CategoryTheory.NonPreadditiveAbelian.add_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id_app, CategoryTheory.Retract.op_i, CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map', CategoryTheory.yoneda_map_app, CategoryTheory.Functor.WellOrderInductionData.map_succ, HomologicalComplex.opSymm_d, CategoryTheory.OplaxFunctor.map₂_associator_app, CategoryTheory.Oplax.LaxTrans.vComp_naturality_id, CategoryTheory.ShortComplex.RightHomologyData.wp_assoc, groupHomology.mapShortComplexH2_zero, CategoryTheory.StrictPseudofunctorCore.map₂_left_unitor, CategoryTheory.unop_tensorHom, CategoryTheory.Bicategory.Lan.existsUnique, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_id_fiber, CategoryTheory.typeEquiv_functor_obj_val_obj, AlgebraicGeometry.Spec.map_surjective, CategoryTheory.MonoidalClosed.ofEquiv_uncurry_def, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_whiskerRight_as_app, CategoryTheory.Oplax.OplaxTrans.Modification.vcomp_app, CategoryTheory.Bicategory.eqToHomTransIso_refl_refl, AlgebraicGeometry.Scheme.Opens.topIso_inv, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀', CategoryTheory.Limits.biproduct.ι_π_assoc, CategoryTheory.curryingIso_hom_toFunctor_obj_map, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition', CategoryTheory.GrothendieckTopology.overMapPullbackId_inv_app_val_app, CategoryTheory.FreeBicategory.mk_left_unitor_inv, AlgebraicGeometry.Scheme.SpecToEquivOfField_eq_iff, CategoryTheory.Equivalence.leftOp_unitIso_inv_app, CategoryTheory.Limits.Cone.equiv_inv_pt, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_inverse, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_naturality_assoc, CategoryTheory.Grp_Class.comp_zpow, CategoryTheory.Functor.Monoidal.RepresentableBy.tensorObj_homEquiv, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality_assoc, CategoryTheory.Bicategory.RightLift.w_assoc, CategoryTheory.op_mono_of_epi, CategoryTheory.Comon.uniqueHomToTrivial_default_hom, CategoryTheory.FreeBicategory.liftHom_id, CategoryTheory.Bicategory.mateEquiv_vcomp, CategoryTheory.Pseudofunctor.StrongTrans.comp_app, CategoryTheory.InducedCategory.homLinearEquiv_apply, HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom_desc_hom_assoc, CategoryTheory.yonedaCommGrpGrpObj_map, CategoryTheory.Functor.WellOrderInductionData.Extension.ofLE_val, CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj, CategoryTheory.ShrinkHoms.id_def, AlgebraicGeometry.pointsPi_surjective_of_isAffine, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHomRight, CategoryTheory.Pseudofunctor.mapComp'_hom_comp_whiskerLeft_mapComp'_hom, CategoryTheory.conjugateEquiv_symm_id, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_right_symm, CategoryTheory.Bicategory.conjugateEquiv_adjunction_id_symm, AlgebraicTopology.DoldKan.PInfty_comp_QInfty, CategoryTheory.ShortComplex.RightHomologyMapData.op_φH, SheafOfModules.pullbackPushforwardAdjunction_homEquiv_pullbackObjUnitToUnit, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_assoc, CochainComplex.IsKInjective.nonempty_homotopy_zero, CategoryTheory.nerve.functorOfNerveMap_map, CategoryTheory.Mon.hom_injective, CategoryTheory.Pretriangulated.shiftFunctorZero_op_inv_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_ι_app, CategoryTheory.Functor.prod'_μ_fst, CategoryTheory.Bicategory.Adj.comp_τl_assoc, CategoryTheory.HasLiftingProperty.op, CategoryTheory.StrictPseudofunctor.mk'_obj, CategoryTheory.ShortComplex.exact_iff_iCycles_pOpcycles_zero, CategoryTheory.Abelian.LeftResolution.chainComplexMap_zero, CategoryTheory.Oplax.OplaxTrans.StrongCore.naturality_hom, CategoryTheory.Bicategory.Adj.forget₁_mapId, CategoryTheory.Limits.BinaryBicone.ofLimitCone_inl, CategoryTheory.ShortComplex.exact_iff_kernel_ι_comp_cokernel_π_zero, CategoryTheory.Localization.liftNatTrans_add, CategoryTheory.Abelian.Ext.mk₀_addEquiv₀_apply, CategoryTheory.MonoidalCategory.externalProductBifunctor_map_app, CategoryTheory.Limits.BinaryBicone.toBiconeFunctor_obj_π, CategoryTheory.sum.inrCompInrCompInverseAssociator_hom_app_down, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id, SimplicialObject.Splitting.PInfty_comp_πSummand_id, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₃, LightCondSet.epi_iff_locallySurjective_on_lightProfinite, CategoryTheory.Limits.IsZero.unique_to, CategoryTheory.Limits.opProdIsoCoprod_hom_snd_assoc, CategoryTheory.Iso.unop2_op2, CategoryTheory.SingleObj.id_as_one, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp_assoc, AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id_assoc, CategoryTheory.Functor.PreservesHomology.preservesKernels, CategoryTheory.Presieve.isSeparatedFor_singleton, CategoryTheory.LocallyDiscrete.id_as, SSet.Subcomplex.range_eq_ofSimplex, CategoryTheory.Oplax.OplaxTrans.homCategory_id_as_app, CategoryTheory.Functor.leftOpRightOpEquiv_counitIso_inv_app_app, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app, HomologicalComplex.dTo_eq_zero, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_apply_f, CategoryTheory.isIso_unop_iff, CategoryTheory.ShortComplex.opcyclesMap_sub, CategoryTheory.NonPreadditiveAbelian.add_def, CategoryTheory.unop_epi_of_mono, SSet.spine_map_subinterval, Opens.mayerVietorisSquare_X₃, AddMonCat.hom_zero, Rep.diagonalHomEquiv_symm_apply, CategoryTheory.BicategoricalCoherence.left'_iso, CategoryTheory.Equivalence.rightOp_functor_map, DerivedCategory.HomologySequence.comp_δ, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app, CategoryTheory.ParametrizedAdjunction.whiskerLeft_map_counit, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_associator, CategoryTheory.ULiftHom.down_map, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapCompIso_inv, AlgebraicGeometry.Scheme.inv_app, CategoryTheory.ShortComplex.opcyclesMap'_sub, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_hom_app, CategoryTheory.ShortComplex.RightHomologyMapData.neg_φQ, CategoryTheory.Functor.RepresentableBy.homEquiv_eq, CategoryTheory.Bicategory.LeftExtension.ofCompId_right, CategoryTheory.Functor.toPrefunctor_map, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_id, CategoryTheory.linearYoneda_obj_map, CategoryTheory.PreOneHypercover.multicospanIndex_fst, CategoryTheory.CostructuredArrow.IsUniversal.existsUnique, CategoryTheory.CountableCategory.countableHom, CategoryTheory.Functor.mapComposableArrowsObjMk₁Iso_inv_app, PresheafOfModules.homEquivOfIsLocallyBijective_symm_apply, CategoryTheory.Limits.widePullbackShapeUnop_map, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp_app, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_comp_naturality_hom, CommRingCat.HomTopology.instCompactSpaceHomOfIsTopologicalRingOfT1SpaceOfCarrier, CategoryTheory.OplaxFunctor.mapComp_naturality_right_assoc, CategoryTheory.prodOpEquiv_inverse_map, HomotopyCategory.isZero_quotient_obj_iff, CategoryTheory.ShortComplex.opMap_τ₁, CategoryTheory.Preadditive.homSelfLinearEquivEndMulOpposite_apply, CategoryTheory.Oplax.LaxTrans.naturality_naturality_assoc, CategoryTheory.CategoryOfElements.map_map_coe, SemiNormedGrp.hom_sub, CategoryTheory.Linear.comp_apply, CategoryTheory.ShortComplex.HasLeftHomology.of_zeros, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left, CategoryTheory.simplicialCosimplicialEquiv_counitIso_inv_app_app, CategoryTheory.DifferentialObject.d_squared_apply, CategoryTheory.Limits.PushoutCocone.unop_π_app, CategoryTheory.Functor.homologySequence_comp_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom, CategoryTheory.CostructuredArrow.w_prod_fst, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app, CategoryTheory.StrictPseudofunctor.id_mapComp_hom, AlgebraicGeometry.Spec.map_injective, CategoryTheory.Presheaf.functorToRepresentables_map, CategoryTheory.op_whiskerRight, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_postcomp, CategoryTheory.ShortComplex.Homotopy.unop_h₂, CategoryTheory.Linear.smulOfRingMorphism_smul_eq', CategoryTheory.simplicialCosimplicialEquiv_inverse_map, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_hom_app_hom_apply, ModuleCat.Iso.homCongr_eq_arrowCongr, CategoryTheory.unop_inv_associator, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp_symm_assoc, CategoryTheory.Limits.Fork.unop_ι_app_zero, CategoryTheory.Subobject.factorThru_eq_zero, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left, TopologicalSpace.OpenNhds.comp_apply, CategoryTheory.finrank_hom_simple_simple_eq_one_iff, CategoryTheory.Adjunction.rightAdjointLaxMonoidal_μ, CategoryTheory.Limits.MulticospanIndex.multicospan_map, CategoryTheory.Functor.FullyFaithful.homMulEquiv_apply, CategoryTheory.Bicategory.InducedBicategory.bicategory_leftUnitor_inv_hom, CategoryTheory.Subgroupoid.full_arrow_eq_iff, CategoryTheory.ShortComplex.leftHomologyMap'_neg, CategoryTheory.IsPullback.op, CategoryTheory.Limits.opCompYonedaSectionsEquiv_symm_apply_coe, CategoryTheory.prodFunctorToFunctorProd_map, CategoryTheory.Adjunction.comp_homEquiv, CategoryTheory.Limits.yonedaCompLimIsoCocones_inv_app, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_app_assoc, CategoryTheory.coyonedaEvaluation_map_down, CategoryTheory.nerve.homEquiv_edgeMk_map_nerveMap, FunctorToFintypeCat.naturality, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id_assoc, HomologicalComplex.mapBifunctor₂₃.d₂_eq, CategoryTheory.Functor.WellOrderInductionData.Extension.map_zero, CategoryTheory.Pseudofunctor.DescentData.pullFunctor_map_hom, CategoryTheory.Grothendieck.grothendieckTypeToCat_inverse_map_base, CategoryTheory.prod_id_fst, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₁₂, CategoryTheory.SimplicialThickening.compFunctor_obj, CategoryTheory.Limits.prod.inl_snd, CategoryTheory.Endofunctor.algebraPreadditive_homGroup_neg_f, CategoryTheory.WithTerminal.map₂_app, CategoryTheory.Pseudofunctor.StrongTrans.leftUnitor_inv_as_app, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_obj, SimplexCategory.instFiniteHom, AlgebraicGeometry.Scheme.stalkMap_congr_assoc, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_symm_assoc, HomologicalComplex.opcyclesOpIso_inv_naturality_assoc, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_whiskerLeft_as_app, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_inverse_obj_str, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id_assoc, CategoryTheory.Limits.KernelFork.condition_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv, CategoryTheory.Functor.FullyFaithful.homEquiv_apply, CategoryTheory.Preadditive.sub_comp_assoc, CategoryTheory.Limits.zero_of_source_iso_zero, CategoryTheory.preadditiveYonedaObj_obj_carrier, LightCondensed.finYoneda_map, CategoryTheory.Monad.algebraPreadditive_homGroup_sub_f, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_inv_app_coe, CategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSet_id, CategoryTheory.tensorRightHomEquiv_symm_naturality, AddCommGrpCat.hom_zero, CategoryTheory.Limits.colimitCoyonedaHomIsoLimit'_π_apply, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_map, CategoryTheory.Limits.HasZeroObject.zeroIsoIsInitial_inv, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_inv_app_hom_apply, CategoryTheory.Functor.cones_map_app, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inr_assoc, CategoryTheory.ShortComplex.LeftHomologyData.f'_π_assoc, CategoryTheory.ShortComplex.LeftHomologyData.unop_ι, MonObj.mopEquivCompForgetIso_hom_app_unmop, CategoryTheory.Types.instReflectsLimitsOfSizeForgetTypeHom, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι_assoc, CategoryTheory.NatTrans.leftOp_app, CochainComplex.IsKProjective.homotopyZero_def, CategoryTheory.Bicategory.pentagon_hom_hom_inv_hom_hom_assoc, CommRingCat.moduleCatRestrictScalarsPseudofunctor_mapComp, SSet.horn.yonedaEquiv_ι, CategoryTheory.Functor.toPseudoFunctor'_obj, AlgebraicGeometry.pointsPi_injective, CategoryTheory.Oplax.OplaxTrans.categoryStruct_id_naturality, HomologicalComplex.biprod_inl_snd_f_assoc, CategoryTheory.Join.isoMkFunctor_hom_app, CategoryTheory.Pseudofunctor.mapId'_inv_naturality_assoc, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy₂_homEquiv, CategoryTheory.Equivalence.leftOp_counitIso_inv_app, CategoryTheory.conjugateEquiv_symm_comp_assoc, CategoryTheory.Limits.coyonedaCompLimIsoCones_inv_app, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_inv_τr, CategoryTheory.Subfunctor.ofSection_eq_range, Homotopy.nullHomotopicMap_f_eq_zero, SemimoduleCat.Iso.homCongr_eq_arrowCongr, TopologicalSpace.Opens.comp_apply, CategoryTheory.Localization.SmallHom.equiv_equiv_symm, CategoryTheory.Bicategory.LeftLift.w_assoc, AlgebraicTopology.AlternatingFaceMapComplex.ε_app_f_succ, HomologicalComplex₂.totalAux.d₂_eq, CategoryTheory.ShortComplex.cyclesMap_neg, CategoryTheory.ShortComplex.toCycles_comp_leftHomologyπ_assoc, CategoryTheory.Abelian.LeftResolution.karoubi.F'_map_f, CochainComplex.mappingCone.d_snd_v, CategoryTheory.OverPresheafAux.YonedaCollection.map₂_yonedaEquivFst, CategoryTheory.Preadditive.isColimitCoforkOfCokernelCofork_desc, CategoryTheory.Bicategory.whiskerRightIso_hom, CategoryTheory.Bicategory.associatorNatIsoLeft_inv_app, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one, CategoryTheory.StrictlyUnitaryPseudofunctor.mk'_map, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app, CategoryTheory.opOp_map, CategoryTheory.Limits.limitOpIsoOpColimit_hom_comp_ι_assoc, HomologicalComplex₂.D₂_totalShift₁XIso_hom_assoc, CategoryTheory.ForgetEnrichment.equivFunctor_map, TopologicalSpace.OpenNhds.val_apply, CategoryTheory.Limits.pushoutIsoUnopPullback_inr_hom, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct, CategoryTheory.Limits.IsColimit.existsUnique, HomotopicalAlgebra.instFibrationOppositeOpOfCofibration, CategoryTheory.Equalizer.firstObjEqFamily_inv, CategoryTheory.Limits.prod.inr_fst_assoc, SheafOfModules.unitHomEquiv_symm_comp, CategoryTheory.MonoidalPreadditive.whiskerLeft_add, CategoryTheory.unop_mono_iff, CategoryTheory.yonedaEquiv_apply, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_hom, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_hom_iCycles_assoc, AlgebraicGeometry.Scheme.IdealSheafData.ideal_le_comap_ideal, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app_assoc, CategoryTheory.Functor.PullbackObjObj.π_fst, CategoryTheory.Functor.partialRightAdjointHomEquiv_symm_comp, CategoryTheory.Bicategory.rightUnitor_inv_naturality, CategoryTheory.OplaxFunctor.mapComp_assoc_left_app_assoc, HomologicalComplex₂.D₂_totalShift₂XIso_hom_assoc, CategoryTheory.sum.inlCompInrCompInverseAssociator_inv_app_down_down, CategoryTheory.Limits.biprod.inlCokernelCofork_π, CategoryTheory.ForgetEnrichment.equivInverse_map, HomologicalComplex₂.d_f_comp_d_f, CategoryTheory.Limits.kernelForkBiproductToSubtype_cone, CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal_ε_unmop_unmop, CategoryTheory.MonoidalCategory.whiskerLeft_dite, CategoryTheory.Pseudofunctor.CoGrothendieck.instIsEquivalenceαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor, HomologicalComplex.add_f_apply, HomologicalComplex.extend_op_d_assoc, CategoryTheory.CatEnriched.id_hComp_id, CategoryTheory.PreGaloisCategory.instEssSurjContActionFintypeCatHomCarrierAutFunctorFunctorToContAction, CategoryTheory.Square.op_f₁₂, CategoryTheory.cokernelUnopUnop_inv, AlgebraicGeometry.StructureSheaf.exists_const, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight_apply, CategoryTheory.InducedCategory.homEquiv_apply, CategoryTheory.Endofunctor.Adjunction.Algebra.homEquiv_naturality_str, CategoryTheory.Limits.KernelFork.IsLimit.isZero_of_mono, CategoryTheory.Bicategory.Adjunction.homEquiv₁_apply, CategoryTheory.StrictPseudofunctorCore.map₂_associator, CategoryTheory.Limits.desc_op_comp_opCoproductIsoProduct'_hom, CategoryTheory.Bicategory.Prod.swap_map₂, AlgebraicGeometry.Scheme.Modules.Hom.zero_app, AlgebraicGeometry.tilde.map_sub, CategoryTheory.Limits.colimit.homIso_hom, CategoryTheory.WithInitial.opEquiv_functor_map, CategoryTheory.LocallyDiscrete.comp_as, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_right_as, SemimoduleCat.hom_zsmul, CategoryTheory.tensorRightHomEquiv_whiskerLeft_comp_evaluation, CategoryTheory.Pseudofunctor.DescentData.isoMk_inv_hom, HomologicalComplex₂.d₁_eq_zero', Mathlib.Tactic.Bicategory.naturality_rightUnitor, CategoryTheory.Bicategory.Pith.whiskerRight_iso_inv, CategoryTheory.Iso.op_inv, AlgebraicGeometry.Scheme.congr_app, CategoryTheory.unop_tensor_unop, SimplicialObject.opFunctor_obj_map, HomologicalComplex₂.D₁_D₁_assoc, TopologicalSpace.Opens.infLELeft_apply_mk, CategoryTheory.Subgroupoid.le_iff, CategoryTheory.Functor.homologySequence_comp, CategoryTheory.kernelOpUnop_hom, CategoryTheory.prod.rightUnitor_map, CategoryTheory.congrArg_cast_hom_right, CategoryTheory.Functor.FullyFaithful.compUliftCoyonedaCompWhiskeringLeft_hom_app_app_down, CategoryTheory.InjectiveResolution.of_def, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHomRight, FintypeCat.instFiniteHom, SemimoduleCat.hom_nsmul, ModuleCat.extendRestrictScalarsAdj_homEquiv_apply, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₁, CategoryTheory.ShortComplex.Homotopy.op_h₀, CategoryTheory.Coyoneda.objOpOp_inv_app, CategoryTheory.toOverPullbackIsoToOver_inv_app_left, SheafOfModules.freeHomEquiv_freeMap, CategoryTheory.Functor.prod'_δ_snd, CategoryTheory.CostructuredArrow.w_prod_fst_assoc, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom_assoc, CategoryTheory.Iso.homCongr_trans, CategoryTheory.Bicategory.rightUnitor_inv_congr, SSet.Truncated.Edge.CompStruct.d₂, CategoryTheory.Limits.isColimitCoconeLeftOpOfCone_desc, CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_app_app, CategoryTheory.GradedObject.zero_apply, CategoryTheory.IsPushout.zero_top, CategoryTheory.Limits.cokernelCoforkBiproductFromSubtype_isColimit, CategoryTheory.Pseudofunctor.map₂_left_unitor, CategoryTheory.Pseudofunctor.CoGrothendieck.map_map_base, CategoryTheory.Limits.pushoutIsoUnopPullback_inl_hom_assoc, CategoryTheory.Bicategory.unitors_inv_equal, CategoryTheory.Bicategory.Adj.forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map, CategoryTheory.Bicategory.Pith.leftUnitor_inv_iso_hom, CategoryTheory.nonempty_hom_of_preconnected_groupoid, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app', CochainComplex.HomComplex.Cochain.toSingleMk_neg, CategoryTheory.Bicategory.leftZigzagIso_symm, CategoryTheory.ShortComplex.homologyMap'_zero, CategoryTheory.CommSq.instHasLift, CategoryTheory.Preadditive.IsIso.comp_right_eq_zero, CategoryTheory.StrictPseudofunctor.mk''_mapId, CategoryTheory.Bicategory.associator_inv_naturality_middle, CategoryTheory.Limits.Sigma.ι_π_assoc, AlgebraicTopology.AlternatingCofaceMapComplex.d_eq_unop_d, CategoryTheory.Bicategory.associator_naturality_right_assoc, CategoryTheory.Pseudofunctor.CoGrothendieck.map_map_fiber, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerLeft_naturality_assoc, HomologicalComplex.unopInverse_map, CategoryTheory.Presheaf.freeYonedaHomEquiv_comp, CategoryTheory.OverPresheafAux.yonedaCollectionPresheaf_map, CategoryTheory.Bicategory.hom_inv_whiskerRight_whiskerRight_assoc, CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_of_mono₂, CategoryTheory.StrictlyUnitaryLaxFunctor.mapId_isIso, CategoryTheory.Groupoid.vertexGroup.inv_eq_inv, CategoryTheory.ShortComplex.RightHomologyData.unop_i, CategoryTheory.Bicategory.prod_id_fst, CategoryTheory.Bicategory.triangle_assoc_comp_left, CategoryTheory.Limits.IsColimit.homIso_hom, CategoryTheory.WithInitial.opEquiv_counitIso_hom_app, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_hom_app, CategoryTheory.Limits.kernel.condition_apply, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom, CategoryTheory.WithInitial.isColimitEquiv_symm_apply_desc, CategoryTheory.Limits.equalizer_as_kernel, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₃_assoc, CategoryTheory.WideSubcategory.id_def, HomologicalComplex.mapBifunctor₂₃.d₃_eq, CategoryTheory.Bicategory.associator_inv_naturality_right, CategoryTheory.CostructuredArrow.unop_left_comp_ofMkLEMk_unop, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivLeft_symm_apply, CategoryTheory.Limits.multicospanIndexEnd_snd, CategoryTheory.GrpObj.comp_zpow, CategoryTheory.leftAdjointOfStructuredArrowInitialsAux_apply, HomologicalComplex.extend.d_none_eq_zero', CategoryTheory.ShortComplex.HomologyMapData.add_left, groupCohomology.congr, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_hom_app_val_app, CategoryTheory.Functor.IsStronglyCocartesian.universal_property', CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIso_hom, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₃, HomologicalComplex₂.D₁_D₁, PresheafOfModules.freeYonedaEquiv_symm_app, CommRingCat.coyoneda_map_app, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapCompIso_hom, CategoryTheory.Limits.biproduct.matrixEquiv_symm_apply, CategoryTheory.zero_map, CategoryTheory.Sheaf.isLocallySurjective_iff_epi, CategoryTheory.InjectiveResolution.complex_d_comp, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app_assoc, CategoryTheory.leftDistributor_hom, TopCat.Presheaf.germ_res', CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapComp_hom, CategoryTheory.FreeBicategory.mk_right_unitor_inv, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_l, CategoryTheory.ShortComplex.unopFunctor_map, CategoryTheory.Limits.PreservesCokernel.of_iso_comparison, CategoryTheory.Bicategory.whiskerLeft_comp, HomologicalComplex.single_obj_d, CategoryTheory.CategoryOfElements.homMk_coe, CategoryTheory.tensorLeftHomEquiv_naturality, HomologicalComplex₂.D₂_D₁_assoc, CochainComplex.IsKInjective.Qh_map_bijective, CategoryTheory.FinCategory.categoryAsType_comp, CategoryTheory.Limits.pushoutIsoUnopPullback_inr_hom_assoc, CategoryTheory.eqToHom_heq_id_cod, HomotopicalAlgebra.cofibration_op_iff, CategoryTheory.leftAdjointOfStructuredArrowInitialsAux_symm_apply, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_left, CategoryTheory.Pseudofunctor.ObjectProperty.ι_app_toFunctor, CategoryTheory.ShortComplex.Homotopy.op_h₂, TopCat.Sheaf.interUnionPullbackCone_fst, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_map_app, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map, CategoryTheory.Bicategory.conjugateEquiv_symm_id, CategoryTheory.Discrete.sumEquiv_inverse_map, CategoryTheory.ShortComplex.ShortExact.comp_δ, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app, CategoryTheory.Limits.kernelBiprodFstIso_hom, CategoryTheory.Oplax.StrongTrans.Modification.whiskerLeft_naturality, CategoryTheory.LaxFunctor.mapComp_naturality_left_app_assoc, CategoryTheory.Bicategory.conjugateEquiv_apply, CategoryTheory.Bicategory.prod_whiskerRight_fst, CategoryTheory.op_epi_iff, CategoryTheory.Limits.monoFactorisationZero_e, CategoryTheory.Functor.FullyFaithful.map_bijective, CategoryTheory.Adjunction.eq_homEquiv_apply, CategoryTheory.Pseudofunctor.DescentData.comp_hom, CategoryTheory.Bicategory.whiskerRight_comp_symm, CategoryTheory.pathComposition_obj, CategoryTheory.Presieve.FamilyOfElements.compatible_singleton_iff, CategoryTheory.Endofunctor.Algebra.ext_iff, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_inv_τl, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv, SimplicialObject.Splitting.cofan_inj_eq, CategoryTheory.Bicategory.Pith.comp₂_iso_hom_assoc, DerivedCategory.subsingleton_hom_of_isStrictlyLE_of_isStrictlyGE, CategoryTheory.MonObj.ofRepresentableBy_one, AlgebraicGeometry.Scheme.LocalRepresentability.instIsLocallySurjectiveHomYonedaGluedToSheafOfIsLocallySurjectiveZariskiTopologyDescFunctorOppositeType, CategoryTheory.ShortComplex.cyclesMap_sub, CategoryTheory.IsPullback.inr_fst, HomologicalComplex₂.D₂_D₂, CategoryTheory.Cat.leftUnitor_hom_app, CategoryTheory.Functor.curry₃_obj_obj_map_app, CategoryTheory.Bicategory.associator_eqToHom_hom_assoc, CategoryTheory.LocallyDiscrete.subsingleton2Hom, CategoryTheory.ShortComplex.Homotopy.g_h₃_assoc, CategoryTheory.CostructuredArrow.prodFunctor_map, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_left_right, CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inr_assoc, CategoryTheory.FinCategory.asTypeToObjAsType_map, CategoryTheory.Bicategory.whiskerRight_id, Homotopy.prevD_succ_cochainComplex, SSet.exists_nonDegenerate, CategoryTheory.Limits.PushoutCocone.op_snd, CategoryTheory.Limits.isColimitOfConeRightOpOfCocone_desc, HomologicalComplex.d_toCycles_assoc, CategoryTheory.Limits.coend.condition, CategoryTheory.kernel_zero_of_nonzero_from_simple, ContinuousMap.Homotopy.heq_path_of_eq_image, CategoryTheory.ShortComplex.Splitting.id, TopCat.Presheaf.germ_res_apply, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f_assoc, CategoryTheory.StructuredArrow.prodInverse_map, CategoryTheory.Limits.PullbackCone.unop_inl, CategoryTheory.Iso.homFromEquiv_symm_apply, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app, CategoryTheory.MonObj.comp_mul_assoc, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivLeft_apply, HomologicalComplex.xPrevIsoSelf_comp_dTo, CategoryTheory.uliftCoyonedaEquiv_uliftCoyoneda_map, SheafOfModules.unitHomEquiv_symm_freeHomEquiv_apply, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality, CochainComplex.homotopyUnop_hom_eq, CategoryTheory.Functor.RepresentableBy.coyoneda_homEquiv, CategoryTheory.TwoSquare.equivNatTrans_apply, CategoryTheory.ShortComplex.Homotopy.add_h₁, CochainComplex.HomComplex.Cochain.toSingleMk_add, CategoryTheory.coyonedaEquiv_comp, CategoryTheory.uliftYonedaEquiv_symm_apply_app, groupHomology.d₃₂_comp_d₂₁_assoc, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₂, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_left, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom, CategoryTheory.Limits.inr_opProdIsoCoprod_inv_assoc, CategoryTheory.Limits.isLimitOfCoconeOfConeRightOp_lift, CategoryTheory.Abelian.Ext.mk₀_neg, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₂, CategoryTheory.Limits.isoZeroOfEpiZero_hom, AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimage, CategoryTheory.Oplax.LaxTrans.naturality_comp_assoc, CategoryTheory.Limits.PushoutCocone.isoMk_inv_hom, CategoryTheory.Limits.colimitYonedaHomIsoLimit'_π_apply, CategoryTheory.Limits.π_comp_colimitLeftOpIsoUnopLimit_inv, CategoryTheory.WithInitial.liftFromUnderComp_inv_app, HomologicalComplex.opcyclesOpIso_inv_naturality, CategoryTheory.conjugateEquiv_symm_apply_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionActionOfMonoidalFunctorToEndofunctorMopIso_hom_app_unmop_app, CategoryTheory.Limits.WalkingParallelPair.inclusionWalkingReflexivePair_map, CategoryTheory.Groupoid.invFunctor_map, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality, FGModuleCat.instFiniteHomModuleCatObjIsFG, HomologicalComplex.extend.XOpIso_hom_d_op, CategoryTheory.Limits.parallelPairOpIso_inv_app_one, CategoryTheory.Oplax.OplaxTrans.categoryStruct_comp_app, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app', CategoryTheory.MonoidalPreadditive.add_whiskerRight, CategoryTheory.LaxFunctor.id_mapId, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_snd_coe, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagram_map, CategoryTheory.nerve.homEquiv_apply, Rep.homEquiv_apply_hom, CategoryTheory.isIso_iff_coyoneda_map_bijective, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π_assoc, CategoryTheory.Limits.Types.binaryCoproductCocone_ι_app, CategoryTheory.conjugateEquiv_apply_app, CategoryTheory.StrictPseudofunctor.id_obj, CategoryTheory.Limits.biproductBiproductIso_hom, CochainComplex.HomComplex.δ_v, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_left, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_id, CategoryTheory.Groupoid.isThin_iff, CategoryTheory.Limits.kernelBiproductπIso_hom, CategoryTheory.Functor.partialLeftAdjointHomEquiv_symm_comp, AlgebraicGeometry.PresheafedSpace.componentwiseDiagram_map, Rep.FiniteCyclicGroup.chainComplexFunctor_obj, CategoryTheory.Abelian.tfae_epi, CategoryTheory.Oplax.StrongTrans.homCategory_id_as_app, CategoryTheory.Limits.compYonedaSectionsEquiv_apply_app, CategoryTheory.Idempotents.add_def, HomologicalComplex.d_comp_d_assoc, CategoryTheory.cokernelOpOp_hom, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_naturality, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, CategoryTheory.ShortComplex.op_pOpcycles_opcyclesOpIso_hom, CategoryTheory.MonoidalOpposite.unmopEquiv_inverse_map_unmop, CategoryTheory.SimplicialObject.δ_def, CategoryTheory.ShortComplex.HomologyMapData.neg_left, HomologicalComplex₂.ιTotal_totalFlipIso_f_inv_assoc, AlgebraicGeometry.AffineSpace.homOverEquiv_symm_apply_coe, CategoryTheory.Limits.BinaryBicone.sndKernelFork_ι, CategoryTheory.Bicategory.InducedBicategory.eqToHom_hom, CochainComplex.fromSingle₀Equiv_apply_coe, CategoryTheory.Functor.FullyFaithful.nonempty_iff_map_bijective, commBialgCatEquivComonCommAlgCat_unitIso_hom_app, SimplexCategory.σ_injective, CategoryTheory.CategoryOfElements.to_comma_map_right, CategoryTheory.Pseudofunctor.Grothendieck.ext_iff, CategoryTheory.Functor.prod'_ε_fst, CategoryTheory.Limits.Cofork.unop_op_π, Rep.coindFunctorIso_hom_app_hom_hom_apply_hom_hom_apply, CategoryTheory.Functor.imageSieve_eq_imageSieve, CategoryTheory.WithTerminal.opEquiv_counitIso_inv_app, CategoryTheory.frobeniusMorphism_mate, CategoryTheory.Subgroupoid.IsWide.eqToHom_mem, HomologicalComplex.dgoToHomologicalComplex_obj_d, CategoryTheory.Bicategory.lanLiftUnit_desc_assoc, CategoryTheory.Localization.liftNatTrans_zero, CategoryTheory.Limits.BinaryFan.IsLimit.lift'_coe, CategoryTheory.tensorRightHomEquiv_whiskerRight_comp_evaluation, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_fst, CategoryTheory.ShortComplex.Homotopy.smul_h₂, CategoryTheory.Equivalence.sheafCongrPreregular_inverse_obj_val_map, CategoryTheory.Bicategory.whiskerLeft_hom_inv, HomotopyCategory.quotient_map_eq_zero_iff, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app, CategoryTheory.Abelian.Pseudoelement.zero_eq_zero', CategoryTheory.Lax.LaxTrans.id_app, CategoryTheory.ShortComplex.RightHomologyMapData.op_φK, CategoryTheory.instSmallHomOfLocallySmall, CategoryTheory.Subobject.factors_add, CategoryTheory.StrictlyUnitaryLaxFunctor.id_obj, CochainComplex.HomComplex.Cochain.neg_v, CochainComplex.HomComplex.Cocycle.equivHomShift'_symm_apply, CategoryTheory.ShortComplex.LeftHomologyMapData.op_φH, CategoryTheory.Pseudofunctor.mapComp'_inv_naturality, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_map, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_snd, SimplexCategory.II_σ, CochainComplex.HomComplex.Cochain.sub_v, CategoryTheory.Linear.units_smul_comp, CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.f', CategoryTheory.Bicategory.mateEquiv_id_comp_right, CategoryTheory.Limits.PullbackCone.op_pt, CategoryTheory.Adjunction.conjugateEquiv_leftAdjointCompIso_inv, CategoryTheory.Linear.leftComp_apply, CategoryTheory.Bicategory.leftUnitor_comp_inv, CochainComplex.mappingCone.liftCochain_v_descCochain_v, CategoryTheory.oppositeShiftFunctorAdd_inv_app, CategoryTheory.Functor.Linear.map_smul, Homotopy.nullHomotopicMap'_f_eq_zero, CategoryTheory.Presheaf.restrictedULiftYoneda_obj_map, CategoryTheory.Pseudofunctor.mapComp_id_left, CategoryTheory.Iso.unop2_inv, CategoryTheory.Limits.IsBilimit.total, CategoryTheory.Sieve.mem_ofObjects_iff, CategoryTheory.Limits.pushoutIsoUnopPullback_inv_snd, CategoryTheory.SemiadditiveOfBinaryBiproducts.comp_add, SheafOfModules.GeneratingSections.epi, CategoryTheory.Bicategory.postcomp_obj, CochainComplex.mappingCone.inl_v_triangle_mor₃_f, CategoryTheory.Limits.FormalCoproduct.Hom.fromIncl_asSigma, HomologicalComplex.extend.XOpIso_hom_d_op_assoc, CategoryTheory.ShortComplex.LeftHomologyMapData.smul_φH, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality_app, CategoryTheory.Comma.opFunctor_map, CategoryTheory.image_ι_op_comp_imageUnopOp_hom, HomologicalComplex₂.d₂_eq_zero, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit, CategoryTheory.Functor.partialRightAdjointHomEquiv_comp_symm_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_app, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_whisker_right, HomologicalComplex.mapBifunctorMapHomotopy.comm₁, CategoryTheory.StrictPseudofunctor.comp_mapComp_hom, CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.hf', CategoryTheory.Biprod.unipotentLower_inv, Action.smul_hom, CategoryTheory.ShortComplex.cyclesMap'_sub, CategoryTheory.Bicategory.leftZigzagIso_hom, CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_mapComp, CategoryTheory.Limits.Cofork.unop_π_app_one, CategoryTheory.ShortComplex.homologyMap'_sub, CategoryTheory.Sieve.equalizer_apply, CategoryTheory.ShortComplex.Splitting.rightHomologyData_ι, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_inl, CategoryTheory.Equalizer.firstObjEqFamily_hom, CategoryTheory.OrthogonalReflection.D₁.ι_comp_t_assoc, CategoryTheory.Subfunctor.Subpresheaf.ofSection_eq_range', CategoryTheory.Functor.toOplaxFunctor'_obj, Rep.coinvariantsAdjunction_homEquiv_symm_apply_hom, CategoryTheory.Limits.isLimitOfCoconeOfConeLeftOp_lift, CategoryTheory.ShortComplex.hasHomology_of_hasCokernel, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd, Bicategory.Opposite.bicategory_associator_hom_unop2, CategoryTheory.Limits.inl_opProdIsoCoprod_inv_assoc, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_hom, LightCondSet.topCatAdjunctionUnit_val_app_apply, CategoryTheory.OplaxFunctor.PseudoCore.mapCompIso_hom, CategoryTheory.StrictPseudofunctor.comp_mapId_hom, CategoryTheory.Idempotents.Karoubi.hom_eq_zero_iff, CategoryTheory.Limits.piConst_map_app, CategoryTheory.Limits.biprod.inr_fst, AlgebraicGeometry.RingedSpace.exists_res_eq_zero_of_germ_eq_zero, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_symm_apply_right, CategoryTheory.ShortComplex.Homotopy.sub_h₁, CategoryTheory.Preadditive.commGrpEquivalence_functor_obj_grp_mul, CategoryTheory.ObjectProperty.isThin_of_isCoseparating_bot, CategoryTheory.Presieve.isSheafFor_singleton, CategoryTheory.Limits.IsBilimit.binary_total, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_symm_apply_φ, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality_assoc, CochainComplex.mappingCone.inr_triangleδ, Bicategory.Opposite.unop2_id_bop, CategoryTheory.kernelCokernelCompSequence.