Basic

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

Statistics

Metric	Count
Definitions comp, id, instInhabited, map, obj, toPrefunctor, «term_⋙_», «term_⥤_», «term𝟭»	9
Theorems comp_id, comp_map, comp_obj, congr_map, id_comp, id_map, id_obj, map_comp, map_comp_assoc, map_dite, map_id, toPrefunctor_comp, toPrefunctor_injective, toPrefunctor_map, toPrefunctor_obj	15
Total	24

CategoryTheory

Definitions

Name	Category	Theorems
«term_⋙_» 📖	CompOp	—
«term_⥤_» 📖	CompOp	—
«term𝟭» 📖	CompOp	—

CategoryTheory.Functor

Definitions

Name	Category	Theorems
comp 📖	CompOp	4960 math math: CategoryTheory.Equivalence.adjointify_η_ε_assoc, CategoryTheory.GrothendieckTopology.coneCompEvaluationOfConeCompDiagramFunctorCompEvaluation_pt, ModuleCat.HasColimit.colimitCocone_pt_isAddCommGroup, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₃, CategoryTheory.MorphismProperty.IsInvertedBy.iff_comp, CategoryTheory.shiftFunctorZero_inv_app_obj_of_induced, HomotopyCategory.spectralObjectMappingCone_δ'_app, PresheafOfModules.Monoidal.tensorObj_obj, CategoryTheory.MorphismProperty.LeftFraction.map_compatibility, CategoryTheory.Adjunction.adjunctionOfEquivLeft_counit_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_eq, CategoryTheory.SingleFunctors.shiftIso_add, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₁, LeftExtension.coconeAtFunctor_map_hom, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_hom_right, CategoryTheory.sum.inrCompInverseAssociator_hom_app, FullyFaithful.homNatIsoMaxRight_inv_app, CommShift.isoAdd_hom_app, PresheafOfModules.instIsRightAdjointPushforwardCompFunctorOppositeRingCatWhiskerLeftOp, CategoryTheory.Adjunction.compUliftCoyonedaIso_hom_app_app_down, smoothSheafCommRing.ι_forgetStalk_inv, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerLeftIso_inv_app, CategoryTheory.whiskeringLeft_comp_evaluation, CategoryTheory.SingleFunctors.postcompPostcompIso_hom_hom_app, CategoryTheory.Equivalence.prod_unitIso, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_map, CategoryTheory.Adjunction.Triple.isIso_unit_iff_isIso_counit, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_hom_app_zero, CategoryTheory.Adjunction.leftOp_unit, CategoryTheory.TwoSquare.equivNatTrans_symm_apply, CategoryTheory.Sum.natTransOfWhiskerLeftInlInr_app, SheafOfModules.pushforward_assoc, rightKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.GlueData.diagramIso_app_right, Initial.extendCone_obj_pt, isoSum_inv_app_inl, CategoryTheory.Limits.IndizationClosedUnderFilteredColimitsAux.exists_nonempty_limit_obj_of_isColimit, CategoryTheory.Limits.Cone.toUnder_pt, CategoryTheory.StructuredArrow.final_pre, CategoryTheory.Equivalence.leftOp_unitIso_hom_app, CategoryTheory.Monad.ForgetCreatesColimits.commuting, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_hom_app_val_app, CategoryTheory.SimplicialObject.whiskering_obj_map_app, CategoryTheory.Monad.monadMonEquiv_unitIso_inv_app_toNatTrans_app, IsDenseSubsite.instIsIsoSheafAppCounitSheafAdjunctionCocontinuous, CategoryTheory.ComposableArrows.opEquivalence_counitIso_inv_app_app, CategoryTheory.mateEquiv_counit_symm, CategoryTheory.Equivalence.preregular_isSheaf_iff, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst_assoc, CategoryTheory.MonoidalCategory.DayConvolution.braidingHomCorepresenting_app, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_apply, coreComp_hom_app_iso_inv, CategoryTheory.Limits.spanCompIso_app_left, CategoryTheory.Discrete.sumEquiv_counitIso_inv_app, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_hom, CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc, CategoryTheory.Presheaf.instIsLocallySurjectiveHomWhiskerRightOppositeForget, HomologicalComplex.singleMapHomologicalComplex_hom_app_ne, CategoryTheory.NatTrans.hcomp_id_app, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_left, CategoryTheory.shiftFunctorAdd'_assoc_inv_app, CategoryTheory.isIso_sheafificationAdjunction_counit, isIso_of_isRightDerivedFunctor_of_inverts, AlgebraicGeometry.StructureSheaf.instIsScalarTowerCarrierStalkCommRingCatStructurePresheafInCommRingCatCarrierAbPresheafOpensCarrierTopModuleStructurePresheaf, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.hasLimit_cospan_forget_of_right', typeToPartialFunIsoPartialFunToPointed_inv_app_toFun, AlgebraicTopology.DoldKan.Compatibility.equivalence₀_unitIso_hom_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_left, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_X₃, CategoryTheory.SingleFunctors.Hom.comm, CategoryTheory.preservesFiniteLimits_iff_lan_preservesFiniteLimits, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app, CategoryTheory.Adjunction.whiskerLeftLCounitIsoOfIsIsoUnit_hom_app, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.Equivalence.sheafCongr.counitIso_hom_app_val_app, CategoryTheory.shift_shiftFunctorCompIsoId_hom_app, CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux_fac, liftOfIsRightKanExtension_fac, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp_inv_app_f, CategoryTheory.Limits.CategoricalPullback.catCommSq_iso_hom_app, CategoryTheory.Join.inlCompFromSum_hom_app, LightProfinite.Extend.functorOp_obj, CategoryTheory.Limits.colimitHomIsoLimitYoneda_hom_comp_π, LightCondensed.lanPresheafIso_hom, rightKanExtensionUniqueOfIso_hom, CategoryTheory.comonEquiv_unitIso, CategoryTheory.ihom.coev_naturality, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_map_right, CategoryTheory.equivOfTensorIsoUnit_unitIso, CategoryTheory.Equivalence.congrFullSubcategory_inverse, comp_obj, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_associator, CategoryTheory.Adjunction.whiskerLeftLCounitIsoOfIsIsoUnit_inv_app, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_hom_hom, FundamentalGroupoid.map_comp, HomotopicalAlgebra.FibrantObject.instIsIsoFunctorWhiskerRightHoCatιCompResolutionNatTransOfIsLocalizationWeakEquivalences, CategoryTheory.ObjectProperty.instCommShiftHomFunctorLiftCompιIso, CategoryTheory.Core.forgetFunctorToCore_map_app, CategoryTheory.reflectsIsomorphisms_comp, hasPointwiseLeftKanExtension_of_preserves, ι_colimitIsoOfIsLeftKanExtension_inv_assoc, shiftIso_add_inv_app, CategoryTheory.Limits.colimitIsoFlipCompColim_inv_app, Monoidal.μNatIso_inv_app, CategoryTheory.MonoidalCategory.DayConvolution.unit_naturality, CategoryTheory.Equivalence.mapGrp_counitIso, Final.colimitCoconeComp_cocone, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceInverseπ_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_hom_app_eq, CategoryTheory.eq_counitIso, CategoryTheory.shiftFunctorComm_zero_hom_app, SSet.OneTruncation₂.ofNerve₂.natIso_hom_app_map, CategoryTheory.Grothendieck.ιCompMap_hom_app_fiber, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app, isoWhiskerRight_twice_assoc, HomologicalComplex.singleMapHomologicalComplex_hom_app_self, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_hom_app, CategoryTheory.regularTopology.equalizerCondition_precomp_of_preservesPullback, mapConeMapCone_hom_hom, CategoryTheory.Limits.coconeEquivalenceOpConeOp_unitIso, AlgebraicGeometry.LocallyRingedSpace.Γ_def, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_hom_app_app_down, IsDense.comp_left_iff_of_isEquivalence, LeftExtension.precomp₂_obj_hom_app, PresheafOfModules.pullback_id_comp, CategoryTheory.CostructuredArrow.toOver_obj_left, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_inv_app_val_app, CategoryTheory.NatTrans.unop_whiskerLeft, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_right_right, CategoryTheory.Limits.Cocone.whisker_pt, CategoryTheory.sheafOver_val, groupHomology.coinfNatTrans_app, CommShift.isoAdd_inv_app, CategoryTheory.Idempotents.toKaroubi_comp_karoubiFunctorCategoryEmbedding, CategoryTheory.Join.pseudofunctorRight_mapComp_inv_toNatTrans_app, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app_assoc, CategoryTheory.MonoidalOpposite.tensorLeftMopIso_hom_app_unmop, instIsIsoAppCounitRanAdjunctionOfHasPointwiseRightKanExtension, CategoryTheory.equivEssImageOfReflective_unitIso, CategoryTheory.Pseudofunctor.map₂_associator_app_assoc, CategoryTheory.Subfunctor.Subpresheaf.range_eq_ofSection', CategoryTheory.LocalizerMorphism.natTransCommShift_hom, Monoidal.commTensorLeft_hom_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_hom, CategoryTheory.Limits.map_id_right_eq_curry_swap_map, AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_inv_app, CategoryTheory.HasShift.Induced.add_inv_app_obj, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_ι_presheafHom, CategoryTheory.Adjunction.Triple.epi_rightToLeft_app_iff_epi_map_adj₁_unit_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_inv_app_hom, CategoryTheory.Adjunction.Localization.ε_app, CategoryTheory.Pseudofunctor.DescentData.pullFunctorCompIso_inv_app_hom, CategoryTheory.Limits.colimitLimitToLimitColimit_isIso, mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app_assoc, CategoryTheory.Monad.free_map_f, CategoryTheory.PullbackShift.adjunction_counit, CategoryTheory.Equivalence.unitIso_hom_app_comp_inverse_map_η_functor_assoc, CategoryTheory.MonoOver.congr_unitIso, final_iff_comp_equivalence, AlgebraicGeometry.coprodSpec_apply, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_app_hom_assoc, CategoryTheory.Adjunction.unit_app_tensor_comp_map_δ_assoc, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_left_app, CategoryTheory.iterated_mateEquiv_conjugateEquiv, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.isMonHom_counitIsoAux, mapCommGrpCompIso_inv_app_hom_hom_hom, CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse, CategoryTheory.Sum.functorEquivFunctorCompFstIso_inv_app_app, CategoryTheory.OverPresheafAux.unitAux_hom, CategoryTheory.Limits.Cones.equivalenceOfReindexing_inverse, Profinite.Extend.cocone_pt, CategoryTheory.Quotient.natIsoLift_inv, CategoryTheory.cocones_map_app_app, LeftExtension.precomp₂_map_right, CategoryTheory.Limits.Cones.whiskeringEquivalence_functor, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_unitIso, CategoryTheory.IndParallelPairPresentation.hf, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.F_obj, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_app_snd_app, AlgebraicGeometry.Scheme.Hom.toNormalization_inl_normalizationCoprodIso_hom_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_whiskerRight, CategoryTheory.Discrete.sumEquiv_unitIso_inv_app, CategoryTheory.MorphismProperty.IsCompatibleWithShift.shiftFunctor_comp_inverts, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_π_app, SSet.Truncated.HomotopyCategory.descOfTruncation_comp, CategoryTheory.MonoidalSingleObj.endMonoidalStarFunctorEquivalence_counitIso, sheafPushforwardContinuousComp'_inv_app_val_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.forgetToPresheafedSpace_preservesPullback_of_right, AlgebraicGeometry.IsOpenImmersion.hasLimit_cospan_forget_of_right', AlgebraicGeometry.instIsIsoSchemeCoprodComparisonOppositeCommRingCatSpec, CategoryTheory.CoverPreserving.comp, instIsRightDerivedFunctorLiftInvFac, CategoryTheory.Limits.DiagramOfCocones.mkOfHasColimits_coconePoints, CategoryTheory.Abelian.LeftResolution.epi_π_app, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app, leftDerivedNatTrans_fac_assoc, CategoryTheory.NonemptyParallelPairPresentationAux.hf, AlgebraicGeometry.ΓSpec.isIso_adjunction_counit, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_hom_app_app_val, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_map, CategoryTheory.Adjunction.isMonoidal_comp, CategoryTheory.MonoidalCategory.tensorRightTensor_hom_app, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₃, CategoryTheory.iterated_mateEquiv_conjugateEquiv_symm, CategoryTheory.MonoidalCategory.tensorLeftTensor_inv_app, CategoryTheory.NatTrans.IsMonoidal.instHomFunctorAssociator, CategoryTheory.Limits.spanCompIso_inv_app_zero, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_app_assoc, CategoryTheory.WithInitial.opEquiv_unitIso_inv_app, CategoryTheory.Monad.ForgetCreatesLimits.liftedConeIsLimit_lift_f, CategoryTheory.Limits.Cocone.toOver_ι_app, CategoryTheory.Equivalence.counitIso_inv_app_comp_functor_map_η_inverse, CategoryTheory.Limits.colimit.ι_pre_assoc, TopCat.Presheaf.germ_stalkPullbackHom, CategoryTheory.Under.postComp_inv_app_right, Rep.coindResAdjunction_counit_app, CategoryTheory.Adjunction.map_ε_comp_counit_app_unit_assoc, AlgebraicGeometry.Scheme.restrictFunctorΓ_inv_app, partialFunEquivPointed_counitIso_inv_app_toFun, isoSum_inv_app_inr, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_counit_app_app, AlgebraicGeometry.Scheme.Hom.inr_toNormalization_normalizationCoprodIso_inv, mapCocone_ι_app, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₂, CategoryTheory.Comma.map_obj_hom, pointedToBipointedFst_comp_swap, commBialgCatEquivComonCommAlgCat_unitIso_inv_app, CategoryTheory.lan_preservesFiniteLimits_of_flat, TopCat.Presheaf.generateEquivalenceOpensLe_unitIso, partialFunEquivPointed_unitIso_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_map_snd_app, CategoryTheory.Limits.parallelPairOpIso_inv_app_zero, CategoryTheory.Limits.HasColimit.isoOfEquivalence_inv_π, shiftIso_add', Rep.resCoindAdjunction_counit_app_hom_hom, CategoryTheory.Comonad.ComonadicityInternal.unitFork_π_app, CategoryTheory.ProdPreservesConnectedLimits.γ₂_app, CategoryTheory.Monoidal.transportStruct_associator, CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse_map_right, CategoryTheory.Adjunction.instIsIsoAppUnitObjOfFaithfulOfFull, CategoryTheory.Idempotents.functorExtension₁CompWhiskeringLeftToKaroubiIso_inv_app_app_f, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_left_hom, CategoryTheory.Limits.ι_colimitCompWhiskeringLeftIsoCompColimit_hom_assoc, CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux_fac_assoc, instIsLeftAdjointDiscreteTensorLeftCompIncl, CategoryTheory.sum.inlCompInrCompInverseAssociator_hom_app_down_down, isLimitConeOfIsRightKanExtension_lift, CategoryTheory.Adjunction.mapMon_unit, Profinite.Extend.functorOp_map, CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_left_app, CategoryTheory.StructuredArrow.ofCommaSndEquivalence_functor, CategoryTheory.comp_comparison_hasColimit, CategoryTheory.Under.forgetMapInitial_inv_app, CategoryTheory.instMonoFunctorWhiskerRightOfPreservesMonomorphisms, rightDerived_fac_app, CategoryTheory.Under.post_comp, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_app_assoc, CategoryTheory.NatIso.op_rightUnitor, CategoryTheory.NatTrans.CommShiftCore.shift_app_comm, map_shiftFunctorComm_hom_app, CategoryTheory.Join.mapPairEquiv_unitIso, CategoryTheory.Comma.map_final, AlgebraicGeometry.instIsAffineSigmaObjScheme, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_hom_app_snd_app, CategoryTheory.Adjunction.derivedε_fac_app_assoc, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₁, CategoryTheory.Join.mapPairEquiv_counitIso, CategoryTheory.PreGaloisCategory.endEquivSectionsFibers_π, sumIsoExt_hom_app_inl, isoWhiskerRight_trans, CategoryTheory.CostructuredArrow.prodEquivalence_counitIso, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_ι_inv, CategoryTheory.Equivalence.rightOp_counitIso_inv_app, CategoryTheory.WithInitial.liftToInitialUnique_hom_app, CategoryTheory.RightExactFunctor.whiskeringRight_obj_obj_obj, CategoryTheory.MonadHom.app_μ, TopologicalSpace.OpenNhds.inclusionMapIso_hom, CategoryTheory.shiftFunctorAdd'_zero_add, curryObjCompIso_hom_app_app, CategoryTheory.GrothendieckTopology.overMapPullback_comp_id, CategoryTheory.Under.equivalenceOfIsInitial_counitIso, uncurryObjFlip_hom_app, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_fst, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id_app, CategoryTheory.MorphismProperty.LeftFraction.Localization.StrictUniversalPropertyFixedTarget.fac, CategoryTheory.OplaxFunctor.map₂_associator_app, CategoryTheory.Comonad.comparison_obj_a, instHasColimitGrothendieckFunctorCompGrothendieckProj, AlgebraicTopology.DoldKan.N₂Γ₂ToKaroubiIso_inv_app, CategoryTheory.MonoidalClosed.ofEquiv_uncurry_def, CategoryTheory.Sum.functorEquiv_functor_map, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_inv_app, CategoryTheory.shiftFunctorComm_eq_refl, CategoryTheory.CostructuredArrow.isEquivalence_pre, Initial.limitIso_hom, CategoryTheory.CatCommSq.hInv_iso_inv_app, CategoryTheory.whiskering_linearCoyoneda, isDense_iff_nonempty_isPointwiseLeftKanExtension, CategoryTheory.Equivalence.leftOp_unitIso_inv_app, PresheafOfModules.pullback_comp_id, CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_cancel_hom_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_counitIso, descOfIsLeftKanExtension_fac_assoc, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_right_left_as, CategoryTheory.Limits.colimit.pre_post, IsDenseAt.iff_of_final, mapTriangleRotateIso_inv_app_hom₂, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_obj_iso_inv, CategoryTheory.Monad.left_comparison, CategoryTheory.ObjectProperty.inverseImage_trW_isInverted, AlgebraicTopology.DoldKan.identity_N₂, CategoryTheory.Limits.PreservesLimit.preserves, shiftIso_hom_app_comp, CategoryTheory.CostructuredArrow.preEquivalence.functor_obj_right_as, Monoidal.commTensorRight_inv_app, StalkSkyscraperPresheafAdjunctionAuxs.counit_app, SSet.opFunctorCompOpFunctorIso_inv_app_app, CategoryTheory.Adjunction.instIsIsoFunctorCounitOfIsEquivalence_1, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₂, CategoryTheory.Under.postCongr_inv_app_right, instIsIsoAppRanCounit, isColimitCoconeOfIsLeftKanExtension_desc, CategoryTheory.Join.inclRightCompOpEquivInverse_inv_app_op, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_inv_app_hom, CategoryTheory.preservesColimit_comp_of_createsColimit, CategoryTheory.CostructuredArrow.pre_obj_hom, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerRightIso_hom_app, CategoryTheory.Pseudofunctor.CoGrothendieck.map_comp_eq, CategoryTheory.Limits.Cocone.whisker_ι, CategoryTheory.cosimplicialSimplicialEquiv_counitIso_hom_app_app, CategoryTheory.GrothendieckTopology.Point.comap_fiber, CategoryTheory.Adjunction.instIsIsoAppCounitOfFullOfFaithful, CategoryTheory.Adjunction.adjunctionOfEquivRight_counit_app, CategoryTheory.StructuredArrow.toUnder_obj_left, CategoryTheory.sum.inrCompInrCompInverseAssociator_hom_app_down, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₃, CategoryTheory.Comonad.ComonadicityInternal.unitFork_pt, mapTriangleCompIso_inv_app_hom₂, pointwiseRightKanExtension_lift_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_leftUnitor, RightExtension.postcompose₂_obj_left_map, pi'CompEval_hom_app, LaxMonoidal.ofBifunctor.leftMapₗ_app, AlgebraicGeometry.sigmaOpenCover_X, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerRight, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app, FullyFaithful.homNatIsoMaxRight_hom_app_down, leftOpRightOpEquiv_counitIso_inv_app_app, CategoryTheory.Adjunction.compCoyonedaIso_inv_app_app, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_unitIso_hom_app_f, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app, CategoryTheory.Grothendieck.map_comp_eq, comp_mapGrp_mul, CategoryTheory.Equivalence.core_inverse_map_iso_hom, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app_assoc, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_map_left, CategoryTheory.Over.forgetMapTerminal_hom_app, DerivedCategory.instCommShiftHomologicalComplexIntUpHomFunctorQuotientCompQhIso, CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_inv_app_app, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app, fullyFaithfulCancelRight_inv_app, CategoryTheory.ParametrizedAdjunction.whiskerLeft_map_counit, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_map_snd, CategoryTheory.FreeGroupoid.map_comp_lift, CategoryTheory.NatTrans.CommShift.leftUnitor, CategoryTheory.GrothendieckTopology.ι_plusCompIso_hom_assoc, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_inv_app_hom_coe, CategoryTheory.Grothendieck.pre_comp_map_assoc, mapTriangle_obj, leftDerived_fac_app, LightCondensed.isoFinYoneda_inv_app, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_app_assoc, CategoryTheory.Over.equivalenceOfIsTerminal_counitIso, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_hom_app, CategoryTheory.Presheaf.isSheaf_iff_isLimit_coverage, CategoryTheory.Comonad.ForgetCreatesLimits'.liftedCone_π_app_f, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_one, AlgebraicGeometry.ι_right_coprodIsoSigma_inv, CondensedMod.isDiscrete_tfae, RightExtension.postcompose₂_obj_right, CategoryTheory.CatCommSq.hId_iso_hom_app, smoothSheafCommRing.ι_evalHom_apply, LeftExtension.postcomp₁_map_right_app, mapCoconePrecomposeEquivalenceFunctor_inv_hom, TopCat.uliftFunctorCompForgetIso_hom_app, AlgebraicGeometry.ι_sigmaSpec, CategoryTheory.NatIso.unop_rightUnitor, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_one, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp_app, CategoryTheory.InjectiveResolution.isoRightDerivedToHomotopyCategoryObj_inv_naturality, leftKanExtensionUnit_leftKanExtension_map_leftKanExtensionObjIsoColimit_hom, AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_hom_app, CategoryTheory.SingleFunctors.shiftIso_add', CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_hom_app, commShiftOp_iso_eq, mapCoconePrecompose_inv_hom, CategoryTheory.simplicialCosimplicialEquiv_counitIso_inv_app_app, CategoryTheory.Limits.PushoutCocone.unop_π_app, CategoryTheory.EnrichedFunctor.forgetComp_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_inv_app, CategoryTheory.Equivalence.precoherent_isSheaf_iff_of_essentiallySmall, CategoryTheory.comp_evaluation, CategoryTheory.MonoidalCategory.tensorLeftTensor_hom_app, CommGrpCat.hasLimit_iff_small_sections, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app, AlgebraicGeometry.coprodSpec_inr, CategoryTheory.NatIso.pi'_inv, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_hom_app_hom_apply, CategoryTheory.Limits.IndObjectPresentation.extend_ι_app_app, CategoryTheory.Join.mapWhiskerRight_leftUnitor_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv, CategoryTheory.Presieve.isSheaf_comp_uliftFunctor, CategoryTheory.Adjunction.rightAdjointLaxMonoidal_μ, OneHypercoverDenseData.isSheaf_iff, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_inv_app, inlCompSum'_inv_app, CondensedSet.instEpiTopCatAppCounitTopCatAdjunction, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.unitIso_inv_app_f_f, AlgebraicGeometry.instIsIsoSchemeSigmaSpecOfFinite, CochainComplex.mappingCone.homologySequenceδ_triangleh, CategoryTheory.Limits.opCompYonedaSectionsEquiv_symm_apply_coe, CategoryTheory.Adjunction.IsMonoidal.leftAdjoint_μ, instIsContinuousCompId_1, CategoryTheory.ObjectProperty.topEquivalence_counitIso, CategoryTheory.Adjunction.comp_homEquiv, CategoryTheory.NatTrans.instCommShiftPullbackShiftHomFunctorNatIsoComp, CategoryTheory.Grothendieck.ιNatTrans_app_fiber, CategoryTheory.MonoidalCategory.externalProductCompDiagIso_hom_app_app, CategoryTheory.Limits.yonedaCompLimIsoCocones_inv_app, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_app_assoc, SSet.Truncated.sk_coreflective, CategoryTheory.Bimon.toMon_forget, CategoryTheory.FreeGroupoid.lift_comp, CategoryTheory.Comon.Comon_EquivMon_OpOp_counitIso, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_left_right, shiftIso_zero_inv_app, CategoryTheory.Iso.isoInverseComp_inv_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_hom_app_fst_app, CategoryTheory.Grothendieck.grothendieckTypeToCat_inverse_map_base, Action.FunctorCategoryEquivalence.counitIso_inv_app_app, Profinite.Extend.cone_π_app, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.g_app, commShift₂_comm, CategoryTheory.comp_comparison_forget_hasLimit, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_obj, OplaxMonoidal.ofBifunctor.bottomMapₗ_app, IsCoverDense.restrictHomEquivHom_naturality_left_symm_assoc, Fiber.fiberInclusionCompIsoConst_inv_app, AlgebraicTopology.DoldKan.instIsIsoFunctorSimplicialObjectKaroubiNatTrans, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_map_app_fst, CategoryTheory.GrothendieckTopology.whiskerRight_toSheafify_sheafifyCompIso_hom_assoc, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_left, pentagon, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.hasLimit_cospan_forget_of_left', CategoryTheory.Equivalence.prod_counitIso, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_inv_app_coe, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_left_hom, mapCoconeWhisker_hom_hom, CategoryTheory.sheafificationNatIso_inv_app_val, CategoryTheory.Limits.colimitCoyonedaHomIsoLimit'_π_apply, pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_inv_app_hom_apply, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₃, MonObj.mopEquivCompForgetIso_hom_app_unmop, CategoryTheory.Bimon.equivMonComonUnitIsoAppXAux_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_inv_app_app_hom_hom, instIsIsoAppUnitLanAdjunctionOfHasPointwiseLeftKanExtension, CommRingCat.moduleCatRestrictScalarsPseudofunctor_mapComp, CategoryTheory.Join.isoMkFunctor_hom_app, AlgebraicTopology.DoldKan.Compatibility.equivalence_functor, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy₂_homEquiv, CategoryTheory.Equivalence.leftOp_counitIso_inv_app, CategoryTheory.NatTrans.unop_whiskerLeft_assoc, CategoryTheory.Limits.coyonedaCompLimIsoCones_inv_app, PresheafOfModules.sections_property, CategoryTheory.CostructuredArrow.toOver_obj_right, CategoryTheory.MonoidalClosed.coev_app_comp_pre_app, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_snd_assoc, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_X₁, CategoryTheory.Monoidal.instIsMonoidalUnitTransportedEquivalenceTransported, CategoryTheory.MorphismProperty.Over.pullbackComp_hom_app_left, CategoryTheory.Localization.SmallHom.equiv_equiv_symm, CommShift.isoZero_hom_app, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_inv_app_op_zero, CategoryTheory.Presheaf.instIsLeftKanExtensionFunctorOppositeTypeLanOpHomCompULiftYonedaIsoULiftYonedaCompLan, AlgebraicTopology.AlternatingFaceMapComplex.ε_app_f_succ, CategoryTheory.LocalizerMorphism.commShift_iso_hom_app, CategoryTheory.Comma.mapRightIso_counitIso_inv_app_left, AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_hom_app, CategoryTheory.Abelian.LeftResolution.karoubi.π_app_toKaroubi_obj, CategoryTheory.Limits.comp_reflectsFiniteProducts, CondensedMod.LocallyConstant.instFullModuleCatSheafCompHausCoherentTopologyConstantSheaf, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.natTrans_app_uliftYoneda_obj, CategoryTheory.TwoSquare.EquivalenceJ.inverse_map, HomotopicalAlgebra.FibrantObject.instIsLocalizationCompHoCatToHoCatWeakEquivalences, CategoryTheory.Bicategory.associatorNatIsoLeft_inv_app, CategoryTheory.Equivalence.cancel_unit_right, CategoryTheory.SimplicialObject.Truncated.whiskering_map_app_app, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_assoc, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_right, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app, TwoP_swap_comp_forget_to_Bipointed, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₂, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_inv_assoc, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct, RightExtension.coneAt_pt, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_inv_app_snd_app, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.isPullback, CategoryTheory.Limits.Cones.functorialityEquivalence_functor, CategoryTheory.Monad.beckCoequalizer_desc, Rep.coinvariantsAdjunction_counit_app, CategoryTheory.coprodMonad_μ_app, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app_assoc, CategoryTheory.ChosenPullbacksAlong.unit_pullbackComp_hom_assoc, SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_inv_app, LaxMonoidal.ofBifunctor.leftMapᵣ_app, CategoryTheory.Comma.mapRightIso_counitIso_inv_app_right, TopologicalSpace.Opens.instIsContinuousCompGrothendieckTopology, CategoryTheory.instIsIsoFunctorOppositeValAppSheafCounitSheafificationAdjunction, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_inv_app_app, instIsLeftKanExtensionSimplexCategoryTopCatSSetToTopInvFunctorToTopSimplex, CategoryTheory.OplaxFunctor.mapComp_assoc_left_app_assoc, CategoryTheory.Limits.Cocone.toCostructuredArrow_comp_proj, CategoryTheory.IsFiltered.iff_nonempty_limit, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_unitIso, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_hom_app, CategoryTheory.FreeGroupoid.functorEquiv_apply, CategoryTheory.sum.inlCompInrCompInverseAssociator_inv_app_down_down, CategoryTheory.Comma.opEquiv_counitIso, CategoryTheory.sheafificationNatIso_hom_app_val, HomologicalComplexUpToQuasiIso.instIsLocalizationHomologicalComplexCompHomotopyCategoryQuotientQhQuasiIso, PresheafOfModules.Derivation.d_map, CategoryTheory.StructuredArrow.map₂_map_right, CategoryTheory.TransportEnrichment.forgetEnrichmentEquiv_counitIso, TopologicalSpace.OpenNhds.inclusionMapIso_inv, commShiftIso_comp_hom_app, CategoryTheory.Monoidal.whiskerRight_fst, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₂_app, CategoryTheory.Monad.monadMonEquiv_counitIso_hom_app_hom, Final.colimitCoconeOfComp_isColimit, CategoryTheory.MonoOver.mapIso_unitIso, CategoryTheory.constantCommuteCompose_hom_app_val, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.unit_app_ev_app_app_assoc, CategoryTheory.WithTerminal.mapComp_hom_app, commShiftIso_map₂CochainComplex_flip_hom_app, CategoryTheory.Equivalence.congrFullSubcategory_counitIso, mapTriangleCommShiftIso_inv_app_hom₁, CategoryTheory.Equivalence.cancel_counit_right, skyscraperPresheafCocone_pt, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_inv_colimit_map_assoc, AlgebraicGeometry.Scheme.Hom.toNormalization_inr_normalizationCoprodIso_hom, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceFunctor_map_fiber, CategoryTheory.Limits.comp_preservesLimitsOfShape, CondensedSet.instIsIsoFunctorCompactlyGeneratedCounitCompactlyGeneratedAdjunction, pointwiseLeftKanExtensionCompIsoOfPreserves_fac_app_assoc, mapConePostcompose_inv_hom, reflective', Monoidal.tensorObjComp_hom_app, CategoryTheory.Join.mapWhiskerLeft_whiskerRight, isEquivalence_trans, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_right_hom, CategoryTheory.Grothendieck.grothendieckTypeToCatFunctor_obj_snd, commGroupAddCommGroupEquivalence_counitIso, IsCoverDense.isoOver_hom_app, AlgebraicGeometry.Scheme.SpecΓIdentity_hom_app, currying₃_unitIso_hom_app_app_app_app, CategoryTheory.Comma.coneOfPreserves_π_app_right, FullyFaithful.compUliftCoyonedaCompWhiskeringLeft_hom_app_app_down, CategoryTheory.Limits.limitIsoLimitCurryCompLim_hom_π_π_assoc, CategoryTheory.Adjunction.instIsIsoFunctorUnitOfIsEquivalence, CategoryTheory.Limits.prodComparisonNatIso_hom, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_unit_app, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_π_app, CategoryTheory.GradedObject.comapEquiv_counitIso, CategoryTheory.toOverPullbackIsoToOver_inv_app_left, ι_leftKanExtensionObjIsoColimit_inv, opComp_inv_app, CategoryTheory.Equivalence.unitInv_naturality, CategoryTheory.Comma.limitAuxiliaryCone_pt, smoothSheaf.ι_evalHom_apply, partialFunEquivPointed_unitIso_inv_app, SemilatInfCat_dual_comp_forget_to_partOrd, LeftExtension.precomp_map_right, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₃, LightCondMod.isDiscrete_tfae, CategoryTheory.Presheaf.isLeftKanExtension_along_yoneda_iff, SSet.opFunctorCompOpFunctorIso_hom_app_app, CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_app_app, CategoryTheory.Limits.coprodComparisonNatTrans_app, CategoryTheory.Equivalence.functor_unit_comp, CategoryTheory.Bimon.instIsMonHomComonHomEquivMonComonCounitIsoAppX, sectionsPrecomp_coe, LeftExtension.precomp₂_obj_left, CategoryTheory.Comonad.right_counit_assoc, CategoryTheory.Limits.colimitCurrySwapCompColimIsoColimitCurryCompColim_ι_ι_hom, CategoryTheory.FreeGroupoid.mapComp_hom_app, CategoryTheory.Comonad.ForgetCreatesLimits'.γ_app, CategoryTheory.Bimon.instIsComonHomHomEquivMonComonCounitIsoAppXAux, RightExtension.coneAt_π_app, SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_hom_app, ModuleCat.restrictScalarsComp'_inv_app, CategoryTheory.Equivalence.inv_fun_map, AlgebraicGeometry.sigmaMk_mk, Final.coconesEquiv_unitIso, CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_right, CategoryTheory.Pseudofunctor.CoGrothendieck.map_map_fiber, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_right, groupHomology.coresNatTrans_app, prod'CompSnd_inv_app, CategoryTheory.Idempotents.KaroubiKaroubi.counitIso_inv_app_f_f, CategoryTheory.Comma.map_map_right, CategoryTheory.Pi.equivalenceOfEquiv_unitIso, CategoryTheory.MonoidalCategory.DayConvolution.whiskerRight_comp_unit_app_assoc, CategoryTheory.CartesianClosed.curry_id_eq_coev, CochainComplex.shiftShortComplexFunctorIso_add'_hom_app, CategoryTheory.SimplicialObject.instIsRightKanExtensionOppositeTruncatedSimplexCategoryObjCoskAppTruncatedCounitCoskAdjTruncation, CategoryTheory.WithInitial.opEquiv_counitIso_hom_app, CategoryTheory.Grothendieck.functor_comp_forget, CategoryTheory.Adjunction.id_counit, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_hom_app, CategoryTheory.prodComonad_δ_app, CategoryTheory.Comma.instEssSurjCompPostOfFull, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_hom_app_hom, CategoryTheory.Quotient.comp_natTransLift_assoc, CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso_hom_app, OplaxMonoidal.ofBifunctor.leftMapᵣ_app, SheafOfModules.instIsRightAdjointPushforwardCompSheafRingCatMapSheafPushforwardContinuous, CategoryTheory.Quotient.lift.isLift_hom, CategoryTheory.Limits.Cocone.toCostructuredArrow_comp_toOver_comp_forget, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι, CategoryTheory.Bimon.equivMonComonUnitIsoApp_hom_hom_hom, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_hom_app_hom_hom_app, CategoryTheory.Limits.colimitIsoSwapCompColim_hom_app, AlgebraicGeometry.Flat.instDescScheme, CategoryTheory.Localization.HasProductsOfShapeAux.adj_counit_app, CategoryTheory.Monad.algebraEquivOfIsoMonads_unitIso, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_hom_app_val_app, instIsDenseCompOfIsEquivalence_1, mapTriangleCompIso_hom_app_hom₂, CategoryTheory.Adjunction.compYonedaIso_hom_app_app, CategoryTheory.Pi.equivalenceOfEquiv_counitIso, CategoryTheory.Sieve.pullback_functorPushforward_equivalence_eq, currying_counitIso_hom_app_app, CategoryTheory.CostructuredArrow.post_obj, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.associator_hom_unit_unit, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.w_app, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_fiber, RightExtension.postcomp₁_map_right, CondensedMod.LocallyConstant.instFaithfulModuleCatCondensedDiscrete, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompCoyoneda, prod'CompSnd_hom_app, CategoryTheory.Iso.isoInverseComp_hom_app, mapActionComp_hom, LeibnizAdjunction.adj_unit_app_left, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app, pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.IsSifted.factorization_prodComparison_colim, CategoryTheory.Limits.Cone.whisker_π, CategoryTheory.Equivalence.core_unitIso_hom_app_iso_inv, ranCompLimIso_inv_app, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_hom_assoc, CategoryTheory.Limits.Cocones.whiskeringEquivalence_unitIso, CategoryTheory.LaxFunctor.mapComp_naturality_left_app_assoc, CategoryTheory.sheafCompose_map_val, hasPointwiseRightKanExtension_of_preserves, ShiftSequence.induced.isoZero_hom_app_obj, CategoryTheory.Sum.functorEquiv_unit_app_app_inr, CategoryTheory.Limits.colimitCurrySwapCompColimIsoColimitCurryCompColim_ι_ι_inv, CategoryTheory.Limits.hasColimitCompEvaluation, Fiber.fiberInclusion_comp_eq_const, whiskeringLeft₃_map_app_app_app_app_app_app, SimplexCategory.revEquivalence_unitIso, CategoryTheory.Adjunction.Triple.rightToLeft_eq_units, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_inv_app_left, CategoryTheory.MonObj.ofRepresentableBy_one, CategoryTheory.HasShift.Induced.zero_inv_app_obj, CategoryTheory.TransfiniteCompositionOfShape.iic_isoBot, CategoryTheory.WithTerminal.mkCommaMorphism_left_app, CategoryTheory.shift_shift_neg', SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_quotMk, CategoryTheory.NatTrans.CommShift.shift_comm, CategoryTheory.evaluationAdjunctionLeft_unit_app_app, CategoryTheory.Limits.hasColimit_equivalence_comp, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_inv_app, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_left_right, CategoryTheory.Sum.functorEquiv_unitIso_inv_app_app_inl, CategoryTheory.LocalizerMorphism.commShift_iso_inv_app, CategoryTheory.Sheaf.isPullback_square_op_map_yoneda_presheafToSheaf_yoneda_iff, CategoryTheory.MonoOver.mapIso_counitIso, bddOrd_dual_comp_forget_to_bipointed, CategoryTheory.HasShift.Induced.add_hom_app_obj, rightKanExtensionCompIsoOfPreserves_hom_fac_app, CategoryTheory.ExponentiableMorphism.comp_pushforward, CategoryTheory.Presheaf.isIso_of_isLeftKanExtension, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₁_app, whiskeringLeft_obj_comp, CategoryTheory.CatCommSq.hComp_iso_hom_app, CategoryTheory.RepresentablyFlat.comp, mapTriangleRotateIso_inv_app_hom₁, CategoryTheory.comp_comparison_forget_hasColimit, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompPointIso_hom_app, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app, CategoryTheory.Discrete.compNatIsoDiscrete_hom_app, leftKanExtensionCompIsoOfPreserves_hom_fac_app, CategoryTheory.CostructuredArrow.mapIso_unitIso_hom_app_left, CategoryTheory.TwoSquare.equivNatTrans_apply, CategoryTheory.CatCommSq.iso_inv_naturality, Rep.resCoindAdjunction_unit_app_hom_hom, CategoryTheory.ReflQuiv.adj_unit_app, mapProjectiveResolution_π, CategoryTheory.Limits.Cocones.whiskeringEquivalence_inverse, CategoryTheory.Adjunction.localization_unit_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₂, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd_assoc, CategoryTheory.Limits.colimitYonedaHomIsoLimit'_π_apply, CategoryTheory.Prod.symmetry_hom_app, CategoryTheory.WithInitial.liftFromUnderComp_inv_app, CategoryTheory.MorphismProperty.Over.pullbackMapHomPullback_app, CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_hom_app_app_val, CategoryTheory.preservesColimitNatIso_inv_app, CategoryTheory.conjugateEquiv_symm_apply_app, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_right, CategoryTheory.Join.mapWhiskerLeft_whiskerLeft, CategoryTheory.Limits.Cone.toStructuredArrowCompProj_inv_app, CategoryTheory.Limits.parallelPairOpIso_inv_app_one, CategoryTheory.StructuredArrow.instEssSurjCompPre, AlgebraicGeometry.Scheme.Modules.pseudofunctor_right_unitality_assoc, CategoryTheory.Join.inrCompFromSum_hom_app, CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatIso_inv, PreservesRightKanExtension.preserves, CategoryTheory.CostructuredArrow.toOver_map_right, CategoryTheory.OppositeShift.adjunction_unit, CategoryTheory.Limits.ColimitPresentation.map_diag, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_hom_whiskerRight_π_assoc, ModuleCat.restrictScalarsComp'_hom_app, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_tensorDec, LightProfinite.Extend.cocone_ι_app, CategoryTheory.Comma.toPUnitIdEquiv_counitIso_hom_app, sheafAdjunctionCocontinuous_counit_app_val, CategoryTheory.coev_expComparison, CategoryTheory.MonoidalCategory.prodCompExternalProduct_inv_app, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.functorToInterchangeIso_inv_app_app, CoconeTypes.precomp_pt, LeftExtension.precomp_obj_hom_app, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.biprodAddEquiv_symm_biprodIsoProd_hom_toBiprod_apply, mapMatComp_hom_app, CategoryTheory.Limits.colimit.ι_post, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π_assoc, CategoryTheory.Adjunction.toCat_comp_toCat, CategoryTheory.Sigma.mapComp_hom_app, CategoryTheory.conjugateEquiv_apply_app, LeibnizAdjunction.adj_counit_app_left, CategoryTheory.Join.mkFunctor_edgeTransform, CategoryTheory.Monad.Algebra.assoc_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_inv_app_app_fst, isoWhiskerLeft_trans_isoWhiskerRight, CategoryTheory.Adjunction.instIsIsoAppCounitObjOfFaithfulOfFull, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom, CategoryTheory.Limits.compYonedaSectionsEquiv_apply_app, CategoryTheory.exp.coev_ev, isRightDerivedFunctor_iff_of_inverts, CategoryTheory.Endofunctor.Algebra.functorOfNatTransComp_hom_app_f, CategoryTheory.Comma.mapSnd_inv_app, Condensed.lanPresheafExt_inv, HomologicalComplex.forgetEval_hom_app, rightKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.Pretriangulated.Triangle.functorMk_map_hom₃, compConstIso_hom_app_app, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_app_assoc, CategoryTheory.Over.iteratedSliceForward_forget, CategoryTheory.NatIso.op_isoWhiskerLeft, FinPartOrd.dualEquiv_unitIso, PresheafOfModules.pushforward₀_obj_obj_carrier, commBialgCatEquivComonCommAlgCat_unitIso_hom_app, costructuredArrowMapCocone_pt, coreComp_hom_app_iso_hom, CategoryTheory.CatCommSq.vId_iso_hom_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_inv_app_snd_app, imageSieve_eq_imageSieve, CategoryTheory.WithTerminal.opEquiv_counitIso_inv_app, CategoryTheory.frobeniusMorphism_mate, CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.liftHom_fac_assoc, CategoryTheory.Adjunction.ε_comp_map_ε_assoc, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_fst, CategoryTheory.toOverIsoToOverUnit_inv_app_left, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_inv_app_hom_left, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorEquivalence_functor, flipping_counitIso_inv_app_app_app, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.presheafHom_naturality, CategoryTheory.Equivalence.congrLeft_counitIso_inv_app, CategoryTheory.NatTrans.hcomp_app, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_snd, CategoryTheory.Localization.Lifting.compLeft_iso, CategoryTheory.Over.postAdjunctionRight_counit_app, CategoryTheory.ofTypeMonad_μ_app, CategoryTheory.Adjunction.conjugateEquiv_leftAdjointCompIso_inv, isoWhiskerLeft_twice, Initial.limitIso_inv, AlgebraicGeometry.Scheme.Modules.instIsIsoFunctorCounitRestrictAdjunction, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_inv_π_assoc, CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences, CategoryTheory.Monad.ForgetCreatesLimits.conePoint_a, curryObjProdComp_hom_app_app, CategoryTheory.RightExactFunctor.whiskeringLeft_map_app, AlgebraicGeometry.Scheme.Modules.pushforwardComp_inv_app_app, CategoryTheory.oppositeShiftFunctorAdd_inv_app, CategoryTheory.Presheaf.isLocallySurjective_whisker, associator_hom_app, shiftIso_zero_hom_app, CategoryTheory.MonoidalClosedFunctor.comparison_iso, assoc, rightOpComp_hom_app, rightAdjointObjIsDefined_iff, comp_flip_uncurry_eq, CategoryTheory.Sieve.functorPullback_comp, isoShift_inv_naturality_assoc, ModuleCat.HasColimit.colimitCocone_ι_app, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality_app, CategoryTheory.CostructuredArrow.toOver_obj_hom, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_comp_mapHomotopyCategory_fst, CategoryTheory.Limits.HasColimit.isoOfEquivalence_hom_π, CategoryTheory.Pretriangulated.Triangle.functorMk_map_hom₁, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_left_as, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_app, ι_colimitIsoColimitGrothendieck_inv_assoc, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_map_fiber, CategoryTheory.Adjunction.Triple.adj₁_counit_app_rightToLeft_app, CategoryTheory.MorphismProperty.map_map, mapContActionComp_inv, AlgebraicTopology.DoldKan.instIsIsoFunctorKaroubiSimplicialObjectNatTrans, IsCoverDense.Types.appHom_valid_glue, CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_mapComp, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_obj_obj, CategoryTheory.Discrete.monoidalFunctorComp_isMonoidal, rightDerived_fac_assoc, CategoryTheory.StructuredArrow.instEssSurjObjCompPostOfFull, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_obj_fiber, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap, CategoryTheory.Comonad.ForgetCreatesColimits'.newCocone_ι_app, LaxMonoidal.ofBifunctor.bottomMapₗ_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app, CategoryTheory.LocalizerMorphism.Derives.isIso, mapMonCompIso_hom_app_hom, initial_comp, CategoryTheory.Cat.freeMap_comp, CategoryTheory.Monoidal.instIsMonoidalTransportedCounitEquivalenceTransported, CategoryTheory.Limits.Cocone.fromCostructuredArrow_ι_app, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_fiber, CategoryTheory.Comma.preRight_obj_left, LeftExtension.coconeAtWhiskerRightIso_inv_hom, CategoryTheory.Limits.Cone.fromStructuredArrow_π_app, CategoryTheory.Equivalence.symm_unitIso, PresheafOfModules.Derivation.postcomp_d_apply, CategoryTheory.WithTerminal.commaFromOver_map_left, CategoryTheory.Adjunction.mapCommMon_unit, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality_assoc, CategoryTheory.Comonad.coassoc, RightExtension.precomp_map_left, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.isPushout, CategoryTheory.LaxFunctor.mapComp_assoc_right_app, CategoryTheory.Limits.Cocone.toCostructuredArrowCompProj_hom_app, PresheafOfModules.Derivation.d_one, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.unit_app_ev_app_app, functorialityCompPostcompose_hom_app_hom, CategoryTheory.Mon.limitConeIsLimit_lift_hom, CategoryTheory.Equivalence.mapHomologicalComplex_unitIso, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d, PresheafOfModules.sectionsMap_coe, swap_comp_bipointedToPointedFst, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app_assoc, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_mul_app, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_right_app, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_zero, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₁, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_unit_app, FullyFaithful.homNatIso_inv_app_down, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_symm_apply, ModuleCat.ExtendRestrictScalarsAdj.Counit.map_hom_apply, CategoryTheory.Cat.opEquivalence_counitIso, isIso_whiskerRight, pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_app, ranCounit_app_whiskerLeft_ranAdjunction_unit_app_assoc, CategoryTheory.IsCofiltered.iff_nonempty_limit, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_right_as, CategoryTheory.Comonad.ForgetCreatesLimits'.newCone_pt, CategoryTheory.StructuredArrow.preEquivalenceFunctor_obj_left_as, bddLat_dual_comp_forget_to_lat, CategoryTheory.Limits.fiberwiseColimitLimitIso_hom_app, CategoryTheory.RightExactFunctor.whiskeringRight_map_app, Final.extendCocone_obj_ι_app, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom, representableByUliftFunctorEquiv_symm_apply_homEquiv, ModuleCat.RestrictionCoextensionAdj.counit'_app, PresheafOfModules.pushforward_map_app_apply', CategoryTheory.MonoidalCategory.DayConvolution.unit_naturality_assoc, CategoryTheory.ProdPreservesConnectedLimits.forgetCone_π, shift_map_op_assoc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_π_app, CategoryTheory.Discrete.equivalence_unitIso, CategoryTheory.Equivalence.funInvIdAssoc_hom_app, CategoryTheory.equivToOverUnit_unitIso, CategoryTheory.Over.postCongr_inv_app_left, Final.coconesEquiv_functor, CategoryTheory.Adjunction.leftAdjointCompNatTrans₀₁₃_eq_conjugateEquiv_symm, CategoryTheory.Localization.Monoidal.lifting_isMonoidal, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app, Initial.hasLimit_comp_iff, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι_assoc, CategoryTheory.GrothendieckTopology.sheafifyCompIso_inv_eq_sheafifyLift, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality, IsCoverDense.Types.pushforwardFamily_def, ι_leftKanExtensionObjIsoColimit_inv_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_inv_app, CoalgCat.comonEquivalence_counitIso, CategoryTheory.Limits.comp_reflectsLimits, CategoryTheory.StructuredArrow.preEquivalence_unitIso, PresheafOfModules.Derivation.d_mul, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_inv_app, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app', CategoryTheory.ihom.ev_coev_assoc, CategoryTheory.Limits.limit.lift_post, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_hom, CategoryTheory.Monad.instReflectsColimitWalkingParallelPairParallelPairMapAAppCounitObjAOfReflectsColimitOfIsSplitPair, CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_hom_app_unmop_unmop, CategoryTheory.WithInitial.inclLift_hom_app, CategoryTheory.MonoidalCategory.DayConvolution.whiskerLeft_comp_unit_app, CategoryTheory.Over.mapComp_hom_app_left, Final.ι_colimitIso_hom_assoc, CategoryTheory.TransfiniteCompositionOfShape.ici_F, CategoryTheory.Limits.Cocones.precomposeEquivalence_unitIso, CategoryTheory.SingleFunctors.postcomp_functor, triangleIso, Condensed.isSheafStonean, BddLat.forget_semilatSup_partOrd_eq_forget_bddOrd_partOrd, CategoryTheory.CategoryOfElements.structuredArrowEquivalence_counitIso, CategoryTheory.Monad.instPreservesColimitWalkingParallelPairParallelPairMapAAppCounitObjAOfPreservesColimitOfIsReflexivePair, CategoryTheory.Limits.walkingCospanOpEquiv_counitIso_hom_app, mapTriangleInvRotateIso_inv_app_hom₃, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_app, TopologicalSpace.Opens.mapComp_hom_app, CategoryTheory.Adjunction.mapCommMon_counit, CategoryTheory.Limits.ι_colimitLimitToLimitColimit_π, CategoryTheory.SimplicialObject.Truncated.rightExtensionInclusion_hom_app, lightDiagramToLightProfinite_obj, CategoryTheory.Presheaf.instIsIsoFunctorOfIsLeftKanExtensionOppositeType, OrderHom.equivalenceFunctor_counitIso_inv_app_app, Action.FunctorCategoryEquivalence.unitIso_inv_app_hom, mapCommGrpCompIso_hom_app_hom_hom_hom, smoothSheaf.ι_evalHom_assoc, Rep.ihom_ev_app_hom, CategoryTheory.Localization.Lifting.ofIsos_iso, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_app_assoc, CategoryTheory.Limits.colimit.toOver_ι_app, CategoryTheory.sheafComposeIso_hom_fac, instIsLeftKanExtensionObjLanAppLanUnit, CategoryTheory.Over.postAdjunctionLeft_unit_app_left, CategoryTheory.Limits.Cone.extend_π, mapActionComp_inv, CategoryTheory.isCocontinuous_comp, CategoryTheory.Idempotents.functorExtension₂CompWhiskeringLeftToKaroubiIso_hom_app_app_f, Initial.conesEquiv_counitIso, hasColimit_map_comp_ι_comp_grothendieckProj, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality, ι_colimitIsoColimitGrothendieck_hom, CategoryTheory.Limits.limit.pre_post, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_tensorHom_app, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_counit_app, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_inv_app, CategoryTheory.Monad.ForgetCreatesColimits.γ_app, CategoryTheory.Pseudofunctor.map₂_associator_app, CategoryTheory.Cat.rightUnitor_hom_toNatTrans, CategoryTheory.Limits.spanCompIso_hom_app_zero, FGModuleCat.instFiniteCarrierSigmaObjModuleCatOfFinite, CategoryTheory.NatTrans.Coequifibered.whiskerRight, CategoryTheory.Adjunction.mkOfHomEquiv_counit_app, ModuleCat.uliftFunctorForgetIso_hom_app, prod'CompFst_hom_app, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.functor_map, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_fst_assoc, CategoryTheory.PullbackShift.adjunction_unit, Bipointed.swapEquiv_counitIso_hom_app_toFun, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_inv_app_hom_hom_app, LeftExtension.postcompose₂_obj_right_map, CategoryTheory.GradedObject.singleCompEval_hom_app, CategoryTheory.MonoidalOpposite.tensorLeftUnmopIso_inv_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_inv_toNatTrans_app_val_app, CategoryTheory.FreeGroupoid.liftNatIso_hom_app, CategoryTheory.compEvaluation_hom_app, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_hom_π_π, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_tensorDesc_app, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_comp_mapHomotopyCategory_snd, LightCondSet.instIsIsoFunctorSequentialCounitSequentialAdjunction, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app_assoc, CategoryTheory.Sheaf.instIsIsoAppCounitConstantSheafAdjOfFaithfulOfFullConstantSheafOfIsConstant, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_iso_inv_app, instIsCorepresentableCompUliftFunctor, AddMonCat.equivalence_counitIso, opUnopEquiv_counitIso, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone_pt, CategoryTheory.LeftExactFunctor.whiskeringRight_map_app, CategoryTheory.StructuredArrow.ofCommaSndEquivalence_unitIso, CategoryTheory.ι_preservesColimitIso_inv_assoc, CategoryTheory.FreeGroupoid.mapCompLift_inv_app, CategoryTheory.StructuredArrow.map₂_map_left, CategoryTheory.TwoSquare.costructuredArrowRightwards_map, CategoryTheory.Limits.spanOp_hom_app, CategoryTheory.Localization.equivalence_counitIso_app, CategoryTheory.Limits.limitIsoSwapCompLim_hom_app, CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieve, CategoryTheory.Presheaf.coherentExtensiveEquivalence_counitIso, CategoryTheory.Adjunction.homEquiv_unit, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_hom_comp_π_assoc, CategoryTheory.Under.postAdjunctionRight_unit_app_right, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_inv_app, CategoryTheory.Limits.limitIsoFlipCompLim_hom_app, CategoryTheory.Limits.Cocones.whiskering_obj, CategoryTheory.NatTrans.shift_comm_assoc, Profinite.Extend.functorOp_obj, CategoryTheory.StructuredArrow.ofCommaSndEquivalence_counitIso, CategoryTheory.Adjunction.mapCommGrp_unit, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app, CategoryTheory.Abelian.LeftResolution.π_naturality_assoc, curry₃ObjProdComp_inv_app_app_app, CategoryTheory.coreFunctor_obj_map_iso_inv, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_inv_colimit_map, CategoryTheory.conjugateEquiv_leftUnitor_hom, CategoryTheory.WithTerminal.coneEquiv_counitIso_inv_app_hom, Final.ι_colimitIso_inv, CategoryTheory.Adjunction.Triple.mono_leftToRight_app_iff_mono_adj₁_counit_app, CategoryTheory.shiftFunctorCompIsoId_add'_inv_app, AlgebraicGeometry.IsOpenImmersion.hasLimit_cospan_forget_of_left, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₃_app, CategoryTheory.shiftFunctorAdd_zero_add_hom_app, initial_comp_equivalence, AlgebraicGeometry.coprodMk_inl, CategoryTheory.Idempotents.functorExtension₁CompWhiskeringLeftToKaroubiIso_hom_app_app_f, instCommShiftHomotopyCategoryIntUpDerivedCategoryHomMapDerivedCategoryFactorsh, CategoryTheory.Adjunction.unit_mono_of_L_faithful, CategoryTheory.Limits.limitCompCoyonedaIsoCone_hom_app, IsCoverDense.restrictHomEquivHom_naturality_right_symm, CategoryTheory.MonoidalClosed.uncurry_eq, HomologicalComplex₂.flipEquivalenceUnitIso_hom_app_f_f, CategoryTheory.prod.associativity_counitIso, sheafPushforwardContinuous_map_val_app, CategoryTheory.Adjunction.leftAdjointUniq_hom_app_counit_assoc, CategoryTheory.Monad.ForgetCreatesLimits.newCone_π_app, Monoidal.μ_comp_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id_app, CategoryTheory.skeletonEquivalence_unitIso, CategoryTheory.WithInitial.mkCommaMorphism_right_app, CategoryTheory.shiftFunctorAdd'_assoc, CategoryTheory.SingleFunctors.Hom.comm_assoc, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_app_π_assoc, CategoryTheory.ι_preservesColimitIso_hom_assoc, CategoryTheory.StructuredArrow.isEquivalence_pre, CategoryTheory.shiftFunctorComm_hom_app_comp_shift_shiftFunctorAdd_hom_app, Initial.limitConeComp_isLimit, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_left, CategoryTheory.Limits.Cocones.equivalenceOfReindexing_functor_obj, AlgebraicGeometry.Scheme.kerAdjunction_unit_app, CategoryTheory.Sigma.mapComp_inv_app, CategoryTheory.LeftExactFunctor.whiskeringRight_obj_map, ModuleCat.HasColimit.colimitCocone_pt_isModule, CategoryTheory.Limits.limit.post_π, CategoryTheory.Limits.Cones.whiskering_map_hom, CategoryTheory.Limits.prodComparison_comp, CategoryTheory.Limits.Cone.toStructuredArrowCompToUnderCompForget_hom_app, CategoryTheory.Comma.equivProd_counitIso_hom_app, mapCoconeOp_inv_hom, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_obj_X₂, CategoryTheory.Limits.spanCompIso_inv_app_left, CategoryTheory.IsCommMonObj.ofRepresentableBy, CategoryTheory.Localization.homEquiv_eq, CategoryTheory.NatTrans.CommShift.whiskerRight, CategoryTheory.CategoryOfElements.CreatesLimitsAux.liftedCone_π_app_coe, CategoryTheory.StructuredArrow.final_post, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_id, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_hom_assoc, CategoryTheory.GrothendieckTopology.whiskerRight_toPlus_comp_plusCompIso_hom, CategoryTheory.NatTrans.op_whiskerRight_assoc, CategoryTheory.preadditiveYoneda_obj, CategoryTheory.regularTopology.equalizerConditionMap_iff_nonempty_isLimit, rightUnitor_hom_app, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp_app, FullyFaithful.compUliftYonedaCompWhiskeringLeft_inv_app_app_down, CategoryTheory.GrothendieckTopology.preservesSheafification_iff_of_adjunctions, initial_iff_equivalence_comp, AlgebraicGeometry.instIsAffineHomDescScheme, CategoryTheory.Over.mapPullbackAdj_counit_app, CategoryTheory.CostructuredArrow.pre_obj_left, CategoryTheory.Over.iteratedSliceBackward_forget, CategoryTheory.WithTerminal.opEquiv_unitIso_hom_app, CategoryTheory.Comma.instFaithfulCompPreLeft, Rep.standardComplex.εToSingle₀_comp_eq, CategoryTheory.Comonad.instPreservesLimitWalkingParallelPairParallelPairMapAAppUnitObjAOfPreservesLimitOfIsCoreflexivePair, Final.colimitIso_hom, isoShift_inv_naturality, CategoryTheory.Equivalence.cancel_counitInv_right, CategoryTheory.Localization.Lifting.compRight_iso, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquiv_counitIso, CategoryTheory.Over.postCongr_hom_app_left, CategoryTheory.Comma.post_obj_right, CategoryTheory.Adjunction.compPreadditiveYonedaIso_inv_app_app_apply, CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.liftHom_fac, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₃, leftOpRightOpEquiv_unitIso_inv_app, map_opShiftFunctorEquivalence_unitIso_inv_app_unop, CategoryTheory.MorphismProperty.Over.map_comp, CategoryTheory.Localization.LeftBousfield.W_adj_unit_app, CategoryTheory.GradedObject.singleCompEval_inv_app, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_app, CategoryTheory.Adjunction.Triple.whiskerRight_rightToLeft_assoc, CategoryTheory.Equivalence.changeFunctor_unitIso_hom_app, CategoryTheory.WithTerminal.opEquiv_counitIso_hom_app, CategoryTheory.Limits.colimit.ι_inv_pre, HasFibers.comp_const, CategoryTheory.Monad.instPreservesColimitWalkingParallelPairParallelPairMapAAppCounitObjAOfPreservesColimitOfIsSplitPair, CategoryTheory.ComposableArrows.opEquivalence_unitIso_inv_app, TopCat.Presheaf.pushforward_map_app, CategoryTheory.Comma.preRight_map_left, AlgebraicGeometry.Scheme.Hom.coequifibered_normalizationDiagramMap, AlgebraicGeometry.ΓSpec.adjunction_counit_app', CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.counitIso_inv, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_inv_app, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_ihom_ev_app_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_hom_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₃, CategoryTheory.instIsIsoFunctorOppositeSheafSheafComposeNatTrans, CategoryTheory.Equivalence.map_η_comp_η, CategoryTheory.Limits.comp_reflectsFiniteCoproducts, CategoryTheory.Cat.HasLimits.limitCone_π_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app_assoc, CategoryTheory.MonoidalCategory.DayConvolution.associator_inv_unit_unit, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_hom, CategoryTheory.Join.pseudofunctorLeft_mapComp_hom_toNatTrans_app, CategoryTheory.CostructuredArrow.post_map, CategoryTheory.Equivalence.counit_naturality_assoc, CategoryTheory.CostructuredArrow.mapIso_unitIso_inv_app_left, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_obj_right, IsCoverDense.restrictHomEquivHom_naturality_left, comp_id, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_hom_app, CategoryTheory.Comma.preLeft_obj_right, HomologicalComplex.cyclesOpNatIso_inv_app, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.iso_hom, CategoryTheory.preadditiveYonedaMap_app, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app', CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_map_base, CategoryTheory.MonoidalCategory.DayFunctor.equiv_counitIso_inv_app, CondensedMod.isDiscrete_iff_isDiscrete_forget, AddCommGrpCat.coyonedaForget_inv_app_app, CategoryTheory.Adjunction.unit_app_shift_commShiftIso_inv_app, CategoryTheory.Comma.mapRightComp_inv_app_right, CategoryTheory.Limits.coprodComparisonNatIso_hom, whiskerRight_id', CategoryTheory.Monad.left_unit, AlgebraicGeometry.isPullback_inl_inl_coprodMap, CategoryTheory.Pi.closedCounit_app, CategoryTheory.NatTrans.CommShift.associator, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π, compFlipUncurryIso_inv_app, CommShift.ofIso_commShiftIso_hom_app, CategoryTheory.Over.iteratedSliceBackward_forget_forget, CategoryTheory.Quotient.LiftCommShift.iso_hom_app, CategoryTheory.Enriched.FunctorCategory.diagram_map_app, CategoryTheory.Comma.instFaithfulCompPost, CategoryTheory.OplaxFunctor.mapComp_assoc_left_app, CategoryTheory.preservesColimitIso_inv_comp_desc, PresheafOfModules.Monoidal.tensorObj_map_tmul, CategoryTheory.LeftExactFunctor.whiskeringLeft_map_app, CategoryTheory.Core.functorToCore_comp_right, Final.hasColimit_comp_iff, lanUnit_app_app_lanAdjunction_counit_app_app, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_snd, CategoryTheory.Adjunction.compUliftCoyonedaIso_inv_app_app_down, bijective_sectionsPrecomp, CategoryTheory.presheafHom_obj, CategoryTheory.StructuredArrow.prodEquivalence_unitIso, ModuleCat.extendScalars_assoc_assoc, pointwiseLeftKanExtension_obj, CategoryTheory.LocalizerMorphism.hasPointwiseRightDerivedFunctorAt_iff_of_isRightDerivabilityStructure, pointwiseLeftKanExtension_map, Final.colimitCoconeComp_isColimit, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_π_app, lanUnit_app_whiskerLeft_lanAdjunction_counit_app, CategoryTheory.CostructuredArrow.preEquivalence.functor_obj_hom, CategoryTheory.Localization.Construction.NatTransExtension.app_eq, CategoryTheory.Cat.HasLimits.homDiagram_map, CategoryTheory.Limits.parallelPairOpIso_hom_app_one, CategoryTheory.Limits.walkingCospanOpEquiv_counitIso_inv_app, mapTriangleInvRotateIso_hom_app_hom₃, groupCohomology.infNatTrans_app, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso_inv_app_f, ι_colimitIsoOfIsLeftKanExtension_inv, CategoryTheory.IsCommMon.ofRepresentableBy, CategoryTheory.Adjunction.instIsIsoFunctorCounitOfIsEquivalence, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.forgetToPresheafedSpace_reflectsPullback_of_right, CategoryTheory.Limits.limit.pre_π_assoc, CategoryTheory.Limits.PullbackCone.op_ι_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_hom_app, constComp_inv_app, Rep.invariantsAdjunction_unit_app, Initial.comp_hasLimit, AlgebraicTopology.DoldKan.Compatibility.equivalence₀_inverse, CategoryTheory.Bimon.equivMonComonCounitIsoAppXAux_inv, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality_app, CategoryTheory.Equivalence.symmEquivInverse_obj_counitIso_hom, pointedToTwoPFst_comp_swap, CondensedMod.LocallyConstant.instFullModuleCatCondensedDiscrete, CategoryTheory.essImage_yonedaMon, CategoryTheory.Comonad.delta_naturality_assoc, CategoryTheory.Join.mapWhiskerRight_whiskerRight, CategoryTheory.ShiftMkCore.add_zero_hom_app, CategoryTheory.Idempotents.DoldKan.N₂_map_isoΓ₀_hom_app_f, liftOfIsRightKanExtension_fac_app, CategoryTheory.Limits.pullbackConeEquivBinaryFan_counitIso, CategoryTheory.Sum.swapCompInl_hom_app, CategoryTheory.CostructuredArrow.ofCommaFstEquivalence_inverse, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counitIso_hom_app_tensor_assoc, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_map_right_left, CategoryTheory.Limits.MultispanIndex.multispanMapIso_inv_app, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_hom_app_f, AlgebraicGeometry.instIsAffineCoprodScheme, CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod_fac, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_apply, CategoryTheory.LocalizerMorphism.functorialRightResolutions.Φ_functor_map_ι_app, CategoryTheory.AsSmall.equiv_unitIso, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_snd, CategoryTheory.Cat.Hom.comp_toFunctor, AddCommGrpCat.coyonedaForget_hom_app_app_hom, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_unitIso_hom_app_f_f, CategoryTheory.Monad.comparisonForget_hom_app, CategoryTheory.GrothendieckTopology.W_isInvertedBy_whiskeringRight_presheafToSheaf, CategoryTheory.Grothendieck.ιNatTrans_app_base, instIsCardinalAccessibleComp, preservesMonomorphisms_comp, CategoryTheory.MonoidalOpposite.tensorIso_hom_app_unmop, CategoryTheory.SimplicialObject.Truncated.rightExtensionInclusion_left, CategoryTheory.Monad.algebraFunctorOfMonadHomComp_hom_app_f, whiskerLeft_comp_whiskerRight_assoc, finBddDistLat_dual_comp_forget_to_bddDistLat, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_right_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π_assoc, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_apply_f, essImage_ι_comp, CommMonCat.instSmallElemForallObjCompMonCatForget₂MonoidHomCarrierCarrierForgetSections, SheafOfModules.pushforwardComp_inv_app_val_app, CategoryTheory.Pi.closedUnit_app, CategoryTheory.Limits.pointwiseCocone_ι_app_app, LightCondensed.internallyProjective_iff_tensor_condition, CategoryTheory.Limits.Cones.whiskeringEquivalence_inverse, CategoryTheory.Presheaf.isSheaf_coherent_of_projective_comp, leftDerived_fac_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_app_fst_app, currying_counitIso_inv_app_app, ihom_ev_app, CategoryTheory.WithTerminal.inclLift_hom_app, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_unit_app, CategoryTheory.Quotient.liftCommShift_compatibility, CategoryTheory.Equivalence.sheafCongrPreregular_functor_map_val_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality_assoc, CategoryTheory.LaxFunctor.mapComp_naturality_right_app_assoc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_inv_app_hom, CategoryTheory.Adjunction.mapGrp_unit, leftKanExtensionCompIsoOfPreserves_hom_fac_assoc, CategoryTheory.CostructuredArrow.instEssSurjCompPre, CategoryTheory.Limits.opHomCompWhiskeringLimYonedaIsoCocones_hom_app_app_app, isoShift_hom_naturality, CategoryTheory.Adjunction.map_restrictFullyFaithful_unit_app_assoc, CategoryTheory.ForgetEnrichment.equiv_unitIso, CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_inv, distLat_dual_comp_forget_to_Lat, CategoryTheory.conjugateEquiv_counit_symm, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_base, LeftExtension.nonempty_isPointwiseLeftKanExtensionAt_compTwoSquare_iff, CommShift.isoZero'_inv_app, CategoryTheory.Grothendieck.ιCompMap_inv_app_fiber, typeToPartialFunIsoPartialFunToPointed_hom_app_toFun, CategoryTheory.TransfiniteCompositionOfShape.iic_isColimit, CategoryTheory.Adjunction.Equivalence.instIsMonoidalCounit, TopCat.Sheaf.extend_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_shift, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₁, AlgebraicGeometry.Surjective.sigmaDesc_of_union_range_eq_univ, CategoryTheory.Limits.opParallelPairIso_hom_app_zero, PartOrdEmb.Limits.CoconePt.fac_apply, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_hom, HomologicalComplex.singleMapHomologicalComplex_inv_app_self, CategoryTheory.PreGaloisCategory.autIsoFibers_inv_app, Initial.extendCone_obj_π_app', MulEquiv.toSingleObjEquiv_unitIso_hom, CategoryTheory.evaluationAdjunctionRight_counit_app_app, LaxMonoidal.ofBifunctor.bottomMapᵣ_app, CategoryTheory.Monad.comparison_obj_a, CategoryTheory.Limits.ColimitPresentation.map_ι, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_counitIso, CategoryTheory.Limits.Cocone.toCostructuredArrowCompToOverCompForget_inv_app, PresheafOfModules.pushforward₀_obj_obj_isAddCommGroup, AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTrans, CategoryTheory.Adjunction.leftAdjointUniq_hom_counit, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_left_as, CategoryTheory.Adjunction.isIso_counit_of_iso, CategoryTheory.NatTrans.CommShift.rightUnitor, CategoryTheory.AsSmall.equiv_counitIso, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_1, CategoryTheory.CatCommSq.hId_iso_inv_app, homEquivOfIsLeftKanExtension_symm_apply, CategoryTheory.MorphismProperty.IsInvertedBy.of_comp, CategoryTheory.OplaxFunctor.map₂_associator_app_assoc, CategoryTheory.Adjunction.unit_app_unit_comp_map_η, CategoryTheory.Limits.limCompFlipIsoWhiskerLim_inv_app_app, CategoryTheory.Monad.adj_counit, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app_assoc, CategoryTheory.StructuredArrow.preEquivalence_inverse, CategoryTheory.LaxFunctor.map₂_associator_app_assoc, CategoryTheory.Presheaf.functorEnrichedHomCoyonedaObjEquiv_naturality, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_unit, commShiftOfLocalization_iso_inv_app, CategoryTheory.Adjunction.map_restrictFullyFaithful_counit_app, CategoryTheory.Over.forgetAdjStar_counit_app, CommMonCat.coyonedaForget_inv_app_app, Quiver.freeGroupoidFunctor_comp, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₁, CategoryTheory.WithInitial.coconeEquiv_counitIso_inv_app_hom, CategoryTheory.Limits.colimit.ι_pre, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₃, CategoryTheory.Equivalence.mapMon_unitIso, AlgebraicGeometry.PresheafedSpace.colimitCocone_ι_app_base, SSet.hoFunctor.unitHomEquiv_eq, commShiftOfLocalization.iso_inv_app, CategoryTheory.flipCompEvaluation_hom_app, CategoryTheory.Bimon.toComon_forget, LaxMonoidal.ofBifunctor.topMapₗ_app, HomotopicalAlgebra.FibrantObject.instWeakEquivalenceHoCatAppιCompResolutionNatTrans, CategoryTheory.StructuredArrow.preEquivalence_functor, instIsIsoAppLanUnit, CategoryTheory.coev_app_comp_pre_app, CategoryTheory.Limits.Cone.fromStructuredArrow_pt, CategoryTheory.WithInitial.commaFromUnder_map_left, CategoryTheory.Equivalence.pi_unitIso, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_whiskerLeft_app, CategoryTheory.simplicialCosimplicialEquiv_unitIso_hom_app, CategoryTheory.Adjunction.leftAdjointUniq_hom_app_counit, LeftExtension.postcompose₂ObjMkIso_inv_right_app, CommShift.comp_commShiftIso_inv_app, CategoryTheory.Cat.HasLimits.limitConeX_α, TopCat.Presheaf.isSheaf_iff_isSheaf_comp, CategoryTheory.Equivalence.counitInv_functor_comp, AlgebraicTopology.DoldKan.N₁Γ₀_hom_app_f_f, CategoryTheory.Adjunction.toComonad_δ, CategoryTheory.Limits.Cone.toStructuredArrow_comp_toUnder_comp_forget, sheafPushforwardContinuousCompSheafToPresheafIso_inv_app_app, essImage_comp_of_essSurj, CategoryTheory.Mon.limit_mon_mul, CategoryTheory.Limits.colimitYonedaHomIsoLimit_π_apply, CategoryTheory.NatTrans.rightOpWhiskerRight, CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_inv_π_π, CategoryTheory.Presheaf.isLocallyInjective_whisker, inlCompSum'_hom_app, CategoryTheory.Equivalence.sheafCongrPreregular_inverse_map_val_app, CategoryTheory.ExponentiableMorphism.pushforwardId_hom_counit_assoc, HomologicalComplex.instIsCorepresentableCompEvalObjOppositeFunctorTypeCoyonedaOp, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_app, CategoryTheory.Quotient.natTransLift_id, Rep.coinvariantsTensorIndNatIso_inv_app, CategoryTheory.Limits.walkingCospanOpEquiv_unitIso_inv_app, CategoryTheory.Join.mapPairComp_hom_app_right, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_hom, sumIsoExt_inv_app_inr, CategoryTheory.ProjectiveResolution.isoLeftDerivedObj_hom_naturality, CategoryTheory.GrothendieckTopology.W_adj_unit_app, CategoryTheory.Comonad.ComonadicityInternal.unitFork_ι, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app, AlgebraicGeometry.ΓSpec.adjunction_counit_app, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app_assoc, CategoryTheory.Adjunction.IsMonoidal.leftAdjoint_ε, CategoryTheory.WithInitial.liftStar_lift_map, CategoryTheory.Under.mapPushoutAdj_unit_app, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_map_left, CategoryTheory.Iso.coreLeftUnitor, CategoryTheory.preservesLimitIso_inv_π_assoc, CategoryTheory.Presheaf.isSheaf_comp_of_isSheaf, CategoryTheory.CategoryOfElements.map_π, leftKanExtensionCompIsoOfPreserves_inv_fac_assoc, ranCompIsoOfPreserves_inv_app, CategoryTheory.Adjunction.Equivalence.instIsMonoidalUnit, CategoryTheory.Comma.mapLeftComp_inv_app_left, CategoryTheory.shiftFunctorComm_hom_app_comp_shift_shiftFunctorAdd_hom_app_assoc, CategoryTheory.CosimplicialObject.Truncated.whiskering_map_app_app, CategoryTheory.Mat_.embeddingLiftIso_hom_app, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_map_fst_app, CategoryTheory.TwoSquare.isIso_lanBaseChange_app, CategoryTheory.CostructuredArrow.initial_post, CategoryTheory.ProjectiveResolution.extMk_hom, instLinearComp, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_map_left_left, CategoryTheory.Grothendieck.grothendieckTypeToCat_functor_obj_fst, CategoryTheory.Adjunction.isIso_counit_app_of_iso, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_obj_X₃, CategoryTheory.Limits.Cocones.functoriality_obj_pt, AlgebraicGeometry.Scheme.Γ_def, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_whiskerLeft, CategoryTheory.MonoidalClosed.curry_id_eq_coev, shiftIso_add_hom_app, CategoryTheory.presheafHom_map_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_app_fst_app, CategoryTheory.shiftFunctorAdd_inv_app_obj_of_induced, mapHomologicalComplex_upToQuasiIso_Q_inverts_quasiIso, CategoryTheory.Join.mapWhiskerLeft_whiskerRight_assoc, CategoryTheory.Limits.opParallelPairIso_hom_app_one, CategoryTheory.typeEquiv_unitIso_hom_app, CategoryTheory.Limits.cospanCompIso_inv_app_left, mapTriangleCompIso_inv_app_hom₃, CategoryTheory.Limits.spanCompIso_app_zero, CategoryTheory.WithInitial.inclLiftToInitial_inv_app, preservesZeroMorphisms_comp, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_unit_app_left, CategoryTheory.Limits.yonedaCompLimIsoCocones_hom_app_app, CategoryTheory.Over.starPullbackIsoStar_hom_app_left, CategoryTheory.Over.postEquiv_inverse, CategoryTheory.TwoSquare.equivalenceJ_counitIso, AlgebraicTopology.DoldKan.Γ₂N₂ToKaroubiIso_hom_app, CategoryTheory.StructuredArrow.mapNatIso_unitIso_hom_app_right, CategoryTheory.Adjunction.functorialityUnit_app_hom, CategoryTheory.Limits.instHasColimitDiscreteOppositeCompInverseOppositeOpFunctor, CategoryTheory.Pi.evalCompEqToEquivalenceFunctor_hom, CategoryTheory.Abelian.Ext.mapExactFunctor_hom, CategoryTheory.Localization.whiskeringLeftFunctor'_eq, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_app, smoothSheafCommRing.ι_evalHom, CategoryTheory.Monad.adj_unit, CategoryTheory.Comma.natTrans_app, CategoryTheory.simplicialCosimplicialEquiv_counitIso_hom_app_app, CategoryTheory.Limits.ι_colimitCompWhiskeringLeftIsoCompColimit_hom, mapTriangleCompIso_hom_app_hom₃, Rep.coindResAdjunction_unit_app, CategoryTheory.Triangulated.Octahedron.map_m₃, CategoryTheory.FunctorToTypes.hcomp, CategoryTheory.OplaxFunctor.mapComp_assoc_right_app, CategoryTheory.Join.isoMkFunctor_inv_app, isoWhiskerLeft_right, CategoryTheory.GrothendieckTopology.W_of_preservesSheafification, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_μ, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_hom_app_app, CategoryTheory.ReflQuiv.adj.unit.map_app_eq, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp_app, PrincipalSeg.cocone_ι_app, HomologicalComplex₂.instHasTotalIntObjUpCompShiftFunctor₁ShiftFunctor₂, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_map_app_snd, CategoryTheory.Localization.lift₂_iso_hom_app_app₂, CategoryTheory.Comma.coneOfPreserves_pt_right, CategoryTheory.Over.forgetMapTerminal_inv_app, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_hom_app, CategoryTheory.Pi.optionEquivalence_unitIso, shiftIso_add'_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app, ProfiniteAddGrp.instIsTopologicalAddGroupCarrierToTopTotallyDisconnectedSpacePtProfiniteLimitConeCompForget₂ContinuousAddMonoidHomToProfiniteContinuousMap, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app, CategoryTheory.NatIso.op_isoWhiskerRight, CategoryTheory.Abelian.full_comp_preadditiveCoyonedaObj, CategoryTheory.LeftExactFunctor.whiskeringLeft_obj_obj_obj, CategoryTheory.Comonad.instPreservesLimitWalkingParallelPairParallelPairMapAAppUnitObjAOfPreservesLimitOfIsCosplitPair, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_inv_app_app, CategoryTheory.Presieve.IsSheafFor.comp_iff_of_preservesPairwisePullbacks, CategoryTheory.ULift.equivalence_unitIso_inv, AlgebraicGeometry.Scheme.Cover.instIsLocallyDirectedI₀CompFunctorOfLocallyDirectedForget, CategoryTheory.Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_one_app, CategoryTheory.TwoSquare.GuitartExact.vComp'_iff_of_equivalences, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₁, CategoryTheory.Adjunction.Triple.leftToRight_app_obj, CategoryTheory.Limits.LimitPresentation.reindex_diag, HomotopicalAlgebra.FibrantObject.instIsLocalizationCompιWeakEquivalences, AlgebraicGeometry.Scheme.SpecΓIdentity_app, AddCommGrpCat.Colimits.quotUliftToQuot_ι, CategoryTheory.Equivalence.sheafCongrPrecoherent_inverse_map_val_app, CategoryTheory.Preadditive.commGrpEquivalenceAux_hom_app_hom_hom_hom, CategoryTheory.Abelian.LeftResolution.instEpiKaroubiAppπ', CategoryTheory.Adjunction.instIsIsoAppUnitOfFullOfFaithful, CategoryTheory.Limits.instPreservesWellOrderContinuousOfShapeComp, CategoryTheory.Sum.natTransOfWhiskerLeftInlInr_id, CommShift.ofComp_compatibility, CategoryTheory.RelCat.unopFunctor_comp_opFunctor_eq, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan_inv_app_app_apply_eq_id, CategoryTheory.Discrete.functorComp_hom_app, CategoryTheory.Limits.spanOp_inv_app, CategoryTheory.Presheaf.isSeparated_iff_subsingleton, BddLat.forget_semilatInf_partOrd_eq_forget_bddOrd_partOrd, mapCoconeMapCocone_hom_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app_assoc, CategoryTheory.GrothendieckTopology.toSheafify_comp_sheafifyCompIso_inv_assoc, LightCondensed.isColimitLocallyConstantPresheafDiagram_desc_apply, CategoryTheory.Equivalence.rightOp_unitIso_hom_app, CategoryTheory.Over.conePostIso_hom_app_hom, CategoryTheory.Join.pseudofunctorLeft_mapComp_inv_toNatTrans_app, CategoryTheory.Limits.Cones.functoriality_obj_π_app, SSet.OneTruncation₂.ofNerve₂.natIso_hom_app_obj, CategoryTheory.Abelian.IsGrothendieckAbelian.OppositeModuleEmbedding.full_embedding, CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_cancel_hom_app, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descAddMonoidHom_quotMk, CategoryTheory.Limits.reflexivePair.compRightIso_hom_app, shiftIso_inv_naturality, IsCoverDense.restrictHomEquivHom_naturality_left_assoc, AlgebraicGeometry.IsZariskiLocalAtSource.sigmaDesc, whiskerLeft_app, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_whiskerRight_app, AlgebraicGeometry.isIso_stalkMap_coprodSpec, CategoryTheory.MonoidalCategory.DayFunctor.equiv_counitIso_hom_app, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInrIso_inv_app_app, CategoryTheory.Limits.colimitLimitToLimitColimitCone_hom, isDenseAt_eq_isPointwiseLeftKanExtensionAt, RightExtension.coneAtFunctor_obj, CategoryTheory.Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor_assoc, CategoryTheory.Over.mapComp_eq, CategoryTheory.GlueData.diagramIso_app_left, CategoryTheory.essImage_yonedaGrp, preservesInjectiveObjects_comp, essImage.liftFunctorCompIso_hom_app, CategoryTheory.shiftFunctorAdd'_zero_add_inv_app, CategoryTheory.Codiscrete.right_triangle_components, PresheafOfModules.Derivation.congr_d, essImage.counit_isIso, CategoryTheory.MonoidalClosed.uncurry_pre, curry₃ObjProdComp_hom_app_app_app, CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_hom_app, CategoryTheory.Adjunction.shift_counit_app, CategoryTheory.SimplicialObject.isoCoskOfIsCoskeletal_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_hom_app_hom_hom_app, LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom, map_shift_unop, IsCoverDense.presheafIso_hom_app, CategoryTheory.TwoSquare.whiskerVertical_app, CategoryTheory.Limits.Cones.equivalenceOfReindexing_counitIso, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_counitIso, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₂, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_base, CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_inv_app, CategoryTheory.GradedObject.comapEquiv_unitIso, bddOrd_dual_comp_forget_to_partOrd, CategoryTheory.Monad.assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_app, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_app, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_map_τ₁, CategoryTheory.Adjunction.map_restrictFullyFaithful_counit_app_assoc, FGModuleCat.instFiniteCarrierLimitModuleCatCompForget₂LinearMapIdObjIsFG, CategoryTheory.Discrete.productEquiv_counitIso_hom_app, toPrefunctor_comp, CategoryTheory.InjectiveResolution.isoRightDerivedObj_hom_naturality, LeftExtension.postcompose₂_map_right_app, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.mk₀_f_comp_biprodAddEquiv_symm_biprodIsoProd_hom, CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatIso_hom, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.image_preimage_is_empty, instIsRepresentableCompOppositeOpObjTypeYonedaObjRightAdjointObjIsDefined, CategoryTheory.ExponentiableMorphism.ev_coev, CategoryTheory.monoOver_terminal_to_subterminals_comp, Rep.indResAdjunction_counit_app_hom_hom, CategoryTheory.Adjunction.counit_naturality, CategoryTheory.Equivalence.CommShift.instCommShiftHomFunctorCounitIso, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_iso_inv_app, CategoryTheory.Localization.functor_additive_iff, CategoryTheory.ULift.equivalence_counitIso_hom_app, CategoryTheory.StructuredArrow.instFaithfulObjCompPost, AlgebraicGeometry.IsOpenImmersion.hasLimit_cospan_forget_of_right, op_commShiftIso_hom_app_assoc, CategoryTheory.WithInitial.mkCommaObject_hom_app, FullyFaithful.compYonedaCompWhiskeringLeftMaxRight_inv_app_app, CategoryTheory.CartesianClosed.curry_eq, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_inv_app, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app_assoc, CategoryTheory.ExactFunctor.whiskeringLeft_map_app, SSet.Truncated.HomotopyCategory.BinaryProduct.left_unitality, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_leftUnitor, SheafOfModules.toSheaf_map_val, CategoryTheory.Comonad.left_counit, FinPartOrd.dualEquiv_counitIso, CategoryTheory.Limits.comp_preservesCofilteredLimits, AlgebraicGeometry.Scheme.kerAdjunction_counit_app, AlgebraicGeometry.opensDiagramι_app, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerLeft_assoc, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.inverseObj_comon_counit_app, PresheafOfModules.pullback_assoc, CategoryTheory.Limits.opSpan_hom_app, CategoryTheory.Comma.instFullCompPreLeft, CategoryTheory.GrothendieckTopology.instIsIsoFunctorOppositeSheafSheafComposeNatTransPlusPlusAdjunction, CategoryTheory.Iso.compInverseIso_inv_app, CategoryTheory.Adjunction.restrictFullyFaithful_homEquiv_apply, CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_hom, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac, TopCat.hasLimit_iff_small_sections, CategoryTheory.Cat.opEquivalence_unitIso, CategoryTheory.GrothendieckTopology.overMapPullback_assoc_assoc, CategoryTheory.LocalizerMorphism.comp_functor, CategoryTheory.Sheaf.isSheaf_of_isLimit, isRightAdjoint_comp, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app_assoc, CategoryTheory.Adjunction.CommShift.commShift_counit, AlgebraicTopology.AlternatingFaceMapComplex.ε_app_f_zero, CategoryTheory.MonoidalClosed.id_tensor_pre_app_comp_ev, AlgebraicGeometry.isCompl_range_inl_inr, CategoryTheory.whiskering_linearYoneda, TopCat.Presheaf.presheafEquivOfIso_unitIso_hom_app_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_counitIso, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom, CategoryTheory.Equivalence.unitInv_naturality_assoc, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_right_as, CategoryTheory.conjugateEquiv_whiskerRight, isLeftDerivedFunctor_iff_of_inverts, CategoryTheory.NatTrans.op_whiskerRight, CategoryTheory.Discrete.sumEquiv_unitIso_hom_app, mapTriangle_map_hom₁, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.inverse_map_app, CategoryTheory.Comma.preRight_map_right, CategoryTheory.Limits.spanCompIso_app_right, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_inv_π_π, rightDerivedNatTrans_app_assoc, AlgebraicGeometry.ΓSpec.adjunction_unit_app, CategoryTheory.NatTrans.CommShiftCore.shift_app, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy₂'_homEquiv, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_left, PartOrdEmb.Limits.cocone_ι_app, CategoryTheory.CatCommSq.vInv_iso_hom_app, CategoryTheory.Over.mapPullbackAdj_unit_app, ShiftSequence.induced_shiftIso_hom_app_obj, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.inverseObj_X, CategoryTheory.MorphismProperty.Over.forget_comp_forget_map, CategoryTheory.Adjunction.whiskerRight_counit_iso_of_L_fully_faithful, CategoryTheory.Sum.natIsoOfWhiskerLeftInlInr_eq, CategoryTheory.NatTrans.shift_comm, ranCompIsoOfPreserves_hom_app, CategoryTheory.lift_comp_preservesLimitIso_hom_assoc, CategoryTheory.preservesLimitIso_inv_π, CategoryTheory.whiskeringRightCompEvaluation_inv_app, associator_inv_app, CategoryTheory.Limits.whiskeringLimYonedaIsoCones_inv_app_app, CategoryTheory.whiskering_linearCoyoneda₂, instCommShiftCochainComplexIntDerivedCategoryHomMapDerivedCategoryFactors, CategoryTheory.Monad.MonadicityInternal.unitCofork_π, CategoryTheory.LocalizerMorphism.homMap_apply, CategoryTheory.typeEquiv_unitIso_inv_app, functorialityCompPrecompose_hom_app_hom, CategoryTheory.NatTrans.unop_whiskerRight, CategoryTheory.Comma.map_map_left, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id_app, CategoryTheory.Sigma.natIso_inv, CategoryTheory.GrothendieckTopology.Cover.multicospanComp_inv_app, CategoryTheory.MorphismProperty.Over.pullbackComp_inv_app_left, CategoryTheory.Limits.Cone.toStructuredArrowCone_π_app, isoWhiskerRight_left_assoc, CategoryTheory.Adjunction.instIsIsoFunctorUnitOfIsEquivalence_1, flipping_counitIso_hom_app_app_app, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_inv_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_map_snd_app, CategoryTheory.Comma.toIdPUnitEquiv_unitIso_inv_app_right, CategoryTheory.Limits.pointwiseCocone_pt, CategoryTheory.Limits.instHasLimitCompOfPreservesLimit, CategoryTheory.Comma.post_map_left, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_inv_app_app, CategoryTheory.Limits.Cones.whiskeringEquivalence_unitIso, isoWhiskerRight_twice, 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, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_obj_left, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_hom_app, corepresentableByUliftFunctorEquiv_apply_homEquiv, CategoryTheory.Comma.toPUnitIdEquiv_unitIso_inv_app_left, AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_right, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_naturality_app, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceFunctor_obj_fiber, CategoryTheory.Comma.colimitAuxiliaryCocone_pt, isIso_ranAdjunction_unit_app_iff, CategoryTheory.mateEquiv_hcomp, CategoryTheory.Limits.colimit.pre_pre, CategoryTheory.Join.mkFunctorLeft_hom_app, CategoryTheory.GrothendieckTopology.uliftYonedaCompSheafToPresheaf_inv_app_app, CategoryTheory.CostructuredArrow.CreatesConnected.natTransInCostructuredArrow_app, CategoryTheory.Adjunction.comp_counit, CategoryTheory.CatCommSq.iso_hom_naturality, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_inv_app_unmop, CategoryTheory.Equivalence.changeFunctor_counitIso_hom_app, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_pt, LeftExtension.postcompose₂_obj_hom_app, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerLeftIso_hom_app, CategoryTheory.GlueData.diagramIso_inv_app_left, CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc, pentagonIso, CategoryTheory.Equivalence.refl_counitIso, IsWellOrderContinuous.nonempty_isColimit, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app_assoc, CategoryTheory.Limits.HasLimit.isoOfEquivalence_hom_π, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_app, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_inv_hom, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_counitIso, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_map_right_right, AlgebraicGeometry.instIsOpenImmersionInrScheme, AlgebraicGeometry.SheafedSpace.ofRestrict_hom_c_app, CategoryTheory.unit_conjugateEquiv_symm, CategoryTheory.Adjunction.mapMon_counit, toCostructuredArrow_comp_proj, CategoryTheory.preservesLimitNatIso_inv_app, shiftIso_zero, CategoryTheory.Limits.opCompYonedaSectionsEquiv_apply_app, CategoryTheory.Grothendieck.grothendieckTypeToCat_inverse_obj_base, TopCat.Presheaf.whiskerIsoMapGenerateCocone_inv_hom, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app_assoc, CategoryTheory.Pretriangulated.preadditiveYoneda_homologySequenceδ_apply, CategoryTheory.Grpd.freeForgetAdjunction_homEquiv_symm_apply, NatTrans.hcomp_eq_whiskerLeft_comp_whiskerRight, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_obj_right, CategoryTheory.toPresheafToSheafCompComposeAndSheafify_app, CategoryTheory.NatTrans.IsMonoidal.hcomp, ι_colimitIsoColimitGrothendieck_hom_assoc, CategoryTheory.forgetEnrichmentOppositeEquivalence_unitIso, HomologicalComplex.instHasLimitDiscreteWalkingPairCompPairEval, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app_assoc, whiskeringLeft₃_obj_obj_map_app_app_app_app, MulEquiv.toSingleObjEquiv_counitIso_hom, CategoryTheory.unit_conjugateEquiv, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_ι_inv_assoc, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct_assoc, CategoryTheory.Iso.coreAssociator, CategoryTheory.Under.postEquiv_counitIso, CategoryTheory.Grothendieck.grothendieckTypeToCatFunctor_map_coe, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone_ι_app, HasFibers.inducedFunctor_comp, CategoryTheory.Bimon.instIsComonHomMonHomEquivMonComonUnitIsoAppX, final_iff_isIso_colimit_pre, CategoryTheory.Comma.coconeOfPreserves_pt_right, CategoryTheory.TransfiniteCompositionOfShape.map_isColimit, CategoryTheory.Join.mapWhiskerLeft_associator_hom, LeibnizAdjunction.adj_counit_app_right, CategoryTheory.instFinalStructuredArrowCompPreOfRepresentablyFlat, LightProfinite.Extend.functor_map, CategoryTheory.Cat.freeReflMap_naturality, CategoryTheory.MonoidalClosed.curry_eq, CategoryTheory.Presheaf.final_toCostructuredArrow_comp_pre, CategoryTheory.GrothendieckTopology.uliftYonedaCompSheafToPresheaf_hom_app_app, mapTriangleRotateIso_hom_app_hom₂, CategoryTheory.Equivalence.counitInv_app_comp_functor_map_η_inverse_assoc, SheafOfModules.pullback_comp_id, CategoryTheory.Under.postComp_hom_app_right, CategoryTheory.shiftFunctorAdd'_add_zero_inv_app, mapCommMonCompIso_inv_app_hom_hom, preservesProjectiveObjects_comp, CategoryTheory.Adjunction.Triple.rightToLeft_eq_counits, CategoryTheory.Comonad.cofree_map_f, comp_mapMon_mul, AlgebraicGeometry.Scheme.Modules.pseudofunctor_right_unitality, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceInverse_obj_fiber, CategoryTheory.Comma.preRight_obj_right, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app, TopologicalSpace.Opens.mapMapIso_unitIso, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τl, CategoryTheory.Limits.PreservesColimit.preserves, SSet.Truncated.rightExtensionInclusion_right_as, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.LocalizerMorphism.commShift_iso_hom_app_assoc, CategoryTheory.Cat.HasLimits.limit_π_homDiagram_eqToHom, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₃, CategoryTheory.NatTrans.op_whiskerLeft_assoc, CategoryTheory.Equivalence.unop_counitIso, CategoryTheory.TwoSquare.hId_app, RightExtension.coneAtWhiskerRightIso_inv_hom, liftOfIsRightKanExtension_fac_app_assoc, FGModuleCat.instFiniteCarrierPiObjModuleCatOfFinite, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_right, shiftIso_add, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInlIso_hom_app_app, AlgebraicGeometry.disjoint_opensRange_sigmaι, SheafOfModules.instPreservesFiniteLimitsFunctorOppositeAddCommGrpCatCompSheafToSheafSheafToPresheaf, CategoryTheory.Adjunction.isIso_unit_app_iff_mem_essImage, CategoryTheory.typeEquiv_counitIso_inv_app_val_app, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_inv_app_left, pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, LeftExtension.postcomp₁_obj_hom_app, whiskerLeft_comp, TopologicalSpace.Opens.overEquivalence_unitIso_hom_app_left, CategoryTheory.Comma.isEquivalence_post, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_left, CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod_fac₂, CategoryTheory.ExactFunctor.whiskeringLeft_obj_obj_obj, CategoryTheory.WithTerminal.liftToTerminalUnique_inv_app, CategoryTheory.ComposableArrows.opEquivalence_inverse_obj, CategoryTheory.Equivalence.mapCommGrp_unitIso, CategoryTheory.Equivalence.cancel_unitInv_right, AlgebraicTopology.DoldKan.N₂Γ₂_inv_app_f_f, CategoryTheory.WithTerminal.mapComp_inv_app, CategoryTheory.Equivalence.invFunIdAssoc_hom_app, CategoryTheory.Comonad.ForgetCreatesColimits'.γ_app, LightCondensed.forget_map_val_app, rightKanExtension_hom_ext_iff, commShiftPullback_iso_eq, CategoryTheory.Limits.Cones.postcomposeEquivalence_unitIso, pointwiseLeftKanExtensionUnit_app, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_unit_app, CategoryTheory.ComonadHom.app_δ_assoc, CategoryTheory.Equivalence.unitIso_hom_app_comp_inverse_map_η_functor, CategoryTheory.CostructuredArrow.mapIso_counitIso_hom_app_left, CategoryTheory.OplaxFunctor.mapComp_naturality_left_app, fullyFaithfulCancelRight_hom_app, CategoryTheory.ExactFunctor.whiskeringLeft_obj_map, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerRightIso_inv_app, AlgebraicGeometry.Scheme.AffineZariskiSite.coequifibered_iff_forall_isLocalizationAway, whiskeringLeft₃_obj_map_app_app_app_app_app, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_germ_apply, CategoryTheory.GrothendieckTopology.toPlus_comp_plusCompIso_inv, CategoryTheory.Iso.compInverseIso_hom_app, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_hom_app_app, CategoryTheory.Grothendieck.pre_map_fiber, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_hom_app_snd_app, CategoryTheory.NatTrans.pi'_app, AlgebraicGeometry.ΓSpec.left_triangle, pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac, CategoryTheory.Limits.colimitIsoSwapCompColim_inv_app, CategoryTheory.CartesianMonoidalCategory.prodComparison_comp, CategoryTheory.Limits.Cones.postcomposeEquivalence_counitIso, SimplexCategory.revCompRevIso_inv_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app, CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj_inv_app, AlgebraicGeometry.ι_left_coprodIsoSigma_inv, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_hom_app_fst_app, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₂, CategoryTheory.Limits.walkingSpanOpEquiv_counitIso_hom_app, postcomposeWhiskerLeftMapCone_inv_hom, CategoryTheory.CostructuredArrow.instFullCompPre, TopCat.uliftFunctorCompForgetIso_inv_app, Initial.limitConeComp_cone, LightCondSet.instEpiTopCatAppCounitTopCatAdjunction, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_one, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquiv_inverse, CategoryTheory.CostructuredArrow.toOver_map_left, CategoryTheory.Limits.Cones.functorialityEquivalence_unitIso, CategoryTheory.Limits.compCoyonedaSectionsEquiv_symm_apply_coe, constCompWhiskeringLeftIso_hom_app_app, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply', CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app_assoc, CategoryTheory.Adjunction.corepresentableBy_homEquiv, CategoryTheory.Over.postComp_inv_app_left, CategoryTheory.TwoSquare.whiskerBottom_app, CochainComplex.shiftFunctorAdd'_inv_app_f', CategoryTheory.Limits.Cocone.equivStructuredArrow_unitIso, pointedToTwoPFst_comp_forget_to_bipointed, Initial.conesEquiv_unitIso, CategoryTheory.Sigma.natTrans_app, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counit_app_assoc, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_app, CategoryTheory.Sieve.functorPushforward_inverse, CategoryTheory.Presheaf.isLocallyInjective_whisker_iff, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_right, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_fst, CategoryTheory.Equivalence.congrFullSubcategory_unitIso, ShiftSequence.induced.shiftIso_hom_app_obj, CategoryTheory.Monad.mu_naturality, coreCompInclusionIso_hom_app, CategoryTheory.lift_comp_preservesLimitIso_hom, CategoryTheory.RanIsSheafOfIsCocontinuous.fac', AlgebraicTopology.DoldKan.N₂Γ₂ToKaroubiIso_hom_app, CategoryTheory.Over.toOverSectionsAdj_unit_app, CategoryTheory.Equivalence.changeInverse_counitIso_inv_app, CategoryTheory.Limits.comp_reflectsFilteredColimits, commShiftIso_hom_naturality_assoc, CategoryTheory.Limits.IndObjectPresentation.yoneda_isColimit_desc, groupCohomology.resNatTrans_app, CategoryTheory.Presheaf.tautologicalCocone'_pt, CategoryTheory.shiftFunctorAdd'_zero_add_hom_app, comp_mapCommMon_mul, CategoryTheory.whiskering_preadditiveYoneda, CategoryTheory.Comonad.Coalgebra.coassoc, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app, lanCompColimIso_inv_app, CategoryTheory.Limits.opCospan_hom_app, mapTriangleCommShiftIso_hom_app_hom₃, CategoryTheory.Adjunction.comp_counit_app, CategoryTheory.isSheaf_pointwiseColimit, CategoryTheory.SingleFunctors.shiftIso_add_inv_app, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π, isLeftDerivedFunctor_of_inverts, CategoryTheory.lan_preservesFiniteLimits_of_preservesFiniteLimits, ShiftSequence.induced_shiftIso_hom_app_obj_assoc, CategoryTheory.Localization.SmallShiftedHom.equiv_shift', CategoryTheory.functorProdToProdFunctor_obj, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.functorToInterchangeIso_hom_app_app, CategoryTheory.Cat.opFunctorInvolutive_hom_app_toFunctor_map, CategoryTheory.ObjectProperty.isColocal_adj_counit_app, AlgebraicGeometry.ΓSpec.unop_locallyRingedSpaceAdjunction_counit_app', CategoryTheory.Monad.mu_naturality_assoc, CategoryTheory.functorProdFunctorEquivUnitIso_hom_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_inv_app_hom, ι_colimitIsoOfIsLeftKanExtension_hom, commShiftIso_comp_inv_app, TwoP.swapEquiv_counitIso_inv_app_hom_toFun, CategoryTheory.Adjunction.mkOfHomEquiv_unit_app, CategoryTheory.CostructuredArrow.instFaithfulCompObjPost, sumIsoExt_hom_app_inr, AlgebraicTopology.DoldKan.compatibility_N₂_N₁_karoubi, CategoryTheory.IsUniversalColimit.whiskerEquivalence, HomotopicalAlgebra.CofibrantObject.instIsLocalizationCompHoCatToHoCatWeakEquivalences, op_comp_isSheaf_of_types, CategoryTheory.Cat.opFunctorInvolutive_hom_app_toFunctor_obj, CategoryTheory.Limits.spanCompIso_inv_app_right, CategoryTheory.GlueData.diagramIso_inv_app_right, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_app_assoc, CategoryTheory.Subobject.lower_comm, CategoryTheory.WithTerminal.lift_map_liftStar, CategoryTheory.WithTerminal.inclLiftToTerminal_inv_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app, CategoryTheory.Adjunction.leftAdjointCompIso_inv_app, CategoryTheory.Sheaf.adjunction_counit_app_val, CategoryTheory.Equivalence.mapCommMon_unitIso, CategoryTheory.CatCommSq.vComp_iso_hom_app, CategoryTheory.Limits.Cones.functoriality_obj_pt, mapCochainComplexShiftIso_inv_app_f, CategoryTheory.LocalizerMorphism.commShift_iso_inv_app_assoc, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_ε, CategoryTheory.LocalizerMorphism.equiv_smallHomMap', map_shiftFunctorCompIsoId_inv_app_assoc, CochainComplex.shiftFunctorAdd'_inv_app_f, CategoryTheory.Presheaf.isLeftKanExtension_along_uliftYoneda_iff, leftDerivedNatTrans_app_assoc, CategoryTheory.Sigma.descUniq_inv_app, CategoryTheory.preservesColimitNatIso_hom_app, CategoryTheory.MonoidalCategory.externalProductCompDiagIso_inv_app_app, LeftExtension.postcompose₂_obj_right_obj, CategoryTheory.Cat.HasLimits.limitConeX_str, prod'CompFst_inv_app, partOrdEmb_dual_comp_forget_to_pardOrd, whiskeringLeft₂_obj_map_app_app_app, AlgebraicGeometry.IsZariskiLocalAtTarget.coprodMap, CategoryTheory.Over.post_comp, AlgebraicGeometry.IsFinite.instDescScheme, mapTriangleCommShiftIso_inv_app_hom₃, CategoryTheory.Comonad.comparisonForget_inv_app, CategoryTheory.Equivalence.changeInverse_unitIso_inv_app, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_hom, CategoryTheory.prod.rightUnitorEquivalence_counitIso, CategoryTheory.Limits.compCoyonedaSectionsEquiv_apply_app, isoSum_hom_app_inl, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_hom_app, pentagonIso_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompPointIso_inv_app, CategoryTheory.WithTerminal.equivComma_functor_obj_hom_app, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso_inv_app_f, CategoryTheory.Over.toOverSectionsAdj_counit_app, AlgebraicGeometry.Scheme.Hom.inl_normalizationCoprodIso_hom_fromNormalization_assoc, pointedToBipointedCompBipointedToPointedSnd_hom_app_toFun, CategoryTheory.Presheaf.isLocallyInjective_forget_iff, CategoryTheory.Adjunction.IsMonoidal.instIsMonoidalUnit, CategoryTheory.instIsCofilteredElementsCompOfRepresentablyFlat, CategoryTheory.Limits.Cocones.reflects_cocone_isomorphism, CategoryTheory.Join.mapPairComp_inv_app_right, CategoryTheory.CartesianClosed.uncurry_eq, map_shiftFunctorComm_assoc, CategoryTheory.Triangulated.TStructure.triangleLTGE_map_hom₃, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_hom_app_coe, ShiftSequence.induced_isoShiftZero_hom_app_obj_assoc, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompYoneda, CategoryTheory.forgetAdjToOver_unit_app, CategoryTheory.Monoidal.associator_hom, IsCoverDense.Types.appHom_restrict, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.e_hom_app, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_hom_eq_germ_apply, AddCommGrpCat.Colimits.quotToQuotUlift_ι, CategoryTheory.Limits.colimitHomIsoLimitYoneda_hom_comp_π_assoc, 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, map_shiftFunctorCompIsoId_hom_app_assoc, CategoryTheory.ShiftMkCore.assoc_inv_app_assoc, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₁, CategoryTheory.Over.iteratedSliceEquivOverMapIso_hom_app_left_left, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.functor_obj, CategoryTheory.Comma.mapLeftComp_inv_app_right, nonemptyFinLinOrd_dual_comp_forget_to_linOrd, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalence_functor, CategoryTheory.Comma.equivProd_counitIso_inv_app, CategoryTheory.Comma.isEquivalence_preLeft, CategoryTheory.CostructuredArrow.map₂_map_right, CategoryTheory.Comma.coconeOfPreserves_ι_app_right, CategoryTheory.Comma.toIdPUnitEquiv_unitIso_hom_app_right, AlgebraicGeometry.HasAffineProperty.coprodDesc_affineAnd, HomologicalComplex₂.instHasTotalIntObjUpCompShiftFunctor₂ShiftFunctor₁, reflectsMonomorphisms_comp, CategoryTheory.Adjunction.toMonad_μ, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_left, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counitIso_hom_app, CategoryTheory.StructuredArrow.toUnder_map_right, MulEquiv.toSingleObjEquiv_unitIso_inv, CategoryTheory.Presheaf.isLocallySurjective_iff_range_sheafify_eq_top, CategoryTheory.Join.mapPairLeft_inv_app, CategoryTheory.cosimplicialSimplicialEquiv_counitIso_inv_app_app, commShiftIso_hom_naturality, ModuleCat.uliftFunctorForgetIso_inv_app, CategoryTheory.Comonad.adj_counit, CommShift.comp_commShiftIso_hom_app, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatTrans_comp, precomposeWhiskerLeftMapCocone_hom_hom, CategoryTheory.ComposableArrows.opEquivalence_unitIso_hom_app, CategoryTheory.TwoSquare.hComp_app, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_left_right_as, CategoryTheory.TwoSquare.natTrans_op, CategoryTheory.SimplicialObject.isCoskeletal_iff, CategoryTheory.Limits.Cocone.toOver_pt, CategoryTheory.Adjunction.adjunctionOfEquivRight_unit_app, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_app_app_germToPullbackStalk_assoc, AddGrpCat.hasLimit_iff_small_sections, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_hom_app_app_hom_hom, AlgebraicTopology.DoldKan.N₂Γ₂_compatible_with_N₁Γ₀, CategoryTheory.CostructuredArrow.pre_obj_right, CategoryTheory.Bimon.ofMonComon_toMonComon_obj_counit, CategoryTheory.Adjunction.unop_counit, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorEquivalence_unitIso, AlgebraicGeometry.Scheme.restrictFunctorΓ_hom_app, CategoryTheory.Comma.coconeOfPreserves_pt_hom, uncurryObjFlip_inv_app, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_inv_app_hom, CategoryTheory.CatCommSq.iso_inv_naturality_assoc, colimitTypePrecomp_ιColimitType, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τr, CategoryTheory.TwoSquare.isIso_lanBaseChange_app_iff, CategoryTheory.TwoSquare.instIsIsoFunctorLanBaseChangeOfGuitartExact, CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_left, instIsRepresentableCompOppositeUliftFunctor, AlgebraicGeometry.instIsIsoSchemeAppUnitOppositeCommRingCatAdjunctionOfIsAffine, rightDerivedNatTrans_fac, CategoryTheory.Localization.liftNatTrans_app, smoothSheafCommRing.ι_forgetStalk_inv_apply, CategoryTheory.Limits.Cones.functoriality_faithful, CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod_fac₁, CategoryTheory.ULift.equivalence_unitIso_hom, PresheafOfModules.unitHomEquiv_apply_coe, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.F_map, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.counitIso_hom_app_app_hom, CategoryTheory.Mat_.embeddingLiftIso_inv_app, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_counitIso_inv_app_f, CategoryTheory.Under.forgetMapInitial_hom_app, Condensed.lanPresheafNatIso_hom_app, CategoryTheory.Limits.fiberwiseColim_map_app, triangle, instIsLeftDerivedFunctorLiftHomFac, CategoryTheory.sum.inrCompInrCompInverseAssociator_inv_app_down, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_hom_π, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_pt, CategoryTheory.Limits.colimCompFlipIsoWhiskerColim_hom_app_app, CategoryTheory.Discrete.sumEquiv_counitIso_hom_app, leftKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, IsLocalization.instCompOfIsEquivalence, isoWhiskerLeft_right_assoc, CategoryTheory.ShortComplex.opEquiv_counitIso, CategoryTheory.Limits.comp_preservesColimits, CategoryTheory.ReflQuiv.forget_forgetToQuiv, AlgebraicGeometry.Scheme.Modules.pushforwardComp_hom_app_app, CategoryTheory.Equivalence.cancel_counitInv_right_assoc, CategoryTheory.Mon.limitCone_π_app_hom, CategoryTheory.Comma.limitAuxiliaryCone_π_app, CategoryTheory.StructuredArrow.isEquivalence_post, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι_assoc, CategoryTheory.Limits.limit.post_π_assoc, CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_map_left, postcompose₃_map_app_app_app_app, AlgebraicGeometry.Scheme.Hom.inl_normalizationCoprodIso_hom_fromNormalization, bddLat_dual_comp_forget_to_semilatSupCat, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_iso_hom_app, CategoryTheory.WithInitial.equivComma_functor_map_right_app, CategoryTheory.frobeniusMorphism_iso_of_preserves_binary_products, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply, CategoryTheory.DifferentialObject.shiftFunctorAdd_hom_app_f, CategoryTheory.Codiscrete.adj_counit_app, CategoryTheory.Over.postEquiv_counitIso, CategoryTheory.ChosenPullbacksAlong.pullbackId_hom_counit, CategoryTheory.ι_colimitCompWhiskeringRightIsoColimitComp_hom, GrpCat.hasLimit_iff_small_sections, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_hom_app_hom_left, ranObjObjIsoLimit_inv_π_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_hom_app_app, CategoryTheory.OplaxFunctor.mapComp_assoc_right_app_assoc, precomposeWhiskerLeftMapCocone_inv_hom, CategoryTheory.Cat.HasLimits.id_def, CategoryTheory.Monoidal.whiskerLeft_snd, CategoryTheory.Quiv.pathComposition_naturality, CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_ω₁, Rep.resIndAdjunction_counit_app, ContAction.resComp_hom, RightExtension.precomp_obj_right, CategoryTheory.Adjunction.rightOp_counit, comp_mapCommGrp_mul, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_inv_π_assoc, mapCoconePrecomposeEquivalenceFunctor_hom_hom, CategoryTheory.Limits.fiberwiseColimitLimitIso_inv_app, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatIso_hom, IsCoverDense.Types.appIso_inv, CategoryTheory.MonoidalOpposite.tensorRightUnmopIso_inv_app, pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_assoc, HomologicalComplex₂.flipEquivalenceUnitIso_inv_app_f_f, CategoryTheory.CosimplicialObject.Truncated.whiskering_obj_map_app, CategoryTheory.Idempotents.whiskeringLeft_obj_preimage_app, 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.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.isoAux_hom_app, AlgebraicGeometry.Scheme.Hom.preservesLocalization_normalizationDiagramMap, Monoidal.tensorObjComp_inv_app, final_iff_equivalence_comp, CategoryTheory.Adjunction.functorialityCounit_app_hom, op_commShiftIso_inv_app_assoc, OplaxMonoidal.ofBifunctor.topMapᵣ_app, StalkSkyscraperPresheafAdjunctionAuxs.unit_app, Profinite.Extend.functor_obj, ModuleCat.RestrictionCoextensionAdj.unit'_app, ModuleCat.matrixEquivalence_unitIso, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₂, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_id, AlgebraicGeometry.