ι_φ, CategoryTheory.LaxFunctor.mapComp_assoc_right_app, CategoryTheory.Bicategory.LeftExtension.ofCompId_left_as, SSet.spine_vertex, CategoryTheory.Oplax.OplaxTrans.associator_hom_as_app, CategoryTheory.Limits.HasZeroObject.zeroIsoTerminal_inv, MonCat.oneHom_apply, CategoryTheory.Idempotents.Karoubi.inclusionHom_apply, CategoryTheory.End.smul_left, HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom, CategoryTheory.Preadditive.isSeparator_iff, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id, HomologicalComplex.fromOpcycles_d_assoc, CategoryTheory.Pseudofunctor.toOplax_mapComp, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app_assoc, Bicategory.Opposite.unopFunctor_map, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_μ_unmop_app, CategoryTheory.Functor.FullyFaithful.homNatIso_inv_app_down, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_symm_apply, CategoryTheory.Grp.Hom.hom_zpow, CategoryTheory.BicategoricalCoherence.tensorRight_iso, CategoryTheory.IsPullback.zero_top, CategoryTheory.Bicategory.inv_hom_whiskerRight_whiskerRight, CategoryTheory.Limits.pushoutIsoUnopPullback_inv_fst, AlgebraicGeometry.Scheme.Hom.appLE_map', CategoryTheory.Functor.IsStronglyCartesian.map_self, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₃_assoc, CategoryTheory.isPullback_of_cofan_isVanKampen, CategoryTheory.Functor.CorepresentableBy.ofIsoObj_homEquiv, CategoryTheory.instIsSplitMonoOppositeOpOfIsSplitEpi, CategoryTheory.Bicategory.Prod.sectR_mapComp_inv, topCatOpToFrm_map, CategoryTheory.Bicategory.Prod.fst_mapComp_hom, CategoryTheory.MonoidalCategory.prodMonoidal_whiskerRight, HomologicalComplex.instQuasiIsoAtMapOppositeSymmUnopFunctorOp, SemimoduleCat.ofHom₂_hom_apply_hom, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality', CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_hom_inv_assoc, CategoryTheory.HomOrthogonal.matrixDecomposition_id, CochainComplex.mappingCone.id_X, CategoryTheory.Functor.Full.map_surjective, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.uliftCoyonedaEquiv_symm_apply_app, CategoryTheory.ShortComplex.leftHomologyMap_op, CategoryTheory.Bicategory.id_whiskerLeft_symm, CategoryTheory.Pseudofunctor.mapComp'_naturality_1, CategoryTheory.Functor.representableByUliftFunctorEquiv_symm_apply_homEquiv, CommRingCat.HomTopology.continuous_precomp, CategoryTheory.ShortComplex.Homotopy.refl_h₃, CochainComplex.HomComplex.Cochain.single_zero, CategoryTheory.ShortComplex.homologyMap'_add, CategoryTheory.actionAsFunctor_map, CategoryTheory.ShortComplex.SnakeInput.δ_L₃_f, CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_sub_f, AddCommGrpCat.asHom_injective, CategoryTheory.Pseudofunctor.isStackFor_ofArrows_iff, CategoryTheory.Limits.opCoproductIsoProduct'_hom_comp_proj, CategoryTheory.Abelian.Pseudoelement.pseudoZero_iff, CategoryTheory.Functor.shift_map_op_assoc, CategoryTheory.Limits.coker.condition_assoc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_π_app, CategoryTheory.Adjunction.leftAdjointCompNatTrans₀₁₃_eq_conjugateEquiv_symm, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality, CategoryTheory.Preadditive.nsmul_comp, CategoryTheory.Functor.IsCoverDense.Types.pushforwardFamily_def, SimplicialObject.Splitting.IndexSet.eqId_iff_len_eq, CategoryTheory.Localization.Preadditive.add'_map, CategoryTheory.ShortComplex.homologyOpIso_inv_naturality, SimplicialObject.Splitting.IndexSet.ext', CategoryTheory.Bicategory.Pith.pseudofunctorToPith_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_of, CategoryTheory.Limits.BinaryBicone.inl_snd_assoc, CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_hom_app_unmop_unmop, CategoryTheory.Bicategory.LeftLift.IsKan.fac_assoc, HomologicalComplex.cyclesOpIso_inv_naturality_assoc, CategoryTheory.linearYoneda_obj_obj_carrier, CategoryTheory.Preadditive.isSeparating_iff, CategoryTheory.Pretriangulated.Triangle.smul_hom₂, CategoryTheory.Limits.Cotrident.IsColimit.homIso_natural, CategoryTheory.Bicategory.postcomposing_obj, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_app, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_inv, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app_assoc, CategoryTheory.Bicategory.Adj.rightUnitor_inv_τl, CategoryTheory.Coyoneda.objOpOp_hom_app, CategoryTheory.Bicategory.Adj.Hom₂.conjugateEquiv_symm_τr, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app, CategoryTheory.ShortComplex.Homotopy.unop_h₃, CategoryTheory.ShortComplex.iCycles_g, CategoryTheory.LaxFunctor.PseudoCore.mapCompIso_inv, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_map, CategoryTheory.Limits.π_comp_colimitUnopIsoOpLimit_inv, SSet.Subcomplex.ofSimplexProd_eq_range, CategoryTheory.nerve.homEquiv_edgeMk, DerivedCategory.HomologySequence.mono_homologyMap_mor₁_iff, CategoryTheory.Join.pseudofunctorLeft_mapId_hom_toNatTrans_app, CategoryTheory.MorphismProperty.RightFraction.unop_s, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_app_assoc, AlgebraicGeometry.pointEquivClosedPoint_apply_coe, CategoryTheory.StrictlyUnitaryLaxFunctor.comp_mapId, CategoryTheory.CostructuredArrow.w_prod_snd_assoc, CategoryTheory.Over.postAdjunctionLeft_unit_app_left, CategoryTheory.Limits.fst_opProdIsoCoprod_hom_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality, ModuleCat.homLinearEquiv_symm_apply, HomologicalComplex.truncGE'.d_comp_d, HomotopicalAlgebra.instWeakEquivalenceUnopOfOpposite, ModuleCat.hom_smul, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_counit_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp_val_app, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_inv_app, CategoryTheory.Limits.cokernel.π_zero_isIso, CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_zero_f, CategoryTheory.Pseudofunctor.map₂_associator_app, CategoryTheory.Cat.rightUnitor_hom_toNatTrans, CategoryTheory.Functor.homObjEquiv_symm_apply_app, CategoryTheory.Adjunction.mkOfHomEquiv_counit_app, CategoryTheory.Bicategory.Prod.snd_map₂, CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullback, Condensed.isoFinYonedaComponents_hom_apply, CategoryTheory.Functor.map_inv', Rep.MonoidalClosed.linearHomEquivComm_hom, CategoryTheory.Preadditive.cokernelCoforkOfCofork_ofπ, CategoryTheory.Lax.OplaxTrans.naturality_comp, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_inv_toNatTrans_app_val_app, HomologicalComplex.extend.d_none_eq_zero, CategoryTheory.ShortComplex.cyclesOpIso_hom_naturality, CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHom_mk, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, SemimoduleCat.homLinearEquiv_apply, CategoryTheory.Iso.op_hom, CategoryTheory.Bicategory.leftUnitor_inv_whiskerRight_assoc, CategoryTheory.StructuredArrow.functor_map, CategoryTheory.Functor.RepresentableBy.comp_homEquiv_symm, CategoryTheory.Bicategory.whiskerRight_comp_symm_assoc, HomologicalComplex.cylinder.πCompι₀Homotopy.nullHomotopicMap_eq, CategoryTheory.Oplax.StrongTrans.Modification.whiskerRight_naturality, CategoryTheory.ShortComplex.Homotopy.neg_h₁, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app_assoc, CategoryTheory.Limits.PullbackCone.unop_inr, HomologicalComplex.mapBifunctor₂₃.ιOrZero_eq_zero, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_naturality_assoc, CochainComplex.ConnectData.d_comp_d, CategoryTheory.NatTrans.app_nsmul, HomologicalComplex.sub_f_apply, CochainComplex.mappingCone.d_snd_v'_assoc, AddCommMonCat.coyonedaType_map_app, CategoryTheory.StrictlyUnitaryPseudofunctor.mk'_mapId, CategoryTheory.whiskerLeft_def, CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inl, CategoryTheory.NatTrans.prod_app_fst, HomologicalComplex.homotopyCofiber.descSigma_ext_iff, CategoryTheory.Comon.MonOpOpToComon_map_hom, CategoryTheory.Limits.spanOp_hom_app, CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapId_inv, AlgebraicGeometry.IsLocalIso.le_of_isZariskiLocalAtSource, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom, CategoryTheory.Bicategory.Adj.rightUnitor_hom_τr, CategoryTheory.Iso.eHomCongr_comp_assoc, CategoryTheory.Adjunction.homEquiv_unit, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_hom_comp_π_assoc, Quiver.Hom.mop_inj, CategoryTheory.Under.postAdjunctionRight_unit_app_right, CategoryTheory.Join.opEquiv_inverse_map_inclRight_op, Profinite.Extend.functorOp_obj, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_left_hom, HomologicalComplex.d_pOpcycles, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapId_inv_iso_inv, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality, AlgebraicGeometry.Scheme.Hom.congr_app, CategoryTheory.Pseudofunctor.mapComp_id_right, CategoryTheory.Preadditive.comp_neg, CategoryTheory.conjugateEquiv_leftUnitor_hom, CategoryTheory.Sum.functorEquiv_inverse_map, CategoryTheory.Limits.isIsoZero_iff_source_target_isZero, CategoryTheory.Bicategory.LeftExtension.whiskering_map, CategoryTheory.Bicategory.comp_whiskerRight, CategoryTheory.BicategoricalCoherence.left_iso, CategoryTheory.Limits.Pi.ι_π_of_ne, CategoryTheory.Presheaf.isLocallySurjective_toSheafify, CategoryTheory.ShortComplex.add_τ₃, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_naturality, CategoryTheory.Over.opEquivOpUnder_inverse_obj, CategoryTheory.Limits.limitCompCoyonedaIsoCone_hom_app, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_symm, CategoryTheory.Pseudofunctor.mapComp'_inv_naturality_assoc, Bicategory.Opposite.bicategory_leftUnitor_hom_unop2, CategoryTheory.uliftYonedaEquiv_apply, CategoryTheory.Limits.ι_comp_colimitRightOpIsoUnopLimit_hom_assoc, CategoryTheory.Limits.WidePullbackShape.mkCone_π_app, AlgebraicGeometry.Scheme.ofRestrict_appLE, CategoryTheory.Iso.homCongr_comp, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_map, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id_app, CategoryTheory.Bicategory.comp_whiskerLeft_symm, Bicategory.Opposite.op2_whiskerRight, CategoryTheory.Bicategory.inv_whiskerRight, CategoryTheory.Limits.FormalCoproduct.powerBifunctor_map_app, CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapComp_inv, CategoryTheory.Bicategory.Pith.id₂_iso_inv, CategoryTheory.StructuredArrow.prodFunctor_map, AlgebraicGeometry.IsAffineOpen.isoSpec_inv, CategoryTheory.ShortComplex.Homotopy.refl_h₂, CategoryTheory.Arrow.equivSigma_apply_snd_snd, CategoryTheory.bijection_natural, HomologicalComplex.fromOpcycles_eq_zero, AlgebraicTopology.DoldKan.PInfty_f_comp_QInfty_f_assoc, ChainComplex.toSingle₀Equiv_apply_coe, HomologicalComplex.homologyι_opcyclesToCycles_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_left, CategoryTheory.Limits.Fork.IsLimit.existsUnique, CategoryTheory.Functor.FullyFaithful.homEquiv_symm_apply, HomologicalComplex₂.ι_totalShift₂Iso_inv_f_assoc, CategoryTheory.Monad.algebraPreadditive_homGroup_add_f, PresheafOfModules.zsmul_app, Condensed.finYoneda_map, FDRep.instFiniteDimensionalHom, CategoryTheory.NormalEpi.w, CategoryTheory.Limits.coequalizer_as_cokernel, CategoryTheory.Localization.small_of_hasSmallLocalizedHom, CategoryTheory.CartesianClosed.homEquiv_apply_eq, CategoryTheory.Classifier.SubobjectRepresentableBy.homEquiv_eq, SimplexCategory.instSubsingletonHomMkOfNatNat, CategoryTheory.op_whiskerLeft, CategoryTheory.Bicategory.mateEquiv_symm_apply', SSet.Subcomplex.instSubsingletonHomToSSetBot, CategoryTheory.Oplax.LaxTrans.naturality_naturality, CategoryTheory.Limits.PullbackCone.combine_π_app, CategoryTheory.Pseudofunctor.mapComp'_comp_id, CategoryTheory.Localization.homEquiv_eq, CategoryTheory.Oplax.StrongTrans.naturality_comp, MonObj.mopEquiv_functor_obj_mon_one_unmop, CategoryTheory.CategoryOfElements.CreatesLimitsAux.liftedCone_π_app_coe, CategoryTheory.Grp.Hom.hom_hom_div, CategoryTheory.Limits.HasZeroObject.zeroIsoTerminal_hom, CategoryTheory.OplaxFunctor.map₂_leftUnitor_assoc, CategoryTheory.Functor.toPseudoFunctor'_map, CategoryTheory.Bicategory.conjugateEquiv_id_comp_right_apply, CategoryTheory.Oplax.OplaxTrans.associator_inv_as_app, CategoryTheory.IsPushout.inl_snd', CategoryTheory.PreGaloisCategory.toAut_surjective_isGalois_finite_family, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality', CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp_app, CategoryTheory.Pseudofunctor.presheafHom_obj, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.fromBiprod_δ_assoc, CategoryTheory.Functor.FullyFaithful.compUliftYonedaCompWhiskeringLeft_inv_app_app_down, CategoryTheory.ShortComplex.π₁Toπ₂_comp_π₂Toπ₃, CompHausLike.LocallyConstant.incl_of_counitAppApp, CategoryTheory.Bicategory.Adjunction.homEquiv₂_apply, CategoryTheory.Over.mapPullbackAdj_counit_app, CategoryTheory.WithTerminal.opEquiv_unitIso_hom_app, CategoryTheory.Limits.Pi.ι_π, CategoryTheory.PreGaloisCategory.toAut_hom_app_apply, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_assoc, SimplicialObject.Splitting.IndexSet.mk_snd_coe, AlgebraicGeometry.Scheme.Hom.app_appIso_inv_assoc, CategoryTheory.Congruence.equivalence, CategoryTheory.Preadditive.smul_iso_hom, CategoryTheory.Oplax.StrongTrans.naturality_id_assoc, CategoryTheory.StrictlyUnitaryLaxFunctorCore.mapComp_naturality_right, CategoryTheory.Adjunction.compPreadditiveYonedaIso_inv_app_app_apply, CategoryTheory.Bicategory.Adj.forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj, CategoryTheory.Functor.leftOpRightOpEquiv_unitIso_inv_app, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_inv_app_unop, FintypeCat.toProfinite_map_hom_hom_apply, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_app, CategoryTheory.WithTerminal.opEquiv_counitIso_hom_app, CategoryTheory.Oplax.LaxTrans.naturality_id, SSet.prodStdSimplex.objEquiv_naturality, CategoryTheory.Preadditive.commGrpEquivalence_functor_obj_grp_inv, CategoryTheory.BicartesianSq.of_has_biproduct₂, Rep.coindVEquiv_symm_apply_coe, CategoryTheory.whiskerRight_def, CategoryTheory.BraidedCategory.unop_tensorμ, CategoryTheory.ComposableArrows.opEquivalence_unitIso_inv_app, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_left_unitor, HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom_desc_hom, HomologicalComplex₂.d_f_comp_d_f_assoc, CategoryTheory.Pseudofunctor.toLax_mapComp, CategoryTheory.PreOneHypercover.multifork_ι, CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse_obj_hom, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₃, CommGrpCat.coyonedaType_map_app, HomologicalComplex.homotopyCofiber.inlX_sndX_assoc, CategoryTheory.Pseudofunctor.isoMapOfCommSq_horiz_id, CategoryTheory.Types.instFullForgetTypeHom, CategoryTheory.Oplax.OplaxTrans.naturality_comp, CategoryTheory.CommSq.shortComplex_f, CategoryTheory.CatEnriched.id_hComp_heq, CategoryTheory.MonObj.comp_one, CategoryTheory.NatTrans.removeLeftOp_app, CategoryTheory.Join.pseudofunctorLeft_mapComp_hom_toNatTrans_app, CategoryTheory.op_tensor_op, CategoryTheory.CommSq.HasLift.iff_op, CategoryTheory.Limits.FintypeCat.productEquiv_apply, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left, CategoryTheory.Discrete.instSubsingletonDiscreteHom, CategoryTheory.uliftYonedaEquiv_symm_map, CategoryTheory.Functor.prod_ε_snd, CategoryTheory.Enriched.FunctorCategory.homEquiv_apply_π, HomologicalComplex.homologyι_comp_fromOpcycles, CategoryTheory.Functor.cones_obj, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app', CategoryTheory.thin_of_isSeparating_empty, CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_neg_f, CategoryTheory.NonPreadditiveAbelian.sub_sub_sub, CategoryTheory.homOfLE_op_comp_eqToHom_assoc, CategoryTheory.Square.unop_f₁₂, CategoryTheory.Lax.LaxTrans.naturality_comp, CategoryTheory.Presieve.preZeroHypercover_I₀, CondensedMod.isDiscrete_iff_isDiscrete_forget, CochainComplex.HomComplex.Cochain.toSingleMk_v_eq_zero, FintypeCat.comp_apply, HomotopicalAlgebra.weakEquivalences_op_iff, CategoryTheory.Limits.zero_of_target_iso_zero', CategoryTheory.Abelian.subobjectIsoSubobjectOp_apply, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_naturality_assoc, CategoryTheory.Limits.biprod.fstKernelFork_ι, CategoryTheory.Limits.biproduct.matrix_desc_assoc, FintypeCat.uSwitchEquiv_naturality, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_right_hom, AlgebraicTopology.DoldKan.QInfty_f_0, CategoryTheory.kernelUnopUnop_inv, HomologicalComplex.homologyMap_neg, CategoryTheory.ShortComplex.RightHomologyData.wι_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π, CategoryTheory.Enriched.FunctorCategory.diagram_map_app, CategoryTheory.Oplax.StrongTrans.id_naturality_inv, CategoryTheory.OplaxFunctor.mapComp_assoc_left_app, CategoryTheory.InjectiveResolution.ι_f_succ, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_snd, CategoryTheory.RetractArrow.op_r_right, CategoryTheory.Adjunction.compUliftCoyonedaIso_inv_app_app_down, CategoryTheory.Lax.OplaxTrans.vComp_naturality_comp, CategoryTheory.MonObj.one_comp_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_assoc, FintypeCat.equivEquivIso_symm_apply_symm_apply, CategoryTheory.presheafHom_obj, CategoryTheory.FinCategory.categoryAsType_id, CategoryTheory.PreGaloisCategory.evaluation_injective_of_isConnected, prevD_eq_toPrev_dTo, CategoryTheory.Limits.IsColimit.homEquiv_apply, Alexandrov.principals_map, CategoryTheory.Limits.comp_zero, CategoryTheory.ObjectProperty.isThin_of_isSeparating_bot, CategoryTheory.Limits.monoFactorisationZero_m, CategoryTheory.Preadditive.neg_iso_hom, CategoryTheory.Groupoid.vertexGroup_inv, CategoryTheory.Limits.PullbackCone.op_inr, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_assoc, CategoryTheory.Oplax.LaxTrans.id_app, CategoryTheory.NatTrans.app_add, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_π_app, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_leftUnitor_inv_as_app, AlgebraicTopology.DoldKan.Γ₂_obj_p_app, CategoryTheory.Functor.whiskerLeft_obj_map_bijective_of_isCoverDense, CategoryTheory.Limits.parallelPairOpIso_hom_app_one, CategoryTheory.Pseudofunctor.map₂_right_unitor_assoc, CategoryTheory.GrothendieckTopology.Cover.Arrow.Relation.ext_iff, CategoryTheory.GrpObj.inv_comp_assoc, CategoryTheory.Bicategory.Prod.sectL_mapComp_hom, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff, CategoryTheory.Limits.preservesKernel_zero, CategoryTheory.ThinSkeleton.thin, CategoryTheory.Abelian.Ext.mk₀_smul, CategoryTheory.prod_id', CategoryTheory.Bicategory.associator_inv_naturality_left, CategoryTheory.ShortComplex.opMap_τ₃, CategoryTheory.Functor.map_zero, CategoryTheory.PreOneHypercover.multicospanIndex_snd, CategoryTheory.opEquiv_apply, CategoryTheory.Pseudofunctor.CoGrothendieck.instFullαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor, CategoryTheory.Limits.PullbackCone.op_ι_app, CategoryTheory.ShortComplex.opcyclesOpIso_hom_naturality_assoc, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_hom_app, SemiNormedGrp.zero_apply, SSet.Truncated.spine_map_subinterval, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_comp_mapComp'_inv, TopCat.Presheaf.presheafEquivOfIso_inverse_obj_map, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality_app, CategoryTheory.Functor.prod_η_snd, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero_assoc, AlgebraicGeometry.Scheme.fromSpecStalk_appTop, AlgebraicTopology.AlternatingFaceMapComplex.d_squared, CategoryTheory.Square.op_f₂₄, CategoryTheory.Limits.inr_pushoutZeroZeroIso_hom, CategoryTheory.Bicategory.leftUnitor_inv_naturality, CategoryTheory.ShortComplex.opcyclesMap_add, CategoryTheory.WithTerminal.lift_map, CategoryTheory.StructuredArrow.IsUniversal.existsUnique, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_inv_hom, CategoryTheory.Limits.biprod.decomp_hom_to, CategoryTheory.Pseudofunctor.DescentData.nonempty_fullyFaithful_toDescentData_iff_of_sieve_eq, CategoryTheory.Biprod.inr_ofComponents, CategoryTheory.Limits.opCoproductIsoProduct_hom_comp_π, CategoryTheory.Equivalence.inverseFunctor_map, TopCat.presheafToTop_obj, CategoryTheory.Bicategory.unitors_equal, CategoryTheory.Oplax.OplaxTrans.Modification.whiskerLeft_naturality_assoc, CategoryTheory.Biprod.ofComponents_snd, CategoryTheory.Arrow.mk_injective, CategoryTheory.ShortComplex.unop_f, CategoryTheory.Cat.associator_inv_app, CategoryTheory.Bicategory.associator_naturality_right, CategoryTheory.Bicategory.whiskerRightIso_inv, CategoryTheory.NonPreadditiveAbelian.sub_add, CategoryTheory.Bicategory.precomposing_map_app, FundamentalGroupoid.instSubsingletonHomPUnit, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_apply, CategoryTheory.Limits.biproduct.lift_matrix_assoc, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_snd, AlgebraicGeometry.PresheafedSpace.Γ_map_op, CategoryTheory.simplicialToCosimplicialAugmented_map_left, CategoryTheory.Bicategory.Prod.sectL_obj, CategoryTheory.Limits.biproduct.lift_desc_assoc, HomologicalComplex.mapBifunctorMapHomotopy.zero₁, CategoryTheory.Subgroupoid.coe_comp_coe, CategoryTheory.OverPresheafAux.YonedaCollection.map₂_snd, CategoryTheory.Preadditive.epi_iff_cancel_zero, Homotopy.dNext_zero_chainComplex, HomologicalComplex.mapBifunctor₂₃.d₃_eq_zero, CategoryTheory.tensorRightHomEquiv_symm_coevaluation_comp_whiskerRight, CategoryTheory.MonoidalOpposite.tensorIso_hom_app_unmop, CategoryTheory.Sheaf.ΓHomEquiv_naturality_left, CategoryTheory.Limits.biproduct.matrixEquiv_apply, CategoryTheory.InjectiveResolution.ι_f_zero_comp_complex_d_assoc, FintypeCat.hom_ext_iff, DerivedCategory.to_singleFunctor_obj_eq_zero_of_injective, CategoryTheory.Cat.rightUnitor_hom_app, CategoryTheory.kernelOpUnop_inv, CategoryTheory.Quiv.lift_obj, CategoryTheory.Limits.Fork.unop_ι_app_one, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π_assoc, CategoryTheory.DifferentialObject.ext_iff, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.g'_eq, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_apply_f, CategoryTheory.Linear.smulOfRingMorphism_smul_eq, CategoryTheory.Preadditive.comp_sum_assoc, HomologicalComplex₂.d₁_eq, CategoryTheory.Oplax.LaxTrans.id_naturality, CategoryTheory.Comon.ComonToMonOpOp_map, MonCat.hom_one, CategoryTheory.Pseudofunctor.ObjectProperty.ι_naturality, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_id, CategoryTheory.Limits.kernelBiprodFstIso_inv, AlgebraicGeometry.Scheme.Spec_map_presheaf_map_eqToHom, CategoryTheory.ShortComplex.Homotopy.smul_h₀, CochainComplex.HomComplex.Cochain.ofHom_neg, CategoryTheory.PreGaloisCategory.instFullContActionFintypeCatHomCarrierAutFunctorFunctorToContAction, CategoryTheory.Pseudofunctor.mapComp_id_right_hom, CategoryTheory.yonedaMonObj_map, Homotopy.prevD_chainComplex, CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_of_mono₃, CategoryTheory.Bicategory.conjugateEquiv_symm_of_iso, CategoryTheory.ShortComplex.homologyMap'_op, SSet.spine_arrow, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp, CategoryTheory.Oplax.StrongTrans.Modification.naturality_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality_assoc, CategoryTheory.ShortComplex.Homotopy.smul_h₃, CategoryTheory.LaxFunctor.mapComp_naturality_right_app_assoc, CategoryTheory.Limits.kernelBiproductToSubtypeIso_hom, CategoryTheory.Subgroupoid.mem_discrete_iff, CategoryTheory.Subfunctor.ofSection_obj, CategoryTheory.uliftYonedaEquiv_naturality, CategoryTheory.OverPresheafAux.OverArrows.map₂_val, CategoryTheory.ShortComplex.cyclesMap_smul, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_associator_hom_as_app, CategoryTheory.Functor.curry₃_obj_map_app_app, CategoryTheory.Grothendieck.map_map, CategoryTheory.Lax.LaxTrans.vComp_naturality_naturality, CategoryTheory.Bicategory.prod_whiskerRight_snd, CategoryTheory.CatEnrichedOrdinary.hComp_id, HomologicalComplex.instQuasiIsoMapOppositeSymmUnopFunctorOp, CategoryTheory.CatCenter.app_add, CategoryTheory.Limits.CokernelCofork.condition, CategoryTheory.conjugateEquiv_counit_symm, CochainComplex.HomComplex.Cochain.zero_v, SimplicialObject.Splitting.IndexSet.eqId_iff_mono, CategoryTheory.Limits.Fork.unop_op_ι, CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_map₂, CategoryTheory.Limits.cokernel.condition, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_hom_τr, CategoryTheory.StrictPseudofunctor.comp_mapId_inv, TopCat.Sheaf.extend_hom_app, CategoryTheory.Functor.map_add, CategoryTheory.OverPresheafAux.YonedaCollection.yonedaEquivFst_eq, CategoryTheory.CatEnrichedOrdinary.hComp_comp, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_val_obj, CategoryTheory.conj_eqToHom_iff_heq', CategoryTheory.NonPreadditiveAbelian.sub_zero, CategoryTheory.op_inv_braiding, CategoryTheory.Limits.opParallelPairIso_hom_app_zero, CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.g, CategoryTheory.Bicategory.Adj.id_τl, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_inr, CategoryTheory.Bicategory.Adj.comp_τl, CategoryTheory.ShortComplex.leftHomologyMap_add, ModuleCat.homAddEquiv_symm_apply_hom, CategoryTheory.IsPushout.zero_bot, CategoryTheory.Limits.BinaryBicone.ofLimitCone_inr, TopCat.Presheaf.map_germ_eq_Γgerm, CategoryTheory.Abelian.LeftResolution.karoubi.F_map_f, CategoryTheory.Preadditive.smul_iso_inv, CategoryTheory.IsPushout.zero_left, CategoryTheory.Pseudofunctor.ObjectProperty.mapId_inv_app, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_map_right_right, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_counitIso, CategoryTheory.PrelaxFunctor.mkOfHomFunctors_toPrelaxFunctorStruct, CategoryTheory.Bicategory.Comonad.comul_assoc_flip_assoc, CategoryTheory.Limits.Fork.IsLimit.homIso_symm_apply, HomotopicalAlgebra.RightHomotopyClass.mk_surjective, CategoryTheory.Limits.Cowedge.condition_assoc, HomologicalComplex.mapBifunctor₁₂.d₂_eq_zero, CategoryTheory.Biprod.unipotentUpper_hom, CategoryTheory.Functor.natTransEquiv_symm_apply_app, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_1, CategoryTheory.Functor.homEquivOfIsLeftKanExtension_symm_apply, AlgebraicGeometry.IsAffineOpen.algebraMap_Spec_obj, CategoryTheory.OplaxFunctor.map₂_associator_app_assoc, CategoryTheory.StrictPseudofunctor.mk'_mapComp, CategoryTheory.Monad.adj_counit, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp, CommRingCat.HomTopology.precompHomeomorph_apply, CategoryTheory.ShortComplex.Homotopy.ofEq_h₂, FintypeCat.id_apply, CategoryTheory.Presieve.preZeroHypercover_X, CategoryTheory.LaxFunctor.map₂_associator_app_assoc, CategoryTheory.Presheaf.functorEnrichedHomCoyonedaObjEquiv_naturality, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_unit, CategoryTheory.Bicategory.conjugateEquiv_comp_id_right_apply, CategoryTheory.Subobject.bot_factors_iff_zero, CategoryTheory.Functor.uncurry_map_app, CategoryTheory.Limits.piConst_obj_map, CategoryTheory.MonoidalPreadditive.whiskerLeft_zero, CategoryTheory.MonoidalOpposite.mopMopEquivalence_inverse_map_unmop_unmop, CategoryTheory.ShortComplex.unopMap_τ₁, CategoryTheory.PreGaloisCategory.functorToContAction_map, CategoryTheory.ActionCategory.uncurry_map, CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans, CategoryTheory.Lax.LaxTrans.id_naturality, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_comp_assoc, HomologicalComplex.iCycles_d, CategoryTheory.NatTrans.removeUnop_app, HomologicalComplex.mapBifunctor₁₂.ιOrZero_eq_zero, CategoryTheory.ShortComplex.LeftHomologyMapData.op_φQ, CategoryTheory.ShortComplex.Homotopy.comm₃, CategoryTheory.NonPreadditiveAbelian.sub_comp, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_assoc, prevD_nat, CategoryTheory.Limits.pullbackZeroZeroIso_inv_fst, CategoryTheory.Bicategory.leftUnitor_inv_whiskerRight, CategoryTheory.InjectiveResolution.extMk_zero, CategoryTheory.Localization.isoOfHom_op_inv, CategoryTheory.ShortComplex.op_pOpcycles_opcyclesOpIso_hom_assoc, CategoryTheory.Idempotents.idem_of_id_sub_idem, ChainComplex.mk_congr_succ_X₃, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality_assoc, CategoryTheory.ShortComplex.homologyMap'_neg, CategoryTheory.CostructuredArrow.toStructuredArrow'_obj, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_associator, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top_assoc, AlgebraicGeometry.ExistsHomHomCompEqCompAux.exists_index, SSet.S.mk_map_eq_iff_of_mono, CategoryTheory.Functor.map_zsmul, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₂_assoc, AlgebraicGeometry.liftCoborder_app, CategoryTheory.CostructuredArrow.prodInverse_obj, CategoryTheory.simplicialCosimplicialEquiv_unitIso_hom_app, CategoryTheory.nerve.homEquiv_comp, CategoryTheory.Limits.pullbackZeroZeroIso_hom_snd, FGModuleCat.instFiniteHom, CategoryTheory.Pretriangulated.Triangle.rotate_mor₃, groupCohomology.cochainsMap_zero, CategoryTheory.pseudofunctorOfIsLocallyDiscrete_obj, CategoryTheory.ShortComplex.homologyι_comp_fromOpcycles_assoc, CategoryTheory.Limits.pullbackIsoOpPushout_inv_fst_assoc, HomologicalComplex.dTo_comp_dFrom, AlgebraicTopology.DoldKan.QInfty_f_comp_PInfty_f, CategoryTheory.nerve.mk₁_homEquiv_apply, CategoryTheory.ShortComplex.LeftHomologyMapData.neg_φH, CategoryTheory.Comonad.coalgebraPreadditive_homGroup_neg_f, CategoryTheory.MorphismProperty.MapFactorizationData.op_Z, CategoryTheory.Preadditive.neg_comp_neg_assoc, CategoryTheory.Preadditive.kernelForkOfFork_ofι, CategoryTheory.Functor.toOplaxFunctor_obj, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_left, CategoryTheory.Bicategory.instIsIsoHomLeftZigzagHom, CategoryTheory.Limits.colimitYonedaHomIsoLimit_π_apply, CategoryTheory.Limits.FintypeCat.productEquiv_symm_comp_π_apply, CategoryTheory.Bicategory.Prod.fst_map₂, HomologicalComplex₂.D₁_shape, CategoryTheory.cokernelUnopOp_hom, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, CategoryTheory.heq_comp_eqToHom_iff, CategoryTheory.Equivalence.sheafCongrPrecoherent_functor_obj_val_map, CategoryTheory.WithTerminal.liftToTerminal_map, CategoryTheory.Precoverage.mem_finite_iff, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_app, AlgebraicGeometry.Spec_map_localization_isIso, CategoryTheory.Bicategory.Equivalence.right_triangle, CategoryTheory.Functor.toPseudoFunctor_mapComp, CategoryTheory.unop_whiskerRight, CategoryTheory.prodFunctor_map, CategoryTheory.Preadditive.neg_comp_neg, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_obj, CategoryTheory.Oplax.OplaxTrans.categoryStruct_id_app, CategoryTheory.Bicategory.InducedBicategory.forget_map, CategoryTheory.ComposableArrows.IsComplex.mono_cokerToKer', CategoryTheory.Pretriangulated.Triangle.sub_hom₁, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_assoc, CategoryTheory.Pseudofunctor.DescentData.instIsIsoαCategoryObjLocallyDiscreteOppositeCatMkOpHom, CategoryTheory.Bicategory.associator_eqToHom_inv, CategoryTheory.Bicategory.Equivalence.left_triangle, CategoryTheory.Limits.coneOfCoconeLeftOp_π_app, CommAlgCat.lift_unop_hom, CategoryTheory.Localization.Preadditive.homEquiv_apply, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app, AlgebraicGeometry.ΓSpec.adjunction_counit_app, SSet.S.le_iff, AddCommGrpCat.homAddEquiv_symm_apply_hom, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app_assoc, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj_condition_assoc, CategoryTheory.Arrow.equivSigma_apply_fst, CategoryTheory.Equivalence.rightOp_inverse_map, CategoryTheory.ShortComplex.RightHomologyMapData.unop_φK, CategoryTheory.InducedCategory.homEquiv_symm_apply_hom, CategoryTheory.OplaxFunctor.mapId'_eq_mapId, CategoryTheory.Under.mapPushoutAdj_unit_app, CategoryTheory.Limits.isColimitOfConeOfCoconeLeftOp_desc, CategoryTheory.Limits.cokernelBiprodInlIso_inv, CategoryTheory.Limits.SequentialProduct.functorMap_commSq_aux, CategoryTheory.DifferentialObject.d_squared, ModuleCat.Tilde.toOpen_res, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one_assoc, AddCommGrpCat.hom_sub, AddGrpCat.zero_apply, CategoryTheory.Presieve.uncurry_singleton, CategoryTheory.Join.mapWhiskerRight_app, CategoryTheory.PrelaxFunctor.map₂_eqToHom, Mathlib.Tactic.Bicategory.naturality_associator, CategoryTheory.Over.opEquivOpUnder_inverse_map, CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIso_inv, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom, CategoryTheory.Equalizer.Presieve.isSheafFor_singleton_iff, CategoryTheory.Presheaf.isLocallyInjective_toSheafify, CommAlgCat.mul_op_of_unop_hom, CategoryTheory.Bicategory.LanLift.existsUnique, CategoryTheory.presheafHom_map_app, CategoryTheory.conjugateEquiv_symm_iso, CategoryTheory.ComposableArrows.IsComplex.zero_assoc, CategoryTheory.ObjectProperty.monoModSerre_zero_iff, CategoryTheory.Oplax.OplaxTrans.categoryStruct_comp_naturality, CategoryTheory.ShortComplex.RightHomologyMapData.zero_φH, CategoryTheory.Limits.opParallelPairIso_hom_app_one, CategoryTheory.Iso.op2_hom_unop2, CategoryTheory.Equivalence.symmEquivFunctor_map, CochainComplex.HomComplex.Cochain.fromSingleMk_add, CategoryTheory.Limits.Cofork.IsColimit.homIso_apply_coe, CategoryTheory.finrank_endomorphism_eq_one, Bicategory.Opposite.bicategory_leftUnitor_inv_unop2, CategoryTheory.CatEnriched.hComp_id_heq, CategoryTheory.Bicategory.Prod.sectR_mapId_inv, CategoryTheory.Limits.isLimitConeOfCoconeUnop_lift, CategoryTheory.Equivalence.sheafCongrPreregular_functor_obj_val_map, CategoryTheory.Functor.toPrefunctor_obj, CategoryTheory.Functor.partialRightAdjointHomEquiv_comp, CategoryTheory.Limits.image.ι_zero, CategoryTheory.Limits.isColimitOfConeUnopOfCocone_desc, CategoryTheory.Abelian.Pseudoelement.zero_morphism_ext, CategoryTheory.Limits.kernel.ι_of_mono, CategoryTheory.Limits.inl_of_isLimit, CategoryTheory.Limits.coend.condition_assoc, CategoryTheory.Pretriangulated.contractibleTriangle_mor₂, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_naturality, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_app, CategoryTheory.Adjunction.conjugateEquiv_leftAdjointIdIso_hom, CategoryTheory.Monad.adj_unit, CategoryTheory.Subfunctor.ofSection_eq_range', CategoryTheory.MonObj.mul_comp, CategoryTheory.simplicialCosimplicialEquiv_counitIso_hom_app_app, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_presheafMap, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zero, groupCohomology.map₁_one, CategoryTheory.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCocone_π_app_eq_sum, CategoryTheory.PrelaxFunctor.map₂_hom_inv, CategoryTheory.Limits.coneOfIsSplitMono_π_app, CategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy.hf, CategoryTheory.Functor.partialRightAdjointHomEquiv_map, CategoryTheory.StrictlyUnitaryLaxFunctor.id_mapComp, CategoryTheory.OplaxFunctor.mapComp_assoc_right_app, AlgebraicGeometry.Scheme.Hom.app_eq, CategoryTheory.linearYoneda_map_app, CategoryTheory.Join.isoMkFunctor_inv_app, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_map_base, TopModuleCat.hom_add, CategoryTheory.Pseudofunctor.StrongTrans.Modification.naturality, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_hom_app_app, CategoryTheory.ReflQuiv.adj.unit.map_app_eq, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp_app, CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse_obj_hom, CategoryTheory.Limits.end_.condition, TopCat.Presheaf.germ_res_assoc, CategoryTheory.Functor.CorepresentableBy.homEquiv_eq, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_right, CategoryTheory.PreGaloisCategory.fiberBinaryProductEquiv_symm_fst_apply, CommRingCat.moduleCatRestrictScalarsPseudofunctor_map, CategoryTheory.ShortComplex.Splitting.g_s, HomologicalComplex.opcyclesOpIso_hom_naturality_assoc, CategoryTheory.Abelian.LeftResolution.karoubi.F'_obj_p, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_hom_app, AlgebraicGeometry.Spec.map_preimage_unop, CategoryTheory.Hom.mul_def, CategoryTheory.Limits.opCoproductIsoProduct'_inv_comp_inj, CochainComplex.IsKInjective.homotopyZero_def, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app, CategoryTheory.ShortComplex.Homotopy.ofEq_h₀, CategoryTheory.ShortComplex.HomologyMapData.zero_left, CategoryTheory.Grp.Hom.hom_hom_inv, HomologicalComplex.opcyclesToCycles_homologyπ, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app, CategoryTheory.MonoidalCategory.dite_whiskerRight, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_inv_app_app, CommRingCat.HomTopology.isEmbedding_pushout, CategoryTheory.Presieve.preZeroHypercover_f, CategoryTheory.Limits.CokernelCofork.mapIsoOfIsColimit_inv, CategoryTheory.Localization.SmallHom.equiv_mkInv, CategoryTheory.ComposableArrows.opEquivalence_functor_obj_map, SSet.Truncated.StrictSegal.spine_δ_arrow_lt, CategoryTheory.SimplicialObject.σ_def, CategoryTheory.Bicategory.pentagon_inv_inv_hom_hom_inv, AlgebraicGeometry.IsLocalIso.le_of_isLocalAtSource, CategoryTheory.Subgroupoid.mem_map_iff, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₁, CategoryTheory.Adjunction.homAddEquiv_sub, CategoryTheory.tensorLeftHomEquiv_tensor, CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_of_epi₁, CategoryTheory.Presheaf.restrictedULiftYoneda_map_app, CategoryTheory.Pseudofunctor.StrongTrans.homCategory_id_as_app, SSet.Subcomplex.yonedaEquiv_coe, CategoryTheory.Pseudofunctor.isPrestackFor_ofArrows_iff, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan_inv_app_app_apply_eq_id, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_assoc, CategoryTheory.CosimplicialObject.Augmented.leftOp_left_map, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac, CategoryTheory.Limits.biprod.sndKernelFork_ι, ComplexShape.Embedding.AreComplementary.hom_ext, CategoryTheory.Limits.spanOp_inv_app, CategoryTheory.Presheaf.isSeparated_iff_subsingleton, CategoryTheory.Preadditive.forkOfKernelFork_pt, CategoryTheory.FreeBicategory.mk_left_unitor_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app_assoc, SimplicialObject.Splitting.IndexSet.mk_fst, CategoryTheory.Equivalence.rightOp_unitIso_hom_app, AddCommGrpCat.hom_nsmul, HomotopyCategory.quot_mk_eq_quotient_map, CategoryTheory.Join.pseudofunctorLeft_mapComp_inv_toNatTrans_app, CategoryTheory.PreGaloisCategory.instIsEquivalenceContActionFintypeCatHomCarrierAutFunctorFunctorToContAction, CategoryTheory.eqToHom_comp_heq_iff, CochainComplex.HomComplex.Cocycle.toSingleMk_zero, HomologicalComplex.units_smul_f_apply, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv, HomologicalComplex.quasiIsoAt_unopFunctor_map_iff, CategoryTheory.Limits.reflexivePair.compRightIso_hom_app, CategoryTheory.RanIsSheafOfIsCocontinuous.fac_assoc, CategoryTheory.Preadditive.sum_comp, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_assoc, AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zero, CategoryTheory.CatEnrichedOrdinary.Hom.mk_comp, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_apply_fst, AlgebraicGeometry.Scheme.Modules.restrict_map, CategoryTheory.Pseudofunctor.CoGrothendieck.map_obj_fiber, TopCat.Sheaf.objSupIsoProdEqLocus_hom_fst, CategoryTheory.Functor.partialLeftAdjointHomEquiv_map, CategoryTheory.Limits.ker.condition, HomologicalComplex.homotopyCofiber.inrX_fstX, CochainComplex.HomComplex.Cochain.leftUnshift_v, CommAlgCat.fst_unop_hom, CategoryTheory.Limits.BinaryBicone.inr_fst_assoc, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_three, DerivedCategory.HomologySequence.comp_δ_assoc, CategoryTheory.Limits.Fork.op_pt, CategoryTheory.Comma.equivProd_inverse_map_left, Quiver.FreeGroupoid.lift_spec, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_map_assoc, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapIdIso_inv, SheafOfModules.freeHomEquiv_symm_comp, CategoryTheory.WithTerminal.map_map, CategoryTheory.cokernel.π_unop, CategoryTheory.oplaxFunctorOfIsLocallyDiscrete_map, CategoryTheory.CosimplicialObject.cechConerveEquiv_symm_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality', CategoryTheory.Pseudofunctor.whiskerLeftIso_mapId, CategoryTheory.Limits.biprod.decomp_hom_from, CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIsoWhisker_hom_right, CategoryTheory.Functor.map_smul, CategoryTheory.Iso.homCongr_refl, CategoryTheory.Bicategory.Prod.swap_map, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_uliftYoneda_map, CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_hom_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHom, CategoryTheory.InitiallySmall.exists_small_weakly_initial_set, CategoryTheory.Bicategory.Pith.rightUnitor_hom_iso, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_id_assoc, CochainComplex.ConnectData.map_f, CategoryTheory.Functor.map_shift_unop, CategoryTheory.Functor.Additive.map_add, CategoryTheory.PreGaloisCategory.toAut_surjective_isGalois, CategoryTheory.Bicategory.Comonad.counit_comul_assoc, CategoryTheory.OplaxFunctor.mapComp_assoc_left, CategoryTheory.Join.opEquiv_functor_map_op_edge, CategoryTheory.ShortComplex.SnakeInput.L₀X₂ToP_comp_φ₁, Bicategory.Opposite.op2_rightUnitor_inv, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_app, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp_assoc, CategoryTheory.Pseudofunctor.id_mapId, CategoryTheory.yonedaMonObj_obj_coe, CategoryTheory.Functor.map_eq_zero_iff, CategoryTheory.Discrete.productEquiv_counitIso_hom_app, CategoryTheory.Functor.homologySequence_epi_shift_map_mor₁_iff, CategoryTheory.Functor.toPrefunctor_comp, SimplicialObject.Splitting.cofan_inj_comp_PInfty_eq_zero, CategoryTheory.Presheaf.app_localPreimage, HomologicalComplex.opcyclesOpIso_hom_toCycles_op, CategoryTheory.Pseudofunctor.DescentData.Hom.comm_assoc, SemiNormedGrp.hom_add, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_comp_map, SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zero, CategoryTheory.Biprod.unipotentLower_hom, CategoryTheory.BicategoricalCoherence.right'_iso, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map, CategoryTheory.Lax.LaxTrans.naturality_comp_assoc, CategoryTheory.Join.mapIsoWhiskerRight_hom_app, CategoryTheory.ShortComplex.Exact.leftHomologyDataOfIsLimitKernelFork_K, CategoryTheory.Limits.zero_of_to_zero, CategoryTheory.unop_inv_leftUnitor, Action.FintypeCat.toEndHom_apply, CategoryTheory.Bicategory.pentagon_assoc, CategoryTheory.Limits.Fork.ofι_π_app, ContinuousMap.yonedaPresheaf_map, CategoryTheory.Functor.op_commShiftIso_hom_app_assoc, CategoryTheory.Functor.FullyFaithful.compYonedaCompWhiskeringLeftMaxRight_inv_app_app, CategoryTheory.Paths.of_map, CategoryTheory.isIso_op, CategoryTheory.WithInitial.prelaxfunctor_toPrelaxFunctorStruct_toPrefunctor_obj, CategoryTheory.yoneda_obj_obj, CategoryTheory.Join.opEquiv_functor_map_op_inclRight, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_inv_app, CategoryTheory.uliftYonedaEquiv_comp, CategoryTheory.Limits.biprod.desc_eq, SSet.stdSimplex.face_obj, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app_assoc, CategoryTheory.Bicategory.Adj.id_τr, CategoryTheory.Functor.sectionsEquivHom_naturality, Homotopy.nullHomotopicMap_f, CategoryTheory.Subgroupoid.IsWide.wide, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff, CategoryTheory.Limits.snd_of_isColimit, CategoryTheory.Oplax.StrongTrans.Modification.id_app, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₃₁, CategoryTheory.Bicategory.prod_rightUnitor_inv_fst, CategoryTheory.Limits.Cofork.op_π_app_zero, AlgebraicGeometry.Scheme.kerAdjunction_counit_app, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_of_epi₂, CategoryTheory.Limits.opSpan_hom_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHom_unop, CategoryTheory.Subgroupoid.isThin_iff, CategoryTheory.Limits.π_comp_colimitLeftOpIsoUnopLimit_inv_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionActionOfMonoidalFunctorToEndofunctorMopIso_inv_app_unmop_app, CategoryTheory.Adjunction.restrictFullyFaithful_homEquiv_apply, CategoryTheory.Limits.biproduct.lift_desc, SSet.stdSimplex.map_apply, HomologicalComplex.d_toCycles, CategoryTheory.LaxFunctor.mapComp'_eq_mapComp, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app_assoc, CategoryTheory.CartesianClosed.homEquiv_symm_apply_eq, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom, CategoryTheory.Limits.isColimitCoconeUnopOfCone_desc, CochainComplex.HomComplex.Cochain.ofHom_sub, CategoryTheory.conjugateEquiv_whiskerRight, LightCondensed.isoFinYonedaComponents_inv_comp, HomologicalComplex.opFunctor_map_f, CategoryTheory.LocalizerMorphism.LeftResolution.unop_w, CategoryTheory.Oplax.LaxTrans.naturality_comp, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_hom_τl, CategoryTheory.WithInitial.prelaxfunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.bijection_symm_apply_id, SSet.Truncated.spine_map_vertex, CategoryTheory.MonoidalPreadditive.add_tensor, AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, TopModuleCat.hom_zsmul, CategoryTheory.ShortComplex.opcyclesMap_neg, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app, CategoryTheory.Limits.id_zero, CategoryTheory.Free.single_comp_single, CategoryTheory.Functor.homObjFunctor_map_app, CategoryTheory.Functor.toPseudoFunctor_map, CategoryTheory.Limits.cokernelBiprodInrIso_inv, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy₂'_homEquiv, CategoryTheory.IsPushout.inr_fst, CategoryTheory.Pretriangulated.contractible_distinguished₂, Rep.resIndAdjunction_homEquiv_symm_apply, CategoryTheory.MorphismProperty.LeftFraction.unop_f, CategoryTheory.Functor.isRepresentedBy_iff, CategoryTheory.instIsSplitEpiOppositeOpOfIsSplitMono, CategoryTheory.ShortComplex.fromOpcycles_op_cyclesOpIso_inv_assoc, CategoryTheory.ShortComplex.homologyι_descOpcycles_eq_zero_of_boundary, CategoryTheory.Localization.homEquiv_comp, CategoryTheory.ShortComplex.Homotopy.symm_h₀, CategoryTheory.rightDistributor_inv, CategoryTheory.quotientPathsTo_obj, CategoryTheory.Limits.limitUnopIsoUnopColimit_inv_comp_π_assoc, CategoryTheory.Bicategory.whiskerLeft_isIso, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_fst, CategoryTheory.Enriched.FunctorCategory.homEquiv_comp, Action.hom_injective, CategoryTheory.ShortComplex.Homotopy.equivSubZero_symm_apply, CategoryTheory.Limits.whiskeringLimYonedaIsoCones_inv_app_app, CategoryTheory.Oplax.StrongTrans.isoMk_hom_as_app, CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp, CategoryTheory.Functor.homologySequenceδ_comp_assoc, Action.nsmul_hom, classifyingSpaceUniversalCover_map, HomologicalComplex.d_pOpcycles_assoc, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app'_assoc, CategoryTheory.Bicategory.conjugateIsoEquiv_apply_inv, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left_assoc, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id_app, CategoryTheory.SemiadditiveOfBinaryBiproducts.isUnital_leftAdd, CategoryTheory.CostructuredArrow.w_prod_snd, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_functor_map, CategoryTheory.ShortComplex.rightHomologyMap'_op, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_inv_app, CategoryTheory.IsPullback.inl_snd, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₁_assoc, CategoryTheory.ShortComplex.opcyclesOpIso_hom_toCycles_op_assoc, CategoryTheory.PrelaxFunctor.map₂_inv_hom_isIso, CategoryTheory.Pseudofunctor.mapComp'_hom_naturality_assoc, CategoryTheory.ProjectiveResolution.of_def, CommRingCat.HomTopology.instT2SpaceHomOfCarrier, CategoryTheory.Pseudofunctor.mapComp'_naturality_2_assoc, CategoryTheory.Pseudofunctor.Grothendieck.categoryStruct_id_fiber, HomologicalComplex₂.totalAux.d₂_eq', CategoryTheory.IsCofiltered.inf_objs_exists, CategoryTheory.Bicategory.eqToHomTransIso_refl_right, CategoryTheory.Limits.colimitCoyonedaHomIsoLimitUnop_π_apply, CategoryTheory.Pseudofunctor.ObjectProperty.map_map_hom, CompHausLike.LocallyConstant.functorToPresheaves_map_app, CategoryTheory.Functor.corepresentableByUliftFunctorEquiv_apply_homEquiv, TopologicalSpace.OpenNhds.id_apply, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_assoc, CategoryTheory.factorThruImage_comp_imageUnopOp_inv, CategoryTheory.Functor.homologySequence_mono_shift_map_mor₁_iff, Homotopy.zero, CondensedSet.topCatAdjunctionUnit_val_app_apply, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_right, Rep.coindMap'_hom, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_naturality_app, CategoryTheory.composePath_comp, CategoryTheory.Limits.imageSubobject_zero_arrow, CategoryTheory.Functor.map_sub, CategoryTheory.Localization.Construction.lift_map, CategoryTheory.ProjectiveResolution.π_f_succ, CategoryTheory.ShortComplex.rightHomologyι_comp_fromOpcycles_assoc, HomologicalComplex₂.totalAux.d₁_eq, CategoryTheory.Limits.limitRightOpIsoOpColimit_hom_comp_ι, CategoryTheory.CatEnriched.hComp_assoc, CategoryTheory.ShortComplex.opcyclesOpIso_hom_naturality, CategoryTheory.yonedaEquiv_yoneda_map, CategoryTheory.Limits.opProdIsoCoprod_inv_inl, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_inv_app_unmop, Preorder.subsingleton_hom, CategoryTheory.OverPresheafAux.unitForward_naturality₂, CategoryTheory.Bicategory.pentagon_inv_inv_hom_inv_inv, CategoryTheory.PrelaxFunctor.map₂_inv_hom_isIso_assoc, CategoryTheory.Limits.isLimitOfCoconeLeftOpOfCone_lift, CategoryTheory.kernelCokernelCompSequence.inr_φ_fst_assoc, CategoryTheory.IsPushout.of_hasBinaryCoproduct, CategoryTheory.unop_comp, CategoryTheory.Idempotents.zero_def, CategoryTheory.Subgroupoid.IsNormal.generatedNormal_le, HomologicalComplex₂.D₁_totalShift₂XIso_hom_assoc, CategoryTheory.Pseudofunctor.CoGrothendieck.Hom.congr, CategoryTheory.Abelian.Ext.mk₀_add, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app_assoc, CategoryTheory.IsPullback.of_hasBinaryProduct, CategoryTheory.Limits.BinaryFan.unop_mk, CategoryTheory.Quotient.functor_homRel_eq_compClosure_eqvGen, CategoryTheory.Limits.imageSubobject_zero, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_app, CategoryTheory.Limits.KernelFork.mapIsoOfIsLimit_inv, AlgebraicGeometry.SheafedSpace.ofRestrict_hom_c_app, CategoryTheory.ShortComplex.rightHomologyι_descOpcycles_π_eq_zero_of_boundary, CategoryTheory.unit_conjugateEquiv_symm, CategoryTheory.CategoryOfElements.comp_val, HomologicalComplex.liftCycles_homologyπ_eq_zero_of_boundary, CategoryTheory.CatEnrichedOrdinary.Hom.id_eq, Homotopy.extend.hom_eq_zero₁, CategoryTheory.PreGaloisCategory.evaluation_aut_bijective_of_isGalois, CategoryTheory.Limits.opCompYonedaSectionsEquiv_apply_app, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app_assoc, SSet.StrictSegal.spineToSimplex_interval, CategoryTheory.Grpd.freeForgetAdjunction_homEquiv_symm_apply, CategoryTheory.Mon_Class.mul_eq_mul, CategoryTheory.Lax.LaxTrans.naturality_id_assoc, CategoryTheory.Groupoid.vertexGroup_one, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_map_hom, CategoryTheory.LaxFunctor.mapComp_naturality_right_assoc, CategoryTheory.Limits.BinaryFan.rightUnitor_inv, AlgebraicGeometry.Scheme.Hom.appIso_inv_app, prevD_eq, CategoryTheory.WideSubcategory.comp_def, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id, CategoryTheory.Preadditive.comp_neg_assoc, CategoryTheory.FreeBicategory.preinclusion_map₂, CategoryTheory.OplaxFunctor.mapComp'_comp_mapComp'_whiskerRight, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_inv_iso_inv, HomologicalComplex.mapBifunctor.d₂_eq, CategoryTheory.Bicategory.prod_whiskerLeft_fst, CategoryTheory.Oplax.OplaxTrans.rightUnitor_hom_as_app, CommRingCat.HomTopology.precompHomeomorph_symm_apply, CategoryTheory.MorphismProperty.LeftFraction.op_f, TopCat.Presheaf.map_germ_eq_Γgerm_assoc, AlgebraicGeometry.Scheme.stalkMap_congr_hom_assoc, CategoryTheory.Limits.pushoutIsoOpPullback_inv_fst, CategoryTheory.unit_conjugateEquiv, HomologicalComplex.instQuasiIsoAtOppositeMapSymmOpFunctorOp, CategoryTheory.OplaxFunctor.map₂_associator_assoc, CategoryTheory.Bicategory.precomp_obj, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct_assoc, AlgebraicTopology.AlternatingCofaceMapComplex.d_squared, CategoryTheory.Free.embedding_map, CategoryTheory.Limits.biprod.total, CategoryTheory.Limits.cokernel.π_of_zero, CategoryTheory.Grothendieck.grothendieckTypeToCatFunctor_map_coe, CategoryTheory.ShortComplex.RightHomologyData.unop_f', CategoryTheory.Pseudofunctor.map₂_whisker_left, CategoryTheory.Limits.BinaryFan.op_mk, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_pt, CategoryTheory.uliftYoneda_obj_map, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_right, TopCat.Sheaf.interUnionPullbackConeLift_right, CategoryTheory.Quiv.adj_homEquiv, CategoryTheory.Triangulated.TStructure.zero, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_inv_app_app, CategoryTheory.Groupoid.isoEquivHom_apply, CategoryTheory.Enriched.FunctorCategory.homEquiv_id, CategoryTheory.regularTopology.mapToEqualizer_eq_comp, CategoryTheory.Groupoid.invEquivalence_functor_map, HomologicalComplex.ι_mapBifunctorFlipIso_inv_assoc, CategoryTheory.Groupoid.isoEquivHom_symm_apply_hom, HomologicalComplex.extend_single_d, CategoryTheory.LaxFunctor.mapComp'_whiskerRight_comp_mapComp'_assoc, CategoryTheory.projective_iff_llp_epimorphisms_zero, AlgebraicGeometry.Scheme.Hom.map_appLE_assoc, CategoryTheory.ComposableArrows.opEquivalence_functor_map_app, CategoryTheory.ShortComplex.liftCycles_leftHomologyπ_eq_zero_of_boundary_assoc, HomologicalComplex.mapBifunctor.d₁_eq_zero, CategoryTheory.GrothendieckTopology.map_yonedaEquiv', CategoryTheory.Pseudofunctor.StrongTrans.isoMk_hom_as_app, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_symm_apply_φ, CategoryTheory.Bicategory.adjointifyCounit_left_triangle, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_assoc, SSet.Truncated.Edge.src_eq, CategoryTheory.EnrichedOrdinaryCategory.homEquiv_id, CategoryTheory.PreGaloisCategory.instFiniteHomOfIsConnected, CategoryTheory.Localization.homEquiv_symm_apply, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τl, CategoryTheory.rightUnitor_def, CategoryTheory.kernelUnopOp_hom, Rep.freeLiftLEquiv_apply, CategoryTheory.Functor.curry₃_obj_obj_obj_map, CategoryTheory.SimplicialObject.Augmented.rightOp_right_map, CategoryTheory.ShortComplex.rightHomologyMap'_add, CategoryTheory.Groupoid.invEquiv_apply, HomologicalComplex₂.d₁_eq_zero, CategoryTheory.Lax.StrongTrans.toLax_naturality, CategoryTheory.Functor.mapComposableArrowsObjMk₂Iso_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app, CommRingCat.HomTopology.isClosedEmbedding_hom, CategoryTheory.WithInitial.coconeEquiv_functor_map_hom, HomologicalComplex.zsmul_f_apply, groupCohomology.mapCocycles₁_one, CategoryTheory.ObjectProperty.epiModSerre_zero_iff, CategoryTheory.Subgroupoid.hom.faithful, CategoryTheory.eHomFunctor_map_app, SSet.Truncated.HomotopyCategory₂.homMk_surjective, CategoryTheory.HomOrthogonal.matrixDecompositionLinearEquiv_symm_apply, CategoryTheory.unitCompPartialBijective_natural, CategoryTheory.SimplicialThickening.functor_map, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id, CategoryTheory.WithTerminal.ofCommaMorphism_app, CochainComplex.singleFunctor_obj_d, CategoryTheory.uliftYoneda_obj_obj, CategoryTheory.typeEquiv_counitIso_inv_app_val_app, CategoryTheory.ShortComplex.homologyOpIso_hom_naturality_assoc, CategoryTheory.Pseudofunctor.toOplax_mapId, CategoryTheory.op_id_unop, CategoryTheory.dite_comp, CategoryTheory.Endofunctor.algebraPreadditive_homGroup_zsmul_f, CategoryTheory.ShortComplex.LeftHomologyData.f'_π, CategoryTheory.Limits.CokernelCofork.mapIsoOfIsColimit_hom, CategoryTheory.FinCategory.objAsTypeToAsType_map, AlgebraicGeometry.Scheme.Hom.map_appLE'_assoc, CategoryTheory.Subobject.mk_eq_bot_iff_zero, CategoryTheory.Localization.SmallHom.equiv_mk, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal, CategoryTheory.eqToHom_comp_heq, CategoryTheory.Preadditive.instMonoNegHom, CategoryTheory.Bicategory.prod_associator_inv_fst, HomologicalComplex.homologyMap_add, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_inv, CategoryTheory.PrelaxFunctor.map₂_hom_inv_assoc, Mathlib.Tactic.Bicategory.evalWhiskerLeft_of_cons, CategoryTheory.tensorRightHomEquiv_symm_coevaluation_comp_whiskerLeft, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map, CategoryTheory.Limits.HasZeroObject.zeroIsoIsTerminal_hom, CategoryTheory.Limits.π_comp_colimitOpIsoOpLimit_inv_assoc, HomotopicalAlgebra.LeftHomotopyClass.mk_surjective, CategoryTheory.Pretriangulated.Triangle.neg_hom₁, CategoryTheory.StrictlyUnitaryLaxFunctor.mapId_eq_eqToHom, SheafOfModules.freeHomEquiv_comp_apply, ContinuousCohomology.MultiInd.d_comp_d_assoc, CategoryTheory.yonedaMon_map_app, SemiNormedGrp.hom_neg, CategoryTheory.shrinkYonedaEquiv_naturality, AlgebraicGeometry.Scheme.zeroLocus_map, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id, CategoryTheory.OplaxFunctor.mapComp_naturality_left_app, AlgebraicGeometry.Scheme.AffineZariskiSite.coequifibered_iff_forall_isLocalizationAway, AlgebraicGeometry.AffineSpace.homOfVector_toSpecMvPoly_assoc, CategoryTheory.Presheaf.imageSieve_apply, HomologicalComplex.extend_d_to_eq_zero, CategoryTheory.yonedaEquiv_naturality', CategoryTheory.Bicategory.InducedBicategory.bicategory_Hom, CategoryTheory.StrictlyUnitaryLaxFunctor.map_id, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerLeft_naturality, Action.sub_hom, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app_assoc, CategoryTheory.OverPresheafAux.restrictedYonedaObj_map, FintypeCat.toLightProfinite_map_hom_hom_apply, CategoryTheory.BicategoricalCoherence.tensorRight'_iso, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_functor_obj, CategoryTheory.Subgroupoid.mem_ker_iff, CategoryTheory.oplaxFunctorOfIsLocallyDiscrete_obj, CategoryTheory.Types.instPreservesLimitsOfSizeForgetTypeHom, PresheafOfModules.toSheaf_map_sheafificationHomEquiv_symm, CategoryTheory.Bicategory.prod_Hom, CategoryTheory.Bicategory.Pith.whiskerRight_iso_hom, CategoryTheory.Functor.mapZeroObject_inv, CategoryTheory.Bicategory.comp_whiskerRight_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv, CategoryTheory.Functor.cocones_obj, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero, CategoryTheory.Limits.compCoyonedaSectionsEquiv_symm_apply_coe, CategoryTheory.tensorHom_def, CategoryTheory.Enriched.Functor.functorHom_whiskerLeft_natTransEquiv_symm_app, CategoryTheory.Limits.coker.condition, CategoryTheory.cokernel.π_op, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply', CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app_assoc, HomologicalComplex.nsmul_f_apply, CategoryTheory.Types.instIsEquivalenceForgetTypeHom, CategoryTheory.NatTrans.mapElements_map_coe, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv, AlgebraicGeometry.Scheme.homOfLE_appTop, CategoryTheory.comp_eqToHom_heq_iff, CategoryTheory.Bicategory.hom_inv_whiskerRight_whiskerRight, Rep.FiniteCyclicGroup.chainComplexFunctor_map_f, CategoryTheory.Bicategory.Pith.rightUnitor_inv_iso_inv, CategoryTheory.Bicategory.LeftExtension.whiskerIdCancel_right, CategoryTheory.Bicategory.prod_rightUnitor_inv_snd, CategoryTheory.Pretriangulated.Triangle.neg_hom₃, CategoryTheory.NatTrans.app_zero, CategoryTheory.NatTrans.prod'_app_fst, CategoryTheory.cosimplicialSimplicialEquiv_functor_map_app, CategoryTheory.Limits.isLimitConeUnopOfCocone_lift, CategoryTheory.Linear.comp_units_smul, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_fst, CategoryTheory.ShortComplex.Homotopy.refl_h₁, CategoryTheory.RanIsSheafOfIsCocontinuous.fac', AlgebraicGeometry.IsAffineOpen.fromSpec_app_self, AlgebraicGeometry.Spec.toPresheafedSpace_map_op, CategoryTheory.ShortComplex.Exact.shortExact, CategoryTheory.Functor.toPreimages_map, CategoryTheory.Bicategory.Pith.associator_hom_iso, CategoryTheory.Limits.KernelFork.condition, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app, CategoryTheory.Limits.opCospan_hom_app, CategoryTheory.Presheaf.FamilyOfElementsOnObjects.IsCompatible.familyOfElements_apply, SSet.Truncated.StrictSegal.spine_δ_arrow_gt, CategoryTheory.Limits.biproduct.fromSubtype_π, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app'_assoc, CategoryTheory.uliftYonedaEquiv_uliftYoneda_map, CategoryTheory.Comon.MonOpOpToComonObj_comon_comul, CategoryTheory.Localization.SmallShiftedHom.equiv_shift', CategoryTheory.Limits.kernel.ι_of_zero, prevD_eq_zero, CategoryTheory.finrank_hom_simple_simple_eq_zero_iff, CategoryTheory.MonObj.one_comp, CategoryTheory.yoneda_obj_map, CategoryTheory.Quotient.compClosure.congruence, CategoryTheory.Cat.opFunctorInvolutive_hom_app_toFunctor_map, CategoryTheory.Lax.LaxTrans.naturality_id, AlgebraicGeometry.ΓSpec.unop_locallyRingedSpaceAdjunction_counit_app', CategoryTheory.ShortComplex.exact_and_epi_g_iff_g_is_cokernel, CategoryTheory.Functor.IsCartesian.universal_property, CategoryTheory.Pseudofunctor.DescentData.ofObj_obj, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_functor_map_f, CategoryTheory.Adjunction.mkOfHomEquiv_unit_app, CategoryTheory.Lax.StrongTrans.naturality_comp_assoc, CategoryTheory.Bicategory.associator_naturality_left_assoc, CategoryTheory.finrank_hom_simple_simple_eq_zero_of_not_iso, CategoryTheory.StrictPseudofunctorCore.map₂_right_unitor, Condensed.epi_iff_locallySurjective_on_compHaus, instIsMonHomOppositeCommAlgCatOpOfHomToAlgHomBialgHom, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_rightUnitor_inv_as_app, groupCohomology.mapShortComplexH2_zero, CategoryTheory.Bicategory.prod_leftUnitor_inv_fst, CategoryTheory.Bicategory.triangle_assoc_comp_right_inv_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_app_assoc, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv, HomologicalComplex.fromOpcycles_op_cyclesOpIso_inv_assoc, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagramOfIsLimit_map, CategoryTheory.NonPreadditiveAbelian.add_zero, CategoryTheory.Limits.Fork.IsLimit.homIso_apply_coe, CategoryTheory.Adjunction.instMonoCoeEquivHomObjHomEquivOfReflectsMonomorphisms, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₂, CategoryTheory.Bicategory.hom_inv_whiskerRight, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_symm_app, CategoryTheory.InducedCategory.homAddEquiv_symm_apply_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app, CategoryTheory.Bicategory.prod_rightUnitor_hom_fst, CategoryTheory.Bicategory.Adjunction.left_triangle, DerivedCategory.HomologySequence.epi_homologyMap_mor₁_iff, Quiver.FreeGroupoid.congr_comp_reverse, CategoryTheory.cokernelOpUnop_inv, CategoryTheory.LocalizerMorphism.equiv_smallHomMap', Rep.resIndAdjunction_homEquiv_apply, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id_val_app, CommRingCat.HomTopology.mvPolynomialHomeomorph_symm_apply_hom, CategoryTheory.coyonedaEquiv_naturality, CategoryTheory.CategoryOfElements.fromCostructuredArrow_obj_snd, Opens.mayerVietorisSquare_X₂, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheaf_map, LightCondensed.isLocallySurjective_iff_locallySurjective_on_lightProfinite, CategoryTheory.Pseudofunctor.CoGrothendieck.ext_iff, CategoryTheory.GrothendieckTopology.yonedaEquiv_comp, HomologicalComplex₂.D₁_totalShift₁XIso_hom_assoc, CategoryTheory.oppositeShiftFunctorZero_inv_app, CategoryTheory.SemiadditiveOfBinaryBiproducts.add_comp, CategoryTheory.HomOrthogonal.matrixDecompositionLinearEquiv_apply, CategoryTheory.Limits.PushoutCocone.mk_ι_app, CategoryTheory.coyonedaEquiv_apply, CategoryTheory.Lax.OplaxTrans.naturality_naturality, PresheafOfModules.pushforward_obj_map_apply, CategoryTheory.InjectiveResolution.ι_f_zero_comp_complex_d, CochainComplex.HomComplex.CohomologyClass.equiv_toSmallShiftedHom_mk, CategoryTheory.Limits.compCoyonedaSectionsEquiv_apply_app, CategoryTheory.Limits.kernelOrderHom_coe, SemimoduleCat.homAddEquiv_apply, CategoryTheory.op_comp_assoc, AddGrpCat.ofHom_injective, CategoryTheory.PreZeroHypercover.shrink_X, AlgebraicGeometry.Scheme.Hom.app_invApp', CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_hom_app, CategoryTheory.Functor.PreservesHomology.preservesCokernels, groupHomology.d₁₀_comp_coinvariantsMk, AlgebraicGeometry.LocallyRingedSpace.Hom.ext_iff, CategoryTheory.ShortComplex.HasLeftHomology.of_hasCokernel, CategoryTheory.Preadditive.cokernelCoforkOfCofork_π, CategoryTheory.LaxFunctor.whiskerLeft_mapComp'_comp_mapComp', CategoryTheory.Limits.biproduct.toSubtype_fromSubtype, CategoryTheory.Bicategory.Prod.fst_mapId_hom, CategoryTheory.Bicategory.triangle_assoc_comp_right_inv, CategoryTheory.Bicategory.associator_naturality_middle, CategoryTheory.Functor.IsStronglyCartesian.universal_property', CategoryTheory.MonObj.comp_pow, HomologicalComplex.homologyOp_hom_naturality_assoc, CategoryTheory.Bicategory.prod_id_snd, CategoryTheory.Presheaf.isLocallyInjective_forget_iff, CategoryTheory.Functor.comp_homologySequenceδ, CategoryTheory.regularTopology.isLocallySurjective_iff, CategoryTheory.StructuredArrow.toCostructuredArrow_map, CategoryTheory.Pseudofunctor.DescentData.hom_comp_assoc, DerivedCategory.HomologySequence.mono_homologyMap_mor₂_iff, CategoryTheory.Limits.cokernelBiprodInrIso_hom, CategoryTheory.Limits.kernel.condition, CategoryTheory.ShortComplex.cyclesOpIso_inv_naturality, HomologicalComplex.homotopyCofiber.inlX_desc_f_assoc, CategoryTheory.MonoOver.bot_arrow_eq_zero, CategoryTheory.ShortComplex.LeftHomologyData.wπ_assoc, CategoryTheory.WithInitial.equivComma_inverse_map_app, CategoryTheory.Biprod.column_nonzero_of_iso, SimplicialObject.Splitting.πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty, CategoryTheory.kernel.ι_unop, CategoryTheory.Pseudofunctor.Grothendieck.map_obj_fiber, CategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy.g', CategoryTheory.ShortComplex.smul_τ₃, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_hom_app_coe, CochainComplex.HomComplex.Cochain.fromSingleMk_zero, CategoryTheory.Oplax.LaxTrans.vComp_naturality_comp, CategoryTheory.ShortComplex.Splitting.unop_r, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp_assoc, CategoryTheory.ShortComplex.homologyMap_neg, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp_assoc, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp, CochainComplex.mappingCone.decomp_from, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp, CategoryTheory.Subgroupoid.IsWide.id_mem, CochainComplex.mappingCone.inl_v_triangle_mor₃_f_assoc, CategoryTheory.Comma.unopFunctor_obj, AlgebraicTopology.DoldKan.P_succ, CategoryTheory.Limits.colimitHomIsoLimitYoneda_hom_comp_π_assoc, CategoryTheory.Bicategory.prod_leftUnitor_inv_snd, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_app_assoc, HomologicalComplex.homotopyCofiber.d_fstX, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_map, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_functor_map, CategoryTheory.unop_neg, CategoryTheory.StrictPseudofunctor.comp_map, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_hom_τl, FGModuleCat.ihom_obj, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₁, CategoryTheory.Bicategory.LeftExtension.IsKan.fac_assoc, SimplicialObject.Splitting.cofan_inj_πSummand_eq_id, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_pt, CategoryTheory.CategoryOfElements.ext_iff, AlgebraicGeometry.RingedSpace.isUnit_res_of_isUnit_germ, CategoryTheory.WithTerminal.isLimitEquiv_symm_apply_lift, CategoryTheory.Limits.biprod.inl_snd, CategoryTheory.Limits.Wedge.condition, CategoryTheory.Bicategory.leftUnitorNatIso_hom_app, CategoryTheory.ShortComplex.Exact.rightHomologyDataOfIsColimitCokernelCofork_Q, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_obj_fiber, CategoryTheory.Iso.unop2_op_inv, CategoryTheory.Abelian.extFunctor_map_app, CochainComplex.mappingCone.inr_triangleδ_assoc, CategoryTheory.PrelaxFunctor.map₂_inv, CategoryTheory.Iso.unop_hom_inv_id_app, CategoryTheory.Biprod.ofComponents_comp, CategoryTheory.StrictPseudofunctorPreCore.map_comp, CategoryTheory.ShortComplex.HomologyMapData.zero_right, CategoryTheory.Limits.limit.existsUnique, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_inv_τl, CochainComplex.mappingCone.inl_v_snd_v_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHomLeft_op, CategoryTheory.ShortComplex.Homotopy.symm_h₃, CategoryTheory.regularTopology.parallelPair_pullback_initial, CategoryTheory.StrictPseudofunctor.mk''_map, HomologicalComplex.cylinder.inlX_π, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_inverse_map, CategoryTheory.Grp_Class.zpow_comp, Rep.leftRegularHomEquiv_symm_apply, CategoryTheory.Oplax.StrongTrans.naturality_naturality_assoc, CategoryTheory.Comonad.adj_counit, CategoryTheory.composePath_nil, CategoryTheory.ShortComplex.SnakeInput.w₁₃_assoc, CategoryTheory.Pseudofunctor.isStackFor_iff, CategoryTheory.Adjunction.homAddEquiv_add, CategoryTheory.Limits.pushoutIsoUnopPullback_inl_hom, Bicategory.Opposite.opFunctor_obj, CategoryTheory.endomorphism_simple_eq_smul_id, CategoryTheory.Bicategory.Prod.sectL_mapId_hom, CategoryTheory.ComposableArrows.opEquivalence_unitIso_hom_app, CategoryTheory.Limits.Sigma.