ΓSpec.isIso_locallyRingedSpaceAdjunction_counit, CategoryTheory.Abelian.LeftResolution.instEpiKaroubiAppπObjToKaroubi, CategoryTheory.prod.prodFunctorToFunctorProdAssociator_inv_app_app, CategoryTheory.LocalizerMorphism.hasPointwiseRightDerivedFunctor_iff_of_isRightDerivabilityStructure, mapGrpCompIso_hom_app_hom_hom, map_shiftFunctorCompIsoId_hom_app, LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom_assoc, CategoryTheory.Subfunctor.range_eq_ofSection', mapTriangleInvRotateIso_inv_app_hom₂, FullyFaithful.homNatIso'_hom_app_down, CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence_inv, Initial.extendCone_map_hom, CategoryTheory.Comonad.comparisonForget_hom_app, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_obj_X₁, SheafOfModules.conjugateEquiv_pullbackComp_inv, CategoryTheory.NatTrans.CommShiftCore.shift_app_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_inv_app_snd_app, AlgebraicTopology.DoldKan.whiskerLeft_toKaroubi_N₂Γ₂_hom, CategoryTheory.Sieve.functorPushforward_comp, CategoryTheory.NatTrans.IsMonoidal.whiskerRight, CategoryTheory.WithTerminal.liftFromOverComp_hom_app, CategoryTheory.equivToOverUnit_counitIso, CategoryTheory.Limits.colimit.map_post, corepresentableByUliftFunctorEquiv_symm_apply_homEquiv, SSet.Truncated.HomotopyCategory.BinaryProduct.mapHomotopyCategory_prod_id_comp_inverse, CategoryTheory.shiftFunctorAdd'_add_zero, AlgebraicGeometry.instIsOpenImmersionMapScheme, essImage_comp_apply_of_essSurj, CategoryTheory.shiftFunctorCompIsoId_add'_hom_app, AlgebraicGeometry.sigmaι_eq_iff, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_comp, CategoryTheory.MonadHom.app_μ_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_iso_hom_app, CategoryTheory.Limits.colimitFlipIsoCompColim_hom_app, CategoryTheory.Equivalence.invFunIdAssoc_inv_app, CategoryTheory.Monad.Algebra.assoc, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.leftUnitor_hom_unit_app, CategoryTheory.Cokleisli.Adjunction.fromCokleisli_map, CategoryTheory.SimplicialObject.instIsIsoAppUnitTruncatedCoskAdj, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_app_app, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_right_as, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_obj, CategoryTheory.MorphismProperty.Over.mapComp_hom_app_left, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₂, CategoryTheory.GrothendieckTopology.sheafToPresheaf_map_sheafComposeNatTrans_eq_sheafifyCompIso_inv, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_inv_app_zero, CategoryTheory.toOverIteratedSliceForwardIsoPullback_hom_app_left, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.unitIso_hom_app_hom_app, PrincipalSeg.cocone_pt, CommShift₂.comm, MonObj.mopEquiv_counitIso_hom_app_hom_unmop, CategoryTheory.pullbackShiftFunctorAdd'_hom_app, Accessible.Limits.isColimitMapCocone.surjective, CategoryTheory.Under.mapComp_hom, limitIsoOfIsRightKanExtension_hom_π_assoc, PresheafOfModules.freeAdjunctionUnit_app, LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv_assoc, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_inv_app, leftExtensionEquivalenceOfIso₁_counitIso_inv_app_right_app, CategoryTheory.Bimon.ofMon_Comon_toMon_Comon_obj_comul, CategoryTheory.ExponentiableMorphism.ev_coev_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_map_left_app, CategoryTheory.Presheaf.isLocallySurjective_iff_whisker_forget, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_hom, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_right_right, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_left_hom, isoWhiskerLeft_inv, isIso_of_isLeftDerivedFunctor_of_inverts, CategoryTheory.shiftFunctorZero_inv_app_shift, CategoryTheory.ObjectProperty.fullSubcategoryCongr_counitIso, CategoryTheory.Presheaf.isSheaf_iff_isLimit, CategoryTheory.Monad.algebra_equiv_of_iso_monads_comp_forget, CategoryTheory.Bimon.equivMonComonUnitIsoAppXAux_inv, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_right_left_as, CategoryTheory.WithInitial.equivComma_functor_obj_hom_app, essImage.unit_isIso, Initial.conesEquiv_inverse, CategoryTheory.Quiv.freeMap_pathsOf_pathComposition, CategoryTheory.Adjunction.commShiftIso_inv_app_counit_app_assoc, SSet.Truncated.HomotopyCategory.BinaryProduct.functor_comp_inverse, leftKanExtension_hom_ext_iff, CategoryTheory.CostructuredArrow.prodEquivalence_unitIso, CategoryTheory.Limits.Cones.whiskeringEquivalence_counitIso, CategoryTheory.Grothendieck.pre_obj_base, CommShift.id_commShiftIso_inv_app, CategoryTheory.Limits.isIndObject_limit_comp_yoneda, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_app_snd_app, CategoryTheory.TransfiniteCompositionOfShape.ici_isoBot, CategoryTheory.Limits.limit.post_post, commShiftIso_inv_naturality_assoc, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₃, HomotopicalAlgebra.CofibrantObject.instIsIsoFunctorWhiskerRightHoCatιCompResolutionNatTransOfIsLocalizationWeakEquivalences, AlgebraicGeometry.instSurjectiveDescI₀SchemeF, whiskerLeft_twice, MulEquiv.toSingleObjEquiv_counitIso_inv, CategoryTheory.skeletonEquivalence_counitIso, CategoryTheory.Limits.Cocone.toCostructuredArrowCocone_ι_app, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_right, CategoryTheory.Limits.PushoutCocone.op_π_app, CategoryTheory.Equivalence.congrLeft_unitIso_inv_app, CategoryTheory.shiftFunctorAdd'_assoc_inv_app_assoc, LeftExtension.postcompose₂ObjMkIso_hom_right_app, CategoryTheory.MonoidalOpposite.unmopEquiv_counitIso_hom_app, CategoryTheory.Comonad.ForgetCreatesLimits'.newCone_π, CategoryTheory.mateEquiv_symm_apply, sheafPushforwardContinuousComp_inv_app_val_app, CategoryTheory.exp.ev_coev, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap_assoc, CategoryTheory.WithInitial.commaFromUnder_obj_hom_app, CategoryTheory.Equivalence.cancel_unit_right_assoc, CategoryTheory.Limits.comp_preservesColimitsOfShape, CompHausLike.LocallyConstant.adjunction_left_triangle, ranCounit_app_app_ranAdjunction_unit_app_app_assoc, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app, AlgebraicTopology.DoldKan.toKaroubiCompN₂IsoN₁_hom_app, mapTriangleInvRotateIso_inv_app_hom₁, CategoryTheory.Equivalence.mapGrp_unitIso, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_left, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_hom_app_app_snd, CategoryTheory.Adjunction.ε_comp_map_ε, CategoryTheory.NatIso.unop_whiskerRight, CategoryTheory.Adjunction.counit_epi_of_R_faithful, CategoryTheory.WithTerminal.inclLift_inv_app, CategoryTheory.Join.InclLeftCompRightOpOpEquivFunctor_hom_app, CategoryTheory.Iso.isoFunctorOfIsoInverse_inv_app, CategoryTheory.Cat.opFunctorInvolutive_inv_app_toFunctor_map, leftOpRightOpEquiv_unitIso_hom_app, HomotopicalAlgebra.CofibrantObject.instIsIsoFunctorHoCatAdjCounit', Final.extendCocone_obj_ι_app', OrderIso.equivalence_counitIso, CategoryTheory.Presheaf.uliftYonedaAdjunction_homEquiv_app, CategoryTheory.WithInitial.commaFromUnder_obj_right, CategoryTheory.Equivalence.counitInv_app_comp_functor_map_η_inverse, SheafOfModules.pullback_id_comp, CategoryTheory.TransfiniteCompositionOfShape.iic_F, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIso_inv_app_hom, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_hom_app_val_app, CategoryTheory.Adjunction.whiskerLeft_counit_iso_of_L_fully_faithful, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.forgetToTop_preservesPullback_of_left, CategoryTheory.Join.mapWhiskerRight_associator_hom, CategoryTheory.CartesianClosed.uncurry_id_eq_ev, leftKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, CategoryTheory.CostructuredArrow.grothendieckProj_map, IsCoverDense.restrictHomEquivHom_naturality_right_assoc, CategoryTheory.SimplicialObject.whiskering_map_app_app, CategoryTheory.toOverPullbackIsoToOver_hom_app_left, SSet.Truncated.hoFunctor₂_naturality, CategoryTheory.Monad.beckCofork_pt, RightExtension.postcomp₁_map_left_app, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π_assoc, CategoryTheory.shiftFunctorAdd'_add_zero_hom_app, FGModuleCat.instFiniteCarrierColimitModuleCatCompForget₂LinearMapIdObjIsFG, CategoryTheory.Comma.toIdPUnitEquiv_counitIso_hom_app, CategoryTheory.Limits.walkingSpanOpEquiv_unitIso_inv_app, CategoryTheory.LocalizerMorphism.homMap_apply_assoc, pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.Limits.comp_preservesLimit, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_obj_iso_inv, HomotopicalAlgebra.CofibrantObject.instIsIsoFunctorHoCatCounitHoCatAdj, CategoryTheory.Limits.Cocones.functoriality_obj_ι_app, CategoryTheory.Limits.opCospan_inv_app, CategoryTheory.Equivalence.congrLeft_unitIso_hom_app, CategoryTheory.Grothendieck.grothendieckTypeToCatFunctor_obj_fst, CategoryTheory.preservesColimitIso_inv_comp_desc_assoc, CategoryTheory.Comma.mapRightComp_hom_app_left, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_left, commAlgCatEquivUnder_counitIso, CategoryTheory.ExponentiableMorphism.pushforwardComp_hom_counit_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_inv_app_snd_app, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_app, CategoryTheory.MonoidalClosed.id_tensor_pre_app_comp_ev_assoc, CategoryTheory.sum.inlCompAssociator_hom_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.forgetToPresheafedSpace_preservesPullback_of_left, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₂, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_inv_app_val_app, mapTriangleRotateIso_hom_app_hom₃, CategoryTheory.ReflQuiv.adj.homEquiv_naturality_left_symm, CategoryTheory.conjugateEquiv_counit, CategoryTheory.NatTrans.CommShiftCore.shift_app_comm_assoc, AlgebraicGeometry.Scheme.Hom.inr_normalizationCoprodIso_hom_fromNormalization_assoc, CategoryTheory.SimplicialObject.Truncated.rightExtensionInclusion_right_as, CategoryTheory.StructuredArrow.post_map, CategoryTheory.whiskerRight_ι_colimitCompWhiskeringRightIsoColimitComp_inv_assoc, Initial.limit_cone_comp_aux, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_left, sheafPushforwardCocontinuousCompSheafToPresheafIso_inv, CategoryTheory.Grpd.freeForgetAdjunction_counit_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_whiskerLeft, CategoryTheory.Adjunction.unit_isIso_of_L_fully_faithful, LaxMonoidal.ofBifunctor.topMapᵣ_app, CategoryTheory.TwoSquare.hCompVCompHComp, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_X, CategoryTheory.Bimon.instIsMonHomHomEquivMonComonUnitIsoAppXAux, CategoryTheory.Equivalence.unitInv_app_inverse, HomotopicalAlgebra.CofibrantObject.instIsIsoFunctorResolutionCompToLocalizationNatTrans, CategoryTheory.Equivalence.sheafCongr.functor_map_val_app, CategoryTheory.Limits.pointwiseProductCompEvaluation_inv_app, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_counitIso_hom, CategoryTheory.Monad.instHasCoequalizerMapAAppCounitObjAOfHasCoequalizerOfIsSplitPair, ranObjObjIsoLimit_hom_π_assoc, sheafPushforwardContinuousComp_hom_app_val_app, CategoryTheory.ExactFunctor.whiskeringRight_obj_obj_obj, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatTrans_id, CategoryTheory.CostructuredArrow.ofCommaFstEquivalence_functor, Condensed.instFinalOppositeDiscreteQuotientCarrierToTopTotallyDisconnectedSpaceCostructuredArrowFintypeCatProfiniteOpToProfiniteOpPtAsLimitConeFunctorOp, AddCommMonCat.instSmallElemForallObjCompMonCatForget₂AddMonoidHomCarrierCarrierForgetSections, CochainComplex.shiftFunctorAdd_inv_app_f, CategoryTheory.Adjunction.compPreadditiveYonedaIso_hom_app_app_apply, CategoryTheory.Limits.IndObjectPresentation.yoneda_ι_app, TopologicalSpace.Opens.overEquivalence_counitIso_inv_app, CategoryTheory.Triangulated.Octahedron.map_m₁, CategoryTheory.uncurry_pre, CategoryTheory.Limits.colimIsoFlipCompWhiskerColim_hom_app_app, CategoryTheory.ReflQuiv.adj_counit_app, CategoryTheory.Equivalence.ext_iff, CategoryTheory.sum.inrCompInlCompAssociator_inv_app_down_down, id_comp, PreservesPointwiseLeftKanExtensionAt.preserves, CategoryTheory.Under.equivalenceOfIsInitial_unitIso, CategoryTheory.whiskeringRightCompEvaluation_hom_app, CategoryTheory.shiftFunctorAdd_assoc_hom_app_assoc, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalence_inverse, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₁, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₂, CategoryTheory.NatTrans.CommShiftCore.shift_comm, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app, CategoryTheory.instIsIsoAppUnitReflectorAdjunctionObjEssImage, CategoryTheory.ihom.coev_naturality_assoc, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd, preservesEpimorphisms_comp, CategoryTheory.Equivalence.symmEquivInverse_obj_counitIso_inv, CategoryTheory.Monad.free_obj_a, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₁, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_inv_π, CategoryTheory.conjugateEquiv_rightUnitor_hom, bddLat_dual_comp_forget_to_semilatInfCat, CategoryTheory.LocalizerMorphism.equiv_smallShiftedHomMap, CategoryTheory.FreeGroupoid.mapComp_inv_app, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₁, CategoryTheory.Adjunction.unit_app_shift_commShiftIso_inv_app_assoc, TopologicalSpace.Opens.adjunction_counit_map_functor, AlgebraicGeometry.coprodSpec_coprodMk, commShiftIso_map₂CochainComplex_inv_app, CategoryTheory.Adjunction.unit_isSplitEpi_of_L_full, commShiftOfLocalization.iso_inv_app_assoc, CategoryTheory.Limits.PullbackCone.unop_ι_app, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_inv_app_hom, isDenseAt_iff, CoalgCat.comonEquivalence_unitIso, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality_assoc, PresheafOfModules.Derivation'.d_app, CategoryTheory.exp.ev_coev_assoc, CategoryTheory.Adjunction.op_unit, CategoryTheory.Bimon.equivMonComonCounitIsoAppX_hom_hom, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_inv_app, IsCoverDense.Types.presheafIso_inv_app, CategoryTheory.cosimplicialSimplicialEquiv_unitIso_hom_app, CategoryTheory.Monad.ForgetCreatesColimits.coconePoint_A, CategoryTheory.Join.inclRightCompOpEquivInverse_hom_app_op, FullyFaithful.comp_preimage, initial_iff_comp_equivalence, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_comp_functor, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_map_fst_app, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_map_right, CategoryTheory.Limits.cospanOp_hom_app, CategoryTheory.Sheaf.isConstant_iff_isIso_counit_app', CategoryTheory.shiftFunctorZero_hom_app_shift, CategoryTheory.NatIso.op_associator, core_comp_inclusion, ModuleCat.homEquiv_extendScalarsComp, CategoryTheory.Equivalence.changeFunctor_unitIso_inv_app, CategoryTheory.unitOfTensorIsoUnit_inv_app, TopologicalSpace.Opens.overEquivalence_unitIso_inv_app_left, AlgebraicGeometry.instMonoObjWalkingSpanCompSchemeSpanForgetNoneWalkingPairSomeMapInitOfIsOpenImmersion, CategoryTheory.Adjunction.hasLimit_comp_equivalence, CategoryTheory.sum.inlCompInlCompAssociator_inv_app_down, CategoryTheory.Grothendieck.pre_comp_map, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_counitIso, CategoryTheory.ShiftedHom.comp_map, smoothSheafCommRing.ι_forgetStalk_inv_assoc, CategoryTheory.Monoidal.transportStruct_leftUnitor, skyscraperPresheafCocone_ι_app, CategoryTheory.Adjunction.CommShift.compatibilityCounit_left, LeftExtension.coconeAtFunctor_obj, flipping_unitIso_hom_app_app_app, CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_obj_hom, CategoryTheory.StructuredArrow.pre_map_left, op_commShiftIso_inv_app, CategoryTheory.Comma.unopFunctorCompSnd_inv_app, PresheafOfModules.map_comp, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_tensorDesc_app_assoc, CategoryTheory.Sieve.mem_functorPushforward_inverse, bijective_colimitTypePrecomp, CategoryTheory.Monoidal.transportStruct_rightUnitor, instIsRightKanExtensionObjRanAppRanCounit, isContinuous_comp, CategoryTheory.LocalizerMorphism.guitartExact_of_isLeftDerivabilityStructure', TopCat.hasColimit_iff_small_colimitType, CategoryTheory.ShiftedHom.opEquiv'_symm_apply, CategoryTheory.Comonad.coassoc_assoc, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_ihom_ev_app, CategoryTheory.ExponentiableMorphism.ev_naturality_assoc, CategoryTheory.Limits.colimitPointwiseProductToProductColimit_app, mapCone_pt, CategoryTheory.Idempotents.DoldKan.η_inv_app_f, CategoryTheory.GrothendieckTopology.W_whiskerLeft_iff, AddCommGrpCat.kernelIsoKer_inv_comp_ι, CategoryTheory.Adjunction.Triple.adj₁_counit_app_rightToLeft_app_assoc, CategoryTheory.Limits.limit.map_post, CategoryTheory.GrothendieckTopology.diagramPullback_app, CategoryTheory.Over.opEquivOpUnder_counitIso, CategoryTheory.Comma.coconeOfPreserves_ι_app_left, closedUnit_app_app, CategoryTheory.ProdPreservesConnectedLimits.forgetCone_pt, CategoryTheory.Adjunction.IsTriangulated.comp, LeftExtension.coconeAtWhiskerRightIso_hom_hom, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_hom_app_left, CategoryTheory.plusPlusAdjunction_counit_app_val, CategoryTheory.Monad.ForgetCreatesColimits.newCocone_pt, instIsEquivalenceLeftExtensionCompPrecomp, CategoryTheory.NatTrans.CommShiftCore.shift_comm_assoc, equiv_unitIso, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_symm_apply, TopologicalSpace.Opens.adjunction_counit_app_self, AlgebraicGeometry.instIsOpenImmersionMapSchemeCompOverOverTopMorphismPropertyForgetForget, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_app, mapHomologicalComplex_commShiftIso_inv_app_f, CategoryTheory.uncurry_expComparison, leftExtensionEquivalenceOfIso₁_inverse_obj_hom_app, CategoryTheory.Comonad.left_comparison, precomp_map_heq, sheafPushforwardCocontinuousCompSheafToPresheafIso_hom, CompHausOpToFrame.faithful, CategoryTheory.Idempotents.KaroubiUniversal₁.counitIso_hom_app_app_f, CommShift.id_commShiftIso_hom_app, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₃, CategoryTheory.Adjunction.commShiftIso_hom_app_counit_app_shift_assoc, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_ε_assoc, CategoryTheory.Limits.Cones.functoriality_full, CategoryTheory.Triangulated.TStructure.triangleLTGE_map_hom₂, CategoryTheory.Coreflective.instIsIsoAppCounitCoreflectorAdjunctionA, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_app_assoc, SheafOfModules.pushforwardComp_hom_app_val_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_inv_app, CategoryTheory.Adjunction.functorialityUnit'_app_hom, CategoryTheory.Limits.colimit.ι_post_assoc, AlgebraicTopology.DoldKan.toKaroubiCompN₂IsoN₁_inv_app, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_unitIso_inv_app_f, OplaxMonoidal.comp_η, CategoryTheory.Idempotents.KaroubiUniversal₁.counitIso_inv_app_app_f, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorEquivalence_inverse, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app, CategoryTheory.MonoidalClosed.uncurry_ihom_map, CategoryTheory.Adjunction.rightAdjointUniq_hom_counit_assoc, CategoryTheory.Localization.Monoidal.isInvertedBy₂, TopCat.Presheaf.stalkFunctor_preserves_mono, isoWhiskerLeft_trans_isoWhiskerRight_assoc, TopCat.Presheaf.pullback_obj_obj_ext_iff, CategoryTheory.forgetEnrichmentOppositeEquivalence_counitIso, triangleIso_assoc, flipIsoCurrySwapUncurry_hom_app_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso_hom_app_app, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_map_left_right, CategoryTheory.SingleFunctors.postcomp_shiftIso_inv_app, CategoryTheory.shiftFunctorAdd_assoc_inv_app_assoc, AlgebraicGeometry.Scheme.ofRestrict_toLRSHom_c_app, CategoryTheory.yonedaGrpObjIsoOfRepresentableBy_hom, CategoryTheory.Limits.Cones.functoriality_map_hom, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_map_left_left, LeftExtension.precomp_obj_right, CategoryTheory.Limits.limitFlipIsoCompLim_inv_app, CategoryTheory.shiftFunctorAdd_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_hom_app, instIsHomologicalCompOfIsTriangulated, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_app_hom, CategoryTheory.toOverIsoToOverUnit_hom_app_left, LightCondMod.LocallyConstant.instIsIsoLightCondSetMapForgetAppLightCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, CategoryTheory.Adjunction.compYonedaIso_inv_app_app, CategoryTheory.GrothendieckTopology.preservesSheafification_iff_of_adjunctions_of_hasSheafCompose, CategoryTheory.yonedaGrpObjIsoOfRepresentableBy_inv, CategoryTheory.MonoidalClosed.uncurry_id_eq_ev, CategoryTheory.Comon.Comon_EquivMon_OpOp_unitIso, CategoryTheory.Equivalence.changeInverse_counitIso_hom_app, CategoryTheory.Limits.colimit.pre_desc_assoc, leftUnitor_inv_app, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₃, mapTriangleRotateIso_hom_app_hom₁, SheafOfModules.Presentation.map_relations_I, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.hasLimit_cospan_forget_of_right, coreCompInclusionIso_inv_app, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_inv, CategoryTheory.Sheaf.adjunction_unit_app_val, CategoryTheory.FreeGroupoid.liftNatIso_inv_app, CategoryTheory.Cat.comp_eq_comp, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceFunctor_obj_base, CategoryTheory.Limits.colimit.pre_desc, TopCat.Presheaf.generateEquivalenceOpensLe_counitIso, CategoryTheory.Equivalence.fun_inv_map, CategoryTheory.StructuredArrow.mapIso_unitIso_inv_app_right, whiskeringRight₂_map_app_app_app, CategoryTheory.Cat.leftUnitor_hom_toNatTrans, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app_assoc, CategoryTheory.MonoidalOpposite.tensorLeftUnmopIso_hom_app, CategoryTheory.MonoidalCategory.DayConvolution.braidingInvCorepresenting_app, toUnder_comp_forget, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.flipFunctorToInterchange_inv_app_app, CategoryTheory.Limits.spanCompIso_hom_app_right, lanUnit_app_whiskerLeft_lanAdjunction_counit_app_assoc, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatIso_inv, Rep.invariantsAdjunction_counit_app_hom, isoWhiskerLeft_trans_assoc, CategoryTheory.Triangulated.TStructure.triangleLTGE_obj_mor₃, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_hom_π_π_assoc, ihom_coev_app, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₁, LightProfinite.Extend.functorOp_map, CategoryTheory.Monoidal.Reflective.instIsIsoAppUnitObjIhom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality_assoc, CategoryTheory.NatIso.unop_leftUnitor, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₂, MonObj.mopEquivCompForgetIso_inv_app_unmop, LeftExtension.postcompose₂_obj_left, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_counitIso, CategoryTheory.NatIso.unop_associator, rightDerivedNatTrans_app, sumIsoExt_inv_app_inl, CategoryTheory.coalgebraEquivOver_counitIso, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_hom_app_fst_app, CategoryTheory.IsVanKampenColimit.whiskerEquivalence, CategoryTheory.TransfiniteCompositionOfShape.ici_isColimit, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app_assoc, Alexandrov.lowerCone_π_app, final_comp, CategoryTheory.Limits.IndObjectPresentation.ofCocone_I, CategoryTheory.Limits.colimitLimitToLimitColimitCone_iso, CategoryTheory.Comma.opFunctorCompSnd_hom_app, CategoryTheory.RepresentablyCoflat.comp, CategoryTheory.NatTrans.IsMonoidal.instHomFunctorRightUnitor, RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π, CategoryTheory.Localization.SmallShiftedHom.equiv_shift, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map_d, LeftExtension.precomp_obj_left, CategoryTheory.instInitialCostructuredArrowCompPreOfRepresentablyCoflat, shiftIso_hom_naturality_assoc, TopologicalSpace.Opens.map_comp_eq, CategoryTheory.WithInitial.opEquiv_counitIso_inv_app, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_right, CategoryTheory.ShiftMkCore.add_zero_inv_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_obj, CategoryTheory.Limits.Cones.functorialityEquivalence_inverse, OplaxMonoidal.ofBifunctor.leftMapₗ_app, CategoryTheory.Limits.instHasLimitDiscreteOppositeCompInverseOppositeOpFunctor, CategoryTheory.HasShift.Induced.zero_hom_app_obj, Bipointed.swapEquiv_counitIso_inv_app_toFun, PresheafOfModules.Elements.fromFreeYoneda_app_apply, CategoryTheory.Localization.Monoidal.lifting₂CurriedTensorPost_iso, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.e_inv_app, flipping_unitIso_inv_app_app_app, CategoryTheory.liftedLimitMapsToOriginal_inv_map_π, CategoryTheory.Bimon.equivMonComonUnitIsoApp_inv_hom_hom, ModuleCat.HasColimit.coconePointSMul_apply, CategoryTheory.Bimon.ofMon_Comon_toMon_Comon_obj_counit, CategoryTheory.Adjunction.CoreUnitCounit.right_triangle, PresheafOfModules.pushforward_obj_obj, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_inv_app_one, CategoryTheory.Adjunction.shift_unit_app, CategoryTheory.Join.inclLeftCompOpEquivInverse_inv_app_op, CategoryTheory.TwoSquare.hasPointwiseLeftKanExtensionAt_iff, CategoryTheory.Adjunction.map_η_comp_η_assoc, CategoryTheory.Quotient.natIsoLift_hom, SheafOfModules.Presentation.mapRelations_mapGenerators, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app_assoc, CategoryTheory.ChosenPullbacksAlong.pullbackId_hom_counit_assoc, CategoryTheory.CostructuredArrow.instEssSurjCompObjPostOfFull, CategoryTheory.CommGrp.forget₂Grp_comp_forget, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_map_hom_hom_app, CategoryTheory.Comonad.Coalgebra.coassoc_assoc, AlgebraicGeometry.PresheafedSpace.colimit_presheaf, CategoryTheory.Adjunction.unit_app_commShiftIso_hom_app_assoc, SSet.Truncated.rightExtensionInclusion_left, FundamentalGroupoid.punitEquivDiscretePUnit_unitIso, CategoryTheory.Monad.algebraEquivOfIsoMonads_counitIso, CategoryTheory.Sigma.inclCompMap_hom_app, final_comp_equivalence, CategoryTheory.FreeGroupoid.lift_id_comp_of, AlgebraicTopology.map_alternatingFaceMapComplex, leftKanExtensionCompIsoOfPreserves_hom_fac, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso_hom_app_f, CategoryTheory.CostructuredArrow.preFunctor_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app_assoc, AlgebraicGeometry.Scheme.Hom.normalizationCoprodIso_inv_coprodDesc_fromNormalization, CategoryTheory.Limits.Cones.postcomposeComp_inv_app_hom, CategoryTheory.Preadditive.commGrpEquivalenceAux_inv_app_hom_hom_hom, leftExtensionEquivalenceOfIso₁_functor_obj_hom_app, CategoryTheory.Presieve.isSheafFor_over_map_op_comp_ofArrows_iff, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_map_right_right, map_opShiftFunctorEquivalence_counitIso_hom_app_unop, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_hom_app_val_app_apply, whiskerRight_zero, mapConePostcomposeEquivalenceFunctor_inv_hom, CategoryTheory.Limits.comp_preservesColimit, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_isoBot, CategoryTheory.NatIso.op_leftUnitor, whiskeringLeft₂_map_app_app_app_app, CategoryTheory.Equivalence.mapCommMon_counitIso, rightKanExtensionCompIsoOfPreserves_hom_fac, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app, CategoryTheory.Adjunction.inv_counit_map, pointedToBipointedCompBipointedToPointedSnd_inv_app_toFun, CategoryTheory.Presieve.isSheafFor_over_map_op_comp_iff, CategoryTheory.Adjunction.leftOp_counit, CategoryTheory.Monad.FreeCoequalizer.bottomMap_f, Monoidal.μ_comp, TopCat.Presheaf.presheafEquivOfIso_unitIso_inv_app_app, CategoryTheory.unit_mateEquiv_symm, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_right, CategoryTheory.Enriched.FunctorCategory.functorEnrichedComp_app, CategoryTheory.Cat.associator_inv_toNatTrans, CategoryTheory.Comma.post_obj_left, CategoryTheory.MonoidalOpposite.mopMopEquivalence_counitIso_inv_app, CategoryTheory.Equivalence.core_functor_map_iso_inv, SheafOfModules.relationsOfIsCokernelFree_I, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_map_left_left, CategoryTheory.Limits.Cone.toStructuredArrowCompProj_hom_app, CategoryTheory.Triangulated.SpectralObject.distinguished', AlgebraicGeometry.instIsOpenImmersionInlScheme, CategoryTheory.Equivalence.symmEquiv_counitIso, map_opShiftFunctorEquivalence_counitIso_inv_app_unop_assoc, CategoryTheory.Adjunction.isIso_unit_of_iso, CategoryTheory.MonoOver.congr_inverse, CategoryTheory.Adjunction.CommShift.instComp, CategoryTheory.Cat.leftUnitor_inv_toNatTrans, Monoidal.commTensorLeft_inv_app, CategoryTheory.Adjunction.Triple.epi_rightToLeft_app_iff, CategoryTheory.Pseudofunctor.map₂_left_unitor_app, CategoryTheory.Adjunction.rightAdjointUniq_hom_counit, CategoryTheory.Equivalence.cancel_unit_right_assoc', CategoryTheory.InjectiveResolution.isoRightDerivedObj_inv_naturality, commShiftOfLocalization.iso_hom_app, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_right, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_map_fst_app, CategoryTheory.Comonad.delta_naturality, fun_inv_map, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π, CategoryTheory.Iso.isoCompInverse_inv_app, CategoryTheory.NatTrans.app_shift_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality, postcompose₂_obj_map_app_app, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_unitIso, mapConePostcomposeEquivalenceFunctor_hom_hom, CategoryTheory.sum.inrCompAssociator_hom_app_down_down, CategoryTheory.cosimplicialSimplicialEquiv_unitIso_inv_app, bddLat_dual_comp_forget_to_bddOrd, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_limit_map, CategoryTheory.Limits.Cocones.functorialityEquivalence_counitIso, mapCone_π_app, CategoryTheory.yonedaMap_app_apply, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceFunctor_map_base, commAlgCatEquivUnder_unitIso, toSheafify_pullbackSheafificationCompatibility, CategoryTheory.Equivalence.mapMon_counitIso, BddLat.forget_lat_partOrd_eq_forget_bddOrd_partOrd, SimplexCategory.revCompRevIso_hom_app, IsCoverDense.Types.naturality_apply, CategoryTheory.MonoidalOpposite.tensorRightIso_hom_app_unmop, SimplicialObject.opFunctorCompOpFunctorIso_hom_app_app, CategoryTheory.Equivalence.induced_unitIso, CategoryTheory.Limits.limit_map_limitObjIsoLimitCompEvaluation_hom_assoc, CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.fac, CategoryTheory.NatTrans.rightOpWhiskerRight_assoc, instIsWellOrderContinuousCompFunctor, pointedToBipointedCompBipointedToPointedFst_inv_app_toFun, CategoryTheory.Iso.isoInverseOfIsoFunctor_inv_app, CategoryTheory.Comonad.comparison_map_f, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_π_app, CategoryTheory.Pretriangulated.Triangle.π₃Toπ₁_app, commShiftIso_id_hom_app, CategoryTheory.Grothendieck.ιCompMap_inv_app_base, CategoryTheory.ComposableArrows.whiskerLeftFunctor_map_app, CategoryTheory.Over.conePostIso_inv_app_hom, PreservesPointwiseRightKanExtensionAt.preserves, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_mapPullbackAdj_unit_app, shiftIso_hom_app_comp_assoc, CategoryTheory.algebraEquivUnder_unitIso, IsWellOrderContinuous.restriction_setIci, CategoryTheory.SimplicialObject.Truncated.trunc_map_app, CategoryTheory.Comonad.ComonadicityInternal.main_pair_coreflexive, AlgebraicGeometry.isOpenImmersion_sigmaDesc, CategoryTheory.prod.leftUnitorEquivalence_counitIso, CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_hom_π_π, curryObjCompIso_inv_app_app, CategoryTheory.Adjunction.Triple.leftToRight_app_map_adj₁_unit_app_assoc, CategoryTheory.Equivalence.core_counitIso_hom_app_iso_hom, CategoryTheory.ChosenPullbacksAlong.pullbackComp_hom_counit, TopCat.Presheaf.germ_stalkPullbackHom_assoc, CategoryTheory.Equivalence.inv_fun_map_assoc, TopCat.Presheaf.whiskerIsoMapGenerateCocone_hom_hom, AlgebraicGeometry.coprodSpec_inr_assoc, CategoryTheory.Equivalence.inverse_counitInv_comp_assoc, CategoryTheory.GrothendieckTopology.Cover.multicospanComp_hom_app, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_inv_app_val_app, HomotopicalAlgebra.CofibrantObject.HoCat.adjCounitIso_inv_app, CategoryTheory.WithTerminal.commaFromOver_obj_hom_app, ModuleCat.ihom_coev_app, AlgebraicGeometry.Scheme.IsLocallyDirected.instIsLocallyDirectedWidePushoutShapeCompForgetOfIsOpenImmersionMap, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app, IsRepresentedBy.uliftYonedaIso_hom, whiskerRight_id, CategoryTheory.Equivalence.core_inverse_map_iso_inv, SimplicialObject.opEquivalence_unitIso, CategoryTheory.functorProdToProdFunctor_map, rightKanExtensionCompIsoOfPreserves_inv_fac, leftOpComp_inv_app, instIsCorepresentableCompObjOppositeTypeCoyonedaOpObjLeftAdjointObjIsDefined, Rep.coinvariantsTensorIndNatIso_hom_app, CommShift.ofIso_commShiftIso_inv_app, CategoryTheory.CartesianMonoidalCategory.preservesTerminalIso_comp, CategoryTheory.MonObj.ofRepresentableBy_mul, CategoryTheory.Comma.opFunctorCompFst_hom_app, CategoryTheory.CostructuredArrow.instFaithfulCompPre, GrpCat.instSmallElemForallObjCompMonCatForget₂MonoidHomCarrierCarrierForgetSections, CategoryTheory.Equivalence.trans_counitIso, CategoryTheory.Over.iteratedSliceEquiv_unitIso, CategoryTheory.ComposableArrows.δlastFunctor_map_app, CategoryTheory.Comma.toPUnitIdEquiv_unitIso_hom_app_left, CategoryTheory.CatCommSq.vInv_iso_inv_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_naturality₂, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse_assoc, CommGrpCat.coyonedaForget_hom_app_app_hom, HomotopicalAlgebra.CofibrantObject.HoCat.adjUnit_app, CategoryTheory.SingleObj.mapHom_comp, constCompEvaluationObj_inv_app, CategoryTheory.Comma.mapRightIso_unitIso_hom_app_left, CategoryTheory.Limits.limitCompYonedaIsoCocone_inv, HomologicalComplex.singleMapHomologicalComplex_inv_app_ne, CategoryTheory.WithInitial.equivComma_unitIso_inv_app_app, CategoryTheory.PreGaloisCategory.FiberFunctor.comp_right, CategoryTheory.MonoidalOpposite.tensorRightIso_inv_app_unmop, CategoryTheory.Limits.fiberwiseColimCompEvaluationIso_hom_app, CategoryTheory.Limits.Fork.op_ι_app, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counitIso_hom_app_assoc, CategoryTheory.IsVanKampenColimit.whiskerEquivalence_iff, CategoryTheory.functorProdFunctorEquivCounitIso_inv_app_app, CategoryTheory.RelCat.opEquivalence_counitIso, CategoryTheory.ι_preservesColimitIso_hom, CategoryTheory.instHasSmallLocalizedShiftedHomHomologicalComplexIntUpQuasiIsoObjCochainComplexCompSingleFunctorOfNatOfHasExt, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.iso_hom_naturality_assoc, CategoryTheory.CartesianMonoidalCategory.instIsIsoFunctorProdComparisonNatTransOfProdComparison, OplaxMonoidal.ofBifunctor.bottomMapᵣ_app, CategoryTheory.WithInitial.commaFromUnder_map_right, CategoryTheory.TwoSquare.whiskerLeft_app, pointwiseRightKanExtensionCounit_app, CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_cancel_inv_app, CategoryTheory.CategoryOfElements.costructuredArrow_yoneda_equivalence_naturality, CategoryTheory.Presheaf.imageSieve_eq_sieveOfSection, lanCompIsoOfPreserves_inv_app, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_assoc, isoWhiskerLeft_refl, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_hom, BddDistLat.forget_bddLat_lat_eq_forget_distLat_lat, CategoryTheory.Limits.coneOfSectionCompYoneda_π, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_map_hom, CategoryTheory.Equivalence.map_η_comp_η_assoc, CategoryTheory.Comma.opFunctorCompFst_inv_app, CategoryTheory.LocalizerMorphism.guitartExact_of_isRightDerivabilityStructure, CategoryTheory.Limits.Cocone.fromCostructuredArrow_pt, CategoryTheory.WithInitial.inclLift_inv_app, CommRingCat.equalizer_ι_isLocalHom', CategoryTheory.NatTrans.Equifibered.whiskerRight, instIsWellOrderContinuousCompFunctorEquivalence, CategoryTheory.instIsFilteredCostructuredArrowCompOfRepresentablyCoflat, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.forgetToPresheafedSpacePreservesOpenImmersion, CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ, CategoryTheory.ParametrizedAdjunction.unit_whiskerRight_map_assoc, mapTriangleCompIso_inv_app_hom₁, CategoryTheory.Comma.preRight_obj_hom, CategoryTheory.Limits.colimit.post_post, CategoryTheory.ShrinkHoms.equivalence_counitIso, pi'CompEval_inv_app, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_app_assoc, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc, CategoryTheory.Limits.IndObjectPresentation.ofCocone_isColimit, CategoryTheory.Join.mapWhiskerRight_whiskerLeft, CategoryTheory.Enriched.FunctorCategory.functorEnrichedHom_obj, AlgebraicTopology.DoldKan.natTransPInfty_f_app, CategoryTheory.Pseudofunctor.Grothendieck.map_comp_forget, CategoryTheory.Bicategory.associatorNatIsoMiddle_hom_app, CategoryTheory.preservesLimitIso_hom_π_assoc, CondensedSet.isDiscrete_tfae, isLeftKanExtensionId, CategoryTheory.Equivalence.precoherent_isSheaf_iff, CategoryTheory.Equivalence.symmEquiv_unitIso, CategoryTheory.Under.postMap_app, pointedToBipointedCompBipointedToPointedFst_hom_app_toFun, LightProfinite.instTotallyDisconnectedSpaceCarrierToTopTruePtCompHausLimitConeCompLightProfiniteToCompHaus, leftOpRightOpEquiv_counitIso_hom_app_app, CategoryTheory.CatCommSq.hComp_iso_inv_app, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_pt, CategoryTheory.Pseudofunctor.map₂_whisker_right_app_assoc, isLeftKanExtension_iff_postcomp₁, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_hom, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_π_app, CategoryTheory.ExactFunctor.whiskeringRight_map_app, CategoryTheory.DifferentialObject.shiftFunctorAdd_inv_app_f, CategoryTheory.shiftFunctorAdd_add_zero_inv_app, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_unitIso, CategoryTheory.Adjunction.leftAdjointUniq_hom_counit_assoc, CategoryTheory.Monad.beckCofork_π, CategoryTheory.Discrete.equivalence_counitIso, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInrIso_hom_app_app, CategoryTheory.ShortComplex.rightHomologyFunctorOpNatIso_hom_app, currying_unitIso_inv_app_app_app, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_hom_app_hom, CategoryTheory.Grothendieck.pre_comp, CategoryTheory.NatTrans.Equifibered.whiskerLeft, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map_val_app, CategoryTheory.Pretriangulated.Triangle.functorMk_map_hom₂, currying_unitIso_hom_app_app_app, CategoryTheory.Limits.Cocones.functoriality_faithful, CategoryTheory.orderDualEquivalence_counitIso, CategoryTheory.Discrete.productEquiv_counitIso_inv_app, CategoryTheory.Equivalence.counitIso_inv_app_comp_functor_map_η_inverse_assoc, CategoryTheory.Join.pseudofunctorRight_mapComp_hom_toNatTrans_app, CategoryTheory.Subobject.lowerEquivalence_counitIso, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_assoc, mapCoconeWhisker_inv_hom, CategoryTheory.Adjunction.Triple.leftToRight_eq_counits, CategoryTheory.Limits.colimit.pre_map', CategoryTheory.Equivalence.mapHomologicalComplex_counitIso, leftDerived_map_eq, SSet.opEquivalence_unitIso, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app, CategoryTheory.WithInitial.inclLiftToInitial_hom_app, CategoryTheory.LocalizerMorphism.isRightDerivabilityStructure_iff, CategoryTheory.Adjunction.counit_isIso_of_R_fully_faithful, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_inv_assoc, PresheafOfModules.restriction_app, CategoryTheory.ShiftedHom.opEquiv_symm_apply_comp, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_hom_hom, CategoryTheory.Comma.instFullCompPreRight, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app, AlgebraicTopology.DoldKan.Γ₂N₂ToKaroubiIso_inv_app, alexDiscEquivPreord_unitIso, CategoryTheory.LiftLeftAdjoint.instIsReflexivePairMapAppCounitOtherMap, CategoryTheory.GrothendieckTopology.toSheafify_comp_sheafifyCompIso_inv, CategoryTheory.Sigma.inclCompMap_inv_app, CategoryTheory.Join.mapWhiskerRight_whiskerLeft_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_map_fst, CategoryTheory.GrothendieckTopology.overMapPullback_comp_id_assoc, rightOpComp_inv_app, CategoryTheory.Limits.cospanCompIso_inv_app_one, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₁, CategoryTheory.Adjunction.rightOp_unit, CategoryTheory.ExponentiableMorphism.coev_ev_assoc, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_inv_app_hom_hom_hom, CategoryTheory.Over.postAdjunctionRight_unit_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_inv_app_fst_app, CategoryTheory.Join.mkFunctor_map_edge, FullyFaithful.hasShift.map_add_hom_app, isoWhiskerRight_hom, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_g, instIsContinuousCompId, CategoryTheory.Cat.Hom.toNatIso_rightUnitor, CategoryTheory.Comma.instFullCompPostOfFaithful, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_inv_app_app, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_pt, CategoryTheory.Join.mapPairComp_hom_app_left, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom.w_assoc, CategoryTheory.unit_mateEquiv, CategoryTheory.conjugateEquiv_associator_hom, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.isPushoutAddCommGrpFreeSheaf, mapTriangle_map_hom₃, mapDifferentialObject_obj_d, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₃, CategoryTheory.sum.inrCompInlCompAssociator_hom_app_down_down, CategoryTheory.Limits.spanCompIso_hom_app_left, OrderHom.equivalenceFunctor_counitIso_hom_app_app, CategoryTheory.Limits.FormalCoproduct.evalOpCompInlIsoId_hom_app_app, CategoryTheory.Comonad.cofree_obj_a, CategoryTheory.Comma.instFaithfulCompPreRight, leftKanExtensionUniqueOfIso_inv, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_right, IsCoverDense.presheafIso_inv, CategoryTheory.Equivalence.counitInv_app_functor, AddGrpCat.instSmallElemForallObjCompMonCatForget₂AddMonoidHomCarrierCarrierForgetSections, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_inv_app_app_snd, CategoryTheory.Over.postComp_hom_app_left, CategoryTheory.flat_iff_lan_flat, CategoryTheory.IndParallelPairPresentation.hg, PresheafOfModules.sectionsMk_coe, HomologicalComplex.singleCompEvalIsoSelf_inv_app, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.hasLimit_cospan_forget_of_left, CategoryTheory.Equivalence.rightOp_counitIso_hom_app, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_obj, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_unit_app_app, CategoryTheory.Limits.limit.lift_pre, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_app_assoc, CategoryTheory.Limits.Cones.functorialityEquivalence_counitIso, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply, CategoryTheory.CostructuredArrow.ofCommaFstEquivalence_counitIso, CategoryTheory.Limits.limIsoFlipCompWhiskerLim_hom_app_app, CategoryTheory.Limits.MultispanIndex.multispanMapIso_hom_app, leftKanExtensionUnit_leftKanExtensionObjIsoColimit_hom, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_counit_app, AlgebraicGeometry.isCompl_opensRange_inl_inr, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerRight_assoc, CategoryTheory.Comma.opEquiv_unitIso, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_hom_app_unmop, Faithful.comp, pointwiseRightKanExtension_obj, CategoryTheory.StructuredArrow.mapNatIso_counitIso_hom_app_right, CategoryTheory.ReflQuiv.adj.homEquiv_naturality_right, CategoryTheory.expComparison_ev, HomologicalComplex₂.totalShift₁Iso_trans_totalShift₂Iso, CategoryTheory.Presheaf.isLeftKanExtension_of_preservesColimits, CategoryTheory.MonoOver.inf_map_app, CategoryTheory.SingleFunctors.postcompPostcompIso_inv_hom_app, CategoryTheory.Sum.functorEquivFunctorCompSndIso_inv_app_app, CategoryTheory.sheafificationAdjunction_unit_app, CategoryTheory.typeEquiv_counitIso_hom_app_val_app, CategoryTheory.Discrete.compNatIsoDiscrete_inv_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_aux_one, MonoidHom.comp_toFunctor, CategoryTheory.Under.postEquiv_inverse, CategoryTheory.Limits.colimIsoFlipCompWhiskerColim_inv_app_app, CategoryTheory.LaxFunctor.mapComp_assoc_left_app, CategoryTheory.Adjunction.unit_naturality, CategoryTheory.Presheaf.uliftYonedaAdjunction_unit_app_app, commShiftIso_map₂CochainComplex_flip_inv_app, opUnopEquiv_unitIso, SSet.Truncated.HomotopyCategory.BinaryProduct.associativity'Iso_hom_app, CategoryTheory.Sum.functorEquiv_unitIso_inv_app_app_inr, CategoryTheory.Localization.Construction.fac, whiskerLeft_id, FullyFaithful.compYonedaCompWhiskeringLeftMaxRight_hom_app_app_down, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_left, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app_assoc, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₃, Final.ι_colimitIso_inv_assoc, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.isConnected, CategoryTheory.Equivalence.counitInv_functor_comp_assoc, LeftExtension.postcompose₂_map_left, CategoryTheory.lan_flat_of_flat, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_app_assoc, CategoryTheory.Limits.LimitPresentation.map_π, CategoryTheory.NatTrans.id_hcomp_app, CategoryTheory.shift_shiftFunctorCompIsoId_inv_app, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_counit_app_left, CategoryTheory.Join.inclLeftCompOpEquivInverse_hom_app_op, CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_left, PresheafOfModules.Derivation.d_app, CategoryTheory.instFaithfulSheafFunctorOppositeCompSheafComposeSheafToPresheaf, CategoryTheory.Adjunction.map_μ_comp_counit_app_tensor, CategoryTheory.LocalizerMorphism.essSurj_of_hasRightResolutions, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counit_app, CategoryTheory.Adjunction.compCoyonedaIso_hom_app_app, CategoryTheory.Kleisli.Adjunction.fromKleisli_map, currying₃_unitIso_inv_app_app_app_app, AlgebraicGeometry.instIsOpenImmersionSigmaSpec, final_iff_comp_final_full_faithful, mapConeWhisker_hom_hom, CategoryTheory.Equivalence.fun_inv_map_assoc, CategoryTheory.Limits.Cone.equivCostructuredArrow_counitIso, closedIhom_map_app, rightKanExtensionCompIsoOfPreserves_hom_fac_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_inv_app_app, CategoryTheory.Cat.opFunctorInvolutive_inv_app_toFunctor_obj, CategoryTheory.Limits.Cocone.toCostructuredArrowCompToOverCompForget_hom_app, CategoryTheory.WithTerminal.mkCommaObject_hom_app, CoconeTypes.precomp_ι, HomotopicalAlgebra.FibrantObject.HoCat.ιCompResolutionNatTrans_app, pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac, bipointedToPointedSnd_comp_forget, CategoryTheory.Comonad.ForgetCreatesColimits'.coconePoint_a, CategoryTheory.Equivalence.ε_comp_map_ε, CategoryTheory.StructuredArrow.toUnder_obj_hom, RightExtension.postcompose₂_obj_hom_app, CategoryTheory.NatTrans.leftOpWhiskerRight, CategoryTheory.Limits.limitCompCoyonedaIsoCone_inv, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_left, Action.resComp_inv_app_hom, CategoryTheory.WithInitial.equivComma_unitIso_hom_app_app, RightExtension.precomp_obj_hom_app, CategoryTheory.Cat.rightUnitor_inv_toNatTrans, whiskerLeft_comp_assoc, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_right_right, final_iff_final_comp, SheafOfModules.pullback_assoc, ranCounit_app_app_ranAdjunction_unit_app_app, Final.colimit_cocone_comp_aux, CategoryTheory.ShiftedHom.opEquiv'_symm_op_opShiftFunctorEquivalence_counitIso_inv_app_op_shift, CategoryTheory.algebraEquivUnder_counitIso, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_map_left, RightExtension.precomp_map_right, CategoryTheory.Presieve.FamilyOfElements.Compatible.functorPullback, CategoryTheory.Monad.MonadicityInternal.unitCofork_pt, CategoryTheory.Presheaf.imageSieve_whisker_forget, CategoryTheory.ProjectiveResolution.leftDerivedToHomotopyCategory_app_eq, CategoryTheory.shiftEquiv'_unitIso, CategoryTheory.Under.postCongr_hom_app_right, AddCommMonCat.coyonedaForget_inv_app_app, CategoryTheory.Limits.colimit.pre_id, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_right, map_opShiftFunctorEquivalence_unitIso_hom_app_unop_assoc, CategoryTheory.instIsIsoPost_1, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_hom_π_π_assoc, CategoryTheory.Subgroupoid.comap_comp, CategoryTheory.Enriched.FunctorCategory.instHasEnrichedHomUnderCompMapForget, CategoryTheory.Limits.Cocones.functoriality_full, CategoryTheory.Pi.optionEquivalence_inverse, AlgebraicGeometry.Scheme.Hom.toNormalization_inr_normalizationCoprodIso_hom_assoc, CategoryTheory.WithTerminal.commaFromOver_map_right, essImage.liftFunctorCompIso_inv_app, CategoryTheory.Grp.forget₂Mon_comp_forget, CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_right, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_hom_app_app_down, CategoryTheory.Limits.comp_preservesFiniteCoproducts, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom.w, CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_hom_assoc, CategoryTheory.CostructuredArrow.map₂_map_left, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_presheafHom_uliftYoneda_obj, representableByUliftFunctorEquiv_apply_homEquiv, shift_map_op, CategoryTheory.Comma.instEssSurjCompPreLeft, CategoryTheory.MorphismProperty.Under.forget_comp_forget_map, CategoryTheory.Limits.limitIsoSwapCompLim_inv_app, mapTriangleCommShiftIso_inv_app_hom₂, CategoryTheory.CosimplicialObject.whiskering_obj_map_app, Action.FunctorCategoryEquivalence.unitIso_hom_app_hom, Lat_dual_comp_forget_to_partOrd, CategoryTheory.Limits.colimit.pre_map, CategoryTheory.Sum.swapCompInl_inv_app, CategoryTheory.Pi.optionEquivalence_counitIso, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_map_right_right, CategoryTheory.Limits.Cocones.whiskeringEquivalence_functor, CategoryTheory.Adjunction.comp_unit_app_assoc, CategoryTheory.InjectiveResolution.extMk_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy_homEquiv_apply_app, PresheafOfModules.Monoidal.tensorHom_app, initial_iff_comp_initial_full_faithful, CategoryTheory.Idempotents.functorExtension₂CompWhiskeringLeftToKaroubiIso_inv_app_app_f, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_whiskerRight, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_right, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_map_snd, CategoryTheory.Limits.cospanCompIso_hom_app_left, CategoryTheory.Iso.coreRightUnitor, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_unitIso, isRepresentable_comp_uliftFunctor_iff, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceFunctorProj_hom_app, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₁, CategoryTheory.Presheaf.isSheaf_iff_isSheaf_comp, HomologicalComplex.homologyFunctorSingleIso_inv_app, pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_assoc, CategoryTheory.exp.coev_ev_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_app_assoc, RightExtension.postcompose₂ObjMkIso_inv_left_app, SimplicialObject.opFunctorCompOpFunctorIso_inv_app_app, CategoryTheory.prod_map_pre_app_comp_ev, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π_assoc, isLeftKanExtensionAlongEquivalence, CategoryTheory.Equivalence.unit_naturality_assoc, CategoryTheory.Enriched.HasConicalLimit.of_equiv, CategoryTheory.Join.mapWhiskerLeft_associator_hom_assoc, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_left_left, CategoryTheory.Equivalence.unit_app_tensor_comp_inverse_map_δ_functor_assoc, CategoryTheory.NatTrans.shift_app_assoc, AlgebraicTopology.DoldKan.Compatibility.υ_hom_app, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_left_left, CategoryTheory.sheafComposeIso_inv_fac_assoc, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_inv_app_eq, CategoryTheory.instIsCofilteredStructuredArrowCompOfRepresentablyFlat, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp_app, CategoryTheory.SimplicialObject.IsCoskeletal.isRightKanExtension, CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_inv_app_unmop_unmop, IsCoverDense.sheafCoyonedaHom_app, AlgebraicGeometry.instIsOpenImmersionAppOverSchemeOpensDiagramι, inrCompSum'_inv_app, CategoryTheory.comp_comparison_hasLimit, constComp_hom_app, finBoolAlg_dual_comp_forget_to_finBddDistLat, CategoryTheory.Adjunction.derivedη_fac_app, CategoryTheory.Grpd.freeForgetAdjunction_homEquiv_apply, AlgebraicGeometry.Scheme.SpecΓIdentity_inv_app, CategoryTheory.Abelian.LeftResolution.instEpiKaroubiAppπ, CategoryTheory.Adjunction.rightAdjointUniq_hom_app_counit, homEquivOfIsRightKanExtension_symm_apply, CategoryTheory.Pseudofunctor.Grothendieck.map_comp_eq, CategoryTheory.simplicialCosimplicialEquiv_unitIso_inv_app, reflective, CategoryTheory.Adjunction.derivedη_fac_app_assoc, CategoryTheory.opOpEquivalence_counitIso, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_map_hom, CategoryTheory.Subobject.lowerEquivalence_unitIso, RightExtension.postcompose₂_map_left_app, CategoryTheory.Equivalence.unit_naturality, completeLat_dual_comp_forget_to_bddLat, TopCat.Presheaf.isSheaf_iff_isSheaf_comp', CategoryTheory.sum.inrCompAssociator_inv_app_down_down, CategoryTheory.Sieve.mem_functorPushforward_functor, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_hom_app_app, CategoryTheory.Equivalence.functor_unitIso_comp, CategoryTheory.Bimon.equivMonComonCounitIsoAppX_inv_hom, CategoryTheory.Comma.mapFst_hom_app, CategoryTheory.GrothendieckTopology.overMapPullbackComp_inv_app_val_app, CategoryTheory.Pseudofunctor.Grothendieck.map_map_fiber, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₃_app, PresheafOfModules.Derivation'.app_apply, CategoryTheory.Limits.limit.map_pre', CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app, CategoryTheory.NatTrans.CommShiftCore.app_shift, CategoryTheory.TwoSquare.hasPointwiseLeftKanExtension, 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, whiskeringRightObjCompIso_hom_app_app, whiskerLeft_id', leftDerived_fac, RightExtension.postcompose₂_obj_left_obj, AlgebraicGeometry.StructureSheaf.instIsLocalizedModuleCarrierStalkAbPresheafOpensCarrierTopModuleStructurePresheafPrimeComplAsIdealToStalkₗ, Rep.unit_iso_comm, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_obj, CategoryTheory.StructuredArrow.preEquivalenceInverse_map_right_right, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app, CategoryTheory.presheafToSheafCompComposeAndSheafifyIso_inv_app, CategoryTheory.Monad.ForgetCreatesLimits.conePoint_A, isoWhiskerRight_symm, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_right, CategoryTheory.Comma.coneOfPreserves_pt_hom, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_symm_apply_f, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceInverse_obj_base, CategoryTheory.Subfunctor.equivalenceMonoOver_unitIso, CategoryTheory.Adjunction.localization_counit_app, CategoryTheory.HasForget₂.forget_comp, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₂, CategoryTheory.Comma.unopFunctorCompFst_inv_app, postcomposeWhiskerLeftMapCone_hom_hom, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIso_hom_app_hom, AlgebraicGeometry.coprodSpec_inl_assoc, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_hom, CategoryTheory.Limits.IndObjectPresentation.extend_isColimit_desc_app, CategoryTheory.Limits.IndObjectPresentation.ofCocone_ι, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_IsMon_Hom, CategoryTheory.ShortComplex.leftHomologyFunctorOpNatIso_hom_app, CategoryTheory.MonoOver.lift_map_hom, TopCat.coneOfConeForget_π_app, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_apply, CategoryTheory.Pi.evalCompEqToEquivalenceFunctor_inv, PreservesLeftKanExtension.preserves, CategoryTheory.Adjunction.instIsIsoMapAppUnitOfFaithfulOfFull, CategoryTheory.Limits.colimitIsoFlipCompColim_hom_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_inv_app_app, CategoryTheory.Monad.algebraFunctorOfMonadHomComp_inv_app_f, CategoryTheory.Sieve.functorPushforward_functor, FullyFaithful.compUliftCoyonedaCompWhiskeringLeft_inv_app_app_down, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_obj_iso_hom, CategoryTheory.Limits.comp_preservesFilteredColimits, whiskerRight_app, LightCondensed.lanPresheafNatIso_hom_app, CategoryTheory.Sum.natTransOfWhiskerLeftInlInr_comp, Final.comp_reflectsColimit, ModuleCat.extendScalars_id_comp_assoc, smoothSheafCommRing.ι_forgetStalk_hom_apply, CategoryTheory.LocalizerMorphism.equiv_smallHomMap, CategoryTheory.NatTrans.IsMonoidal.instHomFunctorLeftUnitor, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.guitartExact', CategoryTheory.plusPlusAdjunction_unit_app, CategoryTheory.Adjunction.CommShift.compatibilityUnit_right, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_inv_app_fst_app, CategoryTheory.CartesianMonoidalCategory.prodComparisonIso_comp, CommShift.isoAdd'_hom_app, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_app, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app_assoc, IsCoverDense.homOver_app, groupAddGroupEquivalence_counitIso, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_inv_app_app, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app, CategoryTheory.Join.mapWhiskerRight_rightUnitor_hom, CategoryTheory.Limits.fiberwiseColimCompColimIso_hom_app, mapTriangleCompIso_hom_app_hom₁, CategoryTheory.ComonadHom.app_δ, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_iso_inv_app, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_hom_app_f, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorEquivalence_counitIso, CategoryTheory.CostructuredArrow.grothendieckProj_obj, CategoryTheory.Adjunction.Triple.map_rightToLeft_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_associator, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app_assoc, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_comp, pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_app, CategoryTheory.Over.equivalenceOfIsTerminal_unitIso, HomotopicalAlgebra.CofibrantObject.instIsIsoHoCatAppAdjCounit', CategoryTheory.TwoSquare.EquivalenceJ.functor_obj, AlgebraicGeometry.sigmaOpenCover_I₀, CategoryTheory.MonoidalOpposite.tensorRightMopIso_inv_app_unmop, CategoryTheory.Adjunction.eq_unit_comp_map_iff, ModuleCat.extendScalars_assoc', CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_id, CategoryTheory.Sum.natIsoOfWhiskerLeftInlInr_hom, CategoryTheory.Equivalence.core_counitIso_hom_app_iso_inv, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_hom_app_val_app, CategoryTheory.Over.iteratedSliceEquiv_counitIso, constCompEvaluationObj_hom_app, leftKanExtensionIsoFiberwiseColimit_hom_app, CategoryTheory.SimplicialObject.Truncated.cosk_reflective, CategoryTheory.Monad.comparisonForget_inv_app, CategoryTheory.Adjunction.functorCategory_inverseImage_isomorphisms_unit, smoothSheafCommRing.ι_forgetStalk_hom_assoc, LaxMonoidal.comp_ε, CategoryTheory.shiftFunctorAdd_add_zero_hom_app, CategoryTheory.Groupoid.invEquivalence_counitIso, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, Final.colimit_pre_isIso, CategoryTheory.StructuredArrow.mapIso_unitIso_hom_app_right, CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ', CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_app_app, CategoryTheory.Equivalence.cancel_counitInv_right_assoc', CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_fst, CategoryTheory.TransfiniteCompositionOfShape.iic_incl_app, Rep.indResAdjunction_unit_app_hom_hom, IsCoverDense.Types.presheafIso_hom_app, CategoryTheory.EnrichedFunctor.forgetComp_hom_app, CategoryTheory.Equivalence.symm_counitIso, pointwiseLeftKanExtensionCompIsoOfPreserves_fac_app, constCompWhiskeringLeftIso_inv_app_app, RightExtension.postcompose₂_map_right, isoWhiskerRight_refl, CategoryTheory.NatTrans.leftOpWhiskerRight_assoc, ModuleCat.extendScalars_id_comp, leftOpComp_hom_app, CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit_assoc, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_F, CategoryTheory.Limits.cospanCompIso_hom_app_one, CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_app_snd_app, RingCat.moduleCatRestrictScalarsPseudofunctor_mapComp, CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatTrans_app, CommShift.isoZero_inv_app, CategoryTheory.TwoSquare.whiskerTop_app, CategoryTheory.WithTerminal.inclLiftToTerminal_hom_app, sheafPushforwardContinuousCompSheafToPresheafIso_hom_app_app, RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π_assoc, LightProfinite.Extend.cocone_pt, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_counitIso_hom_app_f, commShiftIso_inv_naturality, CategoryTheory.GrothendieckTopology.HasSheafCompose.isSheaf, CategoryTheory.expComparison_iso_of_frobeniusMorphism_iso, CategoryTheory.Limits.limitIsoLimitCurryCompLim_inv_π, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_app, AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit_map, CategoryTheory.Adjunction.left_triangle, postcomp_map_heq, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_app_fst_app, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app_assoc, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_mul, AlgebraicTopology.DoldKan.Compatibility.τ₁_hom_app, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj, LeftExtension.precomp_map_left, leftKanExtensionCompIsoOfPreserves_inv_fac, CategoryTheory.Equivalence.unit_app_comp_inverse_map_η_functor, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.unitIso_inv, CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_cancel_inv_app, CategoryTheory.LaxFunctor.map₂_rightUnitor_app_assoc, inv_whiskerLeft, CategoryTheory.Comma.isEquivalence_preRight, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_right, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_hom_app_app_hom, TopCat.Presheaf.presheafEquivOfIso_counitIso_inv_app_app, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk, HomotopyCategory.homologyFunctor_shiftMap_assoc, whiskerRight_comp_assoc, AlgebraicGeometry.ι_sigmaSpec_assoc, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_hom_app_left, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_one, CategoryTheory.ι_colimitCompWhiskeringRightIsoColimitComp_hom_assoc, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_app_assoc, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.unitIso_hom_app_f_f, isRightKanExtensionId, CategoryTheory.eq_unitIso, CategoryTheory.StructuredArrow.pre_map_right, AlgebraicGeometry.ΓSpec.right_triangle, CategoryTheory.TwoSquare.whiskerRight_app, CategoryTheory.Idempotents.KaroubiKaroubi.unitIso_hom_app_f, CategoryTheory.Adjunction.homEquiv_symm_id, CategoryTheory.TwistShiftData.shiftFunctorAdd'_inv_app, CategoryTheory.Localization.HasProductsOfShapeAux.inverts, CompHausLike.LocallyConstant.instIsIsoFunctorTypeUnitSheafCoherentTopologyAdjunction, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₃, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counit_app_tensor_assoc, CategoryTheory.Join.mapPairComp_inv_app_left, AlgebraicGeometry.isPullback_inr_inr_coprodMap, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_inv_app_hom_coe', limitIsoOfIsRightKanExtension_inv_π_assoc, Condensed.isColimitLocallyConstantPresheafDiagram_desc_apply, unopComp_inv_app, CategoryTheory.CatCommSq.vComp_iso_inv_app, CategoryTheory.Equivalence.core_unitIso_hom_app_iso_hom, rightDerived_map_eq, SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_hom_app, LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm, CategoryTheory.Idempotents.DoldKan.isoN₁_hom_app_f, hasRightKanExtension_of_preserves, AlgebraicTopology.DoldKan.N₁Γ₀_hom_app, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_εIso_inv, LeftExtension.precomp₂_obj_right, mapMonCompIso_inv_app_hom, CategoryTheory.BasedFunctor.w, opComp_hom_app, CategoryTheory.ExponentiableMorphism.coev_naturality_assoc, rightDerived_fac_app_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_left, CategoryTheory.Limits.CategoricalPullback.catCommSq_iso_inv_app, CategoryTheory.Monad.comparison_map_f, CategoryTheory.MonoidalCategory.DayFunctor.νNatTrans_app, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_fst, CategoryTheory.Limits.Cocone.mapCoconeToOver_inv_hom, CategoryTheory.StructuredArrow.mapNatIso_unitIso_inv_app_right, ranObjObjIsoLimit_hom_π, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_mapPullbackAdj_counit_app, isLeftAdjoint_comp, CategoryTheory.subterminalsEquivMonoOverTerminal_unitIso, CategoryTheory.Codiscrete.adj_unit_app, CategoryTheory.Equivalence.rightOp_unitIso_inv_app, mapTriangleCommShiftIso_hom_app_hom₁, CategoryTheory.Mon.limit_X, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_map_app_fst, ModuleCat.ExtendRestrictScalarsAdj.counit_app, CategoryTheory.Under.mapForget_eq, CategoryTheory.Adjunction.leftAdjointCompIso_hom, rightKanExtensionUniqueOfIso_inv, CategoryTheory.Adjunction.Triple.whiskerRight_rightToLeft, CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso_hom_app, CategoryTheory.Limits.IndObjectPresentation.ofCocone_F, FullyFaithful.homNatIso'_inv_app_down, CategoryTheory.ReflQuiv.adj.counit.comp_app_eq, CategoryTheory.TwoSquare.hasLeftKanExtension, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.inverseObj_comon_comul_app, isoShift_hom_naturality_assoc, CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj_inv_naturality, CategoryTheory.GrothendieckTopology.whiskerRight_toPlus_comp_plusCompIso_hom_assoc, CommRingCat.equalizer_ι_isLocalHom, CategoryTheory.StructuredArrow.instFaithfulCompPre, CategoryTheory.mateEquiv_vcomp, CategoryTheory.MonoidalClosed.whiskerLeft_curry_ihom_ev_app, IsRepresentedBy.iff_isIso_uliftYonedaEquiv, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_hom_comp_π, CompHausLike.LocallyConstant.counit_app_val, CategoryTheory.Limits.Concrete.small_sections_of_hasLimit, CategoryTheory.Bicategory.associatorNatIsoRight_hom_app, CategoryTheory.Join.InclLeftCompRightOpOpEquivFunctor_inv_app, CategoryTheory.ULift.equivalence_counitIso_inv_app, CategoryTheory.Sum.swapCompInr_hom_app, CategoryTheory.Over.postEquiv_unitIso, LeftExtension.coconeAt_pt, CategoryTheory.Adjunction.homEquiv_apply, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_symm_apply, CategoryTheory.Limits.limit.pre_eq, AlgebraicGeometry.coprodSpec_inl, CategoryTheory.Limits.IndObjectPresentation.ofCocone_ℐ, HomotopyCategory.spectralObjectMappingCone_ω₁, Profinite.Extend.cocone_ι_app, CategoryTheory.equivEssImageOfReflective_inverse, CategoryTheory.Grothendieck.final_pre, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceInverse_map_fiber, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_assoc, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_left, CategoryTheory.Presheaf.isLocallySurjective_whisker_iff, SimplicialObject.Split.natTransCofanInj_app, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_map_app_app, CategoryTheory.Endofunctor.Algebra.functorOfNatTransComp_inv_app_f, CategoryTheory.Equivalence.unit_app_inverse, CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence_hom, CategoryTheory.ExponentiableMorphism.pushforwardComp_hom_counit, CategoryTheory.Limits.whiskeringLimYonedaIsoCones_hom_app_app_app, CategoryTheory.Iso.isoCompInverse_hom_app, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app_assoc, CategoryTheory.Iso.isoInverseOfIsoFunctor_hom_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.forgetToPresheafedSpace_reflectsPullback_of_left, CategoryTheory.Bimon.equivMonComonCounitIsoApp_hom_hom_hom, CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app, CategoryTheory.ComposableArrows.opEquivalence_inverse_map, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_inv_hom, CategoryTheory.δ_iso_of_coreflective, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.counitIso_inv, ModuleCat.HasColimit.colimitCocone_pt_carrier, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_map, CategoryTheory.Idempotents.karoubiUniversal₁_unitIso, CategoryTheory.Comonad.right_counit, CategoryTheory.Bimon.ofMonComon_toMonComon_obj_comul, comp_mapCommGrp_one, CochainComplex.shiftFunctorAdd'_hom_app_f', CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_counit_app, pointwiseRightKanExtension_map, LeftExtension.postcomp₁_map_left, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_π_app_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_app, RightExtension.coneAtFunctor_map_hom, CategoryTheory.Adjunction.CoreUnitCounit.left_triangle, mapConeOp_inv_hom, TopologicalSpace.Opens.mapComp_inv_app, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_hom_app_hom_hom_hom, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackComp_inv, map_shift_unop_assoc, CategoryTheory.ShiftMkCore.zero_add_hom_app, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₁, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalence_unitIso, TopCat.Presheaf.IsSheaf.isSheafPairwiseIntersections, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₁_app, CategoryTheory.Comma.mapRightComp_hom_app_right, CategoryTheory.Comma.opFunctorCompSnd_inv_app, HomotopicalAlgebra.CofibrantObject.instWeakEquivalenceHoCatAppιCompResolutionNatTrans, CochainComplex.shiftEval_hom_app, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app, mapConePostcompose_hom_hom, inv_fun_map, CategoryTheory.CostructuredArrow.instFullCompObjPostOfFaithful, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_counitIso_inv, CategoryTheory.Comonad.ForgetCreatesColimits'.liftedCoconeIsColimit_desc_f, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_assoc, CategoryTheory.Grothendieck.grothendieckTypeToCat_inverse_obj_fiber_as, CategoryTheory.ihom.ev_naturality, HomologicalComplex.singleCompEvalIsoSelf_hom_app, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_app_assoc, Final.coconesEquiv_counitIso, TopCat.Presheaf.isGluing_iff_pairwise, Alexandrov.lowerCone_pt, CategoryTheory.CosimplicialObject.whiskering_map_app_app, CategoryTheory.SimplicialObject.Truncated.sk_coreflective, CategoryTheory.LocalizerMorphism.guitartExact_of_isLeftDerivabilityStructure, isRightKanExtension_iff_precomp, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_assoc, CategoryTheory.Bicategory.associatorNatIsoLeft_hom_app, CategoryTheory.Discrete.addMonoidalFunctorComp_isMonoidal, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π_assoc, CategoryTheory.Adjunction.rightAdjointUniq_hom_app_counit_assoc, HomotopicalAlgebra.CofibrantObject.instWeakEquivalenceHoCatAppAdjUnit, RightExtension.coneAtWhiskerRightIso_hom_hom, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_zero, CategoryTheory.TwistShiftData.shiftFunctorAdd'_hom_app, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_right, CategoryTheory.Cat.HasLimits.comp_def, Action.FunctorCategoryEquivalence.counitIso_hom_app_app, CategoryTheory.CartesianMonoidalCategory.prodComparisonIso_id, CategoryTheory.MonoidalCategory.externalProductSwap_inv_app_app, PresheafOfModules.pushforward_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_hom_app_app, CategoryTheory.ExponentiableMorphism.coev_naturality, CategoryTheory.Limits.Cone.whisker_pt, TopCat.adj₂_counit, CommGrpCat.coyonedaForget_inv_app_app, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app_assoc, CategoryTheory.Limits.fiberwiseColimCompColimIso_inv_app, CommRingCat.moduleCatExtendScalarsPseudofunctor_mapComp, CategoryTheory.sum.inlCompInverseAssociator_inv_app_down_down, shiftIso_hom_app_comp_shiftMap, Condensed.isoFinYoneda_hom_app, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.Adjunction.Triple.whiskerLeft_leftToRight_assoc, isoWhiskerRight_left, shiftIso_add'_inv_app, CategoryTheory.Limits.Cocones.functoriality_map_hom, CategoryTheory.Limits.ι_colimitLimitToLimitColimit_π_apply, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_naturality₂, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, CategoryTheory.Under.mapPushoutAdj_counit_app, CategoryTheory.WithTerminal.pseudofunctor_mapComp, CategoryTheory.LocalizerMorphism.guitartExact_of_isRightDerivabilityStructure', CategoryTheory.Comonad.beckEqualizer_lift, CategoryTheory.Comonad.ForgetCreatesLimits'.conePoint_A, CategoryTheory.subterminalsEquivMonoOverTerminal_counitIso, AlgebraicGeometry.Scheme.Modules.pseudofunctor_left_unitality, CategoryTheory.Adjunction.Triple.map_adj₂_counit_app_leftToRight_app, CategoryTheory.Adjunction.Triple.map_rightToLeft_app_assoc, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_hom_app_app, CategoryTheory.Under.mapComp_eq, Profinite.Extend.cone_pt, leftDerived_fac_app_assoc, CategoryTheory.TwoSquare.structuredArrowDownwards_map, CategoryTheory.evaluationAdjunctionRight_unit_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_associativity_assoc, CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse_map_left, CategoryTheory.MonoidalCategory.DayConvolution.whiskerLeft_comp_unit_app_assoc, CategoryTheory.Adjunction.unit_app_tensor_comp_map_δ, CategoryTheory.Comonad.ForgetCreatesColimits'.coconePoint_A, AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit_obj, lightDiagramToLightProfinite_map, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_f, CategoryTheory.counit_obj_eq_map_counit, AlgebraicGeometry.instIsLocallyDirectedCompSchemeOverOverTopMorphismPropertyForgetForgetForget, CategoryTheory.Join.InclRightCompRightOpOpEquivFunctor_inv_app, mapHomologicalComplex_commShiftIso_hom_app_f, AlgebraicGeometry.Scheme.Hom.normalizationCoprodIso_inv_coprodDesc_fromNormalization_assoc, FullyFaithful.hasShift.map_add_inv_app, CategoryTheory.Monoidal.whiskerRight_snd, CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj_hom_app, CategoryTheory.Pseudofunctor.CoGrothendieck.map_comp_forget, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_left, IsCoverDense.isoOver_inv_app, CategoryTheory.Comonad.beckFork_ι, CategoryTheory.WithTerminal.equivComma_functor_map_left_app, CategoryTheory.Adjunction.whiskerLeftRUnitIsoOfIsIsoCounit_hom_app, CategoryTheory.ExponentiableMorphism.unit_pushforwardId_hom, CategoryTheory.Comma.preLeft_map_left, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_app_assoc, CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app_assoc, CommMonCat.coyonedaForget_hom_app_app_hom, CategoryTheory.MonoidalCategory.DayConvolution.associator_inv_unit_unit_assoc, smoothSheaf.ι_evalHom, isoSum_hom_app_inr, CategoryTheory.Monad.ForgetCreatesColimits.liftedCocone_ι_app_f, AlgebraicGeometry.SheafedSpace.Γ_def, CategoryTheory.Grpd.comp_eq_comp, CategoryTheory.instIsIsoFunctorOppositeSheafToPresheafToSheafCompComposeAndSheafify, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τl, CategoryTheory.Adjunction.functorCategory_inverseImage_isomorphisms_counit, ModuleCat.extendScalarsComp_hom_app_one_tmul, whiskerLeft_comp_whiskerRight, CategoryTheory.LocalizerMorphism.inverts, CategoryTheory.Limits.fiberwiseColimCompEvaluationIso_inv_app, RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π, CategoryTheory.WithInitial.liftFromUnderComp_hom_app, smoothSheafCommRing.ι_evalHom_assoc, CategoryTheory.Equivalence.counitInv_naturality, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom_assoc, CommShift.OfComp.map_iso_hom_app_assoc, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_obj_left, rightDerivedNatTrans_fac_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.corepresentableByLeft_homEquiv, AlgebraicGeometry.sigmaOpenCover_f, CategoryTheory.PresheafHom.IsSheafFor.app_cond, CategoryTheory.Monad.monadMonEquiv_counitIso_inv_app_hom, CategoryTheory.Limits.FormalCoproduct.evalCompInclIsoId_inv_app_app, SSet.Truncated.HomotopyCategory.BinaryProduct.associativity, mapCoconeOp_hom_hom, CategoryTheory.preservesLimitIso_hom_π, MonObj.mopEquiv_counitIso_inv_app_hom_unmop, CategoryTheory.GrothendieckTopology.coneCompEvaluationOfConeCompDiagramFunctorCompEvaluation_π_app, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_inv_app_hom_app, CategoryTheory.Pseudofunctor.DescentData.exists_equivalence_of_sieve_eq, CategoryTheory.Limits.limitIsoLimitCurryCompLim_inv_π_assoc, CategoryTheory.TwoSquare.structuredArrowDownwards_obj, CategoryTheory.Monad.ForgetCreatesLimits.γ_app, CategoryTheory.ForgetEnrichment.equiv_counitIso, AlgebraicTopology.DoldKan.Compatibility.equivalence₁_inverse, CategoryTheory.Equivalence.unit_inverse_comp, CategoryTheory.NatTrans.op_whiskerLeft, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app, CategoryTheory.sheafificationAdjunction_counit_app_val, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_inv_app_app, CategoryTheory.Adjunction.right_triangle_components, CategoryTheory.WithInitial.coconeEquiv_counitIso_hom_app_hom, CategoryTheory.ShortComplex.rightHomologyFunctorOpNatIso_inv_app, CategoryTheory.ihom.ev_naturality_assoc, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_hom_whiskerLeft_π_assoc, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_hom_app_hom_coe, AddCommGrpCat.Colimits.Quot.desc_quotQuotUliftAddEquiv, LightCondensed.lanPresheafExt_inv, CategoryTheory.Limits.Cone.toUnder_π_app, Condensed.lanPresheafExt_hom, CategoryTheory.TransportEnrichment.forgetEnrichmentEquiv_unitIso, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id_app, CategoryTheory.Limits.colimitCoyonedaHomIsoLimit_π_apply, CategoryTheory.ParametrizedAdjunction.unit_whiskerRight_map, CategoryTheory.Adjunction.unit_app_commShiftIso_hom_app, instIsDenseCompOfIsEquivalence, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counitIso_hom_app_tensor, CategoryTheory.Under.postAdjunctionLeft_counit_app, whiskerRight_comp, CategoryTheory.Limits.Cones.equivalenceOfReindexing_unitIso, functorialityCompPrecompose_inv_app_hom, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₃, CategoryTheory.Comonad.beckFork_pt, CategoryTheory.Limits.coneOfSectionCompCoyoneda_π, pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac, CategoryTheory.conjugateEquiv_whiskerLeft, HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_symm_apply, commShiftIso_id_inv_app, CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso_inv_app, op_comp_isSheaf, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_hom_π_assoc, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_inv_app_hom_hom_app, HomotopicalAlgebra.FibrantObject.instIsIsoFunctorResolutionCompToLocalizationNatTrans, CategoryTheory.Adjunction.whiskerLeft_unit_app_app, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app_assoc, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_hom_app_hom, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_left, HomotopyCategory.homologyShiftIso_hom_app, CategoryTheory.Limits.limCompFlipIsoWhiskerLim_hom_app_app, CategoryTheory.Limits.limitIsoLimitCurryCompLim_hom_π_π, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_assoc, CochainComplex.shiftFunctorAdd_hom_app_f, CategoryTheory.Limits.hasLimitCompEvaluation, WellOrderInductionData.map_lift, swap_comp_bipointedToPointedSnd, whiskeringRight_obj_obj, CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_hom_app, CategoryTheory.GrothendieckTopology.whiskerRight_toSheafify_sheafifyCompIso_hom, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_counit_app, smoothSheafCommRing.ι_forgetStalk_hom, CategoryTheory.GrothendieckTopology.overMapPullbackComp_hom_app_val_app, CategoryTheory.Quotient.lift.isLift_inv, CategoryTheory.Adjunction.toMonad_coe, CategoryTheory.Limits.limitCompYonedaIsoCocone_hom_app, lanCompIsoOfPreserves_hom_app, CategoryTheory.Adjunction.isIso_unit_app_of_iso, CategoryTheory.Iso.inverseCompIso_inv_app, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_obj_map, postcompose₃_obj_map_app_app_app, LeibnizAdjunction.adj_unit_app_right, Monoidal.μNatIso_hom_app, postcomp_map_heq', leftExtensionEquivalenceOfIso₁_unitIso_hom_app_right_app, CategoryTheory.Idempotents.KaroubiKaroubi.counitIso_hom_app_f_f, CategoryTheory.ObjectProperty.isLocal_adj_unit_app, AlgebraicGeometry.Scheme.AffineZariskiSite.cocone_ι_app, TopCat.Presheaf.presheafEquivOfIso_counitIso_hom_app_app, CategoryTheory.Join.mkFunctorRight_inv_app, CategoryTheory.PreGaloisCategory.AutGalois.π_apply, Rep.resIndAdjunction_unit_app, SSet.Truncated.HomotopyCategory.BinaryProduct.right_unitality, CategoryTheory.Under.mapComp_inv, HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_apply, CategoryTheory.Pseudofunctor.map₂_whisker_left_app, SheafOfModules.pushforward_comp_id, mapContActionComp_hom, CategoryTheory.preservesLimit_comp_of_createsLimit, SSet.Truncated.cosk_reflective, isRightDerivedFunctor_of_inverts, CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.map_lift, CategoryTheory.MorphismProperty.Over.mapComp_inv_app_left, CategoryTheory.FunctorToTypes.mem_fromOverSubfunctor_iff, CategoryTheory.Limits.colimitYonedaHomIsoLimitOp_π_apply, CategoryTheory.Pseudofunctor.CoGrothendieck.comp_const, ModuleCat.extendScalars_comp_id_assoc, CategoryTheory.MonoidalCategory.tensorRightTensor_inv_app, CategoryTheory.LocalizerMorphism.Derives.isRightDerivedFunctor_iff_isIso, AlgebraicTopology.DoldKan.Γ₂N₁.natTrans_app_f_app, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_inv_π, CategoryTheory.flip_comp_evaluation, CochainComplex.mapBifunctorShift₁Iso_trans_mapBifunctorShift₂Iso, CategoryTheory.shiftFunctorComm_hom_app_of_add_eq_zero, CategoryTheory.MonoidalClosed.compTranspose_eq, CategoryTheory.Iso.isoFunctorOfIsoInverse_hom_app, SheafOfModules.relationsOfIsCokernelFree_s, CategoryTheory.SimplicialObject.instIsLeftKanExtensionOppositeTruncatedSimplexCategoryObjSkAppTruncatedUnitSkAdjTruncation, CategoryTheory.InjectiveResolution.isoRightDerivedToHomotopyCategoryObj_hom_naturality, CategoryTheory.ShiftedHom.opEquiv_symm_apply, CategoryTheory.prodOpEquiv_counitIso_hom_app, CategoryTheory.Over.starPullbackIsoStar_inv_app_left, CategoryTheory.inclusion_comp_decomposedTo, CategoryTheory.FreeGroupoid.of_comp_map, CategoryTheory.Comma.mapSnd_hom_app, CategoryTheory.Join.mapWhiskerLeft_whiskerLeft_assoc, AddCommGrpCat.kernelIsoKer_hom_comp_subtype, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_map_snd_app, CategoryTheory.Limits.coconeEquivalenceOpConeOp_counitIso, CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero_assoc, descOfIsLeftKanExtension_fac_app_assoc, pointedToTwoPSnd_comp_swap, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_snd, HomologicalComplex₂.flipEquivalenceCounitIso_inv_app_f_f, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left, HomologicalComplex.homologyFunctorIso_hom_app, postcompose₂_map_app_app_app, mapGrpCompIso_inv_app_hom_hom, CategoryTheory.Limits.cospanOp_inv_app, CategoryTheory.GrothendieckTopology.overMapPullback_id_comp_assoc, CategoryTheory.Adjunction.homEquiv_counit, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_hom_app, CategoryTheory.Limits.cospanCompIso_hom_app_right, CategoryTheory.shiftFunctorComm_symm, AddCommMonCat.equivalence_counitIso, CategoryTheory.MonoOver.inf_obj, mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app, CategoryTheory.Presheaf.tautologicalCocone_ι_app, CategoryTheory.CostructuredArrow.pre_map_right, CategoryTheory.Equivalence.unit_app_comp_inverse_map_η_functor_assoc, CategoryTheory.Pseudofunctor.CoGrothendieck.compIso_inv_app, Rep.ihom_coev_app_hom, CategoryTheory.ShiftedHom.opEquiv'_apply, core_map_iso_hom, CategoryTheory.Limits.colimit.post_desc, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app_assoc, toReflPrefunctor.map_comp, core_map_iso_inv, CategoryTheory.Cat.HasLimits.limitConeLift_toFunctor, CategoryTheory.Adjunction.leftAdjointCompNatTrans₀₂₃_eq_conjugateEquiv_symm, CategoryTheory.CatCommSq.iso_hom_naturality_assoc, CategoryTheory.Prod.symmetry_inv_app, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_left, CategoryTheory.Adjunction.counit_naturality_assoc, CategoryTheory.Equivalence.leftOp_counitIso_hom_app, CategoryTheory.constantSheafAdj_counit_w, CategoryTheory.Limits.colimit_map_colimitObjIsoColimitCompEvaluation_hom, CategoryTheory.μ_iso_of_reflective, CategoryTheory.Limits.instHasColimitCompOfPreservesColimit, CategoryTheory.Limits.comp_preservesFiniteProducts, CategoryTheory.oppositeShiftFunctorAdd'_hom_app, CategoryTheory.Presheaf.tautologicalCocone'_ι_app, PresheafOfModules.pushforward_obj_map_apply', CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.presheafHom_naturality_assoc, CategoryTheory.sum.inlCompInlCompAssociator_hom_app_down, CategoryTheory.shiftFunctorComm_eq, FinPartOrd_dual_comp_forget_to_partOrd, CategoryTheory.Core.inclusion_comp_functorToCore, CategoryTheory.Comma.toPUnitIdEquiv_counitIso_inv_app, CategoryTheory.Limits.cospanCompIso_app_one, closedCounit_app_app, CategoryTheory.StructuredArrow.preEquivalenceFunctor_map_right, CategoryTheory.toOverIteratedSliceForwardIsoPullback_inv_app_left, mapCoconePrecompose_hom_hom, CategoryTheory.Join.mapWhiskerRight_whiskerRight_assoc, CategoryTheory.FreeGroupoid.lift_spec, CategoryTheory.Limits.Cone.toStructuredArrow_comp_proj, CategoryTheory.CommMon.forget₂Mon_comp_forget, CompHausLike.LocallyConstant.unit_app, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₂, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.instIsLocallyDirectedI₀CompFunctorForgetOfIsThin, HomologicalComplex.cyclesOpNatIso_hom_app, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counit_app_tensor, CategoryTheory.Adjunction.Triple.leftToRight_app, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₃, CategoryTheory.Mon.limit_mon_one, CochainComplex.shiftFunctorAdd'_hom_app_f, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_right_app, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₁, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceInverseπ_inv_app, CategoryTheory.Equivalence.mapCommGrp_counitIso, CategoryTheory.Quotient.LiftCommShift.iso_inv_app, CategoryTheory.GlueData.hasColimit_multispan_comp, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_hom_right, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app, CategoryTheory.Join.mapWhiskerLeft_leftUnitor_hom, descOfIsLeftKanExtension_fac, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_obj_iso_hom, uncurry_obj_curry_obj_flip_flip', CategoryTheory.Idempotents.karoubiChainComplexEquivalence_unitIso_inv_app_f_f, AlgebraicGeometry.Scheme.Modules.pseudofunctor_left_unitality_assoc, CategoryTheory.ProdPreservesConnectedLimits.γ₁_app, CategoryTheory.conjugateEquiv_adjunction_id_symm, CategoryTheory.Limits.Cone.mapConeToUnder_hom_hom, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_symm_apply, CategoryTheory.Monad.right_unit, CategoryTheory.Localization.Monoidal.lifting₂CurriedTensorPre_iso, CategoryTheory.IsVanKampenColimit.mapCocone_iff, CategoryTheory.Grothendieck.map_map_fiber, skyscraperPresheafCoconeOfSpecializes_ι_app, CategoryTheory.PresheafHom.IsSheafFor.exists_app, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompCoyoneda, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_app, CategoryTheory.Limits.ColimitPresentation.reindex_diag, CategoryTheory.Equivalence.core_counitIso_inv_app_iso_hom, CategoryTheory.SmallObject.SuccStruct.ofNatTrans_succ, LightCondSet.isDiscrete_tfae, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_hom_toNatTrans_app_val_app, isLeftKanExtension_iff_precomp, CategoryTheory.yoneda'_comp, AlgebraicTopology.DoldKan.N₁Γ₀_inv_app, AlgebraicGeometry.Scheme.Hom.inl_toNormalization_normalizationCoprodIso_inv_assoc, Types.monoOverEquivalenceSet_unitIso, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₂, ranObjObjIsoLimit_inv_π, CategoryTheory.Sum.natIsoOfWhiskerLeftInlInr_inv, CategoryTheory.CostructuredArrow.ofCommaFstEquivalence_unitIso, CategoryTheory.MonoidalOpposite.tensorLeftIso_hom_app_unmop, ShiftSequence.shiftIso_add, CategoryTheory.Limits.colimit_map_colimitObjIsoColimitCompEvaluation_hom_assoc, CategoryTheory.Iso.inverseCompIso_hom_app, CategoryTheory.TwoSquare.EquivalenceJ.functor_map, boolAlg_dual_comp_forget_to_bddDistLat, CategoryTheory.Equivalence.congrLeft_counitIso_hom_app, mapConeOp_hom_hom, CategoryTheory.Adjunction.right_triangle, CategoryTheory.Sigma.descUniq_hom_app, CategoryTheory.Limits.Cocone.toCostructuredArrowCompProj_inv_app, CategoryTheory.Equivalence.congrFullSubcategory_functor, LightCondensed.instFinalNatCostructuredArrowOppositeFintypeCatLightProfiniteOpToLightProfiniteOpPtAsLimitConeFunctorOp, CategoryTheory.Comma.instEssSurjCompPreRight, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_map_app_snd, CategoryTheory.Cat.asSmallFunctor_map, CategoryTheory.GrothendieckTopology.ι_plusCompIso_hom, leftDerivedNatTrans_app, AlgebraicGeometry.instIsIsoSchemeCoprodSpec, hasLeftKanExtension_of_preserves, AlgebraicTopology.DoldKan.Compatibility.τ₀_hom_app, CategoryTheory.ExponentiableMorphism.unit_pushforwardId_hom_assoc, PresheafOfModules.instReflectsIsomorphismsSheafOfModulesFunctorOppositeAddCommGrpCatCompSheafToSheafSheafToPresheaf, PresheafOfModules.freeAdjunction_unit_app, CategoryTheory.Monoidal.associator_inv, CategoryTheory.ExponentiableMorphism.ev_naturality, CategoryTheory.frobeniusMorphism_iso_of_expComparison_iso, instAdditiveComp, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_ι_inv, commShiftOfLocalization_iso_hom_app, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_left, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₂, CategoryTheory.Join.inrCompFromSum_inv_app, LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv, CategoryTheory.WithTerminal.liftFromOverComp_inv_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_right, Initial.limitConeOfComp_cone, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_map_app_assoc, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_hom_assoc, CategoryTheory.Adjunction.map_restrictFullyFaithful_unit_app, CategoryTheory.Limits.reflexivePair.compRightIso_inv_app, CategoryTheory.Adjunction.CommShift.commShift_unit, partialFunEquivPointed_counitIso_hom_app_toFun, CategoryTheory.Sheaf.sheafifyCocone_ι_app_val_assoc, CategoryTheory.Comma.coneOfPreserves_pt_left, CategoryTheory.LocalizerMorphism.LeftResolution.opEquivalence_counitIso, curryObjProdComp_inv_app_app, TwoP.swapEquiv_counitIso_hom_app_hom_toFun, CategoryTheory.coalgebraEquivOver_unitIso, structuredArrowMapCone_pt, CategoryTheory.Limits.Cone.equivCostructuredArrow_unitIso, CategoryTheory.StructuredArrow.ofCommaSndEquivalence_inverse, CategoryTheory.Prod.braiding_counitIso, CategoryTheory.Limits.Cocone.extend_ι, HomotopicalAlgebra.CofibrantObject.HoCat.ιCompResolutionNatTrans_app, CategoryTheory.Limits.Cocones.functorialityEquivalence_inverse, CategoryTheory.Triangulated.TStructure.triangleLTGE_map_hom₁, CategoryTheory.OplaxFunctor.map₂_rightUnitor_app, CategoryTheory.Limits.prodComparisonNatTrans_app, CochainComplex.shiftFunctorComm_hom_app_f, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_app, CategoryTheory.Comma.post_map_right, CategoryTheory.StructuredArrow.pre_obj_hom, AlgebraicGeometry.Scheme.AffineZariskiSite.cocone_pt, CategoryTheory.LaxFunctor.mapComp_naturality_right_app, CategoryTheory.Limits.comp_preservesLimits, CategoryTheory.Idempotents.KaroubiKaroubi.unitIso_inv_app_f, CategoryTheory.Limits.cospanCompIso_app_left, CategoryTheory.TwoSquare.vComp_app, CategoryTheory.Sum.functorEquiv_unit_app_app_inl, CategoryTheory.Subgroupoid.inclusion_trans, LaxMonoidal.comp_μ, CategoryTheory.Join.mkFunctorLeft_inv_app, AlgebraicGeometry.isEmpty_pullback_sigmaι_of_ne, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₃, leftKanExtensionUniqueOfIso_hom, CategoryTheory.Limits.LimitPresentation.map_diag, CategoryTheory.MonoidalOpposite.unmopEquiv_counitIso_inv_app, CategoryTheory.Equivalence.sheafCongr.inverse_map_val_app, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d_1_0, CategoryTheory.Limits.limitFlipIsoCompLim_hom_app, CategoryTheory.shiftFunctorAdd_assoc_hom_app, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_hom_π_π, CategoryTheory.Limits.limIsoFlipCompWhiskerLim_inv_app_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_unitIso, TopCat.adj₂_unit, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_rightUnitor, CategoryTheory.Abelian.DoldKan.comparisonN_hom_app_f, CategoryTheory.MonoidalOpposite.tensorRightMopIso_hom_app_unmop, CategoryTheory.Equivalence.preregular_isSheaf_iff_of_essentiallySmall, CategoryTheory.Under.opEquivOpOver_counitIso, mapTriangleRotateIso_inv_app_hom₃, isIso_whiskerLeft, CategoryTheory.StructuredArrow.toUnder_map_left, op_comp_isSheaf_of_preservesOneHypercovers, AlgebraicGeometry.IsIntegralHom.instDescScheme, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_hom_left, SSet.Truncated.HomotopyCategory.BinaryProduct.associativityIso_hom_app, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerLeft, CategoryTheory.PreGaloisCategory.PointedGaloisObject.instHasColimitOppositeFunctorTypeCompOpInclCoyoneda, CategoryTheory.Adjunction.Triple.mono_leftToRight_app_iff_mono_adj₂_unit_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_inv_app_app, CategoryTheory.Limits.IndObjectPresentation.cocone_pt, toEssImageCompι_inv_app, CategoryTheory.Adjunction.Triple.epi_rightToLeft_app_iff_epi_map_adj₂_counit_app, Final.extendCocone_obj_pt, CategoryTheory.conjugateEquiv_adjunction_id, final_equivalence_comp, CategoryTheory.Limits.limit.id_pre, CategoryTheory.Comma.toIdPUnitEquiv_counitIso_inv_app, CategoryTheory.CostructuredArrow.preEquivalence.functor_map_left, CategoryTheory.StructuredArrow.preEquivalence_counitIso, CategoryTheory.ShiftMkCore.assoc_hom_app, RightExtension.postcomp₁_obj_hom_app, map_opShiftFunctorEquivalence_counitIso_inv_app_unop, ModuleCat.extendScalars_comp_id, CategoryTheory.NatTrans.commShift_iso_hom_of_localization, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app, CategoryTheory.regularTopology.equalizerCondition_iff_of_equivalence, CategoryTheory.functorProdFunctorEquivUnitIso_inv_app, SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁_inv_app_f_f, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_hom_app_val_app, CategoryTheory.RightExactFunctor.whiskeringLeft_obj_obj_obj, CategoryTheory.Equivalence.core_functor_map_iso_hom, commShiftOfLocalization.iso_hom_app_assoc, ι_leftKanExtensionObjIsoColimit_hom, CategoryTheory.instFullSheafFunctorOppositeCompSheafComposeSheafToPresheafOfFaithful, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₂, CategoryTheory.NatTrans.app_shift, leftDerivedNatTrans_fac, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_mul_app, CategoryTheory.Comma.coconeOfPreserves_pt_left, ι_colimitIsoOfIsLeftKanExtension_hom_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app_assoc, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_left_right_as, instIsIsoAppLanUnit_1, CategoryTheory.LaxFunctor.mapComp_naturality_left_app, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right_assoc, CategoryTheory.Limits.limitIsoFlipCompLim_inv_app, CategoryTheory.Join.mapPairLeft_hom_app, flipIsoCurrySwapUncurry_inv_app_app, CategoryTheory.cones_map_app_app, CategoryTheory.LocalizerMorphism.IsLocalizedEquivalence.isLocalization, AlgebraicGeometry.Scheme.Hom.instIsLocallyDirectedI₀DirectedCoverCompFunctorNormalizationGlueDataForget, CategoryTheory.NatTrans.Coequifibered.whiskerLeft, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_app_snd_app, CategoryTheory.MonoidalClosed.coev_app_comp_pre_app_assoc, CategoryTheory.whiskerRight_ι_colimitCompWhiskeringRightIsoColimitComp_inv, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_left_as, AlgebraicGeometry.PresheafedSpace.colimit_carrier, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₂, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_map_right_app, CategoryTheory.ChosenPullbacksAlong.unit_pullbackComp_hom, bddDistLat_dual_comp_forget_to_distLat, LightProfinite.Extend.functor_obj, LightCondensed.isoFinYoneda_hom_app, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app_assoc, CategoryTheory.Pseudofunctor.DescentData.pullFunctorCompIso_hom_app_hom, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₂, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformPrecomposeObjSquare_iso_hom_comp, CategoryTheory.Limits.limit.map_pre, FundamentalGroupoid.punitEquivDiscretePUnit_counitIso, mapCochainComplexShiftIso_hom_app_f, CategoryTheory.RelCat.opFunctor_comp_unopFunctor_eq, map_opShiftFunctorEquivalence_unitIso_inv_app_unop_assoc, CategoryTheory.SingleFunctors.shiftIso_add_hom_app, AlgebraicGeometry.Scheme.Hom.toNormalization_inl_normalizationCoprodIso_hom, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_apply_app, CategoryTheory.Equivalence.unop_unitIso, CategoryTheory.OppositeShift.adjunction_counit, bifunctorComp₁₂Iso_inv_app_app_app, PresheafOfModules.sheafificationAdjunction_homEquiv_apply, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_inv_app, CategoryTheory.Adjunction.representableBy_homEquiv, CategoryTheory.shiftFunctorCompIsoId_zero_zero_hom_app, AlgebraicGeometry.PresheafedSpace.restrict_presheaf, CategoryTheory.Over.postMap_app, toEssImageCompι_hom_app, CategoryTheory.Equivalence.trans_functor, TopCat.adj₁_unit, CochainComplex.shiftEval_inv_app, AlgebraicGeometry.Scheme.Hom.inr_toNormalization_normalizationCoprodIso_inv_assoc, CategoryTheory.StructuredArrow.preEquivalenceFunctor_obj_right, CategoryTheory.GrothendieckTopology.instIsIsoSheafAppFunctorOppositeSheafComposeNatTransPlusPlusAdjunction, CategoryTheory.Monad.ForgetCreatesLimits.liftedCone_π_app_f, whiskeringRight_obj_comp, CategoryTheory.TwoSquare.vComp'_app, CategoryTheory.Limits.walkingSpanOpEquiv_unitIso_hom_app, CategoryTheory.Limits.CatCospanTransform.comp_right, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app_assoc, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_right_as, ContinuousMap.comp_yonedaPresheaf', TopCat.Presheaf.presheafEquivOfIso_functor_map_app, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_X₂, rightUnitor_inv_app, CategoryTheory.Comonad.ComonadicityInternal.main_pair_F_cosplit, leftUnitor_hom_app, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_map_right, CategoryTheory.Grothendieck.ιCompMap_hom_app_base, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_inv, mapConeMapCone_inv_hom, CategoryTheory.GrothendieckTopology.liftToPlusObjLimitObj_fac, HomotopicalAlgebra.CofibrantObject.instIsLocalizationCompιWeakEquivalences, CategoryTheory.Adjunction.right_triangle_components_assoc, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom, ModuleCat.extendRestrictScalarsAdj_unit_app_apply, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_hom_app, CategoryTheory.TransfiniteCompositionOfShape.map_incl, homEquivOfIsRightKanExtension_apply_app, CategoryTheory.Equivalence.symmEquivInverse_obj_unitIso_inv, CategoryTheory.Adjunction.comp_unit, CategoryTheory.ExponentiableMorphism.unit_pushforwardComp_hom, CategoryTheory.Limits.comp_reflectsLimit, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₁, CategoryTheory.Limits.pointwiseProductCompEvaluation_hom_app, AlgebraicGeometry.instIsQuasicoherentOpensCarrierCarrierCommRingCatSpecTilde, TopCat.adj₁_counit, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceInverse_map_base, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_app, ranCounit_app_whiskerLeft_ranAdjunction_unit_app, CategoryTheory.Monad.MonadicityInternal.main_pair_G_split, alexDiscEquivPreord_counitIso, shiftIso_inv_naturality_assoc, CategoryTheory.Limits.Cocone.toCostructuredArrowCocone_pt, CategoryTheory.Limits.Cones.equivalenceOfReindexing_functor, LeftExtension.coconeAt_ι_app, CategoryTheory.Adjunction.unit_app_unit_comp_map_η_assoc, CategoryTheory.Presheaf.isLimit_iff_isSheafFor, SheafOfModules.Presentation.IsFinite.finite_relations, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_one_app, reflectsEpimorphisms_comp, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_left_as, mapTriangleCommShiftIso_hom_app_hom₂, Rep.coinvariantsAdjunction_unit_app_hom, CategoryTheory.Adjunction.leftAdjointCompIso_hom_app, CategoryTheory.NatTrans.shift_app_comm_assoc, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse, CategoryTheory.ComposableArrows.δ₀Functor_map_app, CategoryTheory.Comonad.instHasEqualizerMapAAppUnitObjAOfHasEqualizerOfIsCosplitPair, whiskerRight_twice, CategoryTheory.NatIso.pi'_hom, CategoryTheory.LocalizerMorphism.instCommShiftLocalizationHomFunctorIsoFunctorQLocalizedFunctor, CategoryTheory.Monad.MonadicityInternal.counitCofork_pt, TopologicalSpace.Opens.mapMapIso_counitIso, CategoryTheory.NatTrans.shift_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app, CategoryTheory.whiskering_linearYoneda₂, SSet.Truncated.HomotopyCategory.homToNerveMk_comp, IsDenseAt.of_final, CategoryTheory.ShortComplex.map_comp, CategoryTheory.Abelian.LeftResolution.π_naturality, isoWhiskerLeft_trans, CategoryTheory.Under.postAdjunctionRight_counit_app_right, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_counitIso, ShiftSequence.induced_shiftMap, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_comp_fiber, commShiftIso_eq_ofInduced, CategoryTheory.SmallObject.coconeOfLE_ι_app, AddCommMonCat.coyonedaForget_hom_app_app_hom, CategoryTheory.unitCompPartialBijectiveAux_symm_apply, CategoryTheory.Square.arrowArrowEquivalence'_counitIso, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.counitIso_hom, CategoryTheory.Pseudofunctor.DescentData.pullFunctorEquivalence_counitIso, CategoryTheory.TwoSquare.EquivalenceJ.inverse_obj, CategoryTheory.ShortComplex.leftHomologyFunctorOpNatIso_inv_app, CategoryTheory.shiftFunctorAdd_hom_app_obj_of_induced, isoWhiskerRight_trans_assoc, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₂, instIsAccessibleComp, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left_assoc, map_shiftFunctorComm, CategoryTheory.MonoOver.congr_counitIso, CategoryTheory.OplaxFunctor.mapComp_naturality_right_app_assoc, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.unitIso_hom, op_commShiftIso_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_app_fst_app, CategoryTheory.instSmallHomFunctorOppositeTypeColimitCompYoneda, AlgebraicTopology.DoldKan.Compatibility.equivalence₀_functor, CategoryTheory.CostructuredArrow.preEquivalence.inverse_map_left_left, CategoryTheory.Equivalence.op_unitIso, CategoryTheory.Groupoid.invEquivalence_unitIso, CategoryTheory.RightExactFunctor.whiskeringLeft_obj_map, skyscraperPresheafCoconeOfSpecializes_pt, CategoryTheory.Comma.preLeft_obj_left, HomotopyCategory.homologyFunctor_shiftMap, CategoryTheory.Adjunction.whiskerRight_counit_app_app, bifunctorComp₁₂Iso_hom_app_app_app, SemilatSupCat_dual_comp_forget_to_partOrd, descOfIsLeftKanExtension_fac_app, CategoryTheory.CatCommSq.hInv_iso_hom_app, CategoryTheory.CartesianMonoidalCategory.preservesTerminalIso_id, CategoryTheory.SimplicialObject.isCoskeletal_iff_isIso, CategoryTheory.Comma.mapLeftComp_hom_app_left, CategoryTheory.Comonad.ForgetCreatesLimits'.commuting, CategoryTheory.Quotient.lift_spec, CategoryTheory.TransfiniteCompositionOfShape.map_F, CategoryTheory.PresheafHom.isAmalgamation_iff, initial_equivalence_comp, CategoryTheory.Monad.MonadicityInternal.counitCofork_ι_app, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app, PresheafOfModules.sections_ext_iff, IsContinuous.op_comp_isSheaf_of_types, bifunctorComp₂₃Iso_hom_app_app_app, CategoryTheory.Adjunction.Triple.rightToLeft_app_adj₂_unit_app, PresheafOfModules.toPresheaf_map_sheafificationAdjunction_unit_app, CategoryTheory.Adjunction.toComonad_coe, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_assoc, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₁, Initial.extendCone_obj_π_app, CategoryTheory.Localization.SmallHom.equiv_shift, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₃, CategoryTheory.Limits.prodComparisonNatIso_inv, CategoryTheory.preserves_lift_mapCone, CochainComplex.shiftShortComplexFunctorIso_zero_add_hom_app, CategoryTheory.Grothendieck.pre_obj_fiber, instSecondCountableTopologyCarrierToTopTotallyDisconnectedSpacePtOppositeNatProfiniteCone, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv_assoc, CategoryTheory.uliftYonedaMap_app_apply, SheafOfModules.pushforward_id_comp, inrCompSum'_hom_app, WellOrderInductionData.Extension.map_limit, whiskeringLeftObjCompIso_hom_app_app, mapTriangleInvRotateIso_hom_app_hom₁, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.rightUnitor_hom_unit_app, functorialityCompPostcompose_inv_app_hom, LeftExtension.precomp₂_map_left, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_inv_app_assoc, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_inv_app_hom_hom, CategoryTheory.Abelian.LeftResolution.karoubi.π'_app_f, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_obj_map_app, IsCoverDense.Types.appIso_hom, CategoryTheory.Monad.MonadicityInternal.main_pair_reflexive, LightCondensed.internallyProjective_iff_tensor_condition', IsCoverDense.restrictHomEquivHom_naturality_right_symm_assoc, Final.extendCocone_map_hom, CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso_inv_app, CategoryTheory.Limits.DiagramOfCones.mkOfHasLimits_conePoints, AlgebraicGeometry.instMonoObjWalkingSpanCompOverSchemeTopMorphismPropertySpanOverForgetForgetForgetNoneWalkingPairSomeMapInitOfIsOpenImmersionLeftDiscretePUnit, CategoryTheory.Grothendieck.grothendieckTypeToCatInverse_obj_base, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_map_fst_app, CategoryTheory.Adjunction.IsMonoidal.instIsMonoidalCounit, SSet.Truncated.rightExtensionInclusion_hom_app, HomotopicalAlgebra.CofibrantObject.instWeakEquivalenceHoCatAppUnitHoCatAdj, CategoryTheory.MonoidalClosed.ofEquiv_curry_def, CategoryTheory.StructuredArrow.prodEquivalence_counitIso, CategoryTheory.Iso.coreWhiskerRight, CategoryTheory.Equivalence.changeInverse_unitIso_hom_app, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso_hom_app_f, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_inv_app_val_app_hom_hom, CategoryTheory.Adjunction.homEquiv_symm_rightAdjointUniq_hom_app, CategoryTheory.Pseudofunctor.map₂_whisker_right_app, CategoryTheory.sheafBotEquivalence_counitIso, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₃, CategoryTheory.unitOfTensorIsoUnit_hom_app, CategoryTheory.preservesLimitNatIso_hom_app, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_counitIso_inv, isoWhiskerLeft_hom, mapCocone_pt, CategoryTheory.Limits.whiskerLeft_ι_colimitCompWhiskeringLeftIsoCompColimit_inv, FullyFaithful.homNatIso_hom_app_down, Final.ι_colimitIso_hom, CategoryTheory.Adjunction.commShiftIso_inv_app_counit_app, CategoryTheory.Limits.IndizationClosedUnderFilteredColimitsAux.exists_nonempty_limit_obj_of_colimit, CategoryTheory.Monad.monadMonEquiv_unitIso_hom_app_toNatTrans_app, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_mul, initial_iff_initial_comp, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d_1_0_assoc, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompYoneda, AlgebraicTopology.DoldKan.Γ₂N₁_inv, CategoryTheory.Comonad.instReflectsLimitWalkingParallelPairParallelPairMapAAppUnitObjAOfReflectsLimitOfIsCosplitPair, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_hom_app, CategoryTheory.CostructuredArrow.initial_map₂_id, CategoryTheory.Comonad.CofreeEqualizer.bottomMap_f, CategoryTheory.MonoidalCategory.externalProductSwap_hom_app_app, coreflective', CategoryTheory.Adjunction.Triple.leftToRight_app_obj_assoc, CategoryTheory.CostructuredArrow.pre_map_left, CategoryTheory.shiftFunctorAdd'_assoc_hom_app_assoc, CategoryTheory.Equivalence.congrRight_unitIso_hom_app, CategoryTheory.IsUniversalColimit.whiskerEquivalence_iff, CategoryTheory.NatTrans.shift_app_comm, CategoryTheory.Join.mapPairRight_hom_app, limitIsoOfIsRightKanExtension_hom_π, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_hom_app_hom, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_hom_app_one, CategoryTheory.sheafComposeIso_hom_fac_assoc, CategoryTheory.Equivalence.sheafCongrPrecoherent_functor_map_val_app, CategoryTheory.sheafification_reflective, CategoryTheory.Limits.Cocone.mapCoconeToOver_hom_hom, mapConeWhisker_inv_hom, linOrd_dual_comp_forget_to_Lat, AlgebraicGeometry.instIsIsoFunctorModuleCatCarrierUnitModulesSpecOfAdjunction, pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_assoc, ShiftSequence.induced_isoShiftZero_hom_app_obj, CategoryTheory.sheafComposeIso_inv_fac, CategoryTheory.Limits.comp_preservesFiniteColimits, CategoryTheory.Limits.walkingSpanOpEquiv_counitIso_inv_app, SmallCategories.instPreservesFiniteLimitsSheafSheafPullbackOfRepresentablyFlat, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.functor_map, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app_assoc, CategoryTheory.WithInitial.pseudofunctor_mapComp, CategoryTheory.Monoidal.whiskerLeft_fst, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality, CategoryTheory.Grpd.freeForgetAdjunction_unit_app, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_hom, CategoryTheory.SingleFunctors.shiftIso_zero_hom_app, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_fst, CategoryTheory.NatTrans.exchange, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app_assoc, CategoryTheory.Pseudofunctor.map₂_left_unitor_app_assoc, CategoryTheory.equivEssImageOfReflective_counitIso, CategoryTheory.Adjunction.leftAdjointIdIso_inv_app, CategoryTheory.Limits.ι_colimitLimitToLimitColimit_π_assoc, map_shiftFunctorCompIsoId_inv_app, CategoryTheory.Equivalence.ε_comp_map_ε_assoc, CategoryTheory.Limits.FintypeCat.instFiniteObjCompFintypeCatIncl, CategoryTheory.Pseudofunctor.map₂_right_unitor_app_assoc, CategoryTheory.Pseudofunctor.map₂_right_unitor_app, CategoryTheory.Equivalence.core_unitIso_inv_app_iso_hom, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_obj, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_naturality_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_unitIso, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.flipFunctorToInterchange_hom_app_app, CategoryTheory.NatTrans.unop_whiskerRight_assoc, CategoryTheory.Limits.Cone.toStructuredArrowCompToUnderCompForget_inv_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_hom_app_app_fst, AlgebraicTopology.DoldKan.identity_N₂_objectwise, CategoryTheory.Subgroupoid.ker_comp, CategoryTheory.MonoidalOpposite.tensorRightUnmopIso_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_iso_hom_app, CategoryTheory.GrothendieckTopology.Point.sheafFiberCompIso_hom_app, CategoryTheory.preserves_desc_mapCocone, TopCat.Presheaf.IsSheaf.isSheafOpensLeCover, SSet.Truncated.HomotopyCategory.BinaryProduct.id_prod_mapHomotopyCategory_comp_inverse, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.hf, CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj_hom_naturality, CategoryTheory.Grpd.hom_to_functor, CategoryTheory.ι_preservesColimitIso_inv, CategoryTheory.MonoidalOpposite.tensorLeftMopIso_inv_app_unmop, CategoryTheory.Bimon.equivMonComonCounitIsoAppXAux_hom, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₃, CategoryTheory.Adjunction.hasColimit_comp_equivalence, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_inv_app_val_app, leftKanExtensionUnit_leftKanExtensionObjIsoColimit_hom_assoc, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCBasicOpens_app, ContinuousCohomology.MultiInd.d_succ, CategoryTheory.Adjunction.comp_counit_app_assoc, CategoryTheory.liftedLimitMapsToOriginal_hom_π, CategoryTheory.Adjunction.whiskerRight_unit_iso_of_R_fully_faithful, CategoryTheory.TwoSquare.GuitartExact.vComp, IsDenseSubsite.isIso_ranCounit_app_of_isDenseSubsite, CategoryTheory.Limits.opParallelPairIso_inv_app_zero, CategoryTheory.Equivalence.trans_unitIso, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_unitIso_inv_app_f_f, CategoryTheory.Comonad.left_counit_assoc, CategoryTheory.Under.postEquiv_unitIso, CategoryTheory.Grothendieck.pre_id, Monoidal.commTensorRight_hom_app, CategoryTheory.constantPresheafAdj_counit_app_app, CategoryTheory.CategoryOfElements.CreatesLimitsAux.map_lift_mapCone, CategoryTheory.Equivalence.sheafCongr.unitIso_inv_app_val_app, CategoryTheory.Sum.functorEquivFunctorCompSndIso_hom_app_app, SheafOfModules.pushforwardSections_coe, AlgebraicTopology.DoldKan.N₁Γ₀_inv_app_f_f, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τr, CategoryTheory.StructuredArrow.instFullCompPre, AlgebraicGeometry.IsLocalAtSource.sigmaDesc, CategoryTheory.WithTerminal.commaFromOver_obj_left, PresheafOfModules.fromFreeYonedaCoproduct_app_mk, CategoryTheory.Cat.HasLimits.homDiagram_obj, TopologicalSpace.Opens.overEquivalence_counitIso_hom_app, CategoryTheory.FreeGroupoid.mapCompLift_hom_app, CategoryTheory.ComposableArrows.opEquivalence_counitIso_hom_app_app, OplaxMonoidal.comp_δ, CategoryTheory.GrothendieckTopology.overMapPullback_assoc, AlgebraicGeometry.Scheme.isLocallyDirected_of_equifibered_of_injective, CategoryTheory.Comonad.ComonadicityInternal.counitFork_pt, CategoryTheory.Presheaf.isSheaf_coherent_of_hasPullbacks_comp, CategoryTheory.Limits.opParallelPairIso_inv_app_one, CategoryTheory.ExponentiableMorphism.pushforwardId_hom_counit, CategoryTheory.TwoSquare.lanBaseChange_app, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π, CategoryTheory.Sum.functorEquivFunctorCompFstIso_hom_app_app, CategoryTheory.whiskeringLeftCompEvaluation_inv_app, AlgebraicGeometry.Scheme.ofRestrict_app, CategoryTheory.CatCommSq.vId_iso_inv_app, CategoryTheory.yonedaYonedaColimit_app_inv, CategoryTheory.Limits.Cone.extensions_app, CategoryTheory.Grothendieck.grothendieckTypeToCatInverse_map_base, CategoryTheory.Limits.pullbackConeEquivBinaryFan_unitIso, CategoryTheory.Limits.CatCospanTransform.comp_left, CategoryTheory.ShrinkHoms.equivalence_unitIso, PresheafOfModules.germ_smul, CategoryTheory.OplaxFunctor.mapComp_naturality_left_app_assoc, CategoryTheory.Adjunction.left_triangle_components_assoc, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_one, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_inv_π, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquiv_functor, CategoryTheory.NatIso.unop_whiskerLeft, Final.comp_hasColimit, CategoryTheory.NatIso.hcomp_inv, CategoryTheory.Presieve.isSheaf_comp_uliftFunctor_iff, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.isIso_post, CategoryTheory.Over.forgetAdjStar_unit_app_left, map_opShiftFunctorEquivalence_counitIso_hom_app_unop_assoc, CategoryTheory.Discrete.functorComp_inv_app, shiftIso_hom_app_comp_shiftMap_of_add_eq_zero, CategoryTheory.mateEquiv_counit, CategoryTheory.Limits.HasLimit.isoOfEquivalence_inv_π, CategoryTheory.Comma.unopFunctorCompSnd_hom_app, CommShift.OfComp.map_iso_inv_app, rightKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, CategoryTheory.NatTrans.CommShift.whiskerLeft, whiskeringLeft_obj_obj, CategoryTheory.LaxFunctor.map₂_associator_app, CategoryTheory.NatTrans.instCommShiftOppositeShiftHomFunctorNatIsoComp, CategoryTheory.Adjunction.whiskerLeftRUnitIsoOfIsIsoCounit_inv_app, Initial.limit_pre_isIso, LightCondensed.lanPresheafExt_hom, CategoryTheory.PreGaloisCategory.PointedGaloisObject.cocone_app, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app, AlgebraicTopology.DoldKan.Compatibility.equivalence₂_functor, pi'_eval, CochainComplex.ShiftSequence.shiftIso_inv_app, CategoryTheory.Comma.preLeft_map_right, CategoryTheory.mateEquiv_square, compConstIso_inv_app_app, ranCompLimIso_hom_app, mapTriangleInvRotateIso_hom_app_hom₂, CategoryTheory.Limits.limit.pre_pre, CategoryTheory.constantSheafAdj_counit_app, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₂_app, Action.resComp_hom_app_hom, CategoryTheory.ProjectiveResolution.isoLeftDerivedObj_inv_naturality, CategoryTheory.Equivalence.funInvIdAssoc_inv_app, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_inv_app_f, CategoryTheory.Grothendieck.grothendieckTypeToCat_functor_map_coe, CategoryTheory.Localization.SmallShiftedHom.equiv_apply, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquiv_unitIso, CategoryTheory.sheafSectionsNatIsoEvaluation_hom_app, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_app_assoc, CategoryTheory.Adjunction.map_η_comp_η, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberCompIso_hom_app_assoc, CategoryTheory.Adjunction.op_counit, CategoryTheory.Presheaf.isSheaf_iff_isSheaf_forget, leftKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.Subgroupoid.inclusion_comp_embedding, CategoryTheory.Limits.colimCompFlipIsoWhiskerColim_inv_app_app, CategoryTheory.GrothendieckTopology.overMapPullback_id_comp, CategoryTheory.sum.inlCompAssociator_inv_app, CategoryTheory.ExactFunctor.whiskeringRight_obj_map, CategoryTheory.Limits.comp_reflectsCofilteredLimits, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.sheafCondition_iff_comp_coyoneda, isoWhiskerRight_inv, HomologicalComplex₂.flipEquivalenceCounitIso_hom_app_f_f, commShift₂_comm_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_inv_app_snd_app, CategoryTheory.NatIso.hcomp_hom, pointedToTwoPSnd_comp_forget_to_bipointed, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_left_right_as, CategoryTheory.WithInitial.liftToInitialUnique_inv_app, CategoryTheory.prod.functorProdToProdFunctorAssociator_inv_app, CategoryTheory.instIsReflexivePairMapAppCounitObj, CategoryTheory.WithInitial.mapComp_inv_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_aux_mul, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_hom_c_app, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_pt, HomologicalComplex.instHasColimitDiscreteWalkingPairCompPairEval, whiskerRight_left, limitIsoOfIsRightKanExtension_inv_π, Types.monoOverEquivalenceSet_counitIso, CategoryTheory.StructuredArrow.post_obj, CategoryTheory.PreservesFiniteLimitsOfFlat.fac, CategoryTheory.Limits.hasLimit_equivalence_comp, PresheafOfModules.pushforward₀_obj_obj_isModule, CategoryTheory.Limits.walkingCospanOpEquiv_unitIso_hom_app, FullyFaithful.hasShift.map_zero_inv_app, CategoryTheory.Comonad.ForgetCreatesLimits'.liftedConeIsLimit_lift_f, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_snd, Initial.comp_reflectsLimit, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app_assoc, curry_obj_comp_flip, CategoryTheory.Adjunction.leftAdjointIdIso_hom_app, CategoryTheory.Pseudofunctor.DescentData.pullFunctorEquivalence_unitIso, CategoryTheory.InjectiveResolution.rightDerivedToHomotopyCategory_app_eq, CategoryTheory.CategoryOfElements.CreatesLimitsAux.map_π_liftedConeElement, CategoryTheory.Comonad.ForgetCreatesColimits'.liftedCocone_ι_app_f, CategoryTheory.Limits.Cones.reflects_cone_isomorphism, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_fst, ShiftSequence.shiftIso_zero, commShiftIso_map₂CochainComplex_hom_app, CategoryTheory.Localization.lift₂_iso_hom_app_app₁, CategoryTheory.TwoSquare.hasPointwiseLeftKanExtension_iff, CategoryTheory.Adjunction.instIsIsoMapAppCounitOfFaithfulOfFull, CategoryTheory.Equivalence.trans_inverse, commBialgCatEquivComonCommAlgCat_counitIso_hom_app, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_left_as, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_left_left, CategoryTheory.Limits.opSpan_inv_app, CategoryTheory.LeftExactFunctor.whiskeringLeft_obj_map, CategoryTheory.Comma.post_obj_hom, Final.comp_preservesColimit, leftExtensionEquivalenceOfIso₁_counitIso_hom_app_right_app, CategoryTheory.SingleFunctors.shiftIso_add'_inv_app, CategoryTheory.Limits.coyonedaCompLimIsoCones_hom_app_app, partOrd_dual_comp_forget_to_preord, CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_right, CategoryTheory.Limits.whiskerLeft_ι_colimitCompWhiskeringLeftIsoCompColimit_inv_assoc, CategoryTheory.toOverUnitPullback_hom_app_left, CategoryTheory.Monad.left_unit_assoc, Condensed.isoFinYoneda_inv_app, CategoryTheory.ExponentiableMorphism.coev_ev, AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_inv_app, CategoryTheory.BasedFunctor.comp_toFunctor, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso_inv_app_app, CategoryTheory.Limits.comp_reflectsColimits, CategoryTheory.compEvaluation_inv_app, leftAdjointObjIsDefined_iff, CategoryTheory.Comonad.adj_unit, AlgebraicTopology.DoldKan.Compatibility.equivalence₂_inverse, CategoryTheory.Adjunction.map_ε_comp_counit_app_unit, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_app, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₂, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, CategoryTheory.Sum.functorEquiv_unitIso, PresheafOfModules.freeAdjunction_homEquiv, CategoryTheory.Cat.associator_hom_toNatTrans, CategoryTheory.Equivalence.op_counitIso, CategoryTheory.Presheaf.isLocallyInjective_forget, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₃, CategoryTheory.MonoidalOpposite.tensorLeftIso_inv_app_unmop, Initial.conesEquiv_functor, CategoryTheory.Sum.swapCompInr_inv_app, CategoryTheory.Limits.colimitYonedaHomIsoLimitRightOp_π_apply, CategoryTheory.WithInitial.opEquiv_unitIso_hom_app, CategoryTheory.ChosenPullbacksAlong.pullbackComp_hom_counit_assoc, CategoryTheory.Limits.FormalCoproduct.evalCompInclIsoId_hom_app_app, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_map_τ₃, CategoryTheory.Limits.comp_reflectsColimit, CategoryTheory.Comma.unopFunctorCompFst_hom_app, TopologicalSpace.OpenNhds.inclusionMapIso_inv_app, CategoryTheory.Sheaf.isConstant_iff_isIso_counit_app, CategoryTheory.Presheaf.tautologicalCocone_pt, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_rightUnitor, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_map, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_map_snd_app, CategoryTheory.Adjunction.homEquiv_leftAdjointUniq_hom_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_hom_app_hom_hom, CategoryTheory.Bicategory.associatorNatIsoMiddle_inv_app, ι_leftKanExtensionObjIsoColimit_hom_assoc, CategoryTheory.ThinSkeleton.map_comp_eq, CategoryTheory.ShiftMkCore.zero_add_inv_app, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.functor_obj, CategoryTheory.Limits.colimit.toOver_pt, comp_map, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_unitIso_hom_app_f_f, CategoryTheory.Adjunction.whiskerRight_unit_app_app, CategoryTheory.Quotient.natTransLift_app, ranAdjunction_unit_app, CategoryTheory.pullbackShiftFunctorAdd'_inv_app, Initial.comp_preservesLimit, CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_app_π, CategoryTheory.LocalizerMorphism.isLeftDerivabilityStructure_iff, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_limit_map_assoc, CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor, shiftIso_hom_naturality, Faithful.div_comp, coreComp_inv_app_iso_hom, CategoryTheory.MonoOver.lift_comm, CategoryTheory.CostructuredArrow.map₂_obj_hom, Full.comp, CategoryTheory.Bimon.toMon_Comon_ofMon_Comon_obj_mul, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_eq, CategoryTheory.Limits.Cocone.equivStructuredArrow_counitIso, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app_assoc, CategoryTheory.prodOpEquiv_counitIso_inv_app, CategoryTheory.Grothendieck.grothendieckTypeToCat_functor_obj_snd, CategoryTheory.MonoidalOpposite.tensorIso_inv_app_unmop, CategoryTheory.MonoidalOpposite.mopMopEquivalence_counitIso_hom_app, CategoryTheory.Comma.map_fst, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_app_assoc, AlgebraicTopology.DoldKan.N₁Γ₀_app, CategoryTheory.MorphismProperty.IsInvertedBy.map_iff, CategoryTheory.Equivalence.core_unitIso_inv_app_iso_inv, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp_hom_app_f, CategoryTheory.Limits.colimitLimitToLimitColimit_injective, lanAdjunction_counit_app, CategoryTheory.Adjunction.unit_comp_map_eq_iff, CategoryTheory.Limits.Cone.toStructuredArrowCone_pt, pointwiseLeftKanExtension_desc_app, RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π_assoc, CategoryTheory.coreFunctor_obj_map_iso_hom, CategoryTheory.Limits.CatCospanTransform.comp_base, isIso_lanAdjunction_counit_app_iff, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk_assoc, CategoryTheory.subterminals_to_monoOver_terminal_comp_forget, CategoryTheory.Adjunction.isIso_counit_app_iff_mem_essImage, CategoryTheory.shiftFunctorCompIsoId_zero_zero_inv_app, CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_inv_app, CategoryTheory.preadditiveCoyoneda_obj, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_obj_base, CategoryTheory.WithTerminal.equivComma_unitIso_hom_app_app, PresheafOfModules.pushforward_id_comp, CategoryTheory.prod.prodFunctorToFunctorProdAssociator_hom_app_app, CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse_assoc, CategoryTheory.TwoSquare.costructuredArrowRightwards_obj, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalence_counitIso, coreComp_inv_app_iso_inv, CategoryTheory.Adjunction.shift_unit_app_assoc, HomologicalComplex.homologyFunctorIso_inv_app, mapCoconeMapCocone_inv_hom, CategoryTheory.oppositeShiftFunctorAdd_hom_app, commShiftUnop_commShiftIso, TopCat.coconeOfCoconeForget_ι_app, CochainComplex.liftCycles_shift_homologyπ_assoc, CategoryTheory.Equivalence.counitInv_naturality_assoc, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_inv_app, CategoryTheory.Comma.colimitAuxiliaryCocone_ι_app, Condensed.isSheafProfinite, isRightKanExtension_iff_postcomp₁, ContAction.resComp_inv, CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatTrans_comp, HomotopicalAlgebra.CofibrantObject.HoCat.adjCounit'_app, CategoryTheory.Sheaf.sheafifyCocone_ι_app_val, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatTrans_app, ι_colimitIsoColimitGrothendieck_inv, ProfiniteGrp.instIsTopologicalGroupCarrierToTopTotallyDisconnectedSpacePtProfiniteLimitConeCompForget₂ContinuousMonoidHomToProfiniteContinuousMap, CategoryTheory.NonemptyParallelPairPresentationAux.hg, coreflective, CategoryTheory.StructuredArrow.instFullObjCompPostOfFaithful, CategoryTheory.Under.postAdjunctionLeft_unit_app, CategoryTheory.Adjunction.unop_unit, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_hom_app_hom_app, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_app, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop, CategoryTheory.WithTerminal.opEquiv_unitIso_inv_app, ShiftSequence.induced_shiftMap_assoc, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.relativeGluingData_natTrans_app, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_map_τ₂, pushforwardContinuousSheafificationCompatibility_hom_app_val, CategoryTheory.MonoidalCategory.DayConvolution.whiskerRight_comp_unit_app, CategoryTheory.Adjunction.commShiftIso_hom_app_counit_app_shift, CategoryTheory.Limits.Cocones.whiskering_map_hom, CategoryTheory.MorphismProperty.Over.pullbackComp_left_fst_fst, mapPresheaf_obj_presheaf, Profinite.Extend.functor_map, CategoryTheory.LaxFunctor.mapComp_assoc_right_app_assoc, CategoryTheory.Enriched.FunctorCategory.functorEnrichedHom_map, CategoryTheory.Limits.coneOfAdj_π, CategoryTheory.Bicategory.associatorNatIsoRight_inv_app, CategoryTheory.Limits.colimitCoyonedaHomIsoLimitLeftOp_π_apply, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_hom, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.convolutionUnitApp_eq, IsCoverDense.restrictHomEquivHom_naturality_right, isCorepresentable_comp_uliftFunctor_iff, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app, CategoryTheory.StructuredArrow.toUnder_obj_right, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_inv_π_assoc, AlgebraicGeometry.IsOpenImmersion.hasLimit_cospan_forget_of_left', CategoryTheory.instIsIsoSSetProdComparisonCatCompNerveFunctorHoFunctorOf, CategoryTheory.Grothendieck.grothendieckTypeToCatInverse_obj_fiber_as, CategoryTheory.Core.functorToCore_comp_left, CategoryTheory.CommGrp.forget₂CommMon_comp_forget, toStructuredArrow_comp_proj, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π_assoc, CategoryTheory.Bimon.toMon_Comon_ofMon_Comon_obj_one, Condensed.locallyConstantIsoFinYoneda_hom_app, CategoryTheory.Pi.comapComp_hom_app, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_left_right, CategoryTheory.GlueData.diagramIso_hom_app_right, 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, essSurj_comp, sheafPushforwardContinuousComp'_hom_app_val_app, AlgebraicGeometry.nonempty_isColimit_Γ_mapCocone, CategoryTheory.nerveAdjunction.isIso_counit, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_inv_app_val_app, CategoryTheory.Equivalence.counit_app_functor, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_apply, OrderIso.equivalence_unitIso, CategoryTheory.Equivalence.CommShift.instCommShiftHomFunctorUnitIso, SSet.StrictSegal.isRightKanExtension, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.Limits.reflexivePair.whiskerRightMkNatTrans, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_assoc, CategoryTheory.Limits.Cocones.functorialityEquivalence_functor, CategoryTheory.piEquivalenceFunctorDiscrete_counitIso, CategoryTheory.SingleFunctors.shiftIso_add'_hom_app, alexDiscEquivPreord_functor, CategoryTheory.Pi.equivalenceOfEquiv_functor, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_inv_app_op_one, AlgebraicGeometry.coprodMk_inr, CategoryTheory.Equivalence.sheafCongr.counitIso_inv_app_val_app, mapMatComp_inv_app, CategoryTheory.Limits.comp_reflectsColimitsOfShape, CategoryTheory.Sieve.functorPushforward_equivalence_eq_pullback, CategoryTheory.Limits.opHomCompWhiskeringLimYonedaIsoCocones_inv_app_app, PresheafOfModules.freeObjDesc_app, CategoryTheory.sheafSectionsNatIsoEvaluation_inv_app, CategoryTheory.Comma.map_snd, CategoryTheory.Presheaf.instIsIsoFunctorLeftKanExtensionUnitOppositeTypeUliftYoneda, CategoryTheory.CostructuredArrow.initial_pre, mapDerivedCategoryFactorsh_hom_app, CategoryTheory.OplaxFunctor.mapComp_naturality_right_app, CategoryTheory.Limits.colimit.ι_inv_pre_assoc, CategoryTheory.Adjunction.Localization.η_app, CategoryTheory.StructuredArrow.map₂_obj_hom, CategoryTheory.sum.inlCompInverseAssociator_hom_app_down_down, sheafAdjunctionCocontinuous_unit_app_val, CategoryTheory.StructuredArrow.mapNatIso_counitIso_inv_app_right, map_opShiftFunctorEquivalence_unitIso_hom_app_unop, CategoryTheory.Limits.comp_preservesFiniteLimits, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_zero, CategoryTheory.Equivalence.pi_counitIso, Condensed.instAB4CondensedMod, mapDifferentialObject_map_f, CategoryTheory.oppositeShiftFunctorAdd'_inv_app, CategoryTheory.Equivalence.symmEquivInverse_obj_unitIso_hom, CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit, whiskeringRight_map_app_app, CategoryTheory.Bimon.equivMonComonCounitIsoApp_inv_hom_hom, CategoryTheory.Limits.Cones.whiskering_obj, lanUnit_app_app_lanAdjunction_counit_app_app_assoc, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_right, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.counitIso_hom, CategoryTheory.Monad.ForgetCreatesColimits.liftedCoconeIsColimit_desc_f, CategoryTheory.GrothendieckTopology.Point.sheafFiberCompIso_inv_app, CategoryTheory.GrothendieckTopology.uliftYoneda_map_val_app_down, CategoryTheory.Limits.FormalCoproduct.evalOpCompInlIsoId_inv_app_app, CategoryTheory.Abelian.DoldKan.comparisonN_inv_app_f, HomologicalComplex.homologyFunctorSingleIso_hom_app, CategoryTheory.Adjunction.homEquiv_id, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_inv_app_fst_app, instIsIsoAppRanCounit_1, CategoryTheory.Limits.Cones.postcomposeComp_hom_app_hom, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_hom_app, SSet.Truncated.HomotopyCategory.homToNerveMk_comp_assoc, TopCat.Presheaf.presheafEquivOfIso_inverse_map_app, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓFreeOpensCarrierCarrierCommRingCat, CategoryTheory.Equivalence.adjointify_η_ε, CategoryTheory.Limits.Cocone.extensions_app, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_map_app, CategoryTheory.LaxFunctor.mapComp_assoc_left_app_assoc, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₁, inv_whiskerRight, CategoryTheory.Equivalence.inverse_counitInv_comp, CategoryTheory.WithTerminal.liftToTerminalUnique_hom_app, TopologicalSpace.OpenNhds.inclusionMapIso_hom_app, CategoryTheory.flipCompEvaluation_inv_app, FullyFaithful.hasShift.map_zero_hom_app, CategoryTheory.instEpiFunctorWhiskerRightOfPreservesEpimorphisms, Fiber.fiberInclusionCompIsoConst_hom_app, leftKanExtensionIsoFiberwiseColimit_inv_app, toOver_comp_forget, CategoryTheory.shiftFunctorAdd_assoc_inv_app, CategoryTheory.LaxFunctor.map₂_leftUnitor_app, HomologicalComplex.isZero_single_comp_eval, CategoryTheory.Adjunction.left_triangle_components, AlgebraicGeometry.PresheafedSpace.colimitCocone_ι_app_c, CategoryTheory.sheafCompose_obj_val, CategoryTheory.Equivalence.core_counitIso_inv_app_iso_inv, FundamentalGroupoidFunctor.coneDiscreteComp_obj_mapCone, CategoryTheory.Join.InclRightCompRightOpOpEquivFunctor_hom_app, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_right_hom, CategoryTheory.Equivalence.unit_app_tensor_comp_inverse_map_δ_functor, CategoryTheory.Join.mapPairRight_inv_app, RightExtension.postcompose₂ObjMkIso_hom_left_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₁, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_inv_app_f, equiv_counitIso, CategoryTheory.WithTerminal.equivComma_unitIso_inv_app_app, CategoryTheory.Limits.Cocones.whiskeringEquivalence_counitIso, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_hom_app, CategoryTheory.Pseudofunctor.Grothendieck.categoryStruct_comp_fiber, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_obj_hom, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right, AlgebraicGeometry.Scheme.Modules.pseudofunctor_associativity, CategoryTheory.NatTrans.CommShiftCore.app_shift_assoc, PresheafOfModules.map_comp_assoc, CategoryTheory.CostructuredArrow.preEquivalence.functor_obj_left, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app, CategoryTheory.Limits.Cocones.functorialityEquivalence_unitIso, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.epi_f, CategoryTheory.Comma.mapLeftComp_hom_app_right, CategoryTheory.Adjunction.whiskerLeft_unit_iso_of_R_fully_faithful, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_μ_assoc, CategoryTheory.ThinSkeleton.comp_toThinSkeleton, CategoryTheory.Limits.colimit.pre_eq, CategoryTheory.shiftFunctorAdd'_assoc_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.iso_hom_naturality, Final.coconesEquiv_inverse, unopComp_hom_app, rightDerived_fac, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_obj_hom, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberCompIso_hom_app, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₁, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_inv_π_π_assoc, AlgebraicTopology.DoldKan.Compatibility.υ_inv_app, compFlipUncurryIso_hom_app, CategoryTheory.LocalizerMorphism.IsLeftDerivabilityStructure.guitartExact', IsCoverDense.Types.pushforwardFamily_apply, CategoryTheory.SingleFunctors.postcomp_shiftIso_hom_app, commBialgCatEquivComonCommAlgCat_counitIso_inv_app, CategoryTheory.Pseudofunctor.CoGrothendieck.compIso_hom_app, CategoryTheory.whiskeringLeftCompEvaluation_hom_app, CategoryTheory.unit_obj_eq_map_unit, CategoryTheory.Pretriangulated.Triangle.functorMk_obj, leftExtensionEquivalenceOfIso₁_unitIso_inv_app_right_app, whiskeringRightObjCompIso_inv_app_app, CategoryTheory.CategoryOfElements.CreatesLimitsAux.liftedCone_pt_fst, CategoryTheory.Equivalence.unit_inverse_comp_assoc, CategoryTheory.Join.mkFunctorRight_hom_app, CategoryTheory.Comma.mapFst_inv_app, CategoryTheory.Iso.coreWhiskerLeft, CategoryTheory.Adjunction.Triple.whiskerLeft_leftToRight, CategoryTheory.MonoidalCategory.DayConvolutionUnit.corepresentableByRight_homEquiv, CategoryTheory.Subfunctor.equivalenceMonoOver_counitIso, CategoryTheory.WithTerminal.coneEquiv_counitIso_hom_app_hom, TopCat.Sheaf.pushforward_forget, CategoryTheory.presheafHom_map_app_op_mk_id, CategoryTheory.Grothendieck.pre_map_base, Condensed.lanPresheafIso_hom, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_app_app_germToPullbackStalk, pointedToBipointedSnd_comp_swap, IsDense.comp_right_iff_of_isEquivalence, CategoryTheory.CostructuredArrow.isEquivalence_post, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_inv_app, CategoryTheory.whiskeringRight_comp_evaluation, CommShift.isoAdd'_inv_app, CategoryTheory.Adjunction.derivedε_fac_app, CategoryTheory.instIsIsoPost, CategoryTheory.Localization.associator_hom_app_app_app, OplaxMonoidal.ofBifunctor.topMapₗ_app, CategoryTheory.StructuredArrow.pre_obj_left, CommShift.OfComp.map_iso_hom_app, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_ι_inv_assoc, CommShift.OfComp.map_iso_inv_app_assoc, CommShift.isoZero'_hom_app, CategoryTheory.Equivalence.congrRight_counitIso_inv_app, CategoryTheory.Equivalence.counit_naturality, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.unitIso_inv_app_hom_app, CategoryTheory.Limits.Cocones.precomposeEquivalence_counitIso, CategoryTheory.Sigma.natIso_hom, CategoryTheory.forgetAdjToOver_counit_app, CategoryTheory.Limits.instIsWellOrderContinuousCompOfPreservesWellOrderContinuousOfShape, CategoryTheory.sum.inrCompInverseAssociator_inv_app, comp_mapMon_one, CategoryTheory.sheafComposeNatTrans_fac, CategoryTheory.Pi.comapEvalIsoEval_inv_app, CategoryTheory.CostructuredArrow.mapIso_counitIso_inv_app_left, CategoryTheory.Limits.widePushoutShapeOpEquiv_unitIso, rightKanExtensionCompIsoOfPreserves_inv_fac_assoc, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₁, CategoryTheory.SimplicialObject.Truncated.whiskering_obj_map_app, CategoryTheory.OplaxFunctor.map₂_rightUnitor_app_assoc, pointwiseLeftKanExtensionCompIsoOfPreserves_inv_fac_assoc, CategoryTheory.Adjunction.map_μ_comp_counit_app_tensor_assoc, CategoryTheory.MonoidalCategory.DayFunctor.ι_comp_isoPointwiseLeftKanExtension_inv, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_map_fst, CategoryTheory.shiftFunctorAdd_zero_add_inv_app, CategoryTheory.Adjunction.homEquiv_symm_apply, CategoryTheory.shiftFunctorComm_hom_app_of_add_eq_zero_assoc, Initial.limitConeOfComp_isLimit, CategoryTheory.Adjunction.counit_isSplitMono_of_R_full, bifunctorComp₂₃Iso_inv_app_app_app, CategoryTheory.ihom.ev_coev, ModuleCat.ihom_ev_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_hom_app_hom, CategoryTheory.MonoidalClosed.whiskerLeft_curry_ihom_ev_app_assoc, CategoryTheory.Limits.limit.pre_π, TopCat.Presheaf.isSheaf_of_isOpenEmbedding, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.w_app_assoc, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_inv_app, CochainComplex.liftCycles_shift_homologyπ, CategoryTheory.Adjunction.inv_map_unit, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app_val_app, AlgebraicTopology.DoldKan.Γ₂N₂_inv, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_right_right, CategoryTheory.prod.functorProdToProdFunctorAssociator_hom_app, CategoryTheory.StructuredArrow.mapIso_counitIso_hom_app_right, CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_inv_assoc, costructuredArrowMapCocone_ι_app, CategoryTheory.Adjunction.mapCommGrp_counit, CategoryTheory.Join.inlCompFromSum_inv_app, mapTriangle_map_hom₂, CategoryTheory.Pi.comapEvalIsoEval_hom_app, comp_mapCommMon_one, PresheafOfModules.pushforward_comp_id, CategoryTheory.Equivalence.congrRight_counitIso_hom_app, CategoryTheory.Adjunction.functorialityCounit'_app_hom, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceFunctorProj_inv_app, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop_assoc, homEquivOfIsLeftKanExtension_apply_app, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_hom_whiskerLeft_π, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_right_app, CategoryTheory.Over.mapForget_eq, CategoryTheory.ExponentiableMorphism.unit_pushforwardComp_hom_assoc, CategoryTheory.Square.arrowArrowEquivalence_counitIso, CategoryTheory.Precoverage.comap_comp, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality, CategoryTheory.Sum.functorEquiv_counitIso, CategoryTheory.WithInitial.mapComp_hom_app, CategoryTheory.Idempotents.DoldKan.η_hom_app_f, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_left, lanCompColimIso_hom_app, CategoryTheory.Pretriangulated.preadditiveCoyoneda_homologySequenceδ_apply, Profinite.exists_hom, LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm_assoc, CategoryTheory.Adjunction.Triple.leftToRight_app_map_adj₁_unit_app, CategoryTheory.Sigma.inclDesc_hom_app, CategoryTheory.Over.postAdjunctionLeft_counit_app_left, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_hom_app_app, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_left_hom, CategoryTheory.LaxFunctor.map₂_leftUnitor_app_assoc, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_hom, CategoryTheory.Comma.mapRightComp_inv_app_left, CategoryTheory.Limits.cospanCompIso_app_right, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_right, CategoryTheory.StructuredArrow.preEquivalenceFunctor_obj_hom, CategoryTheory.StructuredArrow.mapIso_counitIso_inv_app_right, CategoryTheory.ShiftMkCore.assoc_hom_app_assoc, CategoryTheory.Equivalence.changeFunctor_counitIso_inv_app, IsCoverDense.restrictHomEquivHom_naturality_left_symm, CategoryTheory.Reflective.instIsIsoAppUnitReflectorAdjunctionA, CategoryTheory.Sum.functorEquiv_functor_obj, AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_app, CategoryTheory.SingleFunctors.shiftIso_zero_inv_app, AlgebraicGeometry.Scheme.Hom.inl_toNormalization_normalizationCoprodIso_inv, AlgebraicGeometry.Scheme.Hom.inr_normalizationCoprodIso_hom_fromNormalization, isoWhiskerLeft_symm, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply_assoc, 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, CategoryTheory.GlueData.diagramIso_hom_app_left, ModuleCat.extendScalars_assoc, CategoryTheory.Enriched.FunctorCategory.functorEnrichedId_app, CategoryTheory.Equivalence.congrRight_unitIso_inv_app, CategoryTheory.Adjunction.shift_counit_app_assoc, CategoryTheory.shift_neg_shift', CategoryTheory.Monoidal.Reflective.instIsIsoMapTensorHomAppUnit, CategoryTheory.MonoidalOpposite.mopEquiv_counitIso, CategoryTheory.LeftExactFunctor.whiskeringRight_obj_obj_obj, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality_assoc, CategoryTheory.CategoryOfElements.CreatesLimitsAux.π_liftedConeElement', CategoryTheory.ihom.coev_ev_assoc, CategoryTheory.RightExactFunctor.whiskeringRight_obj_map, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_hom_whiskerRight_π, CategoryTheory.LocalizerMorphism.essSurj_of_hasLeftResolutions, CategoryTheory.Join.edgeTransform_app, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_counit, CategoryTheory.Adjunction.mapGrp_counit, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_counitIso_hom, liftOfIsRightKanExtension_fac_assoc, CategoryTheory.Equivalence.functor_unit_comp_assoc, AddCommGrpCat.hasLimit_iff_small_sections, comp_mapGrp_one, CategoryTheory.Pi.comapComp_inv_app, CategoryTheory.Adjunction.unit_naturality_assoc, Final.colimitCoconeOfComp_cocone, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_inv_app_fst_app, CategoryTheory.ShiftMkCore.assoc_inv_app, CategoryTheory.constantPresheafAdj_unit_app, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app_assoc, CategoryTheory.Limits.limit_map_limitObjIsoLimitCompEvaluation_hom, CategoryTheory.Equivalence.symmEquivInverse_map_app, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app_assoc, CategoryTheory.ShiftedHom.opEquiv'_add_symm, CategoryTheory.Sigma.inclDesc_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_hom_app, pointwiseLeftKanExtensionCompIsoOfPreserves_inv_fac, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_hom, CategoryTheory.Adjunction.Triple.mono_leftToRight_app_iff, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app, HomologicalComplex.forgetEval_inv_app, CategoryTheory.colimitYonedaHomEquiv_π_apply, CategoryTheory.Equivalence.induced_counitIso, CategoryTheory.Adjunction.comp_unit_app, CategoryTheory.NatTrans.IsMonoidal.whiskerLeft, CategoryTheory.comonEquiv_counitIso, CategoryTheory.ParametrizedAdjunction.whiskerLeft_map_counit_assoc, CategoryTheory.StructuredArrow.pre_obj_right, AlgebraicGeometry.PresheafedSpace.ofRestrict_c_app, whiskeringLeft_map_app_app, PresheafOfModules.instPreservesFiniteLimitsSheafAddCommGrpCatCompSheafOfModulesSheafificationToSheaf, CategoryTheory.Adjunction.whiskerLeft_counit_app_app, CategoryTheory.TwoSquare.ext_iff, CategoryTheory.Limits.comp_reflectsLimitsOfShape, CategoryTheory.Comma.preLeft_obj_hom, CategoryTheory.FreeGroupoid.map_comp, CategoryTheory.Localization.whiskeringLeftFunctor'_obj, CategoryTheory.Cat.freeMapCompIso_inv_app, IsCoverDense.Types.naturality_assoc, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit, CategoryTheory.Limits.colimitFlipIsoCompColim_inv_app, CategoryTheory.Square.flipEquivalence_counitIso, CategoryTheory.Adjunction.adjunctionOfEquivLeft_unit_app, CategoryTheory.Adjunction.leftAdjointCompNatTrans_app, RightExtension.precomp_obj_left, CategoryTheory.TwoSquare.vId_app, CompHausToLocale.faithful, ModuleCat.ExtendRestrictScalarsAdj.unit_app, CategoryTheory.Limits.colimitLimitToLimitColimit_surjective, instIsEquivalenceRightExtensionCompPrecomp, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_hom_app, mapCommMonCompIso_hom_app_hom_hom, Final.colimitIso_inv, CategoryTheory.evaluationAdjunctionLeft_counit_app, CategoryTheory.functorProdFunctorEquivCounitIso_hom_app_app, PresheafOfModules.pushforward₀_obj_map, SheafOfModules.unitHomEquiv_apply_coe, CategoryTheory.Monad.right_unit_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_app_assoc, CochainComplex.ShiftSequence.shiftIso_hom_app, CategoryTheory.Limits.widePullbackShapeOpEquiv_unitIso, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInlIso_inv_app_app, CategoryTheory.Presheaf.isSheaf_iff_isLimit_pretopology, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_shift, bipointedToPointedFst_comp_forget, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_assoc, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π, CategoryTheory.mateEquiv_apply, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_map_left_right, structuredArrowMapCone_π_app, whiskeringLeftObjCompIso_inv_app_app, CategoryTheory.Presieve.functorPushforward_comp, IsTriangulated.instComp, CategoryTheory.whiskering_preadditiveCoyoneda, uncurry_obj_curry_obj_flip_flip, CategoryTheory.CartesianMonoidalCategory.instIsIsoFunctorProdComparisonBifunctorNatTransOfProdComparison, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_inv_app_fst_app, CategoryTheory.Limits.coprodComparisonNatIso_inv, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_app, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_map_app_app_app, CategoryTheory.Quotient.comp_natTransLift, CategoryTheory.Limits.compYonedaSectionsEquiv_symm_apply_coe, linear_comp_iff_of_full_of_essSurj, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app_assoc, HomotopyCategory.instCommShiftHomologicalComplexIntUpHomFunctorMapHomotopyCategoryFactors, CategoryTheory.Comma.coneOfPreserves_π_app_left, CochainComplex.mappingCone.map_δ, CategoryTheory.unitCompPartialBijective_symm_apply, CategoryTheory.ihom.coev_ev, CategoryTheory.PreGaloisCategory.functorToAction_comp_forget₂_eq, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_εIso_hom, isRightKanExtensionAlongEquivalence, CategoryTheory.Monad.ForgetCreatesColimits.newCocone_ι, CategoryTheory.Limits.parallelPairOpIso_hom_app_zero, IsCoverDense.Types.naturality, CategoryTheory.LiftRightAdjoint.instIsCoreflexivePairMapAppUnitOtherMap, mapComposableArrows_map_app, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_hom
id 📖	CompOp	3104 math math: TopCat.Presheaf.generateEquivalenceOpensLe_functor'_obj_obj, CategoryTheory.Equivalence.adjointify_η_ε_assoc, CommRingCat.tensorProd_map_right, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₃, CategoryTheory.shiftFunctorZero_inv_app_obj_of_induced, CategoryTheory.Limits.Cones.postcomposeId_hom_app_hom, CategoryTheory.Limits.kernelSubobjectMap_arrow_assoc, CategoryTheory.Over.associator_hom_left_snd_fst_assoc, CategoryTheory.Limits.coker.π_app, CategoryTheory.GrothendieckTopology.overMapPullbackId_hom_app_val_app, CategoryTheory.Adjunction.adjunctionOfEquivLeft_counit_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_eq, whiskeringRightObjIdIso_hom_app_app, CategoryTheory.Join.pseudofunctorLeft_mapId_inv_toNatTrans_app, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₁, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_fst, CategoryTheory.SimplicialObject.id_left_app, CategoryTheory.Over.prodLeftIsoPullback_hom_snd_assoc, CategoryTheory.prodComonad_ε_app, CategoryTheory.Adjunction.compUliftCoyonedaIso_hom_app_app_down, CategoryTheory.Equivalence.prod_unitIso, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_map, CategoryTheory.Adjunction.Triple.isIso_unit_iff_isIso_counit, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_hom_app_zero, CategoryTheory.Adjunction.leftOp_unit, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_hom_left, CategoryTheory.Sum.natTransOfWhiskerLeftInlInr_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitNatIso_inv_app, CategoryTheory.Limits.HasImage.of_arrow_iso, CategoryTheory.Equivalence.leftOp_unitIso_hom_app, CategoryTheory.Over.μ_pullback_left_snd', CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_hom_app_val_app, CategoryTheory.WithTerminal.coneEquiv_unitIso_hom_app_hom_left, mapTriangleIdIso_inv_app_hom₃, CategoryTheory.Monad.monadMonEquiv_unitIso_inv_app_toNatTrans_app, IsDenseSubsite.instIsIsoSheafAppCounitSheafAdjunctionCocontinuous, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, CategoryTheory.ComposableArrows.opEquivalence_counitIso_inv_app_app, CategoryTheory.mateEquiv_counit_symm, CategoryTheory.Discrete.sumEquiv_counitIso_inv_app, CategoryTheory.WithTerminal.mkCommaObject_right, CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_left, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst_assoc, leibnizPullback_obj_map, CategoryTheory.isIso_sheafificationAdjunction_counit, CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_p, AlgebraicTopology.DoldKan.Compatibility.equivalence₀_unitIso_hom_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_left, CategoryTheory.WithInitial.equivComma_functor_obj_right_obj, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app, CategoryTheory.Adjunction.whiskerLeftLCounitIsoOfIsIsoUnit_hom_app, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.Equivalence.sheafCongr.counitIso_hom_app_val_app, CategoryTheory.shift_shiftFunctorCompIsoId_hom_app, AlgebraicGeometry.Scheme.Modules.pushforwardId_inv_app_app, CategoryTheory.SmallObject.SuccStruct.prop.arrowIso_hom_left, CategoryTheory.Arrow.equivSigma_symm_apply_left, CategoryTheory.RetractArrow.right_r, CategoryTheory.comonEquiv_unitIso, CategoryTheory.ihom.coev_naturality, CategoryTheory.Monad.id_η_app, CategoryTheory.equivOfTensorIsoUnit_unitIso, mapHomologicalComplexIdIso_hom_app_f, AlgebraicGeometry.Scheme.Cover.pullbackCoverOver_X, CategoryTheory.Join.mapPairId_hom_app, CategoryTheory.Adjunction.whiskerLeftLCounitIsoOfIsIsoUnit_inv_app, CategoryTheory.Over.ConstructProducts.conesEquivInverseObj_pt, CategoryTheory.LocalizerMorphism.id_functor, CategoryTheory.Equivalence.mapGrp_counitIso, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_hom_app_eq, CategoryTheory.eq_counitIso, CategoryTheory.shiftFunctorComm_zero_hom_app, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_hom_app, CategoryTheory.Limits.coconeEquivalenceOpConeOp_unitIso, PresheafOfModules.pullback_id_comp, CategoryTheory.CostructuredArrow.toOver_obj_left, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_inv_app_val_app, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_right_right, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_e, CategoryTheory.MonoOver.mk_coe, CategoryTheory.SmallObject.SuccStruct.prop.arrowIso_inv_left, CategoryTheory.Join.pseudofunctorRight_mapComp_inv_toNatTrans_app, CategoryTheory.Limits.multicospanIndexEnd_fst, CategoryTheory.WithTerminal.equivComma_functor_obj_left_obj, instIsIsoAppCounitRanAdjunctionOfHasPointwiseRightKanExtension, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_fst, CategoryTheory.equivEssImageOfReflective_unitIso, IsLocalization.for_id, CategoryTheory.OverPresheafAux.costructuredArrowPresheafToOver_map, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_hom, AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_inv_app, CategoryTheory.Adjunction.Triple.epi_rightToLeft_app_iff_epi_map_adj₁_unit_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_inv_app_hom, CategoryTheory.Adjunction.Localization.ε_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitNatIso_hom_app, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_pullback_map, CategoryTheory.PullbackShift.adjunction_counit, CategoryTheory.Equivalence.unitIso_hom_app_comp_inverse_map_η_functor_assoc, CategoryTheory.MonoOver.congr_unitIso, CategoryTheory.Adjunction.unit_app_tensor_comp_map_δ_assoc, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_left_app, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.isMonHom_counitIsoAux, CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₁, CategoryTheory.OverPresheafAux.unitAux_hom, CategoryTheory.CosimplicialObject.id_right_app, CategoryTheory.MorphismProperty.FunctorialFactorizationData.i_mapZ_assoc, CategoryTheory.Over.iteratedSliceBackward_map, CategoryTheory.Limits.CatCospanTransform.id_right, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_unitIso, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_map_left_left, CategoryTheory.Over.associator_inv_left_snd, CategoryTheory.Discrete.sumEquiv_unitIso_inv_app, CategoryTheory.Abelian.LeftResolution.epi_π_app, mapArrow_obj, AlgebraicGeometry.ΓSpec.isIso_adjunction_counit, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₃, CategoryTheory.MorphismProperty.map_id, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_app_assoc, CategoryTheory.WithInitial.opEquiv_unitIso_inv_app, CategoryTheory.Equivalence.counitIso_inv_app_comp_functor_map_η_inverse, TopCat.Presheaf.germ_stalkPullbackHom, CategoryTheory.Under.postComp_inv_app_right, CategoryTheory.Over.pullback_obj_left, Rep.coindResAdjunction_counit_app, CategoryTheory.orderDualEquivalence_unitIso, CategoryTheory.Adjunction.map_ε_comp_counit_app_unit_assoc, AddCommMonCat.equivalence_unitIso, partialFunEquivPointed_counitIso_inv_app_toFun, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_counit_app_app, CategoryTheory.Over.inv_left_hom_left_assoc, CategoryTheory.TwistShiftData.z_zero_zero, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₂, commBialgCatEquivComonCommAlgCat_unitIso_inv_app, TopCat.Presheaf.generateEquivalenceOpensLe_unitIso, partialFunEquivPointed_unitIso_hom_app, CategoryTheory.CosimplicialObject.augment_right, CategoryTheory.Limits.HasColimit.isoOfEquivalence_inv_π, CategoryTheory.CatCenter.app_sub, Rep.resCoindAdjunction_counit_app_hom_hom, CategoryTheory.Comonad.ComonadicityInternal.unitFork_π_app, CategoryTheory.Monoidal.transportStruct_associator, CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse_map_right, CategoryTheory.Adjunction.instIsIsoAppUnitObjOfFaithfulOfFull, CategoryTheory.Idempotents.functorExtension₁CompWhiskeringLeftToKaroubiIso_inv_app_app_f, ModuleCat.extendScalarsId_hom_app_one_tmul, CategoryTheory.SimplicialObject.comp_right, CategoryTheory.Adjunction.mapMon_unit, CategoryTheory.SimplicialObject.Augmented.point_map, CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_left_app, CategoryTheory.Under.forgetMapInitial_inv_app, CategoryTheory.Arrow.hom_inv_id_right_assoc, CategoryTheory.RetractArrow.retract_left_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_map_app, CategoryTheory.NatIso.op_rightUnitor, CategoryTheory.WithInitial.isColimitEquiv_apply_desc_right, CategoryTheory.Join.mapPairEquiv_unitIso, CategoryTheory.MonoOver.isIso_left_iff_subobjectMk_eq, CategoryTheory.Adjunction.derivedε_fac_app_assoc, CategoryTheory.Join.mapPairEquiv_counitIso, CategoryTheory.Monad.Algebra.unit_assoc, CategoryTheory.CostructuredArrow.prodEquivalence_counitIso, CategoryTheory.Equivalence.rightOp_counitIso_inv_app, PullbackObjObj.mapArrowRight_right, CategoryTheory.shiftFunctorAdd'_zero_add, CategoryTheory.GrothendieckTopology.overMapPullback_comp_id, CategoryTheory.RetractArrow.left_r, CategoryTheory.Under.equivalenceOfIsInitial_counitIso, CategoryTheory.Sieve.overEquiv_pullback, CategoryTheory.Over.rightUnitor_inv_left_fst_assoc, PushoutObjObj.mapArrowRight_id, PullbackObjObj.mapArrowLeft_id, CategoryTheory.MorphismProperty.Over.hasPullbacks, CategoryTheory.Comonad.comparison_obj_a, CategoryTheory.SmallObject.πObj_ιIteration_app_right, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_id_fiber, CategoryTheory.WithInitial.coconeEquiv_functor_obj_pt, CategoryTheory.MonoidalClosed.ofEquiv_uncurry_def, CategoryTheory.OverPresheafAux.restrictedYoneda_map, CategoryTheory.CatCommSq.hInv_iso_inv_app, isDense_iff_nonempty_isPointwiseLeftKanExtension, CategoryTheory.GrothendieckTopology.overMapPullbackId_inv_app_val_app, CategoryTheory.toOver_obj_hom, CategoryTheory.Equivalence.leftOp_unitIso_inv_app, PresheafOfModules.pullback_comp_id, CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_cancel_hom_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_counitIso, CategoryTheory.Sieve.ofArrows_category', CategoryTheory.Over.comp_left_assoc, CategoryTheory.Under.epi_right_of_epi, AlgebraicTopology.DoldKan.identity_N₂, CategoryTheory.ExponentiableMorphism.id_pushforward, CategoryTheory.MorphismProperty.Over.instHasTerminalTopOfContainsIdentities, StalkSkyscraperPresheafAdjunctionAuxs.counit_app, SSet.opFunctorCompOpFunctorIso_inv_app_app, CategoryTheory.Limits.IsImage.ofArrowIso_lift, CategoryTheory.Pretriangulated.shiftFunctorZero_op_inv_app, CategoryTheory.Adjunction.instIsIsoFunctorCounitOfIsEquivalence_1, CategoryTheory.Under.postCongr_inv_app_right, instIsIsoAppRanCounit, CategoryTheory.Under.mono_right_of_mono, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_inv_app_hom, CategoryTheory.cosimplicialSimplicialEquiv_counitIso_hom_app_app, CategoryTheory.Adjunction.instIsIsoAppCounitOfFullOfFaithful, CategoryTheory.Adjunction.adjunctionOfEquivRight_counit_app, CategoryTheory.Over.hom_left_inv_left, CategoryTheory.StructuredArrow.toUnder_obj_left, CategoryTheory.Comonad.ComonadicityInternal.unitFork_pt, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_leftUnitor, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_inv_left, leftOpRightOpEquiv_counitIso_inv_app_app, CategoryTheory.Adjunction.compCoyonedaIso_inv_app_app, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_unitIso_hom_app_f, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app_assoc, CategoryTheory.Over.whiskerLeft_left, CategoryTheory.CosimplicialObject.Augmented.leftOp_right, CategoryTheory.Monad.algebraFunctorOfMonadHomId_inv_app_f, CategoryTheory.Over.forgetMapTerminal_hom_app, CategoryTheory.ParametrizedAdjunction.whiskerLeft_map_counit, CategoryTheory.ofTypeMonad_η_app, CategoryTheory.Limits.image.map_id, CategoryTheory.OverPresheafAux.restrictedYoneda_obj, CategoryTheory.NatTrans.CommShift.leftUnitor, CategoryTheory.Over.mk_left, CategoryTheory.Over.equivalenceOfIsTerminal_counitIso, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_hom_app, CategoryTheory.Presheaf.isSheaf_iff_isLimit_coverage, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_one, CondensedMod.isDiscrete_tfae, CategoryTheory.MonoOver.isIso_iff_subobjectMk_eq, CategoryTheory.CatCommSq.hId_iso_hom_app, LeftExtension.postcomp₁_map_right_app, CategoryTheory.NatIso.unop_rightUnitor, AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_hom_app, CategoryTheory.SingleObj.mapHom_id, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left, CategoryTheory.simplicialCosimplicialEquiv_counitIso_inv_app_app, mapGrp_id_mul, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_inv_app, CategoryTheory.MonoidalCategory.DayFunctor.equiv_unitIso_hom_app, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app, mapGrpIdIso_hom_app_hom_hom, CategoryTheory.Linear.smulOfRingMorphism_smul_eq', CategoryTheory.SimplicialObject.Augmented.toArrow_map_right, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₃, CategoryTheory.Join.mapWhiskerRight_leftUnitor_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv, CategoryTheory.Over.epi_iff_epi_left, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left, CategoryTheory.Adjunction.rightAdjointLaxMonoidal_μ, CondensedSet.instEpiTopCatAppCounitTopCatAdjunction, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.unitIso_inv_app_f_f, CategoryTheory.Adjunction.IsMonoidal.leftAdjoint_μ, instIsContinuousCompId_1, CategoryTheory.Over.OverMorphism.ext_iff, CategoryTheory.ObjectProperty.topEquivalence_counitIso, SSet.Truncated.sk_coreflective, CategoryTheory.Comon.Comon_EquivMon_OpOp_counitIso, CommRingCat.mkUnder_ext_iff, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_left_right, shiftIso_zero_inv_app, CategoryTheory.Iso.isoInverseComp_inv_app, Action.FunctorCategoryEquivalence.counitIso_inv_app_app, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.g_app, commShift₂_comm, AlgebraicGeometry.Scheme.Cover.pullbackCoverOver'_X, CategoryTheory.SimplicialObject.augment_left, whiskeringRight_obj_id, CategoryTheory.MorphismProperty.Over.map_obj_left, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_left, CategoryTheory.Equivalence.prod_counitIso, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_inv_app_coe, CategoryTheory.sheafificationNatIso_inv_app_val, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_π_app_left, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₃, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_inv_app_app_hom_hom, instIsIsoAppUnitLanAdjunctionOfHasPointwiseLeftKanExtension, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_inv_app_snd_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_left, CategoryTheory.Square.toArrowArrowFunctor_obj_hom_right, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy₂_homEquiv, CategoryTheory.Equivalence.leftOp_counitIso_inv_app, CategoryTheory.Arrow.comp_left, CategoryTheory.CostructuredArrow.toOver_obj_right, CategoryTheory.MonoidalClosed.coev_app_comp_pre_app, CategoryTheory.Monoidal.instIsMonoidalUnitTransportedEquivalenceTransported, CategoryTheory.MorphismProperty.Over.pullbackComp_hom_app_left, CommShift.isoZero_hom_app, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_inv_app_op_zero, CategoryTheory.Comma.mapRightIso_counitIso_inv_app_left, AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_hom_app, whiskeringLeft_obj_id, CategoryTheory.Abelian.LeftResolution.karoubi.π_app_toKaroubi_obj, AlgebraicGeometry.Scheme.locallyCoverDense_of_le, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_inverse_obj, CategoryTheory.Equivalence.cancel_unit_right, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_right, CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse_obj_left, CategoryTheory.GradedObject.mapBifunctorObjObjSingle₀Iso_hom, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₂, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_right, CategoryTheory.Monad.beckCoequalizer_desc, Rep.coinvariantsAdjunction_counit_app, CategoryTheory.ChosenPullbacksAlong.unit_pullbackComp_hom_assoc, CategoryTheory.MorphismProperty.Under.mk_hom, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ₀_assoc, CategoryTheory.Adjunction.IsTriangulated.id, SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_inv_app, CategoryTheory.RetractArrow.r_w_assoc, CategoryTheory.Comma.mapRightIso_counitIso_inv_app_right, CategoryTheory.instIsIsoFunctorOppositeValAppSheafCounitSheafificationAdjunction, CategoryTheory.Limits.Cocone.toCostructuredArrow_comp_proj, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_unitIso, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_hom_app, CategoryTheory.Comma.opEquiv_counitIso, CategoryTheory.sheafificationNatIso_hom_app_val, CategoryTheory.StructuredArrow.map₂_map_right, CategoryTheory.TransportEnrichment.forgetEnrichmentEquiv_counitIso, coreId_hom_app_iso_hom, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₂_app, CategoryTheory.Monad.monadMonEquiv_counitIso_hom_app_hom, CategoryTheory.MonoOver.mapIso_unitIso, CategoryTheory.CatCenter.smul_iso_inv_eq', AlgebraicGeometry.instIsOpenImmersionLeftSchemeDiscretePUnitMapWalkingSpanOverTopMorphismPropertySpan, CategoryTheory.Equivalence.congrFullSubcategory_counitIso, CategoryTheory.Equivalence.cancel_counit_right, CondensedSet.instIsIsoFunctorCompactlyGeneratedCounitCompactlyGeneratedAdjunction, reflective', PullbackObjObj.π_iso_of_iso_left_inv, CategoryTheory.toOver_obj_left, CategoryTheory.Join.mapWhiskerLeft_whiskerRight, CategoryTheory.Endofunctor.Algebra.functorOfNatTransId_inv_app_f, CommRingCat.toAlgHom_comp, CategoryTheory.Monad.algebraFunctorOfMonadHomId_hom_app_f, AlgebraicGeometry.Scheme.SpecΓIdentity_hom_app, currying₃_unitIso_hom_app_app_app_app, CategoryTheory.Limits.image.map_comp, CategoryTheory.Adjunction.instIsIsoFunctorUnitOfIsEquivalence, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_unit_app, CategoryTheory.GradedObject.comapEquiv_counitIso, CategoryTheory.toOverPullbackIsoToOver_inv_app_left, CategoryTheory.Equivalence.unitInv_naturality, partialFunEquivPointed_unitIso_inv_app, CategoryTheory.WithInitial.ofCommaObject_obj, CategoryTheory.Monad.id_μ_app, LeftExtension.precomp_map_right, CategoryTheory.WithTerminal.equivComma_inverse_obj_obj, LightCondMod.isDiscrete_tfae, CategoryTheory.Over.toUnit_left, SSet.opFunctorCompOpFunctorIso_hom_app_app, CategoryTheory.Equivalence.functor_unit_comp, CategoryTheory.Comonad.right_counit_assoc, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_right_right, CategoryTheory.Grpd.id_to_functor, CategoryTheory.Subgroupoid.inclusion_refl, CategoryTheory.SimplicialObject.Augmented.w₀, SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_hom_app, CategoryTheory.Equivalence.inv_fun_map, CategoryTheory.TwoSquare.guitartExact_id', Final.coconesEquiv_unitIso, CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_right, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_right, CategoryTheory.Idempotents.KaroubiKaroubi.counitIso_inv_app_f_f, CategoryTheory.Pseudofunctor.Grothendieck.map_id_eq, CategoryTheory.Pi.equivalenceOfEquiv_unitIso, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd_assoc, CategoryTheory.CartesianClosed.curry_id_eq_coev, CategoryTheory.SimplicialObject.instIsRightKanExtensionOppositeTruncatedSimplexCategoryObjCoskAppTruncatedCounitCoskAdjTruncation, CategoryTheory.WithInitial.opEquiv_counitIso_hom_app, CategoryTheory.Adjunction.id_counit, CategoryTheory.Arrow.leftFunc_obj, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_hom_app_hom, groupCohomology.dArrowIso₀₁_inv_right, CategoryTheory.Limits.Cocone.underPost_ι_app, CategoryTheory.Limits.multicospanIndexEnd_snd, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_hom_app_hom_hom_app, CategoryTheory.Over.braiding_inv_left, CategoryTheory.Localization.HasProductsOfShapeAux.adj_counit_app, CategoryTheory.Monad.algebraEquivOfIsoMonads_unitIso, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_hom_app_val_app, CategoryTheory.Adjunction.compYonedaIso_hom_app_app, CategoryTheory.Pi.equivalenceOfEquiv_counitIso, CategoryTheory.Sieve.pullback_functorPushforward_equivalence_eq, currying_counitIso_hom_app_app, CategoryTheory.MorphismProperty.Over.mapCongr_inv_app_left, CategoryTheory.Over.mapId_eq, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_fiber, RightExtension.postcomp₁_map_right, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompCoyoneda, CategoryTheory.MonoidalCategory.endofunctorMonoidalCategory.evaluationRightAction_actionUnitIso, CategoryTheory.Iso.isoInverseComp_hom_app, CategoryTheory.Over.opEquivOpUnder_unitIso, CategoryTheory.Over.prodLeftIsoPullback_inv_snd, LeibnizAdjunction.adj_unit_app_left, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_map_app, CategoryTheory.Over.iteratedSliceForwardIsoPost_inv_app, CategoryTheory.SimplicialObject.Augmented.toArrow_map_left, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_map_app, CategoryTheory.Equivalence.core_unitIso_hom_app_iso_inv, CategoryTheory.DifferentialObject.shiftZero_hom_app_f, ranCompLimIso_inv_app, CategoryTheory.toOverUnit_map_left, CategoryTheory.Limits.Cocones.whiskeringEquivalence_unitIso, CategoryTheory.Sum.functorEquiv_unit_app_app_inr, CategoryTheory.WithTerminal.equivComma_functor_obj_left_map, SimplexCategory.revEquivalence_unitIso, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε, CategoryTheory.Adjunction.Triple.rightToLeft_eq_units, CategoryTheory.Limits.coker_map, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_inv_app_left, CategoryTheory.HasShift.Induced.zero_inv_app_obj, CategoryTheory.instIsContinuousOverLeftDiscretePUnitIteratedSliceForwardOver, CategoryTheory.Square.toArrowArrowFunctor'_obj_left_hom, CategoryTheory.NatTrans.instCommShiftPullbackShiftHomFunctorNatIsoId, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₃₄, CategoryTheory.WithTerminal.mkCommaMorphism_left_app, CategoryTheory.shift_shift_neg', CategoryTheory.SmallObject.functorialFactorizationData_i_app, CategoryTheory.evaluationAdjunctionLeft_unit_app_app, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_inv_app, CategoryTheory.Sum.functorEquiv_unitIso_inv_app_app_inl, CategoryTheory.SimplicialObject.Augmented.toArrow_obj_left, CategoryTheory.MonoOver.mapIso_counitIso, CategoryTheory.TwoSquare.equivalenceJ_unitIso, CategoryTheory.Abelian.coim_map, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₁_app, CategoryTheory.RetractArrow.map_r_right, CategoryTheory.pullbackShiftFunctorZero_inv_app, CategoryTheory.Triangulated.TStructure.triangleLTGE_obj_mor₁, CategoryTheory.MorphismProperty.under_iff, CategoryTheory.Square.flipEquivalence_unitIso, CategoryTheory.Over.leftUnitor_hom_left, CategoryTheory.CostructuredArrow.mapIso_unitIso_hom_app_left, PullbackObjObj.mapArrowLeft_comp, Rep.resCoindAdjunction_unit_app_hom_hom, CategoryTheory.ReflQuiv.adj_unit_app, CategoryTheory.Kleisli.Adjunction.toKleisli_map, CategoryTheory.Limits.Cocones.whiskeringEquivalence_inverse, CategoryTheory.Adjunction.localization_unit_app, CategoryTheory.WithTerminal.equivComma_functor_obj_right, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₂, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_left, CategoryTheory.Prod.symmetry_hom_app, CategoryTheory.MorphismProperty.Over.pullbackMapHomPullback_app, CategoryTheory.conjugateEquiv_symm_apply_app, CategoryTheory.Over.tensorObj_ext_iff, CategoryTheory.CosimplicialObject.augment_hom_app, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_right, CategoryTheory.Join.mapWhiskerLeft_whiskerLeft, CategoryTheory.Limits.Cone.toStructuredArrowCompProj_inv_app, CategoryTheory.RetractArrow.i_w, AlgebraicGeometry.Scheme.Modules.pseudofunctor_right_unitality_assoc, CategoryTheory.CostructuredArrow.toOver_map_right, CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse_obj_right, CategoryTheory.OppositeShift.adjunction_unit, CategoryTheory.Comma.toPUnitIdEquiv_counitIso_hom_app, sheafAdjunctionCocontinuous_counit_app_val, CategoryTheory.Monad.isSplitMono_iff_isIso_unit, CategoryTheory.coev_expComparison, MonoidHom.id_toFunctor, CategoryTheory.Under.mk_hom, LeftExtension.precomp_obj_hom_app, CategoryTheory.FreeGroupoid.mapId_hom_app, CategoryTheory.WithTerminal.ofCommaObject_obj, CategoryTheory.conjugateEquiv_apply_app, LeibnizAdjunction.adj_counit_app_left, CategoryTheory.CatCenter.mul_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_inv_app_app_fst, CategoryTheory.Adjunction.instIsIsoAppCounitObjOfFaithfulOfFull, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom, CategoryTheory.exp.coev_ev, CategoryTheory.Over.iteratedSliceForward_forget, CategoryTheory.Preadditive.commGrpEquivalence_unitIso_inv_app, FinPartOrd.dualEquiv_unitIso, commBialgCatEquivComonCommAlgCat_unitIso_hom_app, CategoryTheory.CatCommSq.vId_iso_hom_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_inv_app_snd_app, CategoryTheory.WithTerminal.opEquiv_counitIso_inv_app, CategoryTheory.Adjunction.ε_comp_map_ε_assoc, CategoryTheory.toOverIsoToOverUnit_inv_app_left, CategoryTheory.MorphismProperty.Over.mk_hom, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_inv_app_hom_left, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_obj_obj_right_as, CategoryTheory.MorphismProperty.Over.pullback_obj_left, flipping_counitIso_inv_app_app_app, CategoryTheory.Sieve.functorPullback_id, CategoryTheory.MorphismProperty.Over.map_map_left, CategoryTheory.Equivalence.congrLeft_counitIso_inv_app, CategoryTheory.Over.postAdjunctionRight_counit_app, CategoryTheory.Over.conePost_obj_π_app, groupHomology.d₁₀ArrowIso_hom_left, CategoryTheory.Limits.multicospanIndexEnd_right, AlgebraicGeometry.Scheme.Modules.instIsIsoFunctorCounitRestrictAdjunction, shiftIso_zero_hom_app, CategoryTheory.MonoOver.mkArrowIso_hom_hom_left, comp_flip_uncurry_eq, CategoryTheory.NatTrans.instIsClosedUnderLimitsOfShapeOverFunctorEquifiberedHomDiscretePUnitOfHasCoproductsOfShapeHom, CategoryTheory.CostructuredArrow.toOver_obj_hom, CategoryTheory.Limits.HasColimit.isoOfEquivalence_hom_π, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit, CategoryTheory.Adjunction.Triple.adj₁_counit_app_rightToLeft_app, CategoryTheory.Sieve.overEquiv_le_overEquiv_iff, AlgebraicTopology.DoldKan.instIsIsoFunctorKaroubiSimplicialObjectNatTrans, CategoryTheory.MonoOver.map_obj_left, CategoryTheory.ChosenPullbacksAlong.snd'_left, CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_ext_iff, CategoryTheory.OrthogonalReflection.D₁.ι_comp_t_assoc, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap, CategoryTheory.Preadditive.commGrpEquivalence_unitIso_hom_app, CategoryTheory.Square.fromArrowArrowFunctor'_obj_X₂, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd, CategoryTheory.CatCenter.smul_iso_inv_eq'_assoc, CategoryTheory.Over.rightUnitor_inv_left_fst, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_symm_apply_right, CategoryTheory.Monoidal.instIsMonoidalTransportedCounitEquivalenceTransported, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_fiber, CategoryTheory.Equivalence.symm_unitIso, CategoryTheory.WithTerminal.commaFromOver_map_left, CategoryTheory.Adjunction.mapCommMon_unit, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality_assoc, CategoryTheory.WithInitial.equivComma_functor_obj_right_map, RightExtension.precomp_map_left, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_snd_assoc, CategoryTheory.Limits.multicospanShapeEnd_snd, CategoryTheory.Limits.Cocone.toCostructuredArrowCompProj_hom_app, CategoryTheory.Equivalence.mapHomologicalComplex_unitIso, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_right_app, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_zero, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_unit_app, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_symm_apply, CategoryTheory.MonoOver.isIso_hom_left_iff_subobjectMk_eq, CategoryTheory.Under.pushout_map, CategoryTheory.Cat.opEquivalence_counitIso, ranCounit_app_whiskerLeft_ranAdjunction_unit_app_assoc, CategoryTheory.Over.mapCongr_inv_app_left, CategoryTheory.ComonadHom.app_ε, CategoryTheory.StructuredArrow.final_map₂_id, CategoryTheory.MorphismProperty.Over.Hom.ext_iff, CategoryTheory.Cat.freeMapIdIso_hom_app, CategoryTheory.Sieve.ofArrows_category, opId_hom_app, ModuleCat.RestrictionCoextensionAdj.counit'_app, CategoryTheory.CosimplicialObject.Augmented.const_obj_right, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_hom_app_fst_app, CategoryTheory.Limits.image.map_ι, CategoryTheory.Over.mapCongr_hom_app_left, CategoryTheory.Abelian.Pseudoelement.pseudoZero_iff, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd, CategoryTheory.Discrete.equivalence_unitIso, CategoryTheory.Equivalence.funInvIdAssoc_hom_app, CategoryTheory.equivToOverUnit_unitIso, CategoryTheory.Over.postCongr_inv_app_left, CategoryTheory.LocalizerMorphism.LeftResolution.opEquivalence_unitIso, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_η_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality, CategoryTheory.Square.fromArrowArrowFunctor'_obj_X₃, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_hom, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_inv_app, CoalgCat.comonEquivalence_counitIso, CategoryTheory.Over.mk_hom, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_inverse_map_hom, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_obj_left, CategoryTheory.StructuredArrow.preEquivalence_unitIso, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_inv_app, CategoryTheory.ihom.ev_coev_assoc, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_hom, CategoryTheory.Monad.instReflectsColimitWalkingParallelPairParallelPairMapAAppCounitObjAOfReflectsColimitOfIsSplitPair, CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_hom_app_unmop_unmop, CategoryTheory.Over.mapComp_hom_app_left, CategoryTheory.Limits.Cocones.precomposeEquivalence_unitIso, triangleIso, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_obj_obj_hom, CategoryTheory.Monad.instPreservesColimitWalkingParallelPairParallelPairMapAAppCounitObjAOfPreservesColimitOfIsReflexivePair, CategoryTheory.Limits.walkingCospanOpEquiv_counitIso_hom_app, TopologicalSpace.Opens.mapId_hom_app, CategoryTheory.Comma.equivProd_unitIso_hom_app_left, CategoryTheory.Adjunction.mapCommMon_counit, CategoryTheory.SmallObject.SuccStruct.ofNatTrans_X₀, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst, PushoutObjObj.mapArrowRight_left, CategoryTheory.Adjunction.CommShift.instId, unopId_inv_app, Action.FunctorCategoryEquivalence.unitIso_inv_app_hom, CategoryTheory.Over.whiskerRight_left_fst, Rep.ihom_ev_app_hom, CategoryTheory.Join.pseudofunctorLeft_mapId_hom_toNatTrans_app, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_map, instIsLeftKanExtensionObjLanAppLanUnit, CategoryTheory.Over.postAdjunctionLeft_unit_app_left, Initial.conesEquiv_counitIso, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality, CategoryTheory.Comonad.counit_naturality, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right_assoc, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_counit_app, CategoryTheory.Cat.rightUnitor_hom_toNatTrans, groupCohomology.dArrowIso₀₁_hom_right, CategoryTheory.Adjunction.mkOfHomEquiv_counit_app, coreId_inv_app_iso_inv, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.functor_map, CategoryTheory.PullbackShift.adjunction_unit, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_inv_app_hom_hom_app, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp_f, CategoryTheory.Equivalence.refl_inverse, CategoryTheory.GradedObject.singleCompEval_hom_app, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_hom_left, CategoryTheory.Arrow.square_from_iso_invert, CategoryTheory.MonoOver.pullback_obj_arrow, CategoryTheory.Over.preservesTerminalIso_pullback, CategoryTheory.Limits.multispanShapeCoend_snd, PullbackObjObj.π_iso_of_iso_right_hom, LightCondSet.instIsIsoFunctorSequentialCounitSequentialAdjunction, CategoryTheory.Sheaf.instIsIsoAppCounitConstantSheafAdjOfFaithfulOfFullConstantSheafOfIsConstant, CategoryTheory.WithTerminal.commaFromOver_obj_right, CategoryTheory.Sieve.functorPushforward_id, CategoryTheory.Over.prodLeftIsoPullback_inv_fst, opUnopEquiv_counitIso, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone_pt, PushoutObjObj.mapArrowRight_comp_assoc, CategoryTheory.CatCenter.mul_app', CategoryTheory.StructuredArrow.ofCommaSndEquivalence_unitIso, CategoryTheory.Abelian.im_map, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_inv_right, CategoryTheory.StructuredArrow.map₂_map_left, CategoryTheory.Localization.equivalence_counitIso_app, CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieve, CategoryTheory.Adjunction.homEquiv_unit, CategoryTheory.WithTerminal.coneEquiv_functor_obj_π_app_star, CategoryTheory.Under.postAdjunctionRight_unit_app_right, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_inv_app, CategoryTheory.Prod.braiding_unitIso, CategoryTheory.Limits.id_reflectsLimits, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_left_hom, CategoryTheory.StructuredArrow.ofCommaSndEquivalence_counitIso, CategoryTheory.Adjunction.mapCommGrp_unit, CategoryTheory.Abelian.LeftResolution.π_naturality_assoc, CategoryTheory.conjugateEquiv_leftUnitor_hom, PullbackObjObj.mapArrowRight_comp_assoc, CategoryTheory.WithTerminal.coneEquiv_counitIso_inv_app_hom, CategoryTheory.Adjunction.Triple.mono_leftToRight_app_iff_mono_adj₁_counit_app, CategoryTheory.shiftFunctorCompIsoId_add'_inv_app, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₃_app, CategoryTheory.shiftFunctorAdd_zero_add_hom_app, CategoryTheory.Idempotents.functorExtension₁CompWhiskeringLeftToKaroubiIso_hom_app_app_f, CategoryTheory.Under.map_map_right, mapGrp_id_one, CategoryTheory.Adjunction.unit_mono_of_L_faithful, CategoryTheory.Over.opEquivOpUnder_inverse_obj, CategoryTheory.MonoidalClosed.uncurry_eq, OplaxMonoidal.id_δ, HomologicalComplex₂.flipEquivalenceUnitIso_hom_app_f_f, CategoryTheory.Adjunction.leftAdjointUniq_hom_app_counit_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_map, CategoryTheory.skeletonEquivalence_unitIso, CochainComplex.shiftFunctorZero_inv_app_f, CategoryTheory.Arrow.mono_left, CategoryTheory.WithInitial.mkCommaMorphism_right_app, CategoryTheory.CartesianMonoidalCategory.prodComparison_id, CategoryTheory.MorphismProperty.instFaithfulOverTopOverForget, CategoryTheory.Arrow.equivSigma_apply_snd_snd, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_left, CategoryTheory.SimplicialObject.Augmented.toArrow_obj_right, AlgebraicGeometry.Scheme.kerAdjunction_unit_app, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ, CategoryTheory.Over.prodLeftIsoPullback_inv_snd_assoc, CategoryTheory.Over.rightUnitor_inv_left_snd, CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_hom, isContinuous_id, AlgebraicGeometry.instIsClosedImmersionLeftSchemeDiscretePUnitOneOverSpecOf, CategoryTheory.Over.post_map, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_id, CategoryTheory.GrothendieckTopology.OneHypercover.instIsPreservedById, CategoryTheory.prodOpEquiv_unitIso_hom_app, CategoryTheory.Square.toArrowArrowFunctor_obj_left_left, CategoryTheory.regularTopology.equalizerConditionMap_iff_nonempty_isLimit, rightUnitor_hom_app, CategoryTheory.Comma.mapRightId_inv_app_left, CategoryTheory.Pseudofunctor.presheafHom_obj, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_obj, CategoryTheory.GrothendieckTopology.preservesSheafification_iff_of_adjunctions, leftOpId_hom_app, CategoryTheory.Over.mapPullbackAdj_counit_app, CategoryTheory.Over.iteratedSliceBackward_forget, CategoryTheory.WithTerminal.opEquiv_unitIso_hom_app, CategoryTheory.Abelian.Pseudoelement.ModuleCat.eq_range_of_pseudoequal, CategoryTheory.Comonad.instPreservesLimitWalkingParallelPairParallelPairMapAAppUnitObjAOfPreservesLimitOfIsCoreflexivePair, CategoryTheory.Equivalence.cancel_counitInv_right, CategoryTheory.Comma.mapLeftId_hom_app_right, CategoryTheory.Over.postCongr_hom_app_left, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₃, leftOpRightOpEquiv_unitIso_inv_app, map_opShiftFunctorEquivalence_unitIso_inv_app_unop, CategoryTheory.MorphismProperty.Over.map_comp, CategoryTheory.Localization.LeftBousfield.W_adj_unit_app, CategoryTheory.ObjectProperty.fullSubcategoryCongr_unitIso, CategoryTheory.GradedObject.singleCompEval_inv_app, CategoryTheory.Adjunction.Triple.whiskerRight_rightToLeft_assoc, CategoryTheory.Equivalence.changeFunctor_unitIso_hom_app, CategoryTheory.WithTerminal.opEquiv_counitIso_hom_app, CategoryTheory.Monad.instPreservesColimitWalkingParallelPairParallelPairMapAAppCounitObjAOfPreservesColimitOfIsSplitPair, CategoryTheory.ComposableArrows.opEquivalence_unitIso_inv_app, AlgebraicGeometry.ΓSpec.adjunction_counit_app', CategoryTheory.SimplicialObject.Augmented.const_obj_hom, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.counitIso_inv, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_ihom_ev_app_assoc, CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse_obj_hom, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₃, CategoryTheory.toOverUnit_obj_left, CategoryTheory.Equivalence.map_η_comp_η, CommRingCat.moduleCatRestrictScalarsPseudofunctor_mapId, CategoryTheory.Join.pseudofunctorLeft_mapComp_hom_toNatTrans_app, CategoryTheory.Equivalence.counit_naturality_assoc, CategoryTheory.CostructuredArrow.mapIso_unitIso_inv_app_left, comp_id, CategoryTheory.Under.map_obj_right, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app', CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_left, CategoryTheory.WithInitial.mkCommaObject_right_obj, CategoryTheory.prod.associativity_unitIso, CategoryTheory.Under.post_obj, CategoryTheory.Adjunction.unit_app_shift_commShiftIso_inv_app, CategoryTheory.TwistShiftData.assoc, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_right_hom, CategoryTheory.Monad.left_unit, ModuleCat.restrictScalarsId'_inv_app, CategoryTheory.Pi.closedCounit_app, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom, compFlipUncurryIso_inv_app, CategoryTheory.Over.iteratedSliceBackward_forget_forget, CategoryTheory.CosimplicialObject.comp_right_app, CategoryTheory.SimplicialObject.Augmented.whiskering_map_app_right, CategoryTheory.Square.fromArrowArrowFunctor_obj_X₃, lanUnit_app_app_lanAdjunction_counit_app_app, CategoryTheory.RetractArrow.op_r_right, CategoryTheory.Adjunction.compUliftCoyonedaIso_inv_app_app_down, CategoryTheory.StructuredArrow.prodEquivalence_unitIso, CategoryTheory.ObjectProperty.topEquivalence_unitIso, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst, Full.id, CategoryTheory.MorphismProperty.Over.instPreservesFiniteLimitsTopPullback, CategoryTheory.Over.prodLeftIsoPullback_hom_snd, lanUnit_app_whiskerLeft_lanAdjunction_counit_app, CategoryTheory.Limits.walkingCospanOpEquiv_counitIso_inv_app, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso_inv_app_f, CategoryTheory.WithInitial.mapId_inv_app, CategoryTheory.Adjunction.instIsIsoFunctorCounitOfIsEquivalence, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_hom_app, Rep.invariantsAdjunction_unit_app, Bipointed.swapEquiv_unitIso_inv_app_toFun, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_hom_right, CategoryTheory.GradedObject.mapBifunctorRightUnitorCofan_inj, CategoryTheory.Equivalence.symmEquivInverse_obj_counitIso_hom, CategoryTheory.Join.mapWhiskerRight_whiskerRight, CategoryTheory.ShiftMkCore.add_zero_hom_app, CategoryTheory.Limits.pullbackConeEquivBinaryFan_counitIso, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_map_left, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counitIso_hom_app_tensor_assoc, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_map_right_left, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_hom_app_f, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_apply, CategoryTheory.LocalizerMorphism.functorialRightResolutions.Φ_functor_map_ι_app, CategoryTheory.AsSmall.equiv_unitIso, CategoryTheory.simplicialToCosimplicialAugmented_map_left, CategoryTheory.Comonad.isSplitEpi_iff_isIso_counit, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_unitIso_hom_app_f_f, CategoryTheory.Over.whiskerRight_left_snd_assoc, CategoryTheory.Arrow.w_mk_right, CategoryTheory.Under.eqToHom_right, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_right_app, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_apply_f, CategoryTheory.Linear.smulOfRingMorphism_smul_eq, CategoryTheory.ChosenPullbacksAlong.Over.snd_eq_snd', CategoryTheory.SmallObject.SuccStruct.prop.arrowIso_inv_right, CategoryTheory.TwistShiftData.shiftFunctorZero_hom_app, CategoryTheory.Pi.closedUnit_app, CategoryTheory.Limits.IsLimit.pullbackConeEquivBinaryFanFunctor_lift_left, currying_counitIso_inv_app_app, ihom_ev_app, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_unit_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality_assoc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_inv_app_hom, CategoryTheory.Adjunction.mapGrp_unit, CategoryTheory.Over.associator_inv_left_fst_fst_assoc, CategoryTheory.Sieve.overEquiv_symm_iff, coreId_inv_app_iso_hom, CategoryTheory.Under.mapId_inv, CategoryTheory.Adjunction.map_restrictFullyFaithful_unit_app_assoc, CategoryTheory.CatCenter.app_add, CategoryTheory.ForgetEnrichment.equiv_unitIso, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₃, CategoryTheory.conjugateEquiv_counit_symm, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_base, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_inv_left, CategoryTheory.Sieve.functorPushforward_over_map, CategoryTheory.GrothendieckTopology.toSheafification_app, CommShift.isoZero'_inv_app, CategoryTheory.Adjunction.Equivalence.instIsMonoidalCounit, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_shift, CategoryTheory.FreeGroupoid.map_id, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₁, CategoryTheory.Limits.ker.ι_app, CategoryTheory.Over.associator_hom_left_fst, CategoryTheory.TwoSquare.guitartExact_id, MulEquiv.toSingleObjEquiv_unitIso_hom, id_map, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_map_left, CategoryTheory.evaluationAdjunctionRight_counit_app_app, CategoryTheory.SmallObject.functor_map, CategoryTheory.Pseudofunctor.ObjectProperty.mapId_inv_app, CategoryTheory.Monad.comparison_obj_a, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_map_right_right, CategoryTheory.Monoidal.whiskerRight, AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTrans, SSet.Augmented.stdSimplex_map_right, CategoryTheory.Adjunction.leftAdjointUniq_hom_counit, CategoryTheory.Subfunctor.equivalenceMonoOver_inverse_map, CategoryTheory.Adjunction.isIso_counit_of_iso, CategoryTheory.NatTrans.CommShift.rightUnitor, CategoryTheory.AsSmall.equiv_counitIso, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_1, CategoryTheory.CatCommSq.hId_iso_inv_app, CategoryTheory.WithTerminal.equivComma_functor_map_right, CategoryTheory.Adjunction.unit_app_unit_comp_map_η, CategoryTheory.Monad.adj_counit, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_unit, CategoryTheory.Adjunction.map_restrictFullyFaithful_counit_app, CategoryTheory.Over.forgetAdjStar_counit_app, CategoryTheory.WithInitial.coconeEquiv_counitIso_inv_app_hom, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₃, CategoryTheory.Equivalence.mapMon_unitIso, CategoryTheory.Square.fromArrowArrowFunctor_obj_X₂, instIsIsoAppLanUnit, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd, CategoryTheory.WithInitial.mkCommaMorphism_left, CategoryTheory.coev_app_comp_pre_app, CategoryTheory.Arrow.leftToRight_app, CategoryTheory.Abelian.Pseudoelement.pseudoApply_mk', CategoryTheory.WithInitial.commaFromUnder_map_left, CategoryTheory.Equivalence.pi_unitIso, Action.resId_inv_app_hom, CategoryTheory.NatTrans.instIsClosedUnderColimitsOfShapeUnderFunctorCoequifiberedHomDiscretePUnitOfHasProductsOfShapeHom, CategoryTheory.SimplicialObject.Augmented.const_map_left, CategoryTheory.simplicialCosimplicialEquiv_unitIso_hom_app, CategoryTheory.Adjunction.leftAdjointUniq_hom_app_counit, CategoryTheory.NatTrans.instCommShiftOppositeShiftHomFunctorNatIsoId, CategoryTheory.ChosenPullbacksAlong.Over.tensorUnit_hom, CategoryTheory.Over.prodLeftIsoPullback_hom_fst_assoc, CategoryTheory.Over.map_map_left, CategoryTheory.Equivalence.counitInv_functor_comp, SSet.Augmented.stdSimplex_obj_left, CategoryTheory.Adjunction.toComonad_δ, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_snd_assoc, CategoryTheory.MorphismProperty.Over.mapId_inv_app_left, groupCohomology.dArrowIso₀₁_inv_left, CategoryTheory.CosimplicialObject.Augmented.whiskering_map_app_left, CategoryTheory.Under.costar_obj_left, CategoryTheory.SmallObject.objMap_comp_assoc, CategoryTheory.ExponentiableMorphism.pushforwardId_hom_counit_assoc, CategoryTheory.GradedObject.ι_mapBifunctorRightUnitor_hom_apply, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_left_left, CategoryTheory.Limits.ker_obj, CategoryTheory.SmallObject.functorialFactorizationData_Z_obj, CategoryTheory.Limits.walkingCospanOpEquiv_unitIso_inv_app, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst, CategoryTheory.SimplicialObject.Augmented.const_obj_right, CategoryTheory.GrothendieckTopology.W_adj_unit_app, CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan_inj, CategoryTheory.Comonad.ComonadicityInternal.unitFork_ι, CategoryTheory.MonoOver.image_map, AlgebraicGeometry.ΓSpec.adjunction_counit_app, CategoryTheory.ComonadHom.app_ε_assoc, CategoryTheory.Arrow.equivSigma_apply_fst, CategoryTheory.Under.under_left, CategoryTheory.Adjunction.IsMonoidal.leftAdjoint_ε, CategoryTheory.Under.mapPushoutAdj_unit_app, CategoryTheory.Iso.coreLeftUnitor, CategoryTheory.GrothendieckTopology.mem_over_iff, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_obj, CategoryTheory.Adjunction.Equivalence.instIsMonoidalUnit, CategoryTheory.MonoidalOpposite.mopEquiv_unitIso, CategoryTheory.Limits.instHasImageHomMk, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_star, CategoryTheory.Limits.ImageMap.factor_map_assoc, CategoryTheory.Over.tensorUnit_hom, CategoryTheory.Over.opEquivOpUnder_inverse_map, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_map_left_left, CategoryTheory.Adjunction.isIso_counit_app_of_iso, CategoryTheory.MonoidalClosed.curry_id_eq_coev, CategoryTheory.Join.mapWhiskerLeft_whiskerRight_assoc, CategoryTheory.typeEquiv_unitIso_hom_app, CategoryTheory.Limits.CatCospanTransform.id_squareLeft, CategoryTheory.Over.leftUnitor_inv_left_fst, CategoryTheory.Under.post_map, rightOpId_inv_app, CategoryTheory.TwistShiftData.shift_z_app, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_unit_app_left, CategoryTheory.Over.inv_left_hom_left, CategoryTheory.Over.starPullbackIsoStar_hom_app_left, CategoryTheory.Over.postEquiv_inverse, CategoryTheory.Square.toArrowArrowFunctor'_obj_right_right, CommRingCat.mkUnder_hom, CategoryTheory.StructuredArrow.mapNatIso_unitIso_hom_app_right, AlgebraicGeometry.opensDiagram_map, CategoryTheory.Adjunction.functorialityUnit_app_hom, CategoryTheory.Adjunction.conjugateEquiv_leftAdjointIdIso_hom, CategoryTheory.Monad.adj_unit, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left, CategoryTheory.simplicialCosimplicialEquiv_counitIso_hom_app_app, Rep.coindResAdjunction_unit_app, CategoryTheory.GradedObject.mapBifunctorObjSingle₀ObjIso_hom, HomotopicalAlgebra.cofibrations_over_iff, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransId_inv_app_f, CategoryTheory.ReflQuiv.adj.unit.map_app_eq, CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse_obj_hom, CategoryTheory.WithTerminal.coneEquiv_functor_obj_π_app_of, CategoryTheory.Equivalence.refl_functor, CategoryTheory.WithInitial.coconeEquiv_unitIso_hom_app_hom_right, CategoryTheory.Square.toArrowArrowFunctor_map_right_right, CategoryTheory.Over.forgetMapTerminal_inv_app, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_hom_app, CategoryTheory.Pi.optionEquivalence_unitIso, CategoryTheory.MorphismProperty.Over.mapCongr_hom_app_left, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app, CategoryTheory.Comonad.instPreservesLimitWalkingParallelPairParallelPairMapAAppUnitObjAOfPreservesLimitOfIsCosplitPair, CategoryTheory.ULift.equivalence_unitIso_inv, CategoryTheory.Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor, CategoryTheory.Adjunction.Triple.leftToRight_app_obj, CategoryTheory.Subobject.inf_eq_map_pullback', AlgebraicGeometry.Scheme.SpecΓIdentity_app, CategoryTheory.Preadditive.commGrpEquivalenceAux_hom_app_hom_hom_hom, CategoryTheory.Adjunction.instIsIsoAppUnitOfFullOfFaithful, CategoryTheory.RelCat.unopFunctor_comp_opFunctor_eq, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan_inv_app_app_apply_eq_id, CategoryTheory.CosimplicialObject.Augmented.leftOp_left_map, CategoryTheory.Presheaf.isSeparated_iff_subsingleton, CategoryTheory.Equivalence.rightOp_unitIso_hom_app, CategoryTheory.Join.pseudofunctorLeft_mapComp_inv_toNatTrans_app, CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_cancel_hom_app, CategoryTheory.Over.eqToHom_left, CategoryTheory.Sieve.overEquiv_top, leibnizPushout_obj_map, CategoryTheory.Limits.colimitLimitToLimitColimitCone_hom, isDenseAt_eq_isPointwiseLeftKanExtensionAt, CategoryTheory.Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor_assoc, PushoutObjObj.mapArrowLeft_id, essImage_underPost, CategoryTheory.shiftFunctorAdd'_zero_add_inv_app, CategoryTheory.Codiscrete.right_triangle_components, essImage.counit_isIso, CategoryTheory.MonoidalClosed.uncurry_pre, CategoryTheory.Over.tensorHom_left_snd_assoc, whiskeringLeftObjIdIso_hom_app_app, CategoryTheory.Adjunction.shift_counit_app, CategoryTheory.SimplicialObject.isoCoskOfIsCoskeletal_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_hom_app_hom_hom_app, CategoryTheory.Limits.Cones.equivalenceOfReindexing_counitIso, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_counitIso, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_base, CategoryTheory.SmallObject.ε_app, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd_assoc, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_app, CategoryTheory.Adjunction.map_restrictFullyFaithful_counit_app_assoc, CategoryTheory.Discrete.productEquiv_counitIso_hom_app, LeftExtension.postcompose₂_map_right_app, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map, CategoryTheory.Limits.image.map_homMk'_ι, CategoryTheory.ExponentiableMorphism.ev_coev, CategoryTheory.Under.map_obj_hom, Rep.indResAdjunction_counit_app_hom_hom, CategoryTheory.Adjunction.counit_naturality, CategoryTheory.Equivalence.CommShift.instCommShiftHomFunctorCounitIso, CommRingCat.Under.tensorProdEqualizer_ι, CategoryTheory.ULift.equivalence_counitIso_hom_app, CategoryTheory.WithInitial.mkCommaObject_hom_app, CategoryTheory.CartesianClosed.curry_eq, CategoryTheory.pullbackShiftFunctorZero'_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_inv_app, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app_assoc, CategoryTheory.Over.leftUnitor_inv_left_snd, AlgebraicGeometry.AffineTargetMorphismProperty.arrow_mk_iso_iff, SSet.Truncated.HomotopyCategory.BinaryProduct.left_unitality, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_leftUnitor, CategoryTheory.Comonad.left_counit, FinPartOrd.dualEquiv_counitIso, AlgebraicGeometry.Scheme.kerAdjunction_counit_app, CategoryTheory.pullbackShiftFunctorZero_hom_app, AlgebraicGeometry.opensDiagramι_app, CategoryTheory.Monad.unit_naturality, CategoryTheory.Arrow.w, CategoryTheory.Iso.compInverseIso_inv_app, CategoryTheory.Adjunction.restrictFullyFaithful_homEquiv_apply, HomotopicalAlgebra.instCofibrationLeftDiscretePUnitOfOver, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_snd', CategoryTheory.CatCenter.smul_iso_hom_eq'_assoc, CategoryTheory.Cat.opEquivalence_unitIso, CategoryTheory.OverClass.fromOver_over, CategoryTheory.Adjunction.CommShift.commShift_counit, AlgebraicTopology.AlternatingFaceMapComplex.ε_app_f_zero, essImage.of_underPost, CategoryTheory.Comma.equivProd_unitIso_hom_app_right, CategoryTheory.MonoidalClosed.id_tensor_pre_app_comp_ev, CategoryTheory.DifferentialObject.shiftZero_inv_app_f, CategoryTheory.SmallObject.iterationObjRightIso_hom, TopCat.Presheaf.presheafEquivOfIso_unitIso_hom_app_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_counitIso, CategoryTheory.Equivalence.unitInv_naturality_assoc, CategoryTheory.MonoidalCategory.DayConvolution.instIsLeftKanExtensionProdExternalProductConvolutionExtensionUnitRightUnit, CategoryTheory.Discrete.sumEquiv_unitIso_hom_app, CategoryTheory.SmallObject.objMap_id, CategoryTheory.MonoOver.image_obj, TopologicalSpace.Opens.coe_overEquivalence_functor_obj, CategoryTheory.SmallObject.SuccStruct.prop.arrowIso_hom_right, CategoryTheory.OverClass.asOver_left, CategoryTheory.Limits.coker_obj, AlgebraicGeometry.ΓSpec.adjunction_unit_app, CategoryTheory.Over.μ_pullback_left_fst_snd', CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy₂'_homEquiv, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_left, CategoryTheory.Over.comp_left, CategoryTheory.ChosenPullbacksAlong.Over.tensorUnit_left, CategoryTheory.CatCommSq.vInv_iso_hom_app, CategoryTheory.Over.mapPullbackAdj_unit_app, CategoryTheory.MorphismProperty.Over.forget_comp_forget_map, CategoryTheory.Adjunction.whiskerRight_counit_iso_of_L_fully_faithful, CategoryTheory.Sum.natIsoOfWhiskerLeftInlInr_eq, CategoryTheory.Limits.id_reflectsColimits, CategoryTheory.Adjunction.instIsMonoidalId, CategoryTheory.Monad.MonadicityInternal.unitCofork_π, CategoryTheory.typeEquiv_unitIso_inv_app, CategoryTheory.Square.toArrowArrowFunctor'_map_right_left, CategoryTheory.Over.mapId_inv_app_left, CategoryTheory.Limits.multicospanShapeEnd_fst, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left_assoc, CategoryTheory.MorphismProperty.Over.pullbackComp_inv_app_left, CategoryTheory.Limits.imageSubobjectIso_comp_image_map, TwoP.swapEquiv_unitIso_hom_app_hom_toFun, CategoryTheory.Adjunction.instIsIsoFunctorUnitOfIsEquivalence_1, flipping_counitIso_hom_app_app_app, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_inv_app, CommRingCat.toAlgHom_id, CategoryTheory.Comma.toIdPUnitEquiv_unitIso_inv_app_right, CategoryTheory.SmallObject.SuccStruct.toSuccArrow_hom, CategoryTheory.Pseudofunctor.Grothendieck.categoryStruct_id_fiber, CategoryTheory.Limits.Cones.whiskeringEquivalence_unitIso, CategoryTheory.shiftFunctorZero_hom_app_obj_of_induced, SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_inv_app, CategoryTheory.Comma.toPUnitIdEquiv_unitIso_inv_app_left, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_right, isIso_ranAdjunction_unit_app_iff, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst, CategoryTheory.Limits.CatCospanTransform.id_left, Rep.normNatTrans_app, CategoryTheory.Sieve.overEquiv_symm_pullback, CategoryTheory.Adjunction.comp_counit, CategoryTheory.Limits.multispanIndexCoend_snd, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_inv_app_unmop, CategoryTheory.Equivalence.changeFunctor_counitIso_hom_app, CategoryTheory.Subfunctor.equivalenceMonoOver_inverse_obj, CategoryTheory.Over.leftUnitor_inv_left_snd_assoc, CategoryTheory.Limits.CatCospanTransform.id_base, groupCohomology.dArrowIso₀₁_hom_left, CategoryTheory.RetractArrow.r_w, CategoryTheory.CatCenter.mul_app_assoc, LeftExtension.postcompose₂_obj_hom_app, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s₀_comp_δ₁_assoc, CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc, CategoryTheory.Under.mono_iff_mono_right, CategoryTheory.Equivalence.refl_counitIso, CategoryTheory.WithInitial.liftFromUnder_obj_obj, CategoryTheory.Limits.HasLimit.isoOfEquivalence_hom_π, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_counitIso, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_map_right_right, AlgebraicGeometry.SheafedSpace.ofRestrict_hom_c_app, CategoryTheory.unit_conjugateEquiv_symm, CategoryTheory.Adjunction.mapMon_counit, shiftIso_zero, TopCat.Presheaf.whiskerIsoMapGenerateCocone_inv_hom, CategoryTheory.Grpd.freeForgetAdjunction_homEquiv_symm_apply, CategoryTheory.Localization.strictUniversalPropertyFixedTargetId_lift, CategoryTheory.MorphismProperty.instHasPullbackHomDiscretePUnitOfHasPullbacksAlong, CategoryTheory.ChosenPullbacksAlong.iso_pullback_obj, CategoryTheory.forgetEnrichmentOppositeEquivalence_unitIso, CategoryTheory.Arrow.inv_left, CategoryTheory.SimplicialObject.augment_right, MulEquiv.toSingleObjEquiv_counitIso_hom, CategoryTheory.unit_conjugateEquiv, CategoryTheory.SimplicialObject.augment_hom_zero, CategoryTheory.GradedObject.mapBifunctorObjSingle₀ObjIso_inv, CategoryTheory.SmallObject.ιObj_naturality, CategoryTheory.Under.postEquiv_counitIso, CategoryTheory.MonoidalSingleObj.endMonoidalStarFunctorEquivalence_unitIso, CategoryTheory.SmallObject.ιFunctorObj_naturality, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone_ι_app, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_left, CategoryTheory.Join.mapWhiskerLeft_associator_hom, CategoryTheory.CosimplicialObject.Augmented.drop_obj, LeibnizAdjunction.adj_counit_app_right, CategoryTheory.MonoidalClosed.curry_eq, CategoryTheory.Equivalence.counitInv_app_comp_functor_map_η_inverse_assoc, SheafOfModules.pullback_comp_id, CommRingCat.mkUnder_right, CategoryTheory.Over.conePost_map_hom, CategoryTheory.piEquivalenceFunctorDiscrete_unitIso, CategoryTheory.Under.postComp_hom_app_right, CategoryTheory.shiftFunctorAdd'_add_zero_inv_app, Faithful.id, LaxMonoidal.id_ε, CategoryTheory.Adjunction.Triple.rightToLeft_eq_counits, CategoryTheory.sheafBotEquivalence_unitIso, AlgebraicGeometry.Scheme.Modules.pseudofunctor_right_unitality, CategoryTheory.WithTerminal.mkCommaObject_left_map, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app, TopologicalSpace.Opens.mapMapIso_unitIso, CategoryTheory.SimplicialObject.Augmented.rightOp_right_map, CategoryTheory.MonoOver.bot_left, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.Presieve.ofArrows_category, CategoryTheory.WithInitial.coconeEquiv_functor_map_hom, CategoryTheory.Equivalence.unop_counitIso, CategoryTheory.TwoSquare.hId_app, CategoryTheory.Arrow.comp_right_assoc, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_right, CategoryTheory.WithTerminal.ofCommaMorphism_app, CategoryTheory.Adjunction.isIso_unit_app_iff_mem_essImage, CategoryTheory.typeEquiv_counitIso_inv_app_val_app, CategoryTheory.Comonad.id_δ_app, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_inv_app_left, LeftExtension.postcomp₁_obj_hom_app, CategoryTheory.SmallObject.functorMapSrc_functorObjTop, mapCommMonIdIso_hom_app_hom_hom, TopologicalSpace.Opens.overEquivalence_unitIso_hom_app_left, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_left, CategoryTheory.MonoOver.map_obj_arrow, CategoryTheory.Equivalence.mapCommGrp_unitIso, CategoryTheory.Equivalence.cancel_unitInv_right, AlgebraicTopology.DoldKan.N₂Γ₂_inv_app_f_f, CategoryTheory.Equivalence.invFunIdAssoc_hom_app, CategoryTheory.WithTerminal.mkCommaMorphism_right, CategoryTheory.RetractArrow.right_i, CategoryTheory.Arrow.inv_hom_id_right, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_right_left_as, CategoryTheory.Arrow.w_mk_right_assoc, CategoryTheory.MorphismProperty.FunctorialFactorizationData.i_mapZ, CategoryTheory.Square.toArrowArrowFunctor_obj_right_right, CategoryTheory.Limits.pullbackConeEquivBinaryFan_inverse_obj, CategoryTheory.Limits.Cones.postcomposeEquivalence_unitIso, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_unit_app, CategoryTheory.Equivalence.unitIso_hom_app_comp_inverse_map_η_functor, CategoryTheory.CostructuredArrow.mapIso_counitIso_hom_app_left, CategoryTheory.ComposableArrows.arrowEquiv_symm_apply, CategoryTheory.SmallObject.functorMap_π_assoc, CategoryTheory.Iso.compInverseIso_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_inv_app_fst_app, CategoryTheory.WithInitial.equivComma_functor_map_left, AlgebraicGeometry.ΓSpec.left_triangle, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_left_as, CategoryTheory.Over.map_obj_hom, CategoryTheory.Limits.Cones.postcomposeEquivalence_counitIso, SimplexCategory.revCompRevIso_inv_app, CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj_inv_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_hom_app_fst_app, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₁₃, CategoryTheory.Limits.walkingSpanOpEquiv_counitIso_hom_app, CategoryTheory.CosimplicialObject.Augmented.toArrow_map_right, LightCondSet.instEpiTopCatAppCounitTopCatAdjunction, CategoryTheory.Over.associator_hom_left_snd_fst, CategoryTheory.CostructuredArrow.toOver_map_left, CategoryTheory.Limits.Cones.functorialityEquivalence_unitIso, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₃, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply', CategoryTheory.Over.postComp_inv_app_left, CategoryTheory.CosimplicialObject.Augmented.const_map_right, CategoryTheory.Limits.Cocone.equivStructuredArrow_unitIso, Initial.conesEquiv_unitIso, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counit_app_assoc, groupHomology.d₁₀ArrowIso_inv_right, CategoryTheory.Sieve.functorPushforward_inverse, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_right, CategoryTheory.Equivalence.congrFullSubcategory_unitIso, CategoryTheory.Arrow.mk_right, CategoryTheory.Over.toOverSectionsAdj_unit_app, CategoryTheory.Equivalence.changeInverse_counitIso_inv_app, CategoryTheory.shiftFunctorAdd'_zero_add_hom_app, lanCompColimIso_inv_app, CategoryTheory.Adjunction.comp_counit_app, mapArrow_map_left, CategoryTheory.Grothendieck.map_id_eq, CategoryTheory.subterminalsEquivMonoOverTerminal_inverse_map, CategoryTheory.MorphismProperty.over_iso_iff, CategoryTheory.Cat.opFunctorInvolutive_hom_app_toFunctor_map, CategoryTheory.ObjectProperty.isColocal_adj_counit_app, AlgebraicGeometry.ΓSpec.unop_locallyRingedSpaceAdjunction_counit_app', CategoryTheory.functorProdFunctorEquivUnitIso_hom_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_inv_app_hom, CategoryTheory.SmallObject.ιFunctorObj_eq, CategoryTheory.Adjunction.mkOfHomEquiv_unit_app, isEquivalence_refl, CategoryTheory.Cat.opFunctorInvolutive_hom_app_toFunctor_obj, CategoryTheory.underToAlgebra_obj_A, CategoryTheory.EnrichedFunctor.forgetId_inv_app, CategoryTheory.RetractArrow.retract_left, toOver_obj_left, CategoryTheory.Adjunction.leftAdjointCompIso_inv_app, CategoryTheory.Sheaf.adjunction_counit_app_val, CategoryTheory.Equivalence.mapCommMon_unitIso, map_shiftFunctorCompIsoId_inv_app_assoc, AlgEquiv.toUnder_inv_right_apply, CategoryTheory.oppositeShiftFunctorZero_inv_app, CategoryTheory.Arrow.squareToSnd_left, CategoryTheory.Equivalence.changeInverse_unitIso_inv_app, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_hom_app, instEssSurjId, CategoryTheory.Over.rightUnitor_inv_left_snd_assoc, CategoryTheory.WithTerminal.equivComma_functor_obj_hom_app, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso_inv_app_f, CategoryTheory.Over.toOverSectionsAdj_counit_app, pointedToBipointedCompBipointedToPointedSnd_hom_app_toFun, mapMonIdIso_hom_app_hom, CategoryTheory.SimplicialObject.Augmented.hom_ext_iff, CategoryTheory.Limits.ImageMap.factor_map, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_snd, CategoryTheory.Adjunction.IsMonoidal.instIsMonoidalUnit, CategoryTheory.CartesianClosed.uncurry_eq, CategoryTheory.MonoOver.w, CategoryTheory.MonoOver.bot_arrow_eq_zero, CategoryTheory.WithInitial.equivComma_inverse_map_app, CategoryTheory.Triangulated.TStructure.triangleLTGE_map_hom₃, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp'_X, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_hom_app_coe, CategoryTheory.forgetAdjToOver_unit_app, CategoryTheory.Arrow.isIso_left, CategoryTheory.Arrow.isIso_hom_iff_isIso_of_isIso, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_inv_left_app, CategoryTheory.Over.iteratedSliceEquivOverMapIso_inv_app_left_left, map_shiftFunctorCompIsoId_hom_app_assoc, CategoryTheory.Presieve.functorPullback_id, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₁, CategoryTheory.Over.iteratedSliceEquivOverMapIso_hom_app_left_left, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.functor_obj, CategoryTheory.CostructuredArrow.map₂_map_right, CategoryTheory.Comma.toIdPUnitEquiv_unitIso_hom_app_right, CategoryTheory.Bicategory.leftUnitorNatIso_hom_app, CategoryTheory.RetractArrow.retract_right_assoc, CategoryTheory.Adjunction.toMonad_μ, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_left, CommRingCat.toAlgHom_apply, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counitIso_hom_app, CategoryTheory.StructuredArrow.toUnder_map_right, MulEquiv.toSingleObjEquiv_unitIso_inv, CategoryTheory.regularTopology.parallelPair_pullback_initial, CategoryTheory.WithTerminal.liftFromOver_obj_obj, CategoryTheory.cosimplicialSimplicialEquiv_counitIso_inv_app_app, CategoryTheory.overToCoalgebra_map_f, CategoryTheory.Comonad.adj_counit, CategoryTheory.CosimplicialObject.Augmented.toArrow_map_left, CategoryTheory.Pseudofunctor.isStackFor_iff, CategoryTheory.ComposableArrows.opEquivalence_unitIso_hom_app, CategoryTheory.SimplicialObject.augment_hom_app, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_left_right_as, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right_assoc, CategoryTheory.Adjunction.adjunctionOfEquivRight_unit_app, CategoryTheory.Pseudofunctor.isPrestackFor_iff_isSheafFor, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_left_app, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_app_app_germToPullbackStalk_assoc, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_hom_app_app_hom_hom, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_snd_assoc, AlgebraicTopology.DoldKan.N₂Γ₂_compatible_with_N₁Γ₀, CategoryTheory.Adjunction.unop_counit, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorEquivalence_unitIso, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp'_f, CategoryTheory.Cat.freeMap_id, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_fst_assoc, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_inv_app_hom, CategoryTheory.Square.fromArrowArrowFunctor_obj_X₁, CategoryTheory.TwoSquare.isIso_lanBaseChange_app_iff, CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_left, CategoryTheory.Over.pullback_map_left, AlgebraicGeometry.instIsIsoSchemeAppUnitOppositeCommRingCatAdjunctionOfIsAffine, CategoryTheory.SmallObject.instIsIsoRightAppArrowMapToTypeOrdFunctorIterationFunctor, CategoryTheory.instIsContinuousOverLeftDiscretePUnitIteratedSliceBackwardOver, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_inv_app_app, CategoryTheory.ULift.equivalence_unitIso_hom, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.counitIso_hom_app_app_hom, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_counitIso_inv_app_f, CategoryTheory.Join.pseudofunctorRight_mapId_hom_toNatTrans_app, CategoryTheory.Under.forgetMapInitial_hom_app, triangle, mapHomologicalComplexIdIso_inv_app_f, CategoryTheory.Discrete.sumEquiv_counitIso_hom_app, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_fst, CategoryTheory.Pretriangulated.shiftFunctorZero_op_hom_app, CategoryTheory.Equivalence.cancel_counitInv_right_assoc, CategoryTheory.Pseudofunctor.presheafHom_map, CategoryTheory.prodOpEquiv_unitIso_inv_app, CategoryTheory.WithInitial.equivComma_functor_map_right_app, CategoryTheory.GradedObject.mapBifunctorRightUnitor_inv_apply, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply, SSet.Augmented.stdSimplex_obj_right, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_hom, CategoryTheory.Codiscrete.adj_counit_app, CategoryTheory.Over.postEquiv_counitIso, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_ι_app_right, CategoryTheory.ChosenPullbacksAlong.pullbackId_hom_counit, CategoryTheory.Limits.multispanIndexCoend_left, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_hom_app_hom_left, ranObjObjIsoLimit_inv_π_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_hom_app_app, CategoryTheory.Over.sections_obj, AlgebraicGeometry.Scheme.smallGrothendieckTopologyOfLE_eq_toGrothendieck_smallPretopology, Rep.resIndAdjunction_counit_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_map_right, CategoryTheory.Adjunction.rightOp_counit, CochainComplex.shiftFunctorZero'_hom_app_f, HomologicalComplex₂.flipEquivalenceUnitIso_inv_app_f_f, AlgebraicGeometry.opensDiagram_obj, CategoryTheory.MonadHom.app_η_assoc, PushoutObjObj.ι_iso_of_iso_right_hom, CategoryTheory.Equivalence.sheafCongr.unitIso_hom_app_val_app, CategoryTheory.Adjunction.functorialityCounit_app_hom, StalkSkyscraperPresheafAdjunctionAuxs.unit_app, ModuleCat.RestrictionCoextensionAdj.unit'_app, ModuleCat.matrixEquivalence_unitIso, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₂, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_id, CategoryTheory.RetractArrow.op_i_right, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_hom_app_snd_app, AlgebraicGeometry.ΓSpec.isIso_locallyRingedSpaceAdjunction_counit, CategoryTheory.MorphismProperty.instFullUnderTopUnderForget, CategoryTheory.Abelian.LeftResolution.instEpiKaroubiAppπObjToKaroubi, CategoryTheory.prod.prodFunctorToFunctorProdAssociator_inv_app_app, map_shiftFunctorCompIsoId_hom_app, CategoryTheory.SimplicialObject.Augmented.const_map_right, leftOpId_inv_app, CategoryTheory.Abelian.coim_obj, CategoryTheory.Over.star_obj_left, mapArrow_map_right, AlgebraicTopology.DoldKan.whiskerLeft_toKaroubi_N₂Γ₂_hom, RingCat.moduleCatRestrictScalarsPseudofunctor_mapId, CategoryTheory.equivToOverUnit_counitIso, CategoryTheory.Over.iteratedSliceEquiv_functor, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_of, CategoryTheory.MorphismProperty.overObj_iff, SSet.Truncated.HomotopyCategory.BinaryProduct.mapHomotopyCategory_prod_id_comp_inverse, CategoryTheory.shiftFunctorAdd'_add_zero, CategoryTheory.shiftFunctorCompIsoId_add'_hom_app, AlgebraicGeometry.opensCone_π_app, CategoryTheory.Over.tensorHom_left, CategoryTheory.Equivalence.invFunIdAssoc_inv_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_inv_app_snd_app, CategoryTheory.MorphismProperty.instIsLeftAdjointOverTopMapOfHasPullbacksAlongOfIsStableUnderBaseChangeAlong, CategoryTheory.RetractArrow.retract_right, CategoryTheory.SimplicialObject.instIsIsoAppUnitTruncatedCoskAdj, CategoryTheory.MorphismProperty.Over.mapComp_hom_app_left, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_inv_app_zero, CategoryTheory.toOverIteratedSliceForwardIsoPullback_hom_app_left, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.unitIso_hom_app_hom_app, CommShift₂.comm, CategoryTheory.GrothendieckTopology.toPlusNatTrans_app, CategoryTheory.MonoOver.mk'_coe', CategoryTheory.TwistShiftData.z_zero_left, TopologicalSpace.Opens.mapId_inv_app, leftExtensionEquivalenceOfIso₁_counitIso_inv_app_right_app, CategoryTheory.ExponentiableMorphism.ev_coev_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_map_left_app, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_hom, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_left_hom, CategoryTheory.WithInitial.mkCommaObject_right_map, CategoryTheory.shiftFunctorZero_inv_app_shift, CategoryTheory.Presheaf.isSheaf_iff_isLimit, CategoryTheory.Under.opEquivOpOver_functor_obj, CategoryTheory.WithInitial.equivComma_functor_obj_hom_app, essImage.unit_isIso, CategoryTheory.Quiv.freeMap_pathsOf_pathComposition, CategoryTheory.Adjunction.commShiftIso_inv_app_counit_app_assoc, SSet.Truncated.HomotopyCategory.BinaryProduct.functor_comp_inverse, CategoryTheory.MonoidalCategory.DayConvolutionUnit.instIsLeftKanExtensionProdDiscretePUnitExternalProductExtensionUnitLeftφ, CategoryTheory.CostructuredArrow.prodEquivalence_unitIso, CategoryTheory.Limits.Cones.whiskeringEquivalence_counitIso, CommShift.id_commShiftIso_inv_app, CategoryTheory.MonoOver.mono, CategoryTheory.Over.associator_inv_left_fst_snd, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₃, MulEquiv.toSingleObjEquiv_counitIso_inv, CategoryTheory.skeletonEquivalence_counitIso, CategoryTheory.SimplicialObject.comp_left_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_right, CategoryTheory.Equivalence.congrLeft_unitIso_inv_app, CategoryTheory.MonoidalOpposite.unmopEquiv_counitIso_hom_app, CategoryTheory.Square.toArrowArrowFunctor_obj_hom_left, CategoryTheory.mateEquiv_symm_apply, CategoryTheory.exp.ev_coev, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap_assoc, CategoryTheory.Comonad.map_counit_app, CategoryTheory.MonoOver.forget_obj_left, CategoryTheory.WithInitial.commaFromUnder_obj_hom_app, CategoryTheory.Equivalence.cancel_unit_right_assoc, CompHausLike.LocallyConstant.adjunction_left_triangle, ranCounit_app_app_ranAdjunction_unit_app_app_assoc, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app, CategoryTheory.Equivalence.mapGrp_unitIso, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_hom_app_app_snd, CategoryTheory.Adjunction.