ι_π, TopologicalSpace.Opens.coe_id, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_id_naturality_hom, CategoryTheory.CatCenter.smul_eq', CategoryTheory.ShortComplex.LeftHomologyMapData.add_φH, TopCat.presheafToTypes_map, CommRingCat.HomTopology.isEmbedding_hom, CategoryTheory.Bicategory.InducedBicategory.bicategory_rightUnitor_hom_hom, CategoryTheory.Functor.mapComposableArrowsObjMk₁Iso_hom_app, CategoryTheory.Pseudofunctor.isoMapOfCommSq_vert_id, CategoryTheory.Bicategory.LeftExtension.IsKan.uniqueUpToIso_hom_right, CategoryTheory.ShortComplex.unopMap_τ₂, HomologicalComplex.extend.rightHomologyData.d_comp_desc_eq_zero_iff, HomologicalComplex.cyclesOpIso_inv_naturality, AddCommMonCat.coyoneda_map_app, CommRingCat.moduleCatExtendScalarsPseudofunctor_map, CategoryTheory.Mon_Class.one_eq_one, CategoryTheory.Grp.Hom.hom_pow, CategoryTheory.Functor.prod'_δ_fst, CategoryTheory.Under.mapFunctor_map, CategoryTheory.Functor.prod'_μ_snd, CategoryTheory.Limits.Fork.op_π, HomologicalComplex.biprod_inr_fst_f, CategoryTheory.Bicategory.Pith.whiskerLeft_iso_hom, AddCommGrpCat.zero_apply, CategoryTheory.Pseudofunctor.bijective_toDescentData_map_iff, AlgebraicGeometry.Scheme.stalkMap_congr_hom, CategoryTheory.Groupoid.CategoryTheory.Functor.mapVertexGroup_apply, CategoryTheory.Bicategory.mateEquiv_symm_apply, CategoryTheory.Functor.Elements.initialOfCorepresentableBy_snd, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_hom_app_app, CategoryTheory.Pseudofunctor.map₂_whisker_left_assoc, CategoryTheory.Limits.cokernel.condition_assoc, ModuleCat.ExtendRestrictScalarsAdj.homEquiv_symm_apply, CategoryTheory.GrpObj.lift_commutator_eq_mul_mul_inv_inv, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τr, AlgebraicGeometry.Scheme.Γ_map_op, HomologicalComplex.opcyclesOpIso_hom_naturality, PresheafOfModules.homEquivOfIsLocallyBijective_apply, TopModuleCat.comp_cokerπ, CategoryTheory.Limits.kernelSubobject_arrow_comp_apply, CategoryTheory.Bicategory.Strict.rightUnitor_eqToIso, CategoryTheory.Presieve.FamilyOfElements.isAmalgamation_iff_ofArrows, Bicategory.Opposite.bicategory_whiskerRight_unop2, CategoryTheory.Bicategory.leftUnitor_whiskerRight, CategoryTheory.Limits.IsZero.unique_from, Bicategory.Opposite.homCategory_comp_unop2, CategoryTheory.Functor.sheafPushforwardContinuous_obj_val_map, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_inv_app_app, HomologicalComplex.homotopyCofiber.eq_desc, PresheafOfModules.unitHomEquiv_apply_coe, CategoryTheory.Join.pseudofunctorRight_mapId_hom_toNatTrans_app, CategoryTheory.Limits.FormalCoproduct.cochainComplexFunctor_obj_d, Rep.coindResAdjunction_homEquiv_apply, CochainComplex.mappingCone.inr_f_triangle_mor₃_f, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_map_fiber, groupCohomology.inhomogeneousCochains.d_comp_d, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp_assoc, CategoryTheory.sum.inrCompInrCompInverseAssociator_inv_app_down, CategoryTheory.PreGaloisCategory.exists_autMap, AlgebraicGeometry.SheafedSpace.Γ_map, AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id, CategoryTheory.conjugateEquiv_symm_comp, CategoryTheory.StrictPseudofunctor.toFunctor_obj, CategoryTheory.Sieve.functorInclusion_app, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_snd, CategoryTheory.Pretriangulated.shiftFunctorZero_op_hom_app, Opens.coe_mayerVietorisSquare_X₁, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_app_apply, CategoryTheory.Paths.lift_spec, CategoryTheory.Oplax.StrongTrans.naturality_id, CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_homEquiv, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_assoc, CategoryTheory.Bicategory.associator_eqToHom_inv_assoc, AlgebraicTopology.DoldKan.Hσ_eq_zero, CochainComplex.ConnectData.d₀_comp, CategoryTheory.StrictPseudofunctor.map_comp, CategoryTheory.Limits.Trident.IsLimit.homIso_apply_coe, CategoryTheory.associator_def, CategoryTheory.Pseudofunctor.presheafHom_map, CategoryTheory.Functor.toOplaxFunctor'_map, AlgebraicTopology.AlternatingFaceMapComplex.obj_d_eq, HomologicalComplex.tensor_unit_d₂, CategoryTheory.Bicategory.HasLeftKanLift.hasInitial, CategoryTheory.Sheaf.ΓObjEquivHom_naturality_symm, CategoryTheory.Join.opEquiv_inverse_map_inclLeft_op, CategoryTheory.Bicategory.prod_leftUnitor_hom_snd, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply, fintypeToFinBoolAlgOp_map, CategoryTheory.MorphismProperty.LeftFraction.op_s, CategoryTheory.ShortComplex.RightHomologyData.ι_descQ_eq_zero_of_boundary_assoc, ChainComplex.mk'_congr_succ'_d, CategoryTheory.tensorRightHomEquiv_naturality, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_fst, CategoryTheory.Limits.cokernelBiproductιIso_inv, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_assoc, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_hom_app_app, CategoryTheory.OplaxFunctor.mapComp_assoc_right_app_assoc, CochainComplex.IsKProjective.nonempty_homotopy_zero, CategoryTheory.Limits.piPiIso_hom, CategoryTheory.Functor.PullbackObjObj.ofHasPullback_π, SimplicialObject.Splitting.IndexSet.fac_pull, CategoryTheory.Groupoid.vertexGroupIsomOfMap_apply, CategoryTheory.Quiv.pathComposition_naturality, CategoryTheory.StrictlyUnitaryPseudofunctor.mapId_eq_eqToIso, SimplicialObject.Split.cofan_inj_naturality_symm_assoc, CategoryTheory.MorphismProperty.Comma.ext_iff, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_assoc, CategoryTheory.StrictlyUnitaryPseudofunctor.id_obj, CommAlgCat.snd_unop_hom, CategoryTheory.Limits.pullbackIsoOpPushout_inv_fst, CategoryTheory.Bicategory.whiskerLeft_inv_hom_whiskerRight_assoc, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy_homEquiv_symm_apply, CategoryTheory.Equivalence.sheafCongr.unitIso_hom_app_val_app, CategoryTheory.Pseudofunctor.StrongTrans.isoMk_inv_as_app, CategoryTheory.Bicategory.whisker_exchange_assoc, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.isoAux_hom_app, CategoryTheory.AsSmall.up_map_down, typeToBoolAlgOp_map, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_fst, CategoryTheory.op_inv_leftUnitor, CategoryTheory.tensorRightHomEquiv_tensor, CategoryTheory.Hom.mulEquivCongrRight_symm_apply, CategoryTheory.MonObj.mul_comp_assoc, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_rightUnitor_hom_as_app, CategoryTheory.Functor.op_commShiftIso_inv_app_assoc, CategoryTheory.CostructuredArrow.toStructuredArrow'_map, CategoryTheory.Limits.kernelBiproductπIso_inv, CategoryTheory.RetractArrow.op_i_right, CategoryTheory.Pretriangulated.binaryProductTriangle_mor₁, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_symm_apply_f_coe, HomologicalComplex.homologyι_comp_fromOpcycles_assoc, CategoryTheory.Subfunctor.range_eq_ofSection', CategoryTheory.Limits.cokernelBiproductFromSubtypeIso_hom, AlgebraicTopology.DoldKan.QInfty_comp_PInfty, CategoryTheory.unop_add, CategoryTheory.Bicategory.InducedBicategory.bicategory_rightUnitor_inv_hom, CategoryTheory.Functor.FullyFaithful.homNatIso'_hom_app_down, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv, CategoryTheory.Preadditive.kernelForkOfFork_ι, CategoryTheory.Bicategory.pentagon, CategoryTheory.CatEnrichedOrdinary.Hom.base_comp, CategoryTheory.ShortComplex.Homotopy.comp_h₁, CategoryTheory.ULiftHom.up_map_down, CategoryTheory.Oplax.OplaxTrans.homCategory_comp_as_app, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanMap_app, CategoryTheory.Pretriangulated.Triangle.zero_hom₁, CategoryTheory.Bicategory.Prod.snd_obj, HomologicalComplex.cylinder.inlX_π_assoc, CategoryTheory.Limits.pullbackIsoOpPushout_inv_snd, SheafOfModules.conjugateEquiv_pullbackComp_inv, CategoryTheory.typeEquiv_functor_obj_val_map, SSet.const_app, CategoryTheory.Types.instPreservesColimitsOfSizeForgetTypeHom, TopCat.Presheaf.covering_presieve_eq_self, CategoryTheory.WithTerminal.liftFromOverComp_hom_app, CategoryTheory.Functor.coe_mapAddHom, CategoryTheory.ShortComplex.SnakeInput.L₀_g_δ, CategoryTheory.Functor.corepresentableByUliftFunctorEquiv_symm_apply_homEquiv, HomologicalComplex₂.d₂_eq_zero', CategoryTheory.Functor.RepresentableBy.equivUliftYonedaIso_symm_apply_homEquiv, CategoryTheory.MorphismProperty.MapFactorizationData.op_i, CategoryTheory.Bicategory.rightUnitor_naturality_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_assoc, HomologicalComplex₂.ιTotal_totalFlipIso_f_hom_assoc, CategoryTheory.ShortComplex.Splitting.leftHomologyData_π, CategoryTheory.Abelian.Ext.mk₀_sum, CategoryTheory.Lax.OplaxTrans.vComp_naturality_naturality, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_app_app, CategoryTheory.IsPushout.unop, CategoryTheory.leftDualFunctor_map, CategoryTheory.Limits.prod.inl_snd_assoc, FintypeCat.equivEquivIso_symm_apply_apply, CategoryTheory.Types.hom_eq_coe, AlgebraicGeometry.Scheme.Hom.appLE_map_assoc, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₂, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_two, HomologicalComplex.d_comp_d', CategoryTheory.Limits.bicone_ι_π_ne_assoc, MonObj.mopEquiv_counitIso_hom_app_hom_unmop, CategoryTheory.regularTopology.isLocallySurjective_sheaf_of_types, CategoryTheory.Limits.IsColimit.homEquiv_symm_naturality, CategoryTheory.Prod.snd_map, imageToKernel_epi_of_zero_of_mono, CategoryTheory.Limits.HasZeroMorphisms.zero_comp, HomologicalComplex.zero_f, CategoryTheory.Presheaf.isLocallySurjective_iff_range_sheafify_eq_top', CategoryTheory.CatEnrichedOrdinary.id_hComp, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₂₃, CategoryTheory.OplaxFunctor.map₂_rightUnitor_assoc, CategoryTheory.Presieve.FamilyOfElements.singletonEquiv_symm_apply, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom, CategoryTheory.nerve.homEquiv_id, CategoryTheory.StructuredArrow.w_prod_snd, CategoryTheory.MorphismProperty.LeftFraction.unop_s, CochainComplex.mkHom_f_succ_succ, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_id, HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom_eq_zero, CategoryTheory.Limits.BinaryBicone.toBiconeFunctor_map_hom, CategoryTheory.ConcreteCategory.hom_injective, CategoryTheory.Prod.fac'_assoc, CategoryTheory.Functor.isIso_ranAdjunction_homEquiv_iff, CategoryTheory.Presheaf.isLocallySurjective_iff_whisker_forget, CategoryTheory.LocallyDiscrete.mkPseudofunctor_map, CochainComplex.mappingCone.d_snd_v_assoc, CategoryTheory.Lax.LaxTrans.vComp_naturality_id, CategoryTheory.Functor.ofOpSequence_map_homOfLE_succ, CategoryTheory.Under.opEquivOpOver_functor_obj, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHomLeft_unop, CategoryTheory.HomOrthogonal.matrixDecomposition_comp, Representation.coind'_apply_apply, groupCohomology.d₁₂_comp_d₂₃_assoc, CategoryTheory.Quiv.freeMap_pathsOf_pathComposition, CategoryTheory.Oplax.OplaxTrans.Modification.naturality_assoc, CategoryTheory.Limits.Multicofork.map_ι_app, CochainComplex.shiftFunctor_map_f, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_map, CategoryTheory.Enriched.Functor.natTransEquiv_symm_app_app_apply, CategoryTheory.Lax.OplaxTrans.id_naturality, CategoryTheory.isCommMonObj_iff_isMulCommutative, CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIsoWhisker_inv_right, CategoryTheory.ShortComplex.cyclesMap'_zero, CategoryTheory.unop_mono_of_epi, CochainComplex.mappingCone.d_snd_v', CochainComplex.HomComplex.Cocycle.equivHomShift_symm_apply, SheafOfModules.pushforwardPushforwardAdj_unit_app_val_app, CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_iff_epi₁, CategoryTheory.ShortComplex.zero_τ₃, HomologicalComplex.extend_op_d, SSet.Truncated.HomotopyCategory.descOfTruncation_map_homMk, CategoryTheory.FreeGroupoid.eq_mk, CategoryTheory.ShortComplex.HasRightHomology.of_hasCokernel, CategoryTheory.Limits.biproduct.ι_π_ne, CategoryTheory.CoreSmallCategoryOfSet.functor_map, CategoryTheory.Pretriangulated.contractibleTriangleFunctor_map_hom₃, CategoryTheory.GrothendieckTopology.uliftYonedaIsoYoneda_hom_app_val_app, CategoryTheory.Pseudofunctor.DescentData.pullFunctorObj_obj, CategoryTheory.NatTrans.op_app, AlgebraicTopology.DoldKan.Γ₀_map_app, CategoryTheory.uliftYoneda_obj_map_down, CategoryTheory.Limits.PushoutCocone.op_π_app, CategoryTheory.PrelaxFunctor.mapFunctor_map, CategoryTheory.ObjectProperty.leftOrthogonal.map_bijective_of_isTriangulated, CategoryTheory.ShortComplex.Homotopy.sub_h₃, CategoryTheory.Bicategory.whiskerRight_congr, CategoryTheory.Limits.biproduct.fromSubtype_π_assoc, AlgebraicGeometry.Scheme.Hom.appIso_inv_appLE_assoc, CategoryTheory.Oplax.StrongTrans.categoryStruct_comp_naturality, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp, Bicategory.Opposite.op2_rightUnitor, CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois_apply, CategoryTheory.Prod.hom_ext_iff, CategoryTheory.Limits.Cone.equiv_inv_π, CategoryTheory.rightDualFunctor_map, CategoryTheory.ShortComplex.Homotopy.trans_h₂, Action.FintypeCat.quotientToEndHom_mk, CategoryTheory.ShortComplex.kernel_ι_comp_cokernel_π_comp_cokernelToAbelianCoimage, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_assoc, CategoryTheory.Bicategory.LeftLift.whisker_unit, AlgebraicTopology.DoldKan.Q_f_0_eq, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight_symm_apply, CategoryTheory.Triangulated.TStructure.zero_of_isLE_of_isGE, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_assoc, CategoryTheory.ShortComplex.RightHomologyData.wι, CategoryTheory.Oplax.OplaxTrans.naturality_id_assoc, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map_assoc, CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero, CategoryTheory.Limits.π_comp_colimitOpIsoOpLimit_inv, CategoryTheory.Functor.leftOpRightOpEquiv_inverse_map, HomotopicalAlgebra.weakEquivalences_unop_iff, CategoryTheory.SimplicialObject.Truncated.trunc_obj_map, HomologicalComplex.mapBifunctor.d_eq, CategoryTheory.prod_comp_fst, CategoryTheory.Cat.opFunctorInvolutive_inv_app_toFunctor_map, CategoryTheory.Functor.leftOpRightOpEquiv_unitIso_hom_app, HomologicalComplex.unopSymm_d, CategoryTheory.IsPullback.zero_left, CategoryTheory.Presheaf.uliftYonedaAdjunction_homEquiv_app, CategoryTheory.Sheaf.isLocallyInjective_forget, CategoryTheory.ShortComplex.iCycles_g_assoc, CategoryTheory.Bicategory.prod_homCategory_id_fst, CategoryTheory.OplaxFunctor.map₂_leftUnitor, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₁_assoc, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id_assoc, CategoryTheory.Sieve.uliftNatTransOfLe_app_down_coe, CategoryTheory.Bicategory.conjugateEquiv_symm_comp, CategoryTheory.WithInitial.equivComma_inverse_obj_map, AlgebraicGeometry.Scheme.Γ_map, CategoryTheory.ShortComplex.Exact.mono_g_iff, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_hom_app_val_app, ModuleCat.hom_sum, CategoryTheory.ShortComplex.SnakeInput.w₀₂, CategoryTheory.ShortComplex.rightHomologyMap_zero, CategoryTheory.ShortComplex.exact_iff_i_p_zero, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_assoc, CategoryTheory.Limits.Bicone.ofLimitCone_ι, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst_assoc, CategoryTheory.Bicategory.pentagon_hom_hom_inv_inv_hom_assoc, CategoryTheory.CommSq.right_adjoint_hasLift_iff, CategoryTheory.Limits.biprod.map_eq, CochainComplex.homotopyOp_hom_eq, CategoryTheory.cones_obj_map_app, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π_assoc, CategoryTheory.OverPresheafAux.MakesOverArrow.map₂, CategoryTheory.PreGaloisCategory.fiberBinaryProductEquiv_symm_snd_apply, CategoryTheory.StrictPseudofunctor.mk'_map, CategoryTheory.NatTrans.removeRightOp_app, CategoryTheory.Abelian.Pseudoelement.zero_morphism_ext', CategoryTheory.Bicategory.mateEquiv_hcomp, TopCat.Presheaf.germ_res_apply', CategoryTheory.StrictlyUnitaryLaxFunctor.mk'_obj, CategoryTheory.subsingleton_of_unop, CategoryTheory.Iso.homCongr_apply, CategoryTheory.WithTerminal.ofCommaObject_map, CategoryTheory.Lax.LaxTrans.naturality_naturality, CategoryTheory.Bicategory.Adj.leftUnitor_inv_τl, CategoryTheory.Square.opFunctor_map_τ₁, CommRingCat.moduleCatExtendScalarsPseudofunctor_obj, CategoryTheory.Limits.opCospan_inv_app, CategoryTheory.Quiv.lift_map, Bicategory.Opposite.op2_rightUnitor_hom, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀'_assoc, CategoryTheory.PreGaloisCategory.card_hom_le_card_fiber_of_connected, CategoryTheory.Bicategory.whiskerLeft_eqToHom, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_left, CategoryTheory.Limits.limitRightOpIsoOpColimit_hom_comp_ι_assoc, Homotopy.ofEq_hom, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_comp, CategoryTheory.Functor.WellOrderInductionData.Extension.map_succ, CategoryTheory.Bicategory.Pith.id₂_iso_hom, CategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSet_comp, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_inv_app_val_app, HomologicalComplex₂.D₂_shape, CategoryTheory.Adjunction.homEquiv_naturality_right_square_iff, CategoryTheory.conjugateEquiv_counit, CategoryTheory.Mon.Hom.hom_mul, CategoryTheory.Bicategory.associator_hom_congr, CochainComplex.IsKProjective.Qh_map_bijective, Condensed.isoFinYonedaComponents_inv_comp, Mathlib.Tactic.Bicategory.naturality_leftUnitor, Bicategory.Opposite.unopFunctor_obj, Rep.coindIso_inv_hom_hom, CochainComplex.mappingCone.d_fst_v_assoc, CategoryTheory.tensor_sum, CategoryTheory.Preadditive.mono_iff_isZero_kernel', CategoryTheory.ShortComplex.LeftHomologyData.wi, Action.zero_hom, CategoryTheory.Hom.inv_def, CategoryTheory.Limits.WalkingMultispan.instSubsingletonHomRight, CategoryTheory.Prod.fac_assoc, ModuleCat.hom_nsmul, CategoryTheory.Functor.prod_map, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_inl, SimplicialObject.Splitting.IndexSet.id_snd_coe, AlgebraicGeometry.Scheme.Opens.ι_appTop, CategoryTheory.ShortComplex.Exact.leftHomologyDataOfIsLimitKernelFork_π, CategoryTheory.unopHom_apply, CategoryTheory.Bicategory.pentagon_inv_inv_hom_inv_inv_assoc, CategoryTheory.Functor.ranges_directed, HomologicalComplex.cyclesOpIso_hom_naturality_assoc, CategoryTheory.Limits.isLimitConeOfAdj_lift, CategoryTheory.Functor.toOplaxFunctor_mapComp, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_assoc, CategoryTheory.Preadditive.isCoseparating_iff, CategoryTheory.InducedCategory.homAddEquiv_apply, CategoryTheory.Adjunction.compPreadditiveYonedaIso_hom_app_app_apply, CategoryTheory.MonoidalPreadditive.tensor_zero, HomotopicalAlgebra.instFibrationUnopOfCofibrationOpposite, CategoryTheory.Bicategory.Comonad.comul_assoc, groupCohomology.subtype_comp_d₀₁_assoc, CategoryTheory.sum.inrCompInlCompAssociator_inv_app_down_down, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom, HomologicalComplex₂.ι_totalShift₂Iso_hom_f_assoc, CategoryTheory.Limits.pullback_map_diagonal_isPullback, CategoryTheory.Functor.partialLeftAdjointHomEquiv_map_comp, CategoryTheory.Bicategory.comp_whiskerLeft, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₁, CategoryTheory.Adjunction.homAddEquiv_symm_zero, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app, TopCat.Presheaf.presieveOfCovering.indexOfHom_spec, CategoryTheory.Limits.isLimitOfCoconeRightOpOfCone_lift, CategoryTheory.ShortComplex.sub_τ₁, CategoryTheory.Functor.RepresentableBy.homEquiv_comp, AlgebraicGeometry.Scheme.map_basicOpen, CategoryTheory.OplaxFunctor.mapComp_naturality_left, CategoryTheory.conjugateEquiv_rightUnitor_hom, CategoryTheory.Lax.StrongTrans.naturality_id, CategoryTheory.Bicategory.LeftLift.whiskerHom_right, CategoryTheory.Mat_.add_apply, CategoryTheory.Limits.PullbackCone.unop_ι_app, CategoryTheory.Square.unop_f₁₃, SSet.Truncated.StrictSegal.spineToSimplex_vertex, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality_assoc, CategoryTheory.Bicategory.prod_associator_hom_fst, CategoryTheory.Grp_Class.inv_comp, CategoryTheory.CategoryOfElements.π_map, CategoryTheory.IsPushout.of_isBilimit, PresheafOfModules.neg_app, CategoryTheory.Limits.FormalCoproduct.evalOp_map_app, CategoryTheory.Bicategory.LeftExtension.ofCompId_hom, CategoryTheory.Functor.prod_ε_fst, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_leftUnitor_hom_as_app, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_inv_app, CategoryTheory.ShortComplex.opMap_τ₂, CategoryTheory.cosimplicialSimplicialEquiv_unitIso_hom_app, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv, CategoryTheory.Bicategory.prod_homCategory_comp_fst, SimplicialObject.Splitting.cofan_inj_πSummand_eq_zero, CategoryTheory.instIsMonHomInvHomOfIsCommMonObj, HomologicalComplex.homotopyCofiber.inlX_sndX, CategoryTheory.Functor.RepresentableBy.isRepresentedBy, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₂, CategoryTheory.Linear.homCongr_apply, CategoryTheory.Lax.StrongTrans.categoryStruct_id_naturality, CategoryTheory.StrictlyUnitaryLaxFunctor.id_map, CategoryTheory.ShortComplex.Homotopy.add_h₀, CategoryTheory.Limits.cospanOp_hom_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w_apply, HomologicalComplex.truncGE'.d_comp_d_assoc, CategoryTheory.ShortComplex.cyclesMap_zero, CategoryTheory.Limits.asEmptyCocone_ι_app, ModuleCat.homEquiv_extendScalarsComp, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_apply_snd, dNext_comp_left, CategoryTheory.CommSq.left_adjoint_hasLift_iff, CategoryTheory.Pseudofunctor.mapComp_id_left_inv, CategoryTheory.ShortComplex.cyclesMap'_smul, TopCat.Sheaf.objSupIsoProdEqLocus_inv_snd, CategoryTheory.Idempotents.Karoubi.sum_hom, SemimoduleCat.hom_zero, CategoryTheory.ShortComplex.LeftHomologyMapData.zero_φH, CategoryTheory.WithInitial.pseudofunctor_mapId, CategoryTheory.sum.inlCompInlCompAssociator_inv_app_down, CategoryTheory.op_hom_braiding, CategoryTheory.GrothendieckTopology.diagram_map, CategoryTheory.Sieve.uliftFunctorInclusion_app, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_counitIso, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τr, CategoryTheory.Join.pseudofunctorRight_mapId_inv_toNatTrans_app, CategoryTheory.Functor.op_commShiftIso_inv_app, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_whisker_left, CategoryTheory.conjugateEquiv_mateEquiv_vcomp, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_iso, HomologicalComplex.homotopyCofiber.inlX_d, CategoryTheory.isIso_unop, HomologicalComplex.mapBifunctor₂₃.d₁_eq, SSet.Truncated.StrictSegal.spine_δ_vertex_ge, CategoryTheory.ShiftedHom.opEquiv'_symm_apply, SSet.StrictSegal.spineToSimplex_edge, CategoryTheory.GrpObj.div_comp_assoc, CategoryTheory.SemiadditiveOfBinaryBiproducts.add_eq_right_addition, CategoryTheory.ConcreteCategory.hom_bijective, CategoryTheory.Bicategory.Comonad.counit_def, CategoryTheory.NonPreadditiveAbelian.lift_sub_lift, RingCat.moduleCatRestrictScalarsPseudofunctor_map, AddCommGrpCat.kernelIsoKer_inv_comp_ι, CategoryTheory.LaxFunctor.map₂_associator, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, CategoryTheory.Over.opEquivOpUnder_counitIso, CategoryTheory.Bicategory.associator_inv_naturality_left_assoc, CategoryTheory.Monad.algebraPreadditive_homGroup_zsmul_f, TopCat.Presheaf.SheafConditionEqualizerProducts.res_π, CategoryTheory.ShortComplex.HasRightHomology.of_hasKernel, CategoryTheory.Grp_Class.comp_div, CategoryTheory.OplaxFunctor.mapComp_id_right_assoc, TopCat.Presheaf.germ_res, CategoryTheory.CostructuredArrow.prodFunctor_obj, CategoryTheory.Bicategory.whiskerLeftIso_inv, CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_mapId, CategoryTheory.Oplax.StrongTrans.naturality_comp_assoc, CategoryTheory.Comma.equivProd_inverse_map_right, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_left, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapComp_hom, CategoryTheory.tensorObj_def, SSet.Truncated.StrictSegal.spineToSimplex_edge, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_symm_apply, CategoryTheory.mateEquiv_conjugateEquiv_vcomp, CategoryTheory.Iso.unop2_hom, CategoryTheory.CommSq.LiftStruct.opEquiv_symm_apply, CategoryTheory.OplaxFunctor.mapComp_assoc_right, CategoryTheory.Bicategory.mateEquiv_eq_iff, SSet.Truncated.spine_arrow, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_app, HomologicalComplex.ιMapBifunctorOrZero_eq_zero, CategoryTheory.Arrow.equivSigma_symm_apply_hom, CategoryTheory.CategoryOfElements.fromCostructuredArrow_map_coe, CategoryTheory.Preadditive.comp_sum, CategoryTheory.Pretriangulated.binaryProductTriangle_mor₃, CategoryTheory.Equivalence.leftOp_inverse_map, CategoryTheory.Limits.biproduct.fromSubtype_eq_lift, CategoryTheory.Functor.prod_μ_fst, CategoryTheory.Bicategory.LeftLift.ofIdComp_right, CategoryTheory.OplaxFunctor.mapComp_assoc_left_assoc, CategoryTheory.Square.opFunctor_map_τ₂, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₃, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionRight_op, AlgebraicTopology.DoldKan.degeneracy_comp_PInfty_assoc, CategoryTheory.Bicategory.InducedBicategory.forget_mapId_inv, CategoryTheory.Functor.FullyFaithful.homMulEquiv_symm_apply, CategoryTheory.NatTrans.prod_app_snd, CategoryTheory.Pseudofunctor.ObjectProperty.IsClosedUnderMapObj.map_obj, CategoryTheory.Limits.Cotrident.IsColimit.homIso_symm_apply, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_app_assoc, CategoryTheory.RetractArrow.unop_r_right, CategoryTheory.Bicategory.postcomposing_map_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_inv_app, Bicategory.Opposite.op2_comp, CategoryTheory.Paths.lift_cons, CategoryTheory.Bicategory.pentagon_inv_assoc, CategoryTheory.Pseudofunctor.mapComp'_hom_naturality, groupCohomology.d₁₂_comp_d₂₃, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_left, CategoryTheory.yonedaGrpObj_map, CategoryTheory.Functor.unop_map, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_assoc, CategoryTheory.Limits.eq_zero_of_epi_kernel, CategoryTheory.Pseudofunctor.StrongTrans.Modification.id_app, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_id_assoc, CategoryTheory.Limits.isLimitConeOfCoconeRightOp_lift, Representation.linHom.invariantsEquivRepHom_symm_apply_coe, TopCat.Presheaf.pullback_obj_obj_ext_iff, CategoryTheory.Bicategory.whiskerRight_comp, CategoryTheory.ObjectProperty.isLocal.homEquiv_apply, CategoryTheory.MorphismProperty.RightFraction.op_f, CategoryTheory.Limits.IsZero.map, CategoryTheory.CatCenter.smul_eq, CategoryTheory.Bicategory.rightUnitorNatIso_inv_app, CategoryTheory.Functor.RepresentableBy.homEquiv_unop_comp, CondensedMod.LocallyConstant.instFaithfulSheafCompHausCoherentTopologyTypeConstantSheaf, AlgebraicGeometry.Scheme.IdealSheafData.isLocalization_away, CategoryTheory.Pseudofunctor.StrongTrans.associator_inv_as_app, Homotopy.symm_hom, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_map_left_right, Bicategory.Opposite.op2_leftUnitor_hom, SSet.N.le_iff_exists_mono, AlgebraicGeometry.Scheme.ofRestrict_toLRSHom_c_app, CategoryTheory.yonedaGrpObjIsoOfRepresentableBy_hom, CategoryTheory.Linear.comp_smul, CategoryTheory.MonoidalClosed.uncurry_injective, CategoryTheory.Bicategory.Comonad.comul_counit_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHom_unop, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_hom_app, CategoryTheory.regularTopology.equalizerCondition_iff_isIso_lift, CategoryTheory.rightAdjointOfCostructuredArrowTerminalsAux_apply, CategoryTheory.Functor.IsCocartesian.universal_property, CategoryTheory.Bicategory.congr_whiskerLeft, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f, CategoryTheory.yonedaGrpObjIsoOfRepresentableBy_inv, CategoryTheory.Mon.uniqueHomFromTrivial_default_hom, CategoryTheory.ComposableArrows.isComplex₂_iff, CategoryTheory.Functor.FullyFaithful.map_surjective, CategoryTheory.Preadditive.comp_zsmul, CategoryTheory.Pseudofunctor.toLax_mapId, CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_zsmul_f, CategoryTheory.ShiftedHom.mk₀_add, SimplicialObject.Splitting.IndexSet.instEpiSimplexCategoryE, SheafOfModules.Presentation.map_relations_I, HomologicalComplex₂.D₁_totalShift₁XIso_hom, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv, CategoryTheory.Functor.hom_obj, SSet.Truncated.HomotopyCategory.homToNerveMk_app_one, CategoryTheory.Functor.shiftMap_zero, HomologicalComplex₂.D₂_totalShift₁XIso_hom, CategoryTheory.Subgroupoid.mem_sInf, MonObj.mopEquiv_functor_map_hom_unmop, CategoryTheory.Functor.opInv_map, CategoryTheory.Localization.homEquiv_apply, ComplexShape.Embedding.homEquiv_symm_apply, CategoryTheory.Oplax.OplaxTrans.isoMk_hom_as_app, CategoryTheory.Cat.leftUnitor_hom_toNatTrans, CategoryTheory.StructuredArrow.prodFunctor_obj, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_hom_assoc, SSet.prodStdSimplex.objEquiv_map_apply, CategoryTheory.Bicategory.whiskerLeft_inv_hom_whiskerRight, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app_assoc, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_π_app, CategoryTheory.Bicategory.Adj.comp_τr_assoc, CategoryTheory.ShortComplex.toCycles_comp_leftHomologyπ, CategoryTheory.Bicategory.whisker_assoc_assoc, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.δ_toBiprod_assoc, CategoryTheory.Preadditive.add_comp, SSet.stdSimplex.objEquiv_symm_mem_nonDegenerate_iff_mono, SSet.Truncated.Edge.mk'_edge, CategoryTheory.conjugateEquiv_comm, SimplicialObject.Splitting.cofan_inj_comp_app, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_three, CategoryTheory.Limits.limitOpIsoOpColimit_inv_comp_π_assoc, LightProfinite.Extend.functorOp_map, PresheafOfModules.sub_app, CategoryTheory.GrpObj.comp_div, TopCat.Sheaf.interUnionPullbackConeLift_left, AlgebraicTopology.NormalizedMooreComplex.d_squared, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality_assoc, HomologicalComplex.homologyMap_sub, MonObj.mopEquivCompForgetIso_inv_app_unmop, CategoryTheory.Limits.kernelSubobject_factors_iff, CategoryTheory.Functor.isIso_lanAdjunction_homEquiv_symm_iff, CategoryTheory.Preadditive.add_comp_assoc, TopCat.subpresheafToTypes_map_coe, CategoryTheory.MorphismProperty.RightFraction.op_map, CategoryTheory.ShortComplex.opcyclesOpIso_inv_naturality, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_assoc, CategoryTheory.ProjectiveResolution.complex_d_succ_comp, CategoryTheory.Prod.fac, CategoryTheory.MorphismProperty.isLocal_iff, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app_assoc, CategoryTheory.Bicategory.associator_eqToHom_hom, CategoryTheory.Mon_Class.comp_pow, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_fst, AlgebraicTopology.DoldKan.Γ₀.map_app, CategoryTheory.Bicategory.whisker_assoc_symm, ComplexShape.Embedding.homEquiv_apply_coe, CategoryTheory.extendCofan_ι_app, CategoryTheory.LocallySmall.hom_small, CategoryTheory.Limits.ι_comp_colimitRightOpIsoUnopLimit_hom, Homotopy.dNext_succ_chainComplex, CategoryTheory.Lax.StrongTrans.naturality_naturality_assoc, CategoryTheory.op_hom_associator, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.inverse_obj_map, topToLocale_map, HomologicalComplex.homotopyCofiber.shape, CategoryTheory.CommSq.right_adjoint, CategoryTheory.Bicategory.Prod.sectL_mapComp_inv, CategoryTheory.WithInitial.opEquiv_counitIso_inv_app, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac', CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_obj, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_comp, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_snd_coe, CategoryTheory.Functor.sectionsEquivHom_naturality_symm, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id_assoc, CategoryTheory.Functor.IsEventuallyConstantFrom.coconeιApp_eq, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_two_assoc, CategoryTheory.Endofunctor.algebraPreadditive_homGroup_sub_f, CategoryTheory.Limits.coneLeftOpOfCocone_π_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_obj_obj, groupHomology.d₂₁_comp_d₁₀, HomotopicalAlgebra.FibrantObject.homRel_equivalence_of_isCofibrant_src, AlgebraicGeometry.Scheme.homOfLE_app, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.δ_toBiprod, CategoryTheory.ShortComplex.RightHomologyMapData.smul_φH, CategoryTheory.Equivalence.congrLeftFunctor_map, CategoryTheory.Bicategory.id_whiskerLeft_assoc, CategoryTheory.ShortComplex.LeftHomologyData.wπ, HomologicalComplex.cylinder.πCompι₀Homotopy.inrX_nullHomotopy_f, CategoryTheory.CatEnriched.hComp_assoc_heq, CategoryTheory.Bicategory.LeftLift.IsKan.fac, CategoryTheory.unop_epi_iff, CategoryTheory.Adjunction.homAddEquiv_symm_neg, CategoryTheory.Abelian.Ext.mk₀_zero, CategoryTheory.Comonad.coalgebraPreadditive_homGroup_nsmul_f, CategoryTheory.Limits.FormalCoproduct.cech_map, CategoryTheory.Bicategory.Pith.id_of, SSet.Truncated.StrictSegal.spineToSimplex_arrow, AlgebraicGeometry.Scheme.Hom.naturality_assoc, CategoryTheory.MonoidalCategory.prodMonoidal_whiskerLeft, SheafOfModules.Presentation.mapRelations_mapGenerators, CategoryTheory.op_mono_iff, HomologicalComplex.cyclesOpIso_hom_naturality, CategoryTheory.Bicategory.InducedBicategory.forget_mapComp_inv, ModuleCat.hom_add, Bicategory.Opposite.op2_id, CommRingCat.HomTopology.continuous_apply, CategoryTheory.IsPushout.inr_fst', CategoryTheory.op_hom_rightUnitor, CategoryTheory.Pseudofunctor.IsStack.essSurj_of_sieve, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₂₃_assoc, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.sheafCondition_iff_bijective_toPullbackObj, SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero_assoc, CategoryTheory.GrpObj.comp_zpow_assoc, CategoryTheory.Bicategory.toNatTrans_mateEquiv, CategoryTheory.Limits.KernelFork.app_one, CategoryTheory.Functor.RepresentableBy.uniqueUpToIso_hom, CondensedSet.topCatAdjunctionUnit_val_app, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac'_assoc, CategoryTheory.eqToHom_op, AlgebraicGeometry.Scheme.homOfLE_appLE, CategoryTheory.Iso.unop2_op_hom, CategoryTheory.Functor.sheafPushforwardContinuousId'_inv_app_val_app, CategoryTheory.OplaxFunctor.map₂_rightUnitor, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app_assoc, CategoryTheory.uliftYoneda_map_app, CategoryTheory.Functor.prod'_η_snd, CategoryTheory.ShortComplex.RightHomologyData.ι_g'_assoc, CategoryTheory.Localization.SmallHom.equiv_chgUniv, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop, CategoryTheory.Iso.unop_inv, CategoryTheory.Functor.whiskerRight_zero, CategoryTheory.Functor.uliftYonedaReprXIso_hom_app, TopCat.Presheaf.pushforward_obj_map, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_unitIso, CategoryTheory.Limits.opProdIsoCoprod_hom_fst, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app, CategoryTheory.Limits.kernel.ι_zero_isIso, CategoryTheory.equivYoneda_hom_app, CochainComplex.HomComplex.