ε_comp_map_ε, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map_assoc, CategoryTheory.Adjunction.counit_epi_of_R_faithful, CategoryTheory.Iso.isoFunctorOfIsoInverse_inv_app, CategoryTheory.Cat.opFunctorInvolutive_inv_app_toFunctor_map, leftOpRightOpEquiv_unitIso_hom_app, CategoryTheory.Monad.map_unit_app, HomotopicalAlgebra.CofibrantObject.instIsIsoFunctorHoCatAdjCounit', OrderIso.equivalence_counitIso, CategoryTheory.WithInitial.commaFromUnder_obj_right, CategoryTheory.Equivalence.counitInv_app_comp_functor_map_η_inverse, SheafOfModules.pullback_id_comp, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIso_inv_app_hom, CategoryTheory.WithInitial.equivComma_inverse_obj_map, CategoryTheory.Over.forget_obj, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_hom_app_val_app, CategoryTheory.Adjunction.whiskerLeft_counit_iso_of_L_fully_faithful, CategoryTheory.Join.mapWhiskerRight_associator_hom, CategoryTheory.CartesianClosed.uncurry_id_eq_ev, CategoryTheory.CostructuredArrow.grothendieckProj_map, CategoryTheory.MorphismProperty.Over.w_assoc, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst_assoc, CategoryTheory.SimplicialObject.Augmented.rightOp_right_obj, CategoryTheory.toOverPullbackIsoToOver_hom_app_left, CategoryTheory.Over.star_obj_hom, RightExtension.postcomp₁_map_left_app, CategoryTheory.shiftFunctorAdd'_add_zero_hom_app, CategoryTheory.Comma.toIdPUnitEquiv_counitIso_hom_app, CategoryTheory.Limits.walkingSpanOpEquiv_unitIso_inv_app, CategoryTheory.Arrow.mk_hom, CategoryTheory.SmallObject.πObj_ιIteration_app_right_assoc, ComplexShape.Embedding.ιTruncLENatTrans_app, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_right, CategoryTheory.Under.forget_map, CategoryTheory.WithTerminal.ofCommaObject_map, HomotopicalAlgebra.CofibrantObject.instIsIsoFunctorHoCatCounitHoCatAdj, CategoryTheory.Equivalence.congrLeft_unitIso_hom_app, CategoryTheory.MorphismProperty.ofHoms_homFamily, CategoryTheory.Over.associator_hom_left_snd_snd_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_left, commAlgCatEquivUnder_counitIso, CategoryTheory.ExponentiableMorphism.pushforwardComp_hom_counit_assoc, CategoryTheory.MonoidalClosed.id_tensor_pre_app_comp_ev_assoc, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₂, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_inv_app_val_app, CategoryTheory.conjugateEquiv_counit, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_ε_app, mapCommMon_id_mul, CategoryTheory.Grpd.freeForgetAdjunction_counit_app, CategoryTheory.Adjunction.unit_isIso_of_L_fully_faithful, PullbackObjObj.mapArrowRight_comp, CategoryTheory.Equivalence.unitInv_app_inverse, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_counitIso_hom, CategoryTheory.Monad.instHasCoequalizerMapAAppCounitObjAOfHasCoequalizerOfIsSplitPair, ranObjObjIsoLimit_hom_π_assoc, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatTrans_id, CategoryTheory.RetractArrow.map_r_left, TopologicalSpace.Opens.overEquivalence_counitIso_inv_app, CategoryTheory.uncurry_pre, CategoryTheory.ReflQuiv.adj_counit_app, CategoryTheory.Equivalence.ext_iff, id_comp, CategoryTheory.Under.equivalenceOfIsInitial_unitIso, CategoryTheory.Limits.im_obj, CategoryTheory.SmallObject.πObj_naturality_assoc, PullbackObjObj.π_iso_of_iso_right_inv, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_obj, CategoryTheory.instIsIsoAppUnitReflectorAdjunctionObjEssImage, CategoryTheory.ihom.coev_naturality_assoc, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst, CategoryTheory.Equivalence.symmEquivInverse_obj_counitIso_inv, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₁, CategoryTheory.conjugateEquiv_rightUnitor_hom, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₁, CategoryTheory.Adjunction.unit_app_shift_commShiftIso_inv_app_assoc, TopologicalSpace.Opens.adjunction_counit_map_functor, CategoryTheory.Adjunction.unit_isSplitEpi_of_L_full, TopCat.Presheaf.generateEquivalenceOpensLe_functor, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_inv_app_hom, isDenseAt_iff, CoalgCat.comonEquivalence_unitIso, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality_assoc, PresheafOfModules.Derivation'.d_app, CategoryTheory.Limits.multispanShapeCoend_fst, CategoryTheory.exp.ev_coev_assoc, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_hom_right_app, CategoryTheory.Adjunction.op_unit, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_inv_app, LaxMonoidal.id_μ, CategoryTheory.cosimplicialSimplicialEquiv_unitIso_hom_app, CategoryTheory.Over.μ_pullback_left_fst_fst', SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_comp_functor, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_pullback_obj, CategoryTheory.Sheaf.isConstant_iff_isIso_counit_app', CategoryTheory.shiftFunctorZero_hom_app_shift, Types.monoOverEquivalenceSet_functor_map, CategoryTheory.MonadHom.app_η, CategoryTheory.Over.μ_pullback_left_fst_snd, CategoryTheory.Over.whiskerRight_left, CategoryTheory.Mat_.equivalenceSelfOfHasFiniteBiproducts_functor, ModuleCat.homEquiv_extendScalarsComp, CategoryTheory.CosimplicialObject.Augmented.toArrow_obj_left, CategoryTheory.Equivalence.changeFunctor_unitIso_inv_app, CategoryTheory.unitOfTensorIsoUnit_inv_app, CategoryTheory.Square.toArrowArrowFunctor'_map_left_right, TopologicalSpace.Opens.overEquivalence_unitIso_inv_app_left, CategoryTheory.Arrow.id_left, CategoryTheory.WithInitial.pseudofunctor_mapId, CategoryTheory.Abelian.coimageImageComparisonFunctor_obj, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₁₃, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_counitIso, CategoryTheory.Monoidal.transportStruct_leftUnitor, CategoryTheory.Adjunction.CommShift.compatibilityCounit_left, flipping_unitIso_hom_app_app_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τr, CategoryTheory.Join.pseudofunctorRight_mapId_inv_toNatTrans_app, CategoryTheory.Sieve.mem_functorPushforward_inverse, CategoryTheory.Monoidal.transportStruct_rightUnitor, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right, instIsRightKanExtensionObjRanAppRanCounit, CategoryTheory.Limits.imageSubobjectMap_arrow, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_ihom_ev_app, CategoryTheory.ExponentiableMorphism.ev_naturality_assoc, CategoryTheory.Idempotents.DoldKan.η_inv_app_f, CategoryTheory.Limits.imageSubobjectMap_arrow_assoc, mapTriangleIdIso_hom_app_hom₃, CategoryTheory.Adjunction.Triple.adj₁_counit_app_rightToLeft_app_assoc, CategoryTheory.Over.opEquivOpUnder_counitIso, CategoryTheory.SimplicialObject.Augmented.whiskering_map_app_left, closedUnit_app_app, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_hom_app_left, CategoryTheory.plusPlusAdjunction_counit_app_val, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_left, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_σ, commAlgCatEquivUnder_inverse_obj_carrier, CategoryTheory.MorphismProperty.instFaithfulCostructuredArrowTopOverToOver, equiv_unitIso, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_symm_apply, CategoryTheory.MonoidalCategory.tensoringRight_ε, TopologicalSpace.Opens.adjunction_counit_app_self, CategoryTheory.Limits.ImageFactorisation.ofArrowIso_F, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_app, CategoryTheory.uncurry_expComparison, CategoryTheory.Arrow.equivSigma_symm_apply_hom, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_inv_apply, CategoryTheory.CatCenter.smul_iso_inv_eq_assoc, CategoryTheory.Idempotents.KaroubiUniversal₁.counitIso_hom_app_app_f, CommShift.id_commShiftIso_hom_app, CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_p_assoc, CategoryTheory.Adjunction.commShiftIso_hom_app_counit_app_shift_assoc, CategoryTheory.Triangulated.TStructure.triangleLTGE_map_hom₂, CategoryTheory.Coreflective.instIsIsoAppCounitCoreflectorAdjunctionA, CategoryTheory.RetractArrow.unop_r_right, CategoryTheory.Arrow.id_right, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_inv_app, CategoryTheory.Adjunction.functorialityUnit'_app_hom, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_unitIso_inv_app_f, CategoryTheory.Idempotents.KaroubiUniversal₁.counitIso_inv_app_app_f, CategoryTheory.GradedObject.mapBifunctorObjObjSingle₀Iso_inv, PullbackObjObj.mapArrowLeft_left, CategoryTheory.MonoidalClosed.uncurry_ihom_map, CategoryTheory.Adjunction.rightAdjointUniq_hom_counit_assoc, TopCat.Presheaf.pullback_obj_obj_ext_iff, CategoryTheory.forgetEnrichmentOppositeEquivalence_counitIso, triangleIso_assoc, CategoryTheory.Bicategory.rightUnitorNatIso_inv_app, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd, AlgebraicGeometry.Scheme.ofRestrict_toLRSHom_c_app, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_map_left_left, CategoryTheory.FreeGroupoid.mapId_inv_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_hom_app, CategoryTheory.toOverIsoToOverUnit_hom_app_left, LightCondMod.LocallyConstant.instIsIsoLightCondSetMapForgetAppLightCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, CategoryTheory.Adjunction.compYonedaIso_inv_app_app, CategoryTheory.MonoidalClosed.uncurry_id_eq_ev, CategoryTheory.Comon.Comon_EquivMon_OpOp_unitIso, TopCat.Presheaf.id_pushforward, CategoryTheory.Equivalence.changeInverse_counitIso_hom_app, CategoryTheory.Over.w, leftUnitor_inv_app, CategoryTheory.MorphismProperty.CostructuredArrow.toOver_map, CategoryTheory.SimplicialObject.Augmented.drop_obj, CategoryTheory.instIsCorepresentableIdType, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_inv, CategoryTheory.Sheaf.adjunction_unit_app_val, AlgebraicGeometry.instHasCoproductsOfShapeOverSchemeTopMorphismPropertyOfSmall, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_pullback_map, CategoryTheory.Endofunctor.Algebra.functorOfNatTransId_hom_app_f, PullbackObjObj.mapArrowLeft_comp_assoc, TopCat.Presheaf.generateEquivalenceOpensLe_counitIso, CategoryTheory.Equivalence.fun_inv_map, CategoryTheory.StructuredArrow.mapIso_unitIso_inv_app_right, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_m, CategoryTheory.Cat.leftUnitor_hom_toNatTrans, AlgHom.toUnder_right, lanUnit_app_whiskerLeft_lanAdjunction_counit_app_assoc, Rep.invariantsAdjunction_counit_app_hom, ihom_coev_app, instLinearId, CategoryTheory.Limits.CatCospanTransform.id_squareRight, PushoutObjObj.ι_iso_of_iso_left_inv, CategoryTheory.Monoidal.Reflective.instIsIsoAppUnitObjIhom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality_assoc, CategoryTheory.NatIso.unop_leftUnitor, CategoryTheory.Sieve.yonedaFamily_fromCocone_compatible, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_counitIso, CategoryTheory.subterminalsEquivMonoOverTerminal_inverse_obj_obj, CategoryTheory.OverClass.asOverHom_left, CategoryTheory.CosimplicialObject.augment_hom_zero, mapCommGrp_id_one, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_fst_assoc, CategoryTheory.CosimplicialObject.Augmented.toArrow_obj_right, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s₀_comp_δ₁, CategoryTheory.toSheafification_app, CategoryTheory.coalgebraEquivOver_counitIso, CategoryTheory.NatTrans.IsMonoidal.instHomFunctorRightUnitor, CategoryTheory.opOpEquivalence_unitIso, CategoryTheory.WithInitial.opEquiv_counitIso_inv_app, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_right, CategoryTheory.ShiftMkCore.add_zero_inv_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_obj, CategoryTheory.Limits.Cones.functorialityEquivalence_inverse, CategoryTheory.Arrow.mk_eq, CategoryTheory.MorphismProperty.CostructuredArrow.toOver_obj, CategoryTheory.HasShift.Induced.zero_hom_app_obj, Types.monoOverEquivalenceSet_functor_obj, CategoryTheory.MorphismProperty.Under.w, CategoryTheory.CosimplicialObject.Augmented.toArrow_obj_hom, sheafPushforwardContinuousId_hom_app_val_app, flipping_unitIso_inv_app_app_app, AlgEquiv.toUnder_hom_right_apply, CategoryTheory.Adjunction.CoreUnitCounit.right_triangle, AlgebraicGeometry.Scheme.kerFunctor_map, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_inv_app_one, CategoryTheory.Adjunction.shift_unit_app, CategoryTheory.Adjunction.map_η_comp_η_assoc, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app_assoc, CategoryTheory.ChosenPullbacksAlong.pullbackId_hom_counit_assoc, CategoryTheory.Adjunction.unit_app_commShiftIso_hom_app_assoc, FundamentalGroupoid.punitEquivDiscretePUnit_unitIso, CategoryTheory.Pseudofunctor.IsStack.essSurj_of_sieve, CategoryTheory.Monad.algebraEquivOfIsoMonads_counitIso, CategoryTheory.FreeGroupoid.lift_id_comp_of, sheafPushforwardContinuousId'_inv_app_val_app, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso_hom_app_f, CategoryTheory.Over.associator_inv_left_fst_fst, CategoryTheory.Preadditive.commGrpEquivalenceAux_inv_app_hom_hom_hom, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_map_right_right, map_opShiftFunctorEquivalence_counitIso_hom_app_unop, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_unitIso, CategoryTheory.NatIso.op_leftUnitor, CategoryTheory.Equivalence.mapCommMon_counitIso, CategoryTheory.Adjunction.inv_counit_map, pointedToBipointedCompBipointedToPointedSnd_inv_app_toFun, CategoryTheory.Adjunction.leftOp_counit, CategoryTheory.MonoOver.isIso_iff_isIso_hom_left, TopCat.Presheaf.presheafEquivOfIso_unitIso_inv_app_app, CategoryTheory.unit_mateEquiv_symm, CategoryTheory.Comma.mapLeftId_hom_app_left, CategoryTheory.MonoidalOpposite.mopMopEquivalence_counitIso_inv_app, CategoryTheory.Over.snd_left, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_map_left_left, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd, CategoryTheory.Limits.Cone.toStructuredArrowCompProj_hom_app, CategoryTheory.Grpd.id_eq_id, CategoryTheory.Equivalence.symmEquiv_counitIso, map_opShiftFunctorEquivalence_counitIso_inv_app_unop_assoc, CategoryTheory.Limits.ImageMap.map_ι, CategoryTheory.Adjunction.isIso_unit_of_iso, CategoryTheory.MonoOver.congr_inverse, CategoryTheory.Cat.leftUnitor_inv_toNatTrans, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_fst_assoc, CategoryTheory.Adjunction.Triple.epi_rightToLeft_app_iff, leibnizPushout_obj_obj, CategoryTheory.Join.mapPairId_inv_app, CategoryTheory.Over.over_right, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ_assoc, CategoryTheory.Adjunction.rightAdjointUniq_hom_counit, CategoryTheory.Localization.Lifting.id_iso, CategoryTheory.Equivalence.cancel_unit_right_assoc', CategoryTheory.Comma.mapLeftId_inv_app_left, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_right, mapMonIdIso_inv_app_hom, fun_inv_map, CategoryTheory.Iso.isoCompInverse_inv_app, CategoryTheory.instIsCocontinuousOverLeftDiscretePUnitIteratedSliceBackwardOver, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality, CategoryTheory.Arrow.isIso_hom_iff_isIso_hom_of_isIso, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_unitIso, CategoryTheory.cosimplicialSimplicialEquiv_unitIso_inv_app, CategoryTheory.SingleFunctors.shiftIso_zero, CategoryTheory.Limits.Cocones.functorialityEquivalence_counitIso, CategoryTheory.Arrow.inv_hom_id_left_assoc, commAlgCatEquivUnder_unitIso, CategoryTheory.Equivalence.mapMon_counitIso, CategoryTheory.Over.tensorHom_left_fst, CategoryTheory.Sieve.overEquiv_symm_generate, CategoryTheory.Square.fromArrowArrowFunctor_obj_X₄, SimplexCategory.revCompRevIso_hom_app, SimplicialObject.opFunctorCompOpFunctorIso_hom_app_app, CategoryTheory.Equivalence.induced_unitIso, CategoryTheory.ThinSkeleton.map_id_eq, CategoryTheory.MorphismProperty.Over.mk_left, MonObj.mopEquiv_unitIso_hom_app_hom, CategoryTheory.Pseudofunctor.ObjectProperty.mapId_hom_app, CategoryTheory.Over.whiskerRight_left_snd, pointedToBipointedCompBipointedToPointedFst_inv_app_toFun, CategoryTheory.Iso.isoInverseOfIsoFunctor_inv_app, CategoryTheory.Comonad.comparison_map_f, commShiftIso_id_hom_app, AlgebraicGeometry.Scheme.Cover.pullbackCoverOver_f, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_mapPullbackAdj_unit_app, CategoryTheory.algebraEquivUnder_unitIso, CategoryTheory.Comonad.ComonadicityInternal.main_pair_coreflexive, CategoryTheory.SimplicialObject.Augmented.w₀_assoc, CategoryTheory.Adjunction.Triple.leftToRight_app_map_adj₁_unit_app_assoc, CategoryTheory.Equivalence.core_counitIso_hom_app_iso_hom, CategoryTheory.ChosenPullbacksAlong.pullbackComp_hom_counit, TopCat.Presheaf.germ_stalkPullbackHom_assoc, CategoryTheory.Equivalence.inv_fun_map_assoc, CategoryTheory.Square.fromArrowArrowFunctor'_obj_X₄, TopCat.Presheaf.whiskerIsoMapGenerateCocone_hom_hom, CategoryTheory.Equivalence.inverse_counitInv_comp_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd_assoc, mapCommGrpIdIso_hom_app_hom_hom_hom, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_inv_app_val_app, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd, HomotopicalAlgebra.CofibrantObject.HoCat.adjCounitIso_inv_app, CategoryTheory.WithTerminal.commaFromOver_obj_hom_app, ModuleCat.ihom_coev_app, CategoryTheory.Limits.id_preservesLimitsOfSize, AlgebraicGeometry.Scheme.Cover.toPresieveOver_le_arrows_iff, CategoryTheory.MorphismProperty.mem_toSet_iff, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_σ_assoc, SimplicialObject.opEquivalence_unitIso, CategoryTheory.Limits.id_preservesColimitsOfSize, HomotopicalAlgebra.instFibrationLeftDiscretePUnitOfOver, CategoryTheory.Equivalence.trans_counitIso, CategoryTheory.Over.iteratedSliceEquiv_unitIso, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_π_assoc, CategoryTheory.CatCenter.mul_app'_assoc, CategoryTheory.underToAlgebra_obj_a, CategoryTheory.Comma.toPUnitIdEquiv_unitIso_hom_app_left, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit_assoc, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₃, CategoryTheory.CatCommSq.vInv_iso_inv_app, CategoryTheory.CommSq.of_arrow, CochainComplex.shiftFunctorZero'_inv_app_f, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse_assoc, HomotopicalAlgebra.CofibrantObject.HoCat.adjUnit_app, constCompEvaluationObj_inv_app, CategoryTheory.oppositeShiftFunctorZero_hom_app, CategoryTheory.Comma.mapRightIso_unitIso_hom_app_left, CategoryTheory.WithInitial.equivComma_unitIso_inv_app_app, CategoryTheory.prod.rightUnitorEquivalence_unitIso, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counitIso_hom_app_assoc, CategoryTheory.SimplicialObject.Augmented.const_obj_left, CategoryTheory.functorProdFunctorEquivCounitIso_inv_app_app, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_incl, CategoryTheory.WithInitial.commaFromUnder_map_right, CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_cancel_inv_app, CategoryTheory.CatCenter.smul_iso_hom_eq_assoc, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₁, CategoryTheory.WithInitial.equivComma_functor_obj_left, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_fst, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_assoc, CategoryTheory.Under.mk_right, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_hom, CategoryTheory.Equivalence.map_η_comp_η_assoc, CategoryTheory.SmallObject.functorMapSrc_functorObjTop_assoc, toOver_map_left, coreId_hom_app_iso_inv, CategoryTheory.ParametrizedAdjunction.unit_whiskerRight_map_assoc, CategoryTheory.Over.star_map_left, CategoryTheory.ShrinkHoms.equivalence_counitIso, CategoryTheory.Arrow.isIso_of_isIso, CategoryTheory.Arrow.rightFunc_obj, CategoryTheory.Over.tensorHom_left_fst_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd_assoc, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc, CategoryTheory.Join.mapWhiskerRight_whiskerLeft, CategoryTheory.forgetAdjToOver.homEquiv_symm, CondensedSet.isDiscrete_tfae, isLeftKanExtensionId, CategoryTheory.Equivalence.symmEquiv_unitIso, CategoryTheory.Under.postMap_app, pointedToBipointedCompBipointedToPointedFst_hom_app_toFun, AlgebraicGeometry.Scheme.Cover.overEquiv_generate_toPresieveOver_eq_ofArrows, IsTriangulated.instId, leftOpRightOpEquiv_counitIso_hom_app_app, CategoryTheory.shiftFunctorAdd_add_zero_inv_app, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_unitIso, CategoryTheory.Adjunction.leftAdjointUniq_hom_counit_assoc, CategoryTheory.Discrete.equivalence_counitIso, CategoryTheory.Over.prodLeftIsoPullback_inv_fst_assoc, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_inv_right, CategoryTheory.Abelian.im_obj, currying_unitIso_inv_app_app_app, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_hom_left, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_hom_app_hom, CategoryTheory.SmallObject.SuccStruct.toSuccArrow_left, currying_unitIso_hom_app_app_app, CategoryTheory.coprodMonad_η_app, CategoryTheory.Discrete.productEquiv_counitIso_inv_app, CategoryTheory.Equivalence.counitIso_inv_app_comp_functor_map_η_inverse_assoc, CategoryTheory.CosimplicialObject.Augmented.const_map_left, CategoryTheory.Join.pseudofunctorRight_mapComp_hom_toNatTrans_app, CategoryTheory.Subobject.lowerEquivalence_counitIso, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_assoc, CategoryTheory.Adjunction.Triple.leftToRight_eq_counits, CategoryTheory.MorphismProperty.Under.Hom.ext_iff, AlgebraicGeometry.Scheme.Modules.pushforwardId_hom_app_app, CategoryTheory.Equivalence.mapHomologicalComplex_counitIso, CategoryTheory.OverClass.asOver_hom, CategoryTheory.RetractArrow.instIsSplitEpiRightRArrow, SSet.opEquivalence_unitIso, CategoryTheory.Adjunction.counit_isIso_of_R_fully_faithful, CategoryTheory.yonedaPairing_map, CategoryTheory.Over.η_pullback_left, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_hom_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app, alexDiscEquivPreord_unitIso, CategoryTheory.LiftLeftAdjoint.instIsReflexivePairMapAppCounitOtherMap, SSet.Augmented.stdSimplex_obj_hom_app, CategoryTheory.Join.mapWhiskerRight_whiskerLeft_assoc, CategoryTheory.GrothendieckTopology.overMapPullback_comp_id_assoc, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_apply, CategoryTheory.Adjunction.rightOp_unit, toUnder_obj_right, CategoryTheory.Arrow.hom.congr_right, CategoryTheory.ExponentiableMorphism.coev_ev_assoc, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_inv_app_hom_hom_hom, CategoryTheory.Over.postAdjunctionRight_unit_app, instIsContinuousCompId, CategoryTheory.Cat.Hom.toNatIso_rightUnitor, CategoryTheory.Under.hom_right_inv_right, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_inv_app_app, CategoryTheory.Over.id_left, opId_inv_app, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_hom_left, CategoryTheory.unit_mateEquiv, CategoryTheory.Limits.FormalCoproduct.evalOpCompInlIsoId_hom_app_app, CategoryTheory.Arrow.iso_w, CategoryTheory.CosimplicialObject.augment_left, CategoryTheory.MorphismProperty.Under.mk_left, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_right, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_pullback_obj, CategoryTheory.Equivalence.counitInv_app_functor, CategoryTheory.Under.mapId_hom, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_inv_app_app_snd, CategoryTheory.Arrow.comp_left_assoc, CategoryTheory.Over.postComp_hom_app_left, HomologicalComplex.singleCompEvalIsoSelf_inv_app, CategoryTheory.Equivalence.rightOp_counitIso_hom_app, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_unit_app_app, CategoryTheory.CosimplicialObject.Augmented.hom_ext_iff, CategoryTheory.Limits.Cones.functorialityEquivalence_counitIso, CategoryTheory.yonedaPairingExt_iff, CategoryTheory.Over.whiskerLeft_left_fst, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply, CategoryTheory.CostructuredArrow.ofCommaFstEquivalence_counitIso, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_counit_app, CategoryTheory.SmallObject.πFunctorObj_eq, CategoryTheory.Comma.opEquiv_unitIso, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_hom_app_unmop, CategoryTheory.StructuredArrow.mapNatIso_counitIso_hom_app_right, CategoryTheory.expComparison_ev, CategoryTheory.MonoOver.inf_map_app, CategoryTheory.sheafificationAdjunction_unit_app, CategoryTheory.typeEquiv_counitIso_hom_app_val_app, CategoryTheory.Under.postEquiv_inverse, CategoryTheory.Comma.mapRightId_hom_app_right, CategoryTheory.Adjunction.unit_naturality, CategoryTheory.Presheaf.uliftYonedaAdjunction_unit_app_app, opUnopEquiv_unitIso, SSet.Truncated.HomotopyCategory.BinaryProduct.associativity'Iso_hom_app, CategoryTheory.Presheaf.coherentExtensiveEquivalence_unitIso, CategoryTheory.Sum.functorEquiv_unitIso_inv_app_app_inr, CategoryTheory.SmallObject.objMap_comp, ModuleCat.restrictScalarsId'_hom_app, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.isConnected, CategoryTheory.Equivalence.counitInv_functor_comp_assoc, LeftExtension.postcompose₂_map_left, CategoryTheory.CosimplicialObject.Augmented.const_obj_hom, CategoryTheory.shift_shiftFunctorCompIsoId_inv_app, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_counit_app_left, CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_left, CategoryTheory.Over.post_obj, CategoryTheory.Adjunction.map_μ_comp_counit_app_tensor, CategoryTheory.MonoOver.mkArrowIso_inv_hom_left, CategoryTheory.Arrow.inv_left_hom_right, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counit_app, CategoryTheory.Adjunction.compCoyonedaIso_hom_app_app, currying₃_unitIso_inv_app_app_app_app, CategoryTheory.Equivalence.fun_inv_map_assoc, CategoryTheory.Limits.Cone.equivCostructuredArrow_counitIso, whiskeringLeftObjIdIso_inv_app_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_inv_app_app, CategoryTheory.Cat.opFunctorInvolutive_inv_app_toFunctor_obj, CategoryTheory.WithTerminal.mkCommaObject_hom_app, OrderHom.equivalenceFunctor_unitIso_hom_app, CategoryTheory.Equivalence.ε_comp_map_ε, CategoryTheory.WithTerminal.mkCommaObject_left_obj, CategoryTheory.StructuredArrow.toUnder_obj_hom, RightExtension.postcompose₂_obj_hom_app, CategoryTheory.MorphismProperty.Over.instPreservesFiniteLimitsTopOverForget, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_left, CategoryTheory.WithInitial.equivComma_unitIso_hom_app_app, RightExtension.precomp_obj_hom_app, CategoryTheory.Cat.rightUnitor_inv_toNatTrans, CategoryTheory.ShiftedHom.opEquiv'_zero_add_symm, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_right_right, ranCounit_app_app_ranAdjunction_unit_app_app, CategoryTheory.Comma.mapRightId_hom_app_left, CategoryTheory.Pseudofunctor.isPrestackFor_iff, CategoryTheory.ShiftedHom.opEquiv'_symm_op_opShiftFunctorEquivalence_counitIso_inv_app_op_shift, CategoryTheory.algebraEquivUnder_counitIso, RightExtension.precomp_map_right, CategoryTheory.Monad.MonadicityInternal.unitCofork_pt, CategoryTheory.ChosenPullbacksAlong.Over.lift_left, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₁₂, CategoryTheory.prod.leftUnitorEquivalence_unitIso, CategoryTheory.shiftEquiv'_unitIso, CategoryTheory.Under.postCongr_hom_app_right, CategoryTheory.Over.mapId_hom_app_left, CategoryTheory.Square.toArrowArrowFunctor_map_left_left, CategoryTheory.Limits.colimit.pre_id, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_right, map_opShiftFunctorEquivalence_unitIso_hom_app_unop_assoc, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv, CategoryTheory.Abelian.coimageImageComparisonFunctor_map, FundamentalGroupoid.map_id, CategoryTheory.WithTerminal.commaFromOver_map_right, CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_right, CategoryTheory.MonoOver.w_assoc, ComplexShape.Embedding.πTruncGENatTrans_app, CategoryTheory.RetractArrow.map_i_left, CategoryTheory.MorphismProperty.over_iff, CategoryTheory.CostructuredArrow.map₂_map_left, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε_assoc, CategoryTheory.WithInitial.equivComma_inverse_obj_obj, groupAddGroupEquivalence_unitIso, CategoryTheory.MorphismProperty.Under.forget_comp_forget_map, CategoryTheory.Square.fromArrowArrowFunctor'_obj_X₁, CategoryTheory.Over.isPullback_of_binaryFan_isLimit, Action.FunctorCategoryEquivalence.unitIso_hom_app_hom, CategoryTheory.Pseudofunctor.IsStackFor.isEquivalence, CategoryTheory.Presieve.map_id, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_inv_app_fst_app, CategoryTheory.EnrichedFunctor.forgetId_hom_app, CategoryTheory.Adjunction.comp_unit_app_assoc, CategoryTheory.NatTrans.id_comm, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp_assoc, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp_X, CategoryTheory.MorphismProperty.instFullOverTopOverForget, CategoryTheory.CatCenter.smul_iso_inv_eq, CategoryTheory.Iso.coreRightUnitor, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_unitIso, CategoryTheory.CosimplicialObject.Augmented.point_map, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₁, HomologicalComplex.homologyFunctorSingleIso_inv_app, CategoryTheory.exp.coev_ev_assoc, CategoryTheory.Over.whiskerLeft_left_fst_assoc, SimplicialObject.opFunctorCompOpFunctorIso_inv_app_app, CategoryTheory.prod_map_pre_app_comp_ev, CategoryTheory.Equivalence.unit_naturality_assoc, CategoryTheory.Join.mapWhiskerLeft_associator_hom_assoc, CategoryTheory.Under.mapId_eq, CategoryTheory.Equivalence.unit_app_tensor_comp_inverse_map_δ_functor_assoc, CategoryTheory.MonoOver.pullback_obj_left, AlgebraicTopology.DoldKan.Compatibility.υ_hom_app, CategoryTheory.CatCenter.app_neg_one_zpow, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_left_left, CategoryTheory.GradedObject.ι_mapBifunctorLeftUnitor_hom_apply, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_inv_app_eq, CategoryTheory.Under.pushout_obj, CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_inv_app_unmop_unmop, CategoryTheory.MorphismProperty.Over.w, CategoryTheory.Adjunction.derivedη_fac_app, CategoryTheory.Square.toArrowArrowFunctor_obj_right_hom, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ₀, AlgebraicGeometry.Scheme.SpecΓIdentity_inv_app, CategoryTheory.CatCenter.localization_zero, CategoryTheory.Square.toArrowArrowFunctor_obj_right_left, CategoryTheory.Abelian.LeftResolution.instEpiKaroubiAppπ, CategoryTheory.Adjunction.rightAdjointUniq_hom_app_counit, CategoryTheory.simplicialCosimplicialEquiv_unitIso_inv_app, reflective, CategoryTheory.Adjunction.derivedη_fac_app_assoc, CategoryTheory.Subobject.lowerEquivalence_unitIso, RightExtension.postcompose₂_map_left_app, CategoryTheory.Equivalence.unit_naturality, CategoryTheory.Sieve.mem_functorPushforward_functor, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_hom_app_app, CategoryTheory.Equivalence.functor_unitIso_comp, CategoryTheory.Over.coprodObj_obj, AlgebraicGeometry.isClosedImmersion_equalizer_ι_left, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₃_app, PresheafOfModules.Derivation'.app_apply, CategoryTheory.RetractArrow.op_r_left, CategoryTheory.Join.mapWhiskerLeft_rightUnitor_hom, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.trans_app_left, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst, CategoryTheory.RepresentablyCoflat.id, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_pullback_obj, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_obj, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_left_right_as, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_right, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_symm_apply_f, CategoryTheory.Subfunctor.equivalenceMonoOver_unitIso, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₄, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app, CategoryTheory.Adjunction.localization_counit_app, mapGrpIdIso_inv_app_hom_hom, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₂, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIso_hom_app_hom, CategoryTheory.instExponentialIdealId, CategoryTheory.Over.prodComparisonIso_pullback_Spec_inv_left_fst_fst', id_obj, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_hom, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_IsMon_Hom, AlgebraicGeometry.Scheme.instLocallyCoverDenseOverTopMorphismPropertyOverForgetOverGrothendieckTopology, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_apply, CategoryTheory.Adjunction.instIsIsoMapAppUnitOfFaithfulOfFull, PushoutObjObj.ι_iso_of_iso_right_inv, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_inv_app_app, CategoryTheory.MonoOver.subobjectMk_le_mk_of_hom, CategoryTheory.Sieve.functorPushforward_functor, ModuleCat.extendScalars_id_comp_assoc, CategoryTheory.Comma.equivProd_unitIso_inv_app_right, CategoryTheory.Over.whiskerLeft_left_snd_assoc, CategoryTheory.NatTrans.IsMonoidal.instHomFunctorLeftUnitor, CategoryTheory.plusPlusAdjunction_unit_app, CategoryTheory.Adjunction.CommShift.compatibilityUnit_right, CategoryTheory.SmallObject.SuccStruct.toSuccArrow_right, CategoryTheory.WithInitial.commaFromUnder_obj_left, CategoryTheory.Limits.IsColimit.pushoutCoconeEquivBinaryCofanFunctor_desc_right, CategoryTheory.WithTerminal.mapId_hom_app, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_inv_app_app, CategoryTheory.Join.mapWhiskerRight_rightUnitor_hom, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left_assoc, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_hom_app_f, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorEquivalence_counitIso, CategoryTheory.CostructuredArrow.grothendieckProj_obj, CategoryTheory.Adjunction.Triple.map_rightToLeft_app, CategoryTheory.isCocontinuous_id, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_comp, CategoryTheory.Over.equivalenceOfIsTerminal_unitIso, HomotopicalAlgebra.CofibrantObject.instIsIsoHoCatAppAdjCounit', CategoryTheory.Square.toArrowArrowFunctor_obj_left_right, CategoryTheory.Adjunction.eq_unit_comp_map_iff, TopologicalSpace.Opens.coe_overEquivalence_inverse_obj_left, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_id, CategoryTheory.Equivalence.core_counitIso_hom_app_iso_inv, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_hom_app_val_app, CategoryTheory.Over.iteratedSliceEquiv_counitIso, constCompEvaluationObj_hom_app, CategoryTheory.SimplicialObject.Truncated.cosk_reflective, CategoryTheory.Adjunction.functorCategory_inverseImage_isomorphisms_unit, CategoryTheory.shiftFunctorAdd_add_zero_hom_app, CategoryTheory.Groupoid.invEquivalence_counitIso, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, CategoryTheory.StructuredArrow.mapIso_unitIso_hom_app_right, CategoryTheory.Equivalence.cancel_counitInv_right_assoc', id_mapMon_mul, Rep.indResAdjunction_unit_app_hom_hom, CategoryTheory.Equivalence.symm_counitIso, RightExtension.postcompose₂_map_right, ModuleCat.extendScalars_id_comp, CategoryTheory.Square.toArrowArrowFunctor'_map_left_left, CategoryTheory.Over.leftUnitor_inv_left_fst_assoc, CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero, HomologicalComplex.Hom.sqTo_right, CommShift.isoZero_inv_app, commAlgCatEquivUnder_inverse_map, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left, CommRingCat.coyonedaUnique_inv_app_hom_apply, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_counitIso_hom_app_f, CategoryTheory.Adjunction.left_triangle, CategoryTheory.Under.forget_obj, CategoryTheory.Sieve.forallYonedaIsSheaf_iff_colimit, PullbackObjObj.mapArrowRight_id, CategoryTheory.WithTerminal.liftFromOver_obj_map, instIsCardinalAccessibleId, LeftExtension.precomp_map_left, CategoryTheory.Equivalence.unit_app_comp_inverse_map_η_functor, CategoryTheory.BasedFunctor.id_toFunctor, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.unitIso_inv, CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_cancel_inv_app, CategoryTheory.Abelian.Pseudoelement.pseudoZero_aux, mapCommpGrp_id_mul, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_right, CategoryTheory.GradedObject.mapBifunctorRightUnitorCofan_inj_assoc, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_hom_app_app_hom, TopCat.Presheaf.presheafEquivOfIso_counitIso_inv_app_app, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_hom_app_left, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_one, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_app_assoc, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_I, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.unitIso_hom_app_f_f, isRightKanExtensionId, CategoryTheory.eq_unitIso, AlgebraicGeometry.ΓSpec.right_triangle, CategoryTheory.Idempotents.KaroubiKaroubi.unitIso_hom_app_f, CategoryTheory.Adjunction.homEquiv_symm_id, CategoryTheory.TwistShiftData.shiftFunctorAdd'_inv_app, HomologicalComplex.Hom.sqFrom_left, CompHausLike.LocallyConstant.instIsIsoFunctorTypeUnitSheafCoherentTopologyAdjunction, CochainComplex.shiftFunctorZero_hom_app_f, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counit_app_tensor_assoc, CategoryTheory.Arrow.hom_inv_id_left, CategoryTheory.WithInitial.coconeEquiv_inverse_map_hom_right, CategoryTheory.Sigma.mapId_hom_app, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₂₄, CategoryTheory.Comonad.counit_naturality_assoc, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, CategoryTheory.Equivalence.core_unitIso_hom_app_iso_hom, SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_hom_app, Quiver.freeGroupoidFunctor_id, CategoryTheory.MonoidalCategory.DayConvolution.instIsLeftKanExtensionProdExternalProductConvolutionExtensionUnitLeftUnit, CategoryTheory.SmallObject.functorMap_π, CategoryTheory.ExponentiableMorphism.coev_naturality_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_left, CategoryTheory.Monad.comparison_map_f, PushoutObjObj.mapArrowLeft_left, CategoryTheory.StructuredArrow.mapNatIso_unitIso_inv_app_right, ranObjObjIsoLimit_hom_π, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_mapPullbackAdj_counit_app, CategoryTheory.WithTerminal.isLimitEquiv_apply_lift_left, CategoryTheory.subterminalsEquivMonoOverTerminal_unitIso, CategoryTheory.Codiscrete.adj_unit_app, CategoryTheory.overToCoalgebra_obj_A, CategoryTheory.Equivalence.rightOp_unitIso_inv_app, ModuleCat.ExtendRestrictScalarsAdj.counit_app, CategoryTheory.Adjunction.Triple.whiskerRight_rightToLeft, commGroupAddCommGroupEquivalence_unitIso, CategoryTheory.ReflQuiv.adj.counit.comp_app_eq, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitNatIso_hom_app, CategoryTheory.MonoidalClosed.whiskerLeft_curry_ihom_ev_app, CompHausLike.LocallyConstant.counit_app_val, CategoryTheory.underToAlgebra_map_f, CategoryTheory.ULift.equivalence_counitIso_inv_app, CategoryTheory.SimplicialObject.Augmented.rightOp_hom_app, CategoryTheory.Over.postEquiv_unitIso, CategoryTheory.Adjunction.homEquiv_apply, CategoryTheory.WithTerminal.pseudofunctor_mapId, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_left, CategoryTheory.SimplicialObject.Augmented.point_obj, CategoryTheory.Limits.ImageFactorisation.ofArrowIso_isImage, CategoryTheory.Equivalence.unit_app_inverse, CategoryTheory.ExponentiableMorphism.pushforwardComp_hom_counit, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackId_hom, CategoryTheory.Iso.isoCompInverse_hom_app, CategoryTheory.Comonad.Coalgebra.counit_assoc, CategoryTheory.Iso.isoInverseOfIsoFunctor_hom_app, CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app, CategoryTheory.Pseudofunctor.IsStackFor.essSurj, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_inv_hom, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.counitIso_inv, CategoryTheory.Idempotents.karoubiUniversal₁_unitIso, CategoryTheory.Comonad.right_counit, CategoryTheory.CatCenter.smul_iso_hom_eq', CategoryTheory.Over.associator_inv_left_fst_snd_assoc, CategoryTheory.CosimplicialObject.Augmented.leftOp_left_obj, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_counit_app, CategoryTheory.SimplicialObject.Augmented.rightOp_left, CategoryTheory.Arrow.inv_hom_id_left, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_inv_right_app, CategoryTheory.Comma.mapRightId_inv_app_right, LeftExtension.postcomp₁_map_left, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₂, CategoryTheory.Adjunction.CoreUnitCounit.left_triangle, CategoryTheory.CechNerveTerminalFrom.hasWidePullback, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_hom_app_hom_hom_hom, CategoryTheory.MonoOver.forget_obj_hom, CategoryTheory.ShiftMkCore.zero_add_hom_app, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_comp, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalence_unitIso, CategoryTheory.Over.rightUnitor_hom_left, AlgebraicGeometry.Scheme.smallGrothendieckTopology_eq_toGrothendieck_smallPretopology, CategoryTheory.MorphismProperty.Over.pullback_map_left, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₁_app, mapCommGrpIdIso_inv_app_hom_hom_hom, whiskeringRightObjIdIso_inv_app_app, inv_fun_map, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₁, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_counitIso_inv, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_assoc, CategoryTheory.RetractArrow.op_i_left, CategoryTheory.ihom.ev_naturality, HomologicalComplex.singleCompEvalIsoSelf_hom_app, Final.coconesEquiv_counitIso, CategoryTheory.OrthogonalReflection.D₁.ι_comp_t, CategoryTheory.SimplicialObject.Truncated.sk_coreflective, CategoryTheory.Limits.HasImageMaps.has_image_map, SSet.Augmented.stdSimplex_map_left, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_assoc, CategoryTheory.toOver_map_left, CategoryTheory.Over.sections_map, toUnder_map_right, CategoryTheory.Adjunction.rightAdjointUniq_hom_app_counit_assoc, CategoryTheory.ChosenPullbacksAlong.fst'_left, HomotopicalAlgebra.CofibrantObject.instWeakEquivalenceHoCatAppAdjUnit, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_zero, CategoryTheory.TwistShiftData.shiftFunctorAdd'_hom_app, Action.FunctorCategoryEquivalence.counitIso_hom_app_app, CategoryTheory.CartesianMonoidalCategory.prodComparisonIso_id, CategoryTheory.MonoOver.commSqOfHasStrongEpiMonoFactorisation, mapArrowFunctor_map_app_right, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_hom_app_app, CategoryTheory.ExponentiableMorphism.coev_naturality, CategoryTheory.Triangulated.TStructure.triangleLTGE_obj_mor₂, TopCat.adj₂_counit, PresheafOfModules.map_id, HomologicalComplex.Hom.sqFrom_right, CommRingCat.coyonedaUnique_hom_app_hom_apply, CategoryTheory.Over.μ_pullback_left_snd, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.Adjunction.Triple.whiskerLeft_leftToRight_assoc, PushoutObjObj.mapArrowLeft_right, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, CategoryTheory.Under.mapPushoutAdj_counit_app, CategoryTheory.Over.iteratedSliceBackward_obj, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right, CategoryTheory.Comonad.beckEqualizer_lift, CategoryTheory.Comonad.id_ε_app, CategoryTheory.PreGaloisCategory.autEmbedding_range, CategoryTheory.subterminalsEquivMonoOverTerminal_counitIso, AlgebraicGeometry.Scheme.Modules.pseudofunctor_left_unitality, CategoryTheory.Adjunction.Triple.map_adj₂_counit_app_leftToRight_app, CategoryTheory.Adjunction.Triple.map_rightToLeft_app_assoc, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_hom_app_app, CategoryTheory.SmallObject.transfiniteCompositionOfShapeSuccStructPropιIteration_F, CategoryTheory.evaluationAdjunctionRight_unit_app, CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse_map_left, CategoryTheory.Adjunction.unit_app_tensor_comp_map_δ, CategoryTheory.ChosenPullbacksAlong.Over.toUnit_left, CategoryTheory.WithTerminal.coneEquiv_unitIso_inv_app_hom_left, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_π, CategoryTheory.Over.map_obj_left, CategoryTheory.Over.epi_left_of_epi, mapMatId_hom_app, CategoryTheory.counit_obj_eq_map_counit, AlgebraicGeometry.instIsLocallyDirectedCompSchemeOverOverTopMorphismPropertyForgetForgetForget, CategoryTheory.Square.arrowArrowEquivalence'_unitIso, CategoryTheory.SimplicialObject.Augmented.toArrow_obj_hom, CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj_hom_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_left, CategoryTheory.WithTerminal.equivComma_functor_map_left_app, CategoryTheory.Adjunction.whiskerLeftRUnitIsoOfIsIsoCounit_hom_app, CategoryTheory.ExponentiableMorphism.unit_pushforwardId_hom, CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app_assoc, CategoryTheory.MonoidalCategory.endofunctorMonoidalCategory.evaluationRightAction_actionAssocIso, CategoryTheory.Arrow.epi_right, CategoryTheory.Sieve.overEquiv_symm_top, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_fst, OplaxMonoidal.id_η, CategoryTheory.CosimplicialObject.Augmented.whiskering_map_app_right, CategoryTheory.Adjunction.functorCategory_inverseImage_isomorphisms_counit, CategoryTheory.Equivalence.counitInv_naturality, CategoryTheory.MonoidalCategory.DayConvolutionUnit.corepresentableByLeft_homEquiv, CategoryTheory.RetractArrow.map_i_right, CategoryTheory.Monad.monadMonEquiv_counitIso_inv_app_hom, CategoryTheory.Limits.FormalCoproduct.evalCompInclIsoId_inv_app_app, SSet.Truncated.HomotopyCategory.BinaryProduct.associativity, PushoutObjObj.mapArrowLeft_comp_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_right, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_inv_app_hom_app, CategoryTheory.CategoryOfElements.structuredArrowEquivalence_unitIso, CategoryTheory.ForgetEnrichment.equiv_counitIso, CategoryTheory.Equivalence.unit_inverse_comp, CommRingCat.Under.equalizerFork_ι, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst, CategoryTheory.sheafificationAdjunction_counit_app_val, CategoryTheory.Adjunction.right_triangle_components, CategoryTheory.WithInitial.coconeEquiv_counitIso_hom_app_hom, CategoryTheory.ihom.ev_naturality_assoc, CategoryTheory.TransportEnrichment.forgetEnrichmentEquiv_unitIso, 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.postAdjunctionLeft_counit_app, CategoryTheory.Under.inv_right_hom_right, CategoryTheory.Limits.Cones.equivalenceOfReindexing_unitIso, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₃, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isColimit, commShiftIso_id_inv_app, rightOpId_hom_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_inv_app_hom_hom_app, CategoryTheory.Adjunction.whiskerLeft_unit_app_app, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_hom_app_hom, CategoryTheory.instHomIsOverLeftDiscretePUnit, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_left, CategoryTheory.Over.braiding_hom_left, CategoryTheory.MonoOver.instMonoHomDiscretePUnitObjOverForget, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_assoc, CategoryTheory.RetractArrow.instIsSplitMonoRightIArrow, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_obj_hom, CategoryTheory.WithInitial.liftFromUnder_map_app, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIdIso_inv_app_hom, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_counit_app, CategoryTheory.MorphismProperty.Over.pullback_obj_hom, CategoryTheory.Sigma.mapId_inv_app, CategoryTheory.Adjunction.isIso_unit_app_of_iso, CategoryTheory.Iso.inverseCompIso_inv_app, LeibnizAdjunction.adj_unit_app_right, CategoryTheory.pullbackShiftFunctorZero'_inv_app, leftExtensionEquivalenceOfIso₁_unitIso_hom_app_right_app, CategoryTheory.Idempotents.KaroubiKaroubi.counitIso_hom_app_f_f, CategoryTheory.ObjectProperty.isLocal_adj_unit_app, TopCat.Presheaf.presheafEquivOfIso_counitIso_hom_app_app, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_snd, Rep.resIndAdjunction_unit_app, SSet.Truncated.HomotopyCategory.BinaryProduct.right_unitality, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd, SheafOfModules.pushforward_comp_id, CategoryTheory.overToCoalgebra_obj_a, SSet.Truncated.cosk_reflective, CategoryTheory.MorphismProperty.Over.mapComp_inv_app_left, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_obj_right_as, CategoryTheory.FunctorToTypes.mem_fromOverSubfunctor_iff, ModuleCat.extendScalars_comp_id_assoc, CategoryTheory.SimplicialObject.id_right, CategoryTheory.shiftFunctorComm_hom_app_of_add_eq_zero, CategoryTheory.Over.μ_pullback_left_fst_fst, CategoryTheory.MonoidalClosed.compTranspose_eq, CategoryTheory.Iso.isoFunctorOfIsoInverse_hom_app, CategoryTheory.SimplicialObject.instIsLeftKanExtensionOppositeTruncatedSimplexCategoryObjSkAppTruncatedUnitSkAdjTruncation, CategoryTheory.Under.hom_right_inv_right_assoc, CategoryTheory.ShiftedHom.opEquiv_symm_apply, AddMonCat.equivalence_unitIso, CategoryTheory.Over.starPullbackIsoStar_inv_app_left, CategoryTheory.Join.mapWhiskerLeft_whiskerLeft_assoc, CategoryTheory.Limits.coconeEquivalenceOpConeOp_counitIso, CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero_assoc, CategoryTheory.Over.iteratedSliceForward_map, HomologicalComplex₂.flipEquivalenceCounitIso_inv_app_f_f, mapTriangleIdIso_inv_app_hom₁, CategoryTheory.simplicialToCosimplicialAugmented_map_right, CategoryTheory.GrothendieckTopology.overMapPullback_id_comp_assoc, CategoryTheory.coyonedaPairing_map, CategoryTheory.Adjunction.homEquiv_counit, CategoryTheory.MorphismProperty.underObj_iff, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_hom_app, CategoryTheory.MonoOver.inf_obj, CategoryTheory.Equivalence.unit_app_comp_inverse_map_η_functor_assoc, AlgebraicGeometry.Scheme.Cover.pullbackCoverOver'_f, CategoryTheory.Pseudofunctor.CoGrothendieck.map_id_eq, HomologicalComplex.Hom.sqTo_left, Rep.ihom_coev_app_hom, CategoryTheory.CosimplicialObject.Augmented.leftOp_hom_app, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₁, CategoryTheory.WithInitial.mkCommaObject_left, CategoryTheory.SmallObject.ιFunctorObj_naturality_assoc, CategoryTheory.Adjunction.id_unit, CategoryTheory.Prod.symmetry_inv_app, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_left, CategoryTheory.Adjunction.counit_naturality_assoc, CategoryTheory.Equivalence.leftOp_counitIso_hom_app, CategoryTheory.MorphismProperty.Under.w_assoc, CategoryTheory.Arrow.square_to_iso_invert, CategoryTheory.constantSheafAdj_counit_w, CategoryTheory.MonoOver.top_left, CategoryTheory.Over.tensorUnit_left, CategoryTheory.Core.inclusion_comp_functorToCore, CategoryTheory.Comma.toPUnitIdEquiv_counitIso_inv_app, CategoryTheory.MorphismProperty.instFullCostructuredArrowTopOverToOver, CategoryTheory.MonoidalCategory.leftUnitorNatIso_inv_app, closedCounit_app_app, CategoryTheory.toOverIteratedSliceForwardIsoPullback_inv_app_left, CategoryTheory.Over.hom_left_inv_left_assoc, CategoryTheory.Join.mapWhiskerRight_whiskerRight_assoc, CategoryTheory.Arrow.mk_left, CategoryTheory.Limits.Cone.toStructuredArrow_comp_proj, CompHausLike.LocallyConstant.unit_app, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counit_app_tensor, CategoryTheory.Adjunction.Triple.leftToRight_app, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIdIso_hom_app_hom, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_right_app, CategoryTheory.Equivalence.mapCommGrp_counitIso, Action.resId_hom_app_hom, PullbackObjObj.mapArrowRight_left, CategoryTheory.Join.mapWhiskerLeft_leftUnitor_hom, AlgebraicGeometry.Scheme.mem_smallGrothendieckTopology, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_unitIso_inv_app_f_f, AlgebraicGeometry.Scheme.Modules.pseudofunctor_left_unitality_assoc, CategoryTheory.ChosenPullbacksAlong.iso_pullback_map, CategoryTheory.Comonad.Coalgebra.counit, CategoryTheory.conjugateEquiv_adjunction_id_symm, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_symm_apply, CategoryTheory.Monad.right_unit, CategoryTheory.RepresentablyFlat.id, CategoryTheory.Limits.image_map_comp_imageSubobjectIso_inv, CategoryTheory.Under.opEquivOpOver_inverse_obj, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_app, CategoryTheory.Equivalence.core_counitIso_inv_app_iso_hom, LightCondSet.isDiscrete_tfae, Types.monoOverEquivalenceSet_unitIso, ranObjObjIsoLimit_inv_π, CategoryTheory.CostructuredArrow.ofCommaFstEquivalence_unitIso, CategoryTheory.Iso.inverseCompIso_hom_app, CategoryTheory.Under.UnderMorphism.ext_iff, CategoryTheory.Equivalence.congrLeft_counitIso_hom_app, CategoryTheory.Adjunction.right_triangle, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.inverse_obj, CategoryTheory.Limits.Cocone.toCostructuredArrowCompProj_inv_app, CategoryTheory.Over.iteratedSliceEquiv_inverse, CategoryTheory.Square.toArrowArrowFunctor'_map_right_right, CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument.preservesColimit, CategoryTheory.Over.coe_hom, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_obj_obj_left, CategoryTheory.ShiftedHom.id_map, CategoryTheory.WithTerminal.mapId_inv_app, CategoryTheory.RetractArrow.unop_i_left, CategoryTheory.MorphismProperty.instHasPullbackSndHomDiscretePUnitOfHasPullbacksAlongOfIsStableUnderBaseChangeAlong, AlgebraicTopology.DoldKan.Compatibility.τ₀_hom_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_right_map, mapTriangleIdIso_inv_app_hom₂, CategoryTheory.ExponentiableMorphism.unit_pushforwardId_hom_assoc, CategoryTheory.cosimplicialToSimplicialAugmented_map, AlgebraicGeometry.Scheme.kerFunctor_obj, PresheafOfModules.freeAdjunction_unit_app, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst_assoc, CategoryTheory.ExponentiableMorphism.ev_naturality, CategoryTheory.Over.forgetCocone_ι_app, CategoryTheory.SmallObject.functor_obj, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_left, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₂, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_right, CategoryTheory.Arrow.homMk'_right, CategoryTheory.Monoidal.whiskerLeft, CategoryTheory.Arrow.leftFunc_map, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τl, CategoryTheory.Adjunction.map_restrictFullyFaithful_unit_app, CategoryTheory.Adjunction.CommShift.commShift_unit, partialFunEquivPointed_counitIso_hom_app_toFun, SheafOfModules.conjugateEquiv_pullbackId_hom, CategoryTheory.coalgebraEquivOver_unitIso, CategoryTheory.Under.costar_map_left, CategoryTheory.Limits.Cone.equivCostructuredArrow_unitIso, CategoryTheory.Monad.unit_naturality_assoc, CategoryTheory.Limits.Cocones.functorialityEquivalence_inverse, CategoryTheory.Triangulated.TStructure.triangleLTGE_map_hom₁, CategoryTheory.Over.whiskerRight_left_fst_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_left_map, CategoryTheory.WithTerminal.equivComma_inverse_map_app, CategoryTheory.Idempotents.KaroubiKaroubi.unitIso_inv_app_f, CategoryTheory.Sum.functorEquiv_unit_app_app_inl, CategoryTheory.MonoidalOpposite.unmopEquiv_counitIso_inv_app, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d_1_0, PullbackObjObj.mapArrowLeft_right, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_unitIso, TopCat.adj₂_unit, CategoryTheory.Over.tensorHom_left_snd, CategoryTheory.WithInitial.ofCommaObject_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_rightUnitor, CategoryTheory.Abelian.DoldKan.comparisonN_hom_app_f, CategoryTheory.Limits.Cone.overPost_π_app, CategoryTheory.Under.opEquivOpOver_counitIso, CategoryTheory.StructuredArrow.toUnder_map_left, CategoryTheory.Cat.id_eq_id, CategoryTheory.WithTerminal.equivComma_inverse_obj_map, SSet.Truncated.HomotopyCategory.BinaryProduct.associativityIso_hom_app, CategoryTheory.Adjunction.Triple.mono_leftToRight_app_iff_mono_adj₂_unit_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_inv_app_app, CategoryTheory.Adjunction.Triple.epi_rightToLeft_app_iff_epi_map_adj₂_counit_app, CategoryTheory.conjugateEquiv_adjunction_id, CategoryTheory.Limits.limit.id_pre, CategoryTheory.SimplicialObject.Augmented.drop_map, mapArrowFunctor_map_app_left, CategoryTheory.Pretriangulated.exists_iso_of_arrow_iso, CategoryTheory.Comma.toIdPUnitEquiv_counitIso_inv_app, CategoryTheory.StructuredArrow.preEquivalence_counitIso, CategoryTheory.MonoidalCategory.DayFunctor.equiv_unitIso_inv_app, RightExtension.postcomp₁_obj_hom_app, map_opShiftFunctorEquivalence_counitIso_inv_app_unop, ModuleCat.extendScalars_comp_id, CategoryTheory.functorProdFunctorEquivUnitIso_inv_app, CategoryTheory.SmallObject.ιObj_naturality_assoc, CategoryTheory.Over.forget_map, CategoryTheory.Subobject.representative_coe, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₂, CategoryTheory.WithInitial.liftFromUnder_obj_map, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₂, CategoryTheory.RetractArrow.unop_i_right, CategoryTheory.Limits.ImageMap.map_ι_assoc, CategoryTheory.Square.toArrowArrowFunctor'_obj_hom_right, CategoryTheory.Arrow.inv_right, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv_assoc, instIsIsoAppLanUnit_1, CategoryTheory.CatCenter.localization_mul, CategoryTheory.Square.toArrowArrowFunctor_map_left_right, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransId_hom_app_f, CategoryTheory.WithTerminal.liftFromOver_map_app, CategoryTheory.MonoidalClosed.coev_app_comp_pre_app_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_map_right_app, sheafPushforwardContinuousId_inv_app_val_app, CategoryTheory.ChosenPullbacksAlong.unit_pullbackComp_hom, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app_assoc, CategoryTheory.coyonedaPairingExt_iff, CategoryTheory.Sieve.overEquiv_generate, groupHomology.d₁₀ArrowIso_hom_right, CategoryTheory.WithTerminal.coneEquiv_inverse_map_hom_left, CategoryTheory.RelCat.opFunctor_comp_unopFunctor_eq, map_opShiftFunctorEquivalence_unitIso_inv_app_unop_assoc, CategoryTheory.Arrow.left_hom_inv_right, CategoryTheory.Equivalence.unop_unitIso, CategoryTheory.OppositeShift.adjunction_counit, CategoryTheory.Square.toArrowArrowFunctor_map_right_left, CategoryTheory.shiftFunctorCompIsoId_zero_zero_hom_app, CategoryTheory.Arrow.hom_inv_id_right, CategoryTheory.Subobject.inf_eq_map_pullback, CategoryTheory.Over.postMap_app, TopCat.adj₁_unit, CategoryTheory.Square.toArrowArrowFunctor'_obj_left_left, PresheafOfModules.DifferentialsConstruction.instHasDifferentials, PushoutObjObj.mapArrowRight_comp, CategoryTheory.Under.mkIdInitial_to_right, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitNatIso_inv_app, CategoryTheory.Limits.walkingSpanOpEquiv_unitIso_hom_app, CategoryTheory.RetractArrow.left_i, rightUnitor_inv_app, CategoryTheory.Comonad.ComonadicityInternal.main_pair_F_cosplit, leftUnitor_hom_app, CategoryTheory.Over.ConstructProducts.conesEquivInverseObj_π_app, CategoryTheory.Adjunction.right_triangle_components_assoc, CategoryTheory.Arrow.inv_hom_id_right_assoc, CategoryTheory.Equivalence.refl_unitIso, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom, ModuleCat.extendRestrictScalarsAdj_unit_app_apply, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_hom_app, CategoryTheory.Equivalence.symmEquivInverse_obj_unitIso_inv, CategoryTheory.Adjunction.comp_unit, CategoryTheory.ExponentiableMorphism.unit_pushforwardComp_hom, TopologicalSpace.Opens.overEquivalence_inverse_obj_right_as, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₁, TopCat.adj₁_counit, CategoryTheory.RetractArrow.instIsSplitEpiLeftRArrow, ranCounit_app_whiskerLeft_ranAdjunction_unit_app, CategoryTheory.Monad.MonadicityInternal.main_pair_G_split, alexDiscEquivPreord_counitIso, CategoryTheory.Under.costar_obj_hom, CategoryTheory.Pseudofunctor.ObjectProperty.fullsubcategory_mapId, CategoryTheory.Adjunction.unit_app_unit_comp_map_η_assoc, CategoryTheory.Presheaf.isLimit_iff_isSheafFor, CategoryTheory.CatCenter.instIsMulCommutative, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst_assoc, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_left_as, Rep.coinvariantsAdjunction_unit_app_hom, CategoryTheory.Adjunction.leftAdjointCompIso_hom_app, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₂, CategoryTheory.Comonad.instHasEqualizerMapAAppUnitObjAOfHasEqualizerOfIsCosplitPair, CategoryTheory.Over.lift_left, CategoryTheory.Monad.MonadicityInternal.counitCofork_pt, TopologicalSpace.Opens.mapMapIso_counitIso, CategoryTheory.Abelian.LeftResolution.π_naturality, CategoryTheory.Under.postAdjunctionRight_counit_app_right, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_counitIso, CategoryTheory.unitCompPartialBijectiveAux_symm_apply, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.counitIso_hom, CategoryTheory.Pseudofunctor.DescentData.pullFunctorEquivalence_counitIso, mapCommMonIdIso_inv_app_hom_hom, AlgebraicGeometry.Scheme.restrictFunctor_obj_left, CategoryTheory.MonoOver.congr_counitIso, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.unitIso_hom, CategoryTheory.Arrow.w_assoc, CategoryTheory.Equivalence.op_unitIso, CategoryTheory.Groupoid.invEquivalence_unitIso, essentiallySmall_of_le, CategoryTheory.SmallObject.functorialFactorizationData_p_app, CategoryTheory.Adjunction.whiskerRight_counit_app_app, CategoryTheory.Over.opEquivOpUnder_functor_map, CategoryTheory.TwistShiftData.commShift, CategoryTheory.CatCommSq.hInv_iso_hom_app, CategoryTheory.CartesianMonoidalCategory.preservesTerminalIso_id, CategoryTheory.SimplicialObject.isCoskeletal_iff_isIso, CommRingCat.moduleCatExtendScalarsPseudofunctor_mapId, CategoryTheory.Monad.MonadicityInternal.counitCofork_ι_app, CategoryTheory.Adjunction.Triple.rightToLeft_app_adj₂_unit_app, PresheafOfModules.toPresheaf_map_sheafificationAdjunction_unit_app, PushoutObjObj.mapArrowRight_right, CategoryTheory.ShortComplex.opEquiv_unitIso, MonObj.mopEquiv_unitIso_inv_app_hom, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₃, CochainComplex.shiftShortComplexFunctorIso_zero_add_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv_assoc, SheafOfModules.pushforward_id_comp, CategoryTheory.Core.functorToCore_inclusion, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_inv_app_hom_hom, CategoryTheory.Abelian.LeftResolution.karoubi.π'_app_f, CategoryTheory.Monad.MonadicityInternal.main_pair_reflexive, CategoryTheory.MonoidalCategory.rightUnitorNatIso_inv_app, CategoryTheory.OverPresheafAux.costructuredArrowPresheafToOver_obj, CategoryTheory.CatCenter.localization_one, AlgebraicGeometry.instMonoObjWalkingSpanCompOverSchemeTopMorphismPropertySpanOverForgetForgetForgetNoneWalkingPairSomeMapInitOfIsOpenImmersionLeftDiscretePUnit, CategoryTheory.Adjunction.IsMonoidal.instIsMonoidalCounit, HomotopicalAlgebra.CofibrantObject.instWeakEquivalenceHoCatAppUnitHoCatAdj, CategoryTheory.MonoidalClosed.ofEquiv_curry_def, CategoryTheory.StructuredArrow.prodEquivalence_counitIso, CategoryTheory.Limits.multispanIndexCoend_fst, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_pullback_map, CategoryTheory.Equivalence.changeInverse_unitIso_hom_app, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso_hom_app_f, CategoryTheory.Adjunction.homEquiv_symm_rightAdjointUniq_hom_app, CategoryTheory.unitOfTensorIsoUnit_hom_app, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_counitIso_inv, Bipointed.swapEquiv_unitIso_hom_app_toFun, CategoryTheory.Adjunction.commShiftIso_inv_app_counit_app, CategoryTheory.Monad.monadMonEquiv_unitIso_hom_app_toNatTrans_app, AlgebraicGeometry.Scheme.restrictFunctor_map_left, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d_1_0_assoc, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompYoneda, TopCat.Presheaf.generateEquivalenceOpensLe_functor'_map, CategoryTheory.Comonad.instReflectsLimitWalkingParallelPairParallelPairMapAAppUnitObjAOfReflectsLimitOfIsCosplitPair, mapMatId_inv_app, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_hom_app, CategoryTheory.CostructuredArrow.initial_map₂_id, coreflective', CategoryTheory.Adjunction.Triple.leftToRight_app_obj_assoc, CategoryTheory.Equivalence.congrRight_unitIso_hom_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_hom_app_hom, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_hom_app_one, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, CategoryTheory.sheafification_reflective, AlgebraicGeometry.instIsIsoFunctorModuleCatCarrierUnitModulesSpecOfAdjunction, CategoryTheory.idCoverPreserving, CategoryTheory.Limits.walkingSpanOpEquiv_counitIso_inv_app, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.functor_map, OrderHom.equivalenceFunctor_unitIso_inv_app, HomotopicalAlgebra.weakEquivalences_over_iff, CategoryTheory.Under.opEquivOpOver_unitIso, CategoryTheory.Grpd.freeForgetAdjunction_unit_app, CategoryTheory.SingleFunctors.shiftIso_zero_hom_app, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_hom_app_app, CategoryTheory.equivEssImageOfReflective_counitIso, CategoryTheory.Under.inv_right_hom_right_assoc, CategoryTheory.Adjunction.leftAdjointIdIso_inv_app, map_shiftFunctorCompIsoId_inv_app, CategoryTheory.Equivalence.ε_comp_map_ε_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_η_unmop_app, CategoryTheory.Equivalence.core_unitIso_inv_app_iso_hom, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_obj, CategoryTheory.Over.mkIdTerminal_from_left, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_unitIso, CategoryTheory.ChosenPullbacksAlong.Over.fst_eq_fst', CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_hom_app_app_fst, AlgebraicTopology.DoldKan.identity_N₂_objectwise, CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan_inj_assoc, SSet.Truncated.HomotopyCategory.BinaryProduct.id_prod_mapHomotopyCategory_comp_inverse, CategoryTheory.WithTerminal.coneEquiv_functor_obj_pt, CategoryTheory.Under.opEquivOpOver_functor_map, mapCommMon_id_one, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_ε_unmop_app, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_inv_app_val_app, CategoryTheory.Square.toArrowArrowFunctor'_obj_hom_left, CategoryTheory.Square.arrowArrowEquivalence_unitIso, ContinuousCohomology.MultiInd.d_succ, ModuleCat.extendScalarsId_inv_app_apply, CategoryTheory.Adjunction.comp_counit_app_assoc, CategoryTheory.Adjunction.whiskerRight_unit_iso_of_R_fully_faithful, IsDenseSubsite.isIso_ranCounit_app_of_isDenseSubsite, CategoryTheory.Equivalence.trans_unitIso, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_unitIso_inv_app_f_f, CategoryTheory.Comonad.left_counit_assoc, CategoryTheory.Under.postEquiv_unitIso, CategoryTheory.Grothendieck.pre_id, CategoryTheory.constantPresheafAdj_counit_app_app, CategoryTheory.Equivalence.sheafCongr.unitIso_inv_app_val_app, CategoryTheory.ObjectProperty.topEquivalence_inverse, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_hom_app_fst_app, essImage_overPost, CategoryTheory.WithTerminal.commaFromOver_obj_left, TopologicalSpace.Opens.overEquivalence_counitIso_hom_app, CategoryTheory.ComposableArrows.opEquivalence_counitIso_hom_app_app, CategoryTheory.Over.fst_left, CategoryTheory.Over.prodLeftIsoPullback_hom_fst, CategoryTheory.Comonad.ComonadicityInternal.counitFork_pt, CategoryTheory.Arrow.hom_ext_iff, CategoryTheory.Over.associator_hom_left_fst_assoc, CategoryTheory.ExponentiableMorphism.pushforwardId_hom_counit, CategoryTheory.TwoSquare.lanBaseChange_app, CategoryTheory.Linear.toCatCenter_apply_app, AlgebraicGeometry.Scheme.ofRestrict_app, CategoryTheory.CatCommSq.vId_iso_inv_app, CategoryTheory.Comma.equivProd_unitIso_inv_app_left, CategoryTheory.Limits.pullbackConeEquivBinaryFan_unitIso, CategoryTheory.ShrinkHoms.equivalence_unitIso, CategoryTheory.Adjunction.left_triangle_components_assoc, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_symm_apply, CategoryTheory.SmallObject.preservesColimit, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_one, CategoryTheory.CatCenter.app_neg, CategoryTheory.Over.isMonHom_pullbackFst_id_right, CategoryTheory.Over.pullback_obj_hom, CategoryTheory.Over.forgetAdjStar_unit_app_left, map_opShiftFunctorEquivalence_counitIso_hom_app_unop_assoc, shiftIso_hom_app_comp_shiftMap_of_add_eq_zero, CategoryTheory.mateEquiv_counit, CategoryTheory.Precoverage.comap_id, CategoryTheory.CatCenter.smul_iso_hom_eq, HomotopicalAlgebra.instWeakEquivalenceLeftDiscretePUnitOfOver, CategoryTheory.Pseudofunctor.isPrestackFor_iff_isSheafFor', CategoryTheory.Adjunction.whiskerLeftRUnitIsoOfIsIsoCounit_inv_app, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app, ranCompLimIso_hom_app, CategoryTheory.constantSheafAdj_counit_app, leibnizPullback_map_app, CategoryTheory.GradedObject.ι_mapBifunctorRightUnitor_hom_apply_assoc, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₂_app, CategoryTheory.CommShift₂Setup.z_zero₂, CategoryTheory.CommShift₂Setup.int_ε, CategoryTheory.Equivalence.funInvIdAssoc_inv_app, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_inv_app_f, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_app_assoc, CategoryTheory.Adjunction.map_η_comp_η, CategoryTheory.Adjunction.op_counit, SheafOfModules.instIsRightAdjointPushforwardIdSheafRingCat, CategoryTheory.GrothendieckTopology.overMapPullback_id_comp, unopId_hom_app, CategoryTheory.Over.tensorObj_left, HomologicalComplex₂.flipEquivalenceCounitIso_hom_app_f_f, commShift₂_comm_assoc, CategoryTheory.RetractArrow.i_w_assoc, CategoryTheory.prod.functorProdToProdFunctorAssociator_inv_app, CategoryTheory.instIsReflexivePairMapAppCounitObj, CategoryTheory.RetractArrow.unop_r_left, Types.monoOverEquivalenceSet_counitIso, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_hom_app_snd_app, CategoryTheory.Limits.walkingCospanOpEquiv_unitIso_hom_app, FullyFaithful.hasShift.map_zero_inv_app, CategoryTheory.instIsCocontinuousOverLeftDiscretePUnitIteratedSliceForwardOver, CategoryTheory.Adjunction.leftAdjointIdIso_hom_app, CategoryTheory.Pseudofunctor.DescentData.pullFunctorEquivalence_unitIso, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₂, ShiftSequence.shiftIso_zero, CategoryTheory.Adjunction.instIsIsoMapAppCounitOfFaithfulOfFull, PushoutObjObj.mapArrowLeft_comp, CategoryTheory.Abelian.app_hom, commBialgCatEquivComonCommAlgCat_counitIso_hom_app, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_left_left, CategoryTheory.MorphismProperty.map_id_eq_isoClosure, CategoryTheory.SmallObject.hasColimitsOfShape_discrete, leftExtensionEquivalenceOfIso₁_counitIso_hom_app_right_app, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right_assoc, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_snd', CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_right, CategoryTheory.toOverUnitPullback_hom_app_left, sheafPushforwardContinuousId'_hom_app_val_app, CategoryTheory.Monad.left_unit_assoc, CategoryTheory.ExponentiableMorphism.coev_ev, AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_inv_app, CategoryTheory.Comonad.adj_unit, CategoryTheory.Adjunction.map_ε_comp_counit_app_unit, CategoryTheory.SmallObject.πObj_naturality, CategoryTheory.Under.id_right, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₂, PullbackObjObj.π_iso_of_iso_left_hom, CategoryTheory.Sum.functorEquiv_unitIso, CategoryTheory.Arrow.hom.congr_left, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_val_app, CategoryTheory.Equivalence.op_counitIso, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₃, CategoryTheory.WithInitial.opEquiv_unitIso_hom_app, CategoryTheory.instIsDenseSubsiteOverLeftDiscretePUnitOverInverseIteratedSliceEquiv, CategoryTheory.Over.ε_pullback_left, CategoryTheory.ChosenPullbacksAlong.pullbackComp_hom_counit_assoc, CategoryTheory.Limits.FormalCoproduct.evalCompInclIsoId_hom_app_app, id_mapMon_one, CategoryTheory.Sheaf.isConstant_iff_isIso_counit_app, groupHomology.d₁₀ArrowIso_inv_left, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_rightUnitor, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_map, CategoryTheory.Over.coprod_map_app, CategoryTheory.Adjunction.homEquiv_leftAdjointUniq_hom_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_hom_app_hom_hom, CategoryTheory.ShiftMkCore.zero_add_inv_app, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.functor_obj, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_unitIso_hom_app_f_f, CategoryTheory.Adjunction.whiskerRight_unit_app_app, ranAdjunction_unit_app, CategoryTheory.Arrow.equivSigma_apply_snd_fst, CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor, CategoryTheory.WithInitial.ofCommaMorphism_app, CategoryTheory.Monad.Algebra.unit, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_eq, CategoryTheory.Cat.Hom.id_toFunctor, CategoryTheory.Limits.Cocone.equivStructuredArrow_counitIso, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app_assoc, CategoryTheory.MonoidalOpposite.mopMopEquivalence_counitIso_hom_app, CategoryTheory.TwistShiftData.shiftFunctorZero_inv_app, CategoryTheory.Equivalence.core_unitIso_inv_app_iso_inv, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd_assoc, lanAdjunction_counit_app, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst_assoc, CategoryTheory.MonoidalCategory.rightUnitorNatIso_hom_app, CategoryTheory.Adjunction.unit_comp_map_eq_iff, CategoryTheory.CosimplicialObject.Augmented.const_obj_left, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_map, PushoutObjObj.ι_iso_of_iso_left_hom, isIso_lanAdjunction_counit_app_iff, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_val_app, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk_assoc, CategoryTheory.Adjunction.isIso_counit_app_iff_mem_essImage, CategoryTheory.shiftFunctorCompIsoId_zero_zero_inv_app, CategoryTheory.WithTerminal.equivComma_unitIso_hom_app_app, PresheafOfModules.pushforward_id_comp, CategoryTheory.prod.prodFunctorToFunctorProdAssociator_hom_app_app, CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse_assoc, CategoryTheory.Adjunction.shift_unit_app_assoc, CategoryTheory.SmallObject.instIsIsoRightAppArrowιIteration, CategoryTheory.Equivalence.counitInv_naturality_assoc, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_inv_app, AlgebraicGeometry.Scheme.mem_toGrothendieck_smallPretopology, CategoryTheory.Arrow.comp_right, ContinuousCohomology.const_app_hom, CategoryTheory.Square.toArrowArrowFunctor'_obj_right_left, mapTriangleIdIso_hom_app_hom₁, CategoryTheory.RetractArrow.instIsSplitMonoLeftIArrow, HomotopicalAlgebra.CofibrantObject.HoCat.adjCounit'_app, CategoryTheory.MorphismProperty.Over.mapId_hom_app_left, coreflective, CategoryTheory.Under.postAdjunctionLeft_unit_app, CategoryTheory.Adjunction.unop_unit, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_hom_app_hom_app, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_app, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₂₄, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_inv_app, mapTriangleIdIso_hom_app_hom₂, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop, CategoryTheory.WithTerminal.opEquiv_unitIso_inv_app, AlgebraicGeometry.Scheme.restrictFunctor_obj_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom, CategoryTheory.CosimplicialObject.comp_left, CategoryTheory.Adjunction.commShiftIso_hom_app_counit_app_shift, CategoryTheory.MorphismProperty.Over.pullbackComp_left_fst_fst, CategoryTheory.Limits.coneOfAdj_π, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app, CategoryTheory.StructuredArrow.toUnder_obj_right, CategoryTheory.Limits.kernelSubobjectMap_arrow, CategoryTheory.Over.associator_hom_left_snd_snd, CategoryTheory.Over.associator_inv_left_snd_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_map, CategoryTheory.Over.coprodObj_map, CategoryTheory.MorphismProperty.arrow_iso_iff, leibnizPullback_obj_obj, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_left_right, ModuleCat.homEquiv_extendScalarsId, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_hom_app_snd_app, CategoryTheory.toOverUnitPullback_inv_app_left, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app_assoc, CategoryTheory.nerveAdjunction.isIso_counit, CategoryTheory.Equivalence.counit_app_functor, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_apply, OrderIso.equivalence_unitIso, CategoryTheory.Equivalence.CommShift.instCommShiftHomFunctorUnitIso, CategoryTheory.CommShift₂Setup.z_zero₁, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_assoc, CategoryTheory.piEquivalenceFunctorDiscrete_counitIso, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst, CategoryTheory.Under.w_assoc, CategoryTheory.Limits.image.factor_map, CategoryTheory.Comma.mapLeftId_inv_app_right, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_inv_app_op_one, CategoryTheory.Equivalence.sheafCongr.counitIso_inv_app_val_app, CategoryTheory.Arrow.hom_inv_id_left_assoc, CategoryTheory.Sieve.functorPushforward_equivalence_eq_pullback, CategoryTheory.Arrow.homMk'_left, CategoryTheory.GradedObject.ι_mapBifunctorLeftUnitor_hom_apply_assoc, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd_assoc, CategoryTheory.Square.toArrowArrowFunctor'_obj_right_hom, CategoryTheory.Adjunction.Localization.η_app, sheafAdjunctionCocontinuous_unit_app_val, CategoryTheory.StructuredArrow.mapNatIso_counitIso_inv_app_right, map_opShiftFunctorEquivalence_unitIso_hom_app_unop, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_zero, CategoryTheory.Equivalence.pi_counitIso, CategoryTheory.WithInitial.coconeEquiv_unitIso_inv_app_hom_right, CategoryTheory.MorphismProperty.homFamily_apply, CategoryTheory.CosimplicialObject.Augmented.point_obj, CategoryTheory.Equivalence.symmEquivInverse_obj_unitIso_hom, CategoryTheory.Under.opEquivOpOver_inverse_map, lanUnit_app_app_lanAdjunction_counit_app_app_assoc, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.counitIso_hom, CategoryTheory.CommShift₂Setup.hε, CategoryTheory.Limits.FormalCoproduct.evalOpCompInlIsoId_inv_app_app, CategoryTheory.Abelian.DoldKan.comparisonN_inv_app_f, HomologicalComplex.homologyFunctorSingleIso_hom_app, CategoryTheory.Adjunction.homEquiv_id, instIsIsoAppRanCounit_1, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_hom_app, CategoryTheory.Equivalence.adjointify_η_ε, AlgebraicGeometry.instHasFiniteCoproductsOverSchemeTopMorphismProperty, CategoryTheory.Under.forgetCone_π_app, CategoryTheory.Equivalence.inverse_counitInv_comp, CategoryTheory.Over.iteratedSliceForward_obj, FullyFaithful.hasShift.map_zero_hom_app, essImage.of_overPost, CategoryTheory.Adjunction.left_triangle_components, CategoryTheory.Equivalence.core_counitIso_inv_app_iso_inv, CategoryTheory.Equivalence.unit_app_tensor_comp_inverse_map_δ_functor, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τl, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₁, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_inv_app_f, equiv_counitIso, CategoryTheory.WithTerminal.equivComma_unitIso_inv_app_app, CategoryTheory.Limits.Cocones.whiskeringEquivalence_counitIso, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_hom_app, CategoryTheory.Limits.Cocones.functorialityEquivalence_unitIso, CategoryTheory.Adjunction.whiskerLeft_unit_iso_of_R_fully_faithful, CategoryTheory.Over.whiskerLeft_left_snd, CategoryTheory.Pi.comapId_inv_app, leibnizPushout_map_app, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₁, AlgebraicTopology.DoldKan.Compatibility.υ_inv_app, compFlipUncurryIso_hom_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_right_obj, CategoryTheory.Over.w_assoc, CategoryTheory.CatCenter.localization_add, commBialgCatEquivComonCommAlgCat_counitIso_inv_app, CategoryTheory.Square.toArrowArrowFunctor'_obj_left_right, CategoryTheory.unit_obj_eq_map_unit, leftExtensionEquivalenceOfIso₁_unitIso_inv_app_right_app, CategoryTheory.Equivalence.unit_inverse_comp_assoc, CategoryTheory.Pseudofunctor.IsPrestackFor.nonempty_fullyFaithful, CategoryTheory.Limits.Cones.postcomposeId_inv_app_hom, CategoryTheory.Adjunction.Triple.whiskerLeft_leftToRight, CategoryTheory.MonoidalCategory.DayConvolutionUnit.corepresentableByRight_homEquiv, CategoryTheory.Subfunctor.equivalenceMonoOver_counitIso, CategoryTheory.Square.toArrowArrowFunctor_obj_left_hom, CategoryTheory.WithTerminal.coneEquiv_counitIso_hom_app_hom, CategoryTheory.WithInitial.mapId_hom_app, CategoryTheory.MonoidalCategory.tensoringRight_η, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τr, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_app_app_germToPullbackStalk, CategoryTheory.Abelian.coimIsoIm_hom_app, CategoryTheory.Limits.diagonal_pullback_fst, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_inv_app, PresheafOfModules.instIsRightAdjointPushforwardIdFunctorOppositeRingCat, CategoryTheory.Adjunction.derivedε_fac_app, 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.Equivalence.counit_naturality, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.unitIso_inv_app_hom_app, CategoryTheory.MonoidalCategory.leftUnitorNatIso_hom_app, CategoryTheory.Limits.Cocones.precomposeEquivalence_counitIso, CategoryTheory.forgetAdjToOver_counit_app, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.inverse_map, CategoryTheory.RelCat.opEquivalence_unitIso, CategoryTheory.sheafComposeNatTrans_fac, CategoryTheory.CostructuredArrow.mapIso_counitIso_inv_app_left, CategoryTheory.Limits.widePushoutShapeOpEquiv_unitIso, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₁, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_left_obj, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst_assoc, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₁₂, CategoryTheory.MonoOver.mono_obj_hom, CategoryTheory.Sieve.overEquiv_iff, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_snd, CategoryTheory.Adjunction.map_μ_comp_counit_app_tensor_assoc, CategoryTheory.shiftFunctorAdd_zero_add_inv_app, CategoryTheory.Adjunction.homEquiv_symm_apply, CategoryTheory.shiftFunctorComm_hom_app_of_add_eq_zero_assoc, CategoryTheory.Cat.freeMapIdIso_inv_app, CategoryTheory.Over.opEquivOpUnder_functor_obj, CategoryTheory.Adjunction.counit_isSplitMono_of_R_full, CategoryTheory.ihom.ev_coev, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_snd, ModuleCat.ihom_ev_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_hom_app_hom, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι, CategoryTheory.MonoidalClosed.whiskerLeft_curry_ihom_ev_app_assoc, HomotopicalAlgebra.fibrations_over_iff, CategoryTheory.Adjunction.inv_map_unit, AlgebraicTopology.DoldKan.Γ₂N₂_inv, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_right_right, CategoryTheory.Over.ConstructProducts.conesEquivInverse_map_hom, CategoryTheory.prod.functorProdToProdFunctorAssociator_hom_app, CategoryTheory.StructuredArrow.mapIso_counitIso_hom_app_right, CommRingCat.Under.equalizer_comp, CategoryTheory.Adjunction.mapCommGrp_counit, CategoryTheory.Over.iteratedSliceForwardIsoPost_hom_app, CategoryTheory.Cokleisli.Adjunction.toCokleisli_map, PresheafOfModules.pushforward_comp_id, CategoryTheory.Equivalence.congrRight_counitIso_hom_app, CategoryTheory.Adjunction.functorialityCounit'_app_hom, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_right_app, CategoryTheory.ExponentiableMorphism.unit_pushforwardComp_hom_assoc, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_right_as, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality, CategoryTheory.Sum.functorEquiv_counitIso, CategoryTheory.Idempotents.DoldKan.η_hom_app_f, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_left, lanCompColimIso_hom_app, CategoryTheory.Over.tensorObj_hom, CategoryTheory.Adjunction.Triple.leftToRight_app_map_adj₁_unit_app, CategoryTheory.toOverUnit_obj_hom, CategoryTheory.Over.postAdjunctionLeft_counit_app_left, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_hom_app_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.instIsLeftKanExtensionProdDiscretePUnitExternalProductExtensionUnitRightφ, CategoryTheory.Limits.pullbackConeEquivBinaryFan_inverse_map_hom, CategoryTheory.Arrow.iso_w', CategoryTheory.StructuredArrow.mapIso_counitIso_inv_app_right, TopCat.Presheaf.generateEquivalenceOpensLe_inverse, CategoryTheory.Equivalence.changeFunctor_counitIso_inv_app, CategoryTheory.Reflective.instIsIsoAppUnitReflectorAdjunctionA, CategoryTheory.ShortComplex.map_id, AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_app, CategoryTheory.SingleFunctors.shiftIso_zero_inv_app, CategoryTheory.SmallObject.SuccStruct.ofNatTrans_toSucc, CategoryTheory.Limits.kernelSubobjectMap_arrow_apply, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply_assoc, CategoryTheory.Adjunction.Triple.rightToLeft_app_adj₂_unit_app_assoc, CategoryTheory.Comma.mapRightIso_unitIso_hom_app_right, CategoryTheory.Over.mapComp_inv_app_left, TwoP.swapEquiv_unitIso_inv_app_hom_toFun, CategoryTheory.CosimplicialObject.id_left, CategoryTheory.Equivalence.congrRight_unitIso_inv_app, CategoryTheory.Limits.ker_map, CategoryTheory.CosimplicialObject.Augmented.drop_map, CategoryTheory.Adjunction.shift_counit_app_assoc, CategoryTheory.shift_neg_shift', CategoryTheory.Monoidal.Reflective.instIsIsoMapTensorHomAppUnit, CategoryTheory.ihom.coev_ev_assoc, FullyFaithful.id_preimage, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_counit, CategoryTheory.Adjunction.mapGrp_counit, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_counitIso_hom, CategoryTheory.Arrow.isIso_right, CategoryTheory.Equivalence.functor_unit_comp_assoc, CategoryTheory.Under.comp_right, CategoryTheory.Adjunction.unit_naturality_assoc, CategoryTheory.Arrow.squareToSnd_right, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_inv_app_fst_app, CategoryTheory.Over.mono_left_of_mono, CategoryTheory.constantPresheafAdj_unit_app, CategoryTheory.Equivalence.symmEquivInverse_map_app, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app_assoc, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₃₄, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_hom_app, CategoryTheory.MorphismProperty.Over.map_obj_hom, CategoryTheory.Bicategory.rightUnitorNatIso_hom_app, CategoryTheory.Adjunction.Triple.mono_leftToRight_app_iff, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst_assoc, CategoryTheory.Pi.comapId_hom_app, CategoryTheory.Equivalence.induced_counitIso, CategoryTheory.MonoOver.isIso_iff_isIso_left, CategoryTheory.Adjunction.comp_unit_app, CategoryTheory.Abelian.coimIsoIm_inv_app, CategoryTheory.comonEquiv_counitIso, CategoryTheory.ParametrizedAdjunction.whiskerLeft_map_counit_assoc, AlgebraicGeometry.PresheafedSpace.ofRestrict_c_app, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd_assoc, CategoryTheory.Adjunction.whiskerLeft_counit_app_app, CategoryTheory.CommShift₂Setup.int_z, CategoryTheory.MorphismProperty.instFaithfulUnderTopUnderForget, instAdditiveId, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit, CategoryTheory.Adjunction.adjunctionOfEquivLeft_unit_app, CategoryTheory.Adjunction.leftAdjointCompNatTrans_app, CategoryTheory.MonoOver.instIsIsoLeftDiscretePUnitHomFullSubcategoryOverIsMono, CategoryTheory.TwoSquare.vId_app, ModuleCat.ExtendRestrictScalarsAdj.unit_app, CategoryTheory.Arrow.equivSigma_symm_apply_right, CategoryTheory.evaluationAdjunctionLeft_counit_app, CategoryTheory.WithTerminal.coneEquiv_functor_map_hom, CategoryTheory.TwistShiftData.z_zero_right, CategoryTheory.functorProdFunctorEquivCounitIso_hom_app_app, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left, CategoryTheory.Monad.right_unit_assoc, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₄, CategoryTheory.Limits.widePullbackShapeOpEquiv_unitIso, CategoryTheory.Presheaf.isSheaf_iff_isLimit_pretopology, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_shift, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_assoc, CategoryTheory.mateEquiv_apply, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd_assoc, CategoryTheory.unitCompPartialBijective_symm_apply, CategoryTheory.ihom.coev_ev, CategoryTheory.Arrow.rightFunc_map, TopologicalSpace.Opens.map_id_eq, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right, CategoryTheory.LiftRightAdjoint.instIsCoreflexivePairMapAppUnitOtherMap
instInhabited 📖	CompOp	—
map 📖	CompOp	5380 math math: CategoryTheory.Equivalence.adjointify_η_ε_assoc, inr_biprodComparison', CategoryTheory.Localization.Monoidal.leftUnitor_hom_app, CommRingCat.tensorProd_map_right, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_right, CategoryTheory.shiftFunctorZero_inv_app_obj_of_induced, CategoryTheory.Limits.Types.Limit.w_apply', CategoryTheory.Triangulated.SpectralObject.Hom.comm, CategoryTheory.LocalizerMorphism.LeftResolution.opFunctor_map_f, AlgebraicGeometry.Scheme.Hom.resLE_map_assoc, partialFunToPointed_map, CategoryTheory.Cat.freeMap_map, CommGrpCat.uliftFunctor_map, AlgebraicGeometry.Γ_map_morphismRestrict, CategoryTheory.MorphismProperty.LeftFraction.map_compatibility, CategoryTheory.GrothendieckTopology.overMapPullbackId_hom_app_val_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_eq, CategoryTheory.CostructuredArrow.homMk'_id, CategoryTheory.Pseudofunctor.mapComp'_naturality_1_assoc, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π, AlgebraicGeometry.Scheme.Modules.pushforward_obj_presheaf_map, FullyFaithful.preimage_map, LeftExtension.coconeAtFunctor_map_hom, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_hom_right, FullyFaithful.homNatIsoMaxRight_inv_app, CategoryTheory.GrothendieckTopology.W_sheafToPresheaf_map_iff_isIso, CategoryTheory.LeftExactFunctor.ofExact_map, map_homCongr, CommShift.isoAdd_hom_app, CategoryTheory.Adjunction.compUliftCoyonedaIso_hom_app_app_down, CategoryTheory.Pretriangulated.Triangle.π₂_map, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.hπ_assoc, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_map, CategoryTheory.Limits.DiagramOfCones.id, CategoryTheory.PreOneHypercover.forkOfIsColimit_ι_map_inj_assoc, SheafOfModules.pushforward_assoc, rightKanExtensionCompIsoOfPreserves_inv_fac_app, CochainComplex.mappingConeCompTriangleh_comm₁_assoc, CategoryTheory.Mat_.additiveObjIsoBiproduct_hom_π, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.sndFunctor_map, PushoutObjObj.inr_ι, AlgebraicGeometry.Proj.awayMap_awayToSection_assoc, LightCondensed.free_internallyProjective_iff_tensor_condition, CategoryTheory.Monad.ForgetCreatesColimits.commuting, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_hom_app_val_app, CategoryTheory.SimplicialObject.whiskering_obj_map_app, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, CategoryTheory.ComposableArrows.opEquivalence_counitIso_inv_app_app, CategoryTheory.mateEquiv_counit_symm, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst_assoc, CategoryTheory.MonoidalCategory.DayConvolution.braidingHomCorepresenting_app, CategoryTheory.Limits.spanCompIso_app_left, CategoryTheory.Monoidal.InducingFunctorData.rightUnitor_eq, mapComposableArrowsObjMk₂Iso_inv_app, CategoryTheory.Pseudofunctor.DescentData.subtypeCompatibleHomEquiv_toCompatible_presheafHomObjHomEquiv, CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc, CategoryTheory.coyonedaEquiv_symm_app_apply, CategoryTheory.StructuredArrow.map_map_right, CategoryTheory.NatTrans.hcomp_id_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon_map, OplaxMonoidal.δ_comp_tensorHom_η, CategoryTheory.shiftFunctorAdd'_assoc_inv_app, partialRightAdjointHomEquiv_comp_symm, CategoryTheory.Triangulated.Octahedron.mem, leibnizPullback_obj_map, CategoryTheory.Sheaf.ΓHomEquiv_naturality_left_symm, CategoryTheory.preadditiveCoyonedaObj_map, ChainComplex.truncate_map_f, LaxMonoidal.associativity_assoc, CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair_hom_app, OplaxMonoidal.associativity, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.hasLimit_cospan_forget_of_right', AlgebraicTopology.DoldKan.Compatibility.equivalence₀_unitIso_hom_app, CategoryTheory.Sheaf.isLocallySurjective_sheafToPresheaf_map_iff, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_three_assoc, mapBinaryBicone_inl, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_associator_hom_eq_associator_hom, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map, CategoryTheory.CartesianMonoidalCategory.prodComparison_snd, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.Equivalence.sheafCongr.counitIso_hom_app_val_app, groupHomology.mapCycles₂_comp_assoc, CategoryTheory.shift_shiftFunctorCompIsoId_hom_app, ModuleCat.restrictScalars.map_apply, LightProfinite.proj_comp_transitionMap, GrpWithZero.forget_map, CategoryTheory.Limits.biproduct.mapBiproduct_inv_map_desc, CategoryTheory.evaluationLeftAdjoint_map_app, CategoryTheory.DifferentialObject.shiftFunctor_obj_d, CategoryTheory.preserves_epi_of_preservesColimit, CategoryTheory.Limits.colimitHomIsoLimitYoneda_hom_comp_π, CategoryTheory.ShortComplex.SnakeInput.naturality_φ₁, CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj_map_f, AlgebraicGeometry.IsAffineOpen.map_fromSpec_assoc, AlgebraicGeometry.IsAffineOpen.isLocalization_of_eq_basicOpen, CategoryTheory.ShortComplex.RightHomologyData.map_ι, CategoryTheory.DinatTrans.dinaturality_assoc, CategoryTheory.Mod_.comap_map_hom, CategoryTheory.ihom.coev_naturality, CategoryTheory.obj_ε_app_assoc, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_map_right, HomotopyCategory.quotient_map_out_comp_out, CategoryTheory.regularTopology.EqualizerCondition.bijective_mapToEqualizer_pullback', CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_associator, CategoryTheory.Limits.PreservesEqualizer.iso_hom, TopCat.presheafToType_map, OplaxMonoidal.δ_natural_left_assoc, leftOpRightOpEquiv_functor_obj_map, TopCat.Sheaf.interUnionPullbackCone_snd, CategoryTheory.linearCoyoneda_map_app, CategoryTheory.Adjunction.whiskerLeftLCounitIsoOfIsIsoUnit_inv_app, LightCondensed.isoFinYonedaComponents_hom_apply, CategoryTheory.Presieve.functorPullback_mem, DerivedCategory.right_fac, CategoryTheory.Limits.map_ι_comp_inv_sigmaComparison_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionHomLeft, AddGrpCat.forget₂_map, SSet.Truncated.tensor_map_apply_snd, LaxMonoidal.whiskerLeft_μ_comp_μ_assoc, HomotopicalAlgebra.BifibrantObject.inverts_iff_factors, CategoryTheory.Core.forgetFunctorToCore_map_app, CategoryTheory.Limits.PreservesPushout.inr_iso_inv_assoc, CategoryTheory.Sieve.mem_functorPushforward_iff_of_full, shiftIso_add_inv_app, CategoryTheory.Comma.mapLeftIso_inverse_map_right, CategoryTheory.MonoidalCategory.DayConvolution.unit_naturality, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_hom_app_eq, CategoryTheory.shiftFunctorComm_zero_hom_app, CategoryTheory.Grothendieck.ιCompMap_hom_app_fiber, CategoryTheory.shrinkYoneda_map, CategoryTheory.Join.mapWhiskerLeft_app, leftExtensionEquivalenceOfIso₁_functor_map_left, HomologicalComplex.singleMapHomologicalComplex_hom_app_self, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_two, CategoryTheory.GradedObject.ι_mapBifunctorMapMap, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.instIsOpenImmersionCommRingCatMapSheafedSpaceForgetToSheafedSpace, CategoryTheory.Abelian.PreservesCoimage.iso_hom_π_assoc, HomologicalComplex.truncGE.rightHomologyMapData_φQ, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_inv_app_val_app, preimage_map, CategoryTheory.Limits.Cotrident.ofCocone_ι, CategoryTheory.Abelian.LeftResolution.karoubi.F_obj_p, AlgebraicGeometry.RingedSpace.basicOpen_res, CommShift.isoAdd_inv_app, AlgebraicGeometry.Scheme.Hom.app_invApp'_assoc, CategoryTheory.MonadIso.toNatIso_hom, CategoryTheory.Limits.multicospanIndexEnd_fst, CategoryTheory.Presheaf.coherentExtensiveEquivalence_functor_map_val, CategoryTheory.Cat.freeRefl_map, CategoryTheory.Limits.diagramIsoCospan_inv_app, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app_assoc, CategoryTheory.Pseudofunctor.map₂_associator_app_assoc, OplaxMonoidal.δ_comp_η_tensorHom_assoc, AlgebraicGeometry.Scheme.app_eq, whiskeringRight₂_obj_obj_map_app, CategoryTheory.NatTrans.naturality_2, CategoryTheory.OverPresheafAux.costructuredArrowPresheafToOver_map, CategoryTheory.SmallObject.SuccStruct.extendToSucc_map_le_succ, ModuleCat.restrictScalarsId'App_inv_naturality_assoc, CategoryTheory.ExactFunctor.forget_map, relativelyRepresentable.pullback₃.map_p₃_comp, CategoryTheory.Groupoid.invEquivalence_inverse_map, CategoryTheory.CategoryOfElements.fromStructuredArrow_map, DeltaGenerated.topToDeltaGenerated_map_hom_hom_apply, CategoryTheory.Limits.map_id_right_eq_curry_swap_map, AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_inv_app, CategoryTheory.HasShift.Induced.add_inv_app_obj, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_ι_presheafHom, CategoryTheory.Adjunction.Triple.epi_rightToLeft_app_iff_epi_map_adj₁_unit_app, CategoryTheory.Adjunction.Localization.ε_app, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀, CategoryTheory.GrothendieckTopology.Cover.index_fst, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_pullback_map, map_injective_iff, LaxMonoidal.μ_natural_right, mapBifunctorHomologicalComplexObj_map_f_f, mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app_assoc, CategoryTheory.Monad.free_map_f, CategoryTheory.map_is_cosplit_pair, CategoryTheory.CategoryOfElements.map_snd, CategoryTheory.Bicategory.LeftLift.whiskering_map, CategoryTheory.Limits.walkingSpanOpEquiv_inverse_map, LaxMonoidal.right_unitality, CategoryTheory.Equivalence.unitIso_hom_app_comp_inverse_map_η_functor_assoc, AlgebraicGeometry.coprodSpec_apply, CategoryTheory.Adjunction.unit_app_tensor_comp_map_δ_assoc, ιColimitType_map, CategoryTheory.GradedObject.mapTrifunctorMapFunctorObj_obj_map, CategoryTheory.Limits.Cone.ofTrident_π, CategoryTheory.LeftExactFunctor.forget_map, CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse, CategoryTheory.cocones_map_app_app, CategoryTheory.Over.iteratedSliceBackward_map, LeftExtension.precomp₂_map_right, CategoryTheory.Cat.Hom.id_map, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_unitIso, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_map_left_left, TopCat.Presheaf.locally_surjective_iff_surjective_on_stalks, AlgebraicGeometry.Scheme.Hom.toNormalization_inl_normalizationCoprodIso_hom_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_whiskerRight, CategoryTheory.instIsSplitMonoMap, sheafPushforwardContinuousComp'_inv_app_val_app, CategoryTheory.Limits.equalizerComparison_comp_π, AlgebraicGeometry.IsOpenImmersion.hasLimit_cospan_forget_of_right', TopCat.Presheaf.germ_eq_of_isBasis, rightOp_map, SSet.Subcomplex.mem_ofSimplex_obj_iff, HasFibers.inducedMap_comp, flip₁₃_map_app_app, AlgebraicTopology.DoldKan.N₁_map_f, AlgebraicGeometry.instIsIsoSchemeCoprodComparisonOppositeCommRingCatSpec, CategoryTheory.InjectiveResolution.isoRightDerivedToHomotopyCategoryObj_inv_naturality_assoc, CondensedMod.IsSolid.isIso_solidification_map, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app, IsEventuallyConstantFrom.isoMap_hom_inv_id, mapArrow_obj, AddMonCat.uliftFunctor_map, AlgebraicGeometry.IsAffineOpen.map_fromSpec, CategoryTheory.Comma.toPUnitIdEquiv_functor_map, mapCommMon_obj_mon_mul, HomologicalComplex.cyclesFunctor_map, CategoryTheory.MonoidalCategory.endofunctorMonoidalCategory.evaluationRightAction_actionHomLeft, coe_mapLinearMap, AlgebraicGeometry.Spec_Γ_naturality, CategoryTheory.FunctorToTypes.functorHomEquiv_symm_apply_app_app, eqvGen_colimitTypeRel_iff_of_isFiltered, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_map, CategoryTheory.PreservesImage.factorThruImage_comp_hom, CategoryTheory.Limits.spanCompIso_inv_app_zero, map_mul, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_app_assoc, CategoryTheory.Equivalence.counitIso_inv_app_comp_functor_map_η_inverse, SSet.Truncated.mapHomotopyCategory_homMk, CategoryTheory.ShortComplex.isIso_homologyFunctor_map_of_epi_of_isIso_of_mono, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top, CategoryTheory.Adjunction.map_ε_comp_counit_app_unit_assoc, ModuleCat.toMatrixModCat_map, PreservesFiniteEffectiveEpiFamilies.preserves, AlgebraicGeometry.Scheme.restrictFunctorΓ_inv_app, CategoryTheory.Limits.walkingParallelPairOp_left, IsEventuallyConstantTo.coneπApp_eq, CategoryTheory.shrinkYonedaEquiv_symm_map_assoc, SSet.oneTruncation₂_map, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_counit_app_app, OplaxMonoidal.left_unitality, AlgebraicGeometry.Scheme.Hom.inr_toNormalization_normalizationCoprodIso_inv, CategoryTheory.NatTrans.naturality_apply, mapCocone_ι_app, HeytAlg.hasForgetToLat_forget₂_map, CategoryTheory.LocalizerMorphism.homMap_map, CategoryTheory.Limits.reflexivePair.to_isReflexivePair, CategoryTheory.Comma.map_obj_hom, HomologicalComplex₂.totalShift₂Iso_hom_naturality_assoc, LightCondensed.forget_obj_val_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_map_snd_app, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_app_apply, CategoryTheory.shift_shift', CategoryTheory.Limits.HasColimit.isoOfEquivalence_inv_π, MonCat.forget_map, CategoryTheory.CartesianMonoidalCategory.prodComparison_fst, CategoryTheory.Comonad.ComonadicityInternal.unitFork_π_app, CategoryTheory.Endofunctor.Algebra.forget_map, CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse_map_right, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_functor_map_f_f, CategoryTheory.StructuredArrow.w_prod_fst, CategoryTheory.PreOneHypercover.forkOfIsColimit_pt, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_eq_iff', CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionLeft_map, hom_map, mapCommGrp_obj_grp_one, uliftCoyonedaCoreprXIso_hom_app, OplaxRightLinear.δᵣ_unitality_inv, CategoryTheory.eval_map, CategoryTheory.SimplicialObject.Augmented.point_map, Profinite.Extend.functorOp_map, CategoryTheory.StructuredArrow.homMk'_comp, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.hf, groupHomology.mapCycles₁_comp_apply, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_hom_app_app, CategoryTheory.Sigma.incl_map, CategoryTheory.CostructuredArrow.w_assoc, CategoryTheory.Comma.toIdPUnitEquiv_inverse_map_right, PresheafOfModules.restrictScalars_map_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_map_app, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_app_assoc, CategoryTheory.IsHomLift.map, CategoryTheory.NatTrans.CommShiftCore.shift_app_comm, map_shiftFunctorComm_hom_app, AlgebraicGeometry.instIsAffineSigmaObjScheme, CategoryTheory.Idempotents.functorExtension₂_map_app_f, CategoryTheory.Adjunction.derivedε_fac_app_assoc, CategoryTheory.ShortComplex.mapOpcyclesIso_hom_naturality_assoc, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₁, OplaxRightLinear.δᵣ_naturality_right_assoc, SSet.Subcomplex.toSSetFunctor_map, AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf_map, CategoryTheory.CommMon.forget_map, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp, PullbackObjObj.mapArrowRight_right, CategoryTheory.Pretriangulated.Triangle.π₁_map, CategoryTheory.MonadHom.app_μ, FintypeCat.uSwitch_map_uSwitch_map, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_naturality, LightCondensed.ihomPoints_symm_comp, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_map_mkHom_id_homMk, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id_app, CategoryTheory.yoneda_map_app, LaxLeftLinear.μₗ_naturality_right, WellOrderInductionData.map_succ, CategoryTheory.OplaxFunctor.map₂_associator_app, OplaxMonoidal.δ_snd_assoc, CategoryTheory.Comma.mapLeft_map_left, CategoryTheory.Comonad.comparison_obj_a, CategoryTheory.Limits.PreservesPushout.inr_iso_inv, CategoryTheory.TransportEnrichment.eId_eq, CategoryTheory.Sum.functorEquiv_functor_map, AlgebraicGeometry.Scheme.Opens.topIso_inv, CategoryTheory.OverPresheafAux.restrictedYoneda_map, CategoryTheory.curryingIso_hom_toFunctor_obj_map, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition', CategoryTheory.CatCommSq.hInv_iso_inv_app, CategoryTheory.GrothendieckTopology.overMapPullbackId_inv_app_val_app, CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_cancel_hom_app, LaxRightLinear.μᵣ_naturality_right_assoc, CategoryTheory.Localization.isoOfHom_inv_hom_id, CategoryTheory.Limits.colimit.pre_post, ProfiniteGrp.ProfiniteCompletion.lift_eta, CategoryTheory.yonedaCommGrpGrpObj_map, WellOrderInductionData.Extension.ofLE_val, AlgebraicGeometry.Scheme.Hom.opensFunctor_map_homOfLE, whiskeringLeft₃ObjObjObj_obj_map_app_app, CategoryTheory.MonoidalClosed.uncurry_natural_right, shiftIso_hom_app_comp, postcompose₂_obj_obj_obj_map, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_right_symm, pointedToPartialFun_map, HomotopicalAlgebra.CofibrantObject.toHoCat_map_eq_iff, CategoryTheory.ShortComplex.LeftHomologyData.map_leftHomologyMap', CategoryTheory.ShortComplex.Splitting.map_s, CategoryTheory.Preadditive.toCommGrp_map, CategoryTheory.nerve.functorOfNerveMap_map, CategoryTheory.Pretriangulated.contractibleTriangleFunctor_map_hom₂, mapMon_obj_mon_mul, CategoryTheory.NatIso.naturality_1', AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app_assoc, biprodComparison_snd_assoc, CategoryTheory.Endofunctor.Algebra.Hom.h_assoc, OplaxMonoidal.associativity_assoc, ContinuousMap.Homotopy.apply_zero_path, CategoryTheory.MonoidalCategory.externalProductBifunctor_map_app, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.functorObj_map_hom, CategoryTheory.ProjectiveResolution.iso_hom_naturality_assoc, LightCondSet.epi_iff_locallySurjective_on_lightProfinite, HomologicalComplex.quasiIso_map_of_preservesHomology, CategoryTheory.Comonad.ComonadicityInternal.unitFork_pt, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_leftUnitor, RightExtension.postcompose₂_obj_left_map, AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id_assoc, CategoryTheory.Presieve.isSeparatedFor_singleton, CategoryTheory.Over.monObjMkPullbackSnd_mul, AlgebraicGeometry.sigmaOpenCover_X, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app, CategoryTheory.Monad.Algebra.Hom.h, CategoryTheory.InjectiveResolution.iso_hom_naturality, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_inv_left, CategoryTheory.Adjunction.compCoyonedaIso_inv_app_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_map_hom, comp_mapGrp_mul, CategoryTheory.Equivalence.core_inverse_map_iso_hom, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app_assoc, SSet.spine_map_subinterval, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_map_left, TopCat.uliftFunctorObjHomeo_symm_naturality_apply, CategoryTheory.bifunctorComp₁₂FunctorMap_app_app_app_app, CategoryTheory.ShortComplex.SnakeInput.functorL₁'_map_τ₃, CategoryTheory.Limits.piComparison_comp_π, CategoryTheory.Equivalence.rightOp_functor_map, DerivedCategory.HomologySequence.comp_δ, PreOneHypercoverDenseData.w_assoc, CategoryTheory.ParametrizedAdjunction.whiskerLeft_map_counit, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_map_snd, CategoryTheory.ULiftHom.down_map, CategoryTheory.CatCenter.localization_app, AlgebraicGeometry.Scheme.inv_app, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_map_app_app, CategoryTheory.GrothendieckTopology.ι_plusCompIso_hom_assoc, CategoryTheory.GradedObject.singleObjApplyIso_inv_single_map, mapTriangle_obj, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_app_assoc, TopCat.Presheaf.SheafCondition.pairwiseToOpensLeCover_map, RepresentableBy.homEquiv_eq, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_hom_inv_id, toPrefunctor_map, AlgebraicGeometry.ι_right_coprodIsoSigma_inv, CategoryTheory.linearYoneda_obj_map, CategoryTheory.PreOneHypercover.multicospanIndex_fst, LeftExtension.postcomp₁_map_right_app, CategoryTheory.ThinSkeleton.map_map, CategoryTheory.CostructuredArrow.IsUniversal.existsUnique, AlgebraicGeometry.ι_sigmaSpec, mapComposableArrowsObjMk₁Iso_inv_app, PresheafOfModules.homEquivOfIsLocallyBijective_symm_apply, CategoryTheory.Limits.widePullbackShapeUnop_map, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp_app, CategoryTheory.InjectiveResolution.toRightDerivedZero'_naturality_assoc, CategoryTheory.InjectiveResolution.isoRightDerivedToHomotopyCategoryObj_inv_naturality, Rep.coindFunctor_map, CategoryTheory.CostructuredArrow.mkPrecomp_id, leftKanExtensionUnit_leftKanExtension_map_leftKanExtensionObjIsoColimit_hom, CategoryTheory.prodOpEquiv_inverse_map, AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_hom_app, CategoryTheory.CategoryOfElements.map_map_coe, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃'_map_app_app, CategoryTheory.Join.id_right, RingCat.Colimits.cocone_naturality_components, CategoryTheory.eqToHom_map_comp, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_inv_app, homologySequence_comp_assoc, CategoryTheory.CostructuredArrow.w_prod_fst, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app, CategoryTheory.Limits.diagramIsoParallelFamily_inv_app, CategoryTheory.Presheaf.functorToRepresentables_map, AlgebraicGeometry.coprodSpec_inr, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_postcomp, mapHomotopyEquiv_inv, CategoryTheory.simplicialCosimplicialEquiv_inverse_map, CategoryTheory.SimplicialObject.Augmented.toArrow_map_right, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₃, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv, CategoryTheory.GradedObject.shiftFunctor_map_apply, CategoryTheory.Localization.Monoidal.associator_hom_app, CategoryTheory.Limits.MulticospanIndex.multicospan_map, FullyFaithful.homMulEquiv_apply, sum_map_inl, CategoryTheory.Limits.Cocone.ofCotrident_ι, AlgebraicGeometry.instIsIsoSchemeSigmaSpecOfFinite, CategoryTheory.Adjunction.IsMonoidal.leftAdjoint_μ, CategoryTheory.prodFunctorToFunctorProd_map, TopCat.Presheaf.stalkFunctor_map_injective_of_app_injective, CategoryTheory.Grothendieck.ιNatTrans_app_fiber, CategoryTheory.ShortComplex.SnakeInput.functorL₁'_map_τ₁, CategoryTheory.GrothendieckTopology.yoneda_map_val, mapHomologicalComplex_obj_d, closedIhom_obj_map, CategoryTheory.Quotient.Linear.smul_eq, LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition, CondensedSet.hom_naturality_apply, CategoryTheory.Sigma.desc_map_mk, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_app_assoc, CategoryTheory.coyonedaEvaluation_map_down, CategoryTheory.nerve.homEquiv_edgeMk_map_nerveMap, CategoryTheory.Limits.LimitPresentation.w, FunctorToFintypeCat.naturality, CategoryTheory.Over.grpObjMkPullbackSnd_one, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition, HomologicalComplex.mapBifunctor₂₃.d₂_eq, WellOrderInductionData.Extension.map_zero, shiftIso_zero_inv_app, CategoryTheory.Iso.isoInverseComp_inv_app, CategoryTheory.Pseudofunctor.DescentData.pullFunctor_map_hom, CommGrpCat.forget_map, CategoryTheory.Grothendieck.grothendieckTypeToCat_inverse_map_base, Profinite.Extend.cone_π_app, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.g_app, OplaxLeftLinear.δₗ_associativity_inv, commShift₂_comm, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_obj, CategoryTheory.δ_naturalityₗ_assoc, CategoryTheory.Comma.mapLeftIso_functor_map_left, CategoryTheory.ObjectProperty.lift_map, CategoryTheory.Iso.map_inv_hom_id_app_assoc, HomologicalComplex.opcyclesOpIso_inv_naturality_assoc, CategoryTheory.Limits.inl_comp_pushoutComparison_assoc, CategoryTheory.Square.mapFunctor_map, FullyFaithful.homEquiv_apply, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_map_app_fst, PresheafOfModules.pushforward_map_app_apply, CategoryTheory.Limits.Types.Colimit.w_apply, PresheafOfModules.limitPresheafOfModules_map, CategoryTheory.ShortComplex.LeftHomologyMapData.map_φH, LightCondensed.finYoneda_map, SimplexCategoryGenRel.isSplitEpi_toSimplexCategory_map_of_P_σ, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.hasLimit_cospan_forget_of_left', SimplicialObject.Splitting.cofan_inj_epi_naturality_assoc, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_inv_app_coe, CategoryTheory.Grpd.free_map, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂_assoc, groupHomology.mapCycles₁_comp_assoc, CategoryTheory.evaluationRightAdjoint_obj_map, pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_map, CategoryTheory.