δ_zero_cochain_v, CochainComplex.HomComplex.Cochain.units_smul_v, CategoryTheory.NonPreadditiveAbelian.neg_add_cancel, CategoryTheory.GrpObj.inv_eq_inv, HomologicalComplex.smul_f_apply, CategoryTheory.StrictlyUnitaryLaxFunctorCore.mapComp_naturality_left, CategoryTheory.Limits.isLimitOfCoconeOfConeUnop_lift, CategoryTheory.Cat.associator_inv_toNatTrans, CategoryTheory.Limits.isKernelCompMono_lift, CategoryTheory.Limits.FintypeCat.instPreservesFiniteColimitsFintypeCatForgetHomCarrier, CategoryTheory.WithTerminal.prelaxfunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.Limits.walkingCospanOpEquiv_functor_map, CategoryTheory.Iso.homToEquiv_apply, CochainComplex.HomComplex.CohomologyClass.toHom_bijective, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp, CategoryTheory.ShortComplex.LeftHomologyMapData.zero_φK, Compactum.continuous_of_hom, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop_assoc, CategoryTheory.Functor.curryingEquiv_apply_map, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₂, CategoryTheory.ShortComplex.HomologyMapData.add_right, CompHausLike.pullback.cone_π, CategoryTheory.NatTrans.app_sum, Mathlib.Tactic.Bicategory.naturality_id, CategoryTheory.Limits.pushoutIsoOpPullback_inr_hom, CategoryTheory.Cat.leftUnitor_inv_toNatTrans, CategoryTheory.CostructuredArrow.prodInverse_map, CategoryTheory.Functor.initial_iff_of_isCofiltered, CategoryTheory.Join.mapPairId_inv_app, CategoryTheory.Pseudofunctor.map₂_left_unitor_app, CategoryTheory.Pseudofunctor.mapId'_eq_mapId, CategoryTheory.Limits.biproduct.total, CategoryTheory.Functor.CorepresentableBy.equivUliftCoyonedaIso_symm_apply_homEquiv, CategoryTheory.Bicategory.associator_inv_naturality_right_assoc, CategoryTheory.Preadditive.coforkOfCokernelCofork_π, CategoryTheory.ShortComplex.SnakeInput.L₀X₂ToP_comp_φ₁_assoc, CategoryTheory.FunctorToTypes.functorHomEquiv_apply_app, CategoryTheory.GrpObj.zpow_comp, CategoryTheory.Limits.biprod.inrCokernelCofork_π, CategoryTheory.Limits.IsTerminal.subsingleton_to, AlgebraicGeometry.morphismRestrict_appTop, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp, AlgebraicGeometry.Scheme.IdealSheafData.ofIdealTop_ideal, CategoryTheory.ShortComplex.rightHomologyMap_sub, CategoryTheory.ShortComplex.LeftHomologyData.op_p, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π, CategoryTheory.StrictPseudofunctor.toFunctor_map, CategoryTheory.Bicategory.Prod.snd_mapId_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality, CategoryTheory.Bicategory.hom_inv_whiskerRight_assoc, CategoryTheory.MonObj.pow_comp_assoc, CategoryTheory.Bicategory.triangle, CategoryTheory.Pseudofunctor.StrongTrans.leftUnitor_hom_as_app, CategoryTheory.sum.inrCompAssociator_hom_app_down_down, CategoryTheory.cosimplicialSimplicialEquiv_unitIso_inv_app, CategoryTheory.Limits.Pi.ι_π_assoc, CategoryTheory.Comma.fromProd_map_right, CategoryTheory.Bimon.trivialTo_hom, CategoryTheory.Localization.Preadditive.add_eq, SSet.Truncated.spine_vertex, CategoryTheory.Limits.isoZeroOfMonoZero_inv, CategoryTheory.ShortComplex.ShortExact.δ_comp_assoc, CategoryTheory.Limits.BinaryCofan.op_mk, CategoryTheory.Sheaf.ΓHomEquiv_naturality_right_symm, CategoryTheory.Functor.map_units_smul, CategoryTheory.Functor.IsCoverDense.Types.naturality_apply, CategoryTheory.MonoidalOpposite.tensorRightIso_hom_app_unmop, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_symm_apply_f, CategoryTheory.Equivalence.sheafCongr.functor_obj_val_map, CategoryTheory.CatEnrichedOrdinary.Hom.comp_eq, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapId_hom, CategoryTheory.Limits.WidePushoutShape.mkCocone_ι_app, CochainComplex.HomComplex.Cocycle.fromSingleMk_zero, CategoryTheory.Pseudofunctor.ObjectProperty.mapId_hom_app, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_assoc, HomologicalComplex.zero_f_apply, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_apply, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_π_app, CategoryTheory.Bicategory.Prod.sectR_map₂, CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair_inv_app, CategoryTheory.PreGaloisCategory.fiber_in_connected_component, CategoryTheory.instSmallHomDerivedCategoryObjSingleFunctorOfHasExt, CategoryTheory.congrArg_mpr_hom_left, CategoryTheory.Preadditive.hasCokernel_of_hasCoequalizer, CategoryTheory.Limits.biprod.add_eq_lift_desc_id, CategoryTheory.FreeMonoidalCategory.instSubsingletonHomCompDiscreteNormalMonoidalObject, CategoryTheory.ShortComplex.Splitting.g_s_assoc, CategoryTheory.WithInitial.map_map, SSet.stdSimplex.objEquiv_symm_comp, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃_assoc, CategoryTheory.StrictPseudofunctorPreCore.map₂_whisker_right, CategoryTheory.ProjectiveResolution.extMk_zero, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj_condition, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapIdIso_inv, CategoryTheory.PrelaxFunctor.id_toPrelaxFunctorStruct, CategoryTheory.ShortComplex.Homotopy.equivSubZero_apply, CategoryTheory.PresheafOfGroups.OneCochain.ev_precomp, Action.add_hom, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_inv_app_val_app, CategoryTheory.FreeBicategory.normalize_naturality, CategoryTheory.Bicategory.Adj.rIso_hom, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom, CategoryTheory.WithTerminal.subsingleton_hom, CategoryTheory.StrictPseudofunctor.id_map₂, CategoryTheory.Sheaf.ΓObjEquivHom_naturality, CategoryTheory.Limits.sigmaSigmaIso_inv, SimplexCategory.δ_injective, CategoryTheory.HomOrthogonal.matrixDecomposition_apply, CategoryTheory.Bicategory.Prod.sectL_map, CategoryTheory.NatTrans.appHom_apply, HomologicalComplex.toCycles_eq_zero, CategoryTheory.End.smul_right, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_left_symm, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app, CategoryTheory.LocallyDiscrete.mkPseudofunctor_mapComp, CategoryTheory.CommSq.unop, CategoryTheory.Functor.IsRepresentedBy.uliftYonedaIso_hom, CategoryTheory.Bicategory.conjugateIsoEquiv_apply_hom, CategoryTheory.NonPreadditiveAbelian.neg_add, CategoryTheory.Monad.algebraPreadditive_homGroup_zero_f, CategoryTheory.Bicategory.id_whiskerRight, SheafOfModules.pushforwardCongr_symm, CategoryTheory.Bicategory.conjugateIsoEquiv_symm_apply_hom, CategoryTheory.kernelUnopUnop_hom, CochainComplex.mappingCone.inr_f_fst_v_assoc, CategoryTheory.Pseudofunctor.mapComp'_inv_comp_mapComp'_hom, CategoryTheory.Iso.op2_unop_inv_unop2, CategoryTheory.Limits.biproduct.matrix_desc, CategoryTheory.IsPullback.of_hasBinaryBiproduct, CategoryTheory.MonObj.ofRepresentableBy_mul, Homotopy.add_hom, CategoryTheory.Limits.Cofork.IsColimit.homIso_natural, CategoryTheory.Bicategory.Pith.hom₂_ext_iff, CategoryTheory.Localization.homEquiv_refl, groupHomology.congr, CategoryTheory.IsPushout.inl_snd, CategoryTheory.Lax.StrongTrans.naturality_id_assoc, CategoryTheory.ShortComplex.homologyOpIso_inv_naturality_assoc, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit_assoc, CochainComplex.mappingCone.inl_v_d_assoc, CategoryTheory.regularTopology.equalizerCondition_w', CategoryTheory.Localization.homEquiv_trans, CommAlgCat.toUnit_unop_hom, CochainComplex.mappingCone.cocycleOfDegreewiseSplit_triangleRotateShortComplexSplitting_v, CategoryTheory.thin_of_isCoseparating_empty, CategoryTheory.Limits.equalizer.existsUnique, SimplicialObject.Splitting.PInfty_comp_πSummand_id_assoc, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv', CategoryTheory.IsPullback.of_is_bilimit', CategoryTheory.oppositeShiftFunctorZero_hom_app, ChainComplex.mk'_d, CategoryTheory.Limits.limitCompYonedaIsoCocone_inv, HomologicalComplex.singleMapHomologicalComplex_inv_app_ne, CategoryTheory.MonoidalOpposite.tensorRightIso_inv_app_unmop, CategoryTheory.Limits.asEmptyCone_π_app, CategoryTheory.Quotient.inv_mk, CategoryTheory.nerve_map, AlgebraicGeometry.IsOpenImmersion.app_eq_appIso_inv_app_of_comp_eq, CategoryTheory.Limits.Fork.op_ι_app, AlgebraicGeometry.AffineSpace.functor_map_app, CategoryTheory.Comma.fromProd_map_left, CategoryTheory.SimplicialObject.cechNerveEquiv_symm_apply, SheafOfModules.add_val, CategoryTheory.ShortComplex.HasLeftHomology.of_hasKernel, AlgebraicGeometry.Scheme.Modules.Hom.sub_app, CategoryTheory.ShortComplex.rightHomologyMap_op, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id_assoc, CategoryTheory.Functor.prod_δ_snd, CategoryTheory.Bicategory.iterated_mateEquiv_conjugateEquiv_symm, CategoryTheory.conjugateEquiv_comp_assoc, HomologicalComplex.dgoToHomologicalComplex_map_f, CategoryTheory.Limits.BinaryBicone.inrCokernelCofork_π, AlgebraicGeometry.LocallyRingedSpace.restrict_presheaf_map, CategoryTheory.Bicategory.Adj.rightUnitor_inv_τr, CategoryTheory.Oplax.OplaxTrans.naturality_id, CategoryTheory.coyonedaEquiv_coyoneda_map, CategoryTheory.Limits.pullbackZeroZeroIso_hom_fst, CategoryTheory.ShortComplex.Homotopy.op_h₃, CategoryTheory.Bicategory.rightUnitor_comp, CategoryTheory.Bicategory.whiskerRight_id_symm, AlgebraicGeometry.ΓSpec.adjunction_homEquiv_apply, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_app, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_hom_inv, CategoryTheory.Limits.Trident.ofι_π_app, CategoryTheory.Groupoid.vertexGroupIsomOfMap_symm_apply, CategoryTheory.StrictlyUnitaryPseudofunctor.mk'_obj, CategoryTheory.Limits.coneOfSectionCompYoneda_π, CategoryTheory.ShortComplex.sub_τ₂, CategoryTheory.OplaxFunctor.mapComp_id_right, CategoryTheory.op_add, CategoryTheory.Bicategory.triangle_assoc_comp_right, CategoryTheory.CostructuredArrow.toStructuredArrow_obj, CategoryTheory.ShortComplex.Homotopy.trans_h₃, CategoryTheory.MonoidalCategory.tensor_map, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.fac_assoc, CategoryTheory.Pseudofunctor.toDescentData_obj, CategoryTheory.Limits.isIso_kernelSubobject_zero_arrow, CategoryTheory.Bicategory.comp_whiskerLeft_assoc, CategoryTheory.Bicategory.InducedBicategory.forget_mapComp_hom, SSet.Truncated.Edge.id_edge, CategoryTheory.ShortComplex.rightHomologyMap'_sub, CategoryTheory.ParametrizedAdjunction.unit_whiskerRight_map_assoc, CategoryTheory.Pseudofunctor.mapComp_id_right_inv, CategoryTheory.ShortComplex.Homotopy.neg_h₃, CategoryTheory.StrictlyUnitaryPseudofunctor.id_map₂, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inl, CategoryTheory.ShortComplex.Homotopy.unop_h₁, CategoryTheory.Bicategory.whiskerLeft_inv_hom_assoc, CategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy.f, CategoryTheory.Comma.unopFunctor_map, AlgebraicTopology.DoldKan.Q_succ, CategoryTheory.forgetAdjToOver.homEquiv_symm, CategoryTheory.Bicategory.associatorNatIsoMiddle_hom_app, CategoryTheory.ShortComplex.homologyMap_sub, HomologicalComplex.cyclesMap_zero, CondensedSet.isDiscrete_tfae, CategoryTheory.linearCoyoneda_obj_map, Rep.standardComplex.d_comp_ε, CategoryTheory.Bicategory.instHasInitialLeftExtensionOfHasLeftKanExtension, CategoryTheory.simplicialCosimplicialEquiv_functor_map_app, ChainComplex.fromSingle₀Equiv_symm_apply_f_zero, CategoryTheory.Functor.leftOpRightOpEquiv_counitIso_hom_app_app, CochainComplex.HomComplex.Cocycle.equivHomShift'_apply, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_assoc, CategoryTheory.OverPresheafAux.MakesOverArrow.app, CategoryTheory.Pseudofunctor.map₂_whisker_right_app_assoc, FDRep.simple_iff_end_is_rank_one, ContinuousMap.piComparison_fac, CategoryTheory.Limits.isColimitOfConeLeftOpOfCocone_desc, CategoryTheory.Limits.walkingSpanOpEquiv_functor_map, CategoryTheory.Limits.unop_zero, CategoryTheory.Square.unop_f₂₄, CategoryTheory.Grp.Hom.hom_mul, TopologicalSpace.Opens.leSupr_apply_mk, CategoryTheory.Bicategory.mateEquiv_square, PresheafOfModules.comp_toPresheaf_map_sheafifyHomEquiv'_symm_hom, CategoryTheory.Pretriangulated.binaryBiproductTriangle_mor₃, CategoryTheory.Limits.HasZeroObject.zeroIsoInitial_inv, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃_assoc, CategoryTheory.extendFan_π_app, HomologicalComplex.homologyMap_zero, CategoryTheory.Pseudofunctor.StrongTrans.Modification.naturality_assoc, CategoryTheory.ShortComplex.Homotopy.trans_h₀, CategoryTheory.Bicategory.LeftExtension.IsKan.uniqueUpToIso_inv_right, CategoryTheory.Lax.LaxTrans.naturality_naturality_assoc, CategoryTheory.ShortComplex.opcyclesMap_zero, CategoryTheory.Bicategory.Adj.forget₁_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.Bicategory.rightUnitor_naturality, CategoryTheory.MonoidalCategory.leftAssocTensor_map, CategoryTheory.CountableCategory.instCountableHomHomAsType, CategoryTheory.PreGaloisCategory.exists_hom_from_galois_of_fiber, CategoryTheory.OverPresheafAux.OverArrows.app_val, CategoryTheory.StrictlyUnitaryPseudofunctor.id_map, CategoryTheory.Subobject.bot_arrow, CategoryTheory.Presieve.FamilyOfElements.isAmalgamation_singleton_iff, CategoryTheory.Mon.Hom.hom_pow, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map_val_app, CategoryTheory.ShortComplex.neg_τ₂, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_δ_unmop_app, CategoryTheory.Bicategory.whiskerLeft_comp_assoc, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc, CategoryTheory.yonedaCommGrpGrpObj_obj_coe, CategoryTheory.kernelCokernelCompSequence.δ_fac, CategoryTheory.Subfunctor.range_eq_ofSection, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_iso, CategoryTheory.evaluationUncurried_map, CategoryTheory.orderDualEquivalence_counitIso, CategoryTheory.Limits.IsZero.iff_isSplitEpi_eq_zero, CategoryTheory.Bicategory.Pith.whiskerLeft_iso_inv, CategoryTheory.Discrete.productEquiv_counitIso_inv_app, CategoryTheory.FinallySmall.exists_small_weakly_terminal_set, CategoryTheory.ShortComplex.HomologyData.exact_iff_i_p_zero, CategoryTheory.Bicategory.rightZigzagIso_symm, CategoryTheory.Join.pseudofunctorRight_mapComp_hom_toNatTrans_app, HomologicalComplex.toCycles_comp_homologyπ, CategoryTheory.Iso.unop_hom_inv_id_app_assoc, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapIdIso_hom, CochainComplex.ConnectData.d_comp_d_assoc, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_snd, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_assoc, CategoryTheory.Monad.MonadicityInternal.comparisonAdjunction_unit_f_aux, CategoryTheory.MonObj.comp_mul, CategoryTheory.CommSq.op, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_assoc, CommAlgCat.one_op_of_unop_hom, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app, AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_fst_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_assoc, CategoryTheory.Pi.sum_obj_map, CategoryTheory.Lax.StrongTrans.naturality_comp, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.fromBiprod_biprodIsoProd_inv_apply, CategoryTheory.Bicategory.whiskerLeftIso_hom, CategoryTheory.ShiftedHom.opEquiv_symm_apply_comp, CategoryTheory.yonedaPairing_map, CategoryTheory.Monad.MonadicityInternal.comparisonAdjunction_counit, CategoryTheory.Lax.OplaxTrans.naturality_id_assoc, CochainComplex.HomComplex.Cochain.smul_v, Mathlib.Tactic.Bicategory.structuralIso_inv, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.Functor.toOplaxFunctor_map, HomologicalComplex₂.D₂_D₂_assoc, AlgebraicGeometry.Scheme.toOpen_eq, FintypeCat.hom_apply, CategoryTheory.Pretriangulated.Triangle.isZero₂_iff, HomologicalComplex.homotopyCofiber.d_sndX, CategoryTheory.Pseudofunctor.map₂_whisker_right, CategoryTheory.Limits.cokernelIsoOfEq_trans, AlgebraicGeometry.Spec.toSheafedSpace_map, CategoryTheory.Bicategory.whiskerRight_id_assoc, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_π, CategoryTheory.Mon_Class.pow_comp, CategoryTheory.Bicategory.Prod.sectR_obj, HomologicalComplex.extendMap_add, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_apply, CategoryTheory.IsPullback.inl_snd', CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₂_assoc, CategoryTheory.Bicategory.whisker_assoc_symm_assoc, HomologicalComplex.xPrevIsoSelf_comp_dTo_assoc, CategoryTheory.Preadditive.sum_comp_assoc, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_assoc, CategoryTheory.HomOrthogonal.matrixDecompositionAddEquiv_symm_apply, CategoryTheory.MorphismProperty.pullback_map, CategoryTheory.conjugateEquiv_associator_hom, SimplicialObject.Splitting.decomposition_id, CategoryTheory.PreGaloisCategory.surjective_on_fiber_of_epi, SSet.Truncated.Path.arrow_src, CategoryTheory.GrpObj.inv_comp, CategoryTheory.Limits.limitConeOfUnique_isLimit_lift, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app, CategoryTheory.Bicategory.conjugateEquiv_apply', SSet.spine_map_vertex, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₃, CategoryTheory.sum.inrCompInlCompAssociator_hom_app_down_down, HomologicalComplex.mapBifunctor₁₂.d₃_eq_zero, CategoryTheory.Functor.RepresentableBy.ext_iff, CategoryTheory.Bicategory.mateEquiv_conjugateEquiv_vcomp, CochainComplex.HomComplex.Cochain.fromSingleMk_sub, CategoryTheory.ShortComplex.RightHomologyMapData.zero_φQ, CochainComplex.toSingle₀Equiv_symm_apply_f_succ, CategoryTheory.OplaxFunctor.mapComp_assoc_right_assoc, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_hom_τr, CategoryTheory.Limits.zero_of_source_iso_zero', CategoryTheory.ShortComplex.homologyMap'_smul, CochainComplex.mappingCone.inl_v_descShortComplex_f_assoc, CategoryTheory.MonObj.comp_one_assoc, Rep.coindResAdjunction_homEquiv_symm_apply, CategoryTheory.Limits.IsZero.eq_zero_of_tgt, CategoryTheory.FreeMonoidalCategory.subsingleton_hom, CategoryTheory.Equivalence.rightOp_counitIso_hom_app, CategoryTheory.Pretriangulated.Triangle.neg_hom₂, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_unit_app_app, CategoryTheory.Adjunction.homAddEquiv_zero, CategoryTheory.Pseudofunctor.StrongTrans.rightUnitor_inv_as_app, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_app_assoc, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply, CategoryTheory.Iso.op2_unop_hom_unop2, DerivedCategory.from_singleFunctor_obj_eq_zero_of_projective, CategoryTheory.FreeBicategory.mk_associator_hom, CategoryTheory.op_sum, AddCommGrpCat.biprodIsoProd_inv_comp_desc, TopModuleCat.hom_sub, CategoryTheory.Limits.BinaryCofan.unop_mk, TopCat.Presheaf.restrictOpenCommRingCat_apply, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_iff_epi₂, CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIso_hom, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_hom_app_unmop, CategoryTheory.LaxFunctor.map₂_leftUnitor, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_id_naturality_inv, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality, CategoryTheory.Biprod.ofComponents_fst, CategoryTheory.ShortComplex.Splitting.op_s, CategoryTheory.MonoOver.isThin, CategoryTheory.Biprod.unipotentUpper_inv, CategoryTheory.typeEquiv_counitIso_hom_app_val_app, CategoryTheory.Functor.prod_η_fst, CategoryTheory.Limits.Fork.op_ι_app_one, CategoryTheory.IsPullback.of_has_biproduct, SheafOfModules.unitHomEquiv_comp_apply, CategoryTheory.CategoryOfElements.toCostructuredArrow_obj, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_symm_apply_f, CategoryTheory.LaxFunctor.mapComp_assoc_left_app, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_comp_map_assoc, CategoryTheory.Presheaf.uliftYonedaAdjunction_unit_app_app, CategoryTheory.ShiftedHom.opEquiv'_symm_add, AlgebraicGeometry.ΓSpecIso_inv_ΓSpec_adjunction_homEquiv, CategoryTheory.NonPreadditiveAbelian.add_neg, CategoryTheory.Mon_Class.comp_one, CategoryTheory.Bicategory.conjugateEquiv_adjunction_id, CategoryTheory.Cat.rightUnitor_inv_app, AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zero, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app, CategoryTheory.unop_inv, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app_assoc, AlgebraicGeometry.StructureSheaf.res_apply, Rep.coindVEquiv_apply_hom, CategoryTheory.Pseudofunctor.Grothendieck.Hom.ext_iff, CategoryTheory.Functor.uncurry_obj_map, AlgebraicGeometry.Scheme.LocalRepresentability.instIsLocallyInjectiveHomYonedaGluedToSheaf, CategoryTheory.Bicategory.Prod.snd_mapId_inv, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_app_assoc, AlgebraicGeometry.Scheme.Modules.Hom.add_app, CategoryTheory.Presieve.Arrows.toCompatible_coe, SSet.stdSimplex.yonedaEquiv_map, CategoryTheory.Groupoid.isIsomorphic_iff_nonempty_hom, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.kernel_ι_d_comp_d, CategoryTheory.CatEnrichedOrdinary.homEquiv_comp, SemiNormedGrp.completion.map_zero, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_as_app, CategoryTheory.Limits.PullbackCone.op_inl, CategoryTheory.NatTrans.rightOp_app, CategoryTheory.Bicategory.InducedBicategory.bicategory_homCategory_comp_hom, CategoryTheory.Limits.PreservesKernel.of_iso_comparison, CategoryTheory.Enriched.Functor.natTransEquiv_symm_whiskerRight_functorHom_app, AlgebraicTopology.DoldKan.P_add_Q, CategoryTheory.ShortComplex.pOpcycles_π_isoOpcyclesOfIsColimit_inv, AlgebraicTopology.DoldKan.hσ'_eq, HomologicalComplex₂.d₂_eq, CategoryTheory.CommSq.left_adjoint, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_inv_app_app, CategoryTheory.unop_comp_assoc, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_as_app, CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv', AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv, CategoryTheory.Lax.StrongTrans.naturality_naturality, CategoryTheory.Limits.limitCompCoyonedaIsoCone_inv, CategoryTheory.Limits.Cofork.unop_π_app_zero, CategoryTheory.Monad.algebraPreadditive_homGroup_nsmul_f, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_inv_ι_assoc, HomologicalComplex.extend_d_from_eq_zero, HomotopicalAlgebra.RightHomotopyRel.equivalence, CategoryTheory.Bicategory.precomposing_obj, CategoryTheory.NonPreadditiveAbelian.lift_map_assoc, CategoryTheory.Cat.rightUnitor_inv_toNatTrans, CategoryTheory.ShiftedHom.opEquiv'_zero_add_symm, CategoryTheory.Subobject.bot_eq_zero, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_hom_assoc, AlgebraicGeometry.Scheme.Hom.map_appLE', Homotopy.extend.hom_eq_zero₂, CategoryTheory.Functor.toPseudoFunctor_mapId, CategoryTheory.Oplax.OplaxTrans.naturality_naturality, CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inl_assoc, CategoryTheory.Bicategory.conjugateEquiv_of_iso, CategoryTheory.ShortComplex.zero, CategoryTheory.Pseudofunctor.isPrestackFor_iff, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionRight_op, CategoryTheory.ShiftedHom.opEquiv'_symm_op_opShiftFunctorEquivalence_counitIso_inv_app_op_shift, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_assoc, CategoryTheory.Presheaf.imageSieve_whisker_forget, CategoryTheory.MonoidalClosed.homEquiv_symm_apply_eq, CategoryTheory.composePath_cons, CategoryTheory.Subgroupoid.IsNormal.conjugation_bij, TopModuleCat.hom_nsmul, CategoryTheory.ShortComplex.Exact.rightHomologyDataOfIsColimitCokernelCofork_ι, CategoryTheory.GrpObj.lift_commutator_eq_mul_mul_inv_inv_assoc, CategoryTheory.ShortComplex.LeftHomologyData.liftK_π_eq_zero_of_boundary, Mathlib.Tactic.Elementwise.forget_hom_Type, CategoryTheory.bicategoricalComp_refl, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_right, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_hom_app_unop_assoc, CategoryTheory.Limits.Cofork.IsColimit.existsUnique, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_apply, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv, CategoryTheory.WithInitial.map₂_app, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp_assoc, CategoryTheory.Iso.eHomCongr_comp, CategoryTheory.Bicategory.LeftLift.ofIdComp_hom, CategoryTheory.ShortComplex.Homotopy.neg_h₀, CategoryTheory.functorMapReverse, CategoryTheory.Functor.IsRepresentedBy.map_bijective, CategoryTheory.Bicategory.rightZigzagIso_inv, CategoryTheory.Bicategory.prod_comp_fst, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'_inv, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_hom_app_app_down, CategoryTheory.Pseudofunctor.StrongTrans.associator_hom_as_app, HomologicalComplex.toCycles_comp_homologyπ_assoc, CategoryTheory.Functor.PullbackObjObj.ofHasPullback_snd, CategoryTheory.Limits.image.preComp_comp, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_presheafHom_uliftYoneda_obj, CategoryTheory.Pseudofunctor.map₂_right_unitor, CategoryTheory.ShortComplex.exact_and_mono_f_iff_f_is_kernel, CategoryTheory.Functor.representableByUliftFunctorEquiv_apply_homEquiv, CategoryTheory.Functor.shift_map_op, CategoryTheory.Lax.LaxTrans.StrongCore.naturality_hom, CategoryTheory.ShiftedHom.homEquiv_apply, HomologicalComplex₂.D₂_D₁, CategoryTheory.tensorUnit_def, CategoryTheory.Bicategory.Pith.associator_inv_iso_inv, CategoryTheory.Bicategory.rightUnitor_comp_inv, LightCondensed.ihomPoints_symm_apply, CategoryTheory.Pretriangulated.Triangle.add_hom₂, CategoryTheory.Pseudofunctor.IsStackFor.isEquivalence, CategoryTheory.Limits.ι_comp_colimitOpIsoOpLimit_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHom_op, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy_homEquiv_apply_app, CategoryTheory.Pretriangulated.shiftFunctor_op_map, CategoryTheory.Limits.CokernelCofork.condition_assoc, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_inv_comp_π, CategoryTheory.Localization.hasSmallLocalizedHom_iff, CategoryTheory.ShortComplex.RightHomologyData.op_f', CategoryTheory.Subgroupoid.coe_inv_coe', CategoryTheory.Bicategory.whiskerLeft_hom_inv_assoc, AlgebraicTopology.DoldKan.hσ'_eq_zero, CategoryTheory.ShortComplex.add_τ₂, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_comp_naturality_inv, CategoryTheory.NormalMono.w, CategoryTheory.Bicategory.LeftLift.whiskerOfIdCompIsoSelf_hom_right, CategoryTheory.initiallySmall_iff_exists_small_weakly_initial_set, CategoryTheory.uliftCoyonedaEquiv_naturality, CategoryTheory.Pseudofunctor.CoGrothendieck.instEssSurjαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_app_assoc, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_assoc, HomologicalComplex₂.shape_f, CategoryTheory.Limits.opProdIsoCoprod_hom_fst_assoc, Mathlib.Tactic.Bicategory.evalWhiskerRight_nil, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app_assoc, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π_assoc, CategoryTheory.op_inv_rightUnitor, CategoryTheory.Pretriangulated.Triangle.zero_hom₃, SemiNormedGrp₁.zero_apply, CategoryTheory.Pretriangulated.Triangle.add_hom₃, CategoryTheory.Pseudofunctor.mapComp'_eq_mapComp, CategoryTheory.Limits.isLimitConeLeftOpOfCocone_lift, RingCat.moduleCatRestrictScalarsPseudofunctor_obj, CategoryTheory.CatCenter.app_neg_one_zpow, CategoryTheory.cokernelUnopUnop_hom, CategoryTheory.MonoidalPreadditive.zero_tensor, CategoryTheory.pseudofunctorOfIsLocallyDiscrete_map, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_inv_app_eq, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp_app, CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_inv_app_unmop_unmop, CondensedSet.LocallyConstant.instFaithfulCondensedTypeDiscrete, SSet.stdSimplex.objEquiv_toOrderHom_apply, CategoryTheory.Localization.SmallHom.equiv_comp, CategoryTheory.Bicategory.HasLeftKanExtension.hasInitial, CategoryTheory.Limits.fst_of_isColimit, CategoryTheory.IsGrothendieckAbelian.instInjectiveZMonomorphismsRlpMonoMapFactorizationDataRlpOfNatHom, CategoryTheory.ShortComplex.rightHomologyMap_add, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_left, CategoryTheory.NonPreadditiveAbelian.add_comp, CategoryTheory.Pseudofunctor.Grothendieck.Hom.congr, CategoryTheory.Grpd.freeForgetAdjunction_homEquiv_apply, CategoryTheory.Limits.coprod.inr_fst_assoc, CategoryTheory.PrelaxFunctor.map₂_comp, CategoryTheory.Presieve.uncurry_ofArrows, CategoryTheory.Functor.homEquivOfIsRightKanExtension_symm_apply, Bicategory.Opposite.unop2_comp, CategoryTheory.OplaxFunctor.mapComp_naturality_left_assoc, CategoryTheory.simplicialCosimplicialEquiv_unitIso_inv_app, CategoryTheory.Limits.inr_pushoutZeroZeroIso_inv, CategoryTheory.Limits.Bicone.ι_π, CategoryTheory.ComposableArrows.isoMk₀_inv_app, CategoryTheory.StrictlyUnitaryLaxFunctor.mk'_map₂, CategoryTheory.GrpObj.div_comp, HomotopicalAlgebra.instCofibrationOppositeOpOfFibration, CategoryTheory.Limits.limit.homIso_hom, CategoryTheory.Functor.prod'_ε_snd, CategoryTheory.Limits.biprod.inr_fst_assoc, CategoryTheory.sum.inrCompAssociator_inv_app_down_down, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom, CategoryTheory.Limits.colimit.existsUnique, CategoryTheory.PrelaxFunctor.mapFunctor_obj, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_apply, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_val_map, CategoryTheory.GrothendieckTopology.overMapPullbackComp_inv_app_val_app, CategoryTheory.Pseudofunctor.Grothendieck.map_map_fiber, CategoryTheory.uliftYonedaIsoYoneda_hom_app_app, CategoryTheory.ShortComplex.rightHomologyι_descOpcycles_π_eq_zero_of_boundary_assoc, CategoryTheory.IsCodetecting.isIso_iff_of_epi, CategoryTheory.RetractArrow.op_r_left, CategoryTheory.Preadditive.homSelfLinearEquivEndMulOpposite_symm_apply, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_iso_hom, CategoryTheory.Pseudofunctor.StrongTrans.rightUnitor_hom_as_app, CategoryTheory.Functor.FullyFaithful.compUliftYonedaCompWhiskeringLeft_hom_app_app_down, CategoryTheory.Pseudofunctor.map₂_whisker_left_app_assoc, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_α, CategoryTheory.Limits.isLimitConeOfCoconeLeftOp_lift, CochainComplex.mappingCone.decomp_to, CategoryTheory.Bicategory.lanUnit_desc, SemiNormedGrp.explicitCokernelDesc_zero, CategoryTheory.eqToHom_down, CategoryTheory.equivYoneda_inv_app, CategoryTheory.CommSq.shortComplex'_g, CategoryTheory.uliftCoyonedaEquiv_symm_map_assoc, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_obj, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app, Rep.leftRegularHomEquiv_symm_single, CategoryTheory.PreGaloisCategory.comp_autMap_apply, CommMonCat.coyoneda_map_app, AlgebraicGeometry.Spec.homEquiv_apply, CategoryTheory.Subgroupoid.IsNormal.vertexSubgroup, CategoryTheory.StrictPseudofunctor.comp_mapComp_inv, CategoryTheory.Bicategory.whiskerLeft_id, inhomogeneousCochains.d_eq, CategoryTheory.Adjunction.homAddEquiv_symm_apply, CategoryTheory.Functor.Faithful.map_injective, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_symm_apply_f, HomologicalComplex.extend.comp_d_eq_zero_iff, CategoryTheory.NatTrans.appLinearMap_apply, CategoryTheory.unop_inv_braiding, CategoryTheory.MonoidalClosed.curry_injective, CategoryTheory.op_inv, CategoryTheory.Comonad.coalgebraPreadditive_homGroup_zsmul_f, CategoryTheory.Localization.Construction.liftToPathCategory_map, CategoryTheory.Limits.Trident.IsLimit.homIso_symm_apply, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_inv_assoc, CategoryTheory.unop_id_op, CategoryTheory.ActionCategory.comp_val, CategoryTheory.Abelian.Pseudoelement.zero_eq_zero, CategoryTheory.Lax.StrongTrans.vComp_naturality_inv, Mathlib.Tactic.Bicategory.eval_of, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_fst_assoc, CategoryTheory.HasLiftingProperty.iff_op, CategoryTheory.Presieve.FamilyOfElements.comp_of_compatible, CategoryTheory.LaxFunctor.mapComp_assoc_right_assoc, CategoryTheory.shift_zero_eq_zero, CategoryTheory.Functor.Final.zigzag_of_eqvGen_colimitTypeRel, CategoryTheory.Limits.BinaryBicone.inlCokernelCofork_π, CategoryTheory.Pseudofunctor.mapComp'_naturality_2, CategoryTheory.Groupoid.invEquiv_symm_apply, CategoryTheory.Limits.opProdIsoCoprod_inv_inr, AlgebraicGeometry.Spec.coe_toTop_map_hom_apply_asIdeal, AlgebraicGeometry.Scheme.Opens.toScheme_presheaf_map, CategoryTheory.IsPullback.zero_bot, CategoryTheory.Oplax.StrongTrans.vcomp_naturality_hom, CategoryTheory.ObjectProperty.rightOrthogonal.map_bijective_of_isTriangulated, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_apply, CategoryTheory.orderDualEquivalence_functor_map, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_obj_base, CategoryTheory.Functor.CorepresentableBy.homEquiv_comp, CategoryTheory.CatEnrichedOrdinary.hComp_id_heq, CategoryTheory.ShortComplex.LeftHomologyMapData.unop_φH, HomologicalComplex₂.D₁_D₂_assoc, CategoryTheory.Functor.FullyFaithful.compUliftCoyonedaCompWhiskeringLeft_inv_app_app_down, CategoryTheory.Adjunction.homAddEquiv_symm_add, Homotopy.trans_hom, CategoryTheory.Lax.StrongTrans.id_naturality_inv, CategoryTheory.Limits.pushoutIsoOpPullback_inl_hom_assoc, CategoryTheory.LocalizerMorphism.equiv_smallHomMap, CategoryTheory.Monad.beckAlgebraCofork_ι_app, TopCat.Sheaf.objSupIsoProdEqLocus_hom_snd, CategoryTheory.Idempotents.Karoubi.complement_p, CategoryTheory.Sheaf.instIsLocallySurjectiveHomMapTypeSheafComposeForget, CategoryTheory.ite_comp, SSet.Truncated.StrictSegal.spine_δ_arrow_eq, SemiNormedGrp.comp_explicitCokernelπ, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_app, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app_assoc, CategoryTheory.conjugateEquiv_symm_comm, CategoryTheory.Oplax.OplaxTrans.naturality_naturality_assoc, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_norm, CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal_δ_unmop_unmop, CategoryTheory.Limits.Sigma.ι_π_of_ne_assoc, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_inv_app_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w_assoc, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionRight_unop, CategoryTheory.PreGaloisCategory.instFaithfulContActionFintypeCatHomCarrierAutFunctorFunctorToContAction, CategoryTheory.Functor.CorepresentableBy.uniqueUpToIso_hom, CategoryTheory.Limits.MultispanIndex.parallelPairDiagramOfIsColimit_map, CategoryTheory.Bicategory.InducedBicategory.forget_obj, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHomRight, CochainComplex.mappingCone.lift_desc_f, CategoryTheory.imageUnopOp_hom_comp_image_ι, TopCat.Sheaf.objSupIsoProdEqLocus_inv_eq_iff, CategoryTheory.Limits.isColimitCoconeRightOpOfCone_desc, HomologicalComplex.instQuasiIsoOppositeMapSymmOpFunctorOp, CategoryTheory.Limits.limitUnopIsoUnopColimit_hom_comp_ι_assoc, CategoryTheory.Bicategory.Adj.Bicategory.associator_inv_τl, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app_assoc, CategoryTheory.Limits.isColimitCoconeOfConeRightOp_desc, CategoryTheory.Limits.desc_op_comp_opCoproductIsoProduct_hom, CategoryTheory.Equivalence.sheafCongrPrecoherent_inverse_obj_val_map, CategoryTheory.Limits.CokernelCofork.map_condition, CategoryTheory.MonoidalOpposite.tensorRightMopIso_inv_app_unmop, CategoryTheory.Limits.biproduct.lift_matrix, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₃₁_assoc, CategoryTheory.MonoidalCategory.dite_tensor, CategoryTheory.MonObj.pow_comp, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_hom_app_val_app, CategoryTheory.StrictPseudofunctor.id_map, CategoryTheory.Pseudofunctor.toDescentData_map_hom, CategoryTheory.CountableCategory.instCountableHomObjAsType, CategoryTheory.ShortComplex.HomologyMapData.neg_right, CategoryTheory.Pseudofunctor.map₂_associator, CategoryTheory.CommSq.LiftStruct.unop_l, AlgebraicGeometry.Proj.awayMap_awayToSection, CategoryTheory.Groupoid.invEquivalence_counitIso, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, CategoryTheory.ShortComplex.homologyι_comp_fromOpcycles, CategoryTheory.Bicategory.conjugateEquiv_associator_hom, CategoryTheory.Bicategory.Prod.swap_obj, CategoryTheory.HasLiftingProperty.iff_unop, CategoryTheory.epi_from_simple_zero_of_not_iso, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_app_app, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_fst, CategoryTheory.Free.lift_map_single, CategoryTheory.Square.opFunctor_map_τ₃, CategoryTheory.Idempotents.Karoubi.zsmul_hom, CategoryTheory.Presheaf.map_comp_uliftYonedaEquiv_down_assoc, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_obj, CategoryTheory.homOfLE_op_comp_eqToHom, HomologicalComplex₂.