η_naturality_assoc, PreservesEffectiveEpiFamilies.preserves, cones_map_app, TopModuleCat.free_map, CategoryTheory.SmallObject.SuccStruct.arrowMk_iterationFunctor_map, CategoryTheory.Over.grpObjMkPullbackSnd_mul, mapHomologicalComplex_map_f, Monoidal.map_associator_inv_assoc, CategoryTheory.ComonadIso.toNatIso_inv, Monoidal.toUnit_ε_assoc, ContinuousMap.Homotopy.evalAt_eq, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app_apply, CategoryTheory.Pseudofunctor.mapId'_inv_naturality_assoc, CategoryTheory.unmopFunctor_map, CategoryTheory.Comonad.CofreeEqualizer.topMap_f, PresheafOfModules.sections_property, Monoidal.map_associator_assoc, CategoryTheory.Limits.Cofork.ofCocone_ι, CategoryTheory.MonoidalClosed.coev_app_comp_pre_app, CategoryTheory.Localization.SmallHom.equiv_equiv_symm, CommShift.isoZero_hom_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_fst_map, CategoryTheory.LocalizerMorphism.commShift_iso_hom_app, AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_hom_app, CategoryTheory.MorphismProperty.RightFraction.map_ofInv_hom_id, CategoryTheory.Abelian.LeftResolution.karoubi.F'_map_f, CategoryTheory.ShortComplex.mapCyclesIso_hom_iCycles_assoc, CategoryTheory.OverPresheafAux.YonedaCollection.map₂_yonedaEquivFst, CategoryTheory.TwoSquare.EquivalenceJ.inverse_map, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one, CategoryTheory.SimplicialObject.Truncated.whiskering_map_app_app, Condensed.discrete_map, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app, CategoryTheory.GradedObject.mapBifunctorObjObjSingle₀Iso_hom, CategoryTheory.opOp_map, CategoryTheory.ForgetEnrichment.equivFunctor_map, Lat.dual_map, CategoryTheory.Limits.Bicone.toBinaryBiconeFunctor_map_hom, mapHomotopyEquiv_homotopyHomInvId, HomologicalComplex.eval_map, CategoryTheory.Presieve.FunctorPushforwardStructure.fac, CategoryTheory.Monad.beckCoequalizer_desc, CategoryTheory.Limits.PreservesPushout.inr_iso_hom_assoc, AlgebraicGeometry.Scheme.IdealSheafData.ideal_le_comap_ideal, CategoryTheory.ShortComplex.mapHomologyIso_hom_naturality, CategoryTheory.Limits.PreservesKernel.iso_inv_ι, PullbackObjObj.π_fst, CochainComplex.HomComplex.Cochain.map_v, CategoryTheory.OplaxFunctor.mapComp_assoc_left_app_assoc, FundamentalGroupoid.map_map, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_hom_app, CategoryTheory.ForgetEnrichment.equivInverse_map, PresheafOfModules.Derivation.d_map, CategoryTheory.StructuredArrow.map₂_map_right, commShiftIso_comp_hom_app, CategoryTheory.Limits.instIsIsoPushoutComparison, QuadraticModuleCat.forget₂_map_associator_inv, CategoryTheory.Limits.Cone.fromCostructuredArrow_map_hom, CommRingCat.free_map_coe, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity, Monoidal.tensorObj_map, AlgebraicGeometry.instIsOpenImmersionLeftSchemeDiscretePUnitMapWalkingSpanOverTopMorphismPropertySpan, AlgebraicGeometry.StructureSheaf.exists_const, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight_apply, LinOrd.dual_map, CategoryTheory.Endofunctor.Adjunction.Algebra.homEquiv_naturality_str, Monoidal.map_μ_δ_assoc, CategoryTheory.Limits.MultispanIndex.map_fst, CategoryTheory.Limits.ColimitPresentation.bind_diag_map, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_inv_colimit_map_assoc, relativelyRepresentable.hom_ext_iff, Monoidal.lift_μ_assoc, groupCohomology.cochainsMap_comp, AlgebraicGeometry.Scheme.Hom.toNormalization_inr_normalizationCoprodIso_hom, CategoryTheory.MorphismProperty.RightFraction.map_s_comp_map_assoc, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceFunctor_map_fiber, CategoryTheory.InjectiveResolution.toRightDerivedZero'_comp_iCycles, CategoryTheory.Comonad.forget_map, MulEquiv.toSingleObjEquiv_inverse_map, pointwiseLeftKanExtensionCompIsoOfPreserves_fac_app_assoc, CategoryTheory.Limits.colimit.homIso_hom, CategoryTheory.WithInitial.opEquiv_functor_map, TopCat.Sheaf.pushforward_map, CategoryTheory.GlueData.ι_gluedIso_inv, flipping_functor_map_app_app, CochainComplex.mappingConeCompTriangle_mor₃, CategoryTheory.IsHomLift.commSq, CategoryTheory.Factorisation.forget_map, flip₂₃_obj_obj_map, CategoryTheory.Localization.Monoidal.μ_inv_natural_right, AlgebraicGeometry.Scheme.congr_app, SimplicialObject.opFunctor_obj_map, CategoryTheory.GradedObject.mapTrifunctor_map_app_app, CategoryTheory.Limits.Bicones.functoriality_map_hom, CategoryTheory.Limits.PreservesCokernel.π_iso_hom_assoc, homologySequence_comp, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_right_hom, CategoryTheory.ShortComplex.LeftHomologyData.map_π, CategoryTheory.prod.rightUnitor_map, CategoryTheory.Limits.limit.w_assoc, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.F_map, CategoryTheory.Monoidal.transportStruct_tensorHom, DistLat.dual_map, LaxRightLinear.μᵣ_unitality_inv_assoc, CategoryTheory.toOverPullbackIsoToOver_inv_app_left, ι_leftKanExtensionObjIsoColimit_inv, CategoryTheory.Idempotents.functorExtension_map_app, CategoryTheory.Equivalence.unitInv_naturality, CategoryTheory.CostructuredArrow.w_prod_fst_assoc, CategoryTheory.Subobject.wideCospan_map_term, LeftExtension.precomp_map_right, CategoryTheory.Limits.Concrete.colimit_rep_eq_iff_exists, LaxBraided.braided, LaxMonoidal.left_unitality_assoc, SSet.Truncated.Edge.CompStruct.d₂, OplaxMonoidal.δ_snd, CategoryTheory.Equivalence.functor_unit_comp, CategoryTheory.Comonad.right_counit_assoc, CategoryTheory.MonoidalSingleObj.endMonoidalStarFunctor_map, CategoryTheory.MorphismProperty.map_mem_strictMap, CategoryTheory.Pseudofunctor.CoGrothendieck.map_map_base, CategoryTheory.Limits.PreservesCokernel.iso_inv, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app', CategoryTheory.SimplicialObject.Augmented.w₀, RightExtension.coneAt_π_app, CategoryTheory.Comma.mapRightIso_functor_map_left, AlgebraicGeometry.Scheme.forget_map, CategoryTheory.μ_naturality₂_assoc, CategoryTheory.Equivalence.inv_fun_map, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₂_assoc, AlgebraicGeometry.sigmaMk_mk, TopCat.Presheaf.pushforwardToOfIso_app, CategoryTheory.Pseudofunctor.CoGrothendieck.map_map_fiber, AddCommMonCat.hom_forget₂_map, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁_assoc, HomologicalComplex.unopInverse_map, PresheafOfModules.free_map_app, CategoryTheory.MonoidalCategory.externalProductBifunctorCurried_obj_obj_obj_map, CategoryTheory.OverPresheafAux.yonedaCollectionPresheaf_map, CategoryTheory.Limits.lim_map, RingCat.forget₂_map, CategoryTheory.Comma.map_map_right, CategoryTheory.MonoidalCategory.DayConvolution.whiskerRight_comp_unit_app_assoc, CochainComplex.shiftShortComplexFunctorIso_add'_hom_app, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_hom_app, IsEventuallyConstantFrom.isoMap_inv_hom_id_assoc, SheafOfModules.instIsRightAdjointPushforwardCompSheafRingCatMapSheafPushforwardContinuous, HomologicalComplex.mapBifunctor₂₃.d₃_eq, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_right, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivLeft_symm_apply, CategoryTheory.Limits.multicospanIndexEnd_snd, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι, CategoryTheory.leftAdjointOfStructuredArrowInitialsAux_apply, AlgebraicGeometry.Flat.instDescScheme, PresheafOfModules.congr_map_apply, CategoryTheory.Localization.HasProductsOfShapeAux.adj_counit_app, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_hom_app_val_app, RightExtension.postcomp₁_obj_left_map, CategoryTheory.Adjunction.compYonedaIso_hom_app_app, CommRingCat.coyoneda_map_app, CategoryTheory.zero_map, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app_assoc, CategoryTheory.CostructuredArrow.post_obj, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.associator_hom_unit_unit, TopCat.Presheaf.germ_res', CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.w_app, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_fiber, RightExtension.postcomp₁_map_right, CategoryTheory.ShortComplex.unopFunctor_map, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompCoyoneda, Monoidal.map_rightUnitor_inv, CategoryTheory.Limits.colimit.ι_map, PresheafOfModules.restrictScalarsObj_map, CategoryTheory.Iso.isoInverseComp_hom_app, PresheafOfModules.forgetToPresheafModuleCatObj_map, CochainComplex.IsKInjective.Qh_map_bijective, CategoryTheory.Limits.PreservesPullback.iso_inv_fst_assoc, LeibnizAdjunction.adj_unit_app_left, TopCat.Sheaf.interUnionPullbackCone_fst, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_map_app, ModuleCat.restrictScalarsId'App_hom_naturality, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map, HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac', CategoryTheory.Discrete.sumEquiv_inverse_map, CategoryTheory.Limits.span_map_id, pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, whiskeringLeft₃Obj_map, CategoryTheory.SimplicialObject.Augmented.toArrow_map_left, CategoryTheory.NatIso.naturality_1, CategoryTheory.NatIso.inv_map_inv_app, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_map_app, CategoryTheory.GlueData.instHasPullbackMapF, CategoryTheory.Comma.mapRightIso_inverse_map_right, ProfiniteGrp.ProfiniteCompletion.lift_eta_assoc, CategoryTheory.MorphismProperty.RightFraction.map_hom_ofInv_id, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app, CategoryTheory.ShortComplex.HomologyMapData.map_left, CategoryTheory.toOverUnit_map_left, surjective_toEventualRanges, CategoryTheory.FunctorToTypes.map_inv_map_hom_apply, IsMittagLeffler.subset_image_eventualRange, CategoryTheory.LaxFunctor.mapComp_naturality_left_app_assoc, CategoryTheory.sheafCompose_map_val, FullyFaithful.map_bijective, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoColimitUncurryWhiskeringLeft₂_inv_assoc, CategoryTheory.Limits.Cocone.toCostructuredArrow_map, LaxRightLinear.μᵣ_associativity_inv_assoc, CategoryTheory.WithTerminal.equivComma_functor_obj_left_map, shiftMap_comp', whiskeringLeft₃_map_app_app_app_app_app_app, CategoryTheory.ThinSkeleton.fromThinSkeleton_map, SSet.stdSimplex.map_id, CategoryTheory.Presieve.FamilyOfElements.compatible_singleton_iff, LightCondensed.discrete_map, epi_map_iff_epi, SimplicialObject.Splitting.cofan_inj_eq, CategoryTheory.Limits.coker_map, CategoryTheory.HasShift.Induced.zero_inv_app_obj, DerivedCategory.HomologySequence.exact₂, HomologicalComplex.forget_map, CategoryTheory.TransfiniteCompositionOfShape.iic_isoBot, curry₃_obj_obj_map_app, CategoryTheory.Cat.FreeRefl.lift_map, CategoryTheory.shift_shift_neg', LaxMonoidal.ofBifunctor.firstMap₃_app_app_app, CategoryTheory.ShortComplex.RightHomologyData.map_g', CategoryTheory.NatTrans.naturality_2_assoc, CategoryTheory.evaluationAdjunctionLeft_unit_app_app, HomotopicalAlgebra.FibrantObject.toHoCat_map_eq_iff, CategoryTheory.Limits.colimMap_eq, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_inv_app, CategoryTheory.CostructuredArrow.prodFunctor_map, CategoryTheory.mopFunctor_map, AlgebraicGeometry.Scheme.forgetToTop_map, CategoryTheory.LocalizerMorphism.commShift_iso_inv_app, CategoryTheory.FinCategory.asTypeToObjAsType_map, CategoryTheory.Grothendieck.isoMk_inv_fiber, CategoryTheory.GradedObject.ιMapBifunctor₁₂BifunctorMapObj_eq_assoc, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality_assoc, SSet.exists_nonDegenerate, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_hom, CategoryTheory.HasShift.Induced.add_hom_app_obj, CategoryTheory.sum.associator_map_inr, CategoryTheory.ComonadIso.toNatIso_hom, rightKanExtensionCompIsoOfPreserves_hom_fac_app, AddCommMonCat.free_map, CategoryTheory.Limits.limit.toStructuredArrow_map, CategoryTheory.Abelian.coim_map, CategoryTheory.Limits.coend.condition, ContinuousMap.Homotopy.heq_path_of_eq_image, HasFibers.homLift, CategoryTheory.RetractArrow.map_r_right, CategoryTheory.CatCommSq.hComp_iso_hom_app, CategoryTheory.Bimon.toComon_map_hom, CategoryTheory.Under.liftCone_pt, TopCat.Presheaf.germ_res_apply, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f_assoc, CategoryTheory.StructuredArrow.prodInverse_map, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivLeft_apply, CategoryTheory.uliftCoyonedaEquiv_uliftCoyoneda_map, leftKanExtensionCompIsoOfPreserves_hom_fac_app, CochainComplex.homotopyUnop_hom_eq, CategoryTheory.CatCommSq.iso_inv_naturality, CategoryTheory.Kleisli.Adjunction.toKleisli_map, CategoryTheory.NatTrans.mapHomotopyCategory_app, CategoryTheory.uliftYonedaEquiv_symm_apply_app, mapProjectiveResolution_π, CategoryTheory.Adjunction.localization_unit_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₂, CategoryTheory.NatTrans.app_naturality, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π, CategoryTheory.Pretriangulated.Triangle.π₃_map, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd_assoc, lightDiagramToProfinite_map, SimplicialObject.Split.forget_map, AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimage, Monoidal.map_leftUnitor_inv, CategoryTheory.Limits.PushoutCocone.isoMk_inv_hom, HomologicalComplex.opcyclesOpIso_inv_naturality, CategoryTheory.conjugateEquiv_symm_apply_app, CategoryTheory.Presheaf.isLocallyInjective_presheafToSheaf_map_iff, CategoryTheory.Limits.WalkingParallelPair.inclusionWalkingReflexivePair_map, CategoryTheory.Groupoid.invFunctor_map, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality, CategoryTheory.Meq.pullback_refine, flipping_inverse_obj_obj_map, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app', CategoryTheory.CostructuredArrow.toOver_map_right, CommMonCat.coyonedaType_obj_map, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_c_app, CategoryTheory.ε_naturality_assoc, LightProfinite.Extend.cocone_ι_app, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagram_map, CategoryTheory.ShortComplex.π₃_map, CategoryTheory.coev_expComparison, CategoryTheory.MonoidalClosed.uncurry_natural_right_assoc, HomotopicalAlgebra.FibrantObject.weakEquivalence_toHoCat_map_iff, Monoidal.map_associator, CategoryTheory.Limits.colimit.ι_post, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π_assoc, CategoryTheory.conjugateEquiv_apply_app, LeibnizAdjunction.adj_counit_app_left, CategoryTheory.Monad.Algebra.assoc_assoc, CategoryTheory.SmallObject.SuccStruct.ofCocone_map_assoc, partialLeftAdjointHomEquiv_symm_comp, AlgebraicGeometry.PresheafedSpace.componentwiseDiagram_map, groupCohomology.mapShortComplexH2_comp_assoc, CategoryTheory.exp.coev_ev, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_naturality, CategoryTheory.MonoidalOpposite.unmopEquiv_inverse_map_unmop, ContinuousMap.Homotopy.eq_path_of_eq_image, CategoryTheory.SimplicialObject.δ_def, CategoryTheory.MonoidalCategory.tensorμ_comp_μ_tensorHom_μ_comp_μ_assoc, rightKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.Pretriangulated.Triangle.functorMk_map_hom₃, homologySequenceδ_naturality, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_app_assoc, FullyFaithful.nonempty_iff_map_bijective, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app, CategoryTheory.CategoryOfElements.to_comma_map_right, CategoryTheory.evaluationRightAdjoint_map_app, CategoryTheory.Monoidal.InducingFunctorData.associator_eq, IsEventuallyConstantTo.isoMap_inv_hom_id, CategoryTheory.NatIso.naturality_1'_assoc, CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.liftHom_fac_assoc, CategoryTheory.Adjunction.ε_comp_map_ε_assoc, CategoryTheory.MorphismProperty.LeftFraction.map_ofHom, Types.monoOverEquivalenceSet_inverse_map, CategoryTheory.Equivalence.sheafCongrPreregular_inverse_obj_val_map, BoolAlg.hasForgetToBoolRing_forget₂_map, HomotopyCategory.quotient_map_eq_zero_iff, CategoryTheory.MorphismProperty.Over.map_map_left, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.presheafHom_naturality, CategoryTheory.NatTrans.hcomp_app, CategoryTheory.preserves_mono_of_preservesLimit, CategoryTheory.MorphismProperty.baseChange_map, mapBicone_ι, CategoryTheory.Pseudofunctor.mapComp'_inv_naturality, IsDenseSubsite.mapPreimage_map, HomologicalComplex.shortComplexFunctor'_map_τ₂, AddGrpCat.uliftFunctor_map, CategoryTheory.Limits.Cocone.w_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁'_map_app_app, OplaxMonoidal.δ_fst_assoc, CategoryTheory.Presieve.ofArrows_mem_comap_jointlySurjectivePrecoverage_iff, CategoryTheory.RightExactFunctor.whiskeringLeft_map_app, CategoryTheory.Limits.kernel_map_comp_preserves_kernel_iso_inv_assoc, Linear.map_smul, shiftIso_zero_hom_app, CategoryTheory.Presheaf.restrictedULiftYoneda_obj_map, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition_assoc, AddCommGrpCat.forget₂_map, CategoryTheory.obj_zero_map_μ_app_assoc, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_map_app_app, homRel_iff, isoShift_inv_naturality_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality_app, CategoryTheory.Comma.opFunctor_map, CategoryTheory.Limits.HasColimit.isoOfEquivalence_hom_π, partialRightAdjointHomEquiv_comp_symm_assoc, CategoryTheory.Pretriangulated.Triangle.functorMk_map_hom₁, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_app, CategoryTheory.Mat_.ι_additiveObjIsoBiproduct_inv_assoc, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_map_fiber, CategoryTheory.Adjunction.Triple.adj₁_counit_app_rightToLeft_app, TwoP.swapEquiv_functor_map_hom_toFun, IsCoverDense.Types.appHom_valid_glue, PresheafOfModules.toPresheaf_map_toSheafify, obj.ε_def_assoc, sections_property, Lat.forget_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_fst_map, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap, CategoryTheory.eqToHom_map, CategoryTheory.Comonad.ForgetCreatesColimits'.newCocone_ι_app, Monoidal.map_whiskerRight, LaxMonoidal.ofBifunctor.bottomMapₗ_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app, CategoryTheory.ShortComplex.Splitting.map_r, LightCondSet.topCatAdjunctionUnit_val_app_apply, OplaxRightLinear.δᵣ_associativity_inv, CategoryTheory.Limits.inl_comp_pushoutComparison, CategoryTheory.ProjectiveResolution.isoLeftDerivedObj_hom_naturality_assoc, CategoryTheory.LaxBraidedFunctor.forget_map, CommRingCat.coyoneda_obj_map, HomotopyCategory.isoOfHomotopyEquiv_hom, postcompose₃_obj_obj_obj_map_app, CategoryTheory.Limits.piConst_map_app, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_map_hom_app, AlgCat.forget_map, CategoryTheory.CostructuredArrow.homMk'_mk_id, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃'_obj_map_app, QuadraticModuleCat.forget₂_map, AlgebraicGeometry.RingedSpace.exists_res_eq_zero_of_germ_eq_zero, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_fiber, CategoryTheory.Presieve.isSheafFor_singleton, CategoryTheory.WithTerminal.commaFromOver_map_left, lightProfiniteToLightDiagram_map, RingCat.forget_map_apply, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedAction_map_app, CategoryTheory.WithInitial.equivComma_functor_obj_right_map, CategoryTheory.Comonad.coassoc, SimplicialObject.opFunctor_map_app, RightExtension.precomp_map_left, CategoryTheory.Limits.FormalCoproduct.cochainComplexFunctor_map_f, CategoryTheory.μ_naturalityᵣ_assoc, CategoryTheory.Pretriangulated.TriangleMorphism.comm₃, PreOneHypercoverDenseData.toPreOneHypercover_p₂, CategoryTheory.LaxFunctor.mapComp_assoc_right_app, CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj_inv_naturality_assoc, SSet.spine_vertex, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality', CategoryTheory.Join.mapPair_map_inclRight, CategoryTheory.Limits.Cones.forget_map, AddMonCat.FilteredColimits.colimit_add_mk_eq, Bicategory.Opposite.unopFunctor_map, mapBifunctorHomologicalComplexObj_obj_X_d, FullyFaithful.homNatIso_inv_app_down, IsFreeGroupoid.SpanningTree.functorOfMonoidHom_map, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_symm_apply, CategoryTheory.Under.pushout_map, pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_app, CategoryTheory.FreeGroupoid.lift_map_homMk, AlgebraicGeometry.Scheme.Hom.appLE_map', CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.fstFunctor_map, topCatOpToFrm_map, AddGrpCat.FilteredColimits.colimit_add_mk_eq, CategoryTheory.LocalizerMorphism.LeftResolution.Hom.comm, CategoryTheory.Limits.fiberwiseColimitLimitIso_hom_app, CategoryTheory.ShortComplex.HomologyData.map_homologyMap', CategoryTheory.RightExactFunctor.whiskeringRight_map_app, HomologicalComplex.instQuasiIsoAtMapOppositeSymmUnopFunctorOp, CategoryTheory.FreeMonoidalCategory.normalize_naturality, CategoryTheory.ShortComplex.RightHomologyMapData.quasiIso_map_iff, curryingFlipEquiv_symm_apply_map_app, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality', PresheafOfModules.map_comp_apply, CommShift₂.commShift_flip_map, Final.extendCocone_obj_ι_app, Full.map_surjective, DerivedCategory.triangleOfSES_mor₁, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.uliftCoyonedaEquiv_symm_apply_app, CategoryTheory.Pseudofunctor.mapComp'_naturality_1, CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_map_hom, CategoryTheory.actionAsFunctor_map, PresheafOfModules.pushforward_map_app_apply', ofSequence_map_homOfLE_succ, CommAlgCat.forget₂_algCat_map, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoColimitUncurryWhiskeringLeft₂_inv, mapShortComplex_map_τ₁, CategoryTheory.MonoidalCategory.DayConvolution.unit_naturality_assoc, shift_map_op_assoc, AlgebraicGeometry.Scheme.Hom.resLE_map, CategoryTheory.Equivalence.funInvIdAssoc_hom_app, CategoryTheory.CostructuredArrow.homMk'_right, CategoryTheory.Abelian.Ext.mk₀_hom, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality, IsCoverDense.Types.pushforwardFamily_def, ι_leftKanExtensionObjIsoColimit_inv_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_inv_app, SSet.opFunctor_map, ComplexShape.Embedding.restrictionFunctor_map, HomologicalComplex.quasiIso_map_iff_of_preservesHomology, CategoryTheory.Localization.Preadditive.add'_map, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_inverse_map_hom, CategoryTheory.Localization.Monoidal.triangle_aux₃, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app', CategoryTheory.Limits.limit.lift_post, OplaxRightLinear.δᵣ_unitality_hom_assoc, AddCommMonCat.coyonedaType_obj_map, mapPresheaf_map_f, CategoryTheory.Monad.instReflectsColimitWalkingParallelPairParallelPairMapAAppCounitObjAOfReflectsColimitOfIsSplitPair, CategoryTheory.ShortComplex.mapOpcyclesIso_inv_naturality, HomologicalComplex.cyclesOpIso_inv_naturality_assoc, CategoryTheory.MonoidalCategory.DayConvolution.whiskerLeft_comp_unit_app, CategoryTheory.Monad.instPreservesColimitWalkingParallelPairParallelPairMapAAppCounitObjAOfPreservesColimitOfIsReflexivePair, mapGrp_obj_grp_one, AlgebraicGeometry.Scheme.forgetToLocallyRingedSpace_map, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_app, CategoryTheory.Grothendieck.id_fiber, CategoryTheory.ShortComplex.map_f, groupHomology.mapCycles₁_comp, CategoryTheory.Limits.biprod.mapBiprod_hom_desc, Monoidal.map_ε_η_assoc, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app_assoc, CategoryTheory.GradedObject.mapBifunctorMap_obj_map, PushoutObjObj.mapArrowRight_left, groupHomology.map_comp, CoconeTypes.descColimitType_injective_iff_of_isFiltered', CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_map, CategoryTheory.ProjectiveResolution.isoLeftDerivedObj_inv_naturality_assoc, congr_hom_assoc, CategoryTheory.Subfunctor.nat_trans_naturality, CategoryTheory.Limits.Types.binaryProductFunctor_obj_map, DerivedCategory.HomologySequence.mono_homologyMap_mor₁_iff, HomotopicalAlgebra.AttachCells.ofArrowIso_g₂, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_map, whiskeringRight₂_obj_obj_obj_map, CategoryTheory.CostructuredArrow.w_prod_snd_assoc, CategoryTheory.Over.postAdjunctionLeft_unit_app_left, CategoryTheory.Limits.Types.FilteredColimit.isColimit_eq_iff, CategoryTheory.obj_μ_app, Action.FunctorCategoryEquivalence.functor_map_app, hasColimit_map_comp_ι_comp_grothendieckProj, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality, SheafOfModules.ιFree_mapFree_inv_assoc, CategoryTheory.Limits.limit.pre_post, CategoryTheory.μ_naturalityₗ, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_tensorHom_app, CategoryTheory.GradedObject.mapTrifunctorMapFunctorObj_map_app, CategoryTheory.Comonad.counit_naturality, AddMonCat.equivalence_inverse_map, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_inv_app, CategoryTheory.Pseudofunctor.map₂_associator_app, CategoryTheory.Limits.spanCompIso_hom_app_zero, CategoryTheory.Square.evaluation₄_map, CommMonCat.coyoneda_obj_map, CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullback, Condensed.isoFinYonedaComponents_hom_apply, map_inv', CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.functor_map, CategoryTheory.Limits.kernelComparison_comp_ι, LeftExtension.postcompose₂_obj_right_map, CategoryTheory.SmallObject.SuccStruct.extendToSuccObjIso_hom_naturality_assoc, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_inv_toNatTrans_app_val_app, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_hom_left, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, CategoryTheory.Limits.coprodComparison_inl, ModuleCat.smul_naturality, CategoryTheory.MonoidalCategory.DayFunctor.equiv_inverse_map_natTrans, CategoryTheory.flippingIso_inv_toFunctor_obj_map_app, CategoryTheory.AdditiveFunctor.ofLeftExact_map, HomologicalComplex.HomologySequence.mapSnakeInput_f₃, SheafOfModules.pullback_map_ιFree_comp_pullbackObjFreeIso_hom_assoc, HomologicalComplex.singleObjCyclesSelfIso_hom_naturality, CategoryTheory.RightExactFunctor.ofExact_map_hom, CategoryTheory.StructuredArrow.functor_map, RepresentableBy.comp_homEquiv_symm, CompHausLike.LocallyConstantModule.functor_map_val, CompHausLike.LocallyConstant.functor_map_val, HomologicalComplex.singleObjCyclesSelfIso_inv_naturality_assoc, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.functor_obj_obj_map, CategoryTheory.δ_naturalityᵣ_assoc, CategoryTheory.bifunctorComp₂₃_map_app_app, CategoryTheory.Adjunction.hasLiftingProperty_iff, groupCohomology.map_comp, AddCommMonCat.coyonedaType_map_app, CategoryTheory.LeftExactFunctor.whiskeringRight_map_app, HomotopyCategory.eq_of_homotopy, CategoryTheory.ι_preservesColimitIso_inv_assoc, CategoryTheory.Abelian.im_map, CategoryTheory.Comon.MonOpOpToComon_map_hom, CategoryTheory.StructuredArrow.map₂_map_left, CategoryTheory.areEqualizedByLocalization_iff, CategoryTheory.TwoSquare.costructuredArrowRightwards_map, HomotopicalAlgebra.BifibrantObject.toHoCat_map_eq, CategoryTheory.Limits.coprodComparison_inv_natural, Homotopy.map_nullHomotopicMap', CategoryTheory.Adjunction.homEquiv_unit, 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.Join.opEquiv_inverse_map_inclRight_op, CategoryTheory.RelCat.rel_graphFunctor_map, CategoryTheory.Join.mkFunctor_map_inclLeft, AlgebraicGeometry.Scheme.Hom.congr_app, CoreMonoidal.left_unitality, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app, CategoryTheory.Limits.coneOfDiagramInitial_π_app, CategoryTheory.Abelian.LeftResolution.π_naturality_assoc, CategoryTheory.coreFunctor_obj_map_iso_inv, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_inv_colimit_map, CategoryTheory.Sum.functorEquiv_inverse_map, CategoryTheory.shiftFunctorCompIsoId_add'_inv_app, CategoryTheory.Bicategory.LeftExtension.whiskering_map, CategoryTheory.shiftFunctorAdd_zero_add_hom_app, AlgebraicGeometry.coprodMk_inl, CategoryTheory.EnrichedFunctor.forget_map, CategoryTheory.MorphismProperty.relative_map_iff, CategoryTheory.Under.map_map_right, PartOrd.dual_map, CategoryTheory.OrthogonalReflection.iteration_map_succ, CategoryTheory.Pseudofunctor.mapComp'_inv_naturality_assoc, sheafPushforwardContinuous_map_val_app, AlgebraicGeometry.Scheme.ofRestrict_appLE, CategoryTheory.Monad.ForgetCreatesLimits.newCone_π_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_map, Monoidal.μ_comp_assoc, CategoryTheory.CostructuredArrow.mkPrecomp_left, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id_app, CategoryTheory.Limits.FormalCoproduct.powerBifunctor_map_app, CategoryTheory.ObjectProperty.ι_map, CategoryTheory.CostructuredArrow.mapIso_functor_map_left, CategoryTheory.ι_preservesColimitIso_hom_assoc, CategoryTheory.StructuredArrow.prodFunctor_map, CategoryTheory.shiftFunctorComm_hom_app_comp_shift_shiftFunctorAdd_hom_app, CategoryTheory.IsCardinalPresentable.exists_eq_of_isColimit, CategoryTheory.Localization.Monoidal.μ_natural_right, AlgebraicGeometry.IsAffineOpen.isoSpec_inv, currying_inverse_obj_obj_map, PresheafOfModules.unit_map_one, CategoryTheory.left_unitality_app_assoc, CategoryTheory.μ_naturality₂, Condensed.finYoneda_map, CategoryTheory.LeftExactFunctor.whiskeringRight_obj_map, AlgebraicTopology.alternatingFaceMapComplex_map_f, CategoryTheory.Limits.limit.post_π, CategoryTheory.Limits.Cones.whiskering_map_hom, flip₁₃_obj_map_app, MonCat.FilteredColimits.M.map_mk, CategoryTheory.Limits.prodComparison_comp, CategoryTheory.AdditiveFunctor.ofRightExact_map, leftExtensionEquivalenceOfIso₁_inverse_map_left, AddMonCat.forget_map, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂'_obj_map_app, CategoryTheory.Limits.PullbackCone.combine_π_app, CategoryTheory.Limits.spanCompIso_inv_app_left, topCatToSheafCompHausLike_map_val_app, CategoryTheory.Over.post_map, CategoryTheory.Localization.homEquiv_eq, CategoryTheory.CategoryOfElements.CreatesLimitsAux.liftedCone_π_app_coe, HomotopicalAlgebra.BifibrantObject.instIsIsoHoCatMapToHoCatOfWeakEquivalence, CategoryTheory.Bifunctor.map_id_comp, CategoryTheory.Abelian.extFunctorObj_map, toPseudoFunctor'_map, map_hom_inv, LightProfinite.lightToProfinite_map_proj_eq, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality', CategoryTheory.GradedObject.ιMapBifunctorBifunctor₂₃MapObj_eq_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp_app, FullyFaithful.compUliftYonedaCompWhiskeringLeft_inv_app_app_down, CategoryTheory.GrothendieckTopology.preservesSheafification_iff_of_adjunctions, CategoryTheory.AdditiveFunctor.ofExact_map, AlgebraicGeometry.instIsAffineHomDescScheme, CompHausLike.LocallyConstant.incl_of_counitAppApp, CategoryTheory.SplitMono.map_retraction, CategoryTheory.ShortComplex.gFunctor_map, ι_biproductComparison'_assoc, Rep.standardComplex.εToSingle₀_comp_eq, CategoryTheory.Comonad.instPreservesLimitWalkingParallelPairParallelPairMapAAppUnitObjAOfPreservesLimitOfIsCoreflexivePair, isoShift_inv_naturality, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality_apply, CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_exists, AlgebraicGeometry.Scheme.Hom.app_appIso_inv_assoc, PushoutObjObj.ofHasPushout_pt, AddCommMonCat.equivalence_functor_map, CoreMonoidal.μIso_hom_natural_left, postcompose₃_obj_obj_map_app_app, CategoryTheory.μ_naturalityᵣ, Monoidal.map_associator'_assoc, CategoryTheory.JointlyReflectMonomorphisms.mono_iff, CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.liftHom_fac, map_opShiftFunctorEquivalence_unitIso_inv_app_unop, 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.Equivalence.changeFunctor_unitIso_hom_app, SSet.prodStdSimplex.objEquiv_naturality, CategoryTheory.Monad.instPreservesColimitWalkingParallelPairParallelPairMapAAppCounitObjAOfPreservesColimitOfIsSplitPair, TopCat.Presheaf.pushforward_map_app, CategoryTheory.Comma.preRight_map_left, CategoryTheory.ShortComplex.SnakeInput.naturality_φ₁_assoc, CategoryTheory.PreOneHypercover.multifork_ι, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₃, sectionsFunctor_map_coe, CommGrpCat.coyonedaType_map_app, Monoidal.μ_fst_assoc, CategoryTheory.Grp.forget_map, CategoryTheory.Limits.PreservesKernel.iso_inv_ι_assoc, CategoryTheory.Equivalence.map_η_comp_η, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app_assoc, CategoryTheory.Limits.pullbackConeEquivBinaryFan_functor_map_hom, CategoryTheory.MonoidalCategory.DayConvolution.associator_inv_unit_unit, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural, CategoryTheory.CostructuredArrow.post_map, CategoryTheory.Equivalence.counit_naturality_assoc, ModuleCat.restrictScalarsId'App_inv_naturality, CategoryTheory.MorphismProperty.RightFraction.map_hom_ofInv_id_assoc, CategoryTheory.uliftYonedaEquiv_symm_map, CategoryTheory.Limits.ConeMorphism.map_w_assoc, CategoryTheory.Cat.free_map, HomologicalComplex.opcyclesFunctor_map, CategoryTheory.MorphismProperty.RightFraction.map_s_comp_map, map_effectiveEpi, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_map_base, sum'_map_inr, CategoryTheory.Under.post_obj, CategoryTheory.PreservesImage.factorThruImage_comp_hom_assoc, CategoryTheory.Adjunction.unit_app_shift_commShiftIso_inv_app, HomologicalComplex.gradedHomologyFunctor_map, PresheafOfModules.map_smul, HomologicalComplex.quasiIso_iff_evaluation, TopologicalSpace.Opens.map_homOfLE, AddCommGrpCat.free_map_coe, CategoryTheory.ShortComplex.SnakeInput.functorL₀_map, strongEpi_map_iff_strongEpi_of_isEquivalence, FintypeCat.uSwitchEquiv_naturality, AlgebraicGeometry.isPullback_inl_inl_coprodMap, CategoryTheory.GlueData.ι_gluedIso_inv_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π, CategoryTheory.Iso.map_hom_inv_id_assoc, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_right, IsEventuallyConstantTo.isoMap_hom, CommShift.ofIso_commShiftIso_hom_app, CategoryTheory.Enriched.FunctorCategory.diagram_map_app, relativelyRepresentable.pullback₃.map_p₁_comp, CategoryTheory.SimplicialObject.Augmented.whiskering_map_app_right, CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj_hom_naturality_assoc, CommShift₂.commShift_map, CategoryTheory.InjectiveResolution.Hom.ι_comp_hom_assoc, CategoryTheory.OplaxFunctor.mapComp_assoc_left_app, CategoryTheory.preservesColimitIso_inv_comp_desc, PresheafOfModules.Monoidal.tensorObj_map_tmul, CategoryTheory.LeftExactFunctor.whiskeringLeft_map_app, CategoryTheory.Adjunction.compUliftCoyonedaIso_inv_app_app_down, CategoryTheory.PreGaloisCategory.evaluation_injective_of_isConnected, Alexandrov.principals_map, Bipointed.swapEquiv_inverse_map_toFun, CategoryTheory.Endofunctor.Coalgebra.Hom.h_assoc, CategoryTheory.Limits.biprod.lift_mapBiprod, CategoryTheory.FunctorToTypes.naturality, pointwiseLeftKanExtension_map, whiskerLeft_obj_map_bijective_of_isCoverDense, SimplexCategory.toTop_map, CategoryTheory.Cat.HasLimits.homDiagram_map, CategoryTheory.CostructuredArrow.mkPrecomp_right, map_zero, CategoryTheory.PreOneHypercover.multicospanIndex_snd, CategoryTheory.Limits.PreservesPullback.iso_inv_snd, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc, whiskeringLeft₃ObjObjMap_app, CategoryTheory.Limits.HasEqualizersOfHasPullbacksAndBinaryProducts.pullbackFst_eq_pullback_snd, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_hom_app, Monoidal.map_δ_μ_assoc, FullyFaithful.autMulEquivOfFullyFaithful_apply_inv, SSet.Truncated.spine_map_subinterval, CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_eq, CategoryTheory.Limits.π_reflexiveCoequalizerIsoCoequalizer_inv_assoc, CategoryTheory.RightExactFunctor.forget_map, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_hom_right, TopCat.Presheaf.presheafEquivOfIso_inverse_obj_map, TopCat.Presheaf.pushforwardEq_hom_app, id_tensor_π_preserves_coequalizer_inv_colimMap_desc, CategoryTheory.GradedObject.mapBifunctorRightUnitorCofan_inj, CategoryTheory.CommGrp.forget₂CommMon_map_hom, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality_app, CategoryTheory.Discrete.functor_map_id, AlgebraicGeometry.Scheme.fromSpecStalk_appTop, CategoryTheory.Comonad.delta_naturality_assoc, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturality_assoc, CategoryTheory.ShortComplex.mapHomologyIso_hom_naturality_assoc, CategoryTheory.GradedObject.singleObjApplyIsoOfEq_inv_single_map, CategoryTheory.Limits.span_map_snd, CategoryTheory.StructuredArrow.IsUniversal.existsUnique, CategoryTheory.Idempotents.DoldKan.N₂_map_isoΓ₀_hom_app_f, CategoryTheory.CommComon.forget₂Comon_map, CategoryTheory.Limits.PreservesPullback.iso_inv_fst, congr_hom, CategoryTheory.ShortComplex.LeftHomologyData.map_i, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_map_left, CategoryTheory.Equivalence.inverseFunctor_map, FullyFaithful.autMulEquivOfFullyFaithful_apply_hom, OplaxMonoidal.oplax_right_unitality, Monoidal.map_whiskerLeft_assoc, CategoryTheory.ShiftedHom.comp_mk₀, CategoryTheory.StructuredArrow.mapNatIso_functor_map_right, LaxLeftLinear.μₗ_naturality_right_assoc, AddMagmaCat.forget_map, CategoryTheory.Triangulated.Octahedron.comm₄_assoc, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counitIso_hom_app_tensor_assoc, BddOrd.dual_map, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_map_right_left, FintypeCat.incl_map, CategoryTheory.GrothendieckTopology.W_iff_isIso_map_of_adjunction, CategoryTheory.Bicategory.precomposing_map_app, AlgebraicGeometry.instIsAffineCoprodScheme, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_apply, typeToPointed_map_toFun, CategoryTheory.LocalizerMorphism.functorialRightResolutions.Φ_functor_map_ι_app, groupHomology.cyclesMap_comp_assoc, AlgebraicGeometry.PresheafedSpace.Γ_map_op, CategoryTheory.Limits.diagramIsoCospan_hom_app, CategoryTheory.simplicialToCosimplicialAugmented_map_left, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_map_hom, SimplexCategoryGenRel.toSimplexCategory_map_σ, CategoryTheory.Monoidal.tensorUnit_map, CategoryTheory.Grothendieck.ιNatTrans_app_base, CategoryTheory.OverPresheafAux.YonedaCollection.map₂_snd, CategoryTheory.Sheaf.ΓHomEquiv_naturality_left, FundamentalGroupoidFunctor.piToPiTop_map, mapComon_map_hom, HomotopyCategory.Pretriangulated.complete_distinguished_triangle_morphism, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app_apply, CategoryTheory.evaluation_obj_map, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerLeft_assoc, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_apply_f, CategoryTheory.shiftComm_hom_comp_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_map_app_app, CategoryTheory.MonoidalCategory.DayFunctor.equiv_functor_map, CategoryTheory.SmallObject.SuccStruct.extendToSuccObjIso_hom_naturality, DerivedCategory.right_fac_of_isStrictlyLE_of_isStrictlyGE, alexDiscEquivPreord_inverse_map, OplaxMonoidal.δ_comp_whiskerLeft_δ_assoc, GrpCat.toAddGrp_map, CategoryTheory.Limits.coprodComparison_inl_assoc, CategoryTheory.ProjectiveResolution.Hom.hom_comp_π_assoc, mapShortComplex_map_τ₂, CategoryTheory.Comon.ComonToMonOpOp_map, SheafOfModules.pushforwardComp_inv_app_val_app, CategoryTheory.Join.mkFunctor_map_inclRight, CategoryTheory.Presieve.map_map, CommRingCat.Colimits.cocone_naturality, CategoryTheory.Limits.prodComparison_fst, LightCondensed.internallyProjective_iff_tensor_condition, CategoryTheory.CartesianClosed.curry_natural_right_assoc, AlgebraicGeometry.Scheme.Spec_map_presheaf_map_eqToHom, CoconeTypes.ι_naturality_apply, OplaxLeftLinear.δₗ_naturality_left_assoc, CategoryTheory.Square.flipFunctor_map_τ₃, CategoryTheory.yonedaMonObj_map, CategoryTheory.Limits.hasReflexiveCoequalizer_iff_hasCoequalizer, CategoryTheory.CartesianMonoidalCategory.map_toUnit_comp_terminalComparison_assoc, CategoryTheory.sum.inverseAssociator_map_inr_inr, SSet.spine_arrow, CategoryTheory.Equivalence.sheafCongrPreregular_functor_map_val_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality_assoc, CategoryTheory.Limits.FormalCoproduct.eval_map_app, CategoryTheory.Grothendieck.comp_fiber, CategoryTheory.Limits.kernelComparison_comp_kernel_map_assoc, CategoryTheory.Subfunctor.ofSection_obj, CategoryTheory.uliftYonedaEquiv_naturality, ModuleCat.forget₂_map_homMk, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_functor_map_f_f, curry₃_obj_map_app_app, CategoryTheory.Grothendieck.map_map, isoShift_hom_naturality, CategoryTheory.Adjunction.map_restrictFullyFaithful_unit_app_assoc, CategoryTheory.Presheaf.coherentExtensiveEquivalence_inverse_map_val, HomologicalComplex.instQuasiIsoMapOppositeSymmUnopFunctorOp, CategoryTheory.MonoidalClosed.curry'_ihom_map, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₃, CategoryTheory.GradedObject.ι_mapTrifunctorMapMap_assoc, CategoryTheory.conjugateEquiv_counit_symm, CategoryTheory.Idempotents.functorExtension₂_obj_map_f, CategoryTheory.CartesianMonoidalCategory.prodComparison_snd_assoc, CommShift.isoZero'_inv_app, CategoryTheory.Grothendieck.ιCompMap_inv_app_fiber, BoolAlg.hasForgetToHeytAlg_forget₂_map, CategoryTheory.TransfiniteCompositionOfShape.iic_isColimit, AlgebraicTopology.DoldKan.map_Hσ, map_add, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_shift, map_hom_inv_assoc, CategoryTheory.Pseudofunctor.Grothendieck.map_id_map, ContinuousMap.Homotopy.apply_one_path, ModuleCat.restrictScalarsId'App_hom_naturality_assoc, AlgebraicGeometry.Surjective.sigmaDesc_of_union_range_eq_univ, CategoryTheory.Limits.map_id_left_eq_curry_map, HomologicalComplex.singleMapHomologicalComplex_inv_app_self, Initial.extendCone_obj_π_app', CategoryTheory.Limits.parallelPair_map_left, TopCat.Presheaf.map_germ_eq_Γgerm, CategoryTheory.PreOneHypercover.map_p₁, CategoryTheory.Abelian.LeftResolution.karoubi.F_map_f, id_map, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_map_left, CategoryTheory.evaluationAdjunctionRight_counit_app_app, coreprW_hom_app, CategoryTheory.SmallObject.functor_map, LaxMonoidal.ofBifunctor.bottomMapᵣ_app, CategoryTheory.Monad.comparison_obj_a, CategoryTheory.Limits.PreservesLimitPair.iso_inv_fst_assoc, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_map_right_right, CategoryTheory.Limits.PreservesPushout.inl_iso_inv, SSet.Augmented.stdSimplex_map_right, CategoryTheory.Subfunctor.equivalenceMonoOver_inverse_map, RingCat.Colimits.cocone_naturality, CoreMonoidal.associativity_assoc, CategoryTheory.Limits.Cowedge.condition_assoc, CategoryTheory.sheafification_map, CategoryTheory.Limits.DiagramOfCocones.coconePoints_map, CategoryTheory.ShortComplex.LeftHomologyData.map_cyclesMap', CategoryTheory.Grp.forget₂Mon_map_hom, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_1, CategoryTheory.Limits.map_inr_inv_coprodComparison_assoc, AlgebraicGeometry.IsAffineOpen.algebraMap_Spec_obj, CategoryTheory.WithTerminal.equivComma_functor_map_right, CategoryTheory.OplaxFunctor.map₂_associator_app_assoc, CategoryTheory.Adjunction.unit_app_unit_comp_map_η, FinBddDistLat.forget_map, CategoryTheory.Monad.adj_counit, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app_assoc, CommMonCat.val_units_map_hom_apply, whiskeringLeft₂_obj_obj_obj_map_app, CategoryTheory.ShortComplex.exact_iff_of_hasForget, CategoryTheory.LaxFunctor.map₂_associator_app_assoc, CategoryTheory.Presheaf.functorEnrichedHomCoyonedaObjEquiv_naturality, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_unit, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_assoc, commShiftOfLocalization_iso_inv_app, uncurry_map_app, CategoryTheory.Adjunction.map_restrictFullyFaithful_counit_app, CategoryTheory.ShortComplex.RightHomologyData.map_rightHomologyMap', CategoryTheory.Limits.piConst_obj_map, SimplexCategory.toTop₀_map, CategoryTheory.Limits.diagramIsoParallelPair_hom_app, CategoryTheory.ShortComplex.SnakeInput.functorL₁'_map_τ₂, map_epi, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₁, CategoryTheory.MonoidalOpposite.mopMopEquivalence_inverse_map_unmop_unmop, CoreMonoidal.right_unitality_assoc, map.instIsMonHom, CategoryTheory.PreGaloisCategory.functorToContAction_map, CategoryTheory.plusPlusSheaf_map_val, CategoryTheory.ActionCategory.uncurry_map, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_inv_hom_id_assoc, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinset_obj_map, CategoryTheory.Endofunctor.Coalgebra.forget_map, SSet.hoFunctor.unitHomEquiv_eq, commShiftOfLocalization.iso_inv_app, obj.Δ_def_assoc, CategoryTheory.ComposableArrows.whiskerLeftFunctor_obj_map, CategoryTheory.Limits.MultispanIndex.multispan_map_fst, OplaxRightLinear.δᵣ_naturality_left, AlgebraicTopology.DoldKan.Γ₀_obj_map, PresheafOfModules.freeObj_map, CategoryTheory.coev_app_comp_pre_app, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top_assoc, SSet.S.mk_map_eq_iff_of_mono, CategoryTheory.Localization.Monoidal.μ_natural_left_assoc, CategoryTheory.WithInitial.commaFromUnder_map_left, CategoryTheory.StructuredArrow.homMk'_mk_comp, map_zsmul, AlgebraicGeometry.liftCoborder_app, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_whiskerLeft_app, CategoryTheory.SimplicialObject.Augmented.const_map_left, CategoryTheory.Pretriangulated.Triangle.rotate_mor₃, CommShift.comp_commShiftIso_inv_app, DistLat.forget_map, CategoryTheory.Abelian.Ext.singleFunctor_map_comp_hom, SSet.OneTruncation₂.HoRel₂.mk, CategoryTheory.CartesianClosed.curry_natural_right, CategoryTheory.Over.map_map_left, CategoryTheory.Equivalence.counitInv_functor_comp, CategoryTheory.MonoidalCategory.tensorμ_comp_μ_tensorHom_μ_comp_μ, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_left, CategoryTheory.CosimplicialObject.Augmented.whiskering_map_app_left, CategoryTheory.Equivalence.sheafCongrPreregular_inverse_map_val_app, CategoryTheory.Equivalence.sheafCongrPrecoherent_functor_obj_val_map, CategoryTheory.WithTerminal.liftToTerminal_map, groupHomology.map_comp_assoc, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w, CategoryTheory.GradedObject.ι_mapBifunctorRightUnitor_hom_apply, CategoryTheory.Limits.BinaryBicones.functoriality_map_hom, CategoryTheory.ReflQuiv.forget_map, OplaxLeftLinear.δₗ_unitality_hom_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_app, AlgebraicGeometry.Spec_map_localization_isIso, TopCat.Presheaf.stalkFunctor_map_injective_of_isBasis, CategoryTheory.bifunctorComp₁₂_map_app_app, toPseudoFunctor_mapComp, CategoryTheory.prodFunctor_map, CategoryTheory.ShortComplex.mapRightHomologyIso_inv_naturality, CategoryTheory.PreservesImage.iso_hom, CategoryTheory.Triangulated.Localization.complete_distinguished_triangle_morphism, CategoryTheory.Idempotents.Karoubi.decomp_p, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_assoc, mapBinaryBicone_snd, CategoryTheory.ProjectiveResolution.isoLeftDerivedObj_hom_naturality, CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan_inj, CategoryTheory.Comonad.ComonadicityInternal.unitFork_ι, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₂, CategoryTheory.MonoOver.image_map, CategoryTheory.Bifunctor.map_id, SSet.S.le_iff, CoreMonoidal.μIso_hom_natural_left_assoc, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app_assoc, OneHypercoverDenseData.essSurj.presheafObj_condition_assoc, CategoryTheory.Equivalence.rightOp_inverse_map, AlgebraicGeometry.StructureSheaf.algebraMap_self_map, map_conj, CategoryTheory.Limits.hasPushout_of_preservesPushout, CategoryTheory.Adjunction.IsMonoidal.leftAdjoint_ε, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_map_left, CategoryTheory.nerveMap_app_mk₁, CategoryTheory.Limits.SequentialProduct.functorMap_commSq_aux, CategoryTheory.sheafToPresheaf_map, CategoryTheory.DifferentialObject.d_squared, CategoryTheory.preservesLimitIso_inv_π_assoc, CategoryTheory.Limits.ι_comp_sigmaComparison, ModuleCat.Tilde.toOpen_res, CategoryTheory.OverPresheafAux.counitForward_val_snd, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one_assoc, CategoryTheory.Center.ofBraided_map_f, CategoryTheory.Limits.Types.Limit.w_apply, CategoryTheory.shiftFunctorComm_hom_app_comp_shift_shiftFunctorAdd_hom_app_assoc, CategoryTheory.CosimplicialObject.Truncated.whiskering_map_app_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_map_fst_app, CategoryTheory.Join.mapWhiskerRight_app, CategoryTheory.Over.opEquivOpUnder_inverse_map, CommMonCat.val_inv_units_map_hom_apply, CategoryTheory.ProjectiveResolution.extMk_hom, CategoryTheory.SmallObject.SuccStruct.Iteration.subsingleton.MapEq.w, CategoryTheory.Subfunctor.equivalenceMonoOver_functor_map, CategoryTheory.Equalizer.Presieve.isSheafFor_singleton_iff, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_map_left_left, CategoryTheory.StructuredArrow.mkPostcomp_left, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_whiskerLeft, CommMonCat.forget₂_map_ofHom, shiftIso_add_hom_app, mapSquare_map_τ₁, CategoryTheory.presheafHom_map_app, CategoryTheory.Limits.cospan_map_inr, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_app_fst_app, CategoryTheory.shiftFunctorAdd_inv_app_obj_of_induced, CategoryTheory.AreEqualizedByLocalization.map_eq, CategoryTheory.Equivalence.symmEquivFunctor_map, CategoryTheory.Under.post_map, CochainComplex.single₀_map_f_zero, CategoryTheory.Limits.cospanCompIso_inv_app_left, CategoryTheory.Triangulated.Octahedron.triangle_mor₃, CategoryTheory.Limits.spanCompIso_app_zero, map_effectiveEpiFamily, CategoryTheory.Equivalence.sheafCongrPreregular_functor_obj_val_map, partialRightAdjointHomEquiv_comp, CategoryTheory.TwistShiftData.shift_z_app, CategoryTheory.Over.equivalenceOfIsTerminal_inverse_map, CategoryTheory.Limits.PushoutCocone.ofCocone_ι, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_obj_obj_map, AlgebraicTopology.DoldKan.Γ₂N₂ToKaroubiIso_hom_app, CategoryTheory.Limits.coend.condition_assoc, AlgebraicGeometry.opensDiagram_map, postcompose₃_obj_obj_obj_obj_map, CategoryTheory.Abelian.Ext.mapExactFunctor_hom, CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.inductiveSystem_map, TopCat.uliftFunctorObjHomeo_naturality_apply, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_app, CategoryTheory.Monad.adj_unit, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_presheafMap, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.isIso_f, Rep.coindResAdjunction_unit_app, CategoryTheory.GradedObject.mapBifunctorObjSingle₀ObjIso_hom, CategoryTheory.Triangulated.Octahedron.map_m₃, CategoryTheory.FunctorToTypes.hcomp, CategoryTheory.OplaxFunctor.mapComp_assoc_right_app, AlgebraicGeometry.Scheme.Hom.app_eq, CategoryTheory.Join.mapPair_map_inclLeft, CategoryTheory.linearYoneda_map_app, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_map_base, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_μ, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_hom_app_app, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp_app, PrincipalSeg.cocone_ι_app, CategoryTheory.Limits.end_.condition, TopCat.Presheaf.germ_res_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_map_app_snd, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_map_hom, CategoryTheory.SmallObject.SuccStruct.ofCoconeObjIso_hom_naturality, relativelyRepresentable.map_fst', CorepresentableBy.homEquiv_eq, CategoryTheory.Square.toArrowArrowFunctor_map_right_right, CategoryTheory.PreGaloisCategory.fiberBinaryProductEquiv_symm_fst_apply, HomologicalComplex.opcyclesOpIso_hom_naturality_assoc, shiftMap_comp, CategoryTheory.Abelian.LeftResolution.karoubi.F'_obj_p, CategoryTheory.LocalizerMorphism.smallHomMap_mk, shiftIso_add'_hom_app, CategoryTheory.Limits.Cone.ofPullbackCone_pt, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app, CategoryTheory.endofunctorMonoidalCategory_whiskerRight_app, CategoryTheory.MorphismProperty.relative_map, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_obj_obj_map, CategoryTheory.Comonad.instPreservesLimitWalkingParallelPairParallelPairMapAAppUnitObjAOfPreservesLimitOfIsCosplitPair, CategoryTheory.ShortComplex.SnakeInput.composableArrowsFunctor_map, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_inv_app_app, CategoryTheory.FunctorToTypes.binaryCoproductCocone_pt_map, LaxMonoidal.left_unitality, CategoryTheory.ComposableArrows.opEquivalence_functor_obj_map, SSet.Truncated.StrictSegal.spine_δ_arrow_lt, CategoryTheory.SimplicialObject.σ_def, CategoryTheory.Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor, CategoryTheory.Subgroupoid.mem_map_iff, CategoryTheory.NatTrans.naturality_app_app_assoc, partialFunEquivPointed_functor_map_toFun, TopologicalSpace.Opens.map_comp_map, CategoryTheory.Equivalence.sheafCongrPrecoherent_inverse_map_val_app, CategoryTheory.Presheaf.restrictedULiftYoneda_map_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_naturality_assoc, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.ι_map_tensorHom_eq, DerivedCategory.instIsIsoMapCochainComplexIntQ, OplaxMonoidal.δ_comp_δ_whiskerRight_assoc, PresheafOfModules.presheaf_map_apply_coe, LaxMonoidal.μ_natural_right_assoc, CategoryTheory.CosimplicialObject.Augmented.leftOp_left_map, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac, CategoryTheory.IsHomLift.eq_of_isHomLift, CompactlyGenerated.compactlyGeneratedToTop_map, CategoryTheory.right_unitality_app_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app_assoc, CommRingCat.forget_map, inl_biprodComparison', HomotopyCategory.quot_mk_eq_quotient_map, CategoryTheory.Limits.Cones.functoriality_obj_π_app, CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_cancel_hom_app, obj.η_def_assoc, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv, HomologicalComplex.quasiIsoAt_unopFunctor_map_iff, CategoryTheory.Limits.reflexivePair.compRightIso_hom_app, CategoryTheory.RanIsSheafOfIsCocontinuous.fac_assoc, CategoryTheory.DifferentialObject.Hom.comm_assoc, groupCohomology.mapShortComplexH2_comp, shiftIso_inv_naturality, CategoryTheory.η_app_obj, pi_map, AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zero, AlgebraicGeometry.IsZariskiLocalAtSource.sigmaDesc, AlgebraicGeometry.Scheme.Modules.restrict_map, CategoryTheory.ProjectiveResolution.pOpcycles_comp_fromLeftDerivedZero'_assoc, TopCat.Sheaf.objSupIsoProdEqLocus_hom_fst, CategoryTheory.expComparison_whiskerLeft, leibnizPushout_obj_map, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_whiskerRight_app, AlgebraicGeometry.isIso_stalkMap_coprodSpec, isSplitMono_iff, CategoryTheory.Limits.colimitLimitToLimitColimitCone_hom, SheafOfModules.sectionsFunctor_map, CategoryTheory.isIso_iff_isIso_yoneda_map, CategoryTheory.Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor_assoc, CategoryTheory.Limits.cospan_map_inl, CategoryTheory.Localization.isoOfHom_hom, whiskeringLeft₃ObjMap_app, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_three, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃'_obj_obj_map, DerivedCategory.HomologySequence.comp_δ_assoc, CategoryTheory.Comma.equivProd_inverse_map_left, CategoryTheory.shiftFunctorAdd'_zero_add_inv_app, ModuleCat.restrictScalarsComp'App_hom_naturality_assoc, FundamentalGroupoidFunctor.projLeft_map, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_map_assoc, CategoryTheory.Limits.map_inr_inv_coprodComparison, CategoryTheory.Join.fromSum_map_inr, CategoryTheory.WithTerminal.map_map, CategoryTheory.Adjunction.strongEpi_map_of_strongEpi, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_fst_map, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality', map_smul, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided_map_hom_hom_app, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_uliftYoneda_map, OplaxMonoidal.ofBifunctor.secondMap_app_app_app, CategoryTheory.Idempotents.FunctorExtension₁.obj_obj_p, CategoryTheory.Adjunction.shift_counit_app, CategoryTheory.Limits.Cone.ofPullbackCone_π, CategoryTheory.Pretriangulated.contractibleTriangleFunctor_map_hom₁, Monoidal.map_rightUnitor_assoc, LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom, map_shift_unop, Additive.map_add, OplaxMonoidal.lift_δ, CategoryTheory.TwoSquare.whiskerVertical_app, CategoryTheory.Limits.ConeMorphism.map_w, CategoryTheory.Cat.FreeRefl.lift'_map, toEssImage_map_hom, ChainComplex.quasiIsoAt₀_iff, CategoryTheory.Presieve.map_ofArrows, CategoryTheory.curryingIso_inv_toFunctor_obj_map_app, CategoryTheory.Join.opEquiv_functor_map_op_edge, ihom_map, mapCommMonFunctor_map_app, CategoryTheory.Monad.assoc, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_map_τ₁, groupCohomology.cochainsMap_comp_assoc, CategoryTheory.Adjunction.map_restrictFullyFaithful_counit_app_assoc, mapContAction_map, CategoryTheory.endofunctorMonoidalCategory_tensorMap_app, obj.η_def, map_eq_zero_iff, homologySequence_epi_shift_map_mor₁_iff, CategoryTheory.Presheaf.app_localPreimage, LaxRightLinear.μᵣ_associativity_inv, CategoryTheory.Limits.LimitPresentation.ofIso_π, CategoryTheory.InjectiveResolution.isoRightDerivedObj_hom_naturality, LeftExtension.postcompose₂_map_right_app, CategoryTheory.GradedObject.singleObjApplyIso_inv_single_map_assoc, CategoryTheory.Pseudofunctor.DescentData.Hom.comm_assoc, CategoryTheory.Grothendieck.fiber_eqToHom, IsDenseSubsite.mapPreimage_comp_map, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_map_app_app, CategoryTheory.Join.mapIsoWhiskerRight_hom_app, CategoryTheory.ExponentiableMorphism.ev_coev, CategoryTheory.CommaMorphism.w_assoc, mapAction_obj_ρ_apply, CategoryTheory.Adjunction.counit_naturality, OplaxLeftLinear.δₗ_unitality_inv, CategoryTheory.ComposableArrows.δ₀Functor_obj_map, ContinuousMap.yonedaPresheaf_map, biproductComparison_π_assoc, CommRingCat.Under.tensorProdEqualizer_ι, CategoryTheory.MorphismProperty.map_eq_iff_postcomp, CategoryTheory.Limits.pushoutComparison_map_desc, CategoryTheory.Ind.exists_nonempty_arrow_mk_iso_ind_lim, Monoidal.map_leftUnitor_inv_assoc, CategoryTheory.Pretriangulated.invRotate_map_hom₁, op_commShiftIso_hom_app_assoc, AlgebraicGeometry.tilde.functor_map, CategoryTheory.Monad.monadToMon_map_hom, CategoryTheory.WithInitial.mkCommaObject_hom_app, FullyFaithful.compYonedaCompWhiskeringLeftMaxRight_inv_app_app, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.inverse_map, CategoryTheory.CartesianClosed.curry_eq, CategoryTheory.SingleObj.functor_map, CategoryTheory.ShortComplex.map_g, OplaxMonoidal.oplax_associativity, CategoryTheory.Join.opEquiv_functor_map_op_inclRight, PresheafOfModules.forgetToPresheafModuleCatObjMap_apply, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_inv_app, CategoryTheory.CostructuredArrow.map_map_right, CategoryTheory.Limits.FormalCoproduct.incl_map_f, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app_assoc, CategoryTheory.ExactFunctor.whiskeringLeft_map_app, CategoryTheory.μ_naturality, CategoryTheory.SmallObject.SuccStruct.ofCoconeObjIso_hom_naturality_assoc, CategoryTheory.FreeGroupoid.map_map_homMk, sectionsEquivHom_naturality, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_leftUnitor, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₃₁, groupHomology.mapCycles₂_comp, SheafOfModules.toSheaf_map_val, CategoryTheory.Limits.DiagramOfCones.mkOfHasLimits_map_hom, AlgebraicGeometry.opensDiagramι_app, CategoryTheory.Presheaf.freeYoneda_map, shiftMap_comp'_assoc, CategoryTheory.Monoidal.FunctorCategory.tensorObj_map, CategoryTheory.Monad.unit_naturality, CategoryTheory.StructuredArrow.homMk'_left, CategoryTheory.Limits.widePushoutShapeOp_map, CategoryTheory.MonoidalClosed.pre_comm_ihom_map, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃'_obj_map_app, CategoryTheory.obj_zero_map_μ_app, CategoryTheory.Iso.compInverseIso_inv_app, CategoryTheory.Adjunction.restrictFullyFaithful_homEquiv_apply, CategoryTheory.Grothendieck.eqToHom_eq, SSet.stdSimplex.map_apply, CategoryTheory.Square.evaluation₂_map, CategoryTheory.Limits.ColimitPresentation.Total.Hom.w, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app_assoc, CategoryTheory.IsHomLift.fac', SimplexCategory.rev_map_δ, AlgebraicGeometry.isCompl_range_inl_inr, TopCat.Presheaf.presheafEquivOfIso_unitIso_hom_app_app, homologySequence_exact₂, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom, CategoryTheory.Equivalence.unitInv_naturality_assoc, CategoryTheory.TransfiniteCompositionOfShape.map_isoBot, LightCondensed.isoFinYonedaComponents_inv_comp, HomologicalComplex.opFunctor_map_f, mapTriangle_map_hom₁, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.inverse_map_app, CategoryTheory.Comma.preRight_map_right, SSet.Truncated.spine_map_vertex, CategoryTheory.Comonad.Coalgebra.Hom.h, CategoryTheory.Limits.spanCompIso_app_right, AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app, SheafOfModules.pullbackObjFreeIso_hom_naturality_assoc, CategoryTheory.Limits.Concrete.isColimit_exists_of_rep_eq, ModuleCat.FilteredColimits.M.mk_map, CategoryTheory.PreservesImage.hom_comp_map_image_ι, CategoryTheory.NatTrans.CommShiftCore.shift_app, CategoryTheory.GradedObject.eval_map, CategoryTheory.sum.inverseAssociator_map_inl, homObjFunctor_map_app, toPseudoFunctor_map, CategoryTheory.Limits.PreservesPushout.inl_iso_inv_assoc, CommMonCat.forget_map, relativelyRepresentable.map, CategoryTheory.NatTrans.whiskerLeft_app_tensor_app_assoc, AddMonCat.FilteredColimits.M.map_mk, CategoryTheory.CatCommSq.vInv_iso_hom_app, ShiftSequence.induced_shiftIso_hom_app_obj, CategoryTheory.eqToHom_map_comp_assoc, CategoryTheory.prod.leftInverseUnitor_map, isRepresentedBy_iff, CategoryTheory.MorphismProperty.Over.forget_comp_forget_map, Monoidal.map_associator_inv, CategoryTheory.lift_comp_preservesLimitIso_hom_assoc, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.hπ, CategoryTheory.preservesLimitIso_inv_π, CategoryTheory.Abelian.PreservesImage.iso_hom_ι, CategoryTheory.sheafBotEquivalence_inverse_map_val, CochainComplex.mappingConeCompTriangle_mor₃_naturality, CategoryTheory.ShortComplex.mapHomologyIso'_hom_naturality, CategoryTheory.Monad.MonadicityInternal.unitCofork_π, homologySequenceδ_comp_assoc, CategoryTheory.LocalizerMorphism.homMap_apply, CategoryTheory.Square.toArrowArrowFunctor'_map_right_left, classifyingSpaceUniversalCover_map, CategoryTheory.Comma.map_map_left, AlgebraicGeometry.AffineSpace.functor_obj_map, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app'_assoc, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id_app, ModuleCat.localizedModule_functor_map, CategoryTheory.CostructuredArrow.w_prod_snd, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_functor_map, CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_left, CategoryTheory.shift_equiv_triangle, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_app_comp_π, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_hom_assoc, CategoryTheory.Pseudofunctor.mapComp'_hom_naturality_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_map_snd_app, CategoryTheory.Pseudofunctor.mapComp'_naturality_2_assoc, CategoryTheory.Limits.kernelComparison_comp_ι_assoc, CategoryTheory.associator_inv, CategoryTheory.Comma.post_map_left, CategoryTheory.Quiv.forget_map, CategoryTheory.Limits.PreservesPullback.iso_hom_fst, LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition', CommMonCat.hom_forget₂_map, CategoryTheory.shiftFunctorZero_hom_app_obj_of_induced, CategoryTheory.Pseudofunctor.ObjectProperty.map_map_hom, CompHausLike.LocallyConstant.functorToPresheaves_map_app, HomotopicalAlgebra.CofibrantObject.exists_bifibrant_map, CategoryTheory.CommaMorphism.w, homologySequence_mono_shift_map_mor₁_iff, CondensedSet.topCatAdjunctionUnit_val_app_apply, AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_naturality_app, CategoryTheory.ProjectiveResolution.iso_hom_naturality, CategoryTheory.PreGaloisCategory.exists_lift_of_mono_of_isConnected, CategoryTheory.FunctorToTypes.rightAdj_map_app_app, map_sub, CategoryTheory.Localization.Construction.lift_map, TwoP.swap_map, CategoryTheory.LeftExactFunctor.ofExact_map_hom, CategoryTheory.Pairwise.diagram_map, PreOneHypercoverDenseData.w, OplaxLeftLinear.δₗ_associativity, CategoryTheory.Limits.multispanIndexCoend_snd, CategoryTheory.CatCommSq.iso_hom_naturality, CategoryTheory.yonedaEquiv_yoneda_map, CategoryTheory.Cat.exp_map, CategoryTheory.OverPresheafAux.unitForward_naturality₂, CategoryTheory.Limits.FormalCoproduct.eval_obj_map, BddDistLat.forget_map, AlgebraicGeometry.Scheme.Modules.toPresheaf_map, LeftExtension.postcompose₂_obj_hom_app, CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc, SemilatSupCat.dual_map, CategoryTheory.Iso.map_inv_hom_id_app, CategoryTheory.Limits.colim_map, OplaxRightLinear.δᵣ_associativity, CategoryTheory.Limits.HasLimit.isoOfEquivalence_hom_π, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_app, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_map_right_right, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π, CategoryTheory.NatIso.naturality_1_assoc, AlgebraicGeometry.instIsOpenImmersionInrScheme, AlgebraicGeometry.SheafedSpace.ofRestrict_hom_c_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_invApp, CategoryTheory.unit_conjugateEquiv_symm, CategoryTheory.CategoryOfElements.comp_val, CategoryTheory.Localization.Monoidal.μ_natural_left, PresheafOfModules.sheafification_map, CategoryTheory.PreGaloisCategory.evaluation_aut_bijective_of_isGalois, TopCat.Presheaf.whiskerIsoMapGenerateCocone_inv_hom, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app_assoc, CategoryTheory.Pretriangulated.preadditiveYoneda_homologySequenceδ_apply, SSet.StrictSegal.spineToSimplex_interval, AlgebraicTopology.DoldKan.Γ₂_obj_X_map, CategoryTheory.toPresheafToSheafCompComposeAndSheafify_app, CategoryTheory.Iso.map_hom_inv_id, CategoryTheory.PreservesImage.inv_comp_image_ι_map, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_map_hom, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_naturality_assoc, AlgebraicGeometry.Scheme.Hom.appIso_inv_app, TopCat.Presheaf.stalk_mono_of_mono, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app_assoc, CategoryTheory.Limits.Types.Colimit.ι_map_apply', HomologicalComplex.mapBifunctor.d₂_eq, whiskeringLeft₃_obj_obj_map_app_app_app_app, TopCat.Presheaf.map_germ_eq_Γgerm_assoc, CategoryTheory.unit_conjugateEquiv, HomologicalComplex.instQuasiIsoAtOppositeMapSymmOpFunctorOp, map_commSq, DerivedCategory.left_fac_of_isStrictlyLE_of_isStrictlyGE, CategoryTheory.GradedObject.mapBifunctorObjSingle₀ObjIso_inv, CategoryTheory.Square.map_f₁₃, CategoryTheory.Free.embedding_map, CochainComplex.shiftFunctor_map_f', CategoryTheory.Grothendieck.grothendieckTypeToCatFunctor_map_coe, whiskeringLeft₃Map_app_app, CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_inv, pointedToTwoPFst_map_hom_toFun, ComplexShape.Embedding.extendFunctor_map, CategoryTheory.TransfiniteCompositionOfShape.map_isColimit, BialgCat.forget₂_algebra_map, CategoryTheory.uliftYoneda_obj_map, LeibnizAdjunction.adj_counit_app_right, TopCat.Sheaf.interUnionPullbackConeLift_right, HomologicalComplexUpToQuasiIso.Q_map_eq_of_homotopy, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_inv_app_app, LightProfinite.Extend.functor_map, CategoryTheory.regularTopology.mapToEqualizer_eq_comp, CategoryTheory.MonoidalClosed.curry_eq, CategoryTheory.Groupoid.invEquivalence_functor_map, CategoryTheory.ULift.downFunctor_map, CategoryTheory.Equivalence.counitInv_app_comp_functor_map_η_inverse_assoc, UniformSpaceCat.completionFunctor_map, CategoryTheory.GradedObject.mapTrifunctorMap_map_app_app, CategoryTheory.Over.conePost_map_hom, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedAction_obj_map, IsFreeGroupoid.ext_functor_iff, AlgebraicGeometry.Scheme.Hom.map_appLE_assoc, CategoryTheory.ComposableArrows.opEquivalence_functor_map_app, ComplexShape.Embedding.stupidTruncFunctor_map, mapGrpFunctor_map_app, CategoryTheory.Preadditive.epi_iff_surjective, CategoryTheory.GrothendieckTopology.map_yonedaEquiv', CategoryTheory.FunctorToTypes.shrink_map, CategoryTheory.Comonad.cofree_map_f, CategoryTheory.Comma.snd_map, CategoryTheory.bifunctorComp₁₂Functor_map, comp_mapMon_mul, CategoryTheory.FreeMonoidalCategory.tensorFunc_map_app, CategoryTheory.ProjectiveResolution.Hom.hom'_comp_π', CategoryTheory.WithTerminal.mkCommaObject_left_map, CategoryTheory.ShortComplex.quasiIso_map_of_preservesLeftHomology, SSet.Truncated.Edge.src_eq, CategoryTheory.Idempotents.toKaroubi_map_f, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app, preservesFiniteColimits_iff_forall_exact_map_and_epi, Homotopy.map_nullHomotopicMap, curry₃_obj_obj_obj_map, CategoryTheory.SimplicialObject.Augmented.rightOp_right_map, mapComposableArrowsObjMk₂Iso_hom_app, CategoryTheory.LocalizerMorphism.commShift_iso_hom_app_assoc, CategoryTheory.WithInitial.coconeEquiv_functor_map_hom, flip₂₃Functor_obj_obj_obj_map, CategoryTheory.Subgroupoid.hom.faithful, CategoryTheory.eHomFunctor_map_app, PreservesEpimorphisms.preserves, map_isPullback, Monoidal.map_associator_inv', PartOrdEmb.dual_map, AlgebraicGeometry.disjoint_opensRange_sigmaι, Sequential.sequentialToTop_map, pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, LeftExtension.postcomp₁_obj_hom_app, CategoryTheory.ShortComplex.LeftHomologyMapData.quasiIso_map_iff, CategoryTheory.Limits.CategoricalPullback.π₁_map, groupCohomology.cocyclesMap_comp, CategoryTheory.FinCategory.objAsTypeToAsType_map, AlgebraicGeometry.Scheme.Hom.map_appLE'_assoc, CategoryTheory.MorphismProperty.LeftFraction.map_hom_ofInv_id_assoc, CategoryTheory.Preadditive.mono_iff_injective, CategoryTheory.Localization.SmallHom.equiv_mk, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app', CategoryTheory.enrichedFunctorTypeEquivFunctor_apply_map, flippingEquiv_symm_apply_map_app, AlgebraicGeometry.Scheme.Hom.appIso_inv_naturality, CategoryTheory.toThinSkeleton_map, CategoryTheory.Limits.Fork.ofCone_π, CategoryTheory.ProjectiveResolution.pOpcycles_comp_fromLeftDerivedZero', HomotopicalAlgebra.FibrantObject.toHoCat_map_eq, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal, CategoryTheory.Equivalence.invFunIdAssoc_hom_app, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map, LaxMonoidal.right_unitality_inv, DeltaGenerated.deltaGeneratedToTop_map, π_tensor_id_preserves_coequalizer_inv_desc, LightCondensed.forget_map_val_app, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.functor_map_hom_app, CategoryTheory.Limits.PushoutCocone.ofCocone_pt, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinset_obj_map, CategoryTheory.Limits.DiagramOfCocones.comp, CochainComplex.quasiIso_shift_iff, CategoryTheory.SmallObject.SuccStruct.iterationFunctor_map_succ_assoc, Action.FunctorCategoryEquivalence.inverse_obj_ρ_apply, CategoryTheory.yonedaMon_map_app, CategoryTheory.Limits.FormalCoproduct.powerFunctor_map, CategoryTheory.shrinkYonedaEquiv_naturality, CategoryTheory.ComonadHom.app_δ_assoc, CategoryTheory.instIsSplitEpiMap, AlgebraicGeometry.Scheme.zeroLocus_map, CategoryTheory.Equivalence.unitIso_hom_app_comp_inverse_map_η_functor, CategoryTheory.OplaxFunctor.mapComp_naturality_left_app, CategoryTheory.ExactFunctor.whiskeringLeft_obj_map, AlgebraicGeometry.Scheme.AffineZariskiSite.coequifibered_iff_forall_isLocalizationAway, whiskeringLeft₃_obj_map_app_app_app_app_app, ModuleCat.MonModuleEquivalenceAlgebra.functor_map_hom_apply, PreservesEffectiveEpis.preserves, CategoryTheory.Presheaf.imageSieve_apply, CategoryTheory.Limits.coprod.functor_map_app, CategoryTheory.Iso.compInverseIso_hom_app, CategoryTheory.yonedaEquiv_naturality', CategoryTheory.Grothendieck.pre_map_fiber, CategoryTheory.WithInitial.equivComma_functor_map_left, CategoryTheory.CartesianMonoidalCategory.inv_prodComparison_map_fst_assoc, CategoryTheory.ProjectiveResolution.Hom.hom_f_zero_comp_π_f_zero_assoc, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app_assoc, CategoryTheory.OverPresheafAux.restrictedYonedaObj_map, CondensedMod.hom_naturality_apply, CategoryTheory.CartesianMonoidalCategory.prodComparison_comp, FintypeCat.toLightProfinite_map_hom_hom_apply, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app, MonObj.mopEquiv_inverse_map_hom, AlgebraicGeometry.ι_left_coprodIsoSigma_inv, CategoryTheory.Subgroupoid.mem_ker_iff, PresheafOfModules.toSheaf_map_sheafificationHomEquiv_symm, LaxLeftLinear.μₗ_unitality_assoc, CategoryTheory.CosimplicialObject.Augmented.toArrow_map_right, CategoryTheory.Limits.Types.Colimit.ι_map_apply, map₂HomologicalComplex_map_app, PushoutObjObj.isPushout, AlgebraicGeometry.PresheafedSpace.forget_map, CategoryTheory.Limits.ReflexiveCofork.condition, CategoryTheory.ShortComplex.ShortExact.singleTriangle_mor₁, CategoryTheory.CostructuredArrow.toOver_map_left, CategoryTheory.Limits.PreservesLimitPair.iso_inv_snd, CategoryTheory.NatTrans.mapElements_map_coe, CategoryTheory.CosimplicialObject.Augmented.const_map_right, AlgebraicGeometry.Scheme.homOfLE_appTop, Rep.FiniteCyclicGroup.chainComplexFunctor_map_f, map_inv, CategoryTheory.Limits.MultispanIndex.multispan_map_snd, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counit_app_assoc, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_app, CategoryTheory.cosimplicialSimplicialEquiv_functor_map_app, CategoryTheory.Cat.opFunctor_map, mapBifunctorHomologicalComplex_map_app_f_f, ShiftSequence.induced.shiftIso_hom_app_obj, CategoryTheory.Abelian.Ext.hom_comp_singleFunctor_map_shift, CategoryTheory.Monad.mu_naturality, CategoryTheory.ShortComplex.SnakeInput.functorL₁_map, CategoryTheory.lift_comp_preservesLimitIso_hom, CategoryTheory.RanIsSheafOfIsCocontinuous.fac', AlgebraicGeometry.IsAffineOpen.fromSpec_app_self, AlgebraicGeometry.Spec.toPresheafedSpace_map_op, CategoryTheory.Equivalence.changeInverse_counitIso_inv_app, toPreimages_map, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_0, commShiftIso_hom_naturality_assoc, CategoryTheory.decomposedTo_map, QuadraticModuleCat.forget₂_map_associator_hom, CategoryTheory.flippingIso_inv_toFunctor_map_app_app, SSet.OneTruncation₂.nerveEquiv_symm_apply_map, CategoryTheory.shiftFunctorAdd'_zero_add_hom_app, comp_mapCommMon_mul, CategoryTheory.Comonad.Coalgebra.coassoc, CategoryTheory.MonadIso.toNatIso_inv, CategoryTheory.Presheaf.FamilyOfElementsOnObjects.IsCompatible.familyOfElements_apply, CategoryTheory.Adjunction.comp_counit_app, SSet.Truncated.StrictSegal.spine_δ_arrow_gt, mapArrow_map_left, CategoryTheory.Limits.CategoricalPullback.π₂_map, CategoryTheory.Cat.Hom.comp_map, mapBicone_π, CategoryTheory.SingleFunctors.shiftIso_add_inv_app, CategoryTheory.ShortComplex.π₂_map, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app'_assoc, CategoryTheory.subterminalsEquivMonoOverTerminal_inverse_map, CategoryTheory.uliftYonedaEquiv_uliftYoneda_map, CategoryTheory.Limits.instIsIsoEqualizerComparison, ShiftSequence.induced_shiftIso_hom_app_obj_assoc, CategoryTheory.Localization.SmallShiftedHom.equiv_shift', CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂'_map_app_app, CategoryTheory.ShortComplex.mapRightHomologyIso_hom_naturality, CategoryTheory.yoneda_obj_map, CategoryTheory.Cat.opFunctorInvolutive_hom_app_toFunctor_map, OplaxMonoidal.δ_natural_left, CategoryTheory.CartesianClosed.uncurry_natural_right, CategoryTheory.Limits.PreservesPullback.iso_inv_snd_assoc, CategoryTheory.Limits.WidePullbackShape.equivalenceOfEquiv_functor_map_term, CategoryTheory.Monad.mu_naturality_assoc, mapBiproduct_inv, TannakaDuality.FiniteGroup.forget_map, CategoryTheory.SmallObject.ιFunctorObj_eq, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_functor_map_f, commShiftIso_comp_inv_app, CategoryTheory.StructuredArrow.mkPostcomp_comp, leftExtensionEquivalenceOfIso₁_inverse_map_right, Monoidal.toUnit_ε, Condensed.epi_iff_locallySurjective_on_compHaus, CategoryTheory.CartesianMonoidalCategory.inv_prodComparison_map_snd_assoc, CategoryTheory.ComposableArrows.whiskerLeft_map, mapComon_obj_comon_comul, CategoryTheory.Limits.spanCompIso_inv_app_right, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv, CategoryTheory.Limits.MultispanIndex.map_snd, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagramOfIsLimit_map, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_symm_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app, CategoryTheory.Adjunction.leftAdjointCompIso_inv_app, CategoryTheory.Sum.homInduction_left, CochainComplex.mappingCone.map_inr, CategoryTheory.CatCommSq.vComp_iso_hom_app, DerivedCategory.HomologySequence.epi_homologyMap_mor₁_iff, CategoryTheory.LocalizerMorphism.commShift_iso_inv_app_assoc, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_ε, CategoryTheory.LocalizerMorphism.equiv_smallHomMap', map_shiftFunctorCompIsoId_inv_app_assoc, CategoryTheory.coyonedaEquiv_naturality, CategoryTheory.CartesianMonoidalCategory.map_toUnit_comp_terminalComparison, OneHypercoverDenseData.essSurj.presheaf_map, CategoryTheory.Limits.im_map, LightCondensed.isLocallySurjective_iff_locallySurjective_on_lightProfinite, AlgebraicGeometry.Scheme.basicOpen_res_eq, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom_assoc, whiskeringLeft₂_obj_map_app_app_app, AlgebraicGeometry.IsZariskiLocalAtTarget.coprodMap, mapMonFunctor_map_app_hom, AlgebraicGeometry.IsFinite.instDescScheme, IsEventuallyConstantTo.isIso_map, PresheafOfModules.pushforward_obj_map_apply, CategoryTheory.CostructuredArrow.mapIso_functor_map_right, CategoryTheory.endofunctorMonoidalCategory_tensorObj_map, CategoryTheory.ShortComplex.quasiIso_map_iff_of_preservesRightHomology, biprodComparison_fst_assoc, AlgebraicGeometry.Scheme.Hom.app_invApp', CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_hom_app, AlgebraicGeometry.Scheme.Hom.stalkFunctor_toImage_injective, CategoryTheory.Limits.instIsIsoKernelComparison, CategoryTheory.WithTerminal.equivComma_functor_obj_hom_app, mapMon_obj_mon_one, CategoryTheory.CostructuredArrow.functor_map, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂, CategoryTheory.Over.toOverSectionsAdj_counit_app, map.instIsComon_Hom, AlgebraicGeometry.Scheme.Hom.inl_normalizationCoprodIso_hom_fromNormalization_assoc, HomologicalComplex.homologyOp_hom_naturality_assoc, AlgebraicGeometry.exists_appTop_map_eq_zero_of_isAffine_of_isLimit, comp_homologySequenceδ, CategoryTheory.regularTopology.isLocallySurjective_iff, CategoryTheory.StructuredArrow.toCostructuredArrow_map, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app, groupHomology.mapCycles₂_comp_apply, DerivedCategory.HomologySequence.mono_homologyMap_mor₂_iff, TopCat.Presheaf.SubmonoidPresheaf.map, Fiber.fiberInclusion_homMk, mapShortComplex_map_τ₃, map_shiftFunctorComm_assoc, CategoryTheory.WithInitial.equivComma_inverse_map_app, CategoryTheory.Triangulated.TStructure.triangleLTGE_map_hom₃, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_hom_app_coe, CategoryTheory.Comma.left_hom_inv_right, CategoryTheory.prodComonad_map, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompYoneda, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp_assoc, BddOrd.forget_map, OplaxMonoidal.right_unitality_hom, CategoryTheory.Cat.FreeRefl.quotientFunctor_map_id, CategoryTheory.Limits.Types.Colimit.w_apply', Monoidal.map_associator_inv'_assoc, IsCoverDense.Types.appHom_restrict, CategoryTheory.Quotient.functor_map_eq_iff, CategoryTheory.Limits.DiagramOfCones.conePoints_map, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp, AlgebraicTopology.DoldKan.map_PInfty_f, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_map_hom_hom, CategoryTheory.Limits.colimitHomIsoLimitYoneda_hom_comp_π_assoc, CategoryTheory.Limits.Types.binaryProductFunctor_map_app, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_app_assoc, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_map, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_functor_map, map_shiftFunctorCompIsoId_hom_app_assoc, CategoryTheory.ShiftMkCore.assoc_inv_app_assoc, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.NatTrans.sum_app_inl, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₁, CategoryTheory.Retract.map_r, CategoryTheory.CategoryOfElements.ext_iff, AlgebraicGeometry.RingedSpace.isUnit_res_of_isUnit_germ, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functor_map_app_hom, CategoryTheory.CostructuredArrow.map₂_map_right, CategoryTheory.Limits.Wedge.condition, CategoryTheory.Sheaf.ΓObjEquivSections_naturality_symm, CategoryTheory.Limits.HasCoequalizersOfHasPushoutsAndBinaryCoproducts.pushoutInl_eq_pushout_inr, map_mono, HomologicalComplex.shortComplexFunctor_map_τ₁, AlgebraicGeometry.HasAffineProperty.coprodDesc_affineAnd, Braided.braided, CategoryTheory.GradedObject.map_map, AddMonCat.FilteredColimits.cocone_naturality, Rep.quotientToInvariantsFunctor_map_hom, CategoryTheory.Abelian.extFunctor_map_app, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_map_app_app, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counitIso_hom_app, CategoryTheory.StructuredArrow.toUnder_map_right, CategoryTheory.ShortComplex.HomologyMapData.map_right, CategoryTheory.InjectiveResolution.toRightDerivedZero'_naturality, CategoryTheory.PreZeroHypercover.map_f, CategoryTheory.Square.map_f₃₄, CategoryTheory.MorphismProperty.RightFraction.map_ofInv_hom_id_assoc, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_inverse_map, commShiftIso_hom_naturality, CategoryTheory.overToCoalgebra_map_f, CategoryTheory.Comonad.adj_counit, CommShift.comp_commShiftIso_hom_app, CategoryTheory.CosimplicialObject.Augmented.toArrow_map_left, mapHomotopy_hom, CategoryTheory.ProjectiveResolution.Hom.hom'_comp_π'_assoc, CategoryTheory.StructuredArrow.IsUniversal.hom_desc, HomologicalComplex.singleObjOpcyclesSelfIso_inv_naturality, CategoryTheory.TwoSquare.hComp_app, Rep.quotientToCoinvariantsFunctor_map_hom, BddDistLat.dual_map, CategoryTheory.ShortComplex.SnakeInput.functorP_map, TopCat.presheafToTypes_map, CategoryTheory.Limits.colimit.w_apply, SemiNormedGrp.completion.map_normNoninc, CategoryTheory.NatTrans.whiskerRight_app_tensor_app, mapComposableArrowsObjMk₁Iso_hom_app, CategoryTheory.η_naturality, AddGrpCat.toGrp_map, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetObj_map, mapBifunctorHomologicalComplex_obj_obj_X_d, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerRight, HomologicalComplex.cyclesOpIso_inv_naturality, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverse_map_hom_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_map_bijective, AddCommMonCat.coyoneda_map_app, CategoryTheory.Limits.CategoricalPullback.Hom.w_assoc, CategoryTheory.Sheaf.ΓRes_map_assoc, mapComposableArrows_obj_map, CategoryTheory.Under.mapFunctor_map, SimplicialObject.Split.nondegComplexFunctor_map_f, relativelyRepresentable.isPullback, AlgebraicTopology.DoldKan.Γ₀'_map_F, CategoryTheory.Limits.pointwiseProduct_map, AlgebraicGeometry.Scheme.restrictFunctorΓ_hom_app, AlgebraicGeometry.Scheme.Cover.functorOfLocallyDirected_map, CategoryTheory.Pseudofunctor.bijective_toDescentData_map_iff, CategoryTheory.Limits.inv_prodComparison_map_fst, CategoryTheory.Groupoid.CategoryTheory.Functor.mapVertexGroup_apply, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedAction_map_app, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_hom_app_app, CategoryTheory.CatCommSq.iso_inv_naturality_assoc, CategoryTheory.Under.liftCone_π_app, CategoryTheory.ProjectiveResolution.fromLeftDerivedZero'_naturality, CategoryTheory.Limits.Cocone.ofCofork_ι, AlgebraicGeometry.Scheme.Γ_map_op, HomologicalComplex.opcyclesOpIso_hom_naturality, CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_hom_assoc, CategoryTheory.Presieve.FamilyOfElements.isAmalgamation_iff_ofArrows, CategoryTheory.Over.pullback_map_left, sheafPushforwardContinuous_obj_val_map, CategoryTheory.SmallObject.instIsIsoRightAppArrowMapToTypeOrdFunctorIterationFunctor, TopCat.Presheaf.stalkSpecializes_stalkFunctor_map_assoc, CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_inv_assoc, CategoryTheory.NatTrans.naturality_app_assoc, groupHomology.mapShortComplexH1_comp, CategoryTheory.Cat.FreeRefl.quotientFunctor_map_nil, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_inv_app_app, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.F_map, CategoryTheory.Limits.fiberwiseColim_map_app, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_map_fiber, AlgebraicGeometry.SheafedSpace.Γ_map, CategoryTheory.MorphismProperty.Comma.mapLeft_map_right, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_pt, AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id, CategoryTheory.Limits.DiagramOfCocones.mkOfHasColimits_map_hom, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_functor_map_hom, CategoryTheory.Comma.mapRightIso_functor_map_right, leftKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_app_apply, Rep.Tor_map, CategoryTheory.Comma.limitAuxiliaryCone_π_app, CategoryTheory.Square.evaluation₁_map, CategoryTheory.Limits.coequalizerComparison_map_desc, CategoryTheory.Pseudofunctor.presheafHom_map, CategoryTheory.Limits.limit.post_π_assoc, toOplaxFunctor'_map, CategoryTheory.FreeMonoidalCategory.inclusion_map, CategoryTheory.nerveFunctor_map, CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_map_left, postcompose₃_map_app_app_app_app, CategoryTheory.Sheaf.ΓObjEquivHom_naturality_symm, AlgebraicGeometry.Scheme.Hom.inl_normalizationCoprodIso_hom_fromNormalization, relativelyRepresentable.pullback₃.map_p₁_comp_assoc, CategoryTheory.WithInitial.equivComma_functor_map_right_app, CategoryTheory.Join.opEquiv_inverse_map_inclLeft_op, CategoryTheory.GradedObject.mapBifunctorRightUnitor_inv_apply, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply, fintypeToFinBoolAlgOp_map, CategoryTheory.Grothendieck.toTransport_fiber, HomotopicalAlgebra.FibrantObject.HoCat.resolutionObj_hom_ext, IsEventuallyConstantFrom.isoMap_inv_hom_id, CategoryTheory.Comma.toIdPUnitEquiv_functor_map, ranObjObjIsoLimit_inv_π_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_hom_app_app, CategoryTheory.OplaxFunctor.mapComp_assoc_right_app_assoc, complete_distinguished_essImageDistTriang_morphism, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π_assoc, PullbackObjObj.ofHasPullback_π, CategoryTheory.Over.sections_obj, CategoryTheory.Subgroupoid.Map.arrows_iff, Rep.resIndAdjunction_counit_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_map_right, comp_mapCommGrp_mul, CategoryTheory.Limits.fiberwiseColimitLimitIso_inv_app, CategoryTheory.CosimplicialObject.Truncated.whiskering_obj_map_app, FinPartOrd.dual_map, SheafOfModules.freeFunctor_map, AlgebraicGeometry.opensDiagram_obj, CompleteLat.dual_map, CategoryTheory.Idempotents.whiskeringLeft_obj_preimage_app, AlgebraicGeometry.PresheafedSpace.GlueData.f_invApp_f_app_assoc, CategoryTheory.Limits.cospanCompIso_inv_app_right, CategoryTheory.Equivalence.sheafCongr.unitIso_hom_app_val_app, CategoryTheory.AsSmall.up_map_down, typeToBoolAlgOp_map, CategoryTheory.Subfunctor.map, CategoryTheory.Iso.map_hom_inv_id_app, op_commShiftIso_inv_app_assoc, OplaxMonoidal.ofBifunctor.topMapᵣ_app, CategoryTheory.CostructuredArrow.toStructuredArrow'_map, CategoryTheory.ShortComplex.mapRightHomologyIso_inv_naturality_assoc, CommRingCat.monoidAlgebra_map, Bipointed.swapEquiv_functor_map_toFun, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_map_mkHom_homMk_id, map_shiftFunctorCompIsoId_hom_app, LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom_assoc, CategoryTheory.SimplicialObject.Augmented.const_map_right, CategoryTheory.Limits.sigmaConst_obj_map, CategoryTheory.ULiftHom.up_map_down, Initial.extendCone_map_hom, mapArrow_map_right, CommRingCat.Colimits.cocone_naturality_components, SheafOfModules.conjugateEquiv_pullbackComp_inv, CategoryTheory.Limits.Cone.toCostructuredArrow_map, CategoryTheory.NatTrans.CommShiftCore.shift_app_assoc, CategoryTheory.typeEquiv_functor_obj_val_map, SSet.const_app, coe_mapAddHom, HasFibers.Fib.map_homMk, LaxMonoidal.tensorHom_ε_comp_μ_assoc, CategoryTheory.Limits.colimit.map_post, CategoryTheory.Join.homInduction_left, homologySequence_exact₃, AlgebraicGeometry.instIsOpenImmersionMapScheme, CategoryTheory.shiftFunctorCompIsoId_add'_hom_app, AddGrpCat.forget₂_map_ofHom, AlgebraicGeometry.sigmaι_eq_iff, CategoryTheory.ProjectiveResolution.leftDerived_app_eq, CategoryTheory.MonadHom.app_μ_assoc, AlgebraicGeometry.opensCone_π_app, CategoryTheory.CostructuredArrow.w, CategoryTheory.bifunctorComp₂₃Functor_map, HomologicalComplex.shortComplexFunctor_map_τ₃, CategoryTheory.Equivalence.invFunIdAssoc_inv_app, ContinuousCohomology.I_map_hom, CategoryTheory.Monad.Algebra.assoc, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.leftUnitor_hom_unit_app, CategoryTheory.Cokleisli.Adjunction.fromCokleisli_map, AlgebraicGeometry.Scheme.Hom.appIso_inv_naturality_assoc, CategoryTheory.leftDualFunctor_map, AlgebraicGeometry.Scheme.Hom.appLE_map_assoc, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₂, CategoryTheory.GrothendieckTopology.sheafToPresheaf_map_sheafComposeNatTrans_eq_sheafifyCompIso_inv, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_two, CategoryTheory.toOverIteratedSliceForwardIsoPullback_hom_app_left, CategoryTheory.StructuredArrow.homMk'_id, CommShift₂.comm, CategoryTheory.Triangulated.SpectralObject.triangle_mor₂, IsEventuallyConstantFrom.isoMap_hom, CategoryTheory.pullbackShiftFunctorAdd'_hom_app, CategoryTheory.Limits.IsColimit.homEquiv_symm_naturality, CategoryTheory.Prod.snd_map, CategoryTheory.Monoidal.transportStruct_whiskerRight, CategoryTheory.Equivalence.induced_inverse_map, CategoryTheory.ε_naturality, CategoryTheory.Presieve.FamilyOfElements.singletonEquiv_symm_apply, AlgebraicTopology.normalizedMooreComplex_map, LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv_assoc, CategoryTheory.ProjectiveResolution.lift_commutes, CategoryTheory.StructuredArrow.w_prod_snd, CategoryTheory.Localization.Monoidal.μ_inv_natural_left_assoc, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_inv_app, flip₁₃Functor_obj_map_app_app, CategoryTheory.Limits.BinaryBicone.toBiconeFunctor_map_hom, CategoryTheory.ExponentiableMorphism.ev_coev_assoc, CategoryTheory.Limits.reflexiveCoforkEquivCofork_functor_obj_pt, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_map_left_app, CategoryTheory.WithInitial.mkCommaObject_right_map, CategoryTheory.shiftFunctorZero_inv_app_shift, ofOpSequence_map_homOfLE_succ, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.map_f', HomologicalComplex.HomologySequence.mapSnakeInput_f₁, HomotopicalAlgebra.instWeakEquivalenceMapFullSubcategoryι, CategoryTheory.WithInitial.equivComma_functor_obj_hom_app, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_hom_c_app, Representation.coind'_apply_apply, CategoryTheory.Monoidal.InducingFunctorData.tensorHom_eq, Preord.forget_map, HomologicalComplex.homologyFunctor_map, CategoryTheory.Adjunction.commShiftIso_inv_app_counit_app_assoc, CategoryTheory.Limits.Multicofork.map_ι_app, CochainComplex.shiftFunctor_map_f, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_map, CategoryTheory.Limits.reflexivePair_map_left, CochainComplex.quasiIsoAt_shift_iff, LaxMonoidal.ε_tensorHom_comp_μ_assoc, curryingFlipEquiv_symm_apply_obj_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_app_snd_app, chosenProd_map, CategoryTheory.Limits.limit.post_post, SheafOfModules.pushforwardPushforwardAdj_unit_app_val_app, commShiftIso_inv_naturality_assoc, SSet.Truncated.HomotopyCategory.descOfTruncation_map_homMk, AlgebraicGeometry.instSurjectiveDescI₀SchemeF, CategoryTheory.CoreSmallCategoryOfSet.functor_map, CategoryTheory.Pretriangulated.contractibleTriangleFunctor_map_hom₃, OneHypercoverDenseData.SieveStruct.fac, AlgebraicTopology.DoldKan.Γ₀_map_app, CategoryTheory.uliftYoneda_obj_map_down, obj.ε_def, SimplexCategory.rev_map_apply, CategoryTheory.PrelaxFunctor.mapFunctor_map, CategoryTheory.ObjectProperty.leftOrthogonal.map_bijective_of_isTriangulated, AlgebraicGeometry.Scheme.Hom.appIso_inv_appLE_assoc, CategoryTheory.shiftFunctorAdd'_assoc_inv_app_assoc, LightCondensed.free_internallyProjective_iff_tensor_condition', curry₃_map_app_app_app, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_map_mkHom_homMk_homMk, CategoryTheory.Limits.reflexivePair_map_right, CategoryTheory.Iso.map_inv_hom_id, CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois_apply, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap_assoc, MonCat.adjoinOne_map, ProfiniteGrp.profiniteCompletion_map, CategoryTheory.rightDualFunctor_map, CategoryTheory.biconeMk_map, CategoryTheory.Comonad.map_counit_app, CategoryTheory.Limits.CategoricalPullback.Hom.w', CompHausLike.LocallyConstant.adjunction_left_triangle, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight_symm_apply, CategoryTheory.Adjunction.ε_comp_map_ε, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_assoc, LaxRightLinear.μᵣ_naturality_right, HomologicalComplex.complexOfFunctorsToFunctorToComplex_map_app_f, CategoryTheory.Limits.coprodComparison_inr_assoc, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map_assoc, curryingEquiv_symm_apply_map_app, AddCommGrpCat.forget₂_addGrp_map_ofHom, leftOpRightOpEquiv_inverse_map, HomotopicalAlgebra.CofibrantObject.HoCat.resolutionObj_hom_ext, CategoryTheory.SimplicialObject.Truncated.trunc_obj_map, CategoryTheory.Iso.isoFunctorOfIsoInverse_inv_app, CategoryTheory.Cat.opFunctorInvolutive_inv_app_toFunctor_map, CategoryTheory.ProjectiveResolution.Hom.hom_comp_π, CategoryTheory.Monad.map_unit_app, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_comp_π_assoc, Final.extendCocone_obj_ι_app', CategoryTheory.ShortComplex.quasiIso_map_iff_of_preservesLeftHomology, CategoryTheory.Presheaf.uliftYonedaAdjunction_homEquiv_app, CategoryTheory.Sheaf.isLocallyInjective_forget, CategoryTheory.Equivalence.counitInv_app_comp_functor_map_η_inverse, CategoryTheory.flippingIso_hom_toFunctor_obj_obj_map, groupHomology.map_id_comp_H0Iso_hom_assoc, CategoryTheory.TransfiniteCompositionOfShape.iic_F, CategoryTheory.ProjectiveResolution.fromLeftDerivedZero'_naturality_assoc, HasFibers.Fib.hom_ext_iff, CategoryTheory.WithInitial.equivComma_inverse_obj_map, AlgebraicGeometry.Scheme.Γ_map, elementsFunctor_map, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_hom_app_val_app, mapBiproduct_hom, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerRight_assoc, leftKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, CoreMonoidal.associativity, CategoryTheory.CostructuredArrow.grothendieckProj_map, AlgebraicGeometry.AffineScheme.forgetToScheme_map, CategoryTheory.SimplicialObject.whiskering_map_app_app, SheafOfModules.restrictScalars_map_val, ModuleCat.restrictScalarsComp'App_hom_naturality, SSet.Truncated.hoFunctor₂_naturality, flip₁₃_obj_obj_map, CategoryTheory.Monad.beckCofork_pt, CochainComplex.homotopyOp_hom_eq, CategoryTheory.Abelian.PreservesImage.iso_inv_ι_assoc, RightExtension.postcomp₁_map_left_app, CategoryTheory.cones_obj_map_app, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π_assoc, CategoryTheory.PreGaloisCategory.fiberBinaryProductEquiv_symm_snd_apply, CategoryTheory.Limits.sigmaConst_map_app, CategoryTheory.shiftComm', SimplexCategory.rev_map_σ, CategoryTheory.MonoidalCategory.curriedTensor_obj_map, TopCat.Presheaf.stalkFunctor_map_germ_apply, TopCat.Presheaf.germ_res_apply', CategoryTheory.LocalizerMorphism.homMap_apply_assoc, CategoryTheory.Under.forget_map, pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.WithTerminal.ofCommaObject_map, LaxMonoidal.associativity_inv, AlgebraicGeometry.Scheme.LocalRepresentability.yoneda_toGlued_yonedaGluedToSheaf_assoc, CategoryTheory.Square.opFunctor_map_τ₁, CategoryTheory.Limits.Cocones.functoriality_obj_ι_app, CategoryTheory.Limits.coprodComparison_inr, CategoryTheory.Quiv.lift_map, CategoryTheory.preservesColimitIso_inv_comp_desc_assoc, CategoryTheory.Pretriangulated.rotate_map_hom₂, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_app, WellOrderInductionData.Extension.map_succ, CategoryTheory.Limits.instIsIsoCokernelComparison, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_inv_app_val_app, CategoryTheory.Limits.biprod.map_lift_mapBiprod, CategoryTheory.Adjunction.homEquiv_naturality_right_square_iff, CategoryTheory.conjugateEquiv_counit, CategoryTheory.NatTrans.CommShiftCore.shift_app_comm_assoc, AlgebraicGeometry.Scheme.Hom.inr_normalizationCoprodIso_hom_fromNormalization_assoc, CategoryTheory.StructuredArrow.post_map, CochainComplex.IsKProjective.Qh_map_bijective, Condensed.isoFinYonedaComponents_inv_comp, CategoryTheory.LocalizerMorphism.smallHomMap'_mk, Initial.limit_cone_comp_aux, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_left, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂'_map_app_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_whiskerLeft, flippingEquiv_symm_apply_obj_map, prod_map, CategoryTheory.Equivalence.unitInv_app_inverse, CategoryTheory.Square.flipFunctor_map_τ₁, CategoryTheory.ShortComplex.ShortExact.singleTriangle_mor₂, LeftExtension.postcomp₁_obj_right_map, CategoryTheory.Equivalence.sheafCongr.functor_map_val_app, AlgebraicGeometry.Scheme.Opens.ι_appTop, groupHomology.mapShortComplexH2_comp, CategoryTheory.bifunctorComp₁₂Obj_obj_map, ranges_directed, CategoryTheory.Monad.instHasCoequalizerMapAAppCounitObjAOfHasCoequalizerOfIsSplitPair, ranObjObjIsoLimit_hom_π_assoc, HomologicalComplex.cyclesOpIso_hom_naturality_assoc, flip₂₃Functor_obj_obj_map_app, toOplaxFunctor_mapComp, CategoryTheory.RetractArrow.map_r_left, CategoryTheory.Triangulated.Octahedron.map_m₁, LaxMonoidal.tensorUnit_whiskerLeft_comp_leftUnitor_hom, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidalObj_map, CategoryTheory.Limits.preserves_cokernel_iso_comp_cokernel_map, CategoryTheory.Comma.toPUnitIdEquiv_inverse_map_left, AddCommGrpCat.coyonedaType_obj_map, CochainComplex.truncate_map_f, OplaxRightLinear.δᵣ_unitality_hom, CategoryTheory.shiftFunctorAdd_assoc_hom_app_assoc, CategoryTheory.GlueData.mapGlueData_t, CategoryTheory.NatTrans.mapHomologicalComplex_naturality, CategoryTheory.Limits.PreservesPushout.inl_iso_hom_assoc, flip₂₃Functor_map_app_app_app, CategoryTheory.ConcreteCategory.forget₂_comp_apply, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app, CategoryTheory.ihom.coev_naturality_assoc, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd, PresheafOfModules.toPresheaf_map_app_apply, RepresentableBy.homEquiv_comp, MonCat.FilteredColimits.cocone_naturality, AlgebraicGeometry.Scheme.map_basicOpen, CategoryTheory.ShortComplex.FunctorEquivalence.functor_obj_map, CategoryTheory.Limits.FormalCoproduct.cechFunctor_map_app, CategoryTheory.LocalizerMorphism.equiv_smallShiftedHomMap, CategoryTheory.ShortComplex.cyclesFunctor_map, CategoryTheory.SmallObject.restrictionLE_map, CategoryTheory.Adjunction.unit_app_shift_commShiftIso_inv_app_assoc, AlgebraicGeometry.coprodSpec_coprodMk, groupCohomology.map_id_comp_H0Iso_hom, commShiftOfLocalization.iso_inv_app_assoc, CategoryTheory.OrthogonalReflection.iteration_map_succ_assoc, CategoryTheory.Triangulated.SpectralObject.Hom.comm_assoc, Fiber.instIsHomLiftIdMapFiberInclusion, SSet.Truncated.StrictSegal.spineToSimplex_vertex, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality_assoc, CategoryTheory.CategoryOfElements.π_map, CategoryTheory.Idempotents.functorExtension₂_obj_obj_p, CategoryTheory.Localization.Monoidal.μ_inv_natural_right_assoc, CategoryTheory.Limits.FormalCoproduct.evalOp_map_app, CategoryTheory.Pretriangulated.rotate_map_hom₃, partialRightAdjoint_map, CategoryTheory.IsFinitelyPresentable.exists_eq_of_isColimit, AlgebraicGeometry.Scheme.Cover.sigmaFunctor_map, CategoryTheory.Limits.coconeOfDiagramTerminal_ι_app, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₂, LaxMonoidal.μ_natural_left_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_map_fst_app, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_map_right, CategoryTheory.Limits.π_comp_cokernelComparison_assoc, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w_apply, CategoryTheory.shiftFunctorZero_hom_app_shift, Types.monoOverEquivalenceSet_functor_map, ModuleCat.homEquiv_extendScalarsComp, CategoryTheory.Equivalence.changeFunctor_unitIso_inv_app, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_hom_inv_id_assoc, TopCat.Sheaf.objSupIsoProdEqLocus_inv_snd, CategoryTheory.CostructuredArrow.homMk'_left, CategoryTheory.Over.monObjMkPullbackSnd_one, CategoryTheory.unitOfTensorIsoUnit_inv_app, CategoryTheory.Square.toArrowArrowFunctor'_map_left_right, AlgebraicGeometry.instMonoObjWalkingSpanCompSchemeSpanForgetNoneWalkingPairSomeMapInitOfIsOpenImmersion, CategoryTheory.StructuredArrow.homMk'_right, LaxMonoidal.associativity_inv_assoc, QuasiIsoAt.quasiIso, CategoryTheory.NatTrans.naturality_app, AddCommGrpCat.Colimits.Quot.map_ι, CategoryTheory.InjectiveResolution.desc_commutes, ModuleCat.ExtendScalars.map_tmul, CategoryTheory.GrothendieckTopology.diagram_map, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_counitIso, CategoryTheory.Limits.reflexiveCoforkEquivCofork_functor_obj_π, CategoryTheory.Adjunction.CommShift.compatibilityCounit_left, AlgebraicTopology.DoldKan.map_P, CategoryTheory.MonoidalCategory.externalProductBifunctorCurried_map_app_app_app, CategoryTheory.StructuredArrow.pre_map_left, op_commShiftIso_inv_app, QuadraticModuleCat.cliffordAlgebra_map, PresheafOfModules.map_comp, CategoryTheory.cocones_obj_map_app, CategoryTheory.Core.functorToCore_map_iso_hom, LaxRightLinear.μᵣ_associativity_assoc, Monoidal.map_associator', CategoryTheory.obj_η_app_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃'_map_app_app, CategoryTheory.Sieve.mem_functorPushforward_inverse, CategoryTheory.Comma.inv_left_hom_right, HomologicalComplex.mapBifunctor₂₃.d₁_eq, map_braiding_assoc, SSet.Truncated.StrictSegal.spine_δ_vertex_ge, CategoryTheory.Comonad.coassoc_assoc, AlgebraicGeometry.PresheafedSpace.map_id_c_app, SSet.StrictSegal.spineToSimplex_edge, CategoryTheory.ExponentiableMorphism.ev_naturality_assoc, CategoryTheory.Limits.inv_piComparison_comp_map_π, CategoryTheory.Idempotents.DoldKan.η_inv_app_f, BoolAlg.dual_map, mapSquare_map_τ₄, CategoryTheory.typeEquiv_inverse_map, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, CategoryTheory.Adjunction.Triple.adj₁_counit_app_rightToLeft_app_assoc, CategoryTheory.Limits.limit.map_post, TopCat.Presheaf.SheafConditionEqualizerProducts.res_π, CategoryTheory.Limits.map_lift_kernelComparison, CategoryTheory.SimplicialObject.Augmented.whiskering_map_app_left, CategoryTheory.SingleObj.differenceFunctor_map, CategoryTheory.AdditiveFunctor.forget_map, TopCat.Presheaf.germ_res, CategoryTheory.SmallObject.SuccStruct.iterationFunctor_map_succ, ModuleCat.restrictScalarsComp'App_inv_naturality, AlgebraicGeometry.PresheafedSpace.GlueData.f_invApp_f_app, OplaxMonoidal.δ_comp_whiskerLeft_δ, AlgebraicGeometry.Scheme.Hom.resLE_comp_resLE_assoc, CategoryTheory.Comma.equivProd_inverse_map_right, SheafOfModules.pushforward_map_val, CategoryTheory.InjectiveResolution.desc_commutes_assoc, HomologicalComplex.single_map_f_self_assoc, SSet.Truncated.StrictSegal.spineToSimplex_edge, CategoryTheory.GrothendieckTopology.Point.jointly_surjective, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_symm_apply, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_comp_π, SSet.Truncated.spine_arrow, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_app, HomologicalComplex.ι_mapBifunctorMap_assoc, HomologicalComplex.homologicalComplexToDGO_map_f, CategoryTheory.map_functorial_obj, CategoryTheory.uncurry_expComparison, leftExtensionEquivalenceOfIso₁_inverse_obj_hom_app, CategoryTheory.CategoryOfElements.fromCostructuredArrow_map_coe, CategoryTheory.GradedObject.mapBifunctor_map_app, CategoryTheory.Equivalence.leftOp_inverse_map, CategoryTheory.Limits.WidePushoutShape.wideSpan_map, CategoryTheory.CostructuredArrow.proj_map, CategoryTheory.forget₂_comp_apply, whiskeringLeft₃_obj_obj_obj_map_app_app_app, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_inv_apply, CategoryTheory.Idempotents.KaroubiUniversal₁.counitIso_hom_app_app_f, CategoryTheory.FunctorToTypes.map_comp_apply, CategoryTheory.Monad.monToMonad_map_toNatTrans, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_whiskerLeft, CategoryTheory.Square.opFunctor_map_τ₂, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_tensorHom_hom_eq_tensorHom, Action.res_map_hom, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₃, CategoryTheory.Adjunction.commShiftIso_hom_app_counit_app_shift_assoc, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_ε_assoc, AlgebraicTopology.DoldKan.degeneracy_comp_PInfty_assoc, CategoryTheory.ComposableArrows.mk₁_map, CategoryTheory.Triangulated.TStructure.triangleLTGE_map_hom₂, mapBiprod_hom, CategoryTheory.ofTypeMonad_map, CategoryTheory.Join.homInduction_right, CategoryTheory.Limits.ColimitPresentation.w_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_app_assoc, SheafOfModules.pushforwardComp_hom_app_val_app, flipping_functor_obj_map_app, CategoryTheory.Bicategory.postcomposing_map_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_inv_app, CategoryTheory.ShortComplex.π₁_map, CategoryTheory.Limits.colimit.ι_post_assoc, CategoryTheory.MorphismProperty.shift, CategoryTheory.Paths.lift_cons, OplaxMonoidal.comp_η, CategoryTheory.Pseudofunctor.mapComp'_hom_naturality, CategoryTheory.Idempotents.KaroubiUniversal₁.counitIso_inv_app_app_f, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app, CategoryTheory.StructuredArrow.map_map_left, eventualRange_mapsTo, CategoryTheory.GradedObject.mapBifunctorObjObjSingle₀Iso_inv, CategoryTheory.GrothendieckTopology.Point.instIsIsoMapFunctorOppositePresheafFiberToSheafify, PullbackObjObj.mapArrowLeft_left, CategoryTheory.yonedaGrpObj_map, CategoryTheory.Iso.map_hom_inv_id_eval_assoc, unop_map, CategoryTheory.Limits.Types.isPushout_of_bicartSq, CategoryTheory.eHomFunctor_obj_map, CategoryTheory.MonoidalClosed.uncurry_ihom_map, TopCat.Presheaf.pullback_obj_obj_ext_iff, CategoryTheory.Limits.IsZero.map, CategoryTheory.Endofunctor.Algebra.functorOfNatTrans_map_f, CategoryTheory.Limits.PreservesPushout.inr_iso_hom, RepresentableBy.homEquiv_unop_comp, AlgebraicGeometry.Scheme.IdealSheafData.isLocalization_away, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_map_left_right, CategoryTheory.SingleFunctors.postcomp_shiftIso_inv_app, CategoryTheory.shiftFunctorAdd_assoc_inv_app_assoc, SSet.N.le_iff_exists_mono, mapCone₂_π_app, AlgebraicGeometry.Scheme.ofRestrict_toLRSHom_c_app, CategoryTheory.Limits.PreservesLimitPair.iso_inv_snd_assoc, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc, CategoryTheory.Limits.Cones.functoriality_map_hom, CategoryTheory.StructuredArrow.mkPostcomp_right, ModuleCat.restrictScalarsComp'App_inv_naturality_assoc, CategoryTheory.Limits.cokernel_map_comp_cokernelComparison, OplaxMonoidal.δ_comp_η_tensorHom, CategoryTheory.ShortComplex.ShortExact.injective_f, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_map_left_left, GrpCat.forget₂_map, obj.μ_def, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_hom_app, CategoryTheory.regularTopology.equalizerCondition_iff_isIso_lift, CategoryTheory.Idempotents.KaroubiKaroubi.inverse_map_f, CategoryTheory.Limits.cokernelComparison_map_desc, LightCondMod.LocallyConstant.instIsIsoLightCondSetMapForgetAppLightCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, CategoryTheory.Adjunction.compYonedaIso_inv_app_app, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f, LinOrd.forget_map, CategoryTheory.Limits.parallelPair_functor_obj, FullyFaithful.map_surjective, CategoryTheory.Equivalence.changeInverse_counitIso_hom_app, CategoryTheory.MorphismProperty.CostructuredArrow.toOver_map, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_obj_map_app, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.sq, CategoryTheory.Limits.sigmaComparison_map_desc_assoc, SSet.Truncated.HomotopyCategory.homToNerveMk_app_one, ι_biproductComparison', CategoryTheory.ObjectProperty.ihom_map, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_pullback_map, MonObj.mopEquiv_functor_map_hom_unmop, const_map_app, CategoryTheory.GradedObject.ι_mapBifunctorMapMap_assoc, opInv_map, CategoryTheory.Equivalence.fun_inv_map, whiskeringRight₂_map_app_app_app, CategoryTheory.Cat.ihom_map, SSet.prodStdSimplex.objEquiv_map_apply, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π_assoc, CategoryTheory.MonoidalCategory.DayConvolution.braidingInvCorepresenting_app, HomotopicalAlgebra.CofibrantObject.HoCat.bifibrantResolution_map, id_tensor_π_preserves_coequalizer_inv_desc, CategoryTheory.MonoidalOpposite.mopMopEquivalence_functor_map, CategoryTheory.Pretriangulated.invRotate_map_hom₂, CategoryTheory.Limits.PreservesPullback.iso_hom_snd_assoc, CategoryTheory.Limits.spanCompIso_hom_app_right, CategoryTheory.Abelian.PreservesCoimage.iso_inv_π, SSet.Truncated.Edge.mk'_edge, SimplicialObject.Splitting.cofan_inj_comp_app, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_three, HomologicalComplex.mapBifunctor₂₃.ι_eq, CategoryTheory.NatTrans.whiskerLeft_app_tensor_app, CategoryTheory.Limits.prodComparison_snd, LightProfinite.Extend.functorOp_map, CategoryTheory.StructuredArrow.proj_map, TopCat.Sheaf.interUnionPullbackConeLift_left, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObj_map_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality_assoc, relativelyRepresentable.w_assoc, CategoryTheory.fromSkeleton_map, TopCat.subpresheafToTypes_map_coe, CategoryTheory.GradedObject.single_map_singleObjApplyIsoOfEq_hom, CategoryTheory.NatTrans.tensor_naturality_assoc, CategoryTheory.NatTrans.retractArrowApp_r, CategoryTheory.RightExactFunctor.ofExact_map, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_assoc, AlgebraicGeometry.Scheme.monObjAsOverPullback_mul, CategoryTheory.Iso.map_inv_hom_id_assoc, mapCommMon_map_hom_hom, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_inverse_map_f_f, CategoryTheory.Limits.Bicones.functoriality_obj_ι, CategoryTheory.MonoidalCategory.externalProductBifunctorCurried_obj_obj_map_app, CategoryTheory.Limits.reflexiveCoforkEquivCofork_inverse_obj_pt, ιColimitType_eq_iff_of_isFiltered, RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π, CategoryTheory.Localization.SmallShiftedHom.equiv_shift, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map_d, CategoryTheory.Limits.kernelComparison_comp_kernel_map, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.inverse_obj_map, topToLocale_map, CategoryTheory.SmallObject.functorialFactorizationData_Z_map, OplaxMonoidal.left_unitality_hom, LaxLeftLinear.