ι_totalShift₂Iso_inv_f, CategoryTheory.Abelian.coimage.comp_π_eq_zero, CategoryTheory.Join.opEquiv_inverse_map_edge_op, CategoryTheory.ObjectProperty.homMk_surjective, CategoryTheory.PrelaxFunctor.map₂_hom_inv_isIso, CategoryTheory.Functor.curryingFlipEquiv_apply_map, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_assoc, CategoryTheory.Limits.coconeLeftOpOfCone_ι_app, CategoryTheory.MorphismProperty.RightFraction.unop_f, CategoryTheory.Limits.π_comp_colimitRightOpIsoUnopLimit_inv, CategoryTheory.Limits.ι_comp_colimitUnopIsoOpLimit_hom_assoc, CategoryTheory.Limits.zero_of_target_iso_zero, CategoryTheory.ShortComplex.Homotopy.add_h₂, CategoryTheory.yonedaGrpObj_obj_coe, CategoryTheory.LocalizerMorphism.RightResolution.unop_w, CategoryTheory.conjugateEquiv_id, CategoryTheory.Functor.mapAddHom_apply, CategoryTheory.Abelian.Ext.smul_eq_comp_mk₀, CategoryTheory.ShortComplex.Splitting.r_f, CategoryTheory.Bicategory.Pith.inclusion_mapId, CategoryTheory.Oplax.OplaxTrans.Modification.whiskerRight_naturality_assoc, CategoryTheory.Pseudofunctor.ObjectProperty.IsClosedUnderIsomorphisms.isClosedUnderIsomorphisms, CochainComplex.ConnectData.shape, CategoryTheory.Triangulated.TStructure.zero', CondensedSet.LocallyConstant.instFullCondensedTypeDiscrete, AlgebraicGeometry.tilde.map_add, CategoryTheory.Functor.RepresentableBy.uniqueUpToIso_inv, RingCat.moduleCatRestrictScalarsPseudofunctor_mapComp, Action.FintypeCat.quotientToQuotientOfLE_hom_mk, CategoryTheory.IsPullback.zero_right, CochainComplex.HomComplex.Cochain.leftShift_v, CochainComplex.mappingCone.desc_f, AlgebraicGeometry.isIso_SpecMap_stakMap_localization, CochainComplex.mappingCone.d_fst_v'_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHomLeft, CategoryTheory.StrictPseudofunctor.id_mapId_hom, Bicategory.Opposite.op2_leftUnitor_inv, CategoryTheory.Bicategory.InducedBicategory.Hom.category_comp_hom, LightCondMod.epi_iff_locallySurjective_on_lightProfinite, CategoryTheory.Bicategory.Prod.fst_map, AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit_map, SSet.stdSimplex.ofSimplex_yonedaEquiv_δ, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app_assoc, CategoryTheory.Bicategory.Adj.Hom₂.conjugateEquiv_τl, AlgebraicTopology.DoldKan.σ_comp_PInfty, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_iso_inv, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapCompIso_inv, CategoryTheory.WithTerminal.liftFromOver_obj_map, CochainComplex.HomComplex.Cochain.toSingleMk_zero, CategoryTheory.Bicategory.eqToHom_whiskerRight, CategoryTheory.Bicategory.Adj.associator_inv_τl, CategoryTheory.Bicategory.prod_comp_snd, CategoryTheory.Preadditive.comp_add, LightCondensed.ihom_map_val_app, CategoryTheory.Oplax.OplaxTrans.rightUnitor_inv_as_app, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_app_assoc, CategoryTheory.Abelian.Pseudoelement.pseudoZero_aux, CategoryTheory.Abelian.Ext.addEquiv₀_symm_apply, CategoryTheory.ShortComplex.Homotopy.eq_add_nullHomotopic, CategoryTheory.Limits.kernelZeroIsoSource_hom, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk, CategoryTheory.Presieve.FamilyOfElements.isAmalgamation_map_localPreimage, CategoryTheory.Presheaf.isLocallySurjective_toPlus, dNext_eq_dFrom_fromNext, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanIndex_fst, CategoryTheory.Preadditive.sum_comp'_assoc, CochainComplex.mappingCone.inl_v_d, CategoryTheory.Linear.homCongr_symm_apply, AlgebraicGeometry.PresheafedSpace.Γ_map, CategoryTheory.OplaxFunctor.mapComp'_comp_whiskerLeft_mapComp', CategoryTheory.Pretriangulated.contractibleTriangle_mor₃, CategoryTheory.ShortComplex.Homotopy.comp_h₀, CategoryTheory.Adjunction.homAddEquiv_neg, MonObj.mopEquiv_functor_obj_mon_mul_unmop, CategoryTheory.Bicategory.Pith.comp₂_iso_hom, CategoryTheory.Limits.biproduct.desc_eq, CategoryTheory.Bicategory.lanLiftUnit_desc, CategoryTheory.Bicategory.leftUnitor_naturality_assoc, CategoryTheory.Bicategory.conjugateEquiv_id, CategoryTheory.Lax.StrongTrans.id_naturality_hom, AlgebraicGeometry.ΓSpec.right_triangle, CategoryTheory.Functor.IsStronglyCartesian.universal_property, CategoryTheory.Adjunction.homEquiv_symm_id, CategoryTheory.isIso_iff_yoneda_map_bijective, SSet.Truncated.Path₁.arrow_tgt, CategoryTheory.TwistShiftData.shiftFunctorAdd'_inv_app, CategoryTheory.StrictlyUnitaryLaxFunctor.mk'_map, CategoryTheory.Bicategory.whisker_assoc, CategoryTheory.Square.op_f₁₃, CategoryTheory.wideSubcategoryInclusion.map, CategoryTheory.Lax.OplaxTrans.naturality_id, CategoryTheory.Iso.unop_hom, CategoryTheory.comp_ite, CategoryTheory.ShortComplex.ShortExact.δ_comp, CategoryTheory.Subgroupoid.coe_inv_coe, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₃, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_of_eq, CategoryTheory.SemiCartesianMonoidalCategory.default_eq_toUnit, CategoryTheory.StructuredArrow.w_prod_fst_assoc, AlgebraicGeometry.StructureSheaf.comap_id_eq_map, CategoryTheory.MonoidalClosed.internalHom_map, AlgebraicGeometry.Scheme.Hom.appIso_hom, CategoryTheory.ShortComplex.HomologyMapData.smul_right, CategoryTheory.Limits.opProdIsoCoprod_hom_snd, CategoryTheory.Limits.biprod.lift_desc_assoc, CategoryTheory.Preadditive.isLimitForkOfKernelFork_lift, CategoryTheory.ShiftedHom.opEquiv'_symm_comp, CategoryTheory.Preadditive.epi_iff_isZero_cokernel', CategoryTheory.PreOneHypercover.sieve₁_apply, CategoryTheory.Functor.closedSieves_map_coe, SimplicialObject.Splitting.IndexSet.epiComp_snd_coe, CategoryTheory.Limits.CokernelCofork.map_π, CategoryTheory.Bicategory.Adj.comp_τr, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, CategoryTheory.ShortComplex.LeftHomologyMapData.smul_φK, FintypeCat.inv_hom_id_apply, CategoryTheory.OplaxFunctor.PseudoCore.mapIdIso_hom, CategoryTheory.Adjunction.homEquiv_naturality_left_square_iff, CategoryTheory.ShortComplex.homologyι_descOpcycles_eq_zero_of_boundary_assoc, HomologicalComplex.homologyι_descOpcycles_eq_zero_of_boundary_assoc, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm, ModuleCat.hom_zsmul, CategoryTheory.Limits.PullbackCone.unop_pt, CategoryTheory.Preadditive.inv_def, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_apply, CategoryTheory.Endofunctor.Coalgebra.ext_iff, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHom, HomologicalComplex.mapBifunctorMapHomotopy.comm₁_aux, CategoryTheory.Adjunction.homEquiv_naturality_right_symm, InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj, CategoryTheory.Presheaf.instIsLocallySurjectiveHomToRangeSheafify, ChainComplex.linearYonedaObj_d, CategoryTheory.ShortComplex.unop_g, CategoryTheory.ShortComplex.Homotopy.symm_h₂, Action.zsmul_hom, CategoryTheory.PreGaloisCategory.instEssSurjContActionFintypeCatHomCarrierAutFunctorFunctorToContActionOfFiberFunctor, CategoryTheory.Mon_Class.one_comp, CategoryTheory.cokernelOpUnop_hom, CategoryTheory.Preadditive.neg_comp, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_fst, CategoryTheory.Bicategory.conjugateEquiv_symm_iso, CategoryTheory.Bicategory.InducedBicategory.isoMk_inv_hom, Compactum.str_hom_commute, Homotopy.smul_hom, Homotopy.prevD_zero_cochainComplex, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.toBiprod_fromBiprod_assoc, CategoryTheory.Equivalence.rightOp_unitIso_inv_app, CategoryTheory.Bicategory.Prod.sectR_mapComp_hom, CategoryTheory.Limits.MonoFactorisation.kernel_ι_comp, CategoryTheory.HomOrthogonal.eq_zero, CategoryTheory.StrictPseudofunctor.mapComp_eq_eqToIso, AlgebraicGeometry.tilde.toOpen_res, CategoryTheory.Pretriangulated.Triangle.add_hom₁, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_map, AlgebraicGeometry.tilde.toOpen_res_assoc, CategoryTheory.PrelaxFunctor.map₂_comp_assoc, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv_assoc, CategoryTheory.Limits.biproduct.toSubtype_eq_desc, CategoryTheory.LaxFunctor.mapComp_naturality_right, CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_two_symm, CategoryTheory.Functor.FullyFaithful.homNatIso'_inv_app_down, Bicategory.Opposite.unop2_op2, CategoryTheory.Mat.add_apply, CategoryTheory.Preadditive.mul_def, Rep.MonoidalClosed.linearHomEquiv_hom, CategoryTheory.ShortComplex.Homotopy.sub_h₂, CategoryTheory.Abelian.Ext.mk₀_eq_zero_iff, CategoryTheory.congrArg_cast_hom_left, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_as_app, CategoryTheory.StrictPseudofunctorPreCore.map₂_whisker_left, Rep.invariantsAdjunction_homEquiv_apply_hom, CategoryTheory.SemiadditiveOfBinaryBiproducts.add_eq_left_addition, CategoryTheory.Functor.IsRepresentedBy.iff_isIso_uliftYonedaEquiv, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_hom_comp_π, CategoryTheory.Limits.widePushoutShapeUnop_map, CategoryTheory.kernel.ι_op, CategoryTheory.Bicategory.associatorNatIsoRight_hom_app, CategoryTheory.Limits.Bicone.ofColimitCocone_π, CategoryTheory.Bicategory.Adj.lIso_inv, CategoryTheory.Bicategory.instIsIsoHomRightZigzagHom, CategoryTheory.Meq.mk_apply, CategoryTheory.SimplicialObject.Augmented.rightOp_hom_app, CategoryTheory.yonedaEquiv_naturality, SimplicialObject.Splitting.πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty_assoc, SSet.Truncated.StrictSegal.spineToSimplex_interval, CategoryTheory.Adjunction.homEquiv_apply, CategoryTheory.Abelian.preadditiveCoyonedaObj_map_surjective, CategoryTheory.MonoidalLinear.smul_whiskerRight, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_symm_apply, CategoryTheory.unopUnop_map, HomotopicalAlgebra.fibration_unop_iff, SheafOfModules.pushforwardNatTrans_app_val_app, CategoryTheory.Subgroupoid.inv_mem_iff, CategoryTheory.Mat_.comp_apply, CategoryTheory.WithTerminal.pseudofunctor_mapId, CategoryTheory.kernelCokernelCompSequence.φ_π, CategoryTheory.PreGaloisCategory.evaluation_aut_surjective_of_isGalois, HomologicalComplex₂.ιTotal_totalFlipIso_f_hom, SimplicialObject.Split.natTransCofanInj_app, CategoryTheory.MonoidalLinear.whiskerLeft_smul, CategoryTheory.Bicategory.associator_inv_congr, CategoryTheory.Bicategory.inv_whiskerLeft, CochainComplex.ConnectData.d₀_comp_assoc, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackId_hom, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_id_app, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app_assoc, CategoryTheory.Limits.FormalCoproduct.cosimplicialObjectFunctor_obj_map, ModuleCat.Hom.hom₂_apply, ChainComplex.fromSingle₀Equiv_apply, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app_assoc, CochainComplex.mappingCone.d_fst_v', CategoryTheory.ComposableArrows.opEquivalence_inverse_map, CategoryTheory.Pseudofunctor.IsStackFor.essSurj, CategoryTheory.ShortComplex.LeftHomologyMapData.neg_φK, TopModuleCat.hom_smul, CategoryTheory.NonPreadditiveAbelian.add_comm, CondensedMod.epi_iff_locallySurjective_on_compHaus, CategoryTheory.LocalizerMorphism.LeftResolution.op_w, CategoryTheory.Pseudofunctor.id_mapComp, CategoryTheory.Limits.isoZeroOfEpiZero_inv, CategoryTheory.StrictPseudofunctor.mk'_map₂, CategoryTheory.Limits.PushoutCocone.op_pt, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_α, CategoryTheory.Functor.toPseudoFunctor'_mapId, Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply, CategoryTheory.WithInitial.prelaxfunctor_toPrelaxFunctorStruct_toPrefunctor_map, AlgebraicGeometry.ΓSpec.adjunction_homEquiv_symm_apply, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_apply, SemiNormedGrp.hom_zero, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_inv, CategoryTheory.Iso.op2_inv_unop2, Bicategory.Opposite.op2_leftUnitor, CategoryTheory.Limits.kernel.condition_assoc, CategoryTheory.GrpObj.comp_inv_assoc, CategoryTheory.PrelaxFunctor.map₂_isIso, AlgebraicGeometry.Spec_Γ_naturality_assoc, CategoryTheory.types_hom, AlgebraicGeometry.Scheme.Hom.appLE_map'_assoc, CategoryTheory.IsKernelPair.pullback, AlgebraicGeometry.RingedSpace.isUnit_res_basicOpen, CategoryTheory.Bicategory.mateEquiv_leftUnitor_hom_rightUnitor_inv, TopCat.Presheaf.germ_res'_assoc, AlgebraicGeometry.Scheme.Opens.ι_app_self, CategoryTheory.Bicategory.LeftExtension.whisker_unit, CategoryTheory.Bicategory.conjugateEquiv_mateEquiv_vcomp, CategoryTheory.LaxFunctor.map₂_rightUnitor_app, Homotopy.comm, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHomLeft, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_symm_apply, CategoryTheory.Functor.WellOrderInductionData.Extension.compatibility, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_hom_apply, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackComp_inv, TopCat.toSheafCompHausLike_val_map, CategoryTheory.Functor.map_shift_unop_assoc, CategoryTheory.toQuotientPaths_obj_as, CategoryTheory.ActionCategory.id_val, CategoryTheory.ShortComplex.Homotopy.trans_h₁, CategoryTheory.Pseudofunctor.mapComp'_id_comp, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_assoc, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality, HomologicalComplex.mapBifunctor.d₁_eq', AlgebraicGeometry.Scheme.Hom.naturality, CategoryTheory.Limits.cokernelBiprodInlIso_hom, CategoryTheory.Iso.homCongr_symm_apply, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app, CategoryTheory.yonedaCommGrpGrp_map_app, CategoryTheory.regularTopology.equalizerCondition_w, SSet.Truncated.Path.arrow_tgt, CategoryTheory.StrictPseudofunctor.comp_map₂, CategoryTheory.Bicategory.prod_homCategory_id_snd, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_hom_iCycles, CategoryTheory.ShortComplex.Homotopy.comm₂, CategoryTheory.Limits.biproduct.ι_π, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_assoc, CategoryTheory.RetractArrow.op_i_left, HomologicalComplex.d_comp_d, CategoryTheory.Functor.partialRightAdjointHomEquiv_symm_comp_assoc, CategoryTheory.PreZeroHypercover.sumLift_h₀, ChainComplex.mk_congr_succ_d₂, CommRingCat.HomTopology.isHomeomorph_precomp, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app, CategoryTheory.ShortComplex.op_f, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃, CategoryTheory.Bicategory.Adj.Bicategory.associator_hom_τr, SSet.mem_degenerate_iff, SSet.S.le_iff_nonempty_hom, CategoryTheory.Bicategory.InducedBicategory.forget_map₂, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_app_assoc, CategoryTheory.Abelian.image.ι_comp_eq_zero, CategoryTheory.Equivalence.sheafCongr.inverse_obj_val_map, TopCat.Presheaf.isGluing_iff_pairwise, CategoryTheory.GrpObj.comp_div_assoc, CategoryTheory.OrthogonalReflection.D₁.ι_comp_t, Bicategory.Opposite.bicategory_homCategory_id_unop2, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_assoc, CategoryTheory.IsPushout.of_hasBinaryBiproduct, CategoryTheory.composePath_id, CategoryTheory.Bicategory.associatorNatIsoLeft_hom_app, HomologicalComplex.mapBifunctor.d₂_eq_zero, CategoryTheory.ShortComplex.Splitting.s_r, CategoryTheory.Arrow.cechNerve_map, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π_assoc, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, CategoryTheory.LocalizerMorphism.RightResolution.unopFunctor_map_f, CochainComplex.HomComplex.Cocycle.equivHomShift_comp, groupHomology.inhomogeneousChains.d_comp_d, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_fst, ChainComplex.chainComplex_d_succ_succ_zero, CategoryTheory.MonoidalCategory.rightAssocTensor_map, CategoryTheory.Subgroupoid.mem_full_iff, CategoryTheory.Bicategory.LeftLift.whiskerIdCancel_right, CategoryTheory.TwistShiftData.shiftFunctorAdd'_hom_app, AlgebraicGeometry.Scheme.restrict_presheaf_map, CategoryTheory.PrelaxFunctor.comp_toPrelaxFunctorStruct, CategoryTheory.Sheaf.ΓHomEquiv_naturality_right, HomologicalComplex.quasiIso_opFunctor_map_iff, CategoryTheory.MonoidalClosed.curryHomEquiv'_symm_apply, CategoryTheory.ShortComplex.sub_τ₃, CategoryTheory.PrelaxFunctor.map₂_inv_hom_assoc, CategoryTheory.Limits.Pi.ι_π_of_ne_assoc, CategoryTheory.PreGaloisCategory.PointedGaloisObject.Hom.comp, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_hom_app_app, CategoryTheory.map_yonedaEquiv, Homotopy.comp_hom, CategoryTheory.Oplax.StrongTrans.isoMk_inv_as_app, CategoryTheory.CatEnrichedOrdinary.hComp_assoc, CategoryTheory.Bicategory.Prod.fst_mapComp_inv, CategoryTheory.ShortComplex.abelianImageToKernel_comp_kernel_ι_comp_cokernel_π, dNext_eq, CategoryTheory.ComposableArrows.IsComplex.epi_cokerToKer', CategoryTheory.Oplax.StrongTrans.Modification.naturality, CategoryTheory.rightAdjointOfCostructuredArrowTerminalsAux_symm_apply, CategoryTheory.tensorLeftHomEquiv_symm_coevaluation_comp_whiskerRight, CategoryTheory.op_zsmul, CategoryTheory.Sieve.natTransOfLe_app_coe, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv, CategoryTheory.eHomEquiv_comp, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom, CommRingCat.moduleCatExtendScalarsPseudofunctor_mapComp, CategoryTheory.sum.inlCompInverseAssociator_inv_app_down_down, CochainComplex.shiftFunctor_obj_d', CategoryTheory.Pretriangulated.Triangle.smul_hom₃, CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois_symm_fiber, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_comp, CategoryTheory.Hom.one_def, CategoryTheory.NonPreadditiveAbelian.neg_sub, CategoryTheory.Functor.partialLeftAdjointHomEquiv_symm_comp_assoc, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.ShortComplex.homologyMap_op, CategoryTheory.Limits.BinaryCofan.IsColimit.desc'_coe, CategoryTheory.Limits.opProdIsoCoprod_inv_inr_assoc, groupCohomology.mapShortComplexH1_zero, SheafOfModules.pullbackPushforwardAdjunction_homEquiv_symm_unitToPushforwardObjUnit, CategoryTheory.WithTerminal.pseudofunctor_mapComp, CategoryTheory.FunctorToTypes.binaryProductCone_π_app, ModuleCat.binaryProductLimitCone_isLimit_lift, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_α, CategoryTheory.PreGaloisCategory.autEmbedding_range, CategoryTheory.NonPreadditiveAbelian.comp_add, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen', CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_hom_app_app, CategoryTheory.conjugateIsoEquiv_apply_hom, CategoryTheory.WithTerminal.prelaxfunctor_toPrelaxFunctorStruct_toPrefunctor_obj, CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_iff_epi₃, CategoryTheory.Bicategory.Adj.associator_hom_τr, CategoryTheory.op_epi_of_mono, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom, Bicategory.Opposite.unop2_id, AlgebraicTopology.DoldKan.N₂_obj_X_d, CategoryTheory.Limits.FormalCoproduct.evalOp_obj_map, CategoryTheory.Limits.WalkingMultispan.instIsEmptyHomRightLeft, CategoryTheory.BicartesianSq.of_is_biproduct₂, ModuleCat.homLinearEquiv_apply, CategoryTheory.Limits.Multifork.ofι_π_app, CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf_hom_right, CategoryTheory.ShortComplex.RightHomologyMapData.add_φH, CochainComplex.HomComplex.Cocycle.equivHom_apply, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_f, CategoryTheory.Pi.sum_map_app, CategoryTheory.Localization.structuredArrowEquiv_symm_apply, CategoryTheory.Triangulated.instNonemptyOctahedron, CategoryTheory.RanIsSheafOfIsCocontinuous.fac, CategoryTheory.Limits.Cofork.op_unop_π, CategoryTheory.Pretriangulated.Triangle.sub_hom₃, AlgebraicGeometry.AffineSpace.homOverEquiv_apply, CategoryTheory.ShortComplex.rightHomologyMap_neg, CategoryTheory.Bicategory.prod_leftUnitor_hom_fst, SimplicialObject.Splitting.cofan_inj_πSummand_eq_zero_assoc, CategoryTheory.Limits.pullbackZeroZeroIso_inv_snd, CategoryTheory.Limits.KernelFork.mapIsoOfIsLimit_hom, CategoryTheory.CommSq.instHasLift_1, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_app_assoc, CategoryTheory.Limits.limitOpIsoOpColimit_inv_comp_π, CategoryTheory.Limits.biproduct.lift_eq, CategoryTheory.BicartesianSq.of_has_biproduct₁, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_fst, Rep.homEquiv_symm_apply_hom, HomotopicalAlgebra.LeftHomotopyRel.equivalence, CategoryTheory.Grp_Class.inv_eq_inv, Rep.FiniteCyclicGroup.leftRegular.range_norm_eq_ker_applyAsHom_sub, TopCat.Sheaf.objSupIsoProdEqLocus_inv_fst, CategoryTheory.Limits.isColimitOfConeOfCoconeRightOp_desc, GrpCat.ofHom_injective, CategoryTheory.conjugateIsoEquiv_apply_inv, CategoryTheory.Endofunctor.algebraPreadditive_homGroup_zero_f, HomologicalComplex.mapBifunctor₂₃.d_eq, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τl, HomotopicalAlgebra.instCofibrationUnopOfFibrationOpposite, CategoryTheory.WithInitial.liftFromUnderComp_hom_app, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_inv_assoc, CategoryTheory.Oplax.OplaxTrans.naturality_comp_assoc, CategoryTheory.ShortComplex.RightHomologyMapData.smul_φQ, CategoryTheory.Limits.kernelZeroIsoSource_inv, CategoryTheory.Bicategory.Adjunction.comp_left_triangle_aux, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom_assoc, CategoryTheory.Bicategory.whiskerLeft_hom_inv_whiskerRight, CategoryTheory.Limits.BinaryBicone.toBiconeFunctor_obj_ι, CategoryTheory.yonedaEvaluation_map_down, CategoryTheory.CartesianClosed.uncurry_injective, CommRingCat.HomTopology.mvPolynomialHomeomorph_apply_fst, CategoryTheory.MonoidalCategory.DayConvolutionUnit.corepresentableByLeft_homEquiv, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_hom, CategoryTheory.PresheafHom.IsSheafFor.app_cond, CategoryTheory.Iso.homToEquiv_symm_apply, CategoryTheory.PreGaloisCategory.surjective_of_nonempty_fiber_of_isConnected, MonObj.mopEquiv_counitIso_inv_app_hom_unmop, CategoryTheory.unitCompPartialBijective_symm_natural, CategoryTheory.NatTrans.app_smul, CategoryTheory.FunctorToTypes.binaryCoproductCocone_ι_app, CategoryTheory.Subgroupoid.mem_iff, AddCommGrpCat.coyoneda_map_app, CategoryTheory.Functor.sectionsEquivHom_apply_app, CochainComplex.cm5b.I_d, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inr, CategoryTheory.Functor.toPseudoFunctor'_mapComp, CategoryTheory.Pseudofunctor.DescentData.exists_equivalence_of_sieve_eq, CategoryTheory.ShortComplex.Homotopy.ofEq_h₁, CategoryTheory.Bicategory.LeftLift.IsKan.uniqueUpToIso_hom_right, CategoryTheory.IsPullback.of_isBilimit, CategoryTheory.ComposableArrows.Exact.isIso_cokerToKer', CategoryTheory.StrictlyUnitaryPseudofunctor.map_id, CategoryTheory.Iso.homFromEquiv_apply, CochainComplex.mappingCone.mapHomologicalComplexXIso'_hom, groupHomology.d₁₀_eq_zero_of_isTrivial, ContinuousMap.yonedaPresheaf'_map, CategoryTheory.PreGaloisCategory.mulAction_naturality, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst, CategoryTheory.prodOpEquiv_functor_map, CategoryTheory.Comon.ComonToMonOpOpObj_mon_mul, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app, CategoryTheory.Limits.HasZeroObject.zeroIsoIsInitial_hom, Bicategory.Opposite.bicategory_homCategory_comp_unop2, CategoryTheory.ShortComplex.Homotopy.op_h₁, CategoryTheory.GrpObj.comp_inv, CategoryTheory.isIso_iff_isIso_coyoneda_map, AlgebraicGeometry.Scheme.fromSpecStalk_app, HomologicalComplex.homotopyCofiber.inlX_d_assoc, CategoryTheory.Limits.kernelBiprodSndIso_inv, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id_app, CategoryTheory.Limits.colimitCoyonedaHomIsoLimit_π_apply, groupCohomology.d₀₁_comp_d₁₂_assoc, CategoryTheory.ParametrizedAdjunction.unit_whiskerRight_map, CategoryTheory.LocallyDiscrete.mkPseudofunctor_obj, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom, CategoryTheory.IsPullback.unop, CategoryTheory.Functor.prod'_η_fst, CategoryTheory.Limits.inl_pushoutZeroZeroIso_inv, CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_iff_mono₂, CategoryTheory.MonoidalClosed.homEquiv_apply_eq, CategoryTheory.Limits.coneOfSectionCompCoyoneda_π, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_comp, CategoryTheory.conjugateEquiv_whiskerLeft, HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_symm_apply, CategoryTheory.composePath_toPath, AlgebraicGeometry.tilde.map_zero, CategoryTheory.Iso.homCongr_symm, HomologicalComplex.homotopyCofiber.desc_f, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_comp, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app_assoc, CochainComplex.ConnectData.comp_d₀, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom, CategoryTheory.Presheaf.map_comp_uliftYonedaEquiv_down, CategoryTheory.Free.lift_map, CategoryTheory.BraidedCategory.op_tensorμ, AlgebraicGeometry.AffineSpace.homOfVector_toSpecMvPoly, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHom, Opens.mayerVietorisSquare'_toSquare, AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_comp, CategoryTheory.Lax.LaxTrans.vComp_naturality_comp, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_apply, SheafOfModules.pushforwardPushforwardEquivalence_unit_app_val_app, CategoryTheory.WithInitial.liftFromUnder_map_app, CategoryTheory.Functor.WellOrderInductionData.map_lift, HomologicalComplex.ι_mapBifunctorFlipIso_hom, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIdIso_inv_app_hom, CategoryTheory.Bicategory.id_whiskerLeft, CategoryTheory.Quiv.pathsOf_freeMap_toPrefunctor, CategoryTheory.Limits.inr_opProdIsoCoprod_inv, CategoryTheory.GrothendieckTopology.overMapPullbackComp_hom_app_val_app, SimplicialObject.Splitting.comp_PInfty_eq_zero_iff, CategoryTheory.conjugateIsoEquiv_symm_apply_inv, CategoryTheory.ShortComplex.rightHomologyMap'_neg, CategoryTheory.Limits.limitCompYonedaIsoCocone_hom_app, CategoryTheory.GrothendieckTopology.Cover.index_snd, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_snd, CategoryTheory.Limits.fst_opProdIsoCoprod_hom, CategoryTheory.SimplicialObject.cechNerveEquiv_apply, MonObj.mopMonObj_one_unmop, CategoryTheory.Bicategory.Pith.associator_inv_iso_hom, CategoryTheory.Bicategory.whiskerLeft_hom_inv_whiskerRight_assoc, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_right, CategoryTheory.Limits.coconeOfConeLeftOp_ι_app, Opens.coe_mayerVietorisSquare_X₄, CategoryTheory.Pseudofunctor.mapComp_id_left_hom, CondensedMod.LocallyConstant.instFullSheafCompHausCoherentTopologyTypeConstantSheaf, ContinuousCohomology.MultiInd.d_comp_d, CategoryTheory.Functor.IsRepresentedBy.iff_of_isoObj, CategoryTheory.MonoidalPreadditive.zero_whiskerRight, CategoryTheory.Bicategory.prod_associator_inv_snd, CategoryTheory.Abelian.FunctorCategory.imageObjIso_hom, CategoryTheory.OplaxFunctor.id_mapId, CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.map_eq_pullHom_assoc, CategoryTheory.Functor.map_neg, CategoryTheory.Idempotents.DoldKan.Γ_map_app, CommGrpCat.one_apply, CategoryTheory.Oplax.LaxTrans.naturality_id_assoc, CategoryTheory.Functor.homMonoidHom_apply, CategoryTheory.Limits.WidePushoutShape.subsingleton_hom, CategoryTheory.Limits.KernelFork.map_condition, CategoryTheory.Abelian.Ext.mk₀_linearEquiv₀_apply, groupHomology.d₃₂_comp_d₂₁, HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_apply, CategoryTheory.Pseudofunctor.map₂_whisker_left_app, CategoryTheory.Endofunctor.Adjunction.Algebra.toCoalgebraOf_map_f, CategoryTheory.Adjunction.homEquiv_naturality_left_symm, HomologicalComplex.opcyclesToCycles_homologyπ_assoc, CategoryTheory.Enriched.FunctorCategory.homEquiv_apply_π_assoc, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_rightUnitor, CategoryTheory.Limits.colimitYonedaHomIsoLimitOp_π_apply, CategoryTheory.Pseudofunctor.DescentData.isEquivalence_toDescentData_iff_of_sieve_eq, CategoryTheory.Pseudofunctor.CoGrothendieck.comp_const, AlgebraicTopology.DoldKan.Γ₂N₁.natTrans_app_f_app, CategoryTheory.WithTerminal.prelaxfunctor_toPrelaxFunctorStruct_toPrefunctor_map, CategoryTheory.Limits.PushoutCocone.isoMk_hom_hom, CategoryTheory.Limits.biprod.add_eq_lift_id_desc, CategoryTheory.PreGaloisCategory.IsNaturalSMul.naturality, CategoryTheory.StrictlyUnitaryLaxFunctor.ext_iff, CategoryTheory.Bicategory.Prod.snd_mapComp_hom, CochainComplex.mappingCone.inl_v_descShortComplex_f, CategoryTheory.Groupoid.isoEquivHom_symm_apply_inv, AlgebraicGeometry.SpecToEquivOfLocalRing_symm_apply, CategoryTheory.ShiftedHom.opEquiv_symm_apply, CategoryTheory.prodOpEquiv_counitIso_hom_app, CategoryTheory.Bicategory.leftUnitor_hom_congr, CategoryTheory.Subgroupoid.subset_generated, CategoryTheory.Oplax.StrongTrans.Modification.whiskerLeft_naturality_assoc, CategoryTheory.Limits.Sigma.ι_π_of_ne, AddCommGrpCat.kernelIsoKer_hom_comp_subtype, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_functor_obj_str, CategoryTheory.Limits.FintypeCat.jointly_surjective, CategoryTheory.Limits.coconeEquivalenceOpConeOp_counitIso, CategoryTheory.Limits.Fork.op_ι_app_zero, AlgebraicGeometry.Scheme.Hom.stalkMap_congr, CategoryTheory.ActionCategory.homOfPair.val, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_snd, CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapId_hom, CategoryTheory.ShortComplex.Splitting.r_f_assoc, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left, CategoryTheory.simplicialToCosimplicialAugmented_map_right, CategoryTheory.Sieve.functor_map_coe, AlgebraicTopology.DoldKan.degeneracy_comp_PInfty, HomologicalComplex.mapBifunctor₁₂.d₁_eq_zero, CategoryTheory.Adjunction.rightAdjointLaxMonoidal_ε, CategoryTheory.Limits.kernelSubobject_arrow_comp_assoc, CategoryTheory.Limits.cospanOp_inv_app, CategoryTheory.Presheaf.freeYonedaHomEquiv_comp_assoc, CategoryTheory.Subgroupoid.mem_im_iff, CategoryTheory.kernelOpOp_inv, CategoryTheory.coyonedaPairing_map, CategoryTheory.Bicategory.Adj.leftUnitor_inv_τr, CategoryTheory.IsPushout.zero_right, CategoryTheory.Adjunction.homEquiv_counit, CategoryTheory.leftDistributor_inv, CategoryTheory.Bicategory.whiskerRight_isIso, CochainComplex.HomComplex.Cochain.ofHom_add, CategoryTheory.Limits.ker.condition_assoc, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app, CategoryTheory.Pretriangulated.Triangle.sub_hom₂, CategoryTheory.Linear.instEpiHSMulHomOfInvertible, SemiNormedGrp.comp_explicitCokernelπ_assoc, CategoryTheory.PrelaxFunctor.map₂_id, CategoryTheory.Bicategory.rightUnitor_inv_naturality_assoc, CategoryTheory.Localization.Preadditive.add'_zero, CategoryTheory.Limits.coprod.inr_fst, CochainComplex.mappingCone.triangleRotateShortComplexSplitting_s, HomologicalComplex.mapBifunctor.d₂_eq_zero', CategoryTheory.Limits.zero_app, CategoryTheory.Functor.map_injective, CategoryTheory.Limits.isoZeroOfMonoZero_hom, CategoryTheory.Limits.opProdIsoCoprod_inv_inl_assoc, CategoryTheory.Pseudofunctor.CoGrothendieck.compIso_inv_app, CategoryTheory.Oplax.OplaxTrans.isoMk_inv_as_app, CategoryTheory.StrictlyUnitaryLaxFunctor.comp_map, CategoryTheory.StrictPseudofunctor.mk''_mapComp, CategoryTheory.CosimplicialObject.Augmented.leftOp_hom_app, CategoryTheory.ShiftedHom.opEquiv'_apply, CategoryTheory.Presheaf.equalizerSieve_apply, CochainComplex.toSingle₀Equiv_apply, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₁_assoc, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app_assoc, CategoryTheory.Limits.BinaryBicone.fstKernelFork_ι, CategoryTheory.Adjunction.leftAdjointCompNatTrans₀₂₃_eq_conjugateEquiv_symm, CategoryTheory.Functor.leftOp_map, CategoryTheory.Functor.toOplaxFunctor_mapId, CategoryTheory.Prod.fac', CategoryTheory.Equivalence.leftOp_counitIso_hom_app, Rep.leftRegularHomEquiv_apply, SSet.stdSimplex.mem_nonDegenerate_iff_mono, CategoryTheory.Endofunctor.Adjunction.Algebra.toCoalgebraOf_obj_str, CategoryTheory.oppositeShiftFunctorAdd'_hom_app, SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero, PresheafOfModules.pushforward_obj_map_apply', CategoryTheory.sum.inlCompInlCompAssociator_hom_app_down, CategoryTheory.Endofunctor.algebraPreadditive_homGroup_add_f, CategoryTheory.Grp.Hom.hom_inv, CategoryTheory.unop_hom_rightUnitor, CategoryTheory.IsPushout.hom_eq_add_up_to_refinements, CategoryTheory.BicategoricalCoherence.assoc_iso, groupHomology.chainsMap_zero, CochainComplex.HomComplex.Cochain.single_v_eq_zero', CategoryTheory.toOverIteratedSliceForwardIsoPullback_inv_app_left, CategoryTheory.Bicategory.Comonad.comul_assoc_assoc, CategoryTheory.tensorLeftHomEquiv_whiskerLeft_comp_evaluation, CategoryTheory.Presheaf.coconeOfRepresentable_ι_app, CategoryTheory.Preadditive.comp_nsmul, HomologicalComplex.homologyι_opcyclesToCycles, CompHausLike.LocallyConstant.sigmaComparison_comp_sigmaIso, CategoryTheory.Limits.pushoutIsoOpPullback_inv_snd, CategoryTheory.Comonad.ComonadicityInternal.comparisonAdjunction_counit, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₃, CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_of_epi₃, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIdIso_hom_app_hom, CategoryTheory.Limits.Cofork.op_π_app_one, CategoryTheory.Preadditive.forkOfKernelFork_ι, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₁, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_assoc, CategoryTheory.Mat_.id_apply, CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm_assoc, CategoryTheory.Bicategory.Pith.leftUnitor_hom_iso, CategoryTheory.WithInitial.lift_map, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app, CategoryTheory.Bicategory.instHasInitialLeftLiftOfHasLeftKanLift, CochainComplex.HomComplex.Cochain.ofHom_zero, AlgebraicGeometry.Scheme.IsLocallyDirected.exists_of_pullback_V_V, AlgebraicGeometry.Scheme.SpecMap_presheaf_map_eqToHom, HomologicalComplex.mapBifunctor.d₂_eq', CochainComplex.mappingCone.inr_f_triangle_mor₃_f_assoc, CategoryTheory.conjugateEquiv_adjunction_id_symm, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_symm_apply, GrpCat.one_apply, Mathlib.Tactic.BicategoryCoherence.assoc_liftHom₂, CategoryTheory.hasExt_iff, CategoryTheory.Bicategory.lanUnit_desc_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_assoc, CategoryTheory.CompatiblePreserving.compatible, CategoryTheory.IsPushout.op, CategoryTheory.Oplax.LaxTrans.vComp_naturality_naturality, CategoryTheory.Bicategory.associator_naturality_left, CategoryTheory.CategoryOfElements.id_val, HomotopicalAlgebra.cofibration_unop_iff, CategoryTheory.Under.opEquivOpOver_inverse_obj, CategoryTheory.Limits.opProductIsoCoproduct'_inv_comp_lift, TopologicalSpace.Opens.apply_mk, CategoryTheory.PresheafHom.IsSheafFor.exists_app, CochainComplex.cochainComplex_d_succ_succ_zero, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_inv_hom_assoc, TopologicalSpace.Opens.infLELeft_apply, CategoryTheory.ShrinkHoms.comp_def, CategoryTheory.Limits.pullbackIsoOpPushout_inv_snd_assoc, CategoryTheory.Limits.BinaryFan.leftUnitor_inv, CategoryTheory.Abelian.tfae_mono, CategoryTheory.Iso.unop_inv_hom_id_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_hom_toNatTrans_app_val_app, prevD_comp_right, CategoryTheory.Bicategory.Pith.rightUnitor_inv_iso_hom, HomologicalComplex₂.ι_totalShift₂Iso_hom_f, CategoryTheory.Bicategory.Pith.comp₂_iso_inv_assoc, CategoryTheory.ShortComplex.Homotopy.g_h₃, CategoryTheory.Coyoneda.fullyFaithful_preimage, CategoryTheory.IsPushout.of_has_biproduct, SSet.yonedaEquiv_comp, LightCondSet.topCatAdjunctionUnit_val_app, CategoryTheory.MonoidalOpposite.tensorLeftIso_hom_app_unmop, CategoryTheory.StrictlyUnitaryPseudofunctor.mk'_map₂, CategoryTheory.Limits.FintypeCat.instPreservesFiniteLimitsFintypeCatForgetHomCarrier, CategoryTheory.Abelian.Ext.mk₀_bijective, SSet.op_map, CategoryTheory.Preadditive.isCoseparator_iff, CategoryTheory.Limits.isColimitCoconeOfConeLeftOp_desc, SimplicialObject.Splitting.IndexSet.eqId_iff_eq, CategoryTheory.ObjectProperty.isColocal.homEquiv_apply, CategoryTheory.HasLiftingProperty.transfiniteComposition.sqFunctor_map, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_app_apply, HomologicalComplex.fromOpcycles_op_cyclesOpIso_inv, CategoryTheory.Limits.Types.Pushout.cocone_ι_app, CategoryTheory.Bicategory.prod_homCategory_comp_snd, CategoryTheory.unop_hom_braiding, CategoryTheory.Functor.prod_μ_snd, HomologicalComplex₂.total_d, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq, CategoryTheory.Limits.KernelFork.map_ι, CategoryTheory.MarkovCategory.instSubsingletonHomTensorUnit, CategoryTheory.RetractArrow.unop_i_left, CategoryTheory.Oplax.StrongTrans.id_naturality_hom, CategoryTheory.Bicategory.leftUnitor_naturality, CategoryTheory.Limits.zero_comp, CategoryTheory.PreGaloisCategory.functorToContAction_obj_obj, CategoryTheory.Localization.hasSmallLocalizedShiftedHom_iff, CategoryTheory.Bicategory.InducedBicategory.bicategory_homCategory_id_hom, CategoryTheory.CatEnrichedOrdinary.id_hComp_id, CategoryTheory.OverPresheafAux.MakesOverArrow.of_arrow, CategoryTheory.cosimplicialToSimplicialAugmented_map, CategoryTheory.StrictlyUnitaryLaxFunctor.mk'_mapId, CategoryTheory.GrothendieckTopology.instWEqualsLocallyBijectiveTypeHom, CategoryTheory.Bicategory.Adj.Bicategory.associator_inv_τr, SSet.OneTruncation₂.nerveHomEquiv_apply, CochainComplex.HomComplex.CohomologyClass.toHom_mk_eq_zero_iff, FintypeCat.uSwitchEquiv_symm_naturality, TopCat.Presheaf.Γgerm_res_apply, AlgebraicGeometry.Spec.toPresheafedSpace_map, CategoryTheory.MonoOver.initialTo_b_eq_zero, CategoryTheory.Pretriangulated.Triangle.isZero₃_iff, CategoryTheory.Paths.lift_toPath, CategoryTheory.ShrinkHoms.inverse_map, CategoryTheory.WithTerminal.liftFromOverComp_inv_app, CategoryTheory.Monad.algebraPreadditive_homGroup_neg_f, HomologicalComplex.mapBifunctor.d₁_eq_zero', CategoryTheory.WithInitial.liftToInitial_map, CategoryTheory.ShortComplex.Homotopy.comp_h₂, CategoryTheory.ShortComplex.Homotopy.ofEq_h₃, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_assoc, CategoryTheory.Limits.π_comp_colimitRightOpIsoUnopLimit_inv_assoc, CategoryTheory.LaxFunctor.mapComp_assoc_left, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τl, CategoryTheory.Limits.reflexivePair.compRightIso_inv_app, commBialgCatEquivComonCommAlgCat_inverse_map_unop_hom, CategoryTheory.Bicategory.Comonad.counit_comul, ModuleCat.ofHom₂_hom_apply_hom, CategoryTheory.unop_zsmul, SheafOfModules.pushforwardPushforwardAdj_counit_app_val_app, SheafOfModules.conjugateEquiv_pullbackId_hom, CategoryTheory.Sheaf.Hom.add_app, CategoryTheory.PreGaloisCategory.endEquivAutGalois_π, CategoryTheory.ActionCategory.π_map, CategoryTheory.CatEnriched.eqToHom_hComp_eqToHom, CategoryTheory.Prod.swap_map, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapId_inv_iso_hom, CategoryTheory.NatTrans.app_units_zsmul, CategoryTheory.ShortComplex.cyclesMap'_add, CategoryTheory.Presieve.extension_iff_amalgamation, groupCohomology.subtype_comp_d₀₁, HomologicalComplex.quasiIso_unopFunctor_map_iff, CategoryTheory.OplaxFunctor.map₂_rightUnitor_app, SSet.StrictSegalCore.map_mkOfSucc_zero_spineToSimplex, CategoryTheory.prod_comp, CategoryTheory.CatEnrichedOrdinary.eqToHom_hComp_eqToHom, CategoryTheory.Subgroupoid.mem_top, CategoryTheory.NonPreadditiveAbelian.diag_σ_assoc, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_right_unitor, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.SheafCondition.bijective_toPullbackObj, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_app, CategoryTheory.ShortComplex.RightHomologyData.op_i, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_left_map, CategoryTheory.LaxFunctor.mapComp_naturality_right_app, CategoryTheory.WithTerminal.equivComma_inverse_map_app, CategoryTheory.MonoidalClosed.curryHomEquiv'_apply, CategoryTheory.LaxFunctor.mapComp_assoc_right, CategoryTheory.Limits.biproduct.ι_toSubtype, CategoryTheory.Limits.isLimitOfCoconeUnopOfCone_lift, CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIsoWhisker_inv_right, CochainComplex.mappingCone.inl_v_snd_v, CategoryTheory.Discrete.sumEquiv_functor_map, CategoryTheory.CategoryOfElements.fromCostructuredArrow_obj_mk, CategoryTheory.Bicategory.mateEquiv_apply, CategoryTheory.whiskerLeft_sum, CategoryTheory.Bicategory.Adj.associator_hom_τl, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_right, CategoryTheory.Types.instReflectsColimitsOfSizeForgetTypeHom, CategoryTheory.WithInitial.ofCommaObject_map, CategoryTheory.Bicategory.LeftExtension.whiskerHom_right, CategoryTheory.StrictlyUnitaryLaxFunctor.comp_mapComp, CategoryTheory.Bicategory.InducedBicategory.bicategory_associator_hom_hom, CategoryTheory.eHomEquiv_comp_assoc, CategoryTheory.Oplax.StrongTrans.naturality_naturality, CategoryTheory.ShortComplex.RightHomologyData.ι_descQ_eq_zero_of_boundary, CategoryTheory.ShortComplex.neg_τ₁, CategoryTheory.MonoidalOpposite.tensorRightMopIso_hom_app_unmop, CategoryTheory.Under.opEquivOpOver_counitIso, CategoryTheory.Functor.IsDenseSubsite.map_eq_of_eq, HomologicalComplex.unit_tensor_d₁, CategoryTheory.StructuredArrow.w_prod_snd_assoc, CategoryTheory.WithTerminal.equivComma_inverse_obj_map, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanIndex_snd, CategoryTheory.StructuredArrow.prodInverse_obj, CategoryTheory.Bicategory.pentagon_hom_hom_inv_inv_hom, CategoryTheory.Limits.IsZero.eq_zero_of_src, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_inv_app_app, CategoryTheory.SemiadditiveOfBinaryBiproducts.isUnital_rightAdd, CategoryTheory.PrelaxFunctor.map₂Iso_hom, ModuleCat.hom_sub, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapIdIso_hom, CategoryTheory.ShortComplex.LeftHomologyMapData.add_φK, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition'_assoc, CategoryTheory.NonPreadditiveAbelian.sub_def, AlgebraicGeometry.Scheme.Opens.ι_appLE, CategoryTheory.DifferentialObject.d_squared_assoc, CategoryTheory.conjugateEquiv_adjunction_id, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHom_op, CategoryTheory.Oplax.OplaxTrans.leftUnitor_hom_as_app, SSet.StrictSegal.spineToSimplex_arrow, CategoryTheory.Limits.biproduct.ι_toSubtype_assoc, CategoryTheory.Functor.final_iff_of_isFiltered, CategoryTheory.coyonedaEquiv_symm_map, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ_assoc, CategoryTheory.Functor.opHom_map_app, CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_hom_assoc, CategoryTheory.Limits.opCoproductIsoProduct_hom_comp_π_assoc, CategoryTheory.Adjunction.homEquiv_naturality_right_square, CategoryTheory.Abelian.FunctorCategory.functor_category_isIso_coimageImageComparison, CategoryTheory.Limits.proj_comp_opProductIsoCoproduct'_hom, CategoryTheory.ShortComplex.unopMap_τ₃, AlgebraicGeometry.Spec.toLocallyRingedSpace_map, CategoryTheory.rightDistributor_hom, ModuleCat.ofHom₂_compr₂, CategoryTheory.PrelaxFunctor.map₂Iso_inv, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_map, CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.map_eq_pullHom, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app, CategoryTheory.Bicategory.Pith.inclusion_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map, CategoryTheory.Limits.HasZeroObject.zeroIsoIsTerminal_inv, CategoryTheory.Limits.PushoutCocone.unop_pt, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_hom_app_val_app, CategoryTheory.ShortComplex.Homotopy.neg_h₂, CategoryTheory.Limits.SequentialProduct.cone_π_app, PresheafOfModules.freeYonedaEquiv_comp, AlgebraicGeometry.ΓSpec_adjunction_homEquiv_eq, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_assoc, CochainComplex.ConnectData.comp_d₀_assoc, CategoryTheory.MonoidalPreadditive.tensor_add, Bicategory.Opposite.bicategory_associator_inv_unop2, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_assoc, AlgebraicGeometry.Scheme.Opens.ι_app, CategoryTheory.WithInitial.liftFromUnder_obj_map, CategoryTheory.finrank_endomorphism_simple_eq_one, AlgebraicTopology.DoldKan.PInfty_f_comp_QInfty_f, CategoryTheory.ShortComplex.HasRightHomology.of_zeros, CategoryTheory.Limits.IsZero.iff_id_eq_zero, CategoryTheory.RetractArrow.unop_i_right, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_inv_app_app, CategoryTheory.Lax.OplaxTrans.naturality_comp_assoc, CategoryTheory.Pseudofunctor.DescentData.id_hom, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv_assoc, HomologicalComplex₂.d₂_eq', CategoryTheory.Limits.limitRightOpIsoOpColimit_inv_comp_π_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id, CategoryTheory.ShortComplex.zero_τ₁, CategoryTheory.IsFiltered.sup_objs_exists, CategoryTheory.LaxFunctor.mapComp_naturality_left_app, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right_assoc, CategoryTheory.ShortComplex.Exact.rightHomologyDataOfIsColimitCokernelCofork_p, CategoryTheory.Bicategory.pentagon_inv_inv_hom_hom_inv_assoc, CategoryTheory.ShortComplex.smul_τ₁, CategoryTheory.Limits.cokernel.π_of_epi, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_hom_comp_ι_assoc, CochainComplex.HomComplex.Cochain.fromSingleMk_v_eq_zero, SSet.Truncated.Edge.CompStruct.d₀, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp, CategoryTheory.OplaxFunctor.mapComp_id_left_assoc, CategoryTheory.StrictPseudofunctor.mk'_mapId, FintypeCat.hom_inv_id_apply, CategoryTheory.WithTerminal.liftFromOver_map_app, CompHausLike.LocallyConstant.incl_comap, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_of_mono₁, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapCompIso_hom, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₂, CategoryTheory.Limits.coequalizer.existsUnique, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.toBiprod_fromBiprod, CategoryTheory.preadditiveCoyonedaObj_obj_carrier, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app_assoc, AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id_assoc, Homotopy.dNext_cochainComplex, Quiver.FreeGroupoid.of_eq, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_precomp, Homotopy.nullHomotopicMap'_f, CategoryTheory.Bicategory.Prod.swap_mapComp_hom, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_right, CategoryTheory.Enriched.FunctorCategory.homEquiv_comp_assoc, CategoryTheory.Presieve.uncurry_pullbackArrows, CategoryTheory.Pseudofunctor.StrongTrans.Modification.vcomp_app, CategoryTheory.Presieve.IsSheafFor.valid_glue, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHom, CategoryTheory.Pseudofunctor.DescentData.isoMk_hom_hom, AlgebraicGeometry.Scheme.Spec_map, CategoryTheory.CatEnrichedOrdinary.hComp_assoc_heq, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_assoc, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_inv_app_unop_assoc, CategoryTheory.Bicategory.LeftLift.ofIdComp_left_as, CategoryTheory.StrictPseudofunctor.id_mapId_inv, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_apply_app, CategoryTheory.ShortComplex.exact_iff_of_forks, CategoryTheory.cosimplicialSimplicialEquiv_inverse_map, CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf_inv_right, PresheafOfModules.sheafificationAdjunction_homEquiv_apply, CategoryTheory.Adjunction.representableBy_homEquiv, CategoryTheory.Functor.Elements.initialOfRepresentableBy_snd, TopCat.Presheaf.germ_eq, CategoryTheory.Functor.PreservesHomology.preservesCokernel, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.f'_eq, CategoryTheory.Functor.CorepresentableBy.ext_iff, CategoryTheory.ShortComplex.smul_τ₂, HomologicalComplex.extend.leftHomologyData.lift_d_comp_eq_zero_iff, CategoryTheory.Limits.BinaryBicone.inl_snd, CategoryTheory.Functor.CorepresentableBy.homEquiv_symm_comp, CategoryTheory.StrictlyUnitaryLaxFunctor.mapIdIso_inv, CategoryTheory.Abelian.Ext.linearEquiv₀_symm_apply, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_as, CategoryTheory.FreeBicategory.mk_associator_inv, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHomLeft, CategoryTheory.ShiftedHom.mk₀_neg, CategoryTheory.Join.mapIsoWhiskerLeft_inv_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_inv_app', CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_left, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_left, CategoryTheory.eqToHom_comp_homOfLE_op_assoc, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_comp_assoc, CategoryTheory.Functor.toPreimages_obj, CategoryTheory.ShortComplex.liftCycles_homologyπ_eq_zero_of_boundary, CategoryTheory.Bicategory.rightUnitor_comp_assoc, CategoryTheory.HomOrthogonal.matrixDecomposition_symm_apply, CategoryTheory.Over.ConstructProducts.conesEquivInverseObj_π_app, CategoryTheory.NonPreadditiveAbelian.lift_map, CategoryTheory.FreeBicategory.locally_thin, CategoryTheory.Functor.homEquivOfIsRightKanExtension_apply_app, CategoryTheory.Endofunctor.Adjunction.Coalgebra.toAlgebraOf_obj_str, Mathlib.Tactic.Bicategory.evalComp_nil_cons, Rep.diagonalHomEquiv_apply, CategoryTheory.Limits.IsLimit.homEquiv_symm_naturality, HomologicalComplex.homologyι_descOpcycles_eq_zero_of_boundary, CategoryTheory.Bicategory.Adj.leftUnitor_hom_τr, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₁, CategoryTheory.Pseudofunctor.mapId'_hom_naturality, CategoryTheory.IsDiscrete.subsingleton, CategoryTheory.Pseudofunctor.DescentData.hom_self, CategoryTheory.conjugateIsoEquiv_symm_apply_hom, CategoryTheory.HomOrthogonal.matrixDecompositionAddEquiv_apply, Mathlib.Tactic.Bicategory.evalWhiskerRightAux_of, CategoryTheory.Limits.IsZero.iff_isSplitMono_eq_zero, CategoryTheory.Endofunctor.algebraPreadditive_homGroup_nsmul_f, dNext_comp_right, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_hom, HomologicalComplex.homotopyCofiber.inlX_desc_f, CategoryTheory.Pseudofunctor.DescentData.comp_hom_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_app, AlgebraicTopology.DoldKan.QInfty_comp_PInfty_assoc, CategoryTheory.Limits.Cotrident.ofπ_ι_app, AlgebraicGeometry.Scheme.Hom.map_appLE, CategoryTheory.Bicategory.LeftExtension.IsKan.fac, TopologicalSpace.Opens.apply_def, HomologicalComplex.fromOpcycles_d, CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_mapId, CategoryTheory.conj_eqToHom_iff_heq, CategoryTheory.Oplax.StrongTrans.categoryStruct_id_naturality, CategoryTheory.Adjunction.homAddEquiv_apply, CategoryTheory.Functor.PullbackObjObj.ofHasPullback_pt, HomologicalComplex.iCycles_d_assoc, CategoryTheory.Limits.op_zero, CategoryTheory.Functor.linear_iff, CategoryTheory.Iso.unop_inv_hom_id_app_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHomLeft_op, CategoryTheory.ShortComplex.opcyclesOpIso_hom_toCycles_op, HomotopyCategory.quotient_map_out, CategoryTheory.ShortComplex.rightHomologyι_comp_fromOpcycles, CategoryTheory.Pseudofunctor.ObjectProperty.map_obj_obj, CategoryTheory.Bicategory.LeftLift.IsKan.uniqueUpToIso_inv_right, CategoryTheory.Limits.coconeOfIsSplitEpi_ι_app, SheafOfModules.Presentation.IsFinite.finite_relations, SemimoduleCat.hom_add, LightProfinite.proj_comp_transitionMapLE, CategoryTheory.FreeBicategory.lift_mapComp, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₃, CategoryTheory.ShortComplex.Homotopy.add_h₃, HomologicalComplex₂.d₁_eq', CategoryTheory.Limits.π_comp_colimitUnopIsoOpLimit_inv_assoc, CategoryTheory.Bicategory.Comonad.comul_counit, CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_add_f, Rep.freeLiftLEquiv_symm_apply, CategoryTheory.ObjectProperty.rightOrthogonal_iff, CategoryTheory.Preadditive.one_def, CategoryTheory.Over.lift_left, CategoryTheory.Bicategory.leftZigzagIso_inv, CategoryTheory.Functor.toOplaxFunctor'_mapComp, SheafOfModules.pushforwardNatTrans_app_val_app_apply, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_id, CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_iff_mono₃, CategoryTheory.Mat_.id_def, AlgebraicTopology.DoldKan.Γ₂_map_f_app, CategoryTheory.Bicategory.Adjunction.comp_right_triangle_aux, CategoryTheory.Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone_ι_app_eq_sum, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_apply, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app, CategoryTheory.ShortComplex.cyclesMap'_neg, CategoryTheory.DifferentialObject.d_squared_apply_assoc, CategoryTheory.Limits.biproduct.toSubtype_fromSubtype_assoc, CategoryTheory.Adjunction.homEquiv_naturality_right_square_assoc, CategoryTheory.Under.postAdjunctionRight_counit_app_right, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_comp_fiber, CochainComplex.HomComplex.Cochain.equivHomotopy_symm_apply_hom, groupHomology.d₁₀_comp_coinvariantsMk_assoc, CategoryTheory.op_neg, CategoryTheory.Limits.CokernelCofork.map_condition_assoc, CategoryTheory.unitCompPartialBijectiveAux_symm_apply, CategoryTheory.Bicategory.Adj.lIso_hom, AlgebraicTopology.DoldKan.decomposition_Q, CategoryTheory.Limits.hasPullback_over_zero, CategoryTheory.Limits.colimitCoconeOfUnique_cocone_ι, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, HomologicalComplex.extendMap_zero, HomologicalComplex.extendMap_f_eq_zero, CategoryTheory.isCardinalFiltered_iff, CategoryTheory.Bicategory.Prod.sectL_map₂, CategoryTheory.Oplax.StrongTrans.toOplax_naturality, CategoryTheory.ShortComplex.RightHomologyData.unop_π, CategoryTheory.Pseudofunctor.mapId'_hom_naturality_assoc, CategoryTheory.ShortComplex.opcyclesMap'_add, CategoryTheory.ShortComplex.Exact.isZero_X₂_iff, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left_assoc, CategoryTheory.LocalizerMorphism.RightResolution.op_w, CategoryTheory.OplaxFunctor.mapComp_naturality_right_app_assoc, CategoryTheory.prod_id_snd, CategoryTheory.Functor.op_commShiftIso_hom_app, CategoryTheory.instSmallHomFunctorOppositeTypeColimitCompYoneda, AlgebraicTopology.DoldKan.σ_comp_P_eq_zero, CategoryTheory.Groupoid.invEquivalence_unitIso, CategoryTheory.Limits.coconeEquivalenceOpConeOp_inverse_map_hom, CategoryTheory.Bicategory.Adjunction.homEquiv₁_symm_apply, CochainComplex.HomComplex.Cocycle.equivHomShift_comp_shift, CategoryTheory.Oplax.StrongTrans.Modification.whiskerRight_naturality_assoc, CategoryTheory.Bicategory.toNatTrans_conjugateEquiv, CategoryTheory.Lax.StrongTrans.categoryStruct_comp_naturality, CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm, CategoryTheory.Over.opEquivOpUnder_functor_map, CategoryTheory.op_sub, CategoryTheory.Limits.PullbackCone.isoMk_hom_hom, CategoryTheory.ShortComplex.rightHomologyMap'_smul, CategoryTheory.NonPreadditiveAbelian.add_neg_cancel, SSet.S.mk_map_le, CategoryTheory.ShortComplex.Homotopy.unop_h₀, HasFibers.inducedFunctor_map_coe, CategoryTheory.FreeBicategory.lift_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.Subobject.factors_zero, CategoryTheory.IsPullback.inr_fst', CategoryTheory.Pseudofunctor.comp_mapComp, CategoryTheory.Sheaf.instIsLocallyInjectiveHomImageι, CategoryTheory.Limits.SequentialProduct.functorMap_commSq_succ, CategoryTheory.ComposableArrows.isoMk₀_hom_app, CategoryTheory.Bicategory.Prod.swap_mapComp_inv, CategoryTheory.Monad.MonadicityInternal.counitCofork_ι_app, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app, CategoryTheory.PrelaxFunctor.map₂Iso_eqToIso, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp, CategoryTheory.Limits.Cofork.IsColimit.homIso_symm_apply, CategoryTheory.Limits.isColimitOfConeOfCoconeUnop_desc, CategoryTheory.ShortComplex.LeftHomologyData.wi_assoc, CategoryTheory.Functor.PullbackObjObj.π_fst_assoc, CategoryTheory.Pretriangulated.Triangle.isZero₁_iff, CategoryTheory.cokernelUnopOp_inv, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₁, CategoryTheory.Subgroupoid.id_mem_of_nonempty_isotropy, CategoryTheory.Limits.Fork.op_unop_ι, Bicategory.Opposite.opFunctor_map, CategoryTheory.Functor.IsRepresentedBy.of_isoObj, CategoryTheory.Localization.SmallHom.equiv_shift, CategoryTheory.Limits.opProductIsoCoproduct_inv_comp_lift, CategoryTheory.CartesianClosed.curry_injective, HomologicalComplex₂.ιTotalOrZero_eq_zero, HomologicalComplex.double_d_eq_zero₁, HomologicalComplex.unop_d, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₁, CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_mapComp, CategoryTheory.Limits.ι_comp_colimitLeftOpIsoUnopLimit_hom_assoc, AlgebraicGeometry.IsAffineOpen.app_basicOpen_eq_away_map, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv_assoc, CategoryTheory.uliftYonedaMap_app_apply, CategoryTheory.Functor.WellOrderInductionData.Extension.map_limit, CategoryTheory.ShortComplex.Exact.epi_f_iff, CategoryTheory.Preadditive.zsmul_comp, HomologicalComplex.truncGE'.homologyι_truncGE'XIsoOpcycles_inv_d, CategoryTheory.subterminals_thin, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_obj_map_app, CategoryTheory.Limits.Wedge.condition_assoc, CategoryTheory.Bicategory.LeftLift.whiskering_obj, Quiver.Hom.unmop_inj, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_symm_assoc, CategoryTheory.opEquiv_symm_apply, CategoryTheory.Limits.CokernelCofork.π_eq_zero, CategoryTheory.Limits.bicone_ι_π_ne, CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac_assoc, CategoryTheory.InducedWideCategory.category_comp_coe, CategoryTheory.congrArg_mpr_hom_right, CategoryTheory.ShrinkHoms.functor_map, CategoryTheory.ShortComplex.neg_τ₃, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inl_assoc, CategoryTheory.Bicategory.Prod.snd_mapComp_inv, CategoryTheory.Sieve.equalizer_eq_equalizerSieve, CategoryTheory.Bicategory.Adj.Bicategory.associator_hom_τl, CategoryTheory.NonPreadditiveAbelian.lift_σ, CategoryTheory.StrictPseudofunctor.mk''_obj, CategoryTheory.MonoidalClosed.ofEquiv_curry_def, CategoryTheory.Limits.multispanIndexCoend_fst, CategoryTheory.Limits.snd_opProdIsoCoprod_hom_assoc, AlgebraicGeometry.IsAffineOpen.ΓSpecIso_hom_fromSpec_app, AlgebraicGeometry.SpecToEquivOfLocalRing_eq_iff, CategoryTheory.Bicategory.Pith.comp₂_iso_inv, CategoryTheory.Adjunction.homEquiv_symm_rightAdjointUniq_hom_app, CategoryTheory.Pseudofunctor.map₂_whisker_right_app, CategoryTheory.Abelian.Ext.homEquiv₀_symm_apply, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₁, CategoryTheory.kernelOpOp_hom, CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder_map, CategoryTheory.Oplax.OplaxTrans.Modification.whiskerLeft_naturality, CategoryTheory.Bicategory.conjugateEquiv_symm_apply', CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₃, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_r, CategoryTheory.Limits.hasPushout_over_zero, CategoryTheory.cones_obj_obj, Rep.indResHomEquiv_apply_hom, CategoryTheory.NonPreadditiveAbelian.lift_σ_assoc, CategoryTheory.Functor.FullyFaithful.homNatIso_hom_app_down, CategoryTheory.NonPreadditiveAbelian.comp_sub, ModuleCat.homAddEquiv_apply, Quiver.FreeGroupoid.congr_reverse_comp, CategoryTheory.Functor.PreOneHypercoverDenseData.sieve₁₀_apply, CategoryTheory.Pseudofunctor.CoGrothendieck.instFaithfulαCategoryObjLocallyDiscreteOppositeCatMkOpFiberForgetInducedFunctor, CategoryTheory.Adjunction.homAddEquiv_symm_sub, CategoryTheory.Endofunctor.Adjunction.Coalgebra.homEquiv_naturality_str_symm, HomologicalComplex₂.D₁_totalShift₂XIso_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_iso, CategoryTheory.ShortComplex.cyclesOpIso_inv_op_iCycles, CategoryTheory.Bicategory.InducedBicategory.isoMk_hom_hom, CategoryTheory.Limits.opCoproductIsoProduct'_hom_comp_proj_assoc, SSet.Truncated.Path₁.arrow_src, CategoryTheory.Bicategory.Pith.inclusion_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp_assoc, CategoryTheory.Limits.Cofork.ofπ_ι_app, SkyscraperPresheafFunctor.map'_app, CategoryTheory.Subobject.functor_map, CategoryTheory.Bicategory.whiskerLeft_rightUnitor, CategoryTheory.Limits.WalkingCospan.instSubsingletonHom, AlgebraicGeometry.morphismRestrict_app, CategoryTheory.Functor.currying_functor_obj_map, CategoryTheory.SimplicialObject.augmentedCechNerve_obj_left_map, CategoryTheory.Functor.leftOpRightOpEquiv_functor_map_app, CategoryTheory.yonedaGrp_map_app, CategoryTheory.comp_eqToHom_heq, CategoryTheory.Preadditive.comp_sub_assoc, AlgebraicGeometry.tilde.map_neg, CategoryTheory.Equalizer.FirstObj.ext_iff, HomologicalComplex.mapBifunctor₁₂.d₁_eq, AlgebraicTopology.DoldKan.Q_zero, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app_assoc, CategoryTheory.WithInitial.pseudofunctor_mapComp, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality, CategoryTheory.leftUnitor_def, CategoryTheory.Iso.eHomCongr_inv_comp, CategoryTheory.MonObj.one_eq_one, ChainComplex.mkHom_f_succ_succ, HomologicalComplex.opcyclesMap_zero, HomologicalComplex₂.D₂_totalShift₂XIso_hom, CategoryTheory.Limits.IsLimit.existsUnique, CategoryTheory.sheafHomSectionsEquiv_symm_apply_coe_apply, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_fst, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_hom_app_app, TopCat.Sheaf.eq_of_locally_eq_iff, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp, CategoryTheory.Localization.homEquiv_map, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι_assoc, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_inv_comp_π_assoc, CategoryTheory.FreeBicategory.preinclusion_obj, CategoryTheory.Pseudofunctor.map₂_left_unitor_app_assoc, imageToKernel_epi_of_epi_of_zero, CategoryTheory.CatEnriched.hComp_comp, AlgebraicTopology.DoldKan.QInfty_f_comp_PInfty_f_assoc, CategoryTheory.ShortComplex.rightHomologyMap_smul, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_η_unmop_app, CategoryTheory.Pseudofunctor.map₂_right_unitor_app_assoc, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_inv, CategoryTheory.Grp_Class.div_comp, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv_def, CategoryTheory.Pseudofunctor.map₂_right_unitor_app, AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id, SSet.Truncated.Edge.CompStruct.d₁, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_naturality_app, CategoryTheory.unop_hom_associator, CategoryTheory.regularTopology.EqualizerCondition.bijective_mapToEqualizer_pullback, CategoryTheory.Limits.Cofork.unop_ι, CategoryTheory.FreeBicategory.lift_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map, CategoryTheory.LaxFunctor.comp_mapComp, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_iff_mono₁, CategoryTheory.Join.opEquiv_functor_map_op_inclLeft, CategoryTheory.Abelian.Pseudoelement.eq_zero_iff, CategoryTheory.finallySmall_iff_exists_small_weakly_terminal_set, HomologicalComplex.shortComplexTruncLE_shortExact_δ_eq_zero, CategoryTheory.conjugateEquiv_comp, CategoryTheory.map_shrinkYonedaEquiv, CategoryTheory.NatTrans.app_zsmul, CategoryTheory.Mat_.comp_def, CategoryTheory.WithInitial.opEquiv_inverse_map, AlgebraicGeometry.Scheme.Cover.intersectionOfLocallyDirected_f, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.hf, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj, AddCommGrpCat.hom_add_apply, CategoryTheory.PrelaxFunctor.map₂_hom_inv_isIso_assoc, CategoryTheory.Biprod.inl_ofComponents, CategoryTheory.Under.opEquivOpOver_functor_map, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_ε_unmop_app, CategoryTheory.MonoidalOpposite.tensorLeftMopIso_inv_app_unmop, CategoryTheory.Limits.biproduct.map_eq, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_inv_app_val_app, CategoryTheory.Preadditive.comp_sub, CategoryTheory.Limits.WalkingSpan.instSubsingletonHom, CategoryTheory.prod.leftUnitor_map, SSet.OneTruncation₂.id_edge, CategoryTheory.Adjunction.homEquiv_apply_eq, CategoryTheory.yonedaEquiv_symm_map, CategoryTheory.tensorLeftHomEquiv_whiskerRight_comp_evaluation, AlgebraicGeometry.Scheme.Hom.appLE_map, CategoryTheory.Limits.IsLimit.homIso_hom, CategoryTheory.Limits.BinaryBicone.inr_fst, CategoryTheory.Functor.map_nsmul, CategoryTheory.Limits.cokernelZeroIsoTarget_hom, AddCommGrpCat.ofHom_injective, DerivedCategory.HomologySequence.δ_comp_assoc, CategoryTheory.ShortComplex.cyclesOpIso_inv_naturality_assoc, ContinuousCohomology.MultiInd.d_succ, CategoryTheory.Subgroupoid.inclusion_faithful, CategoryTheory.CartesianMonoidalCategory.homEquivToProd_apply, CategoryTheory.Limits.coconeEquivalenceOpConeOp_functor_map, ModuleCat.semilinearMapAddEquiv_symm_apply_apply, CategoryTheory.Limits.CokernelCofork.IsColimit.isZero_of_epi, CategoryTheory.Bicategory.Pith.inclusion_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_snd_assoc, CategoryTheory.Limits.opParallelPairIso_inv_app_zero, CategoryTheory.Limits.cokernelCoforkBiproductFromSubtype_cocone, AlgebraicGeometry.Proj.res_apply, Rep.coinvariantsAdjunction_homEquiv_apply_hom, CategoryTheory.CostructuredArrow.projectQuotient_factors, CategoryTheory.Sieve.toFunctor_app_coe, HomologicalComplex.mapBifunctor₁₂.d₃_eq, CategoryTheory.constantPresheafAdj_counit_app_app, DerivedCategory.HomologySequence.δ_comp, CategoryTheory.Equivalence.sheafCongr.unitIso_inv_app_val_app, AlgebraicGeometry.Scheme.Opens.topIso_hom, CategoryTheory.Join.mapIsoWhiskerLeft_hom_app, HomologicalComplex.biprod_inr_fst_f_assoc, CategoryTheory.PrelaxFunctor.map₂_inv_hom, CategoryTheory.Limits.ι_comp_colimitLeftOpIsoUnopLimit_hom, CategoryTheory.GrothendieckTopology.map_yonedaEquiv, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τr, CategoryTheory.Subgroupoid.mem_sInf_arrows, CategoryTheory.Bicategory.conjugateEquiv_iso, CategoryTheory.Limits.kernelSubobject_arrow_comp, CategoryTheory.effectiveEpi_iff_effectiveEpiFamily, CategoryTheory.Cat.HasLimits.homDiagram_obj, CategoryTheory.Functor.reprW_hom_app, CategoryTheory.Sheaf.isLocallySurjective_iff_isIso, CategoryTheory.ComposableArrows.opEquivalence_counitIso_hom_app_app, CategoryTheory.uliftCoyonedaEquiv_symm_map, CategoryTheory.Bicategory.Prod.sectR_mapId_hom, CategoryTheory.Limits.opParallelPairIso_inv_app_one, CategoryTheory.TwoSquare.lanBaseChange_app, MonObj.mopMonObj_mul_unmop, CategoryTheory.Functor.hcongr_hom, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d_assoc, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π, CategoryTheory.NonPreadditiveAbelian.neg_def, CategoryTheory.Linear.toCatCenter_apply_app, CategoryTheory.OplaxFunctor.mapComp_naturality_right, CategoryTheory.Bicategory.Strict.leftUnitor_eqToIso, AlgebraicGeometry.Scheme.ofRestrict_app, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_apply_coe, CategoryTheory.Grothendieck.grothendieckTypeToCatInverse_map_base, CategoryTheory.yonedaEquiv_symm_naturality_left, CategoryTheory.Limits.inl_opProdIsoCoprod_inv, CategoryTheory.OplaxFunctor.mapComp_naturality_left_app_assoc, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_symm_apply, CategoryTheory.Comonad.coalgebraPreadditive_homGroup_add_f, CategoryTheory.Limits.snd_opProdIsoCoprod_hom, CategoryTheory.imageUnopOp_inv_comp_op_factorThruImage, CategoryTheory.Bicategory.Prod.swap_mapId_hom, CategoryTheory.PreGaloisCategory.exists_galois_representative, CategoryTheory.CatCenter.app_neg, CategoryTheory.Over.isMonHom_pullbackFst_id_right, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand', FundamentalGroupoidFunctor.prodToProdTop_map, TopModuleCat.kerι_comp, HomologicalComplex.homotopyCofiber.d_sndX_assoc, CategoryTheory.zigzag_prefunctor_obj_of_zigzag, CategoryTheory.ShortComplex.Splitting.unop_s, CategoryTheory.ObjectProperty.IsCodetecting.isIso_iff_of_epi, ModuleCat.hom_neg, FDRep.scalar_product_char_eq_finrank_equivariant, CategoryTheory.Limits.isColimitCoconeOfConeUnop_desc, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_hom_comp_ι, CategoryTheory.ShortComplex.Exact.leftHomologyDataOfIsLimitKernelFork_i, CategoryTheory.Bicategory.conjugateEquiv_whiskerLeft, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop_assoc, Quiver.Hom.toLoc_as, CategoryTheory.GrothendieckTopology.diagramNatTrans_zero, CategoryTheory.Equivalence.leftOp_functor_map, AlgebraicGeometry.IsAffineOpen.fromSpec_app_of_le, CondensedSet.epi_iff_locallySurjective_on_compHaus, CategoryTheory.Hom.mulEquivCongrRight_apply, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.fromBiprod_δ, CategoryTheory.StrictlyUnitaryLaxFunctor.id_mapId, dNext_nat, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₁, CategoryTheory.LaxFunctor.map₂_associator_app, CategoryTheory.Comonad.coalgebraPreadditive_homGroup_sub_f, CategoryTheory.FreeBicategory.mk_right_unitor_hom, CategoryTheory.Bicategory.LeftExtension.whiskering_obj, CategoryTheory.Presheaf.instIsLocallyInjectiveHomιOpposite, CategoryTheory.Functor.map_dite, CategoryTheory.yonedaEquiv_symm_naturality_right, CategoryTheory.OplaxFunctor.mapComp'_comp_mapComp'_whiskerRight_assoc, SheafOfModules.pushforwardSections_unitHomEquiv, CategoryTheory.wideInducedFunctor_map, CategoryTheory.PreGaloisCategory.PointedGaloisObject.cocone_app, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₁₂_assoc, HomologicalComplex.extend.mapX_none, CategoryTheory.Prod.fst_map, CategoryTheory.Equalizer.Sieve.SecondObj.ext_iff, CategoryTheory.Functor.leibnizPullback_map_app, HomologicalComplex.neg_f_apply, CategoryTheory.Over.mapCongr_rfl, CategoryTheory.MonoidalCategory.prodMonoidal_tensorHom, AlgebraicGeometry.Scheme.Hom.app_appIso_inv, CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero_assoc, CategoryTheory.Grothendieck.grothendieckTypeToCat_functor_map_coe, TopCat.Sheaf.interUnionPullbackCone_pt, CategoryTheory.Localization.SmallShiftedHom.equiv_apply, LightCondensed.instSmallHom, HomologicalComplex.unopFunctor_map_f, CategoryTheory.Limits.biproduct.