μₗ_associativity, CategoryTheory.TransportEnrichment.eComp_eq, shiftIso_hom_naturality_assoc, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac', CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_obj, sectionsEquivHom_naturality_symm, CategoryTheory.HasShift.Induced.zero_hom_app_obj, groupHomology.chainsMap_comp, TopCat.Presheaf.stalkSpecializes_stalkFunctor_map, IsEventuallyConstantFrom.coconeιApp_eq, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_two_assoc, AlgebraicGeometry.Scheme.homOfLE_app, map_finite_effectiveEpiFamily, CategoryTheory.InjectiveResolution.Hom.ι_f_zero_comp_hom_f_zero, CategoryTheory.StructuredArrow.mapIso_functor_map_left, BoolRing.hasForgetToBoolAlg_forget₂_map, CategoryTheory.Equivalence.congrLeftFunctor_map, CategoryTheory.isIso_iff_of_reflects_iso, CategoryTheory.liftedLimitMapsToOriginal_inv_map_π, SheafOfModules.ιFree_mapFree_inv, AlgebraicGeometry.Scheme.kerFunctor_map, CategoryTheory.PreGaloisCategory.functorToAction_map, obj.ι_def, CategoryTheory.Limits.FormalCoproduct.cech_map, CategoryTheory.Comonad.Coalgebra.Hom.h_assoc, CategoryTheory.Adjunction.shift_unit_app, CategoryTheory.IsPullback.map_iff, mapHomotopyEquiv_homotopyInvHomId, CategoryTheory.InjectiveResolution.iso_hom_naturality_assoc, SSet.Truncated.StrictSegal.spineToSimplex_arrow, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.instIsIsoMapF, CategoryTheory.Adjunction.map_η_comp_η_assoc, AlgebraicGeometry.Scheme.Hom.naturality_assoc, CategoryTheory.OrthogonalReflection.iteration_map_succ_injectivity, CategoryTheory.Sieve.functorPullback_pullback, PushoutObjObj.inl_ι_assoc, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app_assoc, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self_apply, HomologicalComplex.cyclesOpIso_hom_naturality, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_map_hom_hom_app, CategoryTheory.Comonad.Coalgebra.coassoc_assoc, CategoryTheory.Adjunction.unit_app_commShiftIso_hom_app_assoc, TopCat.Presheaf.pushforward_map_app', CategoryTheory.Abelian.PreservesImage.iso_hom_ι_assoc, OplaxLeftLinear.δₗ_unitality_hom, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.sheafCondition_iff_bijective_toPullbackObj, CondensedSet.topCatAdjunctionUnit_val_app, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac'_assoc, AlgebraicGeometry.Scheme.homOfLE_appLE, CategoryTheory.CostructuredArrow.homMk'_mk_comp, sheafPushforwardContinuousId'_inv_app_val_app, NonemptyFinLinOrd.dual_map, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app_assoc, Final.exists_coeq, CategoryTheory.InjectiveResolution.isoRightDerivedObj_hom_naturality_assoc, CategoryTheory.uliftYoneda_map_app, AlgebraicGeometry.Scheme.Hom.normalizationCoprodIso_inv_coprodDesc_fromNormalization, IsEventuallyConstantTo.isoMap_hom_inv_id, leftExtensionEquivalenceOfIso₁_functor_obj_hom_app, CategoryTheory.Presieve.isSheafFor_over_map_op_comp_ofArrows_iff, CategoryTheory.ShortComplex.SnakeInput.functorL₃_map, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_map_right_right, map_opShiftFunctorEquivalence_counitIso_hom_app_unop, mapGrp_map_hom_hom, FundamentalGroupoid.map_eq, uliftYonedaReprXIso_hom_app, TopCat.Presheaf.pushforward_obj_map, CategoryTheory.Sum.homInduction_right, CategoryTheory.Limits.map_π_preserves_coequalizer_inv_assoc, whiskeringLeft₂_map_app_app_app_app, CategoryTheory.NatTrans.naturality_1_assoc, CategoryTheory.Pretriangulated.TriangleMorphism.comm₃_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app, CategoryTheory.Adjunction.inv_counit_map, CategoryTheory.ShortComplex.RightHomologyData.map_p, Monoidal.μ_comp, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_inverse_map_f_f, TopCat.Presheaf.presheafEquivOfIso_unitIso_inv_app_app, CategoryTheory.unit_mateEquiv_symm, prod'_map, CategoryTheory.CommGrp.forget₂Grp_map_hom, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_right, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁'_obj_map_app, CategoryTheory.SmallObject.SuccStruct.Iteration.mapObj_refl, CategoryTheory.Equivalence.core_functor_map_iso_inv, CategoryTheory.Limits.walkingCospanOpEquiv_functor_map, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_map_left_left, CategoryTheory.Limits.Trident.ofCone_π, CategoryTheory.Triangulated.SpectralObject.distinguished', AlgebraicGeometry.instIsOpenImmersionInlScheme, CategoryTheory.eq_functor_map, map_opShiftFunctorEquivalence_counitIso_inv_app_unop_assoc, curryingEquiv_apply_map, CategoryTheory.Bifunctor.diagonal, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₂, PartOrdEmb.forget_map, CategoryTheory.Sieve.functorPushforward_pullback_le, CategoryTheory.Limits.Cocone.w, flip₁₃Functor_obj_obj_map_app, CategoryTheory.Limits.PreservesEqualizer.iso_inv_ι, CategoryTheory.CostructuredArrow.prodInverse_map, initial_iff_of_isCofiltered, CommRingCat.forget_map_apply, CategoryTheory.Pseudofunctor.map₂_left_unitor_app, CategoryTheory.LocalizerMorphism.RightResolution.Hom.comm, LaxMonoidal.tensorUnit_whiskerLeft_comp_leftUnitor_hom_assoc, map_comp_assoc, CategoryTheory.ObjectProperty.IsDetecting.isIso_iff_of_mono, AlgebraicGeometry.morphismRestrict_appTop, CategoryTheory.InjectiveResolution.isoRightDerivedObj_inv_naturality, commShiftOfLocalization.iso_hom_app, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_map_fst_app, AlgebraicGeometry.Scheme.IdealSheafData.ofIdealTop_ideal, CategoryTheory.Comonad.delta_naturality, fun_inv_map, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π, CategoryTheory.MorphismProperty.Comma.mapRight_map_right, CategoryTheory.StrictPseudofunctor.toFunctor_map, CategoryTheory.Iso.isoCompInverse_inv_app, CategoryTheory.NatTrans.app_shift_assoc, CochainComplex.HomComplex.Cochain.fromSingleMk_precomp, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality, postcompose₂_obj_map_app_app, CategoryTheory.Tor'_obj_map, 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, CategoryTheory.ActionCategory.curry_apply_left, SSet.Truncated.spine_vertex, mapCone_π_app, CategoryTheory.yonedaMap_app_apply, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceFunctor_map_base, CategoryTheory.ε_app_obj, CategoryTheory.Sheaf.ΓHomEquiv_naturality_right_symm, CategoryTheory.MorphismProperty.Comma.forget_map, map_units_smul, IsCoverDense.Types.naturality_apply, CategoryTheory.Equivalence.sheafCongr.functor_obj_val_map, CategoryTheory.Limits.limit_map_limitObjIsoLimitCompEvaluation_hom_assoc, HomologicalComplex.singleObjOpcyclesSelfIso_hom_naturality_assoc, TopCat.Presheaf.stalkPushforward.id, CategoryTheory.Iso.isoInverseOfIsoFunctor_inv_app, CategoryTheory.Comonad.comparison_map_f, CategoryTheory.SmallObject.SuccStruct.ofCocone_map_to_top, CategoryTheory.DifferentialObject.shiftFunctor_map_f, CategoryTheory.ComposableArrows.whiskerLeftFunctor_map_app, CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair_inv_app, CategoryTheory.PreGaloisCategory.fiber_in_connected_component, shiftIso_hom_app_comp_assoc, CategoryTheory.SimplicialObject.Truncated.trunc_map_app, LaxLeftLinear.μₗ_naturality_left, CategoryTheory.Comonad.ComonadicityInternal.main_pair_coreflexive, AlgebraicGeometry.isOpenImmersion_sigmaDesc, CategoryTheory.WithInitial.map_map, CategoryTheory.ShortComplex.ShortExact.surjective_g, SSet.stdSimplex.objEquiv_symm_comp, CategoryTheory.SimplicialObject.Augmented.w₀_assoc, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃_assoc, OneHypercoverDenseData.essSurj.presheafObj_condition, CategoryTheory.Adjunction.Triple.leftToRight_app_map_adj₁_unit_app_assoc, CategoryTheory.Equivalence.inv_fun_map_assoc, CategoryTheory.PresheafOfGroups.OneCochain.ev_precomp, CategoryTheory.Limits.pullbackComparison_comp_snd_assoc, biprodComparison_snd, CategoryTheory.GradedObject.mapBifunctorMap_map_app, TopCat.Presheaf.whiskerIsoMapGenerateCocone_hom_hom, CategoryTheory.SimplicialObject.cechNerve_map, AlgebraicGeometry.LocallyRingedSpace.Γ_map, AlgebraicGeometry.coprodSpec_inr_assoc, CategoryTheory.Equivalence.inverse_counitInv_comp_assoc, CategoryTheory.Limits.PreservesKernel.iso_hom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_snd_map, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_inv_app_val_app, ModuleCat.ihom_map_apply, HomotopicalAlgebra.CofibrantObject.HoCat.adjCounitIso_inv_app, CategoryTheory.ShortComplex.zero_apply, CategoryTheory.Pseudofunctor.Grothendieck.forget_map, CategoryTheory.Sheaf.ΓObjEquivHom_naturality, CategoryTheory.obj_μ_inv_app, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_left_symm, OplaxMonoidal.associativity_inv, CategoryTheory.Sheaf.ΓRes_map, CategoryTheory.Equivalence.core_inverse_map_iso_inv, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinset_map_app, CategoryTheory.functorProdToProdFunctor_map, mapCommMon_obj_mon_one, Monoidal.μ_fst, CategoryTheory.Idempotents.DoldKan.Γ_obj_map, const.unop_functor_op_obj_map, CategoryTheory.NatTrans.tensor_naturality, CommShift.ofIso_commShiftIso_inv_app, LightCondSet.hom_naturality_apply, CategoryTheory.ComposableArrows.δlastFunctor_map_app, CategoryTheory.Bimon.ofMonComon_map_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMop_map_unmop_app, CategoryTheory.MorphismProperty.IsStableUnderTransfiniteCompositionOfShape.of_isStableUnderColimitsOfShape.mem_map_bot_le, Rep.standardComplex.quasiIso_forget₂_εToSingle₀, SimplexCategoryGenRel.simplicialEvalσ_of_isAdmissible, CategoryTheory.MonoidalSingleObj.endMonoidalStarFunctorEquivalence_inverse_map, CategoryTheory.CatCommSq.vInv_iso_inv_app, MonCat.uliftFunctor_map, CategoryTheory.regularTopology.equalizerCondition_w', CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_naturality₂, CommSemiRingCat.forget_map, CategoryTheory.Presieve.image_mem_functorPushforward, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse_assoc, CategoryTheory.Limits.BinaryBicones.functoriality_obj_fst, AlgebraicGeometry.instIsOpenImmersionMapWalkingSpanSchemeSpan, HomotopicalAlgebra.CofibrantObject.HoCat.adjUnit_app, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv', CommAlgCat.forget_map, PresheafOfModules.Hom.naturality_assoc, LaxRightLinear.μᵣ_unitality, CategoryTheory.nerve_map, AlgebraicGeometry.IsOpenImmersion.app_eq_appIso_inv_app_of_comp_eq, AlgebraicGeometry.AffineSpace.functor_map_app, CategoryTheory.Comma.fromProd_map_left, LaxMonoidal.μ_whiskerRight_comp_μ_assoc, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counitIso_hom_app_assoc, CategoryTheory.ObjectProperty.isColocal_iff_isIso_map, CategoryTheory.ShortComplex.mapCyclesIso_hom_naturality_assoc, SSet.Truncated.HomotopyCategory.lift_map_homMk, CategoryTheory.ι_preservesColimitIso_hom, AlgebraicGeometry.Scheme.LocalRepresentability.yoneda_toGlued_yonedaGluedToSheaf, HomologicalComplex.dgoToHomologicalComplex_map_f, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.iso_hom_naturality_assoc, AlgebraicGeometry.LocallyRingedSpace.restrict_presheaf_map, CategoryTheory.ReflQuiv.forgetToQuiv_map, sum'_map_inl, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_incl, CategoryTheory.associativity_app_assoc, IsOpenMap.functorNhds_map, CategoryTheory.WithInitial.commaFromUnder_map_right, CategoryTheory.coyonedaEquiv_coyoneda_map, CategoryTheory.Limits.ColimitPresentation.Total.Hom.w_assoc, CategoryTheory.ThinSkeleton.map₂_map, CategoryTheory.TwoSquare.whiskerLeft_app, CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_cancel_inv_app, HomologicalComplex.shortComplexFunctor'_map_τ₁, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_inv_comp_π, CategoryTheory.GrothendieckTopology.plusFunctor_map, CategoryTheory.Subfunctor.toFunctor_map_coe, CategoryTheory.CartesianClosed.uncurry_natural_right_assoc, CategoryTheory.Limits.map_lift_piComparison_assoc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_map_hom, CategoryTheory.Equivalence.map_η_comp_η_assoc, HomotopyCategory.mem_quasiIso_iff, OplaxMonoidal.δ_fst, CategoryTheory.shiftZero', CategoryTheory.Limits.cospan_map_id, CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_hom, CategoryTheory.Monoidal.InducingFunctorData.whiskerRight_eq, HomotopyCategory.composableArrowsFunctor_map, CategoryTheory.MonoidalCategory.tensor_map, OneHypercoverDenseData.isSheaf_iff.fac_assoc, flip_obj_map, CategoryTheory.Mat_.ι_additiveObjIsoBiproduct_inv, CategoryTheory.Limits.diagramIsoParallelFamily_hom_app, SSet.Truncated.Edge.id_edge, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.forgetToPresheafedSpacePreservesOpenImmersion, CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ, CategoryTheory.ParametrizedAdjunction.unit_whiskerRight_map_assoc, CategoryTheory.Over.star_map_left, CategoryTheory.Limits.colimit.post_post, CategoryTheory.Comma.unopFunctor_map, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_app_assoc, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc, CategoryTheory.IsCardinalPresentable.exists_eq_of_isColimit', map_inv_hom_assoc, toEventualRanges_map, Fiber.hom_ext_iff, CategoryTheory.preservesLimitIso_hom_π_assoc, CategoryTheory.linearCoyoneda_obj_map, HomologicalComplex.single_map_f_self, CategoryTheory.Limits.instIsIsoPullbackComparison, GrpCat.FilteredColimits.colimit_mul_mk_eq, CategoryTheory.simplicialCosimplicialEquiv_functor_map_app, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.functor_map_app_hom, CategoryTheory.MorphismProperty.LeftFraction.map_ofInv_hom_id_assoc, CochainComplex.instQuasiIsoIntMapHomologicalComplexUpShiftFunctor, CategoryTheory.CatCommSq.hComp_iso_inv_app, CategoryTheory.Pseudofunctor.map₂_whisker_right_app_assoc, ContinuousMap.piComparison_fac, CategoryTheory.Limits.walkingSpanOpEquiv_functor_map, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app_apply, CategoryTheory.InjectiveResolution.Hom.ι'_comp_hom'_assoc, CategoryTheory.PreOneHypercover.oneToZero_map, AlgebraicGeometry.LocallyRingedSpace.forgetToTop_map, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_π_app, CategoryTheory.ExactFunctor.whiskeringRight_map_app, PresheafOfModules.comp_toPresheaf_map_sheafifyHomEquiv'_symm_hom, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃_assoc, CategoryTheory.Monad.beckCofork_π, Preord.dual_map, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_inv_right, CategoryTheory.Limits.kernel_map_comp_preserves_kernel_iso_inv, CategoryTheory.MonoidalCategory.leftAssocTensor_map, CategoryTheory.MonoidalClosed.curry_natural_right_assoc, CategoryTheory.PreGaloisCategory.exists_hom_from_galois_of_fiber, CategoryTheory.coreFunctor_map_app_iso_inv, CategoryTheory.Presieve.FamilyOfElements.isAmalgamation_singleton_iff, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map_val_app, CategoryTheory.IsDetecting.isIso_iff_of_mono, CategoryTheory.Pretriangulated.Triangle.functorMk_map_hom₂, Monoidal.map_μ_δ, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_obj_obj_map, CategoryTheory.Limits.PreservesCoequalizer.iso_hom, CategoryTheory.evaluationUncurried_map, CategoryTheory.CosimplicialObject.cechConerve_map, CategoryTheory.Equivalence.counitIso_inv_app_comp_functor_map_η_inverse_assoc, CategoryTheory.CosimplicialObject.Augmented.const_map_left, CategoryTheory.PreGaloisCategory.PointedGaloisObject.incl_map, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_whiskerRight_assoc, CategoryTheory.Limits.Cocone.w_apply, DerivedCategory.HomologySequence.exact₁, CategoryTheory.Limits.colimit.pre_map', CategoryTheory.InjectiveResolution.isoRightDerivedToHomotopyCategoryObj_hom_naturality_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app, CategoryTheory.Limits.coprodComparison_inv_natural_assoc, CategoryTheory.subterminalsEquivMonoOverTerminal_functor_map, CategoryTheory.Pi.sum_obj_map, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.fromBiprod_biprodIsoProd_inv_apply, PresheafOfModules.restriction_app, CategoryTheory.yonedaPairing_map, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_obj_map_app, preservesFiniteLimits_iff_forall_exact_map_and_mono, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst, CategoryTheory.Localization.isoOfHom_hom_inv_id, toOplaxFunctor_map, AlgebraicTopology.DoldKan.Γ₂N₂ToKaroubiIso_inv_app, AlgebraicGeometry.Scheme.toOpen_eq, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_rightUnitor_hom_eq_rightUnitor_hom, CategoryTheory.LiftLeftAdjoint.instIsReflexivePairMapAppCounitOtherMap, AlgebraicGeometry.Spec.toSheafedSpace_map, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_map_fst, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_π, CategoryTheory.Limits.CategoricalPullback.Hom.w, CategoryTheory.Limits.cospanCompIso_inv_app_one, CategoryTheory.bifunctorComp₂₃FunctorObj_map_app_app_app, CategoryTheory.ExponentiableMorphism.coev_ev_assoc, CategoryTheory.SimplicialObject.whiskering_obj_obj_map, CategoryTheory.Join.mkFunctor_map_edge, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionRight_map, CategoryTheory.Limits.parallelPair_map_right, FullyFaithful.hasShift.map_add_hom_app, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_g, CategoryTheory.SmallObject.SuccStruct.prop_iterationFunctor_map_succ, groupCohomology.cocyclesMap_comp_assoc, CategoryTheory.uliftYoneda_map_app_down, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_assoc, CategoryTheory.unit_mateEquiv, OplaxRightLinear.δᵣ_associativity_inv_assoc, CategoryTheory.Idempotents.FunctorExtension₁.obj_map_f, CategoryTheory.PreGaloisCategory.surjective_on_fiber_of_epi, SSet.Truncated.Path.arrow_src, mapTriangle_map_hom₃, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app, SSet.spine_map_vertex, CategoryTheory.CosimplicialObject.augmentedCechConerve_map, CategoryTheory.Comon.forget_map, CategoryTheory.Limits.spanCompIso_hom_app_left, whiskeringLeft_obj_map, CategoryTheory.Sum.swap_map_inl, CategoryTheory.Equivalence.counitInv_app_functor, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturality, CategoryTheory.Limits.Cocone.fromStructuredArrow_map_hom, CategoryTheory.Abelian.PreservesImage.iso_inv_ι, flipping_inverse_obj_map_app, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver_map, CategoryTheory.Subfunctor.Subpresheaf.nat_trans_naturality, CategoryTheory.FunctorToTypes.colimit.map_ι_apply, Monoidal.map_tensor_assoc, CategoryTheory.monadToFunctor_map, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_unit_app_app, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinset_map_app, OplaxMonoidal.oplax_left_unitality, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_app_assoc, ComplexShape.Embedding.truncLE'Functor_map, mapComon_obj_comon_counit, CategoryTheory.ProjectiveResolution.lift_commutes_assoc, CategoryTheory.Endofunctor.Coalgebra.Hom.h, MonCat.val_units_map_hom_apply, HomotopicalAlgebra.BifibrantObject.toHoCat_map_eq_iff, AlgebraicGeometry.isCompl_opensRange_inl_inr, TopCat.Presheaf.restrictOpenCommRingCat_apply, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality_assoc, HasFibers.inducedMap_comp_assoc, CategoryTheory.expComparison_ev, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality, CategoryTheory.MonoOver.inf_map_app, CategoryTheory.MorphismProperty.LeftFraction.map_hom_ofInv_id, CategoryTheory.OverPresheafAux.yonedaCollectionFunctor_map, CategoryTheory.Monad.forget_map, CategoryTheory.ShortComplex.mapCyclesIso_inv_naturality_assoc, CategoryTheory.LaxFunctor.mapComp_assoc_left_app, CategoryTheory.Adjunction.unit_naturality, CategoryTheory.Limits.Cone.w, IsDenseSubsite.mapPreimage_comp_map_assoc, CategoryTheory.Presheaf.uliftYonedaAdjunction_unit_app_app, CategoryTheory.Grothendieck.transportIso_inv_fiber, CategoryTheory.GradedObject.single_map_singleObjApplyIso_hom, AugmentedSimplexCategory.inclusion_map, CategoryTheory.left_unitality_app, CategoryTheory.BasedNatTrans.forgetful_map, map_id, CategoryTheory.Limits.PullbackCone.ofCone_π, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app_assoc, AlgebraicGeometry.StructureSheaf.res_apply, groupCohomology.mapShortComplexH1_comp, CategoryTheory.OverPresheafAux.YonedaCollection.mk_snd, SimplexCategoryGenRel.toSimplexCategory_map_δ, AddCommGrpCat.uliftFunctor_map, CategoryTheory.Equivalence.counitInv_functor_comp_assoc, LeftExtension.postcompose₂_map_left, OplaxLeftLinear.δₗ_naturality_right, uncurry_obj_map, CategoryTheory.CartesianMonoidalCategory.inv_prodComparison_map_snd, mapPresheaf_map_c, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_app_assoc, CategoryTheory.Presieve.Arrows.toCompatible_coe, SSet.stdSimplex.yonedaEquiv_map, CategoryTheory.shift_shiftFunctorCompIsoId_inv_app, OplaxLeftLinear.δₗ_associativity_assoc, CategoryTheory.Limits.Concrete.colimit_rep_eq_zero, CategoryTheory.Over.post_obj, CategoryTheory.NatTrans.app_naturality_assoc, SemiNormedGrp.completion.map_zero, CategoryTheory.Adjunction.map_μ_comp_counit_app_tensor, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counit_app, CategoryTheory.Adjunction.compCoyonedaIso_hom_app_app, CategoryTheory.Kleisli.Adjunction.fromKleisli_map, AlgebraicGeometry.instIsOpenImmersionSigmaSpec, CategoryTheory.Equivalence.fun_inv_map_assoc, CategoryTheory.Square.evaluation₃_map, closedIhom_map_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_inv_app_app, CategoryTheory.WithTerminal.mkCommaObject_hom_app, HomotopicalAlgebra.FibrantObject.HoCat.ιCompResolutionNatTrans_app, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural, LightCondMod.hom_naturality_apply, CategoryTheory.Equivalence.ε_comp_map_ε, mapCocone₂_ι_app, RightExtension.postcompose₂_obj_hom_app, CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv', CategoryTheory.ObjectProperty.ColimitOfShape.toCostructuredArrow_map, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv, MagmaCat.forget_map, SheafOfModules.pullback_assoc, AlgebraicGeometry.Scheme.Hom.map_appLE', toPseudoFunctor_mapId, Final.colimit_cocone_comp_aux, CategoryTheory.ShiftedHom.opEquiv'_symm_op_opShiftFunctorEquivalence_counitIso_inv_app_op_shift, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_map_left, RightExtension.precomp_map_right, CategoryTheory.Monad.MonadicityInternal.unitCofork_pt, Rep.trivialFunctor_map_hom, CategoryTheory.ProjectiveResolution.leftDerivedToHomotopyCategory_app_eq, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_leftUnitor_hom_eq_leftUnitor_hom, CategoryTheory.Square.toArrowArrowFunctor_map_left_left, CategoryTheory.Limits.colimit.pre_id, map_opShiftFunctorEquivalence_unitIso_hom_app_unop_assoc, AlgebraicGeometry.Scheme.AffineZariskiSite.opensRange_relativeGluingData_map, CategoryTheory.NatTrans.naturality, CategoryTheory.CompatiblePreserving.apply_map, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv, CategoryTheory.Abelian.coimageImageComparisonFunctor_map, topToPreord_map, whiskeringLeft₃ObjObj_map, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp_assoc, SheafOfModules.forget_map, AlgebraicGeometry.Scheme.Hom.toNormalization_inr_normalizationCoprodIso_hom_assoc, CategoryTheory.WithTerminal.commaFromOver_map_right, IsRepresentedBy.map_bijective, CategoryTheory.Limits.hasPullback_of_preservesPullback, CategoryTheory.CostructuredArrow.map_map_left, ComplexShape.Embedding.truncLEFunctor_map, CategoryTheory.RetractArrow.map_i_left, CategoryTheory.Endofunctor.Algebra.Hom.h, mapEnd_apply, CategoryTheory.CostructuredArrow.map₂_map_left, PullbackObjObj.ofHasPullback_snd, HomologicalComplex.quasiIsoAt_iff_evaluation, shift_map_op, CategoryTheory.MorphismProperty.Comma.mapRight_map_left, CategoryTheory.MorphismProperty.Under.forget_comp_forget_map, LaxRightLinear.μᵣ_naturality_left_assoc, LaxLeftLinear.μₗ_associativity_inv, CategoryTheory.CosimplicialObject.whiskering_obj_map_app, AlgebraicGeometry.RingedSpace.basicOpen_res_eq, CategoryTheory.Limits.colimit.pre_map, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_map_right_right, HomologicalComplex.truncGE.rightHomologyMapData_φH, LaxLeftLinear.μₗ_unitality_inv, CategoryTheory.Adjunction.comp_unit_app_assoc, CategoryTheory.comonadToFunctor_map, SSet.Truncated.tensor_map_apply_fst, CategoryTheory.InjectiveResolution.extMk_hom, CategoryTheory.Localization.isoOfHom_hom_inv_id_assoc, SimplexCategory.rev_map_rev_map, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app, CategoryTheory.Pretriangulated.shiftFunctor_op_map, CategoryTheory.ShortComplex.toComposableArrows_map, CategoryTheory.Limits.pushoutComparison_map_desc_assoc, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map, quasiIsoAt_iff', CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_whiskerRight, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_map_snd, CategoryTheory.Limits.cospanCompIso_hom_app_left, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand, Rep.ihom_map_hom, AlgCat.free_map, CategoryTheory.CosimplicialObject.Augmented.point_map, MonCat.Colimits.cocone_naturality_components, CategoryTheory.uliftCoyonedaEquiv_naturality, CategoryTheory.exp.coev_ev_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_app_assoc, mapMon_map_hom, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π_assoc, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app, CategoryTheory.Equivalence.unit_naturality_assoc, CategoryTheory.shiftComm_hom_comp, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_X_map, CategoryTheory.Limits.BinaryBicones.functoriality_obj_inr, CategoryTheory.Equivalence.unit_app_tensor_comp_inverse_map_δ_functor_assoc, CategoryTheory.NatTrans.shift_app_assoc, CategoryTheory.Sheaf.isLocallyInjective_sheafToPresheaf_map_iff, AlgebraicTopology.DoldKan.Compatibility.υ_hom_app, CategoryTheory.GradedObject.ι_mapBifunctorLeftUnitor_hom_apply, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_inv_app_eq, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp_app, CategoryTheory.NatIso.naturality_2'_assoc, CategoryTheory.CartesianMonoidalCategory.inv_prodComparison_map_fst, CategoryTheory.Adjunction.derivedη_fac_app, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_left, mapIso_inv, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.map_mem, CategoryTheory.ofTypeFunctor_map, obj.μ_def_assoc, CategoryTheory.SmallObject.SuccStruct.extendToSucc_map, CategoryTheory.Adjunction.rightAdjointUniq_hom_app_counit, CategoryTheory.Adjunction.derivedη_fac_app_assoc, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_inv_comp_π_assoc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_map_hom, whiskeringRight_obj_map, RightExtension.postcompose₂_map_left_app, CategoryTheory.Equivalence.unit_naturality, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_snd_map, CategoryTheory.Limits.limit.homIso_hom, CategoryTheory.Sieve.mem_functorPushforward_functor, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_hom_app_app, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom, LaxMonoidal.right_unitality_assoc, CategoryTheory.Equivalence.functor_unitIso_comp, curry_obj_obj_map, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_val_map, CategoryTheory.GrothendieckTopology.overMapPullbackComp_inv_app_val_app, CategoryTheory.Limits.Cocone.ofPushoutCocone_ι, CategoryTheory.Pseudofunctor.Grothendieck.map_map_fiber, CategoryTheory.IsCodetecting.isIso_iff_of_epi, CoalgCat.forget₂_map, CategoryTheory.Limits.limit.map_pre', Monoidal.map_whiskerRight_assoc, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_hom, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app, CategoryTheory.NatTrans.CommShiftCore.app_shift, AlgebraicGeometry.SheafedSpace.forgetToPresheafedSpace_map, LaxRightLinear.μᵣ_associativity, Monoidal.map_leftUnitor, CategoryTheory.GrothendieckTopology.diagramFunctor_map, CategoryTheory.IsSplitCoequalizer.map_leftSection, PushoutObjObj.ofHasPushout_inl, CategoryTheory.uliftCoyonedaEquiv_symm_map_assoc, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_obj, HasCardinalLT.Set.functor_map_coe, CategoryTheory.StructuredArrow.preEquivalenceInverse_map_right_right, CategoryTheory.presheafToSheafCompComposeAndSheafifyIso_inv_app, CategoryTheory.Iso.map_hom_inv_id_eval_app_assoc, CategoryTheory.PreGaloisCategory.comp_autMap_apply, CategoryTheory.Limits.FormalCoproduct.incl_map_φ, CategoryTheory.Comma.mapLeft_map_right, CommMonCat.coyoneda_map_app, Faithful.map_injective, CategoryTheory.Presieve.mem_comap_jointlySurjectivePrecoverage_iff, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_symm_apply_f, relativelyRepresentable.pullback₃.map_p₂_comp_assoc, CategoryTheory.CostructuredArrow.IsUniversal.fac, Monoidal.map_ε_η, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₄, CategoryTheory.ObjectProperty.isLocal_iff_isIso_map, CategoryTheory.Localization.Construction.liftToPathCategory_map, CategoryTheory.ActionCategory.comp_val, CategoryTheory.Adjunction.localization_counit_app, CategoryTheory.Presieve.FamilyOfElements.comp_of_compatible, CochainComplex.quasiIsoAt₀_iff, AlgebraicGeometry.coprodSpec_inl_assoc, CategoryTheory.shift_zero_eq_zero, CategoryTheory.Pseudofunctor.mapComp'_naturality_2, HomologicalComplex.singleObjHomologySelfIso_hom_naturality, AlgebraicGeometry.Spec.coe_toTop_map_hom_apply_asIdeal, AlgebraicGeometry.Scheme.Opens.toScheme_presheaf_map, CategoryTheory.MonoOver.lift_map_hom, CochainComplex.mappingCone.trianglehMapOfHomotopy_hom₃, groupHomology.chainsFunctor_map, CategoryTheory.ObjectProperty.rightOrthogonal.map_bijective_of_isTriangulated, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_apply, CategoryTheory.GradedObject.mapTrifunctorObj_obj_map, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon_map, homologySequence_exact₁, CategoryTheory.orderDualEquivalence_functor_map, CategoryTheory.Adjunction.instIsIsoMapAppUnitOfFaithfulOfFull, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_inv_app_app, CategoryTheory.toSkeletonFunctor_map_hom, CorepresentableBy.homEquiv_comp, FullyFaithful.compUliftCoyonedaCompWhiskeringLeft_inv_app_app_down, CategoryTheory.Sum.swap_map_inr, whiskerRight_app, CategoryTheory.Limits.PreservesLimitPair.iso_inv_fst, CategoryTheory.LocalizerMorphism.equiv_smallHomMap, TopCat.Sheaf.objSupIsoProdEqLocus_hom_snd, CategoryTheory.Sheaf.instIsLocallySurjectiveHomMapTypeSheafComposeForget, SSet.Truncated.StrictSegal.spine_δ_arrow_eq, CategoryTheory.Adjunction.CommShift.compatibilityUnit_right, CommShift.isoAdd'_hom_app, CategoryTheory.flippingIso_hom_toFunctor_obj_map_app, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app_assoc, CategoryTheory.NatIso.naturality_2', CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_inv_app_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w_assoc, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app, CategoryTheory.Limits.Cone.ofFork_π, CategoryTheory.Limits.colimit.ι_map_assoc, CategoryTheory.SplitEpi.map_section_, CategoryTheory.Limits.MultispanIndex.parallelPairDiagramOfIsColimit_map, CategoryTheory.ComonadHom.app_δ, CategoryTheory.FunctorToTypes.rightAdj_obj_map_app, CategoryTheory.Adjunction.Triple.map_rightToLeft_app, TopCat.Sheaf.objSupIsoProdEqLocus_inv_eq_iff, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_associator, HomologicalComplex.instQuasiIsoOppositeMapSymmOpFunctorOp, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app_assoc, CategoryTheory.Subobject.underlying_arrow_assoc, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_comp, pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_app, CategoryTheory.Equivalence.sheafCongrPrecoherent_inverse_obj_val_map, CategoryTheory.Limits.CokernelCofork.map_condition, AlgebraicGeometry.sigmaOpenCover_I₀, CategoryTheory.Adjunction.eq_unit_comp_map_iff, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₃₁_assoc, HomologicalComplex.singleObjHomologySelfIso_hom_naturality_assoc, AlgebraicTopology.DoldKan.map_Q, CategoryTheory.NatTrans.mapHomologicalComplex_naturality_assoc, HomologicalComplex.singleObjHomologySelfIso_inv_naturality_assoc, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_hom_app_val_app, CategoryTheory.SimplicialObject.Truncated.whiskering_obj_obj_map, CategoryTheory.Pseudofunctor.toDescentData_map_hom, CochainComplex.mappingCone.trianglehMapOfHomotopy_hom₁, CategoryTheory.CosimplicialObject.equivalenceRightToLeft_right_app, LaxMonoidal.comp_ε, TwoP.swapEquiv_inverse_map_hom_toFun, AlgebraicGeometry.Proj.awayMap_awayToSection, CategoryTheory.Limits.π_comp_cokernelComparison, SemilatInfCat.dual_map, CategoryTheory.Square.map_f₁₂, CategoryTheory.piEquivalenceFunctorDiscrete_inverse_map, CategoryTheory.Free.lift_map_single, DerivedCategory.right_fac_of_isStrictlyLE, CategoryTheory.Square.opFunctor_map_τ₃, CategoryTheory.Presheaf.map_comp_uliftYonedaEquiv_down_assoc, CategoryTheory.Prod.sectL_map, CategoryTheory.StructuredArrow.w, CategoryTheory.Join.opEquiv_inverse_map_edge_op, CategoryTheory.TransfiniteCompositionOfShape.iic_incl_app, curryingFlipEquiv_apply_map, CompHausLike.compHausLikeToTop_map, CategoryTheory.GlueData.mapGlueData_f, CoreMonoidal.μIso_hom_natural_right, mapAddHom_apply, pointwiseLeftKanExtensionCompIsoOfPreserves_fac_app, RightExtension.postcompose₂_map_right, CategoryTheory.Limits.BinaryBicones.functoriality_obj_snd, CategoryTheory.Limits.map_lift_kernelComparison_assoc, CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit_assoc, CategoryTheory.Limits.cospanCompIso_hom_app_one, CategoryTheory.Square.toArrowArrowFunctor'_map_left_left, CategoryTheory.Limits.ι_comp_coequalizerComparison, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv, OneHypercoverDenseData.SieveStruct.fac_assoc, CategoryTheory.coreFunctor_map_app_iso_hom, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_hom_comp_map_π, Initial.exists_eq, CommShift.isoZero_inv_app, commAlgCatEquivUnder_inverse_map, CategoryTheory.TwoSquare.whiskerTop_app, AlgebraicGeometry.isIso_SpecMap_stakMap_localization, RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π_assoc, LightCondMod.epi_iff_locallySurjective_on_lightProfinite, commShiftIso_inv_naturality, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_app, AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit_map, PresheafOfModules.instHasLimitModuleCatCarrierObjOppositeRingCatCompEvaluationRestrictScalarsHomMap, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_app_fst_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app_assoc, CategoryTheory.WithTerminal.liftFromOver_obj_map, relativelyRepresentable.pullback₃.map_p₂_comp, AlgebraicTopology.DoldKan.Compatibility.τ₁_hom_app, LeftExtension.precomp_map_left, CategoryTheory.Equivalence.unit_app_comp_inverse_map_η_functor, LightCondensed.ihom_map_val_app, mapGrp_obj_grp_mul, CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_cancel_inv_app, LaxLeftLinear.μₗ_unitality, SheafOfModules.map_ιFree_mapFree_hom, CategoryTheory.GradedObject.mapBifunctorRightUnitorCofan_inj_assoc, TopCat.Presheaf.presheafEquivOfIso_counitIso_inv_app_app, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk, CategoryTheory.Iso.map_hom_inv_id_app_assoc, HomotopyCategory.homologyFunctor_shiftMap_assoc, PreOneHypercoverDenseData.multicospanIndex_fst, PreservesMonomorphisms.preserves, AlgebraicGeometry.ι_sigmaSpec_assoc, HomologicalComplex₂.totalShift₂Iso_hom_naturality, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_app_assoc, CategoryTheory.DifferentialObject.Hom.comm, Action.FunctorCategoryEquivalence.inverse_map_hom, AlgebraicGeometry.PresheafedSpace.Γ_map, Fiber.inducedFunctor_comp_map, CategoryTheory.Mat_.lift_map, HopfAlgCat.forget₂_bialgebra_map, mapHomotopyCategory_map, CategoryTheory.StructuredArrow.pre_map_right, AlgebraicGeometry.ΓSpec.right_triangle, CoreMonoidal.right_unitality, ModuleCat.uliftFunctor_map, CategoryTheory.ShortComplex.SnakeInput.functorL₂'_map_τ₃, SSet.Truncated.Path₁.arrow_tgt, CategoryTheory.TwistShiftData.shiftFunctorAdd'_inv_app, CategoryTheory.Limits.PullbackCone.combine_pt_map, CategoryTheory.wideSubcategoryInclusion.map, OplaxRightLinear.δᵣ_naturality_left_assoc, groupHomology.functor_map, mapBiprod_inv, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal', CompHausLike.toCompHausLike_map, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₃, CategoryTheory.CartesianMonoidalCategory.prodComparison_fst_assoc, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counit_app_tensor_assoc, AlgebraicGeometry.isPullback_inr_inr_coprodMap, 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, isMittagLeffler_iff_subset_range_comp, CategoryTheory.Pretriangulated.rotate_map_hom₁, Monoidal.map_whiskerLeft, CategoryTheory.ProjectiveResolution.Hom.hom_f_zero_comp_π_f_zero, CategoryTheory.Comonad.counit_naturality_assoc, CategoryTheory.ShiftedHom.opEquiv'_symm_comp, closedSieves_map_coe, CategoryTheory.δ_naturality_assoc, CategoryTheory.CatCommSq.vComp_iso_inv_app, CategoryTheory.Limits.CokernelCofork.map_π, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, preordToCat_map, CategoryTheory.Over.liftCocone_ι_app, CategoryTheory.Adjunction.homEquiv_naturality_left_square_iff, LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm, CategoryTheory.Limits.inr_comp_pushoutComparison_assoc, CategoryTheory.Iso.map_inv_hom_id_eval, AlgebraicTopology.DoldKan.N₁Γ₀_hom_app, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_εIso_inv, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_apply, SemimoduleCat.forget_map, HomologicalComplex.mapBifunctorMapHomotopy.comm₁_aux, PullbackObjObj.π_snd_assoc, CategoryTheory.Adjunction.homEquiv_naturality_right_symm, InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj, LaxMonoidal.μ_natural_left, CategoryTheory.NatIso.naturality_2, CategoryTheory.ExponentiableMorphism.coev_naturality_assoc, CategoryTheory.ShortComplex.opcyclesFunctor_map, CategoryTheory.Monad.comparison_map_f, PushoutObjObj.mapArrowLeft_left, CategoryTheory.ShortComplex.mapCyclesIso_hom_iCycles, CategoryTheory.ObjectProperty.ιOfLE_map, ranObjObjIsoLimit_hom_π, LaxLeftLinear.μₗ_unitality_inv_assoc, OplaxLeftLinear.δₗ_unitality_inv_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_map_app_fst, OplaxMonoidal.ofBifunctor.secondMap₁_app_app_app, AlgebraicGeometry.tilde.toOpen_res, AlgebraicGeometry.tilde.toOpen_res_assoc, CategoryTheory.PreservesImage.hom_comp_map_image_ι_assoc, CategoryTheory.curryingIso_inv_toFunctor_map_app_app, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv_assoc, CategoryTheory.Idempotents.natTrans_eq, FullyFaithful.homNatIso'_inv_app_down, isoShift_hom_naturality_assoc, CategoryTheory.ShortComplex.quasiIso_iff_evaluation, CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj_inv_naturality, Monoidal.map_δ_μ, CategoryTheory.Limits.CategoricalPullback.Hom.w'_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_hom_comp_π, SSet.Truncated.HomotopyCategory.homToNerveMk_app_edge, CategoryTheory.Limits.span_map_fst, CategoryTheory.Limits.widePushoutShapeUnop_map, CategoryTheory.NatIso.isIso_map_iff, CategoryTheory.underToAlgebra_map_f, mapSquare_map_τ₂, CategoryTheory.Limits.prodComparison_natural, CochainComplex.mappingCone.trianglehMapOfHomotopy_hom₂, CategoryTheory.Meq.mk_apply, CategoryTheory.NatTrans.naturality', CategoryTheory.yonedaEquiv_naturality, SSet.Truncated.StrictSegal.spineToSimplex_interval, CategoryTheory.Adjunction.homEquiv_apply, CategoryTheory.Abelian.preadditiveCoyonedaObj_map_surjective, mapCommGrpFunctor_map, CategoryTheory.unopUnop_map, CategoryTheory.coalgebraToOver_map, AlgebraicGeometry.coprodSpec_inl, SheafOfModules.pushforwardNatTrans_app_val_app, Profinite.Extend.cocone_ι_app, CategoryTheory.GrothendieckTopology.W_iff, CategoryTheory.Idempotents.functorExtension_obj_map, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceInverse_map_fiber, CategoryTheory.PreGaloisCategory.evaluation_aut_surjective_of_isGalois, CategoryTheory.Mod_.forget_map, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_map_app_app, CategoryTheory.Equivalence.unit_app_inverse, CategoryTheory.Iso.isoCompInverse_hom_app, CategoryTheory.ObjectProperty.inverseImage_trW_iff, CategoryTheory.Limits.FormalCoproduct.cosimplicialObjectFunctor_obj_map, AlgebraicTopology.DoldKan.Γ₀.obj_map, CategoryTheory.Iso.isoInverseOfIsoFunctor_hom_app, CategoryTheory.Limits.ColimitPresentation.ofIso_ι, CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app, CategoryTheory.ComposableArrows.opEquivalence_inverse_map, CategoryTheory.δ_naturality, CondensedMod.epi_iff_locallySurjective_on_compHaus, CategoryTheory.Comonad.right_counit, MonCat.FilteredColimits.colimit_mul_mk_eq, comp_mapCommGrp_one, CategoryTheory.Limits.π_reflexiveCoequalizerIsoCoequalizer_inv, CategoryTheory.typeEquiv_functor_map_val_app, toPseudoFunctor'_mapId, ComplexShape.Embedding.truncGE'Functor_map, IsEventuallyConstantFrom.isoMap_hom_inv_id_assoc, CategoryTheory.Comma.mapRight_map_left, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_apply, CategoryTheory.Monoidal.InducingFunctorData.whiskerLeft_eq, pointwiseRightKanExtension_map, CategoryTheory.Iso.map_inv_hom_id_eval_app, AlgebraicGeometry.Spec_Γ_naturality_assoc, CategoryTheory.Abelian.PreservesCoimage.hom_coimageImageComparison, AlgebraicGeometry.Scheme.Hom.appLE_map'_assoc, AlgebraicGeometry.RingedSpace.isUnit_res_basicOpen, CategoryTheory.SmallObject.SuccStruct.Iteration.congr_map, LeftExtension.postcomp₁_map_left, equiv_functor_map, TopCat.Presheaf.germ_res'_assoc, AlgebraicGeometry.Scheme.Opens.ι_app_self, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₂, CategoryTheory.ShortComplex.mapCyclesIso_inv_naturality, RightExtension.coneAtFunctor_map_hom, CategoryTheory.Iso.map_hom_inv_id_eval, CategoryTheory.Limits.ι_reflexiveCoequalizerIsoCoequalizer_hom, CategoryTheory.Limits.reflexiveCoforkEquivCofork_inverse_obj_π, WellOrderInductionData.Extension.compatibility, HomologicalComplex.singleObjCyclesSelfIso_inv_naturality, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_inv, TopCat.toSheafCompHausLike_val_map, map_shift_unop_assoc, SimplicialObject.Split.evalN_map, CategoryTheory.NatTrans.naturality_app_app, CategoryTheory.ActionCategory.id_val, CategoryTheory.ShiftMkCore.zero_add_hom_app, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality, HomologicalComplex.mapBifunctor.d₁_eq', CochainComplex.mappingCone.triangleMapOfHomotopy_comm₃_assoc, AlgebraicGeometry.Scheme.Hom.naturality, CategoryTheory.Idempotents.karoubiFunctorCategoryEmbedding_map, CategoryTheory.MorphismProperty.Over.pullback_map_left, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_snd_map, CategoryTheory.ShortComplex.mapLeftHomologyIso_hom_naturality_assoc, CategoryTheory.yonedaCommGrpGrp_map_app, CategoryTheory.regularTopology.equalizerCondition_w, SSet.Truncated.Path.arrow_tgt, inv_fun_map, CategoryTheory.Limits.pullbackComparison_comp_fst, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₁, CategoryTheory.sum.associator_map_inl_inr, whiskeringLeft₂_obj_obj_obj_obj_map, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_assoc, CategoryTheory.ihom.ev_naturality, AddCommMonCat.forget₂_map_ofHom, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app, CategoryTheory.Pi.ihom_map, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_hom_comp_map_π_assoc, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃, Rep.indFunctor_map, SSet.mem_degenerate_iff, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_app_assoc, LaxMonoidal.associativity, CategoryTheory.Equivalence.sheafCongr.inverse_obj_val_map, mapMat__map, CategoryTheory.CosimplicialObject.whiskering_map_app_app, SSet.Augmented.stdSimplex_map_left, map_isIso, CategoryTheory.toOver_map_left, CategoryTheory.Arrow.cechNerve_map, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π_assoc, CategoryTheory.Over.sections_map, CategoryTheory.LocalizerMorphism.RightResolution.unopFunctor_map_f, CategoryTheory.MorphismProperty.inverseImage_iff, CategoryTheory.ShortComplex.SnakeInput.naturality_φ₂, CategoryTheory.Limits.pullbackComparison_comp_snd, CategoryTheory.Adjunction.rightAdjointUniq_hom_app_counit_assoc, CategoryTheory.MonoidalCategory.rightAssocTensor_map, flipping_inverse_map_app_app, CategoryTheory.Monoidal.InducingFunctorData.leftUnitor_eq, HomologicalComplex.singleObjOpcyclesSelfIso_inv_naturality_assoc, CategoryTheory.TwistShiftData.shiftFunctorAdd'_hom_app, AlgebraicGeometry.Scheme.restrict_presheaf_map, flip₁₃Functor_map_app_app_app, CategoryTheory.Sheaf.ΓHomEquiv_naturality_right, CategoryTheory.GradedObject.mapTrifunctorObj_map_app, HomologicalComplex.quasiIso_opFunctor_map_iff, CategoryTheory.Limits.cokernel_map_comp_cokernelComparison_assoc, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_inv_assoc, MatrixModCat.toModuleCat_map, mapArrowFunctor_map_app_right, AlgebraicTopology.alternatingCofaceMapComplex_map, FundamentalGroupoidFunctor.projRight_map, CategoryTheory.PreGaloisCategory.PointedGaloisObject.Hom.comp, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_hom_app_app, CategoryTheory.Limits.limMap_eq, CategoryTheory.ExponentiableMorphism.coev_naturality, CategoryTheory.map_yonedaEquiv, CategoryTheory.Limits.coequalizerComparison_map_desc_assoc, CategoryTheory.rightAdjointOfCostructuredArrowTerminalsAux_symm_apply, PresheafOfModules.map_id, AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf_map', CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv, CategoryTheory.StructuredArrow.mapIso_inverse_map_right, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app_assoc, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoColimitUncurryWhiskeringLeft₂_hom_assoc, shiftIso_hom_app_comp_shiftMap, CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois_symm_fiber, MonCat.val_inv_units_map_hom_apply, partialLeftAdjointHomEquiv_symm_comp_assoc, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_hom_app, shiftIso_add'_inv_app, CategoryTheory.Limits.Cocones.functoriality_map_hom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_naturality₂, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionHomRight, PushoutObjObj.mapArrowLeft_right, biprodComparison_fst, CategoryTheory.Limits.combineCocones_ι_app_app, CategoryTheory.Comonad.beckEqualizer_lift, CategoryTheory.PreGaloisCategory.autEmbedding_range, HomologicalComplex.singleObjHomologySelfIso_inv_naturality, CategoryTheory.CostructuredArrow.homMk'_comp, CategoryTheory.Adjunction.Triple.map_adj₂_counit_app_leftToRight_app, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen', CategoryTheory.Adjunction.Triple.map_rightToLeft_app_assoc, AddCommGrpCat.forget₂_commMonCat_map_ofHom, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_hom_app_app, CategoryTheory.TwoSquare.structuredArrowDownwards_map, CategoryTheory.SmallObject.SuccStruct.arrowMap_ofCocone, CategoryTheory.Limits.FormalCoproduct.evalOp_obj_map, CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse_map_left, CategoryTheory.MonoidalCategory.DayConvolution.whiskerLeft_comp_unit_app_assoc, CategoryTheory.Adjunction.unit_app_tensor_comp_map_δ, groupCohomology.mapShortComplexH1_comp_assoc, whiskeringLeft₃ObjObjObj_obj_obj_obj_map, lightDiagramToLightProfinite_map, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_obj_obj_map, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_f, CategoryTheory.Pi.sum_map_app, CategoryTheory.counit_obj_eq_map_counit, OplaxLeftLinear.δₗ_naturality_left, CategoryTheory.ShiftedHom.map_mk₀, CategoryTheory.RanIsSheafOfIsCocontinuous.fac, AlgebraicGeometry.Scheme.Hom.normalizationCoprodIso_inv_coprodDesc_fromNormalization_assoc, FullyFaithful.hasShift.map_add_inv_app, Monoidal.μ_snd, CategoryTheory.Comonad.beckFork_ι, CategoryTheory.WithTerminal.equivComma_functor_map_left_app, CategoryTheory.Adjunction.whiskerLeftRUnitIsoOfIsIsoCounit_hom_app, OplaxMonoidal.δ_comp_tensorHom_η_assoc, CategoryTheory.Comma.preLeft_map_left, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_app_assoc, CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app_assoc, flipping_functor_obj_obj_map, AlgebraicGeometry.Scheme.basicOpen_res, CategoryTheory.MonoidalCategory.DayConvolution.associator_inv_unit_unit_assoc, CategoryTheory.ShortComplex.map_leftRightHomologyComparison', AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.map_toTransfiniteCompositionOfShape, TopCat.Sheaf.objSupIsoProdEqLocus_inv_fst, CategoryTheory.Limits.equalizerComparison_comp_π_assoc, postcompose₂_obj_obj_map_app, CategoryTheory.GlueData.ι_gluedIso_hom, CategoryTheory.CosimplicialObject.Augmented.whiskering_map_app_right, AlgCat.forget₂_module_map, CommMonCat.uliftFunctor_map, Rep.invariantsFunctor_map_hom, RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.forgetMapIsOpenImmersion, CategoryTheory.Equivalence.counitInv_naturality, groupHomology.map_id_comp_H0Iso_hom, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom_assoc, CommShift.OfComp.map_iso_hom_app_assoc, CategoryTheory.yonedaEvaluation_map_down, CochainComplex.HomComplex.Cocycle.fromSingleMk_precomp, CategoryTheory.Limits.DiagramOfCones.comp, CochainComplex.ι_mapBifunctorShift₁Iso_hom_f_assoc, AlgebraicGeometry.sigmaOpenCover_f, CategoryTheory.PresheafHom.IsSheafFor.app_cond, CategoryTheory.RetractArrow.map_i_right, Monoidal.map_η_ε_assoc, CategoryTheory.Arrow.cechConerve_map, LaxMonoidal.whiskerRight_tensorUnit_comp_rightUnitor_hom, CategoryTheory.PreGaloisCategory.surjective_of_nonempty_fiber_of_isConnected, CategoryTheory.preservesLimitIso_hom_π, CategoryTheory.Limits.piComparison_comp_π_assoc, CategoryTheory.MonoidalCategory.curriedTensor_map_app, AddCommGrpCat.coyoneda_map_app, toPseudoFunctor'_mapComp, CategoryTheory.TwoSquare.structuredArrowDownwards_obj, CategoryTheory.JointlyReflectIsomorphisms.isIso_iff, CategoryTheory.Presieve.piComparison_fac, CategoryTheory.Equivalence.unit_inverse_comp, CochainComplex.mappingCone.mapHomologicalComplexXIso'_hom, AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp_assoc, map_comp, ContinuousMap.yonedaPresheaf'_map, CategoryTheory.PreGaloisCategory.mulAction_naturality, CoalgCat.toComon_map_hom, CategoryTheory.prodOpEquiv_functor_map, CategoryTheory.Localization.Monoidal.β_hom_app, CategoryTheory.Adjunction.right_triangle_components, CategoryTheory.ihom.ev_naturality_assoc, CategoryTheory.ShortComplex.homologyFunctor_map, CategoryTheory.isIso_iff_isIso_coyoneda_map, AlgebraicGeometry.Scheme.fromSpecStalk_app, Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eq, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id_app, CategoryTheory.Enriched.FunctorCategory.diagram_obj_map, CategoryTheory.ParametrizedAdjunction.unit_whiskerRight_map, CategoryTheory.Adjunction.unit_app_commShiftIso_hom_app, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counitIso_hom_app_tensor, AlgebraicGeometry.StructureSheaf.res_const, IsCoveringMap.monodromyFunctor_map, CategoryTheory.ShortComplex.mapOpcyclesIso_inv_naturality_assoc, CategoryTheory.Comonad.beckFork_pt, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isColimit, flip₂₃_obj_map_app, CategoryTheory.flippingIso_inv_toFunctor_obj_obj_map, CategoryTheory.GrothendieckTopology.sheafification_map, CategoryTheory.CommSq.map, CategoryTheory.Limits.DiagramOfCocones.id, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionLeft_map, Monoidal.μ_snd_assoc, AddCommGrpCat.forget_map, Monoidal.map_η_ε, CategoryTheory.CostructuredArrow.mapNatIso_functor_map_left, CategoryTheory.Adjunction.whiskerLeft_unit_app_app, HomObj.naturality_assoc, CategoryTheory.Limits.CoconeMorphism.map_w_assoc, Monoidal.map_tensor, CategoryTheory.coprodMonad_map, CategoryTheory.MorphismProperty.LeftFraction.map_comp_map_s, HomotopyCategory.homologyShiftIso_hom_app, CategoryTheory.Presheaf.map_comp_uliftYonedaEquiv_down, CategoryTheory.Free.lift_map, CategoryTheory.Limits.instHasCokernelMapOfPreservesColimitWalkingParallelPairParallelPairOfNatHom, CategoryTheory.Limits.prodComparison_natural_assoc, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app, AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_comp, SheafOfModules.pushforwardPushforwardEquivalence_unit_app_val_app, CategoryTheory.WithInitial.liftFromUnder_map_app, WellOrderInductionData.map_lift, CategoryTheory.obj_μ_app_assoc, CategoryTheory.Limits.instIsIsoCoequalizerComparison, CategoryTheory.GrothendieckTopology.overMapPullbackComp_hom_app_val_app, AlgebraicGeometry.Scheme.homOfLE_base, CategoryTheory.GrothendieckTopology.Cover.index_snd, flip₂₃_map_app_app, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.F_obj, CategoryTheory.Iso.inverseCompIso_inv_app, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_obj_map, mono_map_iff_mono, postcompose₃_obj_map_app_app_app, LeibnizAdjunction.adj_unit_app_right, CategoryTheory.StructuredArrow.projectSubobject_factors, CategoryTheory.eq_inverse_map, OplaxMonoidal.δ_natural, LaxLeftLinear.μₗ_naturality_left_assoc, AlgebraicGeometry.PresheafedSpace.congr_app, IsRepresentedBy.iff_of_isoObj, whiskeringLeft₃ObjObjObj_obj_obj_map_app, TopCat.Presheaf.presheafEquivOfIso_counitIso_hom_app_app, CategoryTheory.PreOneHypercover.Homotopy.map_eq_map, CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.map_eq_pullHom_assoc, map_neg, CategoryTheory.Idempotents.DoldKan.Γ_map_app, OplaxMonoidal.δ_natural_right, BialgCat.forget₂_coalgebra_map, homMonoidHom_apply, CategoryTheory.Limits.KernelFork.map_condition, congr_map, CategoryTheory.Limits.PreservesPullback.iso_hom_fst_assoc, PushoutObjObj.ofHasPushout_inr, CategoryTheory.Endofunctor.Adjunction.Algebra.toCoalgebraOf_map_f, CategoryTheory.Adjunction.homEquiv_naturality_left_symm, map₂HomologicalComplex_obj_map, CategoryTheory.FunctorToTypes.mem_fromOverSubfunctor_iff, HomologicalComplex₂.totalShift₁Iso_hom_naturality_assoc, CategoryTheory.NatTrans.congr, Homotopy.map_eq_of_inverts_homotopyEquivalences, AlgebraicTopology.DoldKan.Γ₂N₁.natTrans_app_f_app, CategoryTheory.IsPushout.map, HomologicalComplex.shortComplexFunctor'_map_τ₃, OplaxRightLinear.δᵣ_associativity_assoc, CategoryTheory.NatIso.naturality_2_assoc, CategoryTheory.nerve.functorOfNerveMap_nerveFunctor₂_map, CategoryTheory.Limits.PushoutCocone.isoMk_hom_hom, CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_map_hom, CategoryTheory.InjectiveResolution.iso_inv_naturality_assoc, CategoryTheory.endofunctorMonoidalCategory_tensorUnit_map, CategoryTheory.PreGaloisCategory.IsNaturalSMul.naturality, CategoryTheory.Iso.isoFunctorOfIsoInverse_hom_app, commAlgCatEquivUnder_functor_map, CategoryTheory.InjectiveResolution.isoRightDerivedToHomotopyCategoryObj_hom_naturality, CategoryTheory.ShiftedHom.opEquiv_symm_apply, RingHom.EssFiniteType.exists_comp_map_eq_of_isColimit, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_map_snd_app, CategoryTheory.Over.iteratedSliceForward_map, CategoryTheory.ActionCategory.homOfPair.val, CategoryTheory.simplicialToCosimplicialAugmented_map_right, CategoryTheory.MorphismProperty.RightFraction.map_ofHom, CategoryTheory.Sieve.functor_map_coe, AlgebraicTopology.DoldKan.degeneracy_comp_PInfty, postcompose₂_map_app_app_app, CategoryTheory.Grothendieck.transport_fiber, CategoryTheory.bifunctorComp₁₂FunctorObj_map_app_app_app, CochainComplex.HomComplex.Cochain.toSingleMk_postcomp, Final.exists_coeq_of_locally_small, CategoryTheory.Subgroupoid.mem_im_iff, CategoryTheory.ShortComplex.mapRightHomologyIso_hom_naturality_assoc, CategoryTheory.coyonedaPairing_map, CategoryTheory.Adjunction.homEquiv_counit, CategoryTheory.Localization.Monoidal.μ_natural_right_assoc, CategoryTheory.CosimplicialObject.whiskering_obj_obj_map, HomologicalComplex.HomologySequence.mapSnakeInput_f₂, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_hom_app, CategoryTheory.Limits.cospanCompIso_hom_app_right, AlgebraicGeometry.PresheafedSpace.id_c_app, HomologicalComplex₂.toGradedObjectFunctor_map, mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app, LaxRightLinear.μᵣ_unitality_assoc, CategoryTheory.CostructuredArrow.pre_map_right, CategoryTheory.Equivalence.unit_app_comp_inverse_map_η_functor_assoc, CategoryTheory.Localization.Preadditive.add'_zero, LaxMonoidal.ε_tensorHom_comp_μ, map_injective, HomologicalComplex.asFunctor_map_f, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.functor_map, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₁, CategoryTheory.Presheaf.equalizerSieve_apply, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₁_assoc, core_map_iso_hom, CategoryTheory.Limits.colimit.post_desc, LaxMonoidal.whiskerLeft_μ_comp_μ, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app_assoc, core_map_iso_inv, CategoryTheory.Cat.HasLimits.limitConeLift_toFunctor, leftOp_map, toOplaxFunctor_mapId, CategoryTheory.CatCommSq.iso_hom_naturality_assoc, CategoryTheory.Adjunction.counit_naturality_assoc, obj.ι_def_assoc, CategoryTheory.constantSheafAdj_counit_w, CategoryTheory.Limits.colimit_map_colimitObjIsoColimitCompEvaluation_hom, HomologicalComplex.singleObjCyclesSelfIso_hom_naturality_assoc, PresheafOfModules.pushforward_obj_map_apply', CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.presheafHom_naturality_assoc, curry_obj_map_app, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_comp_assoc, CategoryTheory.Limits.cospanCompIso_app_one, CategoryTheory.StructuredArrow.preEquivalenceFunctor_map_right, PullbackObjObj.π_snd, CompHausLike.LocallyConstant.sigmaComparison_comp_sigmaIso, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂'_obj_obj_map, CategoryTheory.Limits.combineCones_pt_map, CategoryTheory.Limits.reflexivePair_map_reflexion, CategoryTheory.LocalizerMorphism.LeftResolution.Hom.comm_assoc, GrpCat.forget₂_map_ofHom, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counit_app_tensor, CategoryTheory.Adjunction.Triple.leftToRight_app, HomologicalComplex.shortComplexFunctor_map_τ₂, CategoryTheory.Limits.PreservesPushout.inl_iso_hom, CategoryTheory.Comonad.id_map, CategoryTheory.PreGaloisCategory.exists_lift_of_mono, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₁, CategoryTheory.Limits.PreservesCokernel.π_iso_hom, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_hom_right, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app, PullbackObjObj.mapArrowRight_left, AlgebraicGeometry.Scheme.Hom.appLE_comp_appLE_assoc, AlgebraicGeometry.Scheme.SpecMap_presheaf_map_eqToHom, HomologicalComplex.mapBifunctor.d₂_eq', PresheafOfModules.Hom.naturality, CategoryTheory.ChosenPullbacksAlong.iso_pullback_map, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_symm_apply, CategoryTheory.Monad.right_unit, OplaxMonoidal.δ_natural_assoc, CategoryTheory.ShortComplex.mapHomologyIso_inv_naturality, CategoryTheory.Limits.ColimitPresentation.w, LaxMonoidal.right_unitality_inv_assoc, mapBinaryBicone_fst, CategoryTheory.CategoryOfElements.id_val, CategoryTheory.Grothendieck.map_map_fiber, CategoryTheory.PresheafHom.IsSheafFor.exists_app, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompCoyoneda, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_map_injective, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_hom_toNatTrans_app_val_app, AlgebraicTopology.DoldKan.N₁Γ₀_inv_app, Fin.castSuccFunctor_map, partialFunEquivPointed_inverse_map_Dom, CategoryTheory.BasedFunctor.isHomLift_iff, AlgebraicGeometry.Scheme.Hom.inl_toNormalization_normalizationCoprodIso_inv_assoc, SheafOfModules.forgetToSheafModuleCat_map_val, GrpCat.forget_map, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₂, SheafOfModules.pullbackObjFreeIso_hom_naturality, ranObjObjIsoLimit_inv_π, LightCondSet.topCatAdjunctionUnit_val_app, CategoryTheory.Limits.Types.FilteredColimit.colimit_eq_iff, CategoryTheory.IsSplitCoequalizer.map_rightSection, CategoryTheory.Limits.colimit_map_colimitObjIsoColimitCompEvaluation_hom_assoc, SSet.op_map, CategoryTheory.Iso.inverseCompIso_hom_app, CategoryTheory.TwoSquare.EquivalenceJ.functor_map, IsMittagLeffler.eq_image_eventualRange, CommGrpCat.coyonedaType_obj_map, OplaxMonoidal.left_unitality_assoc, CategoryTheory.HasLiftingProperty.transfiniteComposition.sqFunctor_map, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_app_apply, CategoryTheory.Square.toArrowArrowFunctor'_map_right_right, CategoryTheory.Limits.colimit.w_assoc, IsEventuallyConstantTo.isoMap_hom_inv_id_assoc, CategoryTheory.Sieve.mem_functorPushforward_iff_of_full_of_faithful, ModuleCat.free_map_apply, CategoryTheory.InjectiveResolution.Hom.ι_f_zero_comp_hom_f_zero_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_map_app_snd, CategoryTheory.Limits.KernelFork.map_ι, CategoryTheory.Cat.asSmallFunctor_map, CategoryTheory.flipFunctor_map_app_app, CategoryTheory.Prod.sectR_map, CategoryTheory.GrothendieckTopology.ι_plusCompIso_hom, AlgebraicGeometry.instIsIsoSchemeCoprodSpec, condensedSetToTopCat_map, AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.opensRange_map, CategoryTheory.obj_μ_zero_app, CategoryTheory.MorphismProperty.LeftFraction.Localization.Q_map, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_right_map, CategoryTheory.cosimplicialToSimplicialAugmented_map, flippingEquiv_apply_obj_map, CategoryTheory.BasedFunctor.preserves_isHomLift, CochainComplex.HomComplex.Cochain.map_ofHom, CategoryTheory.ExponentiableMorphism.ev_naturality, SSet.OneTruncation₂.nerveHomEquiv_apply, CategoryTheory.Pretriangulated.complete_distinguished_triangle_morphism, CategoryTheory.Grothendieck.map_map_base, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_map_hom, FintypeCat.uSwitchEquiv_symm_naturality, TopCat.Presheaf.Γgerm_res_apply, AlgebraicGeometry.Spec.toPresheafedSpace_map, commShiftOfLocalization_iso_hom_app, CategoryTheory.Paths.lift_toPath, LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv, OplaxRightLinear.δᵣ_unitality_inv_assoc, CategoryTheory.ShrinkHoms.inverse_map, OplaxLeftLinear.δₗ_naturality_right_assoc, FinBoolAlg.hasForgetToFinPartOrd_forget₂_map, CategoryTheory.WithInitial.liftToInitial_map, pointedToTwoPSnd_map_hom_toFun, CategoryTheory.SingleFunctors.evaluation_map, CategoryTheory.Arrow.leftFunc_map, CategoryTheory.StructuredArrow.mapIso_functor_map_right, CategoryTheory.Bifunctor.diagonal', CategoryTheory.Adjunction.map_restrictFullyFaithful_unit_app, CategoryTheory.Limits.reflexivePair.compRightIso_inv_app, commBialgCatEquivComonCommAlgCat_inverse_map_unop_hom, CategoryTheory.Core.forgetFunctorToCore_obj_map, SheafOfModules.pushforwardPushforwardAdj_counit_app_val_app, CategoryTheory.Under.costar_map_left, CategoryTheory.PreGaloisCategory.endEquivAutGalois_π, CategoryTheory.ActionCategory.π_map, CategoryTheory.inducedFunctor_map, CategoryTheory.Monad.unit_naturality_assoc, CategoryTheory.Prod.swap_map, CategoryTheory.Under.equivalenceOfIsInitial_inverse_map, LaxMonoidal.ofBifunctor.firstMap_app_app_app, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_whiskerRight, HomologicalComplex.quasiIso_unopFunctor_map_iff, HomotopicalAlgebra.CofibrantObject.HoCat.ιCompResolutionNatTrans_app, CategoryTheory.Triangulated.TStructure.triangleLTGE_map_hom₁, SSet.StrictSegalCore.map_mkOfSucc_zero_spineToSimplex, CategoryTheory.ShortComplex.mapHomologyIso'_hom_naturality_assoc, CategoryTheory.Limits.Cocones.forget_map, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.SheafCondition.bijective_toPullbackObj, LaxMonoidal.tensorHom_ε_comp_μ, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_app, CategoryTheory.Comma.post_map_right, CategoryTheory.Limits.Cocone.toStructuredArrow_map, CategoryTheory.map_is_split_pair, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_left_map, CategoryTheory.WithTerminal.equivComma_inverse_map_app, CategoryTheory.Limits.cospanCompIso_app_left, CategoryTheory.TwoSquare.vComp_app, Action.isContinuous_def, LaxMonoidal.comp_μ, AlgebraicGeometry.isEmpty_pullback_sigmaι_of_ne, mapCommGrp_map_hom_hom_hom, CategoryTheory.Limits.Cone.w_apply, AlgebraicGeometry.tilde.toOpen_map_app_assoc, CategoryTheory.Equivalence.sheafCongr.inverse_map_val_app, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d_1_0, CategoryTheory.ComposableArrows.mk₀_map, AlgebraicGeometry.LocallyRingedSpace.forgetToSheafedSpace_map, CategoryTheory.shiftFunctorAdd_assoc_hom_app, CategoryTheory.ShortComplex.FunctorEquivalence.functor_map_app, CategoryTheory.Discrete.functor_map, CategoryTheory.Discrete.sumEquiv_functor_map, PullbackObjObj.mapArrowLeft_right, mapGrp_obj_grp_inv, CategoryTheory.sum.associator_map_inl_inl, CategoryTheory.MonoidalOpposite.unmopEquiv_functor_map, CategoryTheory.WithInitial.ofCommaObject_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_rightUnitor, CategoryTheory.Abelian.DoldKan.comparisonN_hom_app_f, CommGrpCat.forget₂_grp_map_ofHom, IsEventuallyConstantFrom.isIso_map, mapAction_map_hom, LaxMonoidal.whiskerRight_tensorUnit_comp_rightUnitor_hom_assoc, CategoryTheory.StructuredArrow.toUnder_map_left, AlgebraicGeometry.LocallyRingedSpace.Γ_map_op, CategoryTheory.StructuredArrow.w_prod_snd_assoc, mapSquare_map_τ₃, AlgebraicGeometry.IsIntegralHom.instDescScheme, CategoryTheory.WithTerminal.equivComma_inverse_obj_map, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_hom_left, SheafOfModules.pullback_map_ιFree_comp_pullbackObjFreeIso_hom, PreOneHypercoverDenseData.multicospanIndex_snd, CategoryTheory.Mat.equivalenceSingleObjInverse_map, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_inv_app_app, CategoryTheory.Adjunction.Triple.epi_rightToLeft_app_iff_epi_map_adj₂_counit_app, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition'_assoc, ProfiniteGrp.diagram_map, AlgebraicGeometry.Scheme.Opens.ι_appLE, CategoryTheory.DifferentialObject.d_squared_assoc, CategoryTheory.Limits.prodComparison_fst_assoc, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_incl_app, CategoryTheory.Limits.limit.id_pre, CategoryTheory.Limits.Cone.toStructuredArrow_map, CategoryTheory.SmallObject.restrictionLT_map, HomologicalComplex.HomologySequence.composableArrows₃Functor_map, SSet.StrictSegal.spineToSimplex_arrow, CategoryTheory.SimplicialObject.Augmented.drop_map, mapArrowFunctor_map_app_left, final_iff_of_isFiltered, CategoryTheory.coyonedaEquiv_symm_map, HomologicalComplex₂.totalShift₁Iso_hom_naturality, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ_assoc, opHom_map_app, FullyFaithful.mulEquivEnd_apply, CategoryTheory.SmallObject.SuccStruct.ofCocone_map, cocones_map_app, CategoryTheory.CostructuredArrow.preEquivalence.functor_map_left, AlgebraicGeometry.Spec.toLocallyRingedSpace_map, AlgebraicGeometry.Scheme.appLE_comp_appLE, CategoryTheory.Limits.coprod.functor_obj_map, CategoryTheory.ShiftMkCore.assoc_hom_app, Monoidal.map_leftUnitor_assoc, CochainComplex.mappingConeCompTriangle_mor₃_naturality_assoc, RightExtension.postcomp₁_obj_hom_app, map_opShiftFunctorEquivalence_counitIso_inv_app_unop, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_map, CategoryTheory.Limits.colimit.w, OplaxMonoidal.right_unitality_assoc, Frm.forget_map, CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.map_eq_pullHom, CategoryTheory.Over.forget_map, partialFunEquivPointed_inverse_map_get_coe, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_obj₂, flip₂₃Functor_obj_map_app_app, AlgebraicGeometry.Scheme.Hom.resLE_comp_resLE, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_hom_app_val_app, CategoryTheory.ObjectProperty.ι_obj_lift_map, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃'_obj_obj_map, CategoryTheory.Equivalence.core_functor_map_iso_hom, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₂, commShiftOfLocalization.iso_hom_app_assoc, ι_leftKanExtensionObjIsoColimit_hom, biproductComparison_π, SimplexCategory.skeletalFunctor_map, AddCommMonCat.coyoneda_obj_map, AddMonCat.equivalence_functor_map, AlgebraicGeometry.Scheme.Opens.ι_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMop_obj_unmop_map, CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctor_map_hom, CategoryTheory.WithInitial.liftFromUnder_obj_map, CategoryTheory.Equivalence.functorFunctor_map, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₃, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_inv_app_app, CategoryTheory.NatTrans.app_shift, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv_assoc, CategoryTheory.uliftFunctor_map, whiskeringLeft₃_obj_obj_obj_obj_obj_map_app, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app_assoc, homologySequenceδ_naturality_assoc, CategoryTheory.Limits.Cone.w_assoc, CategoryTheory.Limits.ofIsReflexivePair_map_left, CategoryTheory.LaxFunctor.mapComp_naturality_left_app, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right_assoc, CategoryTheory.Bimon.toMonComon_map_hom, CategoryTheory.Square.toArrowArrowFunctor_map_left_right, CategoryTheory.cones_map_app_app, SSet.Truncated.Edge.CompStruct.d₀, CommGrpCat.coyoneda_obj_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_app_snd_app, CategoryTheory.Limits.BinaryBicones.functoriality_obj_inl, CategoryTheory.WithTerminal.liftFromOver_map_app, CategoryTheory.typeToCat_map, CategoryTheory.MonoidalClosed.coev_app_comp_pre_app_assoc, relativelyRepresentable.w, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₂, CategoryTheory.Pretriangulated.complete_distinguished_triangle_morphism₁, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_map_right_app, CategoryTheory.GradedObject.ιMapBifunctor₁₂BifunctorMapObj_eq, CommRingCat.commMon_forget₂_map, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app_assoc, AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id_assoc, CategoryTheory.associativity_app, CategoryTheory.SmallObject.prop_iterationFunctor_map_succ, AlgebraicGeometry.SheafedSpace.congr_hom_app, AlgebraicGeometry.IsOpenImmersion.instIsOpenImmersionMapSchemeLocallyRingedSpaceForgetToLocallyRingedSpace, CategoryTheory.Presieve.IsSheafFor.valid_glue, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app, CategoryTheory.MorphismProperty.IsCompatibleWithTriangulation.compatible_with_triangulation, CategoryTheory.Limits.limit.map_pre, AlgebraicGeometry.Scheme.Spec_map, CategoryTheory.WithTerminal.coneEquiv_inverse_map_hom_left, Set.functorToTypes_map, LaxMonoidal.μ_whiskerRight_comp_μ, map_opShiftFunctorEquivalence_unitIso_inv_app_unop_assoc, OplaxMonoidal.δ_comp_δ_whiskerRight, sum_map_inr, CategoryTheory.SingleFunctors.shiftIso_add_hom_app, CategoryTheory.flippingIso_hom_toFunctor_map_app_app, AlgebraicGeometry.Scheme.Hom.toNormalization_inl_normalizationCoprodIso_hom, CategoryTheory.cosimplicialSimplicialEquiv_inverse_map, CategoryTheory.Square.toArrowArrowFunctor_map_right_left, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_inv_app, CategoryTheory.shiftFunctorCompIsoId_zero_zero_hom_app, PushoutObjObj.inr_ι_assoc, CategoryTheory.MonoidalCategory.externalProductBifunctorCurried_obj_map_app_app, TopCat.Presheaf.germ_eq, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one, CategoryTheory.obj_μ_inv_app_assoc, CommBialgCat.forget_map, CategoryTheory.Limits.prod.functor_map_app, CategoryTheory.IsPullback.map, FullyFaithful.map_preimage, CorepresentableBy.homEquiv_symm_comp, whiskeringLeft₃_obj_obj_obj_obj_obj_obj_map, CategoryTheory.δ_naturalityₗ, AlgebraicGeometry.Scheme.Hom.inr_toNormalization_normalizationCoprodIso_inv_assoc, CategoryTheory.InjectiveResolution.toRightDerivedZero'_comp_iCycles_assoc, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁, CategoryTheory.TwoSquare.vComp'_app, DerivedCategory.triangleOfSES_mor₂, CategoryTheory.Join.mapIsoWhiskerLeft_inv_app, imageSieve_map, 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, CategoryTheory.Preadditive.commGrpEquivalence_inverse_map, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_left, TopCat.Presheaf.presheafEquivOfIso_functor_map_app, CommGrpCat.forget₂_commMonCat_map_ofHom, CategoryTheory.Comonad.ComonadicityInternal.main_pair_F_cosplit, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_map_surjective, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_map_right, flippingEquiv_apply_map_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality, CategoryTheory.ShortComplex.SnakeInput.functorL₂'_map_τ₂, toPreimages_obj, CategoryTheory.Limits.WidePullbackShape.wideCospan_map, CommBialgCat.forget₂_commAlgCat_map, CategoryTheory.Adjunction.right_triangle_components_assoc, CategoryTheory.TransfiniteCompositionOfShape.map_incl, CategoryTheory.GradedObject.mapBifunctor_obj_map, SheafOfModules.map_ιFree_mapFree_hom_assoc, CategoryTheory.Subfunctor.Subpresheaf.toPresheaf_map_coe, CategoryTheory.ShortComplex.RightHomologyMapData.map_φH, CategoryTheory.Limits.combineCocones_pt_map, CategoryTheory.Mon.forget_map, CategoryTheory.Limits.IsLimit.homEquiv_symm_naturality, CategoryTheory.MonoidalCategory.curriedTensorPreFunctor_map_app_app, CategoryTheory.Cat.freeReflMap_map, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₁, CategoryTheory.Pseudofunctor.mapId'_hom_naturality, HomotopicalAlgebra.CofibrantObject.exists_bifibrant, HomotopicalAlgebra.CofibrantObject.HoCat.bifibrantResolution'_map, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_hom, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceInverse_map_base, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_app, CategoryTheory.Monad.MonadicityInternal.main_pair_G_split, AlgebraicGeometry.Scheme.Hom.map_appLE, shiftIso_inv_naturality_assoc, PullbackObjObj.ofHasPullback_pt, linear_iff, HomotopyCategory.quotient_map_out, CategoryTheory.ProjectiveResolution.iso_inv_naturality, CategoryTheory.CosimplicialObject.Truncated.whiskering_obj_obj_map, LeftExtension.coconeAt_ι_app, CategoryTheory.ShortComplex.LeftHomologyData.map_f', CategoryTheory.Comma.equivProd_functor_map, CategoryTheory.Adjunction.unit_app_unit_comp_map_η_assoc, LightProfinite.proj_comp_transitionMapLE, CategoryTheory.FunctorToTypes.binaryProductCone_pt_map, CategoryTheory.Localization.isoOfHom_inv_hom_id_assoc, CategoryTheory.Adjunction.leftAdjointCompIso_hom_app, CategoryTheory.NatTrans.shift_app_comm_assoc, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse, CategoryTheory.ComposableArrows.δ₀Functor_map_app, CategoryTheory.Comonad.instHasEqualizerMapAAppUnitObjAOfHasEqualizerOfIsCosplitPair, CategoryTheory.Over.lift_left, toOplaxFunctor'_mapComp, SheafOfModules.pushforwardNatTrans_app_val_app_apply, CategoryTheory.piEquivalenceFunctorDiscrete_functor_map, flip₁₃Functor_obj_obj_obj_map, CategoryTheory.Monad.MonadicityInternal.counitCofork_pt, AlgebraicTopology.DoldKan.Γ₂_map_f_app, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_apply, CategoryTheory.NatTrans.shift_app, PartOrd.forget_map, SSet.Truncated.HomotopyCategory.homToNerveMk_comp, CategoryTheory.MorphismProperty.map_eq_iff_precomp, SSet.Truncated.HomotopyCategory.BinaryProduct.functor_map, CategoryTheory.Abelian.LeftResolution.π_naturality, CategoryTheory.Under.postAdjunctionRight_counit_app_right, ShiftSequence.induced_shiftMap, groupCohomology.cochainsFunctor_map, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_comp_fiber, CategoryTheory.Limits.CokernelCofork.map_condition_assoc, CategoryTheory.SmallObject.coconeOfLE_ι_app, SimplexCategory.skeletalFunctor.coe_map, CategoryTheory.μ_naturality_assoc, quasiIsoAt_iff, CategoryTheory.AreEqualizedByLocalization.map_eq_of_isInvertedBy, CategoryTheory.Pseudofunctor.mapId'_hom_naturality_assoc, CategoryTheory.shiftFunctorAdd_hom_app_obj_of_induced, CategoryTheory.Pi.eval_map, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_succ_succ, CategoryTheory.Comma.mapLeftIso_inverse_map_left, HomologicalComplex.quasiIsoAt_map_of_preservesHomology, CategoryTheory.Limits.biprod.mapBiprod_inv_map_desc, map_shiftFunctorComm, CategoryTheory.instEffectiveEpiFamilyObjMapOfIsEquivalence, LaxRightLinear.μᵣ_naturality_left, CategoryTheory.ShortComplex.SnakeInput.naturality_φ₂_assoc, AddCommMonCat.equivalence_inverse_map, TopologicalSpace.Opens.toTopCat_map, op_commShiftIso_hom_app, CategoryTheory.Limits.biproduct.mapBiproduct_hom_desc, CategoryTheory.Localization.SmallShiftedHom.equiv_mk₀, CategoryTheory.CostructuredArrow.preEquivalence.inverse_map_left_left, HomologicalComplex.mapBifunctor₁₂.ι_eq, CategoryTheory.Limits.coconeEquivalenceOpConeOp_inverse_map_hom, CategoryTheory.RightExactFunctor.whiskeringLeft_obj_map, PushoutObjObj.inl_ι, CategoryTheory.Idempotents.FunctorExtension₁.map_app_f, CochainComplex.HomComplex.Cocycle.equivHomShift_comp_shift, HomotopyCategory.homologyFunctor_shiftMap, CategoryTheory.GradedObject.ιMapBifunctorBifunctor₂₃MapObj_eq, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_inv_hom_id, CategoryTheory.Over.opEquivOpUnder_functor_map, CategoryTheory.Limits.prodComparison_inv_natural_assoc, CategoryTheory.Limits.PullbackCone.isoMk_hom_hom, SSet.S.mk_map_le, HasFibers.inducedFunctor_map_coe, CategoryTheory.CatCommSq.hInv_iso_hom_app, GrpCat.uliftFunctor_map, CategoryTheory.Comonad.ForgetCreatesLimits'.commuting, ModuleCat.forget_map, TopCat.Presheaf.stalkSpecializes_stalkFunctor_map_apply, CategoryTheory.TransfiniteCompositionOfShape.map_F, CategoryTheory.δ_naturalityᵣ, TopCat.Presheaf.stalkFunctor_map_germ, CategoryTheory.Limits.SequentialProduct.functorMap_commSq_succ, CategoryTheory.ShortComplex.mapHomologyIso_inv_naturality_assoc, CoreMonoidal.μIso_hom_natural_right_assoc, CategoryTheory.Monad.MonadicityInternal.counitCofork_ι_app, CategoryTheory.Adjunction.Triple.rightToLeft_app_adj₂_unit_app, PresheafOfModules.toPresheaf_map_sheafificationAdjunction_unit_app, PushoutObjObj.mapArrowRight_right, CategoryTheory.ShortComplex.mapOpcyclesIso_hom_naturality, PullbackObjObj.π_fst_assoc, Initial.extendCone_obj_π_app, Bicategory.Opposite.opFunctor_map, IsRepresentedBy.of_isoObj, CategoryTheory.Localization.SmallHom.equiv_shift, CategoryTheory.ComposableArrows.functorArrows_map, CategoryTheory.preserves_lift_mapCone, CategoryTheory.SingleFunctors.postcompFunctor_map_hom, CochainComplex.shiftShortComplexFunctorIso_zero_add_hom_app, AlgebraicGeometry.IsAffineOpen.app_basicOpen_eq_away_map, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv_assoc, CategoryTheory.uliftYonedaMap_app_apply, CategoryTheory.Limits.diagramIsoSpan_inv_app, WellOrderInductionData.Extension.map_limit, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.rightUnitor_hom_unit_app, LeftExtension.precomp₂_map_left, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_inv_app_assoc, CategoryTheory.Limits.Concrete.colimit_exists_of_rep_eq, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_obj_map_app, CategoryTheory.Under.lift_map, CategoryTheory.Limits.Wedge.condition_assoc, groupHomology.cyclesMap_comp, CategoryTheory.Limits.inv_prodComparison_map_snd_assoc, CategoryTheory.Monad.MonadicityInternal.main_pair_reflexive, LightCondensed.internallyProjective_iff_tensor_condition', LaxLeftLinear.μₗ_associativity_assoc, CategoryTheory.PreservesImage.iso_inv, Final.extendCocone_map_hom, CategoryTheory.ShrinkHoms.functor_map, AlgebraicGeometry.instMonoObjWalkingSpanCompOverSchemeTopMorphismPropertySpanOverForgetForgetForgetNoneWalkingPairSomeMapInitOfIsOpenImmersionLeftDiscretePUnit, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_map_fst_app, CategoryTheory.Limits.multispanIndexCoend_fst, TopCat.Presheaf.toPushforwardOfIso_app, CategoryTheory.OrthogonalReflection.iteration_map_succ_surjectivity, AlgebraicGeometry.Scheme.monObjAsOverPullback_one, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_obj_map_app, CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_left_assoc, AlgebraicGeometry.IsAffineOpen.ΓSpecIso_hom_fromSpec_app, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_pullback_map, CategoryTheory.Pseudofunctor.map₂_whisker_right_app, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₁, CategoryTheory.PreGaloisCategory.autGaloisSystem_map, CategoryTheory.curryingIso_inv_toFunctor_obj_obj_map, CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder_map, CategoryTheory.Abelian.PreservesCoimage.iso_inv_π_assoc, CategoryTheory.unitOfTensorIsoUnit_hom_app, CategoryTheory.StructuredArrow.mapIso_inverse_map_left, ModuleCat.MonModuleEquivalenceAlgebra.inverse_map_hom, CategoryTheory.Limits.coprodComparison_natural_assoc, CategoryTheory.AdditiveFunctor.ofExact_map_hom, CategoryTheory.Adjunction.commShiftIso_inv_app_counit_app, CategoryTheory.SimplicialObject.augmentedCechNerve_map_left_app, LaxMonoidal.μ_natural_assoc, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₁, AlgebraicGeometry.Scheme.restrictFunctor_map_left, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d_1_0_assoc, CategoryTheory.Endofunctor.Adjunction.Coalgebra.homEquiv_naturality_str_symm, HeytAlg.forget_map, CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_eHomWhiskerLeft, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompYoneda, TopCat.Presheaf.generateEquivalenceOpensLe_functor'_map, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionRight_map, CategoryTheory.Comonad.instReflectsLimitWalkingParallelPairParallelPairMapAAppUnitObjAOfReflectsLimitOfIsCosplitPair, Monoidal.lift_μ, CategoryTheory.Limits.PreservesPullback.iso_hom_snd, CategoryTheory.Limits.map_inl_inv_coprodComparison, CategoryTheory.InjectiveResolution.isoRightDerivedObj_inv_naturality_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionHomRight, CategoryTheory.CostructuredArrow.pre_map_left, SSet.Truncated.Path₁.arrow_src, CategoryTheory.shiftFunctorAdd'_assoc_hom_app_assoc, CategoryTheory.Monoidal.tensorObj_map, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp_assoc, CategoryTheory.NatTrans.shift_app_comm, shiftMap_comp_assoc, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_whiskerLeft_assoc, CategoryTheory.Subobject.functor_map, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂'_obj_obj_map, AlgebraicGeometry.morphismRestrict_app, CategoryTheory.Equivalence.sheafCongrPrecoherent_functor_map_val_app, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, currying_functor_obj_map, CategoryTheory.SimplicialObject.augmentedCechNerve_obj_left_map, leftOpRightOpEquiv_functor_map_app, CategoryTheory.Limits.prodComparison_inv_natural, CategoryTheory.yonedaGrp_map_app, CommRingCat.forgetToRingCat_map_hom, AlgebraicGeometry.Scheme.Hom.appLE_comp_appLE, CochainComplex.mappingConeCompTriangleh_comm₁, HomologicalComplex.mapBifunctor₁₂.d₁_eq, CochainComplex.HomComplex.Cocycle.toSingleMk_postcomp, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.functor_map, CategoryTheory.Limits.map_lift_pullbackComparison, SemiRingCat.forget₂_monCat_map, CategoryTheory.nerve.nerveFunctor₂_map_functorOfNerveMap, CategoryTheory.Monoidal.transportStruct_whiskerLeft, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality, ModuleCat.directLimitDiagram_map, CategoryTheory.MorphismProperty.map_mem_map, CategoryTheory.sheafHomSectionsEquiv_symm_apply_coe_apply, CategoryTheory.MonoidalClosed.curry_natural_right, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_hom_app_app, TopCat.Sheaf.eq_of_locally_eq_iff, flip_map_app, partialLeftAdjointHomEquiv_comp, CategoryTheory.Localization.homEquiv_map, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app_assoc, CategoryTheory.Pseudofunctor.map₂_left_unitor_app_assoc, CategoryTheory.Limits.preserves_cokernel_iso_comp_cokernel_map_assoc, LightCondensed.underlying_map, HomotopicalAlgebra.CofibrantObject.weakEquivalence_toHoCat_map_iff, CategoryTheory.subterminalInclusion_map, CategoryTheory.Bifunctor.map_comp_id, PresheafOfModules.naturality_apply, MonCat.Colimits.cocone_naturality, map_shiftFunctorCompIsoId_inv_app, CategoryTheory.Equivalence.ε_comp_map_ε_assoc, mapIso_hom, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv_def, AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id, SSet.Truncated.Edge.CompStruct.d₁, CategoryTheory.Pretriangulated.invRotate_map_hom₃, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_naturality_app, CategoryTheory.PreOneHypercover.map_f, CategoryTheory.regularTopology.EqualizerCondition.bijective_mapToEqualizer_pullback, FinBddDistLat.dual_map, AlgebraicTopology.DoldKan.identity_N₂_objectwise, CategoryTheory.Join.opEquiv_functor_map_op_inclLeft, CategoryTheory.Localization.Monoidal.μ_inv_natural_left, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_invApp, CategoryTheory.map_shrinkYonedaEquiv, CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan_inj_assoc, SimpleGraph.componentComplFunctor_map, CategoryTheory.Mat_.embedding_map, Condensed.underlying_map, CategoryTheory.preserves_desc_mapCocone, CategoryTheory.OverPresheafAux.YonedaCollection.map₁_snd, MulEquiv.toSingleObjEquiv_functor_map, CategoryTheory.WithInitial.opEquiv_inverse_map, CategoryTheory.CostructuredArrow.mapNatIso_functor_map_right, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_obj_map_app, CategoryTheory.Limits.prod.functor_obj_map, mapBifunctorHomologicalComplex_obj_map_f_f, AlgebraicGeometry.PresheafedSpace.comp_c, CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj_hom_naturality, CategoryTheory.ObjectProperty.LimitOfShape.toStructuredArrow_map, HomObj.naturality, CategoryTheory.Under.opEquivOpOver_functor_map, CategoryTheory.ι_preservesColimitIso_inv, CategoryTheory.Limits.biproduct.map_lift_mapBiprod, CategoryTheory.Limits.Cocone.ofPushoutCocone_pt, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₃, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_inv_app_val_app, lightCondSetToTopCat_map, CategoryTheory.prod.leftUnitor_map, SSet.OneTruncation₂.id_edge, HomologicalComplex.cylinder.map_ι₀_eq_map_ι₁, CategoryTheory.yonedaEquiv_symm_map, CategoryTheory.Limits.ι_reflexiveCoequalizerIsoCoequalizer_hom_assoc, relativelyRepresentable.isPullback', AlgebraicGeometry.Scheme.Hom.appLE_map, AlgebraicGeometry.Scheme.Pullback.forget_comparison_surjective, pi'_map, CategoryTheory.NatTrans.whiskerRight_app_tensor_app_assoc, map_nsmul, CategoryTheory.obj_ε_app, CategoryTheory.RelCat.rel_iso_iff, DerivedCategory.HomologySequence.δ_comp_assoc, CategoryTheory.Subgroupoid.inclusion_faithful, CategoryTheory.Limits.coconeEquivalenceOpConeOp_functor_map, CategoryTheory.Limits.PullbackCone.ofCone_pt, CategoryTheory.Adjunction.comp_counit_app_assoc, CategoryTheory.liftedLimitMapsToOriginal_hom_π, CategoryTheory.MorphismProperty.LeftFraction.map_ofInv_hom_id, LaxBraided.braided_assoc, IsDenseSubsite.isIso_ranCounit_app_of_isDenseSubsite, CategoryTheory.Pseudofunctor.CoGrothendieck.map_id_map, CategoryTheory.Join.id_left, AlgebraicGeometry.Proj.res_apply, CategoryTheory.CostructuredArrow.projectQuotient_factors, TopCat.Presheaf.app_injective_iff_stalkFunctor_map_injective, CategoryTheory.NatTrans.naturality_1, HomologicalComplex.mapBifunctor₁₂.d₃_eq, CategoryTheory.constantPresheafAdj_counit_app_app, CategoryTheory.CategoryOfElements.CreatesLimitsAux.map_lift_mapCone, DerivedCategory.HomologySequence.δ_comp, CategoryTheory.Equivalence.sheafCongr.unitIso_inv_app_val_app, AlgebraicGeometry.Scheme.Opens.topIso_hom, CategoryTheory.Join.mapIsoWhiskerLeft_hom_app, CategoryTheory.Quotient.sound, CategoryTheory.GrothendieckTopology.map_yonedaEquiv, SimplexCategory.toCat_map, AlgebraicGeometry.IsLocalAtSource.sigmaDesc, CategoryTheory.CostructuredArrow.mkPrecomp_comp, mapCommGrp_obj_grp_mul, reprW_hom_app, PresheafOfModules.Sheafify.map_smul, CategoryTheory.ComposableArrows.opEquivalence_counitIso_hom_app_app, CategoryTheory.uliftCoyonedaEquiv_symm_map, OplaxMonoidal.comp_δ, AlgebraicGeometry.StructureSheaf.toOpen_res, CategoryTheory.Comonad.ComonadicityInternal.counitFork_pt, curry_map_app_app, hcongr_hom, CategoryTheory.ShortComplex.SnakeInput.functorL₂'_map_τ₁, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.tensorHom_eq, AlgebraicGeometry.Scheme.ofRestrict_app, Monoidal.map_rightUnitor, AlgebraicGeometry.SheafedSpace.congr_app, CategoryTheory.Limits.map_lift_pullbackComparison_assoc, CategoryTheory.Sheaf.ΓObjEquivSections_naturality, CategoryTheory.Limits.Cone.extensions_app, CategoryTheory.Grothendieck.grothendieckTypeToCatInverse_map_base, CategoryTheory.yonedaEquiv_symm_naturality_left, CategoryTheory.ShortComplex.RightHomologyData.map_opcyclesMap', CategoryTheory.OplaxFunctor.mapComp_naturality_left_app_assoc, CategoryTheory.Adjunction.left_triangle_components_assoc, HomotopicalAlgebra.BifibrantObject.HoCat.ιCofibrantObject_map_toHoCat_map, CategoryTheory.PreGaloisCategory.exists_galois_representative, CategoryTheory.Limits.PreservesPullback.iso_hom, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand', FundamentalGroupoidFunctor.prodToProdTop_map, CategoryTheory.Limits.cokernelComparison_map_desc_assoc, OplaxMonoidal.lift_δ_assoc, CategoryTheory.ObjectProperty.IsCodetecting.isIso_iff_of_epi, instCommShiftCochainComplexIntMapMap₂CochainComplex, CategoryTheory.Pretriangulated.Opposite.complete_distinguished_triangle_morphism, CategoryTheory.Cat.whiskerRight_app, CategoryTheory.Limits.pullbackComparison_comp_fst_assoc, CoreMonoidal.left_unitality_assoc, map_opShiftFunctorEquivalence_counitIso_hom_app_unop_assoc, CategoryTheory.Equivalence.leftOp_functor_map, AlgebraicGeometry.IsAffineOpen.fromSpec_app_of_le, mapBifunctorHomologicalComplexObj_obj_d_f, CondensedSet.epi_iff_locallySurjective_on_compHaus, shiftIso_hom_app_comp_shiftMap_of_add_eq_zero, CategoryTheory.IsSplitEqualizer.map_rightRetraction, CategoryTheory.Limits.ι_comp_sigmaComparison_assoc, CategoryTheory.mateEquiv_counit, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₁, CommShift.OfComp.map_iso_inv_app, rightKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, CategoryTheory.LaxFunctor.map₂_associator_app, CategoryTheory.Limits.ofIsReflexivePair_map_right, map_dite, CategoryTheory.Presieve.map_singleton, CategoryTheory.ObjectProperty.trW.shift, SheafOfModules.pushforwardSections_unitHomEquiv, CategoryTheory.wideInducedFunctor_map, CategoryTheory.PreGaloisCategory.PointedGaloisObject.cocone_app, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app, CategoryTheory.Comma.preLeft_map_right, CategoryTheory.Prod.fst_map, CategoryTheory.constantSheafAdj_counit_app, CategoryTheory.Grothendieck.congr, leibnizPullback_map_app, CategoryTheory.GradedObject.ι_mapBifunctorRightUnitor_hom_apply_assoc, CategoryTheory.Over.mapFunctor_map, TopCat.Presheaf.isIso_iff_stalkFunctor_map_iso, AlgebraicGeometry.Scheme.Hom.app_appIso_inv, CategoryTheory.ProjectiveResolution.isoLeftDerivedObj_inv_naturality, CategoryTheory.Equivalence.funInvIdAssoc_inv_app, CategoryTheory.MorphismProperty.LeftFraction.map_comp_map_s_assoc, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.functor_map, CategoryTheory.Grothendieck.grothendieckTypeToCat_functor_map_coe, TopCat.Sheaf.interUnionPullbackCone_pt, HomologicalComplex.unopFunctor_map_f, HomologicalComplex.homologyOp_hom_naturality, CategoryTheory.MorphismProperty.Comma.mapLeft_map_left, CategoryTheory.StructuredArrow.toCostructuredArrow'_map, CategoryTheory.Adjunction.map_η_comp_η, CategoryTheory.Square.opFunctor_map_τ₄, map_isPushout, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberCompIso_hom_app_assoc, Semigrp.forget_map, OplaxMonoidal.right_unitality, CategoryTheory.Core.inclusion_map, leftKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.Limits.FormalCoproduct.cosimplicialObjectFunctor_map_app, CategoryTheory.Triangulated.Octahedron.comm₄, CategoryTheory.ExactFunctor.whiskeringRight_obj_map, instCommShiftCochainComplexIntMapFlipMap₂CochainComplex, OplaxRightLinear.δᵣ_naturality_right, CategoryTheory.IsPushout.map_iff, CategoryTheory.AsSmall.down_map, essImage.liftFunctor_map, CategoryTheory.Center.forget_map, commShift₂_comm_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionHomLeft, AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInfty_assoc, CategoryTheory.Limits.colimit.toCostructuredArrow_map, CategoryTheory.instIsReflexivePairMapAppCounitObj, CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_right, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv_assoc, CategoryTheory.Localization.Preadditive.map_add, CategoryTheory.OverPresheafAux.OverArrows.map_val, CategoryTheory.sum.inverseAssociator_map_inr_inl, CategoryTheory.PreOneHypercover.forkOfIsColimit_ι_map_inj, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one_assoc, CategoryTheory.StructuredArrow.post_obj, AlgebraicGeometry.Scheme.OpenCover.instIsOpenImmersionMapI₀FunctorOfLocallyDirected, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app_assoc, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_yonedaULift_map, DerivedCategory.HomologySequence.exact₃, AlgebraicTopology.DoldKan.map_hσ', FullyFaithful.hasShift.map_zero_inv_app, CategoryTheory.ShortComplex.rightHomologyFunctor_map, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_inverse_map_f, CategoryTheory.ProjectiveResolution.iso_inv_naturality_assoc, AlgebraicTopology.DoldKan.N₂_map_f_f, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app_assoc, CategoryTheory.Adjunction.leftAdjointIdIso_hom_app, CategoryTheory.InjectiveResolution.rightDerivedToHomotopyCategory_app_eq, CategoryTheory.CategoryOfElements.CreatesLimitsAux.map_π_liftedConeElement, CategoryTheory.CostructuredArrow.mapIso_inverse_map_right, DerivedCategory.Q_map_eq_of_homotopy, CategoryTheory.Paths.lift_nil, CategoryTheory.Limits.Cocones.precompose_map_hom, CategoryTheory.uliftYonedaEquiv_symm_map_assoc, CategoryTheory.Sieve.image_mem_functorPushforward, CategoryTheory.Adjunction.instIsIsoMapAppCounitOfFaithfulOfFull, HomologicalComplex.mapBifunctor₁₂.d₂_eq, CategoryTheory.Adjunction.strongEpi_map_of_isEquivalence, HasFibers.fiber_factorization, AlgebraicGeometry.PresheafedSpace.map_comp_c_app, CategoryTheory.IsSplitEqualizer.map_leftRetraction, CategoryTheory.Iso.map_inv_hom_id_eval_assoc, curryingEquiv_symm_apply_obj_map, CategoryTheory.LeftExactFunctor.whiskeringLeft_obj_map, CategoryTheory.Comma.post_obj_hom, CategoryTheory.SingleFunctors.shiftIso_add'_inv_app, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app, IsEventuallyConstantTo.isoMap_inv_hom_id_assoc, CategoryTheory.IsPullback.of_isLimit_cone, CategoryTheory.Limits.coendFunctor_map, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoColimitUncurryWhiskeringLeft₂_hom, FinBoolAlg.dual_map, LaxMonoidal.μ_natural, sheafPushforwardContinuousId'_hom_app_val_app, HomologicalComplex.quasiIsoAt_opFunctor_map_iff, SSet.Truncated.StrictSegal.spine_δ_vertex_lt, CategoryTheory.ExponentiableMorphism.coev_ev, CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_map_hom, CategoryTheory.algebraToUnder_map, CategoryTheory.LocalizerMorphism.RightResolution.Hom.comm_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_inv_app, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι, CategoryTheory.pathComposition_map, FundamentalGroupoidFunctor.proj_map, TopCat.Presheaf.stalkFunctor_map_germ_apply', CategoryTheory.Comonad.adj_unit, CategoryTheory.MorphismProperty.IsCompatibleWithShift.iff, CategoryTheory.prod.rightInverseUnitor_map, CategoryTheory.Adjunction.map_ε_comp_counit_app_unit, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_app, mem_eventualRange_iff, DerivedCategory.HomologySequence.epi_homologyMap_mor₂_iff, CategoryTheory.Limits.map_π_epi, CategoryTheory.SmallObject.SuccStruct.Iteration.prop_map_succ, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_val_app, CategoryTheory.Square.flipFunctor_map_τ₂, CategoryTheory.toQuotientPaths_map, mapHomotopyEquiv_hom, Action.FunctorCategoryEquivalence.functor_obj_map, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_invApp, CategoryTheory.Pseudofunctor.CoGrothendieck.forget_map, CategoryTheory.Localization.Preadditive.zero_add', CategoryTheory.ComposableArrows.precomp_map, CategoryTheory.Limits.LimitPresentation.w_assoc, CommGrpCat.coyoneda_map_app, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃, skyscraperPresheafFunctor_map, const_obj_map, CategoryTheory.Limits.parallelFamily_map_left, commBialgCatEquivComonCommAlgCat_functor_map_unop_hom, CategoryTheory.Localization.Preadditive.neg'_add'_self, CategoryTheory.obj_η_app, AlgebraicGeometry.Scheme.Opens.eq_presheaf_map_eqToHom, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_map_τ₃, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_rightUnitor, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_map, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.mem_map, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_map_snd_app, CategoryTheory.Over.coprod_map_app, CategoryTheory.yoneda'_map_val, Rep.coindFunctor'_map, ComplexShape.Embedding.truncGEFunctor_map, ι_leftKanExtensionObjIsoColimit_hom_assoc, LaxRightLinear.μᵣ_unitality_inv, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ, DerivedCategory.isIso_Q_map_iff_quasiIso, CategoryTheory.Limits.map_π_preserves_coequalizer_inv, CategoryTheory.ShiftMkCore.zero_add_inv_app, CategoryTheory.Limits.map_lift_equalizerComparison_assoc, Rep.coinvariantsFunctor_map_hom, AlgebraicGeometry.map_injective_of_isIntegral, comp_map, CategoryTheory.CostructuredArrow.mapIso_inverse_map_left, CategoryTheory.Subobject.underlying_arrow, DerivedCategory.isIso_Qh_map_iff, CategoryTheory.GrothendieckTopology.uliftYoneda_obj_val_map_down, CategoryTheory.Limits.inv_prodComparison_map_snd, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraidedObj_map, CategoryTheory.Limits.Types.FilteredColimit.isColimit_eq_iff', CategoryTheory.pullbackShiftFunctorAdd'_inv_app, CategoryTheory.StructuredArrow.IsUniversal.fac_assoc, CategoryTheory.OverPresheafAux.map_mkPrecomp_eqToHom, 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, shiftIso_hom_naturality, AlgebraicGeometry.Scheme.pullbackComparison_forget_surjective, CategoryTheory.Sheaf.ΓRes_naturality, CategoryTheory.CostructuredArrow.map₂_obj_hom, SimplicialObject.Splitting.cofan_inj_comp_app_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_eq, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTrans_map_f, CategoryTheory.AdditiveFunctor.ofLeftExact_map_hom, CategoryTheory.Grothendieck.isoMk_hom_fiber, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_obj₁, CategoryTheory.TwistShiftData.shiftFunctor_map, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_app_assoc, CommAlgCat.forget₂_commRingCat_map, CochainComplex.HomComplex.CohomologyClass.toHom_mk, CategoryTheory.bifunctorComp₂₃Obj_map_app, CategoryTheory.Adjunction.homEquiv_naturality_right, CategoryTheory.Equalizer.Presieve.isSheafFor_singleton_iff_of_hasPullback, CategoryTheory.GradedObject.single_map_singleObjApplyIso_hom_assoc, CategoryTheory.Adjunction.unit_comp_map_eq_iff, HomotopicalAlgebra.AttachCells.ofArrowIso_g₁, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_map, Monoidal.map_rightUnitor_inv_assoc, CategoryTheory.Subfunctor.sieveOfSection_apply, CategoryTheory.ShortComplex.RightHomologyMapData.map_φQ, RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π_assoc, CategoryTheory.coreFunctor_obj_map_iso_hom, Rep.linearization_map_hom_single, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_obj_map_app, OplaxMonoidal.δ_natural_right_assoc, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_map, rightOp_map_unop, CategoryTheory.Bicategory.precomp_map, CategoryTheory.Discrete.productEquiv_functor_map, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_val_app, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk_assoc, CategoryTheory.shiftFunctorCompIsoId_zero_zero_inv_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_inv_app'_assoc, HomotopyCategory.quotient_map_mem_quasiIso_iff, groupCohomology.map_id_comp_H0Iso_hom_assoc, CategoryTheory.Limits.map_lift_equalizerComparison, CategoryTheory.cosimplicialSimplicialEquiv_functor_obj_map, CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse_assoc, CategoryTheory.GlueData.ι_gluedIso_hom_assoc, CategoryTheory.DinatTrans.dinaturality, CategoryTheory.TwoSquare.costructuredArrowRightwards_obj, DerivedCategory.left_fac_of_isStrictlyGE, LaxMonoidal.left_unitality_inv, CategoryTheory.Adjunction.shift_unit_app_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionHom, CategoryTheory.Preadditive.commGrpEquivalence_functor_map_hom_hom_hom, AlgebraicGeometry.Scheme.Modules.pushforward_map_app, CategoryTheory.Equivalence.counitInv_naturality_assoc, BddLat.dual_map, CategoryTheory.Comma.colimitAuxiliaryCocone_ι_app, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map_assoc, CategoryTheory.curryingIso_hom_toFunctor_map_app, CategoryTheory.quotientPathsTo_map, HomotopicalAlgebra.CofibrantObject.HoCat.adjCounit'_app, ChainComplex.alternatingConst_map_f, CategoryTheory.Meq.condition, CategoryTheory.ULift.upFunctor_map, CategoryTheory.Localization.Monoidal.rightUnitor_hom_app, CategoryTheory.Idempotents.DoldKan.N_map, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_map_of_preserves, AlgebraicGeometry.Scheme.Hom.inv_app, homologySequenceδ_comp, CategoryTheory.StructuredArrow.IsUniversal.fac, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app', CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_app, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop, AddCommMonCat.forget_map, ShiftSequence.induced_shiftMap_assoc, CategoryTheory.Limits.map_ι_comp_inv_sigmaComparison, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_map_τ₂, CategoryTheory.Limits.diagramIsoParallelPair_inv_app, CategoryTheory.InjectiveResolution.iso_inv_naturality, CategoryTheory.MonoidalCategory.DayConvolution.whiskerRight_comp_unit_app, CategoryTheory.Adjunction.commShiftIso_hom_app_counit_app_shift, CategoryTheory.Limits.Cocones.whiskering_map_hom, Profinite.Extend.functor_map, CategoryTheory.LaxFunctor.mapComp_assoc_right_app_assoc, CategoryTheory.GlueData.mapGlueData_t', SheafOfModules.pushforwardPushforwardEquivalence_counit_app_val_app, ContAction.res_map, CategoryTheory.Enriched.FunctorCategory.functorEnrichedHom_map, CategoryTheory.Limits.inv_prodComparison_map_fst_assoc, AlgebraicGeometry.Scheme.IdealSheafData.subschemeFunctor_map, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app, TopCat.Presheaf.mono_iff_stalk_mono, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂'_obj_map_app, AlgebraicGeometry.IsOpenImmersion.hasLimit_cospan_forget_of_left', CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₁_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_map, inr_biprodComparison'_assoc, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π_assoc, CategoryTheory.PreGaloisCategory.endMulEquivAutGalois_pi, CategoryTheory.Over.coprodObj_map, CategoryTheory.Comma.fst_map, map_braiding, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_two_assoc, CategoryTheory.Limits.sigmaComparison_map_desc, CategoryTheory.NatTrans.naturality_assoc, PresheafOfModules.evaluation_map, CategoryTheory.ShortComplex.opFunctor_map, Bipointed.swap_map_toFun, CategoryTheory.Comma.mapRightIso_inverse_map_left, sheafPushforwardContinuousComp'_hom_app_val_app, SemiNormedGrp.completion_map, mapBinaryBicone_inr, OneHypercoverDenseData.isSheaf_iff.lift_map, HomRel.IsCompatibleWithShift.condition, CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv, HomologicalComplex.opInverse_map, CategoryTheory.Grothendieck.forget_map, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_inv_app_val_app, CategoryTheory.Equivalence.counit_app_functor, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_apply, CategoryTheory.Join.fromSum_map_inl, CategoryTheory.FunctorToTypes.eqToHom_map_comp_apply, LaxMonoidal.left_unitality_inv_assoc, CategoryTheory.GrothendieckTopology.Plus.toPlus_apply, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom, HomologicalComplex₂.flipFunctor_map_f_f, CategoryTheory.Limits.instHasKernelMapOfPreservesLimitWalkingParallelPairParallelPairOfNatHom, CategoryTheory.Square.flipFunctor_map_τ₄, CategoryTheory.SingleFunctors.shiftIso_add'_hom_app, whiskeringLeft₃_obj_obj_obj_obj_map_app_app, CategoryTheory.StructuredArrow.w_assoc, AlgebraicGeometry.coprodMk_inr, CategoryTheory.Equivalence.sheafCongr.counitIso_inv_app_val_app, CommGrpCat.forget₂_map, AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInfty, CategoryTheory.StructuredArrow.mapNatIso_functor_map_left, groupCohomology.functor_map, CategoryTheory.OverPresheafAux.YonedaCollection.map₂_fst, CategoryTheory.Tor_map, HomotopyCategory.isoOfHomotopyEquiv_inv, CategoryTheory.GradedObject.ι_mapBifunctorLeftUnitor_hom_apply_assoc, TopCat.Presheaf.presheafEquivOfIso_functor_obj_map, mapDerivedCategoryFactorsh_hom_app, CategoryTheory.Adjunction.Localization.η_app, CategoryTheory.StructuredArrow.map₂_obj_hom, CategoryTheory.Discrete.productEquiv_inverse_map, map_opShiftFunctorEquivalence_unitIso_hom_app_unop, OneHypercoverDenseData.isSheaf_iff.lift_map_assoc, CategoryTheory.Tor'_map_app, CategoryTheory.InjectiveResolution.Hom.ι_comp_hom, CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit, whiskeringRight_map_app_app, Fin.succFunctor_map, CategoryTheory.LocalizerMorphism.smallShiftedHomMap_mk₀, CategoryTheory.Under.opEquivOpOver_inverse_map, SimplicialObject.Splitting.cofan_inj_eq_assoc, diag_map, CategoryTheory.Cat.FreeRefl.quotientFunctor_map_cons, leftExtensionEquivalenceOfIso₁_functor_map_right, CategoryTheory.GrothendieckTopology.uliftYoneda_map_val_app_down, CategoryTheory.Abelian.DoldKan.comparisonN_inv_app_f, whiskeringLeft₂_obj_obj_map_app_app, CategoryTheory.right_unitality_app, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal_basicOpen, CategoryTheory.CommMon.forget₂Mon_map_hom, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_hom_app, SSet.Truncated.HomotopyCategory.homToNerveMk_comp_assoc, CommGrpCat.toAddCommGrp_map, TopCat.Presheaf.presheafEquivOfIso_inverse_map_app, CategoryTheory.Equivalence.adjointify_η_ε, TopCat.Presheaf.stalkFunctor_map_germ_assoc, CategoryTheory.Limits.Cocone.extensions_app, CategoryTheory.LaxFunctor.mapComp_assoc_left_app_assoc, CategoryTheory.Retract.map_i, CategoryTheory.FunctorToTypes.map_hom_map_inv_apply, CategoryTheory.Adjunction.homEquiv_naturality_left, HomologicalComplex.mapBifunctor.d₁_eq, CategoryTheory.Equivalence.inverse_counitInv_comp, CategoryTheory.MorphismProperty.LeftFraction.Localization.Q_map_comp_Qinv, PullbackObjObj.ofHasPullback_fst, OplaxMonoidal.left_unitality_hom_assoc, IsRepresentedBy.representableBy_homEquiv_apply, CategoryTheory.Limits.diagramIsoSpan_hom_app, CategoryTheory.Limits.limit.w_apply, CategoryTheory.ConcreteCategory.forget_map_eq_coe, SemiRingCat.forget_map, ChainComplex.single₀_map_f_zero, FullyFaithful.hasShift.map_zero_hom_app, CategoryTheory.ShortComplex.SnakeInput.functorL₂_map, CategoryTheory.ShortComplex.fFunctor_map, map_one, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality'_assoc, CategoryTheory.orderDualEquivalence_inverse_map, CategoryTheory.Monad.id_map, CategoryTheory.shiftFunctorAdd_assoc_inv_app, CategoryTheory.ShortComplex.quasiIso_map_of_preservesRightHomology, CategoryTheory.LaxFunctor.map₂_leftUnitor_app, CategoryTheory.Limits.Cones.postcompose_map_hom, CategoryTheory.Adjunction.left_triangle_components, CategoryTheory.Limits.endFunctor_map, CompHausLike.LocallyConstant.functorToPresheaves_obj_map, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₂_assoc, CategoryTheory.Limits.walkingParallelPairOp_right, CategoryTheory.WithTerminal.opEquiv_functor_map, CategoryTheory.PreGaloisCategory.evaluation_aut_injective_of_isConnected, CategoryTheory.Equivalence.unit_app_tensor_comp_inverse_map_δ_functor, CategoryTheory.Sigma.map_map, CategoryTheory.PreOneHypercover.map_p₂, CategoryTheory.Iso.map_hom_inv_id_eval_app, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_hom_app, CategoryTheory.Pseudofunctor.Grothendieck.categoryStruct_comp_fiber, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'_assoc, CategoryTheory.NatTrans.CommShiftCore.app_shift_assoc, AlgebraicGeometry.Scheme.presheaf_map_eqToHom_op, PresheafOfModules.map_comp_assoc, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app, map_preimage, AlgebraicTopology.DoldKan.Γ₀'_map_f, homologySequence_mono_shift_map_mor₂_iff, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_μ_assoc, CategoryTheory.Endofunctor.Adjunction.Coalgebra.toAlgebraOf_map_f, CategoryTheory.GlueData.ι_jointly_surjective, obj.Δ_def, HomologicalComplex.singleObjOpcyclesSelfIso_hom_naturality, whiskeringRight₂_obj_map_app_app, CategoryTheory.shiftFunctorAdd'_assoc_hom_app, CategoryTheory.CostructuredArrow.toStructuredArrow_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.iso_hom_naturality, CategoryTheory.NatTrans.retractArrowApp_i, OplaxMonoidal.right_unitality_hom_assoc, leibnizPushout_map_app, AddCommMonCat.uliftFunctor_map, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberCompIso_hom_app, CategoryTheory.μ_naturalityₗ_assoc, AlgebraicTopology.DoldKan.Compatibility.υ_inv_app, CategoryTheory.Grothendieck.transportIso_hom_fiber, CategoryTheory.Localization.LeftBousfield.W_iff_isIso_map, CategoryTheory.Comma.mapRight_map_right, CochainComplex.mappingCone.mapHomologicalComplexXIso'_inv, IsCoverDense.Types.pushforwardFamily_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_yoneda_map, CategoryTheory.SingleFunctors.postcomp_shiftIso_hom_app, CategoryTheory.Limits.CoconeMorphism.map_w, CategoryTheory.Equivalence.congrRightFunctor_map, HomologicalComplexUpToQuasiIso.isIso_Q_map_iff_mem_quasiIso, CategoryTheory.unit_obj_eq_map_unit, essImage_ext_iff, CategoryTheory.StructuredArrow.homMk'_mk_id, PreservesZeroMorphisms.map_zero, CategoryTheory.CostructuredArrow.IsUniversal.fac_assoc, CategoryTheory.Equivalence.unit_inverse_comp_assoc, Alexandrov.projSup_map, CategoryTheory.SimplicialObject.equivalenceLeftToRight_left_app, inl_biprodComparison'_assoc, Topology.IsInducing.functorNhds_map, CategoryTheory.Over.liftCocone_pt, eventualRange_eq_iff, comp_homologySequenceδ_assoc, TopCat.Presheaf.SheafConditionEqualizerProducts.res_π_apply, CategoryTheory.Square.map_f₂₄, AlgebraicGeometry.Scheme.zeroLocus_map_of_eq, CategoryTheory.toOver_map, PresheafOfModules.forgetToPresheafModuleCat_map, CategoryTheory.ObjectProperty.ihom_map_hom, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv, AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.isOpenImmersion, CategoryTheory.Core.functorToCore_map_iso_inv, OplaxLeftLinear.δₗ_associativity_inv_assoc, CategoryTheory.presheafHom_map_app_op_mk_id, SemimoduleCat.forget₂_map, CategoryTheory.Grothendieck.pre_map_base, CategoryTheory.InjectiveResolution.rightDerived_app_eq, CategoryTheory.Limits.diagonal_pullback_fst, CategoryTheory.InjectiveResolution.Hom.ι'_comp_hom', CategoryTheory.PreservesImage.inv_comp_image_ι_map_assoc, CategoryTheory.ShortComplex.mapLeftHomologyIso_inv_naturality, CommShift.isoAdd'_inv_app, CategoryTheory.Adjunction.derivedε_fac_app, CategoryTheory.Localization.associator_hom_app_app_app, OplaxMonoidal.ofBifunctor.topMapₗ_app, CommShift.OfComp.map_iso_hom_app, Rep.linearization_map_hom, CommShift.OfComp.map_iso_inv_app_assoc, CommShift.isoZero'_hom_app, CategoryTheory.Equivalence.counit_naturality, SheafOfModules.Presentation.map_π_eq, CategoryTheory.MonoidalCategory.externalProductBifunctor_obj_map, CoconeTypes.ι_naturality, CategoryTheory.MorphismProperty.LeftFraction.map_eq, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.inverse_map, AlgebraicGeometry.IsOpenImmersion.lift_app, CategoryTheory.JointlyReflectEpimorphisms.epi_iff, comp_mapMon_one, CoconeTypes.descColimitType_injective_iff_of_isFiltered, CategoryTheory.MonoidalCategory.DayFunctor.ι_map, CategoryTheory.sheafComposeNatTrans_fac, CategoryTheory.PreGaloisCategory.autGaloisSystem_map_surjective, CategoryTheory.Mat_.additiveObjIsoBiproduct_hom_π_assoc, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_app_comp_π_assoc, OplaxMonoidal.associativity_inv_assoc, CategoryTheory.SimplicialObject.Truncated.whiskering_obj_map_app, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_map_app_hom_hom, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_obj_obj_map, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.toBiprod_apply, CategoryTheory.shrinkYonedaEquiv_symm_map, TopModuleCat.hom_forget₂_TopCat_map, CategoryTheory.IsPushout.of_isColimit_cocone, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_assoc, CategoryTheory.Adjunction.map_μ_comp_counit_app_tensor_assoc, HomologicalComplex.ι_mapBifunctorMap, CategoryTheory.Comma.mapLeftIso_functor_map_right, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.epi_f, isMittagLeffler_iff_eventualRange, currying_functor_map_app, SimplicialObject.Splitting.cofan_inj_epi_naturality, CategoryTheory.map_coyonedaEquiv, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_map_fst, CategoryTheory.shiftFunctorAdd_zero_add_inv_app, CategoryTheory.Adjunction.homEquiv_symm_apply, CategoryTheory.StructuredArrow.mkPostcomp_id, CategoryTheory.Limits.limit.w, CategoryTheory.ShortComplex.leftHomologyFunctor_map, CategoryTheory.Limits.inv_piComparison_comp_map_π_assoc, CategoryTheory.Limits.combineCones_π_app_app, AddCommGrpCat.coyonedaType_map_app, Topology.IsInducing.functor_map, SSet.Truncated.Edge.CompStruct.idCompId_simplex, SimplexCategoryGenRel.isSplitMono_toSimplexCategory_map_of_P_δ, mem_homologicalKernel_trW_iff, CategoryTheory.SimplicialObject.augmentedCechNerve_map_right, CategoryTheory.Yoneda.obj_map_id, HomologicalComplex₂.total.forget_map, CategoryTheory.Limits.prodComparison_snd_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.w_app_assoc, isSplitEpi_iff, CategoryTheory.Pseudofunctor.Grothendieck.map_map_base, CategoryTheory.Adjunction.inv_map_unit, CategoryTheory.Limits.widePullbackShapeOp_map, CategoryTheory.map_yonedaEquiv', HomologicalComplex₂.totalFunctor_map, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionHom, CategoryTheory.bifunctorComp₂₃Obj_obj_map, CategoryTheory.Over.ConstructProducts.conesEquivInverse_map_hom, CategoryTheory.Limits.Cowedge.condition, CommMonCat.coyonedaType_map_app, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.instIsOpenImmersionMapI₀Functor, costructuredArrowMapCocone_ι_app, CategoryTheory.AdditiveFunctor.ofRightExact_map_hom, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_fst_map, map_sum, CategoryTheory.Cokleisli.Adjunction.toCokleisli_map, CategoryTheory.Limits.map_lift_piComparison, CategoryTheory.evaluation_map_app, CategoryTheory.CategoryOfElements.toCostructuredArrow_map, mapTriangle_map_hom₂, toOplaxFunctor'_mapId, CategoryTheory.evaluationLeftAdjoint_obj_map, Action.forget_map, comp_mapCommMon_one, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop_assoc, CategoryTheory.Iso.map_inv_hom_id_eval_app_assoc, ModuleCat.FilteredColimits.colimit_add_mk_eq, DerivedCategory.left_fac, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality, CategoryTheory.Idempotents.DoldKan.η_hom_app_f, AddCommGrpCat.toCommGrp_map, CategoryTheory.Limits.walkingCospanOpEquiv_inverse_map, CategoryTheory.simplicialCosimplicialEquiv_functor_obj_map, CategoryTheory.Over.lift_map, AlgebraicGeometry.SheafedSpace.Γ_map_op, CategoryTheory.ShortComplex.mapLeftHomologyIso_inv_naturality_assoc, CategoryTheory.Pretriangulated.preadditiveCoyoneda_homologySequenceδ_apply, Profinite.exists_hom, CategoryTheory.Idempotents.functorExtension₁_map, LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm_assoc, CategoryTheory.Monad.Algebra.Hom.h_assoc, CategoryTheory.Adjunction.Triple.leftToRight_app_map_adj₁_unit_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedAction_obj_map, CategoryTheory.Over.postAdjunctionLeft_counit_app_left, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_left_hom, CategoryTheory.LaxFunctor.map₂_leftUnitor_app_assoc, HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac'_assoc, CategoryTheory.Limits.cospanCompIso_app_right, CategoryTheory.Limits.pullbackConeEquivBinaryFan_inverse_map_hom, skyscraperPresheaf_map, CategoryTheory.ShiftMkCore.assoc_hom_app_assoc, CategoryTheory.GradedObject.ι_mapTrifunctorMapMap, AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_app, AlgebraicGeometry.Scheme.Hom.inl_toNormalization_normalizationCoprodIso_inv, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_three_assoc, AlgebraicGeometry.Scheme.Hom.inr_normalizationCoprodIso_hom_fromNormalization, mapCommGrp_obj_grp_inv, AlgebraicGeometry.Scheme.Hom.appIso_inv_appLE, CategoryTheory.ShortComplex.mapHomologyIso'_inv_naturality_assoc, whiskeringLeft₃ObjObjObj_map_app_app_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply_assoc, CategoryTheory.Adjunction.Triple.rightToLeft_app_adj₂_unit_app_assoc, CategoryTheory.Bicategory.postcomp_map, AlgebraicGeometry.Scheme.Modules.map_smul, CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_right_assoc, CategoryTheory.Limits.ker_map, CategoryTheory.Presheaf.isLocallySurjective_presheafToSheaf_map_iff, CategoryTheory.CosimplicialObject.Augmented.drop_map, CategoryTheory.Adjunction.shift_counit_app_assoc, CategoryTheory.shift_neg_shift', CategoryTheory.Monoidal.Reflective.instIsIsoMapTensorHomAppUnit, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerLeft, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality_assoc, CategoryTheory.Grothendieck.ι_map, CategoryTheory.ihom.coev_ev_assoc, CategoryTheory.RightExactFunctor.whiskeringRight_obj_map, CategoryTheory.shrinkYonedaEquiv_shrinkYoneda_map, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_counit, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_obj_obj_map, CategoryTheory.Equivalence.functor_unit_comp_assoc, HomotopicalAlgebra.CofibrantObject.toHoCat_map_eq, comp_mapGrp_one, CategoryTheory.enrichedNatTransYoneda_map_app, AddMonCat.adjoinZero_map, homologySequence_epi_shift_map_mor₂_iff, CategoryTheory.Pi.comap_map, CategoryTheory.Adjunction.unit_naturality_assoc, currying_inverse_map_app_app, CategoryTheory.WithTerminal.opEquiv_inverse_map, RingCat.forget_map, PullbackObjObj.isPullback, ChainComplex.map_chain_complex_of, CategoryTheory.ShiftMkCore.assoc_inv_app, Subobject.presheaf_map, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app_assoc, CategoryTheory.MorphismProperty.quotient_iff, CategoryTheory.Limits.limit_map_limitObjIsoLimitCompEvaluation_hom, CategoryTheory.Equivalence.symmEquivInverse_map_app, CategoryTheory.prod.associator_map, SSet.StrictSegal.spineToSimplex_vertex, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_hom_app, functorHomEquiv_symm_apply_app_app, PushoutObjObj.ofHasPushout_ι, CategoryTheory.CostructuredArrow.IsUniversal.hom_desc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app, SSet.Truncated.Edge.tgt_eq, CategoryTheory.Limits.coprodComparison_natural, SemiRingCat.forget₂_addCommMonCat_map, CategoryTheory.ShortComplex.LeftHomologyMapData.map_φK, CategoryTheory.Adjunction.comp_unit_app, CategoryTheory.CommGrp.forget_map, ModuleCat.exteriorPower.functor_map, ιColimitType_eq_iff_of_isFiltered', CategoryTheory.ParametrizedAdjunction.whiskerLeft_map_counit_assoc, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_apply, AlgebraicGeometry.PresheafedSpace.ofRestrict_c_app, whiskeringLeft_map_app_app, CategoryTheory.Limits.SequentialProduct.functorMap_commSq, HomotopicalAlgebra.BifibrantObject.HoCat.ιFibrantObject_map_toHoCat_map, CategoryTheory.Adjunction.whiskerLeft_counit_app_app, π_tensor_id_preserves_coequalizer_inv_colimMap_desc, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_obj₃, OneHypercoverDenseData.isSheaf_iff.fac, CategoryTheory.FreeMonoidalCategory.tensorFunc_obj_map, CategoryTheory.IsHomLift.fac, ContinuousMap.Homotopy.eq_diag_path, IsCoverDense.Types.naturality_assoc, CategoryTheory.Abelian.PreservesCoimage.iso_hom_π, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetObj_map, CategoryTheory.enrichedFunctorTypeEquivFunctor_symm_apply_map, AlgebraicGeometry.LocallyRingedSpace.comp_c, CategoryTheory.yonedaEquiv_symm_app_apply, CategoryTheory.Adjunction.leftAdjointCompNatTrans_app, CategoryTheory.Limits.PreservesPushout.iso_hom, map_inv_hom, HomologicalComplex.HomologySequence.mapSnakeInput_f₀, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_snd_map, CategoryTheory.ComposableArrows.δlastFunctor_obj_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_hom_app, CategoryTheory.associator_hom, CategoryTheory.Limits.inr_comp_pushoutComparison, CategoryTheory.WithTerminal.coneEquiv_functor_map_hom, BoolAlg.forget_map, CategoryTheory.Join.mapIsoWhiskerRight_inv_app, CategoryTheory.Pseudofunctor.mapId'_inv_naturality, map_surjective, mapBifunctorHomologicalComplex_obj_obj_d_f, CategoryTheory.Monad.algebraFunctorOfMonadHom_map_f, AlgebraicGeometry.exists_lift_of_germInjective, ModuleCat.CoextendScalars.map_apply, op_map, PresheafOfModules.pushforward₀_obj_map, CochainComplex.ι_mapBifunctorShift₁Iso_hom_f, PreOneHypercoverDenseData.toPreOneHypercover_p₁, CategoryTheory.Monad.right_unit_assoc, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₄, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_app_assoc, CategoryTheory.preadditiveYonedaObj_map, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁'_obj_obj_map, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_app, CategoryTheory.Limits.Bicones.functoriality_obj_π, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_shift, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_assoc, CategoryTheory.prod.inverseAssociator_map, CategoryTheory.Monad.FreeCoequalizer.topMap_f, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_map_left_right, structuredArrowMapCone_π_app, groupCohomology.map_comp_assoc, CategoryTheory.ShortComplex.mapHomologyIso'_inv_naturality, CategoryTheory.ShortComplex.mapCyclesIso_hom_naturality, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_app, ModuleCat.forget₂_map, CategoryTheory.NatTrans.sum_app_inr, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_map_app_app_app, CategoryTheory.Pseudofunctor.DescentData.Hom.comm, AlgebraicGeometry.tilde.toOpen_map_app, CategoryTheory.Limits.KernelFork.map_condition_assoc, CategoryTheory.ComposableArrows.Precomp.map_one_one, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app_assoc, CategoryTheory.OverPresheafAux.counitForward_naturality₂, partialLeftAdjoint_map, CochainComplex.mappingCone.map_δ, AddCommGrpCat.coyoneda_obj_map, CategoryTheory.ihom.coev_ev, CategoryTheory.bifunctorComp₁₂Obj_map_app, CategoryTheory.Arrow.rightFunc_map, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_εIso_hom, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map, currying_inverse_obj_map_app, IsCoverDense.Types.naturality, CategoryTheory.LiftRightAdjoint.instIsCoreflexivePairMapAppUnitOtherMap, HomologicalComplex.quasiIsoAt_map_iff_of_preservesHomology, mapComposableArrows_map_app