ι_π_ne_assoc, CategoryTheory.StrictPseudofunctor.comp_obj, CategoryTheory.ShortComplex.leftHomologyMap_zero, HomologicalComplex.homologyOp_hom_naturality, Bicategory.Opposite.homCategory_id_unop2, CategoryTheory.StructuredArrow.toCostructuredArrow'_map, CategoryTheory.Square.opFunctor_map_τ₄, CategoryTheory.Limits.cokernelZeroIsoTarget_inv, CategoryTheory.Grp.Hom.hom_one, CategoryTheory.ShortComplex.fromOpcycles_op_cyclesOpIso_inv, AlgebraicTopology.DoldKan.PInfty_comp_QInfty_assoc, CategoryTheory.StrictPseudofunctor.id_mapComp_inv, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp_symm, CategoryTheory.instIsThin, CategoryTheory.Bicategory.InducedBicategory.mkHom_eqToHom, CategoryTheory.Bicategory.comp_whiskerLeft_symm_assoc, HomologicalComplex.shape, CategoryTheory.AsSmall.down_map, SSet.stdSimplex.objEquiv_symm_apply, AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInfty_assoc, CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac, CategoryTheory.FintypeCat.instFiberFunctorActionFintypeCatForget₂HomSubtypeHomCarrierV, AlgebraicGeometry.pointEquivClosedPoint_symm_apply_coe, Homotopy.refl_hom, CategoryTheory.Localization.HasSmallLocalizedHom.small, CategoryTheory.Localization.Preadditive.map_add, CochainComplex.HomComplex.Cochain.toSingleEquiv_toSingleMk, CategoryTheory.RetractArrow.unop_r_left, CommRingCat.moduleCatRestrictScalarsPseudofunctor_obj, CategoryTheory.Functor.sheafAdjunctionCocontinuous_homEquiv_apply_val, CategoryTheory.PreOneHypercover.forkOfIsColimit_ι_map_inj, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one_assoc, CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_nsmul_f, CategoryTheory.CostructuredArrow.unop_left_comp_underlyingIso_hom_unop, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_yonedaULift_map, SemimoduleCat.homLinearEquiv_symm_apply, CategoryTheory.ShortComplex.LeftHomologyData.unop_g', CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_inverse_map_f, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app_assoc, CochainComplex.HomComplex.Cochain.ofHoms_zero, CategoryTheory.GrothendieckTopology.uliftYoneda_obj_val_obj, CategoryTheory.Paths.lift_nil, CategoryTheory.uliftYonedaEquiv_symm_map_assoc, CategoryTheory.comp_dite, HomologicalComplex.mapBifunctor₁₂.d₂_eq, CategoryTheory.StructuredArrow.toCostructuredArrow'_obj, commBialgCatEquivComonCommAlgCat_counitIso_hom_app, Representation.linHom.invariantsEquivRepHom_apply_hom, AlgebraicGeometry.PresheafedSpace.map_comp_c_app, TopCat.Presheaf.coveringOfPresieve_apply, CategoryTheory.Limits.WalkingMultispan.instSubsingletonHomLeft, Bicategory.Opposite.op2_id_unbop, CategoryTheory.isIso_prod_iff, CategoryTheory.Comonad.ComonadicityInternal.comparisonAdjunction_counit_f_aux, CategoryTheory.ShortComplex.liftCycles_leftHomologyπ_eq_zero_of_boundary, CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inr, HomologicalComplex.opcyclesOpIso_hom_toCycles_op_assoc, CategoryTheory.Limits.opSpan_inv_app, CategoryTheory.unop_inv_rightUnitor, CategoryTheory.Sieve.generate_apply, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app, CategoryTheory.Limits.colimitCoconeOfUnique_isColimit_desc, CategoryTheory.Pretriangulated.contractible_distinguished₁, CategoryTheory.Functor.sheafPushforwardContinuousId'_hom_app_val_app, HomologicalComplex.quasiIsoAt_opFunctor_map_iff, SSet.Truncated.StrictSegal.spine_δ_vertex_lt, CategoryTheory.Bicategory.leftUnitor_comp, CategoryTheory.Presheaf.isLocallyInjective_toPlus, HomologicalComplex.mapBifunctor₂₃.d₁_eq_zero, CategoryTheory.BicategoricalCoherence.assoc'_iso, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.restriction_map, CategoryTheory.Bicategory.LeftExtension.w, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι, CategoryTheory.Lax.OplaxTrans.vComp_naturality_id, CategoryTheory.pathComposition_map, CategoryTheory.Comonad.adj_unit, CategoryTheory.NonPreadditiveAbelian.neg_neg, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_app, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id, CategoryTheory.Sum.functorEquiv_unitIso, DerivedCategory.HomologySequence.epi_homologyMap_mor₂_iff, TopModuleCat.hom_neg, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_val_app, CategoryTheory.Limits.coprod.inl_snd_assoc, CategoryTheory.toQuotientPaths_map, CategoryTheory.Cat.associator_hom_toNatTrans, CategoryTheory.Presheaf.isLocallyInjective_forget, Mathlib.Tactic.Bicategory.evalComp_nil_nil, CategoryTheory.unop_sub, CategoryTheory.Localization.Preadditive.zero_add', dNext_eq_zero, CategoryTheory.ActionCategory.hom_as_subtype, SimplicialObject.Split.cofan_inj_naturality_symm, CategoryTheory.MonoidalOpposite.tensorLeftIso_inv_app_unmop, CategoryTheory.Pseudofunctor.isoMapOfCommSq_eq, CommGrpCat.coyoneda_map_app, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃, CategoryTheory.cocones_obj_obj, commBialgCatEquivComonCommAlgCat_functor_map_unop_hom, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_hom, CategoryTheory.Limits.colimitYonedaHomIsoLimitRightOp_π_apply, CategoryTheory.WithInitial.opEquiv_unitIso_hom_app, CategoryTheory.Localization.Preadditive.neg'_add'_self, CategoryTheory.LaxFunctor.mapComp_naturality_left, CategoryTheory.LaxFunctor.mapComp_assoc_left_assoc, CategoryTheory.Bicategory.LeftLift.whiskerOfIdCompIsoSelf_inv_right, CategoryTheory.Abelian.subobjectIsoSubobjectOp_symm_apply, CategoryTheory.GrothendieckTopology.plusMap_zero, CategoryTheory.Functor.RepresentableBy.ofIsoObj_homEquiv, AlgebraicGeometry.Scheme.Opens.eq_presheaf_map_eqToHom, CategoryTheory.unop_hom_leftUnitor, CochainComplex.mappingCone.lift_f, CategoryTheory.ComposableArrows.IsComplex.zero, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_functor, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_map, CategoryTheory.Limits.cokernelBiproductFromSubtypeIso_inv, CategoryTheory.Functor.CorepresentableBy.coyoneda_homEquiv, ModuleCat.monoidalClosed_pre_app, CategoryTheory.Adjunction.homEquiv_leftAdjointUniq_hom_app, AlgebraicGeometry.pointsPi_surjective, CategoryTheory.Bicategory.associatorNatIsoMiddle_inv_app, SemimoduleCat.hom_smul, CategoryTheory.Limits.pullback_fst_map_snd_isPullback, HomologicalComplex₂.totalAux.d₁_eq', CategoryTheory.ShortComplex.add_τ₁, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ, AlgebraicGeometry.map_injective_of_isIntegral, CategoryTheory.GrothendieckTopology.uliftYoneda_obj_val_map_down, SSet.stdSimplex.nonDegenerateEquiv_symm_apply_coe, CategoryTheory.InducedCategory.homLinearEquiv_symm_apply_hom, CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map, CategoryTheory.Pseudofunctor.map₂_whisker_right_assoc, CategoryTheory.OverPresheafAux.map_mkPrecomp_eqToHom, CategoryTheory.Limits.end_.condition_assoc, CategoryTheory.Arrow.equivSigma_apply_snd_fst, CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor, CategoryTheory.WithInitial.ofCommaMorphism_app, SimplicialObject.Splitting.cofan_inj_comp_app_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_eq, HomologicalComplex.ι_mapBifunctorFlipIso_hom_assoc, CategoryTheory.prodOpEquiv_counitIso_inv_app, CategoryTheory.Comonad.beckCoalgebraFork_π_app, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_apply_φ, TopologicalSpace.OpenNhds.apply_mk, CategoryTheory.Paths.of_obj, CategoryTheory.MonoidalOpposite.tensorIso_inv_app_unmop, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_app_assoc, CommGrpCat.ofHom_injective, CochainComplex.HomComplex.CohomologyClass.toHom_mk, CategoryTheory.ShortComplex.leftHomologyMap'_zero, CategoryTheory.Limits.prod.inr_fst, CategoryTheory.Adjunction.homEquiv_naturality_right, CategoryTheory.Bicategory.InducedBicategory.forget_mapId_hom, CategoryTheory.Equalizer.Presieve.isSheafFor_singleton_iff_of_hasPullback, CategoryTheory.GrpObj.zpow_comp_assoc, CategoryTheory.Limits.cokernelOrderHom_coe, CategoryTheory.Functor.IsRepresentedBy.iff_exists_representableBy, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_assoc, CategoryTheory.Subfunctor.sieveOfSection_apply, CochainComplex.HomComplex.Cochain.add_v, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_inv_iso_hom, CategoryTheory.CosimplicialObject.cechConerveEquiv_apply, CategoryTheory.Bicategory.prod_rightUnitor_hom_snd, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_map, CategoryTheory.Functor.rightOp_map_unop, CategoryTheory.Bicategory.precomp_map, CategoryTheory.Discrete.productEquiv_functor_map, CategoryTheory.Bicategory.pentagon_hom_hom_inv_hom_hom, CategoryTheory.Bicategory.conjugateEquiv_symm_apply, CategoryTheory.Comon.MonOpOpToComonObj_comon_counit, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_val_app, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk_assoc, CategoryTheory.Bicategory.prod_associator_hom_snd, CategoryTheory.Bicategory.Adjunction.right_triangle, CategoryTheory.Bicategory.triangle_assoc_comp_left_inv, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerRight_naturality, CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_inv_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_inv_app'_assoc, CategoryTheory.injective_iff_rlp_monomorphisms_zero, CategoryTheory.cosimplicialSimplicialEquiv_functor_obj_map, CategoryTheory.ShortComplex.rightHomologyMap'_zero, HomologicalComplex.biprod_inl_snd_f, CategoryTheory.DinatTrans.dinaturality, CochainComplex.toSingle₀Equiv_symm_apply_f_zero, CategoryTheory.oppositeShiftFunctorAdd_hom_app, CategoryTheory.ComposableArrows.homMk₀_app, CategoryTheory.Limits.preservesCokernel_zero, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map_assoc, ModuleCat.semilinearMapAddEquiv_apply, CategoryTheory.Preadditive.comp_add_assoc, CategoryTheory.curryingIso_hom_toFunctor_map_app, CategoryTheory.quotientPathsTo_map, CategoryTheory.Oplax.OplaxTrans.Modification.naturality, CategoryTheory.Quotient.comp_mk, CategoryTheory.ShortComplex.HomologyMapData.smul_left, CategoryTheory.Functor.mapZeroObject_hom, Rep.coindIso_hom_hom_hom, ChainComplex.alternatingConst_map_f, CategoryTheory.Meq.condition, CategoryTheory.BicategoricalCoherence.right_iso, CategoryTheory.Bicategory.Equivalence.right_triangle_hom, ModuleCat.freeHomEquiv_symm_apply, CategoryTheory.Bicategory.Prod.fst_obj, AlgebraicGeometry.Scheme.Hom.inv_app, CategoryTheory.MonObj.comp_pow_assoc, CategoryTheory.Functor.homologySequenceδ_comp, CategoryTheory.CommSq.LiftStruct.opEquiv_apply, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop, CategoryTheory.WithTerminal.opEquiv_unitIso_inv_app, CategoryTheory.Limits.PushoutCocone.unop_snd, CategoryTheory.Square.op_f₃₄, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_inv, ChainComplex.fromSingle₀Equiv_symm_apply_f_succ, CategoryTheory.LaxFunctor.mapComp_assoc_right_app_assoc, CategoryTheory.ShortComplex.opcyclesOpIso_inv_naturality_assoc, SheafOfModules.pushforwardPushforwardEquivalence_counit_app_val_app, CategoryTheory.NatTrans.removeOp_app, SemimoduleCat.hom_sum, CategoryTheory.instEffectiveEpiFamily, CategoryTheory.Bicategory.associatorNatIsoRight_inv_app, CategoryTheory.Comma.ext_iff, CategoryTheory.Limits.colimitCoyonedaHomIsoLimitLeftOp_π_apply, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app, CategoryTheory.ExponentiableMorphism.homEquiv_apply_eq, CategoryTheory.Groupoid.vertexGroup_mul, CategoryTheory.ShortComplex.Homotopy.symm_h₁, CategoryTheory.PreZeroHypercover.shrink_I₀, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_map, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π_assoc, CategoryTheory.PreGaloisCategory.endMulEquivAutGalois_pi, CategoryTheory.Localization.homEquiv_isoOfHom_inv, CategoryTheory.Bicategory.leftUnitor_comp_inv_assoc, CategoryTheory.Localization.homEquiv_id, CategoryTheory.NatTrans.app_sub, CategoryTheory.Bicategory.leftUnitor_whiskerRight_assoc, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_two_assoc, AlgebraicTopology.DoldKan.P_add_Q_f, CategoryTheory.ShortComplex.opFunctor_map, ModuleCat.homEquiv_extendScalarsId, CategoryTheory.NatTrans.app_neg, CategoryTheory.Limits.kernelForkBiproductToSubtype_isLimit, CategoryTheory.Functor.sheafPushforwardContinuousComp'_hom_app_val_app, CategoryTheory.ShortComplex.SnakeInput.w₁₃, groupHomology.d₂₁_comp_d₁₀_assoc, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.lift_map, AddCommGrpCat.hom_neg, CategoryTheory.Limits.hasImage_zero, AlgebraicTopology.DoldKan.hσ'_eq', CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv, HomologicalComplex.opInverse_map, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_inv_app_val_app, CategoryTheory.MorphismProperty.RightFraction.op_s, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_apply, CategoryTheory.Bicategory.leftUnitor_inv_congr, CategoryTheory.GrothendieckTopology.Plus.toPlus_apply, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.Bicategory.conjugateIsoEquiv_symm_apply_inv, CategoryTheory.Limits.kernelBiproductToSubtypeIso_inv, CategoryTheory.Limits.limitUnopIsoUnopColimit_inv_comp_π, CategoryTheory.Subfunctor.Subpresheaf.ofSection_eq_range, CategoryTheory.Bicategory.Adj.forget₁_mapComp, CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_hom, CategoryTheory.Limits.Trident.IsLimit.homIso_natural, HomologicalComplex.dFrom_comp_xNextIsoSelf_assoc, CategoryTheory.Bicategory.rightUnitor_hom_congr, SemiNormedGrp.hom_zsum, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapComp_inv, CategoryTheory.Equivalence.sheafCongr.counitIso_inv_app_val_app, CategoryTheory.Preadditive.sum_comp', CategoryTheory.unop_whiskerLeft, CategoryTheory.CatEnrichedOrdinary.homEquiv_id, AlgebraicTopology.DoldKan.HigherFacesVanish.induction, CategoryTheory.Limits.opHomCompWhiskeringLimYonedaIsoCocones_inv_app_app, AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInfty, CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp_assoc, CategoryTheory.Pseudofunctor.comp_mapId, HomologicalComplex₂.D₁_D₂, CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal_μ_unmop_unmop, CategoryTheory.eqToHom_unop, TopCat.Presheaf.presheafEquivOfIso_functor_obj_map, CategoryTheory.Bicategory.Prod.swap_mapId_inv, CategoryTheory.NatTrans.unop_app, CategoryTheory.OplaxFunctor.mapComp_naturality_right_app, CochainComplex.HomComplex.Cochain.toSingleMk_sub, CategoryTheory.Limits.HasZeroMorphisms.comp_zero, CategoryTheory.sum.inlCompInverseAssociator_hom_app_down_down, CategoryTheory.unop_sum, CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal_η_unmop_unmop, CategoryTheory.Discrete.productEquiv_inverse_map, CategoryTheory.Bicategory.Prod.sectR_map, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_hom_app_unop, CategoryTheory.Sieve.toUliftFunctor_app_down_coe, CategoryTheory.ShortComplex.leftHomologyMap'_add, CategoryTheory.kernelCokernelCompSequence.inr_φ_fst, CategoryTheory.StrictPseudofunctor.mk''_map₂, CategoryTheory.Linear.rightComp_apply, CategoryTheory.ShiftedHom.mk₀_smul, CategoryTheory.OplaxFunctor.mapComp'_comp_whiskerLeft_mapComp'_assoc, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.lift_map_assoc, CategoryTheory.MonoidalCategory.tensor_dite, CategoryTheory.NonPreadditiveAbelian.sub_self, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapId_inv, CategoryTheory.oppositeShiftFunctorAdd'_inv_app, CategoryTheory.Under.opEquivOpOver_inverse_map, CategoryTheory.ShortComplex.Homotopy.h₀_f, Bicategory.Opposite.op2_associator_hom, CategoryTheory.ShortComplex.opcyclesMap'_neg, AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_toGlued, SimplicialObject.Splitting.cofan_inj_eq_assoc, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_hom, FintypeCat.homMk_apply, CategoryTheory.GrothendieckTopology.uliftYoneda_map_val_app_down, CategoryTheory.PreZeroHypercover.sum_f, CategoryTheory.Abelian.Ext.mk₀_homEquiv₀_apply, SimplexCategory.II_δ, CochainComplex.HomComplex.Cocycle.equivHomShift_apply, CategoryTheory.Limits.Cofork.op_ι, ComplexShape.Embedding.AreComplementary.hom_ext', AlgebraicGeometry.Scheme.IdealSheafData.map_ideal_basicOpen, CategoryTheory.Abelian.FunctorCategory.imageObjIso_inv, CategoryTheory.MorphismProperty.MapFactorizationData.op_p, CategoryTheory.Adjunction.homEquiv_id, CommRingCat.coproductCocone_ι, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_inv_τr, CategoryTheory.CatEnriched.hComp_id, CategoryTheory.instReflectsIsomorphismsForgetTypeHom, CategoryTheory.LaxFunctor.mapComp_assoc_left_app_assoc, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₁, CategoryTheory.Adjunction.homEquiv_naturality_left, CategoryTheory.Comon.monoidal_tensorObj_comon_counit, HomologicalComplex.mapBifunctor.d₁_eq, CategoryTheory.Lax.OplaxTrans.id_app, CategoryTheory.Oplax.StrongTrans.homCategory_comp_as_app, CategoryTheory.Bicategory.rightZigzagIso_hom, CategoryTheory.LaxFunctor.id_mapComp, CategoryTheory.Functor.PullbackObjObj.ofHasPullback_fst, CategoryTheory.Functor.IsRepresentedBy.representableBy_homEquiv_apply, CategoryTheory.Preadditive.sub_comp, CategoryTheory.Functor.map_one, ChainComplex.alternatingConst_obj, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHomLeft, CategoryTheory.Retract.op_r, CategoryTheory.Cat.leftUnitor_inv_app, CategoryTheory.Functor.toPseudoFunctor_obj, CategoryTheory.GradedObject.ιMapObjOrZero_eq_zero, CategoryTheory.Limits.WidePullbackShape.subsingleton_hom, CategoryTheory.Bicategory.associator_inv_naturality_middle_assoc, CategoryTheory.LaxFunctor.map₂_leftUnitor_app, CategoryTheory.Preadditive.mono_iff_cancel_zero, CategoryTheory.BicategoricalCoherence.refl_iso, CompHausLike.LocallyConstant.functorToPresheaves_obj_map, CategoryTheory.Bicategory.rightUnitor_comp_inv_assoc, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj, CategoryTheory.op_comp_unop, CategoryTheory.Limits.inl_pushoutZeroZeroIso_hom, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₂_assoc, CategoryTheory.Limits.walkingParallelPairOp_right, CategoryTheory.WithTerminal.opEquiv_functor_map, CategoryTheory.PreGaloisCategory.evaluation_aut_injective_of_isConnected, PresheafOfModules.zero_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τl, CategoryTheory.Lax.OplaxTrans.naturality_naturality_assoc, CategoryTheory.Limits.opCoproductIsoProduct_inv_comp_ι, CategoryTheory.CostructuredArrow.projectQuotient_mk, CategoryTheory.Limits.Cotrident.IsColimit.homIso_apply_coe, CategoryTheory.CatEnrichedOrdinary.Hom.base_eqToHom, AddCommGrpCat.homAddEquiv_apply, CategoryTheory.Over.coreHomEquivToOverSections_homEquiv, CategoryTheory.Functor.PreservesHomology.preservesKernel, CategoryTheory.MorphismProperty.isColocal_iff, Homotopy.nullHomotopy'_hom, CategoryTheory.Bicategory.InducedBicategory.bicategory_leftUnitor_hom_hom, CategoryTheory.Limits.IsInitial.subsingleton_to, CategoryTheory.Pseudofunctor.Grothendieck.categoryStruct_comp_fiber, CategoryTheory.Preadditive.neg_comp_assoc, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right, CategoryTheory.StrictlyUnitaryLaxFunctor.comp_map₂, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'_assoc, CategoryTheory.Abelian.Pseudoelement.zero_apply, CategoryTheory.Limits.biprod.lift_desc, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app, CategoryTheory.Preadditive.instEpiNegHom, CategoryTheory.eqToHom_heq_id_dom, CategoryTheory.Functor.homologySequence_mono_shift_map_mor₂_iff, Bicategory.Opposite.bicategory_rightUnitor_hom_unop2, CategoryTheory.Endofunctor.Adjunction.Coalgebra.toAlgebraOf_map_f, CategoryTheory.Quiv.forget_obj, CategoryTheory.Limits.HasZeroObject.zeroIsoInitial_hom, CategoryTheory.Functor.prod_δ_fst, CategoryTheory.Preadditive.neg_iso_inv, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv, SemiNormedGrp.hom_nsum, CategoryTheory.CostructuredArrow.toStructuredArrow_map, CategoryTheory.cokernel_zero_of_nonzero_to_simple, CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_three, CategoryTheory.ShortComplex.zero_τ₂, CochainComplex.mappingCone.mapHomologicalComplexXIso'_inv, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHomLeft_unop, CategoryTheory.Functor.IsCoverDense.Types.pushforwardFamily_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_yoneda_map, commBialgCatEquivComonCommAlgCat_counitIso_inv_app, CategoryTheory.Pseudofunctor.CoGrothendieck.compIso_hom_app, CategoryTheory.Pseudofunctor.DescentData.hom_comp, CategoryTheory.Functor.IsStronglyCocartesian.map_self, CategoryTheory.Bicategory.Strict.associator_eqToIso, CategoryTheory.Linear.smul_comp, CategoryTheory.Pretriangulated.Triangle.smul_hom₁, CategoryTheory.ShortComplex.RightHomologyMapData.add_φQ, CategoryTheory.Functor.PreservesZeroMorphisms.map_zero, CategoryTheory.Pseudofunctor.IsPrestackFor.nonempty_fullyFaithful, Rep.FiniteCyclicGroup.resolution.π_f, Alexandrov.projSup_map, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_linearCombination, CategoryTheory.SimplicialObject.equivalenceLeftToRight_left_app, CategoryTheory.Limits.Fork.unop_π, CategoryTheory.ShortComplex.leftHomologyMap_smul, CategoryTheory.MonoidalCategory.DayConvolutionUnit.corepresentableByRight_homEquiv, CategoryTheory.Functor.comp_homologySequenceδ_assoc, TopCat.Presheaf.SheafConditionEqualizerProducts.res_π_apply, HomologicalComplex.homotopyCofiber.d_fstX_assoc, AlgebraicGeometry.Scheme.zeroLocus_map_of_eq, CategoryTheory.Pseudofunctor.mapComp'_hom_comp_mapComp'_hom_whiskerRight, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τr, CategoryTheory.presheafHom_map_app_op_mk_id, CategoryTheory.OplaxFunctor.mapComp'_eq_mapComp, CategoryTheory.ShortComplex.opcyclesMap'_smul, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_comp, CategoryTheory.InducedWideCategory.category_id_coe, CategoryTheory.Bicategory.RightLift.w, CategoryTheory.CartesianMonoidalCategory.homEquivToProd_symm_apply, CategoryTheory.ShortComplex.LeftHomologyData.liftK_π_eq_zero_of_boundary_assoc, CategoryTheory.Pseudofunctor.ObjectProperty.map₂_app_hom, CategoryTheory.ShortComplex.RightHomologyMapData.unop_φH, CategoryTheory.cokernelOpOp_inv, SSet.stdSimplex.face_singleton_compl, CategoryTheory.Functor.partialRightAdjointHomEquiv_map_comp, CategoryTheory.Bicategory.triangle_assoc, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_inr, CategoryTheory.Bicategory.leftUnitorNatIso_inv_app, TopologicalSpace.Opens.val_apply, HomologicalComplex.Hom.fAddMonoidHom_apply, CategoryTheory.down_comp, CategoryTheory.Pseudofunctor.CoGrothendieck.Hom.ext_iff, CategoryTheory.equiv_punit_iff_unique, CategoryTheory.Limits.PushoutCocone.unop_fst, CategoryTheory.MonoidalCategory.externalProductBifunctor_obj_map, CategoryTheory.isIso_op_iff, AlgebraicGeometry.IsOpenImmersion.lift_app, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff, CochainComplex.shiftFunctor_obj_d, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_left_left_as, CategoryTheory.Limits.limitOpIsoOpColimit_hom_comp_ι, CategoryTheory.Comonad.coalgebraPreadditive_homGroup_zero_f, CategoryTheory.GrothendieckTopology.yonedaEquiv_apply, CategoryTheory.PreZeroHypercover.shrink_f, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_obj_π_app, CategoryTheory.OplaxFunctor.map₂_rightUnitor_app_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.toBiprod_apply, CategoryTheory.shrinkYonedaEquiv_symm_map, CategoryTheory.ComposableArrows.IsComplex.zero', CategoryTheory.Oplax.StrongTrans.vcomp_naturality_inv, Bicategory.Opposite.bicategory_whiskerLeft_unop2, CategoryTheory.ShortComplex.leftHomologyMap'_smul, CategoryTheory.Functor.currying_functor_map_app, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv, CategoryTheory.map_coyonedaEquiv, CategoryTheory.Adjunction.homEquiv_symm_apply, CategoryTheory.CommSq.HasLift.iff_unop, CategoryTheory.Limits.PushoutCocone.op_fst, CategoryTheory.ShortComplex.cyclesMap_add, CategoryTheory.ShortComplex.LeftHomologyData.op_ι, FintypeCat.instFullForgetHomCarrier, CochainComplex.mappingCone.d_fst_v, CategoryTheory.unop_id, CategoryTheory.DifferentialObject.zero_f, CategoryTheory.Oplax.OplaxTrans.whiskerRight_as_app, CategoryTheory.ShortComplex.RightHomologyData.op_π, CategoryTheory.Limits.isCokernelEpiComp_desc, AddCommGrpCat.coyonedaType_map_app, CategoryTheory.MonObj.mul_eq_mul, CategoryTheory.Over.opEquivOpUnder_functor_obj, SSet.Truncated.Edge.CompStruct.idCompId_simplex, AlgebraicGeometry.Scheme.stalkMap_congr, CategoryTheory.Bicategory.associator_naturality_middle_assoc, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_snd, AlgebraicGeometry.Spec.homEquiv_symm_apply, ModuleCat.ihom_ev_app, Bicategory.Opposite.bicategory_rightUnitor_inv_unop2, CategoryTheory.ShortComplex.hasHomology_of_hasKernel, HomologicalComplex.mapBifunctor₂₃.d₂_eq_zero, CategoryTheory.Yoneda.obj_map_id, SimplicialObject.Splitting.IndexSet.eqId_iff_len_le, CategoryTheory.ObjectProperty.smul_mem_trW_iff, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι, CategoryTheory.Pseudofunctor.whiskerRightIso_mapId, CategoryTheory.Pseudofunctor.Grothendieck.map_map_base, CategoryTheory.map_yonedaEquiv', CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_associator_inv_as_app, CategoryTheory.Limits.Cowedge.condition, CommMonCat.coyonedaType_map_app, CategoryTheory.Oplax.OplaxTrans.leftUnitor_inv_as_app, CategoryTheory.ObjectProperty.leftOrthogonal_iff, CategoryTheory.Limits.initial.subsingleton_to, CategoryTheory.Functor.map_sum, Rep.indResHomEquiv_symm_apply_hom, CategoryTheory.FreeBicategory.lift_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom, CategoryTheory.kernelCokernelCompSequence.ι_φ_assoc, CategoryTheory.op_id, CategoryTheory.CategoryOfElements.toCostructuredArrow_map, CategoryTheory.Functor.toOplaxFunctor'_mapId, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom, CategoryTheory.Bicategory.RightExtension.w, CategoryTheory.Bicategory.Prod.fst_mapId_inv, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom, CategoryTheory.Bicategory.Adj.leftUnitor_hom_τl, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop_assoc, CategoryTheory.Functor.homEquivOfIsLeftKanExtension_apply_app, CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIso_inv, CategoryTheory.Oplax.OplaxTrans.Modification.id_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality, CategoryTheory.Sum.functorEquiv_counitIso, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_right, CategoryTheory.Limits.π_comp_opProductIsoCoproduct_hom, CategoryTheory.StrictlyUnitaryLaxFunctor.comp_obj, CategoryTheory.simplicialCosimplicialEquiv_functor_obj_map, AlgebraicGeometry.SheafedSpace.Γ_map_op, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_hom_iso, CategoryTheory.Bicategory.mateEquiv_apply', CategoryTheory.StructuredArrow.toCostructuredArrow_obj, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.liftAux_fac, CategoryTheory.nerve.edgeMk_surjective, CategoryTheory.Bicategory.Equivalence.left_triangle_hom, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm_assoc, CategoryTheory.Over.postAdjunctionLeft_counit_app_left, CategoryTheory.Preadditive.coforkOfCokernelCofork_pt, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_symm_apply, CategoryTheory.Pretriangulated.Triangle.zero_hom₂, CategoryTheory.Square.unop_f₃₄, CategoryTheory.Bicategory.conjugateEquiv_comp, CategoryTheory.OplaxFunctor.mapComp_id_left, CategoryTheory.LaxFunctor.map₂_leftUnitor_app_assoc, CategoryTheory.epi_iff_forall_injective, skyscraperPresheaf_map, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_symm, CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_fst, HomologicalComplex.ι_mapBifunctorFlipIso_inv, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_three_assoc, StalkSkyscraperPresheafAdjunctionAuxs.toSkyscraperPresheaf_app, CategoryTheory.Functor.IsStronglyCocartesian.universal_property, AlgebraicGeometry.Scheme.Hom.appIso_inv_appLE, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply_assoc, CategoryTheory.Bicategory.postcomp_map, AlgebraicGeometry.Scheme.Modules.map_smul, CochainComplex.HomComplex.CohomologyClass.homAddEquiv_apply, CategoryTheory.LaxFunctor.map₂_rightUnitor, CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIsoWhisker_hom_right, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality_assoc, CategoryTheory.Bicategory.triangle_assoc_comp_right_assoc, CategoryTheory.LaxFunctor.mapId'_eq_mapId, CategoryTheory.ShortComplex.f_pOpcycles, CategoryTheory.Functor.mapLinearMap_apply, CategoryTheory.ShortComplex.leftHomologyMap'_op, CategoryTheory.shrinkYonedaEquiv_shrinkYoneda_map, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_counit, CategoryTheory.enrichedNatTransYoneda_map_app, CategoryTheory.Functor.homologySequence_epi_shift_map_mor₂_iff, HomologicalComplex.cylinder.πCompι₀Homotopy.inlX_nullHomotopy_f, CategoryTheory.WithTerminal.opEquiv_inverse_map, CategoryTheory.Functor.PullbackObjObj.isPullback, Subobject.presheaf_map, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app_assoc, CategoryTheory.Limits.limitRightOpIsoOpColimit_inv_comp_π, CategoryTheory.Equivalence.symmEquivInverse_map_app, CategoryTheory.prod.associator_map, SSet.StrictSegal.spineToSimplex_vertex, CategoryTheory.FreeBicategory.liftHom_comp, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app_assoc, CategoryTheory.ShiftedHom.opEquiv'_add_symm, CategoryTheory.Functor.functorHomEquiv_symm_apply_app_app, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_map₂, CategoryTheory.Mon.Hom.hom_one, CategoryTheory.Bicategory.rightUnitorNatIso_hom_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app, AddCommGrpCat.hom_zsmul, SSet.Truncated.Edge.tgt_eq, CategoryTheory.colimitYonedaHomEquiv_π_apply, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_inv_assoc, CategoryTheory.heq_eqToHom_comp_iff, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_inv_ι, CategoryTheory.ParametrizedAdjunction.whiskerLeft_map_counit_assoc, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_apply, AlgebraicGeometry.PresheafedSpace.ofRestrict_c_app, CategoryTheory.Limits.SequentialProduct.functorMap_commSq, CategoryTheory.ShortComplex.Splitting.s_r_assoc, CategoryTheory.mono_iff_forall_injective, CategoryTheory.ShortComplex.opcyclesMap'_zero, CategoryTheory.ShortComplex.leftHomologyMap_neg, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.fac, CategoryTheory.kernelCokernelCompSequence.φ_π_assoc, CategoryTheory.Comon.monoidal_tensorObj_comon_comul, CategoryTheory.uliftCoyonedaEquiv_comp, CategoryTheory.Functor.IsCoverDense.Types.naturality_assoc, Action.FintypeCat.ofMulAction_apply, HomologicalComplex.liftCycles_homologyπ_eq_zero_of_boundary_assoc, CategoryTheory.LaxFunctor.PseudoCore.mapIdIso_inv, CategoryTheory.CatEnrichedOrdinary.Hom.base_id, CategoryTheory.yonedaEquiv_symm_app_apply, CategoryTheory.Bicategory.leftUnitor_comp_assoc, SemimoduleCat.homAddEquiv_symm_apply_hom, CategoryTheory.Arrow.equivSigma_symm_apply_right, FDRep.finrank_hom_simple_simple, CategoryTheory.WithTerminal.coneEquiv_functor_map_hom, CategoryTheory.Bicategory.LeftLift.w, CategoryTheory.Join.mapIsoWhiskerRight_inv_app, CategoryTheory.Limits.ι_comp_colimitUnopIsoOpLimit_hom, AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_fst, CategoryTheory.Pseudofunctor.mapId'_inv_naturality, CategoryTheory.LaxFunctor.mapComp_naturality_left_assoc, CategoryTheory.tensorLeftHomEquiv_symm_naturality, CategoryTheory.Functor.map_surjective, AlgebraicGeometry.exists_lift_of_germInjective, CategoryTheory.nerve.homEquiv_symm_apply, CategoryTheory.Functor.op_map, CategoryTheory.mono_to_simple_zero_of_not_iso, SheafOfModules.unitHomEquiv_apply_coe, AlgebraicTopology.DoldKan.PInfty_add_QInfty, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_app_assoc, CategoryTheory.preadditiveYonedaObj_map, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_app, CategoryTheory.ShortComplex.f_pOpcycles_assoc, CategoryTheory.ShortComplex.ShortExact.comp_δ_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_assoc, CategoryTheory.prod.inverseAssociator_map, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π, CategoryTheory.Limits.IsLimit.homEquiv_apply, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd_assoc, CochainComplex.HomComplex.Cochain.single_v_eq_zero, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_app, CategoryTheory.ShortComplex.cyclesOpIso_hom_naturality_assoc, CategoryTheory.Adjunction.homEquiv_naturality_left_square_assoc, CategoryTheory.Limits.cokernel.condition_apply, CategoryTheory.Pseudofunctor.DescentData.Hom.comm, CategoryTheory.Limits.compYonedaSectionsEquiv_symm_apply_coe, CategoryTheory.Limits.KernelFork.map_condition_assoc, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_comp, groupCohomology.d₀₁_eq_zero, CategoryTheory.yonedaEquiv_comp, CategoryTheory.OverPresheafAux.counitForward_naturality₂, CategoryTheory.prod_comp_snd, HomologicalComplex₂.ιTotal_totalFlipIso_f_inv, CategoryTheory.unitCompPartialBijective_symm_apply, CategoryTheory.PreGaloisCategory.functorToAction_comp_forget₂_eq, CategoryTheory.Comon.ComonToMonOpOpObj_mon_one, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map, CategoryTheory.Bicategory.triangle_assoc_comp_left_inv_assoc, CategoryTheory.Limits.parallelPairOpIso_hom_app_zero, CategoryTheory.Functor.IsCoverDense.Types.naturality, CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_map, CategoryTheory.Localization.structuredArrowEquiv_apply, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerRight_naturality_assoc, CategoryTheory.Limits.kernelSubobject_zero, CategoryTheory.Limits.Bicone.ι_of_isLimit

CategoryTheory.Epi

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
left_cancellation 📖	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct	—	—	—

CategoryTheory.Mono

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
right_cancellation 📖	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct	—	—	—

LibraryNote

Definitions

Name	Category	Theorems
category_theory_universes 📖	CompOp	—

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