obj 📖	CompOp	12867 math math: CategoryTheory.Mod_.comap_obj_mod, TopCat.Presheaf.generateEquivalenceOpensLe_functor'_obj_obj, CategoryTheory.Equivalence.adjointify_η_ε_assoc, CategoryTheory.GrothendieckTopology.coneCompEvaluationOfConeCompDiagramFunctorCompEvaluation_pt, CategoryTheory.Grp.mkIso_inv_hom, inr_biprodComparison', CategoryTheory.Limits.Trident.condition_assoc, CategoryTheory.Limits.limMap_π, CategoryTheory.Localization.Monoidal.leftUnitor_hom_app, SSet.OneTruncation₂.nerveEquiv_apply, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₃, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_right, CategoryTheory.shiftFunctorZero_inv_app_obj_of_induced, CategoryTheory.Limits.Cones.postcomposeId_hom_app_hom, Condensed.finYoneda_obj, CategoryTheory.Triangulated.SpectralObject.Hom.comm, AlgebraicGeometry.Scheme.toSpecΓ_apply, HomotopyCategory.spectralObjectMappingCone_δ'_app, PresheafOfModules.Monoidal.tensorObj_obj, CommSemiRingCat.forget_obj, CategoryTheory.Classifier.pullback_χ_obj_mk_truth, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen, CategoryTheory.Limits.kernelSubobjectMap_arrow_assoc, SSet.op_δ, CategoryTheory.Over.associator_hom_left_snd_fst_assoc, CategoryTheory.Limits.parallelFamily_obj_zero, AlgebraicGeometry.Γ_map_morphismRestrict, CategoryTheory.Adjunction.adjToComonadIso_inv_toNatTrans_app, CategoryTheory.Limits.instPreservesMonomorphismsObjFunctorTypeSigmaConst, Action.resCongr_inv, CategoryTheory.MorphismProperty.LeftFraction.map_compatibility, CategoryTheory.Limits.coker.π_app, CategoryTheory.Limits.Cocones.precompose_obj_ι, CategoryTheory.GrothendieckTopology.overMapPullbackId_hom_app_val_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_eq, CategoryTheory.CostructuredArrow.homMk'_id, CategoryTheory.Pseudofunctor.mapComp'_naturality_1_assoc, whiskeringRightObjIdIso_hom_app_app, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π, AlgebraicGeometry.Scheme.Modules.pushforward_obj_presheaf_map, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraidedObj_obj, Action.forget_η, CategoryTheory.Join.pseudofunctorLeft_mapId_inv_toNatTrans_app, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₁, TopCat.binaryCofan_isColimit_iff, Rep.resCoindHomEquiv_symm_apply_hom, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_fst, LeftExtension.coconeAtFunctor_map_hom, CochainComplex.acyclic_op, functorHomEquiv_apply_app, GrpCat.FilteredColimits.colimit_inv_mk_eq, CategoryTheory.SimplicialObject.id_left_app, Rep.resCoindHomEquiv_apply_hom, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_hom_right, CategoryTheory.sum.inrCompInverseAssociator_hom_app, FullyFaithful.homNatIsoMaxRight_inv_app, CategoryTheory.Over.prodLeftIsoPullback_hom_snd_assoc, CategoryTheory.MorphismProperty.exists_isPushout_of_isFiltered, CategoryTheory.GrothendieckTopology.W_sheafToPresheaf_map_iff_isIso, CategoryTheory.prodComonad_ε_app, CategoryTheory.LeftExactFunctor.ofExact_map, map_homCongr, CommShift.isoAdd_hom_app, CategoryTheory.Adjunction.compUliftCoyonedaIso_hom_app_app_down, DiscreteContAction.instDiscreteTopologyCarrierObjTopCatForget₂ContinuousMap, CategoryTheory.Monoidal.tensorHom_app, CategoryTheory.Tor'_obj_obj, smoothSheafCommRing.ι_forgetStalk_inv, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerLeftIso_inv_app, CategoryTheory.whiskeringLeft_comp_evaluation, CategoryTheory.SingleFunctors.postcompPostcompIso_hom_hom_app, CategoryTheory.GrothendieckTopology.Plus.toPlus_mk, CategoryTheory.Enriched.Functor.associator_inv_apply, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.hπ_assoc, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_map, CategoryTheory.uliftCoyonedaEquiv_apply, CategoryTheory.Limits.DiagramOfCones.id, CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_app, CategoryTheory.PreOneHypercover.forkOfIsColimit_ι_map_inj_assoc, CategoryTheory.Sum.natTransOfWhiskerLeftInlInr_app, SheafOfModules.pushforward_assoc, CategoryTheory.instSmallOppositeObjFunctorTypeYoneda, CategoryTheory.PresheafOfGroups.OneCochain.one_ev, CategoryTheory.Subobject.map_mk, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverse_obj, CategoryTheory.TwoSquare.instInitialStructuredArrowObjStructuredArrowDownwardsOfGuitartExact, CategoryTheory.Limits.HasImage.of_arrow_iso, rightKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.Grp.mkIso_hom_hom, AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality_assoc, CategoryTheory.GlueData.diagramIso_app_right, CochainComplex.mappingConeCompTriangleh_comm₁_assoc, Initial.extendCone_obj_pt, Rep.invariantsAdjunction_homEquiv_symm_apply_hom, CategoryTheory.Mat_.additiveObjIsoBiproduct_hom_π, PushoutObjObj.inr_ι, isoSum_inv_app_inl, CategoryTheory.Limits.IndizationClosedUnderFilteredColimitsAux.exists_nonempty_limit_obj_of_isColimit, AddCommGrpCat.coyoneda_obj_obj_coe, AlgebraicGeometry.Proj.awayMap_awayToSection_assoc, HomologicalComplex.extendSingleIso_inv_f, pointedToTwoPFst_obj_toTwoPointing_toProd, LightCondensed.free_internallyProjective_iff_tensor_condition, CategoryTheory.Equivalence.leftOp_unitIso_hom_app, CategoryTheory.Over.μ_pullback_left_snd', CategoryTheory.linearCoyoneda_obj_additive, CategoryTheory.Monad.ForgetCreatesColimits.commuting, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_hom_app_val_app, CategoryTheory.WithTerminal.coneEquiv_unitIso_hom_app_hom_left, mapTriangleIdIso_inv_app_hom₃, CategoryTheory.SimplicialObject.whiskering_obj_map_app, CategoryTheory.Monad.monadMonEquiv_unitIso_inv_app_toNatTrans_app, IsDenseSubsite.instIsIsoSheafAppCounitSheafAdjunctionCocontinuous, CategoryTheory.Limits.limitConeOfUnique_cone_π, CochainComplex.HomComplex.Cochain.rightShiftAddEquiv_symm_apply, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, CategoryTheory.ComposableArrows.opEquivalence_counitIso_inv_app_app, CategoryTheory.mateEquiv_counit_symm, CategoryTheory.Pseudofunctor.DescentData.ofObj_hom, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst_assoc, CategoryTheory.MonoidalCategory.DayConvolution.braidingHomCorepresenting_app, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_apply, OplaxMonoidal.ofBifunctor.firstMap₂_app_app_app, coreComp_hom_app_iso_inv, CategoryTheory.Limits.spanCompIso_app_left, CategoryTheory.ComposableArrows.threeδ₂Toδ₁_app_zero, CategoryTheory.Monoidal.InducingFunctorData.rightUnitor_eq, natTransEquiv_apply_app, mapComposableArrowsObjMk₂Iso_inv_app, AlgebraicGeometry.Scheme.map_PrimeSpectrum_basicOpen_of_affine, CategoryTheory.uliftCoyonedaIsoCoyoneda_hom_app_app, CategoryTheory.Pseudofunctor.DescentData.subtypeCompatibleHomEquiv_toCompatible_presheafHomObjHomEquiv, CategoryTheory.Discrete.sumEquiv_counitIso_inv_app, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_hom, ModuleCat.directLimitDiagram_obj_isModule, CategoryTheory.WithTerminal.mkCommaObject_right, CategoryTheory.Limits.imageSubobject_arrow_assoc, CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc, CategoryTheory.coyonedaEquiv_symm_app_apply, CategoryTheory.Subobject.factorThru_right, CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_right, HomologicalComplex.singleMapHomologicalComplex_hom_app_ne, CategoryTheory.StructuredArrow.map_map_right, CategoryTheory.NatTrans.hcomp_id_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon_map, CategoryTheory.MonoidalCategory.leftAssocTensor_obj, OplaxMonoidal.δ_comp_tensorHom_η, CategoryTheory.ObjectProperty.prop_shift_iff_of_isStableUnderShift, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_left, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_injective, CategoryTheory.PreGaloisCategory.mulAction_def, CategoryTheory.shiftFunctorAdd'_assoc_inv_app, CommRingCat.KaehlerDifferential.map_d, partialRightAdjointHomEquiv_comp_symm, CategoryTheory.Subobject.factors_iff, CategoryTheory.Triangulated.Octahedron.mem, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst_assoc, leibnizPullback_obj_map, CategoryTheory.Sheaf.ΓHomEquiv_naturality_left_symm, CategoryTheory.isIso_sheafificationAdjunction_counit, LaxMonoidal.associativity_assoc, CategoryTheory.CosimplicialObject.δ_comp_δ_self_assoc, Rep.coe_linearization_obj_ρ, CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair_hom_app, OplaxMonoidal.associativity, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.hasLimit_cospan_forget_of_right', typeToPartialFunIsoPartialFunToPointed_inv_app_toFun, AlgebraicTopology.DoldKan.Compatibility.equivalence₀_unitIso_hom_app, CategoryTheory.ObjectProperty.ColimitOfShape.toCostructuredArrow_obj, CategoryTheory.Sheaf.isLocallySurjective_sheafToPresheaf_map_iff, CategoryTheory.Idempotents.app_idem_assoc, homObjEquiv_apply_app, CategoryTheory.Limits.imageSubobjectCompIso_hom_arrow, instIsSplitEpiBiproductComparison, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_three_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_left, CategoryTheory.WithInitial.equivComma_functor_obj_right_obj, CategoryTheory.CoreSmallCategoryOfSet.functor_obj, mapBinaryBicone_inl, CategoryTheory.Limits.SingleObj.Types.sections.equivFixedPoints_apply_coe, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app', CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_associator_hom_eq_associator_hom, CategoryTheory.NatIso.mapHomologicalComplex_inv_app_f, CategoryTheory.ComposableArrows.exact_iff_δlast, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_X₃, CategoryTheory.GrothendieckTopology.Cover.index_left, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app, CategoryTheory.whiskeringRightPreservesLimits, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map, CategoryTheory.CartesianMonoidalCategory.prodComparison_snd, CategoryTheory.Adjunction.whiskerLeftLCounitIsoOfIsIsoUnit_hom_app, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app, ModuleCat.FilteredColimits.colimit_smul_mk_eq, CategoryTheory.Equivalence.sheafCongr.counitIso_hom_app_val_app, groupHomology.mapCycles₂_comp_assoc, CategoryTheory.shift_shiftFunctorCompIsoId_hom_app, ModuleCat.restrictScalars.map_apply, AlgebraicGeometry.Spec.toPresheafedSpace_obj, CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux_fac, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_appTop, LightProfinite.proj_comp_transitionMap, CategoryTheory.TwoSquare.instIsConnectedStructuredArrowCostructuredArrowObjCostructuredArrowRightwardsOfGuitartExact, CategoryTheory.Subobject.underlyingIso_hom_comp_eq_mk_assoc, CategoryTheory.Limits.PreservesColimitsOfSize.underPost, CategoryTheory.Limits.biproduct.mapBiproduct_inv_map_desc, CategoryTheory.endofunctorMonoidalCategory_tensorUnit_obj, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp_inv_app_f, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo, TopologicalSpace.Opens.map_id_obj_unop, CochainComplex.HomComplex.Cochain.fromSingleMk_neg, CategoryTheory.yoneda_preservesLimit, CategoryTheory.evaluationLeftAdjoint_map_app, CategoryTheory.NatTrans.prod'_app_snd, CategoryTheory.Limits.CategoricalPullback.catCommSq_iso_hom_app, LightProfinite.Extend.functorOp_obj, CategoryTheory.DifferentialObject.shiftFunctor_obj_d, CategoryTheory.preserves_epi_of_preservesColimit, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.cover_X, AlgebraicGeometry.Scheme.zeroLocus_iInf, CategoryTheory.StructuredArrow.map_comp, CategoryTheory.Limits.colimitHomIsoLimitYoneda_hom_comp_π, AlgebraicGeometry.Scheme.Modules.pushforwardId_inv_app_app, AddCommMonCat.coyoneda_obj_obj_coe, CategoryTheory.ShortComplex.SnakeInput.naturality_φ₁, CategoryTheory.Limits.CatCospanTransform.associator_hom_right_app, CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj_map_f, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_neg, AlgebraicGeometry.IsAffineOpen.map_fromSpec_assoc, LightCondensed.lanPresheafIso_hom, CategoryTheory.Equivalence.symmEquivFunctor_obj, AlgebraicGeometry.IsAffineOpen.isLocalization_of_eq_basicOpen, CategoryTheory.DinatTrans.dinaturality_assoc, CategoryTheory.Cat.Hom₂.comp_app, TopologicalSpace.Opens.inclusion'_hom_apply, CategoryTheory.Limits.diagramIsoPair_hom_app, SimplexCategory.instNonemptyCarrierObjTopCatToTop₀, CategoryTheory.ihom.coev_naturality, CategoryTheory.obj_ε_app_assoc, SSet.stdSimplex.mem_nonDegenerate_iff_strictMono, ComplexShape.Embedding.truncLEFunctor_obj, SSet.stdSimplex.coe_triangle_down_toOrderHom, HasPointwiseLeftDerivedFunctorAt.hasLimit', Set.functorToTypes_obj, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_map_right, AlgebraicGeometry.Scheme.Hom.opensRange_pullbackSnd, CategoryTheory.equivOfTensorIsoUnit_unitIso, CategoryTheory.SimplicialObject.δ_comp_δ_self_assoc, CategoryTheory.Presheaf.isSheaf_of_isTerminal, mapHomologicalComplexIdIso_hom_app_f, comp_obj, CategoryTheory.Comma.snd_obj, mapExtLinearMap_toAddMonoidHom, CategoryTheory.regularTopology.EqualizerCondition.bijective_mapToEqualizer_pullback', CategoryTheory.Limits.limitUnopIsoUnopColimit_hom_comp_ι, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_associator, AlgebraicGeometry.Scheme.Hom.germ_stalkMap_assoc, CategoryTheory.Limits.PreservesEqualizer.iso_hom, CategoryTheory.Join.mapPairId_hom_app, CategoryTheory.Bimon.toMonComonObj_mon_mul_hom, CategoryTheory.Limits.Bicone.toCocone_ι_app_mk, AddGrpCat.uliftFunctor_obj, OplaxMonoidal.δ_natural_left_assoc, leftOpRightOpEquiv_functor_obj_map, TopCat.Sheaf.interUnionPullbackCone_snd, CategoryTheory.Bimon.Bimon_ClassAux_comul, CategoryTheory.Adjunction.whiskerLeftLCounitIsoOfIsIsoUnit_inv_app, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_add, CategoryTheory.linearCoyoneda_obj_obj_carrier, mapMonNatTrans_app_hom, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_hom_hom, LightCondensed.isoFinYonedaComponents_hom_apply, CategoryTheory.Limits.isIso_ι_terminal, CategoryTheory.Cat.asSmallFunctor_obj, TopologicalSpace.Opens.map_coe, CategoryTheory.Presieve.functorPullback_mem, DerivedCategory.right_fac, CategoryTheory.Limits.map_ι_comp_inv_sigmaComparison_assoc, AlgebraicGeometry.Scheme.Hom.image_preimage_eq_opensRange_inter, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_apply, CategoryTheory.Abelian.Ext.homLinearEquiv_apply, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionHomLeft, AddGrpCat.forget₂_map, TopCat.Sheaf.pushforward_sheaf_of_sheaf, CategoryTheory.Limits.WalkingMultispan.functorExt_hom_app, SimplexCategoryGenRel.toSimplexCategory_len, Rep.MonoidalClosed.linearHomEquiv_symm_hom, CategoryTheory.CosimplicialObject.whiskering_obj_obj_obj, SSet.Truncated.tensor_map_apply_snd, LaxMonoidal.whiskerLeft_μ_comp_μ_assoc, CategoryTheory.CosimplicialObject.comp_app, instIsSplitMonoBiprodComparison', CategoryTheory.Core.forgetFunctorToCore_map_app, CategoryTheory.Comma.mapLeftEq_inv_app_right, CategoryTheory.Limits.PreservesPushout.inr_iso_inv_assoc, CategoryTheory.Square.map_X₄, CategoryTheory.Sieve.mem_functorPushforward_iff_of_full, ι_colimitIsoOfIsLeftKanExtension_inv_assoc, shiftIso_add_inv_app, CategoryTheory.Limits.colimitIsoFlipCompColim_inv_app, CategoryTheory.Comma.mapLeftIso_inverse_map_right, HomologicalComplex.isZero_single_obj_X, SSet.oneTruncation₂_obj, CategoryTheory.Subobject.imageFactorisation_F_m, CategoryTheory.MonoidalCategory.DayConvolution.unit_naturality, AlgebraicGeometry.PresheafedSpace.stalkMap_germ, HomotopicalAlgebra.BifibrantObject.HoCat.ιCofibrantObject_obj, CategoryTheory.nerve.σ_obj, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_hom_app_eq, CategoryTheory.shiftFunctorComm_zero_hom_app, SSet.OneTruncation₂.ofNerve₂.natIso_hom_app_map, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionAssocIso_hom, CategoryTheory.Grothendieck.ιCompMap_hom_app_fiber, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app, CategoryTheory.shrinkYoneda_map, CochainComplex.HomComplex.Cocycle.fromSingleMk_add, CategoryTheory.isSeparator_iff_faithful_preadditiveCoyoneda, flip₂₃Functor_obj_obj_obj_obj, Bipointed.swapEquiv_functor_obj_toProd, CategoryTheory.Join.mapWhiskerLeft_app, CategoryTheory.NatTrans.isIso_app_iff_of_iso, leftExtensionEquivalenceOfIso₁_functor_map_left, HomologicalComplex.singleMapHomologicalComplex_hom_app_self, CategoryTheory.ShiftedHom.neg_comp, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_hom_app, CategoryTheory.Subobject.underlyingIso_arrow_assoc, mapConeMapCone_hom_hom, CategoryTheory.Codiscrete.left_triangle_components, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_two, Monoidal.rightUnitor_inv_app, CategoryTheory.Limits.coconeEquivalenceOpConeOp_unitIso, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_hom_app_app_down, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.instIsOpenImmersionCommRingCatMapSheafedSpaceForgetToSheafedSpace, AlgebraicGeometry.Scheme.IsQuasiAffine.toIsImmersion, groupHomology.map₁_quotientGroupMk'_epi, AlgebraicGeometry.StructureSheaf.globalSectionsIso_inv, CategoryTheory.Abelian.PreservesCoimage.iso_hom_π_assoc, CategoryTheory.ComposableArrows.IsComplex.zero'_assoc, CategoryTheory.Preadditive.commGrpEquivalence_functor_obj_grp_one, LeftExtension.precomp₂_obj_hom_app, HomologicalComplex.singleObjHomologySelfIso_hom_singleObjOpcyclesSelfIso_hom_assoc, CategoryTheory.CostructuredArrow.map_comp, AlgebraicGeometry.Scheme.ofRestrict_appIso, CategoryTheory.Limits.Types.binaryCofan_isColimit_iff, HomologicalComplex.truncGE.rightHomologyMapData_φQ, ContinuousCohomology.I_obj_V_isAddCommGroup, SSet.PtSimplex.RelStruct.δ_map_of_lt, CategoryTheory.ULift.upFunctor_obj_down, CategoryTheory.CostructuredArrow.toOver_obj_left, TannakaDuality.FiniteGroup.toRightFDRepComp_in_rightRegular, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_inv_app_val_app, CategoryTheory.isCardinalPresentable_of_isEquivalence, CategoryTheory.Limits.Cotrident.ofCocone_ι, CategoryTheory.Abelian.LeftResolution.karoubi.F_obj_p, BoolRing.hasForgetToBoolAlg_forget₂_obj_coe, CategoryTheory.ObjectProperty.prop_map_iff, CategoryTheory.Localization.Preadditive.homEquiv_symm_apply, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_right_right, ContinuousMap.yonedaPresheaf'_obj, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_e, HomObj.comp_app, CategoryTheory.sheafOver_val, AlgebraicGeometry.RingedSpace.basicOpen_res, groupHomology.coinfNatTrans_app, CategoryTheory.Limits.colimit.isoColimitCocone_ι_inv, CategoryTheory.Comma.opFunctor_obj, CommShift.isoAdd_inv_app, AlgebraicGeometry.Scheme.Hom.app_invApp'_assoc, CategoryTheory.Classifier.SubobjectRepresentableBy.pullback_homEquiv_symm_obj_Ω₀, AlgebraicGeometry.LocallyRingedSpace.restrict_presheaf_obj, CategoryTheory.ReflQuiv.adj_homEquiv, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_inverse_obj_X_d, FullyFaithful.mapMon_preimage_hom, HomologicalComplex.singleObjCyclesSelfIso_hom_singleObjOpcyclesSelfIso_hom_assoc, CategoryTheory.Idempotents.toKaroubi_comp_karoubiFunctorCategoryEmbedding, CategoryTheory.Join.pseudofunctorRight_mapComp_inv_toNatTrans_app, CategoryTheory.Limits.PreservesBinaryBiproduct.preserves, CategoryTheory.Limits.multicospanIndexEnd_fst, AlgebraicTopology.DoldKan.σ_comp_PInfty_assoc, IsDenseSubsite.mapPreimage_id, CategoryTheory.Limits.FormalCoproduct.incl_obj_I, CategoryTheory.Equalizer.Sieve.equalizer_sheaf_condition, opUnopIso_hom_app, CategoryTheory.WithTerminal.equivComma_functor_obj_left_obj, CategoryTheory.Pairwise.diagram_obj, CategoryTheory.Limits.limit.toStructuredArrow_obj, CategoryTheory.Limits.diagramIsoCospan_inv_app, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app_assoc, CategoryTheory.MonoidalOpposite.tensorLeftMopIso_hom_app_unmop, CategoryTheory.SimplicialObject.δ_comp_δ''_assoc, instIsIsoAppCounitRanAdjunctionOfHasPointwiseRightKanExtension, CochainComplex.HomComplex.Cocycle.leftShiftAddEquiv_symm_apply, 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, UniformSpaceCat.completionHom_val, CategoryTheory.Pseudofunctor.map₂_associator_app_assoc, CategoryTheory.Pretriangulated.Opposite.mem_distinguishedTriangles_iff, OplaxMonoidal.δ_comp_η_tensorHom_assoc, LightCondensed.ihomPoints_apply, AlgebraicGeometry.Scheme.app_eq, CategoryTheory.Limits.IsColimit.fac, CategoryTheory.shrinkYonedaEquiv_comp, CategoryTheory.StructuredArrow.map_obj_right, CategoryTheory.Subobject.ofLE_arrow, CategoryTheory.StructuredArrow.mapIso_functor_obj_left, whiskeringRight₂_obj_obj_map_app, CategoryTheory.NatTrans.naturality_2, CategoryTheory.ShortComplex.SnakeInput.functorL₁_obj, CategoryTheory.Subfunctor.Subpresheaf.range_eq_ofSection', CategoryTheory.SmallObject.SuccStruct.extendToSucc_map_le_succ, ModuleCat.restrictScalarsId'App_inv_naturality_assoc, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberDesc, CategoryTheory.Localization.isoOfHom_unop, AlgebraicTopology.NormalizedMooreComplex.obj_d, CategoryTheory.CategoryOfElements.fromStructuredArrow_map, Monoidal.commTensorLeft_hom_app, CategoryTheory.prod.inverseAssociator_obj, CategoryTheory.SimplicialObject.δ_comp_σ_of_gt, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_hom, CategoryTheory.eqToIso_map, CategoryTheory.Limits.map_id_right_eq_curry_swap_map, AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_inv_app, CategoryTheory.HasShift.Induced.add_inv_app_obj, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_ι_presheafHom, CategoryTheory.Limits.FormalCoproduct.fullyFaithfulIncl_preimage, CategoryTheory.Adjunction.Triple.epi_rightToLeft_app_iff_epi_map_adj₁_unit_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_inv_app_hom, AlgebraicGeometry.opensCone_pt, CategoryTheory.Adjunction.Localization.ε_app, CategoryTheory.Pseudofunctor.DescentData.pullFunctorCompIso_inv_app_hom, CategoryTheory.Limits.Cone.unop_ι, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_isLimit_lift, curryingEquiv_symm_apply_obj_obj, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_pullback_map, groupHomology.coinvariantsMk_comp_H0Iso_inv_apply, CategoryTheory.Limits.colimitLimitToLimitColimit_isIso, LaxMonoidal.μ_natural_right, mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app_assoc, CategoryTheory.Monad.free_map_f, CategoryTheory.map_is_cosplit_pair, CategoryTheory.CategoryOfElements.map_snd, AlgebraicGeometry.Scheme.zeroLocus_empty_eq_univ, LaxMonoidal.right_unitality, CategoryTheory.Equivalence.unitIso_hom_app_comp_inverse_map_η_functor_assoc, CategoryTheory.Square.mapFunctor_obj, CategoryTheory.Limits.widePushoutShapeUnop_obj, CategoryTheory.MonoOver.congr_unitIso, AlgebraicGeometry.coprodSpec_apply, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_app_hom_assoc, CategoryTheory.instGuitartExactOverObjOverPostOfHasBinaryProductOfPreservesLimitDiscreteWalkingPairPair, CategoryTheory.Adjunction.unit_app_tensor_comp_map_δ_assoc, Monoidal.whiskerLeft_η_ε, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_left_app, CategoryTheory.Limits.colimit.eqToHom_comp_ι_assoc, Monoidal.whiskerLeft_app_fst_assoc, AlgebraicGeometry.morphismRestrict_base_coe, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.isMonHom_counitIsoAux, CategoryTheory.FunctorToTypes.prodMk_fst, CategoryTheory.Limits.Cone.ofTrident_π, mapCommGrpCompIso_inv_app_hom_hom_hom, CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse, CategoryTheory.Sum.functorEquivFunctorCompFstIso_inv_app_app, CategoryTheory.ShiftedHom.map_comp, mapCommMonNatIso_inv_app_hom_hom, CategoryTheory.sum.associator_obj_inr, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₁, AlgebraicGeometry.StructureSheaf.comap_id, CategoryTheory.OverPresheafAux.unitAux_hom, Profinite.Extend.cocone_pt, CategoryTheory.CosimplicialObject.id_right_app, CategoryTheory.cocones_map_app_app, CategoryTheory.Over.iteratedSliceBackward_map, FundamentalGroupoidFunctor.piIso_hom, LeftExtension.precomp₂_map_right, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_unitIso, CategoryTheory.Sieve.functor_obj, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_map_left_left, PresheafOfModules.instIsLocallySurjectiveToSheafify, PresheafOfModules.add_app, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.F_obj, CategoryTheory.Monoidal.leftUnitor_hom_app, TopCat.Presheaf.locally_surjective_iff_surjective_on_stalks, HomologicalComplex.pOpcycles_singleObjOpcyclesSelfIso_inv, AddMonCat.FilteredColimits.M.mk_surjective, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_app_snd_app, AlgebraicGeometry.Scheme.Hom.toNormalization_inl_normalizationCoprodIso_hom_assoc, mapTriangleOpCompTriangleOpEquivalenceFunctorApp_inv_hom₁, CategoryTheory.InjectiveResolution.homotopyEquiv_inv_ι, CategoryTheory.whiskeringRightPreservesColimits, MonCat.FilteredColimits.colimit_mul_mk_eq', mapTriangleIso_inv_app_hom₁, AlgebraicGeometry.SheafedSpace.forgetToPresheafedSpace_obj, CategoryTheory.Subfunctor.Subpresheaf.range_eq_ofSection, IsEventuallyConstantFrom.cocone_ι_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_whiskerRight, CategoryTheory.wideSubcategoryInclusion.obj, CategoryTheory.ShortComplex.map_X₃, CategoryTheory.Over.associator_inv_left_snd, CategoryTheory.instIsSplitMonoMap, SSet.ι₀_snd_assoc, CategoryTheory.Discrete.sumEquiv_unitIso_inv_app, CategoryTheory.Limits.ReflexiveCofork.app_one_eq_π, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_π_app, SSet.Truncated.HomotopyCategory.descOfTruncation_comp, CategoryTheory.NatIso.cancel_natIso_hom_right, sheafPushforwardContinuousComp'_inv_app_val_app, CategoryTheory.Limits.equalizerComparison_comp_π, HomologicalComplex.isZero_single_obj_homology, condensedSetToTopCat_obj_carrier, AlgebraicGeometry.IsOpenImmersion.hasLimit_cospan_forget_of_right', CategoryTheory.Mon.forget_obj, CategoryTheory.MonoidalCategory.externalProductBifunctor_obj_obj, CategoryTheory.PreGaloisCategory.card_fiber_eq_of_iso, rightOp_map, SSet.Subcomplex.mem_ofSimplex_obj_iff, HasFibers.inducedMap_comp, flip₁₃_map_app_app, CategoryTheory.Limits.isIso_app_coconePt_of_preservesColimit, CategoryTheory.ComposableArrows.isIso_iff₂, AlgebraicGeometry.instIsIsoSchemeCoprodComparisonOppositeCommRingCatSpec, CondensedMod.IsSolid.isIso_solidification_map, CategoryTheory.Abelian.LeftResolution.epi_π_app, CategoryTheory.Limits.pointwiseProduct_obj, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app, CategoryTheory.Dial.tensorObjImpl_rel, IsEventuallyConstantFrom.isoMap_hom_inv_id, mapArrow_obj, groupCohomology.cocyclesMap_id_comp_assoc, CategoryTheory.FreeMonoidalCategory.inclusion_obj, AlgebraicGeometry.IsAffineOpen.map_fromSpec, CategoryTheory.ExponentiableMorphism.homEquiv_symm_apply_eq, AlgebraicGeometry.StructureSheaf.const_mul_rev, mapCommMon_obj_mon_mul, CategoryTheory.MonoidalOpposite.mopMopEquivalence_functor_obj, coe_mapLinearMap, mapMat__obj_X, CategoryTheory.CosimplicialObject.δ_comp_δ''_assoc, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_hom_app_app_val, AlgebraicGeometry.Spec_Γ_naturality, SSet.degenerate_eq_top_of_hasDimensionLT, CategoryTheory.FunctorToTypes.functorHomEquiv_symm_apply_app_app, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec_fromSpecStalk_assoc, eqvGen_colimitTypeRel_iff_of_isFiltered, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_map, TopCat.Presheaf.Pushforward.id_inv_app, CategoryTheory.PreservesImage.factorThruImage_comp_hom, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₃, CategoryTheory.MorphismProperty.LeftFraction.op_map, CochainComplex.isStrictlyGE_shift, CategoryTheory.Limits.spanCompIso_inv_app_zero, map_mul, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_app_assoc, CategoryTheory.Limits.CatCospanTransform.rightUnitor_inv_left_app, CategoryTheory.Limits.limitSubobjectProduct_mono, ModuleCat.freeHomEquiv_apply, CategoryTheory.Limits.Cocone.toOver_ι_app, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_functor_obj_X_X, CategoryTheory.Equivalence.counitIso_inv_app_comp_functor_map_η_inverse, CategoryTheory.NatTrans.flipApp_app, mapComon_obj_X, AlgebraicTopology.DoldKan.HigherFacesVanish.inclusionOfMooreComplexMap, AlgebraicGeometry.IsLocallyArtinian.isArtinianRing_presheaf_obj, mapTriangleIso_inv_app_hom₃, AlgebraicGeometry.Scheme.Opens.toSpecΓ_naturality, CategoryTheory.Limits.colimit.ι_pre_assoc, CategoryTheory.ShortComplex.isIso_homologyFunctor_map_of_epi_of_isIso_of_mono, CategoryTheory.Pretriangulated.Triangle.invRotate_obj₁, TopCat.Presheaf.germ_stalkPullbackHom, CategoryTheory.Under.postComp_inv_app_right, CategoryTheory.Over.pullback_obj_left, Rep.coindResAdjunction_counit_app, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top, CategoryTheory.Adjunction.map_ε_comp_counit_app_unit_assoc, CategoryTheory.CosimplicialObject.δ_comp_δ_assoc, skyscraperPresheaf_obj, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_distinguished, AlgebraicGeometry.LocallyRingedSpace.notMem_prime_iff_unit_in_stalk, CategoryTheory.Limits.Multicofork.ofπ_ι_app, CategoryTheory.Limits.Fork.IsLimit.lift_ι'_assoc, HomologicalComplex.singleObjOpcyclesSelfIso_hom, CategoryTheory.opOp_obj, PreservesFiniteEffectiveEpiFamilies.preserves, AlgebraicGeometry.Scheme.restrictFunctorΓ_inv_app, CategoryTheory.Sheaf.instIsLocallySurjectiveAppArrowILocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, HomologicalComplex.singleObjCyclesSelfIso_inv_iCycles, CategoryTheory.SimplicialObject.σ_naturality_assoc, partialFunEquivPointed_counitIso_inv_app_toFun, CategoryTheory.Arrow.augmentedCechNerve_hom_app, TopCat.coe_of_of, isoSum_inv_app_inr, imageToKernel_unop, CategoryTheory.ran_isSheaf_of_isCocontinuous, TopCat.Presheaf.stalkSpecializes_stalkPushforward, IsEventuallyConstantTo.coneπApp_eq, SSet.instIsDiscreteHomotopyCategoryObjTruncatedOfNatNatTruncationSimplexCategoryStdSimplexMk, CategoryTheory.nerve.δ₂_zero, CategoryTheory.shrinkYonedaEquiv_symm_map_assoc, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_counit_app_app, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_specStalkEquiv, OplaxMonoidal.left_unitality, AlgebraicGeometry.Scheme.Hom.inr_toNormalization_normalizationCoprodIso_inv, groupHomology.chainsMap_f_3_comp_chainsIso₃_apply, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedAction_obj_obj, CategoryTheory.Limits.ι_comp_colimitOpIsoOpLimit_hom_assoc, CategoryTheory.NatTrans.naturality_apply, mapCocone_ι_app, AlgebraicGeometry.instGeometricallyIrreducibleMorphismRestrict, CategoryTheory.LocalizerMorphism.homMap_map, CategoryTheory.Limits.reflexivePair.to_isReflexivePair, CategoryTheory.GrothendieckTopology.diagram_obj, AlgebraicGeometry.instIsDomainCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTopOfIsIntegral, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₂, CategoryTheory.Comma.map_obj_hom, HomologicalComplex₂.totalShift₂Iso_hom_naturality_assoc, LightCondensed.forget_obj_val_map, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_apply, SSet.horn.faceSingletonComplIso_inv_ι_assoc, full_whiskeringRight_obj, ContinuousCohomology.I_obj_V_carrier, TopCat.Presheaf.generateEquivalenceOpensLe_unitIso, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_map_snd_app, AlgebraicTopology.DoldKan.MorphComponents.preComp_a, AlgebraicGeometry.StructureSheaf.comap_comp, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_app_apply, AlgebraicGeometry.Scheme.Opens.mem_ι_image_iff, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_hom_eq_germ, CategoryTheory.Limits.parallelPairOpIso_inv_app_zero, CategoryTheory.Subfunctor.Subpresheaf.toPresheaf_obj, CategoryTheory.shift_shift', CategoryTheory.Limits.HasColimit.isoOfEquivalence_inv_π, CategoryTheory.InjectiveResolution.ι'_f_zero, CategoryTheory.CartesianMonoidalCategory.prodComparison_fst, Rep.resCoindAdjunction_counit_app_hom_hom, SheafOfModules.pushforwardNatIso_inv, CategoryTheory.FreeMonoidalCategory.normalizeIsoAux_inv_app, CategoryTheory.Comonad.ComonadicityInternal.unitFork_π_app, CategoryTheory.ProdPreservesConnectedLimits.γ₂_app, CategoryTheory.Prod.sectL_obj, CategoryTheory.Monoidal.transportStruct_associator, CategoryTheory.ProjectiveResolution.quasiIso, CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse_map_right, CategoryTheory.StructuredArrow.w_prod_fst, CategoryTheory.Adjunction.instIsIsoAppUnitObjOfFaithfulOfFull, CategoryTheory.Arrow.mapCechNerve_app, CorepresentableBy.uniqueUpToIso_inv, CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_left, CategoryTheory.PreOneHypercover.forkOfIsColimit_pt, SSet.degenerate_iff_of_mono, CategoryTheory.Idempotents.functorExtension₁CompWhiskeringLeftToKaroubiIso_inv_app_app_f, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_eq_iff', CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_left_hom, CategoryTheory.Limits.ι_colimitCompWhiskeringLeftIsoCompColimit_hom_assoc, CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux_fac_assoc, AlgebraicGeometry.Scheme.Hom.exists_isIso_morphismRestrict_toNormalization, CategoryTheory.Limits.colimit.cocone_ι, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_symm_apply, mapCommGrp_obj_grp_one, AlgebraicGeometry.morphismRestrict_ι_assoc, PresheafOfModules.Sheafify.add_smul, CategoryTheory.MorphismProperty.FunctorialFactorizationData.hi, CategoryTheory.sum.inlCompInrCompInverseAssociator_hom_app_down_down, uliftCoyonedaCoreprXIso_hom_app, CochainComplex.augmentTruncate_inv_f_zero, CategoryTheory.instMonoMap'KernelCokernelCompSequenceOfNatNat, Monoidal.εIso_hom, isLimitConeOfIsRightKanExtension_lift, OplaxRightLinear.δᵣ_unitality_inv, CategoryTheory.FunctorToTypes.shrinkMap_app, CategoryTheory.Limits.Pi.cone_π, ModuleCat.extendScalarsId_hom_app_one_tmul, CategoryTheory.isCoseparator_iff_faithful_preadditiveYoneda, Profinite.Extend.functorOp_map, Monoidal.tensorHom_app_fst_assoc, AlgebraicGeometry.functionField_isFractionRing_of_isAffineOpen, CategoryTheory.Iso.core_inv_app_iso_hom, CategoryTheory.StructuredArrow.homMk'_comp, AlgebraicGeometry.Scheme.IdealSheafData.ideal_sSup, AlgebraicTopology.singularChainComplexFunctor_exactAt_of_totallyDisconnectedSpace, CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_left_app, CategoryTheory.Cat.associator_hom_app, AlgebraicGeometry.Scheme.fromSpecStalk_toSpecΓ_assoc, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_fromSpec, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.hf, CategoryTheory.Limits.colimit_ι_zero_cokernel_desc_assoc, CategoryTheory.Enriched.Functor.whiskerLeft_app_apply, CategoryTheory.Limits.equalizerSubobject_arrow'_assoc, SSet.stdSimplex.faceSingletonIso_zero_hom_comp_ι_eq_δ, groupHomology.mapCycles₁_comp_apply, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_hom_app_app, CategoryTheory.MorphismProperty.LeftFraction₂.map_add, CategoryTheory.prodComparison_iso, AugmentedSimplexCategory.inclusion_obj, CategoryTheory.CostructuredArrow.w_assoc, AlgebraicGeometry.AffineSpace.SpecIso_hom_appTop, rightDerived_fac_app, CategoryTheory.Limits.HasLimit.isoOfNatIso_inv_π_assoc, CategoryTheory.Comma.toIdPUnitEquiv_inverse_map_right, PresheafOfModules.restrictScalars_map_app, groupHomology.mapShortComplexH1_zero, CategoryTheory.Under.post_comp, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_map_app, AlgebraicGeometry.LocallyRingedSpace.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_app_assoc, AddMonCat.equivalence_functor_obj_coe, CategoryTheory.IsHomLift.map, SSet.σ_mem_degenerate, CategoryTheory.NatTrans.CommShiftCore.shift_app_comm, map_shiftFunctorComm_hom_app, CategoryTheory.WithInitial.isColimitEquiv_apply_desc_right, AlgebraicGeometry.SheafedSpace.colimit_exists_rep, AlgebraicGeometry.instIsAffineSigmaObjScheme, Monoidal.whiskerLeft_μ_δ_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_hom_app_snd_app, CategoryTheory.MonoOver.isIso_left_iff_subobjectMk_eq, CochainComplex.HomComplex.Cochain.leftShift_smul, AlgebraicGeometry.Scheme.Modules.pushforward_obj_obj, CategoryTheory.Idempotents.functorExtension₂_map_app_f, CategoryTheory.Adjunction.derivedε_fac_app_assoc, CategoryTheory.ShortComplex.mapOpcyclesIso_hom_naturality_assoc, CategoryTheory.biconeMk_obj, HomologicalComplex.coneOfHasLimitEval_pt_d, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₁, CategoryTheory.Limits.Fork.π_comp_hom, CategoryTheory.Monad.Algebra.unit_assoc, CategoryTheory.Comon.MonOpOpToComon_obj, CategoryTheory.PreGaloisCategory.endEquivSectionsFibers_π, ProfiniteGrp.limit_one_val, OplaxRightLinear.δᵣ_naturality_right_assoc, CategoryTheory.CostructuredArrow.prodEquivalence_counitIso, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app, CategoryTheory.ShiftedHom.mk₀_zero, CategoryTheory.unmopFunctor_obj, CategoryTheory.Limits.CoconeMorphism.w, TopologicalSpace.Opens.coe_inclusion', CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_ι_inv, AlgebraicGeometry.Scheme.Hom.preimage_bot, CategoryTheory.Equivalence.rightOp_counitIso_inv_app, CategoryTheory.WithInitial.liftToInitialUnique_hom_app, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_inv_eq_germ_assoc, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp, CategoryTheory.RightExactFunctor.whiskeringRight_obj_obj_obj, PullbackObjObj.mapArrowRight_right, FullyFaithful.mapGrp_preimage, CategoryTheory.MonadHom.app_μ, ModuleCat.restrictScalarsComp'App_hom_apply, FintypeCat.uSwitch_map_uSwitch_map, CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_base, curryObjCompIso_hom_app_app, unopOpIso_inv_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_naturality, PresheafOfModules.epi_iff_surjective, CategoryTheory.Under.equivalenceOfIsInitial_counitIso, Bipointed.swapEquiv_inverse_obj_toProd, groupHomology.cyclesMap_id_comp, SSet.Truncated.Path.mk₂_arrow, AlgebraicGeometry.StructureSheaf.const_self, uncurryObjFlip_hom_app, HomologicalComplex.homologyι_singleObjOpcyclesSelfIso_inv_assoc, AlgebraicGeometry.Scheme.mem_basicOpen', PushoutObjObj.mapArrowRight_id, CategoryTheory.NatTrans.epi_iff_epi_app, 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, PullbackObjObj.mapArrowLeft_id, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id_app, CategoryTheory.Subobject.inf_le_left, CategoryTheory.Limits.BinaryBicone.toCone_π_app_right, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom, LaxLeftLinear.μₗ_naturality_right, CategoryTheory.Localization.Construction.lift_obj, ComplexShape.Embedding.truncGE'Functor_obj, CategoryTheory.OplaxFunctor.map₂_associator_app, OplaxMonoidal.δ_snd_assoc, Rep.indFunctor_obj, CategoryTheory.Comma.mapLeft_map_left, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIso_inv_app_hom, CategoryTheory.Limits.Cones.postcompose_obj_pt, groupHomology.mapShortComplexH2_zero, CategoryTheory.Comonad.comparison_obj_a, CategoryTheory.SmallObject.πObj_ιIteration_app_right, CategoryTheory.Limits.PreservesPushout.inr_iso_inv, CategoryTheory.NatIso.isIso_app_of_isIso, AlgebraicTopology.DoldKan.N₂Γ₂ToKaroubiIso_inv_app, CategoryTheory.typeEquiv_functor_obj_val_obj, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_morphismRestrict_assoc, CategoryTheory.WithInitial.coconeEquiv_functor_obj_pt, CategoryTheory.TransportEnrichment.eId_eq, CategoryTheory.MonoidalClosed.ofEquiv_uncurry_def, AlgebraicGeometry.Scheme.zeroLocus_eq_univ_iff_subset_nilradical, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_inv_app, CategoryTheory.ObjectProperty.prop_map_obj, AlgebraicGeometry.Scheme.Opens.topIso_inv, CategoryTheory.OverPresheafAux.restrictedYoneda_map, CategoryTheory.curryingIso_hom_toFunctor_obj_map, SSet.stdSimplex.obj₀Equiv_symm_apply, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition', CategoryTheory.CatCommSq.hInv_iso_inv_app, CategoryTheory.whiskering_linearCoyoneda, CategoryTheory.Discrete.opposite_functor_obj_as, CategoryTheory.GrothendieckTopology.overMapPullbackId_inv_app_val_app, CategoryTheory.toOver_obj_hom, CategoryTheory.Limits.ColimitPresentation.changeDiag_ι, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_preimage_basicOpen, CategoryTheory.Equivalence.leftOp_unitIso_inv_app, CategoryTheory.PreGaloisCategory.autEmbedding_injective, CategoryTheory.Limits.Cone.equiv_inv_pt, CategoryTheory.unopUnop_obj, CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_cancel_hom_app, AlgebraicGeometry.Proj.pow_apply, LaxRightLinear.μᵣ_naturality_right_assoc, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_inverse, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_counitIso, alexDiscEquivPreord_inverse_obj_carrier, CategoryTheory.yonedaGrp_obj, CategoryTheory.Localization.isoOfHom_inv_hom_id, SSet.OneTruncation₂.nerveHomEquiv_id, Monoidal.RepresentableBy.tensorObj_homEquiv, CategoryTheory.MorphismProperty.LeftFraction.Localization.homMk_comp_homMk, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_right_left_as, CategoryTheory.Limits.colimit.pre_post, ProfiniteGrp.ProfiniteCompletion.lift_eta, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_inl, AlgebraicGeometry.PresheafedSpace.isoOfComponents_inv, sectionsFunctor_obj, CategoryTheory.Sieve.ofArrows_category', HomologicalComplex.shortComplexFunctor'_obj_X₁, mapTriangleRotateIso_inv_app_hom₂, PresheafOfModules.evaluation_preservesColimitsOfShape, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_obj_iso_inv, CategoryTheory.Subfunctor.Subpresheaf.max_obj, CategoryTheory.ProjectiveResolution.lift_commutes_zero_assoc, CategoryTheory.Limits.BinaryFan.braiding_hom_snd_assoc, CategoryTheory.Comon.ComonToMonOpOp_obj, TopCat.Presheaf.SheafConditionEqualizerProducts.piOpens.hom_ext_iff, AlgebraicGeometry.Scheme.Hom.opensFunctor_map_homOfLE, CategoryTheory.μ_def, CategoryTheory.Limits.PushoutCocone.mk_ι_app_zero, whiskeringLeft₃ObjObjObj_obj_map_app_app, CategoryTheory.Subobject.map_comp, CategoryTheory.MonoidalClosed.uncurry_natural_right, PresheafOfModules.comp_app, shiftIso_hom_app_comp, CategoryTheory.Limits.FormalCoproduct.cosimplicialObjectFunctor_obj_obj, HomologicalComplex₂.shiftFunctor₂XXIso_refl, postcompose₂_obj_obj_obj_map, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_right_symm, AddCommMonCat.free_obj_coe, CategoryTheory.CostructuredArrow.preEquivalence.functor_obj_right_as, Monoidal.commTensorRight_inv_app, CategoryTheory.ShortComplex.LeftHomologyData.map_leftHomologyMap', CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom_assoc, SheafOfModules.pullbackPushforwardAdjunction_homEquiv_pullbackObjUnitToUnit, CategoryTheory.Comonad.beckCoalgebraFork_pt, CategoryTheory.Monad.algebraFunctorOfMonadHom_obj_A, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.sndFunctor_obj, CategoryTheory.nerve.functorOfNerveMap_map, CategoryTheory.Limits.PreservesColimitPair.iso_hom, CommMonCat.coe_forget₂_obj, SSet.opFunctorCompOpFunctorIso_inv_app_app, CategoryTheory.Limits.IsImage.ofArrowIso_lift, CategoryTheory.Pretriangulated.shiftFunctorZero_op_inv_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_ι_app, prod'_μ_fst, toOrderHom_coe, CategoryTheory.Free.embedding_obj, CategoryTheory.Idempotents.instIsEquivalenceFunctorKaroubiObjWhiskeringLeftToKaroubi, CategoryTheory.Sieve.generate_functorPullback_le, CategoryTheory.StructuredArrow.mapIso_inverse_obj_hom, CommGrpTypeEquivalenceCommGrp.inverse_obj_one, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₂, HomologicalComplex.unopFunctor_obj, LightCondSet.continuous_coinducingCoprod, imageToKernel'_kernelSubobjectIso, CategoryTheory.Under.postCongr_inv_app_right, instIsIsoAppRanCounit, mapMon_obj_mon_mul, isColimitCoconeOfIsLeftKanExtension_desc, SimplicialObject.Split.evalN_obj, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_inv_app_hom, CategoryTheory.Equivalence.leftOp_functor_obj, CategoryTheory.NatIso.naturality_1', CategoryTheory.Subobject.isPullback_aux, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app_assoc, CategoryTheory.Limits.IsLimit.map_π, biprodComparison_snd_assoc, SSet.Truncated.StrictSegal.spine_spineToSimplex, CategoryTheory.CostructuredArrow.pre_obj_hom, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerRightIso_hom_app, CategoryTheory.Endofunctor.Algebra.Hom.h_assoc, AlgebraicGeometry.Scheme.Hom.resLE_eq_morphismRestrict, CategoryTheory.Limits.Cocone.whisker_ι, CategoryTheory.Limits.end_.map_π, Rep.coe_res_obj_ρ, CategoryTheory.SimplicialObject.Truncated.whiskering_obj_obj_obj, OplaxMonoidal.associativity_assoc, ContinuousMap.Homotopy.apply_zero_path, Rep.invariantsFunctor_obj_carrier, CategoryTheory.cosimplicialSimplicialEquiv_counitIso_hom_app_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.comp_snd_app, CategoryTheory.MonoidalCategory.externalProductBifunctor_map_app, CategoryTheory.Adjunction.instIsIsoAppCounitOfFullOfFaithful, CategoryTheory.ForgetEnrichment.equivFunctor_obj, CategoryTheory.StructuredArrow.toUnder_obj_left, CategoryTheory.Limits.BinaryBicone.toBiconeFunctor_obj_π, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₃, CategoryTheory.Monoidal.FunctorCategory.whiskerLeft_app, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left, CategoryTheory.Comonad.ComonadicityInternal.unitFork_pt, CategoryTheory.WithTerminal.opEquiv_inverse_obj, CochainComplex.instIsStrictlyLEObjHomologicalComplexIntUpSingle, CategoryTheory.Over.instIsEquivalenceObjPost, mapTriangleCompIso_inv_app_hom₂, CategoryTheory.Presieve.CoverByImageStructure.fac, CategoryTheory.InjectiveResolution.self_ι, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_leftUnitor, RightExtension.postcompose₂_obj_left_map, pi'CompEval_hom_app, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_obj_obj_obj, ModuleCat.monoidalClosed_uncurry, CategoryTheory.Iso.app_inv, CategoryTheory.Limits.PreservesLimitsOfShape.overPost, LaxMonoidal.ofBifunctor.leftMapₗ_app, AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id_assoc, CategoryTheory.Mod_.comap_obj_X, CategoryTheory.Presieve.isSeparatedFor_singleton, CategoryTheory.Limits.mono_of_isLimit_parallelFamily, CategoryTheory.Over.monObjMkPullbackSnd_mul, AlgebraicGeometry.sigmaOpenCover_X, SSet.Subcomplex.range_eq_ofSimplex, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap_apply, BoolAlg.hasForgetToBoolRing_forget₂_obj_carrier, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app, mapAction_δ_hom, CategoryTheory.CosimplicialObject.δ_comp_δ', CategoryTheory.Monad.Algebra.Hom.h, FullyFaithful.homNatIsoMaxRight_hom_app_down, mapMat__obj_ι, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_inv_left, 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.Pretriangulated.Opposite.mem_distinguishedTriangles_iff', CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app, CategoryTheory.IsPullback.of_isLimit_binaryFan_of_isTerminal, CategoryTheory.ShortComplex.hasHomology_of_preserves', comp_mapGrp_mul, CategoryTheory.Equivalence.core_inverse_map_iso_hom, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app_assoc, CategoryTheory.Over.whiskerLeft_left, CategoryTheory.Monad.algebraFunctorOfMonadHomId_inv_app_f, CochainComplex.exactAt_op, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_map_left, TopCat.uliftFunctorObjHomeo_symm_naturality_apply, CategoryTheory.bifunctorComp₁₂FunctorMap_app_app_app_app, CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_inv_app_app, CategoryTheory.Limits.piComparison_comp_π, CategoryTheory.Equivalence.rightOp_functor_map, DerivedCategory.HomologySequence.comp_δ, SSet.PtSimplex.MulStruct.δ_map_of_gt, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app, fullyFaithfulCancelRight_inv_app, PreOneHypercoverDenseData.w_assoc, CategoryTheory.ParametrizedAdjunction.whiskerLeft_map_counit, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_map_snd, CategoryTheory.Limits.image.map_id, CategoryTheory.OverPresheafAux.restrictedYoneda_obj, CategoryTheory.CatCenter.localization_app, LightCondensed.finYoneda_obj, AlgebraicGeometry.Scheme.inv_app, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_map_app_app, CategoryTheory.GrothendieckTopology.ι_plusCompIso_hom_assoc, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_inv_app_hom_coe, CategoryTheory.GradedObject.singleObjApplyIso_inv_single_map, mapTriangle_obj, CategoryTheory.Abelian.Ext.preadditiveYoneda_homologySequenceδ_singleTriangle_apply, leftDerived_fac_app, LightCondensed.isoFinYoneda_inv_app, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_app_assoc, CategoryTheory.Over.equivalenceOfIsTerminal_counitIso, CategoryTheory.BraidedCategory.ofBifunctor.Forward.secondMap₃_app_app_app, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_hom_app, OneHypercoverDenseData.essSurj.presheaf_obj, CategoryTheory.Grpd.free_obj, AlgebraicGeometry.Scheme.Hom.id_appTop, CategoryTheory.Subfunctor.toFunctor_obj, RepresentableBy.homEquiv_eq, SSet.nonDegenerate_iff_of_mono, CategoryTheory.Presheaf.imageSieve_app, CategoryTheory.Presheaf.isSheaf_iff_isLimit_coverage, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_hom_inv_id, Monoidal.instIsIsoδ, CategoryTheory.Comonad.ForgetCreatesLimits'.liftedCone_π_app_f, TannakaDuality.FiniteGroup.forget_obj, AlgebraicGeometry.ι_right_coprodIsoSigma_inv, CondensedMod.isDiscrete_tfae, CategoryTheory.MonoOver.isIso_iff_subobjectMk_eq, RightExtension.postcompose₂_obj_right, AlgebraicGeometry.Proj.basicOpenIsoAway_hom, CategoryTheory.CatCommSq.hId_iso_hom_app, CategoryTheory.linearYoneda_obj_map, smoothSheafCommRing.ι_evalHom_apply, LeftExtension.postcomp₁_map_right_app, CategoryTheory.ThinSkeleton.map_map, CategoryTheory.CostructuredArrow.IsUniversal.existsUnique, mapCoconePrecomposeEquivalenceFunctor_inv_hom, AlgebraicGeometry.ι_sigmaSpec, CategoryTheory.WithInitial.liftToInitial_obj, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_one, mapComposableArrowsObjMk₁Iso_inv_app, TopCat.Presheaf.germ_exist_of_isBasis, IsEventuallyConstantFrom.isIso_ι_of_isColimit', PresheafOfModules.homEquivOfIsLocallyBijective_symm_apply, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp_app, CategoryTheory.Limits.PullbackCone.π_app_right, CategoryTheory.CostructuredArrow.mkPrecomp_id, CategoryTheory.Square.evaluation₁_obj, CategoryTheory.piEquivalenceFunctorDiscrete_inverse_obj, leftKanExtensionUnit_leftKanExtension_map_leftKanExtensionObjIsoColimit_hom, CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_π_assoc, CategoryTheory.Mat_.embedding_obj_ι, AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_hom_app, HomotopyCategory.isZero_quotient_obj_iff, Monoidal.η_ε_assoc, CategoryTheory.ObjectProperty.LimitOfShape.prop_diag_obj, CategoryTheory.CategoryOfElements.map_map_coe, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃'_map_app_app, AlgebraicGeometry.image_morphismRestrict_preimage, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_hom_app, CategoryTheory.Pretriangulated.Triangle.functorHomMk'_app_hom₁, RingCat.Colimits.cocone_naturality_components, mapCoconePrecompose_inv_hom, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left, CategoryTheory.simplicialCosimplicialEquiv_counitIso_inv_app_app, CategoryTheory.DifferentialObject.d_squared_apply, mapGrp_id_mul, CategoryTheory.Limits.PushoutCocone.unop_π_app, CategoryTheory.eqToHom_map_comp, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_inv_app, CategoryTheory.ShiftedHom.opEquiv_symm_add, LeftLinear.instIsIsoδₗ, homologySequence_comp_assoc, Preorder.conePt_mem_lowerBounds, CategoryTheory.Limits.kernelSubobject_arrow'_apply, CategoryTheory.Comma.fromProd_obj_hom, CategoryTheory.comp_evaluation, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_hom_apply_asIdeal, HasCardinalLT.Set.functor_obj, CategoryTheory.PresheafOfGroups.Cochain₀.inv_apply, CategoryTheory.CostructuredArrow.w_prod_fst, AlgebraicGeometry.Scheme.zeroLocus_mul, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app, CategoryTheory.Limits.diagramIsoParallelFamily_inv_app, CategoryTheory.Sieve.functorPushforward_ofObjects_le, CategoryTheory.Presheaf.functorToRepresentables_map, CategoryTheory.NatTrans.mapSquare_app_τ₁, SSet.tensorHom_app_apply, AlgebraicGeometry.coprodSpec_inr, mapGrpIdIso_hom_app_hom_hom, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_postcomp, CategoryTheory.whiskeringLeft_preservesLimitsOfShape, mapHomotopyEquiv_inv, CategoryTheory.CostructuredArrow.mapNatIso_inverse_obj_left, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_hom_app_hom_apply, AlgebraicGeometry.Proj.mul_apply, AlgebraicGeometry.StructureSheaf.comap_id', TopologicalSpace.Opens.map_functor_eq', CategoryTheory.SimplicialObject.Augmented.toArrow_map_right, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₃, CategoryTheory.Limits.IndObjectPresentation.extend_ι_app_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv, SimplicialObject.opFunctor_obj_σ, partialLeftAdjointHomEquiv_comp_symm_assoc, CategoryTheory.Limits.Fork.unop_ι_app_zero, CategoryTheory.Subobject.factorThru_eq_zero, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left, CategoryTheory.Localization.Monoidal.associator_hom_app, CategoryTheory.Limits.CatCospanTransform.rightUnitor_hom_left_app, CategoryTheory.Adjunction.rightAdjointLaxMonoidal_μ, DerivedCategory.isLE_iff, FullyFaithful.homMulEquiv_apply, CategoryTheory.MonoidalCategory.tensor_obj, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_inv_app, inlCompSum'_inv_app, CondensedSet.instEpiTopCatAppCounitTopCatAdjunction, sum_map_inl, CategoryTheory.Limits.Cocone.ofCotrident_ι, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.unitIso_inv_app_f_f, AlgebraicGeometry.instIsIsoSchemeSigmaSpecOfFinite, CategoryTheory.PreGaloisCategory.PointedGaloisObject.incl_obj, CochainComplex.mappingCone.homologySequenceδ_triangleh, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_pos_assoc, CategoryTheory.Limits.opCompYonedaSectionsEquiv_symm_apply_coe, ModuleCat.CoextendScalars.smul_apply', CategoryTheory.Yoneda.naturality, CategoryTheory.Adjunction.IsMonoidal.leftAdjoint_μ, CategoryTheory.Cat.Hom₂.id_app, curry_obj_obj_obj, CategoryTheory.StructuredArrow.map₂_obj_right, CategoryTheory.Adjunction.comp_homEquiv, groupHomology.comap_coinvariantsKer_pOpcycles_range_subtype_pOpcycles_eq_top, CategoryTheory.Grothendieck.ιNatTrans_app_fiber, CategoryTheory.GrothendieckTopology.yoneda_map_val, CategoryTheory.CostructuredArrow.mapIso_functor_obj_hom, mapHomologicalComplex_obj_d, CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_self_succ, closedIhom_obj_map, CategoryTheory.Pretriangulated.Triangle.shift_distinguished, CategoryTheory.Quotient.Linear.smul_eq, LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition, CategoryTheory.Discrete.natIsoFunctor_hom_app, CategoryTheory.MonoidalCategory.externalProductCompDiagIso_hom_app_app, CategoryTheory.Limits.yonedaCompLimIsoCocones_inv_app, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_app_assoc, CategoryTheory.coyonedaEvaluation_map_down, CategoryTheory.Limits.mapPairIso_inv_app, CategoryTheory.Limits.LimitPresentation.w, FunctorToFintypeCat.naturality, AlgebraicGeometry.SpecMap_preimage_basicOpen, CategoryTheory.Over.grpObjMkPullbackSnd_one, CategoryTheory.Abelian.extFunctorObj_obj_coe, CategoryTheory.Comon.Comon_EquivMon_OpOp_counitIso, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_isModule, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_left_right, shiftIso_zero_inv_app, CategoryTheory.Iso.isoInverseComp_inv_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_hom_app_fst_app, CategoryTheory.Comma.fst_obj, Monoidal.coreMonoidalTransport_εIso_inv, CategoryTheory.Grothendieck.grothendieckTypeToCat_inverse_map_base, ModuleCat.toMatrixModCat_obj_carrier, Action.FunctorCategoryEquivalence.counitIso_inv_app_app, Profinite.Extend.cone_π_app, CompHausLike.LocallyConstant.adjunction_counit, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.g_app, CommRingCat.free_obj_coe, CategoryTheory.SimplicialThickening.compFunctor_obj, functorPushforward_imageSieve_mem, OplaxLeftLinear.δₗ_associativity_inv, projective_obj, commShift₂_comm, CategoryTheory.WithTerminal.map₂_app, AlgebraicGeometry.Scheme.ideal_ker_le_ker_ΓSpecIso_inv_comp, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_obj, SSet.prodStdSimplex.instHasDimensionLETensorObjObjSimplexCategoryStdSimplexMkHAddNat, CategoryTheory.δ_naturalityₗ_assoc, CategoryTheory.Comma.mapLeftIso_functor_map_left, OplaxMonoidal.ofBifunctor.bottomMapₗ_app, SSet.Truncated.Edge.map_fst, CategoryTheory.Iso.map_inv_hom_id_app_assoc, CategoryTheory.Triangulated.TStructure.instIsLEObjTruncLTHSubIntOfNat, CategoryTheory.Abelian.Ext.smul_hom, LaxMonoidal.ofBifunctor.secondMap₁_app_app_app, HomologicalComplex.opcyclesOpIso_inv_naturality_assoc, CategoryTheory.Limits.inl_comp_pushoutComparison_assoc, CategoryTheory.Pretriangulated.Triangle.functorHomMk_app_hom₂, smoothSheafCommRing.eval_germ, ModuleCat.instSmallSubtypeForallCarrierObjMemSubmoduleSectionsSubmodule, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_inverse_obj_str, Fiber.fiberInclusionCompIsoConst_inv_app, Monoidal.inv_μ, whiskeringRight_obj_id, CategoryTheory.Limits.KernelFork.condition_assoc, CategoryTheory.Limits.Cocone.unop_π, CategoryTheory.MorphismProperty.Over.map_obj_left, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_surjective, FullyFaithful.homEquiv_apply, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_map_app_fst, PresheafOfModules.pushforward_map_app_apply, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_left, CategoryTheory.CostructuredArrow.functor_obj, CategoryTheory.ShortComplex.LeftHomologyMapData.map_φH, IsLocalization.instDiscreteObjWhiskeringRightFunctorCategoryOfFiniteOfContainsIdentities, CategoryTheory.preadditiveYonedaObj_obj_carrier, LightCondensed.finYoneda_map, CategoryTheory.PreGaloisCategory.initial_iff_fiber_empty, SimplexCategoryGenRel.isSplitEpi_toSimplexCategory_map_of_P_σ, CategoryTheory.Subobject.ofLEMk_comp_ofMkLEMk, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.hasLimit_cospan_forget_of_left', Preorder.hasColimit_iff_hasLUB, SimplicialObject.Splitting.cofan_inj_epi_naturality_assoc, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_inv_app_coe, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_left_hom, mapCoconeWhisker_hom_hom, CategoryTheory.sheafificationNatIso_inv_app_val, CategoryTheory.Limits.colimitCoyonedaHomIsoLimit'_π_apply, CategoryTheory.NatIso.cancel_natIso_inv_right_assoc, groupHomology.mapCycles₁_comp_assoc, CategoryTheory.evaluationRightAdjoint_obj_map, pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_map, Action.leftUnitor_inv_hom, CategoryTheory.η_naturality_assoc, leftExtensionEquivalenceOfIso₁_functor_obj_left, AlgebraicGeometry.Scheme.isoSpec_inv_toSpecΓ, CategoryTheory.endofunctorMonoidalCategory_tensorObj_obj, SSet.Subcomplex.image_obj, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_π_app_left, PreservesEffectiveEpiFamilies.preserves, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_inv_app_hom_apply, cones_map_app, AlgebraicGeometry.Scheme.Hom.image_le_image_of_le, CategoryTheory.SmallObject.SuccStruct.arrowMk_iterationFunctor_map, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₃, MonObj.mopEquivCompForgetIso_hom_app_unmop, AlgCat.forget_obj, CategoryTheory.Over.grpObjMkPullbackSnd_mul, mapHomologicalComplex_map_f, Monoidal.map_associator_inv_assoc, CategoryTheory.Bimon.equivMonComonUnitIsoAppXAux_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_inv_app_app_hom_hom, instIsIsoAppUnitLanAdjunctionOfHasPointwiseLeftKanExtension, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.instIsIsoInvApp, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι_assoc, CategoryTheory.μ_δ_app_assoc, Monoidal.toUnit_ε_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_inv_app_snd_app, CategoryTheory.NatTrans.leftOp_app, ContinuousMap.Homotopy.evalAt_eq, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_left, IsRightKanExtension.nonempty_isUniversal, CategoryTheory.instIsFinitelyPresentableObjFullSubcategoryIsFinitelyPresentableι, CategoryTheory.Monoidal.associator_hom_app, CategoryTheory.Sieve.functorPushforward_apply, SSet.horn.yonedaEquiv_ι, toPseudoFunctor'_obj, closedSieves_obj, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app_apply, CategoryTheory.Square.toArrowArrowFunctor_obj_hom_right, CategoryTheory.Join.isoMkFunctor_hom_app, CategoryTheory.Pseudofunctor.mapId'_inv_naturality_assoc, CategoryTheory.Center.forget_η, CategoryTheory.LocalizerMorphism.homMap_id, CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_π, CategoryTheory.Comonad.CofreeEqualizer.topMap_f, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy₂_homEquiv, SimplexCategory.instPathConnectedSpaceCarrierObjTopCatToTop, CategoryTheory.Equivalence.leftOp_counitIso_inv_app, CategoryTheory.TransfiniteCompositionOfShape.fac_assoc, CategoryTheory.η_ε_app_assoc, AlgebraicGeometry.StructureSheaf.const_add, CategoryTheory.Limits.coyonedaCompLimIsoCones_inv_app, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.functorObj_obj, Rep.instIsTrivialObjModuleCatTrivialFunctor, PresheafOfModules.sections_property, Monoidal.map_associator_assoc, TopologicalSpace.Opens.map_obj, CategoryTheory.Subfunctor.ofSection_eq_range, CategoryTheory.Limits.Cofork.ofCocone_ι, groupHomology.H0π_comp_map, CategoryTheory.CostructuredArrow.toOver_obj_right, CategoryTheory.MonoidalClosed.coev_app_comp_pre_app, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_snd_assoc, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_X₁, CategoryTheory.MorphismProperty.Over.pullbackComp_hom_app_left, CategoryTheory.Localization.SmallHom.equiv_equiv_symm, CategoryTheory.ObjectProperty.prop_shift_iff, CommShift.isoZero_hom_app, CategoryTheory.Subgroupoid.inclusion_inj_on_objects, LeftExtension.IsPointwiseLeftKanExtensionAt.isIso_hom_app, AlgebraicTopology.AlternatingFaceMapComplex.ε_app_f_succ, AlgebraicGeometry.isIso_ΓSpec_adjunction_unit_app_basicOpen, IsEventuallyConstantFrom.cocone_pt, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_fst_map, AlgebraicGeometry.isNoetherian_iff_of_finite_affine_openCover, CategoryTheory.LocalizerMorphism.commShift_iso_hom_app, CategoryTheory.Limits.inl_comp_pushoutObjIso_hom, CategoryTheory.Comma.mapRightIso_counitIso_inv_app_left, AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_hom_app, whiskeringLeft_obj_id, CategoryTheory.MorphismProperty.RightFraction.map_ofInv_hom_id, CategoryTheory.Limits.multispanIndexCoend_right, CategoryTheory.Abelian.LeftResolution.karoubi.π_app_toKaroubi_obj, CategoryTheory.Abelian.LeftResolution.karoubi.F'_map_f, mapCommMonNatTrans_app_hom_hom, CategoryTheory.ShortComplex.mapCyclesIso_hom_iCycles_assoc, CondensedMod.LocallyConstant.instFullModuleCatSheafCompHausCoherentTopologyConstantSheaf, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.natTrans_app_uliftYoneda_obj, CategoryTheory.TwoSquare.EquivalenceJ.inverse_map, CategoryTheory.Limits.MonoCoprod.binaryCofan_inl, CategoryTheory.Bicategory.associatorNatIsoLeft_inv_app, CochainComplex.HomComplex.Cochain.rightUnshift_neg, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_inverse_obj, CategoryTheory.Equivalence.cancel_unit_right, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one, CategoryTheory.SimplicialObject.Truncated.whiskering_map_app_app, Condensed.discrete_map, PresheafOfModules.toSheafify_app_apply', SSet.Finite.instIsFinitelyPresentableObjSimplexCategoryStdSimplex, IsPreFibered.exists_isCartesian', AlgebraicGeometry.Scheme.Hom.preimage_le_preimage_of_le, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_functor_obj, CategoryTheory.Limits.limitConstTerminal_inv_π_assoc, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_right, CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse_obj_left, CategoryTheory.Limits.Fork.isoForkOfι_hom_hom, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app, CategoryTheory.GradedObject.mapBifunctorObjObjSingle₀Iso_hom, CategoryTheory.Limits.limitOpIsoOpColimit_hom_comp_ι_assoc, PresheafOfModules.instPreservesLimitsOfShapeModuleCatCarrierObjOppositeRingCatEvaluation, CategoryTheory.ThinSkeleton.map_obj, HomologicalComplex₂.D₂_totalShift₁XIso_hom_assoc, Monoidal.whiskerRight_app_fst_assoc, CommAlgCat.forget₂_commRingCat_obj, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₂, CochainComplex.HomComplex.Cochain.δ_fromSingleMk, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_inv_assoc, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct, RightExtension.coneAt_pt, CategoryTheory.Comma.mapRightEq_hom_app_right, CategoryTheory.CostructuredArrow.eq_mk, mapHomotopyEquiv_homotopyHomInvId, AlgebraicGeometry.Scheme.Cover.functorOfLocallyDirected_obj, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_inv_app_snd_app, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.secondMap₁_app_app_app, TopCat.Presheaf.Pushforward.comp_eq, CategoryTheory.Equalizer.firstObjEqFamily_inv, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.isPullback, HomologicalComplex.map_isStrictlySupported, AlgebraicGeometry.SmoothOfRelativeDimension.exists_isStandardSmoothOfRelativeDimension, CategoryTheory.Presieve.FunctorPushforwardStructure.fac, CategoryTheory.Limits.BinaryFan.braiding_hom_fst_assoc, CategoryTheory.yonedaEquiv_apply, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_right, AlgebraicGeometry.Scheme.Hom.preimageIso_hom_ι_assoc, CategoryTheory.Limits.CompleteLattice.colimit_eq_iSup, CategoryTheory.Monad.beckCoequalizer_desc, Rep.coinvariantsAdjunction_counit_app, CategoryTheory.Limits.PreservesPushout.inr_iso_hom_assoc, CategoryTheory.coprodMonad_μ_app, AlgebraicGeometry.Scheme.IdealSheafData.ideal_le_comap_ideal, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app_assoc, currying_inverse_obj_obj_obj, CommGrpCat.uliftFunctor_obj, CommRingCat.forget_obj, CategoryTheory.ShortComplex.mapHomologyIso_hom_naturality, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ₀_assoc, CategoryTheory.Limits.Sigma.ι_isoColimit_inv, CategoryTheory.ObjectProperty.isLocalization_isColocal, SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_inv_app, opInv_obj, CategoryTheory.Limits.PreservesKernel.iso_inv_ι, HomologicalComplex.to_single_hom_ext_iff, PullbackObjObj.π_fst, LeftExtension.postcomp₁_obj_left, partialRightAdjointHomEquiv_symm_comp, TopCat.GlueData.ofOpenSubsets_toGlueData_U, LaxMonoidal.ofBifunctor.leftMapᵣ_app, WellOrderInductionData.surjective, FullyFaithful.monObj_mul, CategoryTheory.Comma.mapRightIso_counitIso_inv_app_right, CategoryTheory.Enriched.FunctorCategory.isLimitConeFunctorEnrichedHom.fac, Monoidal.transport_μ, CochainComplex.HomComplex.Cochain.map_v, CategoryTheory.Limits.Fork.IsLimit.mono, CategoryTheory.instIsIsoFunctorOppositeValAppSheafCounitSheafificationAdjunction, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_inv_app_app, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_inverse_obj_p_f, CategoryTheory.OplaxFunctor.mapComp_assoc_left_app_assoc, CategoryTheory.IsFiltered.iff_nonempty_limit, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_unitIso, HomologicalComplex₂.D₂_totalShift₂XIso_hom_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_hom_app, CategoryTheory.sum.inlCompInrCompInverseAssociator_inv_app_down_down, CategoryTheory.Comon.monoidal_rightUnitor_inv_hom, CochainComplex.truncate_obj_X, CategoryTheory.Comma.opEquiv_counitIso, CategoryTheory.sheafificationNatIso_hom_app_val, CategoryTheory.Limits.reflexivePair_obj_one, PresheafOfModules.Derivation.d_map, CategoryTheory.StructuredArrow.map₂_map_right, CategoryTheory.Discrete.functor_obj, CategoryTheory.DifferentialObject.shiftFunctor_obj_obj, biproductComparison'_comp_biproductComparison, commShiftIso_comp_hom_app, AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine_apply, AlgebraicGeometry.structureSheafInType.mul_apply, CategoryTheory.Comma.mapLeftEq_hom_app_left, coreId_hom_app_iso_hom, CategoryTheory.Limits.instIsIsoPushoutComparison, TopCat.Presheaf.germ_stalkSpecializes_apply, DerivedCategory.isZero_of_isGE, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₂_app, SSet.Subcomplex.topIso_inv_app_coe, SSet.prodStdSimplex.orderHomOfSimplex_coe, CategoryTheory.Monad.monadMonEquiv_counitIso_hom_app_hom, CategoryTheory.NatTrans.mapSquare_app_τ₂, CategoryTheory.Subobject.ofMkLEMk_comp_ofMkLE, Final.colimitCoconeOfComp_isColimit, CommRingCat.free_map_coe, CategoryTheory.Limits.Cone.toCostructuredArrow_obj, Monoidal.tensorObj_map, CategoryTheory.Limits.CatCospanTransform.rightUnitor_inv_base_app, CategoryTheory.constantCommuteCompose_hom_app_val, ModuleCat.RestrictionCoextensionAdj.HomEquiv.toRestriction_hom_apply, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.unit_app_ev_app_app_assoc, CategoryTheory.WithTerminal.mapComp_hom_app, AlgebraicGeometry.instIsOpenImmersionLeftSchemeDiscretePUnitMapWalkingSpanOverTopMorphismPropertySpan, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight_apply, CategoryTheory.Limits.coconeOfCoconeCurry_pt, functorPushforward_mem_iff, CategoryTheory.Endofunctor.Adjunction.Algebra.homEquiv_naturality_str, IsOpenMap.functorNhds_obj_coe, CategoryTheory.Equivalence.congrFullSubcategory_counitIso, mapTriangleCommShiftIso_inv_app_hom₁, Monoidal.map_μ_δ_assoc, CategoryTheory.Equivalence.cancel_counit_right, CategoryTheory.MonoidalCategory.curriedAssociatorNatIso_hom_app_app_app, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_inv_colimit_map_assoc, relativelyRepresentable.hom_ext_iff, CategoryTheory.Subobject.top_arrow_isIso, Monoidal.lift_μ_assoc, CategoryTheory.ShiftedHom.comp_add, Monoidal.instIsIsoη, groupCohomology.cochainsMap_comp, CategoryTheory.Equivalence.map_injective_iff, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right, AlgebraicGeometry.Scheme.Hom.toNormalization_inr_normalizationCoprodIso_hom, CategoryTheory.MorphismProperty.RightFraction.map_s_comp_map_assoc, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceFunctor_map_fiber, CategoryTheory.InjectiveResolution.toRightDerivedZero'_comp_iCycles, CategoryTheory.CosimplicialObject.σ_naturality_assoc, AlgebraicGeometry.Scheme.Modules.Hom.zero_app, pointwiseLeftKanExtensionCompIsoOfPreserves_fac_app_assoc, CategoryTheory.Limits.colimit.homIso_hom, mapConePostcompose_inv_hom, CategoryTheory.Limits.WidePullbackShape.functorExt_hom_app, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_inv_app_hom₂, CategoryTheory.PreGaloisCategory.card_aut_le_card_fiber_of_connected, TopCat.Sheaf.pushforward_map, reflective', PullbackObjObj.π_iso_of_iso_left_inv, CategoryTheory.GlueData.ι_gluedIso_inv, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_right_as, flipping_functor_map_app_app, CochainComplex.mappingConeCompTriangle_mor₃, CategoryTheory.toOver_obj_left, CategoryTheory.IsHomLift.commSq, ModuleCat.toMatrixModCat_obj_isAddCommGroup, Monoidal.tensorObjComp_hom_app, CategoryTheory.Endofunctor.Algebra.functorOfNatTransId_inv_app_f, CochainComplex.HomComplex.Cochain.shift_add, AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine_symm_apply, flip₂₃_obj_obj_map, AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex_inv, CategoryTheory.Localization.Monoidal.μ_inv_natural_right, AlgebraicGeometry.Scheme.congr_app, SimplicialObject.opFunctor_obj_map, SimplicialObject.Split.forget_obj, CategoryTheory.GradedObject.mapTrifunctor_map_app_app, AlgebraicGeometry.Scheme.IdealSheafData.ideal_mul, CategoryTheory.Cat.Hom₂.comp_app_assoc, CategoryTheory.Limits.Bicones.functoriality_map_hom, CategoryTheory.Limits.PreservesCokernel.π_iso_hom_assoc, homologySequence_comp, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_right_hom, Sequential.sequentialToTop_obj, FullyFaithful.autMulEquivOfFullyFaithful_symm_apply_hom, CategoryTheory.Grothendieck.grothendieckTypeToCatFunctor_obj_snd, CategoryTheory.Monad.algebraFunctorOfMonadHomId_hom_app_f, IsEventuallyConstantTo.cone_π_app, AlgebraicGeometry.IsZariskiLocalAtTarget.restrict, Monoidal.whiskerRight_η_ε, IsCoverDense.isoOver_hom_app, CategoryTheory.Limits.limit.w_assoc, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.F_map, AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.structurePresheafInCommRing_obj_carrier, Rep.linearization_single, CategoryTheory.Limits.ι_colimitPointwiseProductToProductColimit_π, AlgebraicGeometry.Scheme.SpecΓIdentity_hom_app, currying₃_unitIso_hom_app_app_app_app, CategoryTheory.Limits.image.map_comp, CategoryTheory.Comma.coneOfPreserves_π_app_right, FullyFaithful.compUliftCoyonedaCompWhiskeringLeft_hom_app_app_down, CategoryTheory.Monoidal.transportStruct_tensorHom, CategoryTheory.InjectiveResolution.of_def, CategoryTheory.Limits.limitIsoLimitCurryCompLim_hom_π_π_assoc, LaxRightLinear.μᵣ_unitality_inv_assoc, AlgebraicGeometry.locallyQuasiFinite_iff, ModuleCat.extendRestrictScalarsAdj_homEquiv_apply, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_unit_app, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_π_app, CategoryTheory.Coyoneda.objOpOp_inv_app, CategoryTheory.toOverPullbackIsoToOver_inv_app_left, AlgebraicGeometry.Scheme.preimage_comp, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_add, prod'_δ_snd, ι_leftKanExtensionObjIsoColimit_inv, opComp_inv_app, CategoryTheory.Idempotents.functorExtension_map_app, CategoryTheory.Equivalence.unitInv_naturality, CategoryTheory.Comma.limitAuxiliaryCone_pt, CategoryTheory.CostructuredArrow.w_prod_fst_assoc, CategoryTheory.TwoSquare.instIsConnectedCostructuredArrowStructuredArrowObjStructuredArrowDownwardsOfGuitartExact, AddGrpCat.toGrp_obj_coe, curry_obj_uncurry_obj, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.toBase_preimage_eq_opensRange_ι, CategoryTheory.ProjectiveResolution.self_π, CategoryTheory.WithInitial.ofCommaObject_obj, CategoryTheory.FunctorToTypes.binaryProductEquiv_apply, LeftExtension.precomp_map_right, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₃, CategoryTheory.Limits.Concrete.colimit_rep_eq_iff_exists, LaxBraided.braided, LaxMonoidal.left_unitality_assoc, CategoryTheory.WithTerminal.equivComma_inverse_obj_obj, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_π_app_walkingParallelPair_one, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_sub, LightCondMod.isDiscrete_tfae, OplaxMonoidal.δ_snd, SSet.opFunctorCompOpFunctorIso_hom_app_app, CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_app_app, CategoryTheory.Limits.coprodComparisonNatTrans_app, CategoryTheory.Equivalence.functor_unit_comp, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.fstFunctor_obj, CategoryTheory.Bimon.instIsMonHomComonHomEquivMonComonCounitIsoAppX, sectionsPrecomp_coe, CategoryTheory.FinitaryExtensive.mono_ι, FullyFaithful.isoEquiv_apply, LeftExtension.precomp₂_obj_left, CategoryTheory.Comonad.right_counit_assoc, CategoryTheory.MorphismProperty.map_mem_strictMap, CategoryTheory.Limits.MulticospanIndex.sectionsEquiv_apply_coe, HomologicalComplex.singleObjCyclesSelfIso_inv_homologyπ, CategoryTheory.Pseudofunctor.CoGrothendieck.map_map_base, AlgebraicGeometry.IsFinite.instMorphismRestrict, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σ, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_right_right, CategoryTheory.Limits.PreservesCokernel.iso_inv, CategoryTheory.Limits.colimitCurrySwapCompColimIsoColimitCurryCompColim_ι_ι_hom, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app', CochainComplex.HomComplex.Cochain.toSingleMk_neg, CategoryTheory.FreeGroupoid.mapComp_hom_app, CategoryTheory.Comonad.ForgetCreatesLimits'.γ_app, CategoryTheory.Bimon.instIsComonHomHomEquivMonComonCounitIsoAppXAux, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap, CategoryTheory.FinitaryExtensive.isPullback_initial_to_binaryCofan, CategoryTheory.SimplicialObject.Augmented.w₀, CategoryTheory.BraidedCategory.curriedBraidingNatIso_inv_app_app, RightExtension.coneAt_π_app, Action.whiskerRight_hom, SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_hom_app, ModuleCat.restrictScalarsComp'_inv_app, CategoryTheory.Cat.freeReflMap_obj, CategoryTheory.Comma.mapRightIso_functor_map_left, CategoryTheory.Regular.frobeniusStrongEpiMonoFactorisation_I, CategoryTheory.μ_naturality₂_assoc, CategoryTheory.Equivalence.inv_fun_map, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₂_assoc, Monoidal.δ_μ, AlgebraicTopology.AlternatingCofaceMapComplex.d_eq_unop_d, AlgebraicGeometry.sigmaMk_mk, TopCat.Presheaf.pushforwardToOfIso_app, Final.coconesEquiv_unitIso, SSet.Subcomplex.toRange_app_val, CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_right, CategoryTheory.Pseudofunctor.CoGrothendieck.map_map_fiber, AlgebraicGeometry.affineLocally_iff_forall_isAffineOpen, AddCommMonCat.hom_forget₂_map, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_right, groupHomology.coresNatTrans_app, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality, prod'CompSnd_inv_app, CategoryTheory.Idempotents.KaroubiKaroubi.counitIso_inv_app_f_f, CategoryTheory.Presheaf.freeYonedaHomEquiv_comp, CategoryTheory.zigzag_obj_of_zigzag, PresheafOfModules.free_map_app, CategoryTheory.MonoidalCategory.externalProductBifunctorCurried_obj_obj_obj_map, CategoryTheory.SimplicialObject.σ_naturality, RingCat.forget₂_map, CategoryTheory.NatTrans.mapHomologicalComplex_app_f, 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.SimplicialObject.instIsRightKanExtensionOppositeTruncatedSimplexCategoryObjCoskAppTruncatedCounitCoskAdjTruncation, CochainComplex.HomComplex.Cochain.map_zero, CategoryTheory.Limits.IsColimit.homIso_hom, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_hom_app, CategoryTheory.NatIso.ofComponents_inv_app, CategoryTheory.prodComonad_δ_app, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.ofRestrict_invApp, IsEventuallyConstantFrom.isoMap_inv_hom_id_assoc, CategoryTheory.WithInitial.isColimitEquiv_symm_apply_desc, CategoryTheory.uliftCoyonedaIsoCoyoneda_inv_app_app_down, CategoryTheory.Arrow.leftFunc_obj, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_hom_app_hom, CategoryTheory.monoidalOfHasFiniteProducts.δ_eq, CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso_hom_app, CategoryTheory.Localization.instHasSmallLocalizedHomObjShiftFunctor_1, OplaxMonoidal.ofBifunctor.leftMapᵣ_app, SheafOfModules.instIsRightAdjointPushforwardCompSheafRingCatMapSheafPushforwardContinuous, groupCohomology.map_H0Iso_hom_f_apply, CategoryTheory.Quotient.lift.isLift_hom, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_right, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivLeft_symm_apply, HomologicalComplex.natIsoSc'_inv_app_τ₂, CategoryTheory.Limits.Cocone.underPost_ι_app, mem_homologicalKernel_iff, CategoryTheory.Limits.multicospanIndexEnd_snd, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι, CategoryTheory.Bimon.equivMonComonUnitIsoApp_hom_hom_hom, CategoryTheory.leftAdjointOfStructuredArrowInitialsAux_apply, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_hom_app_hom_hom_app, CategoryTheory.Limits.colimitIsoSwapCompColim_hom_app, CategoryTheory.Over.braiding_inv_left, AlgebraicGeometry.Scheme.isoSpec_inv_preimage_zeroLocus, CochainComplex.HomComplex.Cochain.toSingleMk_v, AlgebraicGeometry.Flat.instDescScheme, CategoryTheory.Limits.SingleObj.Types.colimitEquivQuotient_symm_apply, PresheafOfModules.congr_map_apply, CategoryTheory.Localization.HasProductsOfShapeAux.adj_counit_app, Monoidal.whiskerLeft_μ_δ, groupCohomology.congr, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_hom_app_val_app, IsStronglyCocartesian.universal_property', mapTriangleCompIso_hom_app_hom₂, CategoryTheory.PresheafOfGroups.OneCocycle.ev_trans, RightExtension.postcomp₁_obj_left_map, CategoryTheory.Limits.kernelSubobjectIsoComp_hom_arrow, CategoryTheory.Adjunction.compYonedaIso_hom_app_app, PresheafOfModules.freeYonedaEquiv_symm_app, CategoryTheory.Sieve.pullback_functorPushforward_equivalence_eq, TopCat.toSheafCompHausLike_val_obj, currying_counitIso_hom_app_app, CochainComplex.IsKInjective.rightOrthogonal, CategoryTheory.zero_map, CategoryTheory.CosimplicialObject.eqToIso_refl, CategoryTheory.MorphismProperty.Over.mapCongr_inv_app_left, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app_assoc, CategoryTheory.CostructuredArrow.post_obj, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.associator_hom_unit_unit, TopCat.Presheaf.germ_res', CategoryTheory.Limits.Cotrident.π_eq_app_one, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.w_app, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_fiber, CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.inductiveSystem_obj, AlgebraicGeometry.PresheafedSpace.Γ_obj_op, CategoryTheory.MonoidalCategory.DayFunctor.ν_comp_unitDesc_assoc, RightExtension.postcomp₁_map_right, CondensedMod.LocallyConstant.instFaithfulModuleCatCondensedDiscrete, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompCoyoneda, TopologicalSpace.Opens.map_comp_obj_unop, CategoryTheory.Limits.imageSubobject_arrow_comp_eq_zero, Monoidal.map_rightUnitor_inv, CategoryTheory.Limits.colimit.ι_map, prod'CompSnd_hom_app, SSet.RelativeMorphism.Homotopy.h₀_assoc, CategoryTheory.Cat.freeMap_obj, PresheafOfModules.restrictScalarsObj_map, CategoryTheory.Subobject.ofMkLE_arrow, CategoryTheory.FunctorToTypes.binaryProductCone_pt_obj, HomologicalComplex.single_obj_d, CategoryTheory.CommMon.mkIso'_inv_hom_hom, CategoryTheory.Iso.isoInverseComp_hom_app, CategoryTheory.Over.prodLeftIsoPullback_inv_snd, mapActionComp_hom, PresheafOfModules.forgetToPresheafModuleCatObj_map, CategoryTheory.StructuredArrow.mapNatIso_functor_obj_right, CochainComplex.IsKInjective.Qh_map_bijective, CategoryTheory.AdditiveFunctor.ofExact_obj_fst, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionActionOfMonoidalFunctorToEndofunctorIso_inv_app_app, CategoryTheory.Limits.PreservesPullback.iso_inv_fst_assoc, CategoryTheory.Limits.constCone_pt, Profinite.NobelingProof.spanFunctorIsoIndexFunctor_hom_app_hom_hom_apply_coe, CategoryTheory.Limits.piObjIso_hom_comp_π, Action.FunctorCategoryEquivalence.functor_obj_obj, CategoryTheory.leftAdjointOfStructuredArrowInitialsAux_symm_apply, LeibnizAdjunction.adj_unit_app_left, CategoryTheory.MonoidalClosed.uncurry_natural_left_assoc, CategoryTheory.Join.mkFunctor_obj_left, TopCat.Sheaf.interUnionPullbackCone_fst, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_map_app, ModuleCat.restrictScalarsId'App_hom_naturality, CategoryTheory.Subobject.map_top, AlgebraicGeometry.functionField_isScalarTower, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map, HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac', CategoryTheory.Limits.span_map_id, CategoryTheory.Over.iteratedSliceForwardIsoPost_inv_app, CochainComplex.HomComplex.Cochain.leftShiftLinearEquiv_apply, pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.IsSifted.factorization_prodComparison_colim, CategoryTheory.SimplicialObject.Augmented.toArrow_map_left, AlgebraicTopology.alternatingFaceMapComplex_obj_d, CategoryTheory.Comma.mapRight_obj_hom, CategoryTheory.NatIso.naturality_1, CategoryTheory.NatIso.inv_map_inv_app, CochainComplex.HomComplex.Cochain.shift_neg, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_map_app, CategoryTheory.GlueData.instHasPullbackMapF, CategoryTheory.Limits.Cone.whisker_π, CategoryTheory.Comma.mapRightIso_inverse_map_right, CategoryTheory.Equivalence.core_unitIso_hom_app_iso_inv, ProfiniteGrp.ProfiniteCompletion.lift_eta_assoc, CategoryTheory.DifferentialObject.shiftZero_hom_app_f, ranCompLimIso_inv_app, CategoryTheory.MorphismProperty.RightFraction.map_hom_ofInv_id, CategoryTheory.Limits.PreservesProduct.iso_hom, imageToKernel_op, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app, TopCat.Presheaf.stalkPushforward_germ_apply, CategoryTheory.ShortComplex.HomologyMapData.map_left, InfiniteGalois.toAlgEquivAux_eq_proj_of_mem, CategoryTheory.MonoidalClosed.uncurry_pre_app_assoc, surjective_toEventualRanges, IsMittagLeffler.subset_image_eventualRange, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_hom_assoc, CategoryTheory.Limits.Cocones.whiskeringEquivalence_unitIso, CategoryTheory.LaxFunctor.mapComp_naturality_left_app_assoc, CategoryTheory.InjectiveResolution.desc_commutes_zero_assoc, FullyFaithful.map_bijective, CategoryTheory.Adjunction.eq_homEquiv_apply, ShiftSequence.induced.isoZero_hom_app_obj, CategoryTheory.Sum.functorEquiv_unit_app_app_inr, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoColimitUncurryWhiskeringLeft₂_inv_assoc, CategoryTheory.Limits.colimitCurrySwapCompColimIsoColimitCurryCompColim_ι_ι_inv, factorThruImageSubobject_comp_imageToKernel, CategoryTheory.ObjectProperty.isColocal_eq_inverseImage_isomorphisms, CategoryTheory.Monoidal.transportStruct_tensorObj, CategoryTheory.Limits.Cocone.toCostructuredArrow_map, CategoryTheory.pathComposition_obj, LaxRightLinear.μᵣ_associativity_inv_assoc, CategoryTheory.Limits.hasColimitCompEvaluation, Fiber.fiberInclusion_comp_eq_const, CategoryTheory.WithTerminal.equivComma_functor_obj_left_map, shiftMap_comp', whiskeringLeft₃_map_app_app_app_app_app_app, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε, StalkSkyscraperPresheafAdjunctionAuxs.germ_fromStalk, SSet.prodStdSimplex.objEquiv_apply_fst, SSet.stdSimplex.map_id, SheafOfModules.evaluationPreservesLimitsOfShape, CategoryTheory.NatTrans.vcomp_app', LightCondensed.discrete_map, epi_map_iff_epi, CategoryTheory.Limits.PreservesTerminal.iso_hom, CategoryTheory.monoidalOpOp_δ, SimplicialObject.Splitting.cofan_inj_eq, CategoryTheory.Equivalence.toOrderIso_apply, CategoryTheory.Limits.coker_map, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_inv_app_left, DerivedCategory.subsingleton_hom_of_isStrictlyLE_of_isStrictlyGE, CategoryTheory.MonObj.ofRepresentableBy_one, CategoryTheory.HasShift.Induced.zero_inv_app_obj, DerivedCategory.HomologySequence.exact₂, CategoryTheory.Limits.Types.pUnitCocone_ι_app, HomologicalComplex₂.toGradedObjectFunctor_obj, CategoryTheory.Square.toArrowArrowFunctor'_obj_left_hom, CategoryTheory.TransfiniteCompositionOfShape.iic_isoBot, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_single, CategoryTheory.Subobject.ofLE_arrow_assoc, AlgebraicGeometry.Scheme.exists_germ_injective, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₃₄, CategoryTheory.Cat.leftUnitor_hom_app, curry₃_obj_obj_map_app, CategoryTheory.WithTerminal.mkCommaMorphism_left_app, CategoryTheory.ComposableArrows.threeδ₃Toδ₂_app_one, CategoryTheory.shift_shift_neg', SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_quotMk, CategoryTheory.SmallObject.functorialFactorizationData_i_app, LaxMonoidal.ofBifunctor.firstMap₃_app_app_app, CategoryTheory.NatTrans.naturality_2_assoc, CategoryTheory.Bimon.toComon_obj_comon_counit, CategoryTheory.evaluationAdjunctionLeft_unit_app_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocNatIso_hom_app_app_app, CategoryTheory.CostructuredArrow.hasTerminal, CategoryTheory.Localization.Construction.wInv_eq_isoOfHom_inv, 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.CoproductsFromFiniteFiltered.liftToFinsetColimIso_aux_assoc, CategoryTheory.SimplicialObject.Augmented.toArrow_obj_left, CategoryTheory.LocalizerMorphism.commShift_iso_inv_app, CategoryTheory.ComposableArrows.whiskerLeft_obj, CategoryTheory.Grothendieck.isoMk_inv_fiber, CategoryTheory.Sheaf.isPullback_square_op_map_yoneda_presheafToSheaf_yoneda_iff, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality_assoc, SSet.exists_nonDegenerate, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.sheafedSpace_pullback_to_base_isOpenImmersion, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_hom, SheafOfModules.toSheaf_obj_val, CategoryTheory.HasShift.Induced.add_hom_app_obj, CategoryTheory.sum.associator_map_inr, rightKanExtensionCompIsoOfPreserves_hom_fac_app, CategoryTheory.TwoSquare.equivalenceJ_unitIso, AlgebraicGeometry.StructureSheaf.instIsLocalizedModuleObjOppositeOpensCarrierTopValStructureSheafInTypeOpBasicOpenPowersToOpenₗ, CategoryTheory.Abelian.coim_map, CategoryTheory.Limits.coend.condition, CategoryTheory.IsSifted.instIsIsoObjFunctorTypeColimTensorObjProdComparison, CategoryTheory.Pi.sum_obj_obj, CategoryTheory.sheafToPresheaf_μ, ContinuousMap.Homotopy.heq_path_of_eq_image, CategoryTheory.GradedObject.mapTrifunctorObj_obj_obj, HasFibers.homLift, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_eq, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, HomologicalComplex.asFunctor_obj_X, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₁_app, whiskeringLeft_obj_comp, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isoBot, CategoryTheory.RetractArrow.map_r_right, CategoryTheory.CatCommSq.hComp_iso_hom_app, LightProfinite.proj_comp_transitionMapLE', CategoryTheory.pullbackShiftFunctorZero_inv_app, CategoryTheory.Bimon.toComon_map_hom, CategoryTheory.Subobject.ofMkLE_comp_ofLEMk_assoc, mapTriangleRotateIso_inv_app_hom₁, CategoryTheory.Under.liftCone_pt, TopCat.Presheaf.germ_res_apply, CategoryTheory.CostructuredArrow.map₂_obj_right, CategoryTheory.Triangulated.TStructure.triangleLTGE_obj_mor₁, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompPointIso_hom_app, CategoryTheory.StructuredArrow.prodInverse_map, CategoryTheory.OverPresheafAux.OverArrows.val_mk, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivLeft_apply, groupHomology.π_comp_H0Iso_hom_assoc, CategoryTheory.Discrete.compNatIsoDiscrete_hom_app, CategoryTheory.uliftCoyonedaEquiv_uliftCoyoneda_map, leftKanExtensionCompIsoOfPreserves_hom_fac_app, CochainComplex.homotopyUnop_hom_eq, RepresentableBy.coyoneda_homEquiv, CategoryTheory.Over.leftUnitor_hom_left, CategoryTheory.CostructuredArrow.mapIso_unitIso_hom_app_left, SSet.Subcomplex.lift_app_coe, CategoryTheory.CatCommSq.iso_inv_naturality, PullbackObjObj.mapArrowLeft_comp, Rep.resCoindAdjunction_unit_app_hom_hom, CochainComplex.HomComplex.Cochain.toSingleMk_add, AlgebraicGeometry.Scheme.Hom.preimage_top, CategoryTheory.Kleisli.Adjunction.toKleisli_map, CategoryTheory.NatTrans.mapHomotopyCategory_app, CategoryTheory.coyonedaEquiv_comp, HomologicalComplex₂.ι_totalShift₁Iso_hom_f_assoc, CategoryTheory.uliftYonedaEquiv_symm_apply_app, CategoryTheory.flippingIso_inv_toFunctor_obj_obj_obj, mapProjectiveResolution_π, CategoryTheory.Adjunction.localization_unit_app, CategoryTheory.WithTerminal.equivComma_functor_obj_right, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₂, CategoryTheory.NatTrans.app_naturality, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_left, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd_assoc, HomologicalComplex.complexOfFunctorsToFunctorToComplex_obj, AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimage, OneHypercoverDenseData.essSurj.presheafMap_π_assoc, Monoidal.map_leftUnitor_inv, CategoryTheory.Limits.PushoutCocone.isoMk_inv_hom, CategoryTheory.Join.opEquiv_functor_obj_op_right, CategoryTheory.Limits.colimitYonedaHomIsoLimit'_π_apply, CategoryTheory.Limits.π_comp_colimitLeftOpIsoUnopLimit_inv, AlgebraicGeometry.Proj.one_apply, Condensed.epi_iff_surjective_on_stonean, CategoryTheory.WithInitial.liftFromUnderComp_inv_app, HomologicalComplex.opcyclesOpIso_inv_naturality, CategoryTheory.MorphismProperty.Over.pullbackMapHomPullback_app, AlgebraicGeometry.Scheme.Hom.toImage_app_injective, CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_hom_app_app_val, AlgebraicGeometry.Scheme.isoSpec_hom, CategoryTheory.preservesColimitNatIso_inv_app, CategoryTheory.conjugateEquiv_symm_apply_app, CategoryTheory.Presheaf.isLocallyInjective_presheafToSheaf_map_iff, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionActionOfMonoidalFunctorToEndofunctorMopIso_hom_app_unmop_app, AlgebraicGeometry.Scheme.Hom.id_preimage, AlgebraicGeometry.Flat.instMorphismRestrict, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality, AlgebraicGeometry.StructureSheaf.to_basicOpen_epi, CategoryTheory.Meq.pullback_refine, CategoryTheory.bifunctorComp₂₃_obj, CategoryTheory.Over.tensorObj_ext_iff, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_right, AlgebraicGeometry.IsAffineOpen.opensRange_fromSpec, CategoryTheory.instIsIsoToRightDerivedZero', CategoryTheory.Limits.parallelPairOpIso_inv_app_one, CategoryTheory.PreOneHypercover.map_I₀, CategoryTheory.ε_η_app_assoc, CategoryTheory.Limits.PullbackCone.mk_π_app, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec_fromSpecStalk, CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatIso_inv, flipping_inverse_obj_obj_map, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app', CategoryTheory.CostructuredArrow.toOver_map_right, CommMonCat.coyonedaType_obj_map, SemimoduleCat.forget_obj, AlgebraicGeometry.Scheme.IdealSheafData.ideal_le_ker_glueDataObjι, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_c_app, CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse_obj_right, CategoryTheory.plusPlusSheaf_obj_val, TopCat.Presheaf.germ_stalkPullbackInv_assoc, CategoryTheory.Limits.ColimitPresentation.map_diag, CategoryTheory.CostructuredArrow.map_obj_hom, injective_obj_of_injective, CategoryTheory.ε_naturality_assoc, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_hom_whiskerRight_π_assoc, ModuleCat.restrictScalarsComp'_hom_app, LightProfinite.Extend.cocone_ι_app, groupHomology.H1CoresCoinfOfTrivial_X₁, sheafAdjunctionCocontinuous_counit_app_val, CategoryTheory.Monad.isSplitMono_iff_isIso_unit, AlgebraicGeometry.instQuasiCompactMorphismRestrict, CategoryTheory.coev_expComparison, CategoryTheory.MonoidalCategory.prodCompExternalProduct_inv_app, AlgebraicGeometry.Scheme.forget_obj, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.functorToInterchangeIso_inv_app_app, AlgebraicGeometry.Scheme.eqToHom_c_app, LeftExtension.precomp_obj_hom_app, CategoryTheory.MonoidalClosed.uncurry_natural_right_assoc, HomotopicalAlgebra.FibrantObject.weakEquivalence_toHoCat_map_iff, Rep.homEquiv_apply_hom, Monoidal.map_associator, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.biprodAddEquiv_symm_biprodIsoProd_hom_toBiprod_apply, CategoryTheory.Limits.IsColimit.ι_map, TopCat.GlueData.ofOpenSubsets_toGlueData_t, CategoryTheory.Presieve.map_functorPullback, CategoryTheory.WithTerminal.ofCommaObject_obj, mapMatComp_hom_app, CategoryTheory.Limits.colimit.ι_post, CategoryTheory.PreOneHypercover.oneToZero_obj, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π_assoc, CategoryTheory.Limits.Types.binaryCoproductCocone_ι_app, CategoryTheory.conjugateEquiv_apply_app, CategoryTheory.BinaryCofan.isVanKampen_iff, AlgebraicGeometry.IsAffineOpen.self_le_iSup_basicOpen_iff, ModuleCat.FilteredColimits.colimit_zero_eq, LeibnizAdjunction.adj_counit_app_left, AlgebraicGeometry.Scheme.zeroLocus_biInf, CategoryTheory.Monad.Algebra.assoc_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_inv_app_app_fst, AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_hom_π, CategoryTheory.SmallObject.SuccStruct.ofCocone_map_assoc, partialLeftAdjointHomEquiv_symm_comp, AlgebraicGeometry.PresheafedSpace.componentwiseDiagram_map, groupCohomology.mapShortComplexH2_comp_assoc, AlgebraicGeometry.PresheafedSpace.stalkMap_germ_assoc, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_incl, Rep.FiniteCyclicGroup.chainComplexFunctor_obj, CategoryTheory.Adjunction.instIsIsoAppCounitObjOfFaithfulOfFull, CategoryTheory.Idempotents.app_p_comp, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom, AlgebraicGeometry.Proj.basicOpenToSpec_app_top, SimpleGraph.componentComplFunctor_obj, CategoryTheory.Limits.compYonedaSectionsEquiv_apply_app, CategoryTheory.exp.coev_ev, CategoryTheory.Join.mapPair_obj_right, CochainComplex.instIsStrictlyGEObjHomologicalComplexIntUpSingle, CategoryTheory.Endofunctor.Algebra.functorOfNatTransComp_hom_app_f, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.ofRestrict_invApp, CategoryTheory.Comma.mapSnd_inv_app, CategoryTheory.ShortComplex.SnakeInput.functorP_obj, CategoryTheory.GradedObject.mapBifunctor_obj_obj, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_naturality, CategoryTheory.SimplicialObject.δ_comp_σ_succ'_assoc, AlgebraicGeometry.Scheme.Hom.image_preimage_le, ContinuousMap.Homotopy.eq_path_of_eq_image, CategoryTheory.Sieve.functorPullback_arrows, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp, HomologicalComplex.homologyι_singleObjOpcyclesSelfIso_inv, AlgebraicGeometry.Scheme.AffineZariskiSite.generate_presieveOfSections, CategoryTheory.MonoidalCategory.tensorμ_comp_μ_tensorHom_μ_comp_μ_assoc, rightKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, Preorder.coconePt_mem_upperBounds, CategoryTheory.Pretriangulated.Triangle.functorMk_map_hom₃, homologySequenceδ_naturality, compConstIso_hom_app_app, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_app_assoc, CategoryTheory.PreOneHypercover.map_X, CochainComplex.fromSingle₀Equiv_apply_coe, CategoryTheory.mopFunctor_obj, FinPartOrd.dualEquiv_unitIso, PresheafOfModules.pushforward₀_obj_obj_carrier, FullyFaithful.nonempty_iff_map_bijective, costructuredArrowMapCocone_pt, AlgebraicGeometry.Scheme.Hom.image_top_eq_opensRange, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app, coreComp_hom_app_iso_hom, CategoryTheory.CatCommSq.vId_iso_hom_app, CategoryTheory.CategoryOfElements.to_comma_map_right, CategoryTheory.StructuredArrow.eq_mk, CategoryTheory.ComposableArrows.fourδ₄Toδ₃_app_two, prod'_ε_fst, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_inv_app_snd_app, CategoryTheory.evaluationRightAdjoint_map_app, AlgebraicGeometry.Scheme.forgetToTop_obj, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_apply, Rep.coindFunctorIso_hom_app_hom_hom_apply_hom_hom_apply, CategoryTheory.Comma.fromProd_obj_right, imageSieve_eq_imageSieve, CategoryTheory.frobeniusMorphism_mate, CategoryTheory.Monoidal.InducingFunctorData.associator_eq, IsEventuallyConstantTo.isoMap_inv_hom_id, groupCohomology.mapCocycles₂_comp_i_apply, HomologicalComplex.dgoToHomologicalComplex_obj_d, CategoryTheory.NatIso.naturality_1'_assoc, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right', CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.liftHom_fac_assoc, CategoryTheory.Monad.monadToMon_obj, CategoryTheory.Adjunction.ε_comp_map_ε_assoc, CategoryTheory.Limits.BinaryFan.IsLimit.lift'_coe, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_fst, CategoryTheory.toOverIsoToOverUnit_inv_app_left, CategoryTheory.MonoidalCategory.DayFunctor.equiv_inverse_obj_functor, CategoryTheory.Equivalence.sheafCongrPreregular_inverse_obj_val_map, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_inv_app_hom_left, PresheafOfModules.id_app, CategoryTheory.Codiscrete.natIsoFunctor_hom_app, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_obj_obj_right_as, CategoryTheory.MorphismProperty.Over.pullback_obj_left, CategoryTheory.Subobject.inf_comp_left, flipping_counitIso_inv_app_app_app, CategoryTheory.Limits.colimit.map_desc, HomotopyCategory.quotient_map_eq_zero_iff, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app, CategoryTheory.Abelian.isoModSerre_kernel_eq_isLocal_of_rightAdjoint, CategoryTheory.FunctorToTypes.coprod.inr_app, CategoryTheory.Under.mapCongr_inv_app, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.presheafHom_naturality, SSet.Truncated.StrictSegal.spineToSimplex_spine, CategoryTheory.Equivalence.congrLeft_counitIso_inv_app, CategoryTheory.NatTrans.hcomp_app, CochainComplex.HomComplex.Cocycle.equivHomShift'_symm_apply, CategoryTheory.preserves_mono_of_preservesLimit, AlgebraicGeometry.Scheme.Opens.isoOfLE_hom_ι_assoc, CategoryTheory.MorphismProperty.baseChange_map, CategoryTheory.Comma.mapRightIso_functor_obj_right, mapBicone_ι, CategoryTheory.Pseudofunctor.mapComp'_inv_naturality, CategoryTheory.Limits.Bicones.functoriality_faithful, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_snd, CategoryTheory.Over.postAdjunctionRight_counit_app, AlgebraicGeometry.Scheme.Hom.fromNormalization_preimage, CategoryTheory.Over.conePost_obj_π_app, FullyFaithful.preimage_comp, initial_const_initial, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_apply, CategoryTheory.ShortComplex.RightHomologyData.map_H, CategoryTheory.SmallObject.SuccStruct.arrowMap_refl, AlgebraicGeometry.Scheme.Hom.iSup_preimage_eq_top, CategoryTheory.Localization.SmallShiftedHom.equiv_comp, CategoryTheory.Limits.multicospanIndexEnd_right, CategoryTheory.Subfunctor.Subpresheaf.iSup_obj, CategoryTheory.Limits.Cocone.w_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁'_map_app_app, AlgebraicGeometry.Scheme.toSpecΓ_naturality_assoc, OplaxMonoidal.δ_fst_assoc, CategoryTheory.PreZeroHypercover.map_I₀, CategoryTheory.PresheafOfGroups.Cochain₀.one_apply, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_inv_π_assoc, CategoryTheory.Presieve.ofArrows_mem_comap_jointlySurjectivePrecoverage_iff, CategoryTheory.PreOneHypercover.multicospanIndex_right, curryObjProdComp_hom_app_app, CategoryTheory.RightExactFunctor.whiskeringLeft_map_app, SSet.Subcomplex.degenerate_eq_top_iff, CategoryTheory.Limits.kernel_map_comp_preserves_kernel_iso_inv_assoc, AlgebraicGeometry.Scheme.Modules.pushforwardComp_inv_app_app, CategoryTheory.ShortComplex.map_X₂, CategoryTheory.Limits.span_right, AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_f, CategoryTheory.oppositeShiftFunctorAdd_inv_app, CategoryTheory.Idempotents.app_p_comm, associator_hom_app, Linear.map_smul, shiftIso_zero_hom_app, CategoryTheory.Presheaf.restrictedULiftYoneda_obj_map, CategoryTheory.Limits.inr_comp_pushoutObjIso_hom_assoc, obj_mem_essImage, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition_assoc, CategoryTheory.leftDualFunctor_obj, ModuleCat.HasLimit.productLimitCone_cone_π, CategoryTheory.MonoidalClosedFunctor.comparison_iso, CommRingCat.coyoneda_obj_obj_carrier, AddCommGrpCat.forget₂_map, AlgebraicGeometry.SurjectiveOnStalks.iff_of_isAffine, rightOpComp_hom_app, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetObj_obj, rightAdjointObjIsDefined_iff, CategoryTheory.obj_zero_map_μ_app_assoc, comp_flip_uncurry_eq, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand_assoc, CategoryTheory.Sieve.functorPullback_comp, SSet.Edge.ofTruncated_edge, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_map_app_app, CategoryTheory.Abelian.LeftResolution.exactAt_map_chainComplex_succ, star_obj_as, CategoryTheory.NatTrans.instIsClosedUnderLimitsOfShapeOverFunctorEquifiberedHomDiscretePUnitOfHasCoproductsOfShapeHom, CategoryTheory.Bicategory.postcomp_obj, AlgebraicGeometry.SpecMap_ΓSpecIso_hom, isoShift_inv_naturality_assoc, ModuleCat.HasColimit.colimitCocone_ι_app, CochainComplex.mappingCone.inl_v_triangle_mor₃_f, CategoryTheory.Limits.kernelSubobject_arrow_assoc, CategoryTheory.ExactFunctor.forget_obj, CategoryTheory.LeftExactFunctor.forget_obj, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality_app, CategoryTheory.Comma.opFunctor_map, CategoryTheory.CostructuredArrow.toOver_obj_hom, CategoryTheory.OverPresheafAux.unitAuxAuxAux_hom, HeytAlg.hasForgetToLat_forget₂_obj_str, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_functor_obj_X_p, AlgebraicGeometry.IsAffineOpen.isLocalization_basicOpen, CategoryTheory.Limits.HasColimit.isoOfEquivalence_hom_π, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit, partialRightAdjointHomEquiv_comp_symm_assoc, leftOp_obj, CategoryTheory.Pretriangulated.Triangle.functorMk_map_hom₁, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_left_as, CategoryTheory.Equivalence.inverseFunctor_obj, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_app, CategoryTheory.Mat_.ι_additiveObjIsoBiproduct_inv_assoc, ι_colimitIsoColimitGrothendieck_inv_assoc, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_map_fiber, AlgebraicTopology.DoldKan.PInfty_f_naturality_assoc, CategoryTheory.Adjunction.Triple.adj₁_counit_app_rightToLeft_app, SSet.horn₂₂.sq, CochainComplex.XIsoOfEq_shift, HomologicalComplex₂.ι_totalShift₁Iso_inv_f, CategoryTheory.NatTrans.id_app', HomologicalComplex.extendSingleIso_inv_f_assoc, CategoryTheory.Subfunctor.homOfLe_app_coe, alexDiscEquivPreord_inverse_obj_str, hasBiproduct_of_preserves', CategoryTheory.ComposableArrows.IsComplex.opcyclesToCycles_fac_assoc, CategoryTheory.Monad.FreeCoequalizer.condition, IsCoverDense.Types.appHom_valid_glue, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_apply, CategoryTheory.Limits.Cofork.unop_π_app_one, AlgebraicGeometry.Scheme.zeroLocus_iUnion, AddCommGrpCat.Colimits.colimitCocone_ι_app, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_obj_obj, PresheafOfModules.toPresheaf_map_toSheafify, mapGrpFunctor_obj, CategoryTheory.MonoOver.map_obj_left, CategoryTheory.ChosenPullbacksAlong.snd'_left, CategoryTheory.PreGaloisCategory.card_fiber_coprod_eq_sum, rightOpLeftOpIso_hom_app, obj.ε_def_assoc, Monoidal.ε_η, CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_ext_iff, PresheafOfModules.restrictScalarsObj_obj, TopCat.sigmaCofan_ι_app, AlgebraicGeometry.IsReduced.component_reduced, CategoryTheory.Equalizer.firstObjEqFamily_hom, FullyFaithful.grpObj_inv, uncurry_obj_curry_obj, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_fst_map, CategoryTheory.StructuredArrow.instEssSurjObjCompPostOfFull, HomologicalComplex.natIsoSc'_inv_app_τ₃, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_obj_fiber, CategoryTheory.Subfunctor.Subpresheaf.ofSection_eq_range', AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap, core_obj_of, CategoryTheory.Square.fromArrowArrowFunctor'_obj_X₂, CategoryTheory.Abelian.Ext.mapExactFunctor_zero, CategoryTheory.eqToHom_map, toOplaxFunctor'_obj, Rep.coinvariantsAdjunction_homEquiv_symm_apply_hom, CategoryTheory.CartesianMonoidalCategory.prodComparisonIso_hom, AlgebraicGeometry.SheafedSpace.comp_hom_c_app, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd, CategoryTheory.Comonad.ForgetCreatesColimits'.newCocone_ι_app, Profinite.injective_of_light, CategoryTheory.Localization.LeftBousfield.W_eq_inverseImage_isomorphisms, Monoidal.map_whiskerRight, LaxMonoidal.ofBifunctor.bottomMapₗ_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app, CompHausLike.LocallyConstant.locallyConstantIsoContinuousMap_inv_apply, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_hom, SSet.nonDegenerateEquivOfIso_symm_apply_coe, LightCondSet.topCatAdjunctionUnit_val_app_apply, OplaxRightLinear.δᵣ_associativity_inv, CategoryTheory.Limits.inl_comp_pushoutComparison, CategoryTheory.LocalizerMorphism.Derives.isIso, CategoryTheory.Over.rightUnitor_inv_left_fst, CategoryTheory.LocalizerMorphism.smallHomMap_comp, CommRingCat.coyoneda_obj_map, HomotopyCategory.isoOfHomotopyEquiv_hom, postcompose₃_obj_obj_obj_map_app, CategoryTheory.Injective.injective_of_adjoint, CategoryTheory.CostructuredArrow.homMk'_mk_id, mapMonCompIso_hom_app_hom, AlgebraicGeometry.IsIntegralHom.isIntegral_app, AlgebraicGeometry.Scheme.ker_ideal_of_isPullback_of_isOpenImmersion, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃'_obj_map_app, CategoryTheory.TwoSquare.guitartExact_iff_initial, CochainComplex.HomComplex.Cochain.rightUnshift_comp, CochainComplex.HomComplex.Cochain.rightUnshift_units_smul, TopCat.colimit_topology, CategoryTheory.Subobject.ofMkLEMk_comp_ofMkLE_assoc, CategoryTheory.Limits.Cofork.IsColimit.epi, HeytAlg.hasForgetToLat_forget₂_obj_carrier, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_symm_apply_right, CategoryTheory.Limits.Cocone.fromCostructuredArrow_ι_app, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_fiber, AlgebraicTopology.DoldKan.N₁_obj_p, CategoryTheory.Comma.preRight_obj_left, LeftExtension.coconeAtWhiskerRightIso_inv_hom, CategoryTheory.Subfunctor.Subpresheaf.min_obj, CategoryTheory.Limits.Cone.fromStructuredArrow_π_app, CategoryTheory.Under.mapFunctor_obj, CategoryTheory.Preadditive.commGrpEquivalence_functor_obj_grp_mul, CategoryTheory.Cat.exp_obj, CategoryTheory.Sieve.functorPullback_bot, CategoryTheory.Presieve.isSheafFor_singleton, PresheafOfModules.Derivation.postcomp_d_apply, CategoryTheory.WithTerminal.commaFromOver_map_left, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_symm_apply_φ, CategoryTheory.AsSmall.down_obj, CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_right, TopCat.Sheaf.id_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality_assoc, CategoryTheory.WithInitial.equivComma_functor_obj_right_map, CochainComplex.mappingCone.inr_triangleδ, CategoryTheory.Comonad.coassoc, SimplicialObject.opFunctor_map_app, RightExtension.precomp_map_left, CategoryTheory.Limits.FormalCoproduct.cochainComplexFunctor_map_f, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_snd_assoc, CategoryTheory.μ_naturalityᵣ_assoc, CategoryTheory.Pretriangulated.TriangleMorphism.comm₃, TopologicalSpace.Opens.isOpenEmbedding_obj_top, AlgebraicGeometry.LocallyRingedSpace.Γ_obj_op, CategoryTheory.LaxFunctor.mapComp_assoc_right_app, SemilatInfCat.dual_obj_isOrderBot, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_appTop_coord, LeftExtension.IsPointwiseLeftKanExtension.isLeftKanExtension, SSet.Truncated.HomotopyCategory₂.mk_surjective, CategoryTheory.Limits.pullbackObjIso_inv_comp_fst_assoc, CategoryTheory.Iso.hom_inv_id_app_app_assoc, PresheafOfModules.Derivation.d_one, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.unit_app_ev_app_app, functorialityCompPostcompose_hom_app_hom, mapTriangleOpCompTriangleOpEquivalenceFunctorApp_inv_hom₃, Profinite.exists_locallyConstant_finite_aux, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_hom_hom₂, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_sub, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isIso_of_subset, CategoryTheory.Limits.Cone.fromCostructuredArrow_obj_π, PresheafOfModules.sectionsMap_coe, CategoryTheory.NatTrans.epi_iff_epi_app', SimpleGraph.infinite_iff_in_eventualRange, CategoryTheory.Limits.kernelSubobjectMap_comp, CategoryTheory.SimplicialObject.δ_comp_δ_assoc, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality', AlgebraicGeometry.SheafedSpace.IsOpenImmersion.ofRestrict_invApp_apply, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app_assoc, CategoryTheory.FunctorToTypes.binaryCoproductEquiv_apply, CategoryTheory.Join.mapPair_map_inclRight, AlgebraicGeometry.PresheafedSpace.isoOfComponents_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_mul_app, CategoryTheory.Presieve.FamilyOfElements.singletonEquiv_symm_apply_self, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_inverse_obj_p_f, AddMonCat.FilteredColimits.colimit_add_mk_eq, HomologicalComplex.opFunctor_obj, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_right_app, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.const_s', AlgebraicGeometry.Scheme.Hom.image_preimage_eq_opensRange_inf, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over_assoc, groupHomology.d₁₀_comp_coinvariantsMk_apply, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_μ_unmop_app, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_unit_app, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ_ΓToStalk, Monoidal.whiskerRight_μ_δ_assoc, FullyFaithful.homNatIso_inv_app_down, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_symm_apply, CategoryTheory.MonoOver.isIso_hom_left_iff_subobjectMk_eq, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_sub, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionUnitIso_inv, CategoryTheory.Under.pushout_map, ModuleCat.ExtendRestrictScalarsAdj.Counit.map_hom_apply, CategoryTheory.Cat.opEquivalence_counitIso, pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_app, AlgebraicTopology.DoldKan.comp_P_eq_self_iff, ranCounit_app_whiskerLeft_ranAdjunction_unit_app_assoc, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_inv, CategoryTheory.Over.mapCongr_inv_app_left, CategoryTheory.Limits.kernelSubobject_comp_mono_isIso, CategoryTheory.Comonad.instIsCoreflexivePairCoalgebraTopMapBottomMap, CategoryTheory.IsCofiltered.iff_nonempty_limit, CategoryTheory.ComonadHom.app_ε, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp, AlgebraicGeometry.StructureSheaf.comap_const, CategoryTheory.Limits.Types.FilteredColimit.colimit_eq_iff_aux, CategoryTheory.sheafificationIso_inv_val, SSet.Subcomplex.eq_top_iff_of_hasDimensionLT, AlgebraicGeometry.Scheme.Hom.image_iSup₂, CategoryTheory.Limits.Cocones.precompose_obj_pt, CorepresentableBy.ofIsoObj_homEquiv, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_right_as, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.id_fst_app, AlgebraicGeometry.Scheme.isoSpec_hom_naturality, CategoryTheory.StructuredArrow.preEquivalenceFunctor_obj_left_as, HomologicalComplex.natIsoSc'_hom_app_τ₃, CategoryTheory.Limits.PreservesFiniteLimits.overPost, AlgebraicGeometry.Scheme.zeroLocus_singleton, CategoryTheory.Sum.inl__obj, SSet.stdSimplex.ext_iff, AddGrpCat.FilteredColimits.colimit_add_mk_eq, CategoryTheory.LocalizerMorphism.LeftResolution.Hom.comm, CategoryTheory.ShortComplex.HomologyData.map_homologyMap', CategoryTheory.Endofunctor.Coalgebra.functorOfNatTrans_obj_str, CategoryTheory.RightExactFunctor.whiskeringRight_map_app, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃'_obj_obj_obj, HomologicalComplex.instQuasiIsoAtMapOppositeSymmUnopFunctorOp, CategoryTheory.FreeMonoidalCategory.normalize_naturality, CategoryTheory.StructuredArrow.map₂_obj_left, CategoryTheory.Triangulated.TStructure.isGE_shift_iff, AlgebraicGeometry.PresheafedSpace.comp_c_app, CategoryTheory.ShortComplex.RightHomologyMapData.quasiIso_map_iff, curryingFlipEquiv_symm_apply_map_app, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality', PresheafOfModules.map_comp_apply, CategoryTheory.Subfunctor.max_obj, CategoryTheory.MonoidalClosed.uncurry_pre_app, CommShift₂.commShift_flip_map, AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv_assoc, Final.extendCocone_obj_ι_app, AlgebraicGeometry.LocallyRingedSpace.component_nontrivial, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_hom_app_hom₃, CategoryTheory.Sieve.ofArrows_category, Full.map_surjective, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.uliftCoyonedaEquiv_symm_apply_app, CategoryTheory.InjectiveResolution.toRightDerivedZero_eq, CategoryTheory.Factorisation.forget_obj, AlgebraicGeometry.Scheme.IdealSheafData.ideal_map, CategoryTheory.Pseudofunctor.mapComp'_naturality_1, representableByUliftFunctorEquiv_symm_apply_homEquiv, ModuleCat.RestrictionCoextensionAdj.counit'_app, CategoryTheory.CosimplicialObject.Augmented.const_obj_right, AlgebraicGeometry.IsOpenImmersion.range_pullbackSnd, CategoryTheory.Core.forgetFunctorToCore_obj_obj, PresheafOfModules.pushforward_map_app_apply', CategoryTheory.Under.lift_obj, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoColimitUncurryWhiskeringLeft₂_inv, AlgebraicGeometry.Proj.sub_apply, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_hom_app_fst_app, groupHomology.mapCycles₁_id_comp_assoc, CategoryTheory.Limits.image.map_ι, AlgebraicGeometry.isLocallyArtinian_iff_of_isOpenCover, CategoryTheory.Over.mapCongr_hom_app_left, CategoryTheory.Abelian.Pseudoelement.pseudoZero_iff, AlgebraicGeometry.IsImmersion.instMorphismRestrict, CategoryTheory.MonoidalCategory.DayConvolution.unit_naturality_assoc, CategoryTheory.ProdPreservesConnectedLimits.forgetCone_π, PreservesInjectiveObjects.injective_obj, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd, shift_map_op_assoc, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_jointly_surjective, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_π_app, CategoryTheory.FunctorToTypes.prodMk_snd, CategoryTheory.Discrete.equivalence_unitIso, CategoryTheory.Equivalence.funInvIdAssoc_hom_app, CategoryTheory.equivToOverUnit_unitIso, CategoryTheory.Limits.ConeMorphism.w, CategoryTheory.CostructuredArrow.homMk'_right, CategoryTheory.Abelian.Ext.mk₀_hom, CategoryTheory.Over.postCongr_inv_app_left, CategoryTheory.Subobject.inf_arrow_factors_right, IsDenseSubsite.mapPreimage_comp_assoc, CategoryTheory.SimplicialObject.Truncated.trunc_obj_obj, SSet.mem_degenerate_iff_notMem_nonDegenerate, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app, opUnopIso_inv_app, CategoryTheory.monadToFunctor_obj, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι_assoc, CategoryTheory.Triangulated.TStructure.triangleLTGE_obj_obj₃, AlgebraicGeometry.Scheme.Hom.comp_app, ChainComplex.single₀ObjXSelf, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality, CategoryTheory.Square.fromArrowArrowFunctor'_obj_X₃, FullyFaithful.preimageIso_inv, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_hom, IsCoverDense.Types.pushforwardFamily_def, CategoryTheory.Limits.equalizerSubobject_arrow_comp, ι_leftKanExtensionObjIsoColimit_inv_assoc, LeftLinear.μₗ_comp_δₗ_assoc, CategoryTheory.Limits.LimitPresentation.self_π, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_inv_app, SSet.opFunctor_map, CoalgCat.comonEquivalence_counitIso, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_inverse_map_hom, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_obj_left, CategoryTheory.StructuredArrow.preEquivalence_unitIso, CategoryTheory.Localization.Monoidal.triangle_aux₃, PresheafOfModules.Derivation.d_mul, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_inv_app, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app', CategoryTheory.ihom.ev_coev_assoc, CategoryTheory.Limits.limit.lift_post, OplaxRightLinear.δᵣ_unitality_hom_assoc, AddCommMonCat.coyonedaType_obj_map, CategoryTheory.Comonad.cofree_obj_A, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_hom, CategoryTheory.Limits.ι_comp_sigmaObjIso_inv, mapPresheaf_map_f, FullyFaithful.preimageIso_hom, CategoryTheory.eqToHom_app, AlgebraicGeometry.instIsScalarTowerObjOppositeOpensCarrierTopValStructureSheafInType, CategoryTheory.CosimplicialObject.δ_comp_σ_self', CategoryTheory.Monad.instReflectsColimitWalkingParallelPairParallelPairMapAAppCounitObjAOfReflectsColimitOfIsSplitPair, CategoryTheory.Limits.ι_colimitLimitIso_limit_π, CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_hom_app_unmop_unmop, CategoryTheory.ShortComplex.mapOpcyclesIso_inv_naturality, HomologicalComplex.cyclesOpIso_inv_naturality_assoc, CategoryTheory.MonoidalCategory.DayConvolution.whiskerLeft_comp_unit_app, CategoryTheory.Over.mapComp_hom_app_left, Final.ι_colimitIso_hom_assoc, CategoryTheory.Comma.mapLeftIso_inverse_obj_left, CategoryTheory.TransfiniteCompositionOfShape.ici_F, CategoryTheory.Limits.Cocones.precomposeEquivalence_unitIso, CompactlyGenerated.compactlyGeneratedToTop_obj, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_obj_obj_hom, CategoryTheory.Monad.instPreservesColimitWalkingParallelPairParallelPairMapAAppCounitObjAOfPreservesColimitOfIsReflexivePair, mapGrp_obj_grp_one, CategoryTheory.CostructuredArrow.mapIso_inverse_obj_right, CategoryTheory.linearYoneda_obj_obj_carrier, TopologicalSpace.Opens.mapId_hom_app, CategoryTheory.Comma.mapRight_obj_left, CategoryTheory.CosimplicialObject.Truncated.whiskering_obj_obj_obj, biprodComparison'_comp_biprodComparison_assoc, Rep.instLinearModuleCatObjFunctorCoinvariantsTensor, AlgebraicGeometry.IsOpenImmersion.range_pullback_fst_of_right, CategoryTheory.Limits.LimitPresentation.changeDiag_π, CategoryTheory.Bicategory.postcomposing_obj, mapTriangleInvRotateIso_inv_app_hom₃, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_app, CategoryTheory.Limits.instIsIsoTerminalComparison, CategoryTheory.Grothendieck.id_fiber, groupHomology.mapCycles₁_comp, CategoryTheory.Limits.prodComparison_natural_of_natTrans_assoc, prod_obj, CoconeTypes.IsColimit.exists_desc, CategoryTheory.Comma.equivProd_unitIso_hom_app_left, CategoryTheory.FunctorToTypes.binaryCoproductEquiv_symm_apply, TopologicalSpace.Opens.mapComp_hom_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionUnitIso_hom, AlgebraicGeometry.Scheme.toSpecΓ_naturality, CategoryTheory.Limits.biprod.mapBiprod_hom_desc, Monoidal.map_ε_η_assoc, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app_assoc, SSet.prodStdSimplex.strictMono_orderHomOfSimplex_iff, CategoryTheory.Limits.ι_colimitLimitToLimitColimit_π, CategoryTheory.SimplicialObject.Truncated.rightExtensionInclusion_hom_app, lightDiagramToLightProfinite_obj, CategoryTheory.Coyoneda.objOpOp_hom_app, mapCommGrpFunctor_obj, CategoryTheory.Idempotents.Karoubi.retract_r_f, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst, PushoutObjObj.mapArrowRight_left, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app, HomologicalComplex.singleObjHomologySelfIso_hom_singleObjOpcyclesSelfIso_hom, groupHomology.map_comp, CommGrpCat.μ_forget_apply, CategoryTheory.Subobject.ofLE_comp_ofLEMk_assoc, CategoryTheory.Monad.algebraFunctorOfMonadHomEq_hom_app_f, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_map, OrderHom.equivalenceFunctor_counitIso_inv_app_app, CategoryTheory.Cat.ihom_obj, Action.FunctorCategoryEquivalence.unitIso_inv_app_hom, mapCommGrpCompIso_hom_app_hom_hom_hom, congr_hom_assoc, CategoryTheory.Limits.BinaryBicone.toCocone_ι_app_right, CategoryTheory.Limits.π_comp_colimitUnopIsoOpLimit_inv, SSet.Subcomplex.ofSimplexProd_eq_range, smoothSheaf.ι_evalHom_assoc, CategoryTheory.Subfunctor.nat_trans_naturality, CategoryTheory.Limits.Types.binaryProductFunctor_obj_map, CategoryTheory.Over.whiskerRight_left_fst, Rep.ihom_ev_app_hom, DerivedCategory.HomologySequence.mono_homologyMap_mor₁_iff, CategoryTheory.Join.pseudofunctorLeft_mapId_hom_toNatTrans_app, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_map, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_app_assoc, CategoryTheory.Limits.colimit.toOver_ι_app, whiskeringRight₂_obj_obj_obj_map, CochainComplex.mappingConeCompHomotopyEquiv_comm₂_assoc, instIsLeftKanExtensionObjLanAppLanUnit, SSet.Truncated.Edge.CompStruct.tensor_simplex_snd, CategoryTheory.CostructuredArrow.w_prod_snd_assoc, CategoryTheory.Over.postAdjunctionLeft_unit_app_left, CategoryTheory.Limits.Types.FilteredColimit.isColimit_eq_iff, CategoryTheory.Limits.Cone.extend_π, mapActionComp_inv, CategoryTheory.obj_μ_app, CategoryTheory.Idempotents.functorExtension₂CompWhiskeringLeftToKaroubiIso_hom_app_app_f, CategoryTheory.Limits.Multicofork.snd_app_right_assoc, Initial.conesEquiv_counitIso, hasColimit_map_comp_ι_comp_grothendieckProj, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality, ι_colimitIsoColimitGrothendieck_hom, SheafOfModules.ιFree_mapFree_inv_assoc, CategoryTheory.Limits.limit.pre_post, CategoryTheory.μ_naturalityₗ, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_tensorHom_app, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_sub, CategoryTheory.Limits.Bicone.toCone_π_app_mk, CategoryTheory.Comonad.counit_naturality, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right_assoc, SSet.stdSimplex.face_eq_ofSimplex, CategoryTheory.Limits.coneOfCoconeRightOp_π, CategoryTheory.Bimon.toComon_obj_X, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_counit_app, CategoryTheory.extensiveTopology.isSheaf_yoneda_obj, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp_val_app, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_inv_app, AlgebraicGeometry.Scheme.Hom.ι_toNormalization, CategoryTheory.Limits.limitConstTerminal_hom, CompHausLike.LocallyConstant.counitApp_app, CategoryTheory.Monad.ForgetCreatesColimits.γ_app, CategoryTheory.Pseudofunctor.map₂_associator_app, CategoryTheory.GrothendieckTopology.Plus.toPlus_eq_mk, CategoryTheory.Equalizer.Sieve.w, CategoryTheory.BasedNatTrans.isHomLift', CategoryTheory.Limits.spanCompIso_hom_app_zero, homObjEquiv_symm_apply_app, const.opObjUnop_hom_app, AlgebraicGeometry.LocallyRingedSpace.Γ_Spec_left_triangle, AlgebraicGeometry.StructureSheaf.comap_apply, CategoryTheory.Adjunction.mkOfHomEquiv_counit_app, CommMonCat.coyoneda_obj_map, HomologicalComplex.coconeOfHasColimitEval_pt_d, CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullback, prod'CompFst_hom_app, CategoryTheory.FunctorToTypes.coprod.desc_app, SemilatInfCat.dual_obj_X, coreId_inv_app_iso_inv, SSet.PtSimplex.RelStruct.δ_castSucc_map, CategoryTheory.eHomFunctor_obj_obj, CategoryTheory.instReflectsIsomorphismsFunctorObjWhiskeringRight, Condensed.isoFinYonedaComponents_hom_apply, CategoryTheory.CosimplicialObject.δ_comp_σ_self_assoc, map_inv', CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.functor_map, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_fst_assoc, Bipointed.swapEquiv_counitIso_hom_app_toFun, CategoryTheory.PreGaloisCategory.PreservesIsConnected.preserves, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_inv_app_hom_hom_app, HomologicalComplex.shortComplexFunctor_obj_X₂, CategoryTheory.Limits.kernelComparison_comp_ι, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.sigma_ι_isOpenImmersion, CategoryTheory.Adjunction.isCardinalPresentable_leftAdjoint_obj, SSet.stdSimplex.obj₀Equiv_apply, LeftExtension.postcompose₂_obj_right_map, CategoryTheory.SmallObject.SuccStruct.extendToSuccObjIso_hom_naturality_assoc, Rep.MonoidalClosed.linearHomEquivComm_hom, CategoryTheory.GradedObject.singleCompEval_hom_app, CategoryTheory.Limits.Trident.condition, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_inv_toNatTrans_app_val_app, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_hom_left, CategoryTheory.compEvaluation_hom_app, AlgebraicGeometry.Scheme.IdealSheafData.ideal_pow, AlgebraicGeometry.RingedSpace.mem_top_basicOpen, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_hom_π_π, CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHom_mk, CategoryTheory.Arrow.square_from_iso_invert, CategoryTheory.Limits.coprodComparison_inl, CategoryTheory.Limits.instMonoLiftπ, SSet.Truncated.HomotopyCategory.lift_obj_mk, CategoryTheory.Localization.Preadditive.add'_comp_assoc, ModuleCat.smul_naturality, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv, CategoryTheory.MonoOver.pullback_obj_arrow, CategoryTheory.flippingIso_inv_toFunctor_obj_map_app, CategoryTheory.Over.preservesTerminalIso_pullback, CategoryTheory.AdditiveFunctor.ofLeftExact_map, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_tensorDesc_app, CommGrpTypeEquivalenceCommGrp.inverse_obj_X, SheafOfModules.pullback_map_ιFree_comp_pullbackObjFreeIso_hom_assoc, HomologicalComplex.singleObjCyclesSelfIso_hom_naturality, CategoryTheory.RightExactFunctor.ofExact_map_hom, RepresentableBy.comp_homEquiv_symm, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_hom_hom₁, CategoryTheory.Pseudofunctor.DescentData.iso_hom, CategoryTheory.Equivalence.sheafCongrPrecoherent_functor_obj_val_obj, sheafPushforwardContinuousNatTrans_app_val, CompHausLike.LocallyConstantModule.functor_map_val, CategoryTheory.Limits.Cofork.condition_assoc, PullbackObjObj.π_iso_of_iso_right_hom, CompHausLike.LocallyConstant.functor_map_val, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app_assoc, CochainComplex.HomComplex.Cochain.fromSingleMk_postcomp, Rep.coe_linearization_obj, HomologicalComplex.singleObjCyclesSelfIso_inv_naturality_assoc, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.functor_obj_obj_map, CategoryTheory.Sheaf.instIsIsoAppCounitConstantSheafAdjOfFaithfulOfFullConstantSheafOfIsConstant, SSet.prodStdSimplex.objEquiv_δ_apply, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv, CategoryTheory.WithTerminal.commaFromOver_obj_right, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_iso_inv_app, CategoryTheory.NatTrans.app_nsmul, CategoryTheory.Enriched.FunctorCategory.enrichedId_π_assoc, CoconeTypes.postcomp_ι, CategoryTheory.δ_naturalityᵣ_assoc, CategoryTheory.bifunctorComp₂₃_map_app_app, Subobject.presheaf_obj, CategoryTheory.Adjunction.hasLiftingProperty_iff, CategoryTheory.Over.prodLeftIsoPullback_inv_fst, groupCohomology.map_comp, PushoutObjObj.mapArrowRight_comp_assoc, CategoryTheory.LeftExactFunctor.whiskeringRight_map_app, CategoryTheory.StructuredArrow.ofCommaSndEquivalence_unitIso, CategoryTheory.NatTrans.prod_app_fst, FundamentalGroupoidFunctor.prodToProdTop_obj, CategoryTheory.ι_preservesColimitIso_inv_assoc, SheafOfModules.evaluationPreservesLimitsOfSize, CategoryTheory.FreeGroupoid.mapCompLift_inv_app, groupHomology.map_id_comp, CategoryTheory.Limits.Fork.ι_postcompose, CategoryTheory.Abelian.im_map, ContinuousCohomology.I_obj_ρ_apply, CategoryTheory.Mat_.embedding_obj_X, CategoryTheory.StructuredArrow.map₂_map_left, CategoryTheory.Limits.BinaryBicone.toCone_π_app_left, CategoryTheory.TwoSquare.costructuredArrowRightwards_map, CategoryTheory.ComposableArrows.precomp_obj, HomologicalComplex.HomologySequence.snakeInput_L₁, CategoryTheory.Limits.spanOp_hom_app, AlgebraicGeometry.IsAffineOpen.ideal_le_iff, CategoryTheory.Localization.equivalence_counitIso_app, CategoryTheory.Limits.limitIsoSwapCompLim_hom_app, CategoryTheory.Limits.coprodComparison_inv_natural, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_coproductIsoSelf_inv_assoc, CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieve, CategoryTheory.Limits.Fork.equivOfIsos_functor_obj_ι, TopCat.Presheaf.IsSheaf.isSheafUniqueGluing_types, Homotopy.map_nullHomotopicMap', CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_coproductIsoSelf_inv, AlgebraicTopology.karoubi_alternatingFaceMapComplex_d, CategoryTheory.Adjunction.homEquiv_unit, CategoryTheory.Abelian.Ext.preadditiveCoyoneda_homologySequenceδ_singleTriangle_apply, LaxLeftLinear.μₗ_associativity_inv_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_hom_comp_π_assoc, CategoryTheory.WithTerminal.coneEquiv_functor_obj_π_app_star, CategoryTheory.Under.postAdjunctionRight_unit_app_right, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_inv_app, CategoryTheory.Limits.limitIsoFlipCompLim_hom_app, CategoryTheory.Limits.Cocones.whiskering_obj, CategoryTheory.Join.opEquiv_inverse_map_inclRight_op, CategoryTheory.ComposableArrows.Precomp.map_zero_succ_succ, Profinite.Extend.functorOp_obj, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_left_hom, CategoryTheory.Join.mkFunctor_map_inclLeft, AlgebraicGeometry.Scheme.Hom.congr_app, CoreMonoidal.left_unitality, CategoryTheory.StructuredArrow.ofCommaSndEquivalence_counitIso, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app, CategoryTheory.Limits.coneOfDiagramInitial_π_app, CategoryTheory.Abelian.LeftResolution.π_naturality_assoc, curry₃ObjProdComp_inv_app_app_app, CategoryTheory.coreFunctor_obj_map_iso_inv, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_inv_colimit_map, AlgebraicGeometry.Scheme.Hom.preimage_iSup, ModuleCat.CoextendScalars.smul_apply, CochainComplex.HomComplex.Cochain.shift_zero, PullbackObjObj.mapArrowRight_comp_assoc, CategoryTheory.Limits.CategoricalPullback.mkNatIso_inv_app_snd, CategoryTheory.WithTerminal.coneEquiv_counitIso_inv_app_hom, Final.ι_colimitIso_inv, CategoryTheory.Adjunction.Triple.mono_leftToRight_app_iff_mono_adj₁_counit_app, CategoryTheory.shiftFunctorCompIsoId_add'_inv_app, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₃_app, CategoryTheory.shiftFunctorAdd_zero_add_hom_app, CategoryTheory.Abelian.LeftResolution.karoubi_π, AlgebraicGeometry.coprodMk_inl, CategoryTheory.Idempotents.functorExtension₁CompWhiskeringLeftToKaroubiIso_hom_app_app_f, Rep.coinvariantsTensorIndIso_inv, CategoryTheory.MorphismProperty.relative_map_iff, CategoryTheory.Under.map_map_right, mapGrp_id_one, CategoryTheory.Adjunction.unit_mono_of_L_faithful, CategoryTheory.Over.opEquivOpUnder_inverse_obj, CategoryTheory.Limits.limitCompCoyonedaIsoCone_hom_app, CategoryTheory.ComposableArrows.threeδ₂Toδ₁_app_two, SSet.op_σ, CategoryTheory.ThinSkeleton.fromThinSkeleton_obj, CategoryTheory.OrthogonalReflection.iteration_map_succ, CategoryTheory.MonoidalClosed.uncurry_eq, CategoryTheory.Pseudofunctor.mapComp'_inv_naturality_assoc, Bicategory.Opposite.bicategory_leftUnitor_hom_unop2, TopologicalSpace.Opens.map_id_obj', OplaxMonoidal.id_δ, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionAssocIso_inv, CategoryTheory.uliftYonedaEquiv_apply, CategoryTheory.Limits.ι_comp_colimitRightOpIsoUnopLimit_hom_assoc, CategoryTheory.Limits.instHasColimitObjFunctorConstInitial, HomologicalComplex₂.flipEquivalenceUnitIso_hom_app_f_f, sheafPushforwardContinuous_map_val_app, AlgebraicGeometry.Scheme.Opens.toSpecΓ_naturality_assoc, CategoryTheory.eq_functor_obj, CategoryTheory.isZero_Tor'_succ_of_projective, CategoryTheory.Adjunction.leftAdjointUniq_hom_app_counit_assoc, CategoryTheory.Monad.ForgetCreatesLimits.newCone_π_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_map, Monoidal.μ_comp_assoc, CategoryTheory.CostructuredArrow.mkPrecomp_left, CategoryTheory.NatTrans.comp_app_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id_app, CategoryTheory.skeletonEquivalence_unitIso, CategoryTheory.Limits.SingleObj.Types.colimitEquivQuotient_apply, CategoryTheory.CosimplicialObject.id_app, ModuleCat.binaryProductLimitCone_cone_π_app_right, CategoryTheory.ShiftedHom.zero_comp, CochainComplex.shiftFunctorZero_inv_app_f, CategoryTheory.WithInitial.mkCommaMorphism_right_app, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_app_π_assoc, CategoryTheory.CostructuredArrow.mapIso_functor_map_left, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.functor_obj_obj_obj, CategoryTheory.ι_preservesColimitIso_hom_assoc, CategoryTheory.StructuredArrow.prodFunctor_map, CategoryTheory.shiftFunctorComm_hom_app_comp_shift_shiftFunctorAdd_hom_app, CategoryTheory.Localization.Monoidal.μ_natural_right, AlgebraicGeometry.IsAffineOpen.isoSpec_inv, CategoryTheory.Monad.monToMonad_obj, CategoryTheory.Arrow.equivSigma_apply_snd_snd, CategoryTheory.bijection_natural, AlgebraicGeometry.Scheme.Hom.id_app, TopCat.Presheaf.comp_app, currying_inverse_obj_obj_map, ChainComplex.toSingle₀Equiv_apply_coe, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObjObj_mon_one, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_fst_obj, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_left, CategoryTheory.Presheaf.isSheaf_yoneda', AlgebraicGeometry.Scheme.Γ_obj, CategoryTheory.Limits.Fork.IsLimit.existsUnique, PresheafOfModules.unit_map_one, CategoryTheory.Monoidal.transportStruct_tensorUnit, mapProjectiveResolution_complex, SSet.horn.faceSingletonComplIso_inv_ι, CategoryTheory.NatTrans.CommShift₂.commShift_flipApp, CategoryTheory.piEquivalenceFunctorDiscrete_functor_obj, CategoryTheory.Limits.Types.FilteredColimit.jointly_surjective_of_isColimit₂, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_zero, CategoryTheory.SimplicialObject.Augmented.toArrow_obj_right, FullyFaithful.homEquiv_symm_apply, SSet.Subcomplex.toSSetFunctor_obj, CategoryTheory.left_unitality_app_assoc, HomologicalComplex₂.ι_totalShift₂Iso_inv_f_assoc, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_hom_app_hom₁, groupHomology.functor_obj, PresheafOfModules.zsmul_app, CategoryTheory.Limits.Cocones.equivalenceOfReindexing_functor_obj, CategoryTheory.μ_naturality₂, AlgebraicGeometry.isLocallyNoetherian_iff_of_affine_openCover, AlgebraicGeometry.Scheme.kerAdjunction_unit_app, Condensed.finYoneda_map, CategoryTheory.LeftExactFunctor.whiskeringRight_obj_map, AlgebraicTopology.alternatingFaceMapComplex_map_f, CochainComplex.HomComplex.Cochain.leftShift_comp, CategoryTheory.Limits.limit.post_π, CategoryTheory.Localization.small_of_hasSmallLocalizedHom, CategoryTheory.CartesianClosed.homEquiv_apply_eq, CategoryTheory.Classifier.SubobjectRepresentableBy.homEquiv_eq, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ, CategoryTheory.Over.prodLeftIsoPullback_inv_snd_assoc, CategoryTheory.Comma.mapLeftIso_inverse_obj_right, EffectivePresentation.effectiveEpi, RightExtension.mk_hom, PresheafOfModules.toPresheaf_obj_coe, diag_δ, flip₁₃_obj_map_app, MonCat.FilteredColimits.M.map_mk, CategoryTheory.Limits.prodComparison_comp, mapCommMonNatIso_hom_app_hom_hom, CategoryTheory.AdditiveFunctor.ofRightExact_map, CategoryTheory.Over.rightUnitor_inv_left_snd, CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_hom, leftExtensionEquivalenceOfIso₁_inverse_map_left, OplaxMonoidal.ofBifunctor.secondMap₂_app_app_app, CategoryTheory.Over.coprod_obj, CategoryTheory.Limits.Cone.toStructuredArrowCompToUnderCompForget_hom_app, SSet.Truncated.Edge.id_tensor_id, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂'_obj_map_app, CategoryTheory.ProjectiveResolution.extAddEquivCohomologyClass_symm_apply, mapCoconeOp_inv_hom, CategoryTheory.Limits.PullbackCone.combine_π_app, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_obj_X₂, CategoryTheory.Limits.spanCompIso_inv_app_left, AlgebraicGeometry.Scheme.IdealSheafData.mem_support_iff_of_mem, CategoryTheory.MonoidalOpposite.unmopEquiv_inverse_obj_unmop, instIsMonHomμ, Action.FunctorCategoryEquivalence.functor_δ, topCatToSheafCompHausLike_map_val_app, CategoryTheory.Presieve.HasPairwisePullbacks.map_of_preservesPairwisePullbacks, CategoryTheory.Over.post_map, TopCat.Presheaf.germ_stalkSpecializes_assoc, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone_isColimit_desc, CategoryTheory.FreeGroupoid.lift_obj_mk, CategoryTheory.Localization.homEquiv_eq, MonObj.mopEquiv_functor_obj_mon_one_unmop, CategoryTheory.CategoryOfElements.CreatesLimitsAux.liftedCone_π_app_coe, HomotopicalAlgebra.BifibrantObject.instIsIsoHoCatMapToHoCatOfWeakEquivalence, CategoryTheory.StructuredArrow.final_post, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_hom_assoc, CategoryTheory.Presieve.FamilyOfElements.singletonEquiv_apply, CategoryTheory.Bifunctor.map_id_comp, CategoryTheory.Subobject.ofLEMk_comp, CategoryTheory.Adjunction.leftAdjointUniq_trans_app_assoc, CategoryTheory.preadditiveYoneda_obj, CategoryTheory.bifunctorComp₁₂Obj_obj_obj, imageToKernel_comp_right, SemimoduleCat.forget₂_obj_moduleCat_of, CategoryTheory.Square.toArrowArrowFunctor_obj_left_left, CategoryTheory.regularTopology.equalizerConditionMap_iff_nonempty_isLimit, map_hom_inv, LightProfinite.lightToProfinite_map_proj_eq, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetObj_obj, rightUnitor_hom_app, CategoryTheory.Comma.mapRightId_inv_app_left, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality', CategoryTheory.NatTrans.vcomp_app, CategoryTheory.preservesColimitsOfShape_of_isCardinalPresentable_of_essentiallySmall, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp_app, CategoryTheory.Pseudofunctor.presheafHom_obj, CategoryTheory.isFinitelyPresentable_iff_preservesFilteredColimitsOfSize, AlgebraicGeometry.IsLocallyArtinian.isArtinianRing_of_isAffine, CategoryTheory.linearCoyoneda_obj_obj_isAddCommGroup, FullyFaithful.compUliftYonedaCompWhiskeringLeft_inv_app_app_down, AlgebraicGeometry.StructureSheaf.toPushforwardStalkAlgHom_apply, AlgebraicGeometry.Scheme.Hom.germ_stalkMap_apply, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_obj, CategoryTheory.GrothendieckTopology.preservesSheafification_iff_of_adjunctions, CategoryTheory.Limits.IsColimit.ι_map_assoc, CategoryTheory.AdditiveFunctor.ofExact_map, AlgebraicGeometry.instIsAffineHomDescScheme, CompHausLike.LocallyConstant.incl_of_counitAppApp, CategoryTheory.SplitMono.map_retraction, CategoryTheory.Over.mapPullbackAdj_counit_app, AlgebraicGeometry.Scheme.preimage_basicOpen_top, ι_biproductComparison'_assoc, CategoryTheory.CostructuredArrow.pre_obj_left, CategoryTheory.Over.iteratedSliceBackward_forget, CategoryTheory.Abelian.Pseudoelement.ModuleCat.eq_range_of_pseudoequal, Rep.standardComplex.εToSingle₀_comp_eq, CategoryTheory.Comonad.instPreservesLimitWalkingParallelPairParallelPairMapAAppUnitObjAOfPreservesLimitOfIsCoreflexivePair, OplaxMonoidal.ofBifunctor.firstMap₁_app_app_app, CategoryTheory.PreGaloisCategory.toAut_hom_app_apply, CategoryTheory.Limits.CokernelCofork.IsColimit.isIso_π, isoShift_inv_naturality, AlgebraicTopology.DoldKan.Γ₀'_obj, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality_apply, leftExtensionEquivalenceOfIso₁_inverse_obj_left, CategoryTheory.Equivalence.cancel_counitInv_right, CategoryTheory.Comma.mapLeftId_hom_app_right, CategoryTheory.tensoringRight_linear, AlgebraicGeometry.Scheme.ΓSpecIso_inv, CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_exists, AlgebraicGeometry.Scheme.Hom.app_appIso_inv_assoc, CategoryTheory.Over.postCongr_hom_app_left, PushoutObjObj.ofHasPushout_pt, CompHausLike.sigmaComparison_eq_comp_isos, CategoryTheory.Limits.Fork.hom_comp_ι, CoreMonoidal.μIso_hom_natural_left, map_isoCongr, CategoryTheory.Comma.post_obj_right, postcompose₃_obj_obj_map_app_app, CategoryTheory.μ_naturalityᵣ, Monoidal.map_associator'_assoc, CategoryTheory.JointlyReflectMonomorphisms.mono_iff, CategoryTheory.Adjunction.compPreadditiveYonedaIso_inv_app_app_apply, CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.liftHom_fac, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₃, map_opShiftFunctorEquivalence_unitIso_inv_app_unop, CategoryTheory.Localization.LeftBousfield.W_adj_unit_app, AlgebraicGeometry.IsAffineOpen.basicOpen_fromSpec_app, FundamentalGroupoidFunctor.prodIso_hom, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_comp, CategoryTheory.ShortComplex.mapLeftHomologyIso_hom_naturality, PresheafOfModules.isoMk_hom_app, CategoryTheory.GradedObject.singleCompEval_inv_app, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_app, TopologicalSpace.OpenNhds.map_obj, CategoryTheory.Equivalence.changeFunctor_unitIso_hom_app, CategoryTheory.Limits.colimit.ι_inv_pre, HasFibers.comp_const, TopCat.Presheaf.stalkPushforward_germ_assoc, SSet.prodStdSimplex.objEquiv_naturality, Bipointed.swap_obj_X, imageToKernel_comp_hom_inv_comp, ChainComplex.exactAt_succ_single_obj, CategoryTheory.Preadditive.commGrpEquivalence_functor_obj_grp_inv, CategoryTheory.Monad.instPreservesColimitWalkingParallelPairParallelPairMapAAppCounitObjAOfPreservesColimitOfIsSplitPair, CategoryTheory.ObjectProperty.strictMap_obj, AlgebraicGeometry.Scheme.opensRange_homOfLE, Rep.coindVEquiv_symm_apply_coe, CategoryTheory.ComposableArrows.opEquivalence_unitIso_inv_app, TopCat.Presheaf.pushforward_map_app, CategoryTheory.Comma.preRight_map_left, CategoryTheory.ShortComplex.SnakeInput.naturality_φ₁_assoc, LeftLinear.inv_μₗ, CategoryTheory.SimplicialObject.Augmented.const_obj_hom, TopologicalSpace.OpenNhds.op_map_id_obj, CategoryTheory.LocalizerMorphism.smallShiftedHomMap_mk, OneHypercoverDenseData.essSurj.presheafMap_restriction_assoc, CategoryTheory.Limits.FormalCoproduct.homOfPiHom_φ, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_inv_app, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_ihom_ev_app_assoc, AlgebraicGeometry.Scheme.isoSpec_hom_naturality_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_hom_app, CategoryTheory.ParametrizedAdjunction.hasLiftingProperty_iff, SimplexCategory.toTop_obj, CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse_obj_hom, CategoryTheory.prod.associator_obj, AlgebraicGeometry.Scheme.isoSpec_inv_image_zeroLocus, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₃, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι_ι, splitEpiBiproductComparison_section_, CategoryTheory.instIsIsoFunctorOppositeSheafSheafComposeNatTrans, CategoryTheory.toOverUnit_obj_left, AlgebraicGeometry.Scheme.germToFunctionField_injective, Monoidal.μ_fst_assoc, CategoryTheory.Limits.factorThruKernelSubobject_comp_arrow, CategoryTheory.Limits.PreservesKernel.iso_inv_ι_assoc, CategoryTheory.ShortComplex.Exact.isIso_imageToKernel, CategoryTheory.Equivalence.map_η_comp_η, CategoryTheory.Limits.Multiequalizer.multifork_π_app_left, map_distinguished_iff, CategoryTheory.CosimplicialObject.δ_comp_δ, CategoryTheory.Cat.HasLimits.limitCone_π_app, CategoryTheory.NatTrans.removeLeftOp_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app_assoc, ProfiniteGrp.denseRange_toLimit, CategoryTheory.MonoidalCategory.DayConvolution.associator_inv_unit_unit, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_hom, CategoryTheory.Join.pseudofunctorLeft_mapComp_hom_toNatTrans_app, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural, CategoryTheory.CostructuredArrow.post_map, CategoryTheory.Equivalence.counit_naturality_assoc, CategoryTheory.StructuredArrow.mapNatIso_functor_obj_hom, SSet.modelCategoryQuillen.instHasLiftingPropertyιHornHAddNatOfNatOfFibration, ModuleCat.restrictScalarsId'App_inv_naturality, CategoryTheory.CostructuredArrow.mapIso_unitIso_inv_app_left, CategoryTheory.Limits.Bicone.toBinaryBiconeFunctor_obj_inr, CategoryTheory.MorphismProperty.RightFraction.map_hom_ofInv_id_assoc, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_obj_right, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObjObj_mon_mul, CategoryTheory.uliftYonedaEquiv_symm_map, CategoryTheory.Under.map_obj_right, CategoryTheory.Limits.ConeMorphism.map_w_assoc, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_hom_app, CategoryTheory.Comma.preLeft_obj_right, prod_ε_snd, CategoryTheory.Enriched.FunctorCategory.homEquiv_apply_π, IsLocallyFull.functorPushforward_imageSieve_mem, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.iso_hom, CategoryTheory.MorphismProperty.RightFraction.map_s_comp_map, cones_obj, CategoryTheory.preadditiveYonedaMap_app, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app', CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_left, CategoryTheory.StructuredArrow.mapIso_inverse_obj_right, postcompose₃_obj_obj_obj_obj_obj, map_effectiveEpi, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_map_base, CategoryTheory.WithInitial.mkCommaObject_right_obj, SSet.stdSimplex.spineId_arrow_apply_zero, sum'_map_inr, CategoryTheory.shrinkYoneda_obj, ChainComplex.truncateAugment_inv_f, CategoryTheory.Under.post_obj, SSet.comp_app_assoc, CondensedMod.isDiscrete_iff_isDiscrete_forget, CochainComplex.HomComplex.Cochain.toSingleMk_v_eq_zero, AddCommGrpCat.coyonedaForget_inv_app_app, TopCat.Presheaf.stalkFunctor_obj, SSet.nonDegenerate_eq_bot_of_hasDimensionLT, CategoryTheory.PreservesImage.factorThruImage_comp_hom_assoc, CategoryTheory.PreGaloisCategory.obj_discreteTopology, CategoryTheory.bifunctorComp₁₂Functor_obj, CategoryTheory.Subobject.factorThru_mk_self, CategoryTheory.Adjunction.unit_app_shift_commShiftIso_inv_app, PresheafOfModules.map_smul, ProfiniteAddGrp.limit_zero_val, CategoryTheory.Comma.mapRightComp_inv_app_right, HomologicalComplex.quasiIso_iff_evaluation, DerivedCategory.isZero_of_isLE, CategoryTheory.Pseudofunctor.DescentData.iso_inv, CategoryTheory.Subobject.ofLEMk_comp_ofMkLE, TopologicalSpace.Opens.map_homOfLE, imageToKernel_arrow_assoc, AlgebraicGeometry.isIso_morphismRestrict_iff_isIso_app, CategoryTheory.Grp.mkIso_hom_hom_hom, AddCommGrpCat.free_map_coe, CategoryTheory.SmallObject.SuccStruct.restrictionLTOfCoconeIso_inv_app, mapTriangleIso_hom_app_hom₁, CategoryTheory.Limits.BinaryFan.braiding_hom_snd, strongEpi_map_iff_strongEpi_of_isEquivalence, FintypeCat.uSwitchEquiv_naturality, AlgebraicGeometry.morphismRestrict_base, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_right_hom, CategoryTheory.Monad.left_unit, AlgebraicGeometry.isPullback_inl_inl_coprodMap, ModuleCat.restrictScalarsId'_inv_app, AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex_homotopyHomInvId, CategoryTheory.ShortComplex.exact_iff_isIso_imageToKernel, CategoryTheory.GlueData.ι_gluedIso_inv_assoc, HomologicalComplex.HomologySequence.instEpiMap'ComposableArrows₃OfNatNat, congr_obj, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π, CategoryTheory.Iso.map_hom_inv_id_assoc, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_right, CategoryTheory.CostructuredArrow.map_obj_right, IsEventuallyConstantTo.isoMap_hom, compFlipUncurryIso_inv_app, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_inverse_obj_a, CommShift.ofIso_commShiftIso_hom_app, CategoryTheory.Limits.limit.isoLimitCone_hom_π_assoc, CategoryTheory.Quotient.LiftCommShift.iso_hom_app, CategoryTheory.Enriched.FunctorCategory.diagram_map_app, CategoryTheory.CosimplicialObject.comp_right_app, CategoryTheory.SimplicialObject.Augmented.whiskering_map_app_right, CommShift₂.commShift_map, CategoryTheory.InjectiveResolution.Hom.ι_comp_hom_assoc, CategoryTheory.OplaxFunctor.mapComp_assoc_left_app, CategoryTheory.preservesColimitIso_inv_comp_desc, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen_topIso_inv, PresheafOfModules.Monoidal.tensorObj_map_tmul, CategoryTheory.Square.fromArrowArrowFunctor_obj_X₃, CategoryTheory.LeftExactFunctor.whiskeringLeft_map_app, CategoryTheory.ShortComplex.rightHomologyFunctor_obj, AlgebraicGeometry.Scheme.zeroLocus_setMul, Monoidal.coreMonoidalTransport_μIso_hom, CategoryTheory.CostructuredArrow.proj_obj, CategoryTheory.NatTrans.IsMonoidal.unit, AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ, CategoryTheory.InjectiveResolution.ι_f_succ, lanUnit_app_app_lanAdjunction_counit_app_app, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_snd, CategoryTheory.Adjunction.compUliftCoyonedaIso_inv_app_app_down, CochainComplex.isKInjective_shift_iff, CategoryTheory.ComposableArrows.exact_iff_δ₀, HomologicalComplex.from_single_hom_ext_iff, CategoryTheory.Pretriangulated.Triangle.functorHomMk'_app_hom₃, CategoryTheory.presheafHom_obj, CategoryTheory.IsUniversalColimit.precompose_isIso, CategoryTheory.StructuredArrow.prodEquivalence_unitIso, CategoryTheory.PreGaloisCategory.evaluation_injective_of_isConnected, CategoryTheory.Limits.IsColimit.homEquiv_apply, CategoryTheory.PreZeroHypercover.presieve₀_map, groupHomology.H1CoresCoinf_X₁, pointwiseLeftKanExtension_obj, CategoryTheory.Endofunctor.Coalgebra.Hom.h_assoc, AlgebraicTopology.DoldKan.MorphComponents.preComp_b, CategoryTheory.CosimplicialObject.σ_naturality, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst, CommBialgCat.forget₂_commAlgCat_obj, AlgebraicGeometry.Scheme.ι_image_homOfLE_le_ι_image, Rep.ofModuleMonoidAlgebra_obj_coe, CategoryTheory.Limits.biprod.lift_mapBiprod, AlgebraicGeometry.Scheme.toSpecΓ_preimage_zeroLocus, CategoryTheory.LocalizerMorphism.hasPointwiseRightDerivedFunctorAt_iff_of_isRightDerivabilityStructure, CategoryTheory.Subfunctor.sSup_obj, pointwiseLeftKanExtension_map, CategoryTheory.NatTrans.app_add, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_π_app, AlgebraicTopology.DoldKan.Γ₂_obj_p_app, CategoryTheory.Limits.ι_colimMap, CategoryTheory.Over.prodLeftIsoPullback_hom_snd, lanUnit_app_whiskerLeft_lanAdjunction_counit_app, whiskerLeft_obj_map_bijective_of_isCoverDense, mapCommGrp_obj_X, AlgebraicGeometry.Scheme.Hom.preimage_image_eq, CategoryTheory.ShortComplex.map_X₁, CategoryTheory.CostructuredArrow.preEquivalence.functor_obj_hom, CategoryTheory.Localization.Construction.NatTransExtension.app_eq, CategoryTheory.Cat.HasLimits.homDiagram_map, CategoryTheory.Limits.parallelPairOpIso_hom_app_one, AddGrpCat.FilteredColimits.colimit_neg_mk_eq, mapTriangleInvRotateIso_hom_app_hom₃, Bipointed.swapEquiv_inverse_obj_X, AlgebraicGeometry.IsOpenImmersion.instπWalkingCospanSchemeCospanOne, SimplexCategory.instPathConnectedSpaceCarrierObjTopCatToTop₀, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc_assoc, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_assoc, commAlgCatEquivUnder_functor_obj, groupCohomology.infNatTrans_app, TopologicalSpace.Opens.inclusion'_top_functor, CategoryTheory.comonadToFunctor_obj, CategoryTheory.CostructuredArrow.mkPrecomp_right, CategoryTheory.ThinSkeleton.map₂_obj, TopCat.Presheaf.stalk_open_algebraMap, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso_inv_app_f, ι_colimitIsoOfIsLeftKanExtension_inv, map_zero, CategoryTheory.Limits.PreservesPullback.iso_inv_snd, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc, CategoryTheory.Limits.pair_obj_right, sum_obj_inl, AlgebraicGeometry.Scheme.Hom.app_surjective, CategoryTheory.Limits.coneOfDiagramInitial_pt, CategoryTheory.Limits.limit.pre_π_assoc, CategoryTheory.Limits.PullbackCone.op_ι_app, whiskeringLeft₃ObjObjMap_app, CategoryTheory.Limits.HasEqualizersOfHasPullbacksAndBinaryProducts.pullbackFst_eq_pullback_snd, Monoidal.coreMonoidalTransport_εIso_hom, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_hom_app, constComp_inv_app, Monoidal.map_δ_μ_assoc, CategoryTheory.coprodComparison_tensorRight_braiding_hom, Rep.invariantsAdjunction_unit_app, CategoryTheory.eqToIso_map_trans, FullyFaithful.autMulEquivOfFullyFaithful_apply_inv, CategoryTheory.Monad.id_obj, groupHomology.mapCycles₂_id_comp, TopCat.GlueData.instIsIsoT, CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_eq, CategoryTheory.Limits.π_reflexiveCoequalizerIsoCoequalizer_inv_assoc, Bipointed.swapEquiv_unitIso_inv_app_toFun, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_hom_right, TopCat.Presheaf.presheafEquivOfIso_inverse_obj_map, TopCat.Presheaf.pushforwardEq_hom_app, CategoryTheory.Bimon.equivMonComonCounitIsoAppXAux_inv, id_tensor_π_preserves_coequalizer_inv_colimMap_desc, CategoryTheory.typeEquiv_inverse_obj, SSet.Subcomplex.eq_top_iff_contains_nonDegenerate, CategoryTheory.CommGrp.forget₂CommMon_map_hom, SSet.stdSimplex.range_δ, SSet.PtSimplex.RelStruct.δ_castSucc_map_assoc, CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality_app, CategoryTheory.Equivalence.symmEquivInverse_obj_counitIso_hom, AlgebraicGeometry.affineLocally_iff_affineOpens_le, prod_η_snd, CategoryTheory.Discrete.functor_map_id, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero_assoc, AlgebraicGeometry.Scheme.fromSpecStalk_appTop, AlgebraicTopology.AlternatingFaceMapComplex.d_squared, CategoryTheory.Limits.evaluationPreservesLimits, CondensedMod.LocallyConstant.instFullModuleCatCondensedDiscrete, AlgebraicGeometry.RingedSpace.basicOpen_pow, CategoryTheory.Comonad.delta_naturality_assoc, CategoryTheory.Endofunctor.Algebra.Initial.right_inv, ModuleCat.monoidalClosed_curry, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturality_assoc, CategoryTheory.ShiftMkCore.add_zero_hom_app, CategoryTheory.ShortComplex.mapHomologyIso_hom_naturality_assoc, CategoryTheory.GradedObject.singleObjApplyIsoOfEq_inv_single_map, UniformSpaceCat.extension_comp_coe, CategoryTheory.FinitaryExtensive.mono_inl_of_isColimit, CategoryTheory.StructuredArrow.IsUniversal.existsUnique, CategoryTheory.Idempotents.DoldKan.N₂_map_isoΓ₀_hom_app_f, AlgebraicGeometry.Scheme.Modules.toPresheaf_obj, liftOfIsRightKanExtension_fac_app, CategoryTheory.Limits.pullbackConeEquivBinaryFan_counitIso, CategoryTheory.Limits.PreservesPullback.iso_inv_fst, AlgebraicGeometry.pullbackRestrictIsoRestrict_inv_fst, congr_hom, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_map_left, SSet.PtSimplex.MulStruct.δ_succ_succ_map_assoc, TopCat.presheafToTop_obj, FullyFaithful.autMulEquivOfFullyFaithful_apply_hom, OplaxMonoidal.oplax_right_unitality, Monoidal.map_whiskerLeft_assoc, AlgebraicGeometry.HasRingHomProperty.iff_of_iSup_eq_top, CategoryTheory.ShiftedHom.comp_mk₀, CategoryTheory.StructuredArrow.mapNatIso_functor_map_right, LaxLeftLinear.μₗ_naturality_right_assoc, CategoryTheory.Triangulated.Octahedron.comm₄_assoc, CochainComplex.HomComplex.Cochain.leftShift_rightShift_eq_negOnePow_rightShift_leftShift, CategoryTheory.Cat.associator_inv_app, AlgebraicGeometry.Scheme.Opens.toScheme_presheaf_obj, PresheafOfModules.instPreservesLimitsOfSizeModuleCatCarrierObjOppositeRingCatEvaluation, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counitIso_hom_app_tensor_assoc, CategoryTheory.Idempotents.FunctorExtension₁.obj_obj_X, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_map_right_left, CategoryTheory.Limits.coneOfConeCurry_pt, CategoryTheory.CostructuredArrow.mapIso_functor_obj_left, CategoryTheory.GrothendieckTopology.W_iff_isIso_map_of_adjunction, CategoryTheory.Limits.MultispanIndex.multispanMapIso_inv_app, HomologicalComplex.singleObjHomologySelfIso_hom_singleObjHomologySelfIso_inv_assoc, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.ι_toBase, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_hom_app_f, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_ideal, AlgebraicGeometry.instIsAffineCoprodScheme, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_apply, CategoryTheory.flipFunctor_obj, CategoryTheory.LocalizerMorphism.functorialRightResolutions.Φ_functor_map_ι_app, CategoryTheory.AsSmall.equiv_unitIso, groupHomology.cyclesMap_comp_assoc, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_snd, AlgebraicGeometry.PresheafedSpace.Γ_map_op, CategoryTheory.Limits.diagramIsoCospan_hom_app, CategoryTheory.Comonad.isSplitEpi_iff_isIso_counit, CategoryTheory.Equivalence.sheafCongrPreregular_functor_obj_val_obj, AddCommGrpCat.coyonedaForget_hom_app_app_hom, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_unitIso_hom_app_f_f, CategoryTheory.Monad.comparisonForget_hom_app, CategoryTheory.GrothendieckTopology.W_isInvertedBy_whiskeringRight_presheafToSheaf, CategoryTheory.Grothendieck.ιNatTrans_app_base, CategoryTheory.OverPresheafAux.YonedaCollection.map₂_snd, CategoryTheory.Mat_.lift_obj, CategoryTheory.Dial.comp_le_lemma, CategoryTheory.MonoidalOpposite.tensorIso_hom_app_unmop, CategoryTheory.Over.whiskerRight_left_snd_assoc, CategoryTheory.Sheaf.ΓHomEquiv_naturality_left, FundamentalGroupoidFunctor.piToPiTop_map, CategoryTheory.Arrow.w_mk_right, CategoryTheory.SimplicialObject.Truncated.rightExtensionInclusion_left, CategoryTheory.Monad.algebraFunctorOfMonadHomComp_hom_app_f, CategoryTheory.InjectiveResolution.ι_f_zero_comp_complex_d_assoc, mapComon_map_hom, CategoryTheory.Limits.IsColimit.isIso_colimMap_ι, HomotopyCategory.Pretriangulated.complete_distinguished_triangle_morphism, DerivedCategory.to_singleFunctor_obj_eq_zero_of_injective, CategoryTheory.Cat.rightUnitor_hom_app, groupHomology.cyclesMap_comp_cyclesIso₀_hom_apply, Rep.coinvariantsFunctor_obj_carrier, Monoidal.whiskerLeft_ε_η_assoc, CategoryTheory.Quiv.lift_obj, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_right_app, CategoryTheory.Limits.Fork.unop_ι_app_one, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app_assoc, CategoryTheory.InjectiveResolution.instIsIsoToRightDerivedZero'Self, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app_apply, AlgebraicGeometry.Scheme.id_appTop, CategoryTheory.evaluation_obj_map, CategoryTheory.Arrow.cechNerve_obj, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerLeft_assoc, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_apply_f, CategoryTheory.shiftComm_hom_comp_assoc, TwoP.swap_obj_toTwoPointing, groupHomology.chainsMap_f_single, CategoryTheory.CommGrp.forget₂Grp_obj_mul, CategoryTheory.yonedaMon_naturality_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_map_app_app, CategoryTheory.ChosenPullbacksAlong.Over.snd_eq_snd', CategoryTheory.SmallObject.SuccStruct.extendToSuccObjIso_hom_naturality, DerivedCategory.right_fac_of_isStrictlyLE_of_isStrictlyGE, SSet.instFiniteElemObjOppositeSimplexCategoryOpMkNonDegenerateOfFinite, CategoryTheory.ShortComplex.RightHomologyData.mapOpcyclesIso_eq, OplaxMonoidal.δ_comp_whiskerLeft_δ_assoc, CategoryTheory.Limits.MulticospanIndex.multiforkOfParallelHomsEquivFork_inverse_obj_ι, CategoryTheory.coyoneda_preservesLimits, CategoryTheory.ShortComplex.SnakeInput.functorL₁'_obj, ModuleCat.restrictScalarsId'App_hom_apply, CategoryTheory.Triangulated.TStructure.isLE_shift_iff, CategoryTheory.Limits.coprodComparison_inl_assoc, CategoryTheory.TwistShiftData.shiftFunctorZero_hom_app, CategoryTheory.ProjectiveResolution.Hom.hom_comp_π_assoc, SheafOfModules.pushforwardComp_inv_app_val_app, CategoryTheory.Join.mkFunctor_map_inclRight, CategoryTheory.Presieve.map_map, AddCommGrpCat.HasLimit.productLimitCone_isLimit_lift, CommRingCat.Colimits.cocone_naturality, CategoryTheory.Limits.prodComparison_fst, CochainComplex.HomComplex.Cochain.leftShift_rightShift, Monoidal.transport_ε, CategoryTheory.Limits.pointwiseCocone_ι_app_app, LightCondensed.internallyProjective_iff_tensor_condition, CategoryTheory.CartesianClosed.curry_natural_right_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, CategoryTheory.NatTrans.app_homology, SSet.id_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_app_fst_app, currying_counitIso_inv_app_app, OplaxLeftLinear.δₗ_naturality_left_assoc, CategoryTheory.Limits.hasReflexiveCoequalizer_iff_hasCoequalizer, CategoryTheory.CartesianMonoidalCategory.map_toUnit_comp_terminalComparison_assoc, CategoryTheory.Limits.Types.Colimit.ι_desc_apply', CategoryTheory.sum.inverseAssociator_map_inr_inr, CochainComplex.isSplitEpi_to_singleFunctor_obj_of_projective, CategoryTheory.Sheaf.isConstant_iff_forget, CategoryTheory.CostructuredArrow.map_obj_left, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_unit_app, TopologicalSpace.Opens.map_functor_eq, CategoryTheory.Cat.opFunctor_obj, CategoryTheory.Equivalence.sheafCongrPreregular_functor_map_val_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality_assoc, TopCommRingCat.forgetToTopCatTopologicalRing, CategoryTheory.Limits.FormalCoproduct.eval_map_app, CategoryTheory.LaxFunctor.mapComp_naturality_right_app_assoc, CategoryTheory.Grothendieck.comp_fiber, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_inv_app_hom, CochainComplex.HomComplex.Cocycle.toSingleMk_add, CategoryTheory.Limits.kernelComparison_comp_kernel_map_assoc, CategoryTheory.instIsIsoAppToRightDerivedZeroOfInjective, CategoryTheory.Subfunctor.ofSection_obj, CategoryTheory.uliftYonedaEquiv_naturality, CategoryTheory.SimplicialObject.δ_comp_σ_self'_assoc, CategoryTheory.Limits.opHomCompWhiskeringLimYonedaIsoCocones_hom_app_app_app, CategoryTheory.Over.associator_inv_left_fst_fst_assoc, DerivedCategory.triangleOfSES_obj₃, curry₃_obj_map_app_app, coreId_inv_app_iso_hom, HomologicalComplex.homologyπ_singleObjHomologySelfIso_hom_assoc, HomologicalComplex₂.instHasTotalIntObjUpShiftFunctor₂, CategoryTheory.Grothendieck.map_map, isoShift_hom_naturality, CategoryTheory.Adjunction.map_restrictFullyFaithful_unit_app_assoc, HomologicalComplex.instQuasiIsoMapOppositeSymmUnopFunctorOp, CategoryTheory.MonoidalClosed.curry'_ihom_map, CategoryTheory.ForgetEnrichment.equiv_unitIso, mapIso_injective, HomologicalComplex.single_obj_X_self, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionRight_obj, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₃, CategoryTheory.Limits.CokernelCofork.condition, CategoryTheory.toSkeleton_eq_iff, CategoryTheory.conjugateEquiv_counit_symm, CategoryTheory.Limits.isIso_limit_cone_parallelPair_of_epi, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_base, LeftExtension.nonempty_isPointwiseLeftKanExtensionAt_compTwoSquare_iff, CategoryTheory.Sieve.functorPushforward_over_map, flip₂₃_obj_obj_obj, CategoryTheory.Idempotents.functorExtension₂_obj_map_f, CategoryTheory.CartesianMonoidalCategory.prodComparison_snd_assoc, SSet.RelativeMorphism.ofSimplex₀_map, CategoryTheory.Limits.FormalCoproduct.powerBifunctor_obj, CategoryTheory.sum.inverseAssociator_obj_inr_inl, CommShift.isoZero'_inv_app, CategoryTheory.Grothendieck.ιCompMap_inv_app_fiber, typeToPartialFunIsoPartialFunToPointed_hom_app_toFun, CategoryTheory.TransfiniteCompositionOfShape.iic_isColimit, AlgebraicTopology.DoldKan.map_Hσ, mapBicone_whisker, map_add, CategoryTheory.OverPresheafAux.YonedaCollection.yonedaEquivFst_eq, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_shift, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_val_obj, map_hom_inv_assoc, ContinuousMap.Homotopy.apply_one_path, CategoryTheory.SimplicialObject.Augmented.whiskering_obj, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₁, CategoryTheory.id_app, Monoidal.whiskerRight_η_ε_assoc, ModuleCat.restrictScalarsId'App_hom_naturality_assoc, AlgebraicGeometry.Surjective.sigmaDesc_of_union_range_eq_univ, CategoryTheory.Limits.ker.ι_app, CategoryTheory.Limits.opParallelPairIso_hom_app_zero, PartOrdEmb.Limits.CoconePt.fac_apply, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_hom, HomotopicalAlgebra.CofibrantObject.instIsFibrantObjιBifibrantObjectιCofibrantObject, AlgebraicGeometry.IsAffineOpen.primeIdealOf_isMaximal_of_isClosed, CategoryTheory.Limits.cospan_left, CategoryTheory.Over.associator_hom_left_fst, CategoryTheory.Limits.walkingCospanOpEquiv_inverse_obj, CategoryTheory.Limits.map_id_left_eq_curry_map, HomologicalComplex.singleMapHomologicalComplex_inv_app_self, AlgebraicGeometry.Scheme.fromSpecStalk_toSpecΓ, AlgebraicGeometry.Scheme.ker_toSpecΓ, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_snd_obj, CategoryTheory.StructuredArrow.mapNatIso_inverse_obj_left, HomotopicalAlgebra.CofibrantObject.toHoCat_obj_surjective, CategoryTheory.PreGaloisCategory.autIsoFibers_inv_app, Initial.extendCone_obj_π_app', TopCat.Presheaf.map_germ_eq_Γgerm, CategoryTheory.PreOneHypercover.map_p₁, AlgebraicGeometry.Scheme.IdealSheafData.ideal_bot, CategoryTheory.Enriched.FunctorCategory.coneFunctorEnrichedHom_π_app, CategoryTheory.Abelian.LeftResolution.karoubi.F_map_f, CategoryTheory.evaluationAdjunctionRight_counit_app_app, groupHomology.coinvariantsMk_comp_H0Iso_inv, coreprW_hom_app, LaxMonoidal.ofBifunctor.bottomMapᵣ_app, CategoryTheory.Pseudofunctor.ObjectProperty.mapId_inv_app, CategoryTheory.Monad.comparison_obj_a, CategoryTheory.Limits.ColimitPresentation.map_ι, CategoryTheory.Limits.PreservesLimitPair.iso_inv_fst_assoc, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_map_right_right, AlgebraicGeometry.Spec.toLocallyRingedSpace_obj, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_counitIso, CategoryTheory.Limits.Cocone.toCostructuredArrowCompToOverCompForget_inv_app, CategoryTheory.ShortComplex.unopFunctor_obj, CategoryTheory.Limits.PreservesPushout.inl_iso_inv, PresheafOfModules.pushforward₀_obj_obj_isAddCommGroup, CategoryTheory.Nerve.instIsStrictSegalObjCatTruncatedOfNatNatNerveFunctor₂, TwoP.swapEquiv_inverse_obj_X, CategoryTheory.Limits.CatCospanTransform.rightUnitor_inv_right_app, AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTrans, SSet.Augmented.stdSimplex_map_right, CategoryTheory.CategoryOfElements.toStructuredArrow_obj, LightProfinite.instCountableDiscreteQuotient, AddCommGrpCat.toCommGrp_obj_coe, CategoryTheory.Limits.Fork.IsLimit.homIso_symm_apply, SSet.Subcomplex.toImage_app_coe, CategoryTheory.Limits.walkingSpanOpEquiv_inverse_obj, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_left_as, AlgebraicGeometry.Scheme.ker_of_isAffine, CategoryTheory.PreGaloisCategory.IsFundamentalGroup.transitive_of_isGalois, RingCat.Colimits.cocone_naturality, CategoryTheory.Monad.beckAlgebraCofork_pt, CoreMonoidal.associativity_assoc, CategoryTheory.Limits.Cowedge.condition_assoc, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_left, CategoryTheory.Limits.DiagramOfCocones.coconePoints_map, CategoryTheory.AsSmall.equiv_counitIso, natTransEquiv_symm_apply_app, CategoryTheory.ShortComplex.LeftHomologyData.map_cyclesMap', CategoryTheory.Grp.forget₂Mon_map_hom, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_1, CategoryTheory.CatCommSq.hId_iso_inv_app, CategoryTheory.GrothendieckTopology.PreservesSheafification.le, SSet.PtSimplex.MulStruct.δ_succ_succ_map, CategoryTheory.Limits.CategoricalPullback.π₂_obj, CategoryTheory.Limits.map_inr_inv_coprodComparison_assoc, HomotopicalAlgebra.CofibrantObject.HoCat.bifibrantResolution'_obj, CategoryTheory.δ_μ_app, AlgebraicGeometry.IsAffineOpen.algebraMap_Spec_obj, CategoryTheory.OplaxFunctor.map₂_associator_app_assoc, mapExtLinearMap_coe, AlgebraicGeometry.isBasis_basicOpen, CategoryTheory.Comon.monoidal_whiskerLeft_hom, 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, TopologicalSpace.Opens.map_id_obj, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.exists_larger_subobject, CategoryTheory.Coyoneda.colimitCocone_ι_app, whiskeringLeft₂_obj_obj_obj_map_app, CategoryTheory.ShortComplex.exact_iff_of_hasForget, CategoryTheory.MonoidalClosed.assoc, CategoryTheory.Pretriangulated.instIsHomologicalOppositeAddCommGrpCatObjFunctorPreadditiveYoneda, SheafOfModules.pushforwardNatTrans_id, CategoryTheory.LaxFunctor.map₂_associator_app_assoc, HomologicalComplex.extendSingleIso_hom_f_assoc, CategoryTheory.Presheaf.functorEnrichedHomCoyonedaObjEquiv_naturality, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_unit, CategoryTheory.Monoidal.whiskerRight_app, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_assoc, commShiftOfLocalization_iso_inv_app, leftDerivedZeroIsoSelf_hom_inv_id_app, CategoryTheory.IsHomLift.codomain_eq, CategoryTheory.Limits.ι_colimMap_assoc, uncurry_map_app, whiskeringLeft₂_obj_obj_obj_obj_obj, CategoryTheory.Adjunction.map_restrictFullyFaithful_counit_app, CategoryTheory.ShortComplex.RightHomologyData.map_rightHomologyMap', CategoryTheory.Limits.CompleteLattice.colimitCocone_cocone_pt, CategoryTheory.Limits.piConst_obj_map, CategoryTheory.Limits.diagramIsoParallelPair_hom_app, AlgebraicGeometry.Scheme.Hom.mem_preimage, CommMonCat.coyonedaForget_inv_app_app, map_epi, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₁, PartialOrder.mem_nerve_nonDegenerate_iff_injective, CategoryTheory.GrothendieckTopology.plusFunctor_obj, CategoryTheory.Adjunction.gc, CategoryTheory.MonoidalOpposite.mopMopEquivalence_inverse_map_unmop_unmop, CoreMonoidal.right_unitality_assoc, map.instIsMonHom, CategoryTheory.Equalizer.Presieve.Arrows.compatible_iff, SSet.prodStdSimplex.objEquiv_apply_snd, CategoryTheory.PreGaloisCategory.functorToContAction_map, CategoryTheory.ComposableArrows.twoδ₂Toδ₁_app_zero, CategoryTheory.WithInitial.coconeEquiv_counitIso_inv_app_hom, CategoryTheory.ActionCategory.uncurry_map, CategoryTheory.Limits.colimit.ι_pre, Rep.coinvariantsTensorIndIso_hom, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₃, groupCohomology.map_H0Iso_hom_f, AlgebraicGeometry.PresheafedSpace.colimitCocone_ι_app_base, AlgebraicGeometry.Scheme.Γevaluation_naturality_apply, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_inv_hom_id_assoc, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinset_obj_map, hasBinaryBiproduct_of_preserves, CategoryTheory.NatTrans.removeUnop_app, SSet.hoFunctor.unitHomEquiv_eq, commShiftOfLocalization.iso_inv_app, AlgebraicGeometry.locallyOfFiniteType_iff, CategoryTheory.Comma.toPUnitIdEquiv_functor_obj, CategoryTheory.flipCompEvaluation_hom_app, SheafOfModules.restrictScalars_obj_val, AlgebraicGeometry.SheafedSpace.comp_c_app, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁'_obj_obj_obj, obj.Δ_def_assoc, CategoryTheory.Square.fromArrowArrowFunctor_obj_X₂, LaxMonoidal.ofBifunctor.topMapₗ_app, CategoryTheory.ComposableArrows.whiskerLeftFunctor_obj_map, HomologicalComplex.instHasHomologyObjSingle, AlgebraicGeometry.Flat.flat_and_surjective_iff_faithfullyFlat_of_isAffine, HomotopicalAlgebra.FibrantObject.instWeakEquivalenceHoCatAppιCompResolutionNatTrans, CategoryTheory.Mat_.instHasBiproductιObjEmbeddingXOfAdditive, PresheafOfModules.mono_iff_surjective, instIsIsoAppLanUnit, CategoryTheory.MonoidalOpposite.mopFunctor_η, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd, TopCat.Presheaf.SheafConditionEqualizerProducts.w, OplaxRightLinear.δᵣ_naturality_left, CategoryTheory.CartesianClosed.curry_natural_left_assoc, CategoryTheory.Localization.isoOfHom_op_inv, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_inv_assoc, AlgebraicTopology.DoldKan.Γ₀_obj_map, CategoryTheory.cosimplicialSimplicialEquiv_functor_obj_obj, CategoryTheory.CostructuredArrow.toStructuredArrow'_obj, CategoryTheory.PreGaloisCategory.continuous_mapAut_whiskeringRight, CategoryTheory.ObjectProperty.strictMap_singleton, PresheafOfModules.freeObj_map, CategoryTheory.coev_app_comp_pre_app, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top_assoc, CategoryTheory.Abelian.Pseudoelement.pseudoApply_mk', CategoryTheory.Subobject.pullback_id, CategoryTheory.Localization.Monoidal.μ_natural_left_assoc, CategoryTheory.WithInitial.commaFromUnder_map_left, RightLinear.μᵣ_comp_δᵣ, CategoryTheory.StructuredArrow.homMk'_mk_comp, map_zsmul, mapArrowFunctor_obj, AlgebraicGeometry.liftCoborder_app, Action.resId_inv_app_hom, CategoryTheory.NatTrans.instIsClosedUnderColimitsOfShapeUnderFunctorCoequifiberedHomDiscretePUnitOfHasProductsOfShapeHom, AlgebraicGeometry.LocallyRingedSpace.coe_toΓSpecSheafedSpace_hom_base_hom_apply_asIdeal, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_whiskerLeft_app, CategoryTheory.SimplicialObject.Augmented.const_map_left, CategoryTheory.CostructuredArrow.prodInverse_obj, CategoryTheory.Adjunction.leftAdjointUniq_hom_app_counit, CategoryTheory.Triangulated.SpectralObject.triangle_obj₂, LeftExtension.postcompose₂ObjMkIso_inv_right_app, CategoryTheory.Pretriangulated.Triangle.rotate_mor₃, groupCohomology.cochainsMap_zero, mapCommMon_obj_X, CategoryTheory.Monoidal.tensorUnit_obj, CommShift.comp_commShiftIso_inv_app, CategoryTheory.Over.prodLeftIsoPullback_hom_fst_assoc, CategoryTheory.Abelian.Ext.singleFunctor_map_comp_hom, AlgebraicGeometry.Scheme.Opens.toSpecΓ_preimage_basicOpen, SSet.OneTruncation₂.HoRel₂.mk, CategoryTheory.Limits.Bicone.toBinaryBiconeFunctor_obj_inl, CategoryTheory.CartesianClosed.curry_natural_right, CochainComplex.shiftFunctor_obj_X, CategoryTheory.Over.map_map_left, CategoryTheory.Limits.factorThruImageSubobject_comp_self_assoc, CategoryTheory.Equivalence.counitInv_functor_comp, CategoryTheory.Limits.CompleteLattice.finiteColimitCocone_cocone_ι_app, AlgebraicTopology.DoldKan.N₁Γ₀_hom_app_f_f, SSet.Augmented.stdSimplex_obj_left, sheafPushforwardContinuousCompSheafToPresheafIso_inv_app_app, CategoryTheory.yonedaMon_naturality, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_snd_assoc, CategoryTheory.Mon.limit_mon_mul, CategoryTheory.MorphismProperty.Over.mapId_inv_app_left, CategoryTheory.MonoidalCategory.tensorμ_comp_μ_tensorHom_μ_comp_μ, toOplaxFunctor_obj, CategoryTheory.PreGaloisCategory.nonempty_fiber_of_isConnected, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_left, CategoryTheory.Subobject.pullback_obj, CategoryTheory.Limits.colimitYonedaHomIsoLimit_π_apply, CategoryTheory.Limits.Cotrident.condition_assoc, AlgebraicGeometry.isIntegral_appTop_of_universallyClosed, CategoryTheory.Limits.BinaryFan.braiding_inv_snd, CategoryTheory.equivYoneda'_inv_val, Monoidal.transport_δ, CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_inv_π_π, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.ofRestrict_invApp_apply, CategoryTheory.CosimplicialObject.Augmented.whiskering_map_app_left, AlgebraicGeometry.SheafedSpace.id_hom_c_app, inlCompSum'_hom_app, CategoryTheory.Equivalence.sheafCongrPreregular_inverse_map_val_app, CategoryTheory.Under.costar_obj_left, CategoryTheory.Equivalence.sheafCongrPrecoherent_functor_obj_val_map, CategoryTheory.WithTerminal.liftToTerminal_map, groupHomology.map_comp_assoc, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w, AlgebraicGeometry.Scheme.zeroLocus_def, CategoryTheory.Subfunctor.Subpresheaf.mem_ofSection_obj, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_left_left, CategoryTheory.Limits.BinaryBicones.functoriality_map_hom, CategoryTheory.WithInitial.opEquiv_inverse_obj, HomologicalComplex.instIsCorepresentableCompEvalObjOppositeFunctorTypeCoyonedaOp, CochainComplex.exactAt_succ_single_obj, OplaxLeftLinear.δₗ_unitality_hom_assoc, CategoryTheory.Limits.ker_obj, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_app, Rep.coinvariantsTensorIndNatIso_inv_app, CategoryTheory.SmallObject.functorialFactorizationData_Z_obj, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_continuous, AlgebraicGeometry.Spec_map_localization_isIso, CategoryTheory.Join.mapPairComp_hom_app_right, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_hom, CategoryTheory.bifunctorComp₁₂_map_app_app, toPseudoFunctor_mapComp, AlgebraicGeometry.StructureSheaf.isLocalizedModule_toPushforwardStalkAlgHom_aux, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst, mapMon_obj_X, AddCommGrpCat.binaryProductLimitCone_cone_π_app_left, CategoryTheory.ShortComplex.mapRightHomologyIso_inv_naturality, CategoryTheory.PreservesImage.iso_hom, CategoryTheory.Triangulated.Localization.complete_distinguished_triangle_morphism, CategoryTheory.SimplicialObject.Augmented.const_obj_right, CategoryTheory.ComposableArrows.IsComplex.mono_cokerToKer', AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_assoc, CategoryTheory.IsSeparator.of_equivalence, CategoryTheory.Pseudofunctor.DescentData.instIsIsoαCategoryObjLocallyDiscreteOppositeCatMkOpHom, mapBinaryBicone_snd, CategoryTheory.GrothendieckTopology.W_adj_unit_app, CategoryTheory.Limits.CoconeMorphism.w_assoc, CategoryTheory.Comma.fromProd_obj_left, mapHomologicalComplex_obj_X, instIsSplitMonoApp, CategoryTheory.Limits.coneOfCoconeLeftOp_π_app, CategoryTheory.Limits.LimitPresentation.reindex_π, CategoryTheory.Comonad.ComonadicityInternal.unitFork_ι, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₂, CategoryTheory.MonoOver.image_map, CategoryTheory.Localization.Preadditive.homEquiv_apply, CategoryTheory.Bifunctor.map_id, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app, CategoryTheory.SmallObject.SuccStruct.extendToSuccRestrictionLEIso_hom_app, CoreMonoidal.toOplaxMonoidal_δ, AlgebraicGeometry.ΓSpec.adjunction_counit_app, CoreMonoidal.μIso_hom_natural_left_assoc, CochainComplex.HomComplex.Cocycle.toSingleMk_mem_coboundaries_iff, CategoryTheory.ComonadHom.app_ε_assoc, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app_assoc, OneHypercoverDenseData.essSurj.presheafObj_condition_assoc, CategoryTheory.Limits.coneOfCoconeUnop_π, CategoryTheory.Equivalence.rightOp_inverse_map, AlgebraicGeometry.StructureSheaf.algebraMap_self_map, map_conj, CategoryTheory.sheafToPresheaf_obj, CategoryTheory.Limits.hasPushout_of_preservesPushout, ContinuousCohomology.I_obj_V_isModule, AlgebraicGeometry.Scheme.Hom.preimage_smoothLocus_eq, AlgebraicGeometry.tilde.isoTop_hom, AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInfty_assoc, CategoryTheory.OverPresheafAux.unitAuxAuxAux_inv, CategoryTheory.Adjunction.IsMonoidal.leftAdjoint_ε, AlgebraicGeometry.Scheme.restrict_presheaf_obj, CategoryTheory.Under.mapPushoutAdj_unit_app, CategoryTheory.additive_yonedaObj', SSet.hasDimensionLT_iff, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_map_left, CategoryTheory.MonoidalCategory.tensoringRight_δ, CategoryTheory.Idempotents.functorExtension_obj_obj, CategoryTheory.nerveMap_app_mk₁, AlgebraicGeometry.ProjectiveSpectrum.Proj.isLocalization_atPrime, CategoryTheory.Limits.SequentialProduct.functorMap_commSq_aux, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.secondMap₂_app_app_app, CategoryTheory.DifferentialObject.d_squared, CategoryTheory.Limits.Types.isLimitEquivSections_apply, CategoryTheory.preservesLimitIso_inv_π_assoc, CategoryTheory.Limits.ι_comp_sigmaComparison, CategoryTheory.Center.ofBraided_ε_f, leftOpRightOpIso_hom_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_obj, ranCompIsoOfPreserves_inv_app, ModuleCat.Tilde.toOpen_res, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one_assoc, CategoryTheory.Mat.equivalenceSingleObjInverse_obj_carrier, 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.Limits.instHasImageHomMk, CategoryTheory.shiftFunctorComm_hom_app_comp_shift_shiftFunctorAdd_hom_app_assoc, HomotopicalAlgebra.CofibrantObject.instIsCofibrantObjι, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_star, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv_assoc, CategoryTheory.CosimplicialObject.Truncated.whiskering_map_app_app, CochainComplex.HomComplex.Cochain.map_add, CategoryTheory.Mat_.embeddingLiftIso_hom_app, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_map_fst_app, CategoryTheory.Join.mapWhiskerRight_app, CategoryTheory.TwoSquare.isIso_lanBaseChange_app, AlgebraicGeometry.germ_comp_stalkToFiberRingHom, CategoryTheory.CostructuredArrow.initial_post, HopfAlgCat.MonoidalCategory.inducingFunctorData_μIso, CategoryTheory.Over.opEquivOpUnder_inverse_map, CategoryTheory.Limits.CompleteLattice.colimitCocone_cocone_ι_app, CategoryTheory.ProjectiveResolution.extMk_hom, AlgebraicGeometry.Scheme.IdealSheafData.mem_supportSet_iff, CategoryTheory.SmallObject.SuccStruct.Iteration.subsingleton.MapEq.w, CategoryTheory.Equalizer.Presieve.isSheafFor_singleton_iff, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_map_left_left, CategoryTheory.Projective.projective_iff_preservesEpimorphisms_coyoneda_obj, CategoryTheory.StructuredArrow.mkPostcomp_left, map_conjAut, CategoryTheory.Grothendieck.grothendieckTypeToCat_functor_obj_fst, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_neg_assoc, CategoryTheory.Adjunction.isIso_counit_app_of_iso, AlgebraicGeometry.Scheme.Opens.toSpecΓ_appTop, instIsEquivalenceRightExtensionPostcomp₁OfIsIso, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_obj_X₃, CategoryTheory.Limits.Cocones.functoriality_obj_pt, CochainComplex.HomComplex.Cochain.fromSingleMk_v, commBialgCatEquivComonCommAlgCat_functor_obj_unop_X, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_whiskerLeft, CategoryTheory.MonoidalClosed.curry_id_eq_coev, shiftIso_add_hom_app, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_inv_hom₃, CategoryTheory.AdditiveFunctor.forget_obj_of, mapMonNatIso_hom_app_hom, CategoryTheory.ComposableArrows.map'_comp, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_app_fst_app, CategoryTheory.shiftFunctorAdd_inv_app_obj_of_induced, CategoryTheory.ComposableArrows.IsComplex.zero_assoc, AlgebraicGeometry.Scheme.IdealSheafData.mem_support_iff, mapTriangleIso_hom_app_hom₂, CondensedMod.epi_iff_surjective_on_stonean, CategoryTheory.Limits.opParallelPairIso_hom_app_one, CategoryTheory.Iso.op2_hom_unop2, CategoryTheory.typeEquiv_unitIso_hom_app, AlgebraicGeometry.PresheafedSpace.GlueData.ι_image_preimage_eq, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_hom_assoc, CochainComplex.HomComplex.Cochain.fromSingleMk_add, CategoryTheory.Limits.Cofork.IsColimit.homIso_apply_coe, SSet.instFiniteObjOppositeSimplexCategoryTensorObj, CategoryTheory.Over.leftUnitor_inv_left_fst, Rep.instAdditiveModuleCatObjFunctorCoinvariantsTensor, CategoryTheory.Under.post_map, CochainComplex.single₀_map_f_zero, Bicategory.Opposite.bicategory_leftUnitor_inv_unop2, CategoryTheory.Limits.cospanCompIso_inv_app_left, CategoryTheory.Limits.CatCospanTransform.associator_hom_left_app, mapTriangleCompIso_inv_app_hom₃, preservesZeroMorphisms_evaluation_obj, CompHausLike.LocallyConstant.functor_obj_val, CategoryTheory.Triangulated.Octahedron.triangle_mor₃, CategoryTheory.ShortComplex.LeftHomologyData.exact_map_iff, CategoryTheory.Limits.spanCompIso_app_zero, map_effectiveEpiFamily, CategoryTheory.Equivalence.sheafCongrPreregular_functor_obj_val_map, CategoryTheory.WithInitial.inclLiftToInitial_inv_app, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_neg, InfiniteGalois.mulEquivToLimit_symm_continuous, CategoryTheory.Comma.mapLeftIso_functor_obj_left, toPrefunctor_obj, partialRightAdjointHomEquiv_comp, CategoryTheory.TwistShiftData.shift_z_app, CategoryTheory.Ind.isIndObject_inclusion_obj, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_unit_app_left, CategoryTheory.Limits.yonedaCompLimIsoCocones_hom_app_app, CategoryTheory.Over.starPullbackIsoStar_hom_app_left, PresheafOfModules.instEpiModuleCatCarrierObjOppositeRingCatApp, CategoryTheory.Limits.PushoutCocone.ofCocone_ι, CategoryTheory.Over.postEquiv_inverse, CategoryTheory.ObjectProperty.isLocalization_isLocal, CategoryTheory.Square.toArrowArrowFunctor'_obj_right_right, CategoryTheory.SmallObject.SuccStruct.extendToSucc_obj_eq, CategoryTheory.TwoSquare.equivalenceJ_counitIso, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_obj_obj_map, AlgebraicTopology.DoldKan.Γ₂N₂ToKaroubiIso_hom_app, CategoryTheory.StructuredArrow.mapNatIso_unitIso_hom_app_right, CategoryTheory.Limits.coend.condition_assoc, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec_assoc, AlgebraicGeometry.opensDiagram_map, CategoryTheory.Adjunction.functorialityUnit_app_hom, postcompose₃_obj_obj_obj_obj_map, CategoryTheory.Abelian.Ext.mapExactFunctor_hom, rightOp_obj, CategoryTheory.AdditiveFunctor.forget_obj, CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_hom_apply, mapTriangleOpCompTriangleOpEquivalenceFunctorApp_hom_hom₁, TopCat.uliftFunctorObjHomeo_naturality_apply, CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_hom_apply, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_app, smoothSheafCommRing.ι_evalHom, CochainComplex.HomComplex.Cochain.shift_smul, AlgebraicGeometry.Γ_restrict_isLocalization, CategoryTheory.Monad.adj_unit, CategoryTheory.Subfunctor.ofSection_eq_range', 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.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCocone_π_app_eq_sum, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.isIso_f, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_hom_hom₃, CategoryTheory.Limits.ι_colimitCompWhiskeringLeftIsoCompColimit_hom, mapTriangleCompIso_hom_app_hom₃, Rep.coindResAdjunction_unit_app, CategoryTheory.Subobject.map_pullback, CategoryTheory.Limits.coneOfIsSplitMono_π_app, CategoryTheory.Limits.ι_comp_sigmaObjIso_hom, CategoryTheory.coreFunctor_obj_obj_of, CategoryTheory.Localization.Monoidal.map_hexagon_reverse, CategoryTheory.GradedObject.mapBifunctorObjSingle₀ObjIso_hom, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagram_obj, partialRightAdjointHomEquiv_map, CategoryTheory.Comma.map_obj_right, CategoryTheory.Triangulated.Octahedron.map_m₃, CategoryTheory.FunctorToTypes.hcomp, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone_cocone_ι_app, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.ι_toBase_assoc, CategoryTheory.OplaxFunctor.mapComp_assoc_right_app, AlgebraicGeometry.Scheme.Hom.app_eq, CategoryTheory.Join.mapPair_map_inclLeft, CategoryTheory.Endofunctor.Algebra.Initial.str_isIso, CategoryTheory.Localization.faithful_whiskeringLeft, CategoryTheory.Join.isoMkFunctor_inv_app, AlgebraicGeometry.RingedSpace.res_zero, CategoryTheory.OverPresheafAux.yonedaCollectionFunctor_obj, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_hom_eq_germ, CategoryTheory.SimplicialObject.δ_naturality, AlgebraicGeometry.morphismRestrict_ι, CochainComplex.HomComplex.Cochain.leftShiftAddEquiv_apply, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_μ, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransId_inv_app_f, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_hom_app_app, CategoryTheory.ReflQuiv.adj.unit.map_app_eq, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp_app, PrincipalSeg.cocone_ι_app, AlgebraicGeometry.Scheme.Hom.preimageIso_inv_ι, CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse_obj_hom, CommRingCat.instIsLocalHomCarrierObjWalkingParallelPairFunctorConstPtEqualizerForkZeroParallelPairRingHomHomι, BialgCat.forget₂_coalgebra_obj, CategoryTheory.Limits.end_.condition, SSet.horn.spineId_map_hornInclusion, SSet.Truncated.HomotopyCategory.mk_surjective, HomologicalComplex₂.instHasTotalIntObjUpCompShiftFunctor₁ShiftFunctor₂, TopCat.Presheaf.germ_res_assoc, CategoryTheory.WithTerminal.coneEquiv_functor_obj_π_app_of, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec, CategoryTheory.Limits.Multicofork.ofSigmaCofork_π, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_map_app_snd, CategoryTheory.SmallObject.SuccStruct.ofCoconeObjIso_hom_naturality, CategoryTheory.WithInitial.coconeEquiv_unitIso_hom_app_hom_right, CorepresentableBy.homEquiv_eq, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_right, CategoryTheory.Sheaf.instMonoAppArrowPLocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, CategoryTheory.PreGaloisCategory.fiberBinaryProductEquiv_symm_fst_apply, AlgebraicGeometry.Scheme.Hom.apply_mem_image_iff, HomologicalComplex.opcyclesOpIso_hom_naturality_assoc, CategoryTheory.Localization.lift₂_iso_hom_app_app₂, shiftMap_comp, CategoryTheory.Abelian.LeftResolution.karoubi.F'_obj_p, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_hom_app, CategoryTheory.Limits.Concrete.isColimit_exists_rep, CategoryTheory.LocalizerMorphism.smallHomMap_mk, HomologicalComplex.dgoToHomologicalComplex_obj_X, CategoryTheory.MorphismProperty.Over.mapCongr_hom_app_left, shiftIso_add'_hom_app, CategoryTheory.Limits.Cone.ofPullbackCone_pt, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app, SemiNormedGrp.completion.norm_incl_eq, Monoidal.transport_μ_assoc, CategoryTheory.endofunctorMonoidalCategory_whiskerRight_app, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app, SSet.horn_obj, CategoryTheory.sectionsFunctorNatIsoCoyoneda_inv_app_coe, TopCat.Presheaf.germToPullbackStalk_stalkPullbackHom, ModuleCat.directLimitIsColimit_desc, CategoryTheory.MorphismProperty.relative_map, CategoryTheory.BraidedCategory.ofBifunctor.Forward.secondMap₂_app_app_app, CategoryTheory.Limits.Pi.isoLimit_inv_π, CategoryTheory.LeftExactFunctor.whiskeringLeft_obj_obj_obj, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_obj_obj_map, CategoryTheory.Pretriangulated.Triangle.distinguished_iff_of_isZero₂, CondensedSet.epi_iff_surjective_on_stonean, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app, SimplexCategory.instNonemptyCarrierObjTopCatToTop, CategoryTheory.Comonad.instPreservesLimitWalkingParallelPairParallelPairMapAAppUnitObjAOfPreservesLimitOfIsCosplitPair, ChainComplex.augmentTruncate_inv_f_succ, CategoryTheory.preadditiveYonedaObj_obj_isModule, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_inv_app_app, AlgebraicGeometry.ΓSpecIso_obj_hom, CategoryTheory.eq_inverse_obj, CategoryTheory.Presieve.IsSheafFor.comp_iff_of_preservesPairwisePullbacks, functorPushforward_equalizer_mem, CategoryTheory.FunctorToTypes.binaryCoproductCocone_pt_map, groupHomology.mapCycles₁_id_comp_apply, LaxMonoidal.left_unitality, CategoryTheory.Localization.SmallHom.equiv_mkInv, CategoryTheory.ComposableArrows.opEquivalence_functor_obj_map, CategoryTheory.Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor, AddCommGrpCat.free_obj_coe, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_one_app, SSet.leftUnitor_inv_app_apply, CategoryTheory.NatTrans.naturality_app_app_assoc, CategoryTheory.Limits.PreservesLimitPair.iso_hom, CategoryTheory.SmallObject.SuccStruct.Iteration.obj_bot, TopologicalSpace.Opens.map_comp_map, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₁, CategoryTheory.Adjunction.Triple.leftToRight_app_obj, SSet.ι₀_fst_assoc, SSet.ι₁_comp, CategoryTheory.Comon.monoidal_leftUnitor_hom_hom, CategoryTheory.Subobject.inf_eq_map_pullback', AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackToBaseIsOpenImmersion, CategoryTheory.Adjunction.homAddEquiv_sub, AddCommGrpCat.Colimits.quotUliftToQuot_ι, CategoryTheory.Equivalence.sheafCongrPrecoherent_inverse_map_val_app, CategoryTheory.Preadditive.commGrpEquivalenceAux_hom_app_hom_hom_hom, CategoryTheory.Presheaf.restrictedULiftYoneda_map_app, CategoryTheory.Adjunction.map_injective, CategoryTheory.Abelian.LeftResolution.instEpiKaroubiAppπ', CategoryTheory.Adjunction.instIsIsoAppUnitOfFullOfFaithful, SSet.skeleton_obj_eq_top, groupCohomology.cochainsMap_id_comp, SSet.Subcomplex.yonedaEquiv_coe, SSet.Augmented.StandardSimplex.nonempty_extraDegeneracy_stdSimplex, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_naturality_assoc, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.ι_map_tensorHom_eq, DerivedCategory.instIsIsoMapCochainComplexIntQ, OplaxMonoidal.δ_comp_δ_whiskerRight_assoc, AlgebraicGeometry.Spec.germ_stalkMapIso_hom_assoc, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan_inv_app_app_apply_eq_id, PresheafOfModules.presheaf_map_apply_coe, CategoryTheory.Pi.comap_obj, AlgebraicGeometry.Scheme.IdealSheafData.le_ofIdeals_iff, SheafOfModules.sectionsFunctor_obj, LaxMonoidal.μ_natural_right_assoc, CategoryTheory.CosimplicialObject.Augmented.leftOp_left_map, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac, AlgebraicGeometry.Scheme.Hom.preimage_basicOpen_top, InfiniteGalois.isOpen_mulEquivToLimit_image_fixingSubgroup, CategoryTheory.Limits.spanOp_inv_app, CategoryTheory.Presheaf.isSeparated_iff_subsingleton, HasFibers.inducedFunctor_obj_coe, CategoryTheory.Abelian.Ext.homEquiv_chgUniv, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom, CategoryTheory.Pretriangulated.Triangle.shift_distinguished_iff, CategoryTheory.right_unitality_app_assoc, mapCoconeMapCocone_hom_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app_assoc, ofOpSequence_obj, LightCondensed.isColimitLocallyConstantPresheafDiagram_desc_apply, AlgebraicGeometry.StructureSheaf.IsLocalization.to_basicOpen, CategoryTheory.Limits.Cocones.forget_obj, CategoryTheory.Equivalence.rightOp_unitIso_hom_app, CategoryTheory.Over.conePostIso_hom_app_hom, inl_biprodComparison', CategoryTheory.SmallObject.SuccStruct.Iteration.subsingleton.MapEq.tgt, HomotopyCategory.quot_mk_eq_quotient_map, CategoryTheory.Join.pseudofunctorLeft_mapComp_inv_toNatTrans_app, CategoryTheory.Limits.Cones.functoriality_obj_π_app, SSet.OneTruncation₂.ofNerve₂.natIso_hom_app_obj, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv_assoc, CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_cancel_hom_app, HomotopicalAlgebra.CofibrantObject.instIsCofibrantObjFunctorWeakEquivalencesLocalizerMorphism, CochainComplex.HomComplex.Cocycle.toSingleMk_zero, CategoryTheory.Presieve.isSheafFor_arrows_iff, CochainComplex.HomComplex.Cochain.rightShiftAddEquiv_apply, obj.η_def_assoc, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descAddMonoidHom_quotMk, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv, HomologicalComplex.quasiIsoAt_unopFunctor_map_iff, CategoryTheory.Limits.reflexivePair.compRightIso_hom_app, CategoryTheory.RanIsSheafOfIsCocontinuous.fac_assoc, CategoryTheory.DifferentialObject.Hom.comm_assoc, CategoryTheory.preservesLimits_preadditiveCoyoneda_obj, groupCohomology.mapShortComplexH2_comp, shiftIso_inv_naturality, OplaxMonoidal.ofBifunctor.secondMap₃_app_app_app, CategoryTheory.enrichedFunctorTypeEquivFunctor_symm_apply_obj, CategoryTheory.η_app_obj, CategoryTheory.bifunctorComp₂₃Obj_obj_obj, AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zero, AlgebraicGeometry.IsZariskiLocalAtSource.sigmaDesc, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_apply_fst, CategoryTheory.ShortComplex.fFunctor_obj, AlgebraicGeometry.Scheme.Modules.restrict_map, CategoryTheory.ProjectiveResolution.pOpcycles_comp_fromLeftDerivedZero'_assoc, CategoryTheory.FinCategory.asTypeToObjAsType_obj, CategoryTheory.Pseudofunctor.CoGrothendieck.map_obj_fiber, TopCat.Sheaf.objSupIsoProdEqLocus_hom_fst, whiskerLeft_app, imageToKernel_epi_comp, TopCat.nonempty_isLimit_iff_eq_induced, CategoryTheory.Groupoid.invEquivalence_inverse_obj, CategoryTheory.expComparison_whiskerLeft, partialLeftAdjointHomEquiv_map, leibnizPushout_obj_map, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_whiskerRight_app, CategoryTheory.linearYoneda_obj_obj_isAddCommGroup, CochainComplex.HomComplex.Cochain.leftUnshift_v, AlgebraicGeometry.isIso_stalkMap_coprodSpec, toEventualRanges_obj, isSplitMono_iff, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInrIso_inv_app_app, SimplexCategory.toTop₀_obj, CategoryTheory.Limits.colimitLimitToLimitColimitCone_hom, AlgebraicGeometry.PresheafedSpace.forget_obj, CategoryTheory.NatIso.mapHomologicalComplex_hom_app_f, CategoryTheory.isIso_iff_isIso_yoneda_map, RightExtension.coneAtFunctor_obj, CategoryTheory.Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor_assoc, TopologicalSpace.Opens.functor_obj_map_obj, CategoryTheory.GlueData.diagramIso_app_left, smoothSheafCommRing.evalHom_germ, CategoryTheory.Localization.isoOfHom_hom, whiskeringLeft₃ObjMap_app, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_three, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃'_obj_obj_map, HomotopicalAlgebra.BifibrantObject.instIsCofibrantObjFibrantObjectsObjFibrantObjectιFibrantObject, DerivedCategory.HomologySequence.comp_δ_assoc, CategoryTheory.Sheaf.natTransΓRes_app, PushoutObjObj.mapArrowLeft_id, CategoryTheory.Quotient.lift_map_functor_map, essImage_underPost, SSet.instFiniteObjOppositeSimplexCategoryOfFinite, CategoryTheory.Comma.equivProd_inverse_map_left, CategoryTheory.shiftFunctorAdd'_zero_add_inv_app, ModuleCat.restrictScalarsComp'App_hom_naturality_assoc, FundamentalGroupoidFunctor.projLeft_map, CategoryTheory.Subobject.instMonoOfLE, AlgebraicGeometry.HasRingHomProperty.iff_appLE, PresheafOfModules.Derivation.congr_d, CategoryTheory.cosimplicialSimplicialEquiv_inverse_obj, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_map_assoc, CategoryTheory.Limits.map_inr_inv_coprodComparison, CategoryTheory.PreGaloisCategory.exists_lift_of_continuous, CategoryTheory.Join.fromSum_map_inr, essImage.counit_isIso, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_mapIso_mkNatIso_eq_mkIso, CategoryTheory.Limits.Multicofork.π_eq_app_right, CategoryTheory.WithTerminal.map_map, CategoryTheory.MonoidalClosed.uncurry_pre, CategoryTheory.Adjunction.strongEpi_map_of_strongEpi, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_fst_map, mapAction_η_hom, CategoryTheory.Limits.instPreservesFiniteLimitsFunctorObjEvaluationOfHasFiniteLimits, curry₃ObjProdComp_hom_app_app_app, CategoryTheory.Over.tensorHom_left_snd_assoc, CategoryTheory.CosimplicialObject.cechConerveEquiv_symm_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality', map_smul, whiskeringLeftObjIdIso_hom_app_app, preimage_comp, CategoryTheory.BraidedCategory.curriedBraidingNatIso_hom_app_app, TopCat.Presheaf.pushforward_eq', AlgebraicGeometry.Scheme.Hom.image_mono, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_uliftYoneda_map, OplaxMonoidal.ofBifunctor.secondMap_app_app_app, CategoryTheory.Grp.μ_def, CategoryTheory.Idempotents.FunctorExtension₁.obj_obj_p, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap_assoc, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided_obj, CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_snd_apply, CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_hom_app, mapMonNatIso_inv_app_hom, CategoryTheory.Adjunction.shift_counit_app, CategoryTheory.SimplicialObject.isoCoskOfIsCoskeletal_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_hom_app_hom_hom_app, CategoryTheory.Limits.Cone.ofPullbackCone_π, CategoryTheory.ShortComplex.hasRightHomology_of_preserves', mapIso_refl, CategoryTheory.Subobject.mapIsoToOrderIso_apply, Monoidal.map_rightUnitor_assoc, LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom, map_shift_unop, Additive.map_add, CategoryTheory.LocalizerMorphism.LeftResolution.opFunctor_obj, CategoryTheory.PreGaloisCategory.toAut_surjective_isGalois, CategoryTheory.CosimplicialObject.δ_naturality_assoc, OplaxMonoidal.lift_δ, AlgebraicGeometry.IsAffineOpen.self_le_basicOpen_union_iff, CategoryTheory.Presieve.FamilyOfElements.Compatible.functorPushforward, IsCoverDense.presheafIso_hom_app, CategoryTheory.TwoSquare.whiskerVertical_app, CategoryTheory.Limits.ConeMorphism.map_w, CategoryTheory.FunctorToTypes.binaryProductEquiv_symm_apply, SheafOfModules.Presentation.quasicoherentData_presentation, AddMonCat.FilteredColimits.colimit_zero_eq, toEssImage_map_hom, CategoryTheory.Limits.Cones.equivalenceOfReindexing_counitIso, partialRightAdjoint_obj, ChainComplex.quasiIsoAt₀_iff, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_base, HomologicalComplex.singleObjCyclesSelfIso_hom_singleObjOpcyclesSelfIso_hom, CategoryTheory.SmallObject.ε_app, CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_inv_app, TopologicalSpace.Opens.map_comp_obj', CategoryTheory.Presieve.map_ofArrows, SSet.Truncated.id_app, CategoryTheory.curryingIso_inv_toFunctor_obj_map_app, CategoryTheory.Under.instFaithfulObjPost, CategoryTheory.prodComonad_obj, mapCommMonFunctor_map_app, AlgebraicGeometry.StructureSheaf.const_mul_cancel, CategoryTheory.Monad.assoc, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd_assoc, CategoryTheory.Classifier.χ_pullback_obj_mk_truth_arrow, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_app, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_app, groupCohomology.cochainsMap_comp_assoc, CategoryTheory.Limits.ColimitPresentation.self_diag, CategoryTheory.Adjunction.map_restrictFullyFaithful_counit_app_assoc, CategoryTheory.Iso.inv_hom_id_app_app, CategoryTheory.Subobject.factorThru_arrow_assoc, monotone, CategoryTheory.endofunctorMonoidalCategory_tensorMap_app, obj.η_def, CategoryTheory.yonedaMonObj_obj_coe, map_eq_zero_iff, FGModuleCat.instFiniteCarrierLimitModuleCatCompForget₂LinearMapIdObjIsFG, homologySequence_epi_shift_map_mor₁_iff, CategoryTheory.Presheaf.app_localPreimage, LaxRightLinear.μᵣ_associativity_inv, CategoryTheory.Limits.limit.isoLimitCone_hom_π, CategoryTheory.Limits.LimitPresentation.ofIso_π, LeftExtension.postcompose₂_map_right_app, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.mk₀_f_comp_biprodAddEquiv_symm_biprodIsoProd_hom, CategoryTheory.GradedObject.singleObjApplyIso_inv_single_map_assoc, CategoryTheory.Pseudofunctor.DescentData.Hom.comm_assoc, ModuleCat.forget₂_obj, CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatIso_hom, CategoryTheory.Grothendieck.fiber_eqToHom, SSet.whiskerRight_app_apply, topToLocale_obj, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functor_obj, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.image_preimage_is_empty, CategoryTheory.Sieve.functorPullback_inter, IsDenseSubsite.mapPreimage_comp_map, CategoryTheory.δ_app, instIsRepresentableCompOppositeOpObjTypeYonedaObjRightAdjointObjIsDefined, CategoryTheory.Limits.pullbackConeOfRightIso_π_app_right, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_map_app_app, CategoryTheory.ComposableArrows.Exact.opcyclesIsoCycles_hom_fac_assoc, CategoryTheory.Presheaf.functorToRepresentables_obj, AlgebraicGeometry.HasAffineProperty.restrict, CategoryTheory.Limits.image.map_homMk'_ι, CategoryTheory.Join.mapIsoWhiskerRight_hom_app, CategoryTheory.ExponentiableMorphism.ev_coev, CategoryTheory.Preadditive.commGrpEquivalence_functor_obj_X, CategoryTheory.Under.map_obj_hom, CategoryTheory.CommaMorphism.w_assoc, Rep.indResAdjunction_counit_app_hom_hom, CategoryTheory.CommGrp.forget₂Grp_obj_X, mapAction_obj_ρ_apply, CategoryTheory.Idempotents.app_p_comp_assoc, CategoryTheory.Adjunction.counit_naturality, CompHausLike.LocallyConstantModule.functor_obj_val, CategoryTheory.GlueData.mapGlueData_U, final_const_of_isTerminal, CategoryTheory.Limits.Fork.ofι_π_app, CategoryTheory.Equivalence.congrLeft_functor, OplaxLeftLinear.δₗ_unitality_inv, Monoidal.whiskeringLeft_ε_app, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_iso_inv_app, CategoryTheory.ComposableArrows.δ₀Functor_obj_map, ContinuousMap.yonedaPresheaf_map, biproductComparison_π_assoc, CommRingCat.Under.tensorProdEqualizer_ι, CategoryTheory.Limits.pushoutComparison_map_desc, CategoryTheory.ULift.equivalence_counitIso_hom_app, CategoryTheory.StructuredArrow.instFaithfulObjCompPost, CategoryTheory.Ind.exists_nonempty_arrow_mk_iso_ind_lim, Monoidal.map_leftUnitor_inv_assoc, HomologicalComplex₂.totalFunctor_obj, op_commShiftIso_hom_app_assoc, CategoryTheory.WithInitial.mkCommaObject_hom_app, FullyFaithful.compYonedaCompWhiskeringLeftMaxRight_inv_app_app, CategoryTheory.CartesianClosed.curry_eq, SSet.rightUnitor_inv_app_apply, CategoryTheory.NatTrans.IsMonoidal.tensor, CategoryTheory.pullbackShiftFunctorZero'_hom_app, CochainComplex.HomComplex.Cochain.rightShift_leftShift, OplaxMonoidal.oplax_associativity, groupHomology.pOpcycles_comp_opcyclesIso_hom_apply, HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac, CategoryTheory.yoneda_obj_obj, PresheafOfModules.forgetToPresheafModuleCatObjMap_apply, CategoryTheory.Limits.pullback_factors_iff, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_inv_app, groupHomology.mapCycles₁_comp_i_apply, CategoryTheory.uliftYonedaEquiv_comp, CategoryTheory.CostructuredArrow.map_map_right, CategoryTheory.Subobject.arrow_mono, CategoryTheory.Subobject.isIso_top_arrow, SSet.stdSimplex.face_obj, Monoidal.whiskerRight_ε_η_assoc, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app_assoc, CategoryTheory.Limits.IsLimit.hom_lift, SheafOfModules.pushforwardCongr_hom_app_val_app, CategoryTheory.Over.leftUnitor_inv_left_snd, SSet.stdSimplex.nonDegenerateEquiv_apply_apply, CategoryTheory.CostructuredArrow.closedUnderLimitsOfShape_discrete_empty, CategoryTheory.Limits.coconePointwiseProduct_ι_app, CategoryTheory.ExactFunctor.whiskeringLeft_map_app, CategoryTheory.Monoidal.tensorObj_obj, CategoryTheory.μ_naturality, CategoryTheory.FinitaryExtensive.mono_inr_of_isColimit, CategoryTheory.SmallObject.SuccStruct.ofCoconeObjIso_hom_naturality_assoc, CategoryTheory.FreeGroupoid.map_map_homMk, sectionsEquivHom_naturality, SSet.modelCategoryQuillen.horn_ι_mem_J, TopCat.Presheaf.SheafCondition.pairwiseToOpensLeCover_obj, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_leftUnitor, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₃₁, CategoryTheory.evalEquiv_apply, groupHomology.mapCycles₂_comp, CategoryTheory.Comonad.left_counit, FinPartOrd.dualEquiv_counitIso, CategoryTheory.Limits.PullbackCone.mk_π_app_right, CategoryTheory.Limits.Cofork.op_π_app_zero, ModuleCat.restrictScalarsCongr_hom_app, AlgebraicGeometry.Scheme.Γevaluation_naturality_assoc, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.instIsIsoAppIncl, AlgebraicGeometry.Scheme.kerAdjunction_counit_app, CategoryTheory.Limits.DiagramOfCones.mkOfHasLimits_map_hom, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_of_epi₂, CategoryTheory.pullbackShiftFunctorZero_hom_app, CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_obj_right_as, AlgebraicGeometry.opensDiagramι_app, CategoryTheory.Presheaf.freeYoneda_map, mapSkeleton_obj_toSkeleton, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.inverseObj_comon_counit_app, shiftMap_comp'_assoc, CategoryTheory.Monoidal.FunctorCategory.tensorObj_map, CategoryTheory.ComposableArrows.fourδ₄Toδ₃_app_one, CategoryTheory.Monad.unit_naturality, TopologicalSpace.Opens.mapIso_inv_app, CategoryTheory.Arrow.w, CategoryTheory.StructuredArrow.homMk'_left, CategoryTheory.Limits.opSpan_hom_app, CategoryTheory.Limits.π_comp_colimitLeftOpIsoUnopLimit_inv_assoc, CategoryTheory.GrothendieckTopology.instIsIsoFunctorOppositeSheafSheafComposeNatTransPlusPlusAdjunction, CategoryTheory.MonoidalClosed.pre_comm_ihom_map, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃'_obj_map_app, AlgebraicGeometry.Scheme.IdealSheafData.coe_support_ofIdealTop, CategoryTheory.obj_zero_map_μ_app, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.fromExtendScalars_hom_apply, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionActionOfMonoidalFunctorToEndofunctorMopIso_inv_app_unmop_app, CategoryTheory.Iso.compInverseIso_inv_app, CategoryTheory.Adjunction.restrictFullyFaithful_homEquiv_apply, CategoryTheory.Grothendieck.eqToHom_eq, CategoryTheory.Limits.Cofork.IsColimit.π_desc_assoc, CategoryTheory.curryingIso_hom_toFunctor_obj_obj, SSet.stdSimplex.map_apply, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_snd', groupHomology.cyclesIso₀_inv_comp_cyclesMap_apply, CategoryTheory.Cat.opEquivalence_unitIso, CategoryTheory.Limits.piObjIso_inv_comp_π, rightDerivedZeroIsoSelf_hom_inv_id_app, CategoryTheory.Limits.ColimitPresentation.Total.Hom.w, CategoryTheory.Limits.coneOfConeCurry_π_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_snd_obj, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app_assoc, CategoryTheory.Limits.coconeEquivalenceOpConeOp_functor_obj, CategoryTheory.ActionCategory.coe_back, AlgebraicTopology.AlternatingFaceMapComplex.ε_app_f_zero, Monoidal.whiskeringLeft_μ_app, CategoryTheory.Limits.IsZero.obj, ContAction.resCongr_hom, CategoryTheory.Limits.limMap_π_assoc, CategoryTheory.IsHomLift.fac', CategoryTheory.Comma.equivProd_unitIso_hom_app_right, CategoryTheory.Under.instEssSurjObjPostOfFull, CategoryTheory.ShortComplex.SnakeInput.functorL₀_obj, CategoryTheory.MonoidalClosed.id_tensor_pre_app_comp_ev, AlgebraicGeometry.Scheme.component_nontrivial, CategoryTheory.DifferentialObject.shiftZero_inv_app_f, CategoryTheory.SmallObject.iterationObjRightIso_hom, AlgebraicGeometry.isCompl_range_inl_inr, CategoryTheory.Bimon.Bimon_ClassAux_counit, CategoryTheory.whiskering_linearYoneda, TopCat.Presheaf.presheafEquivOfIso_unitIso_hom_app_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_counitIso, CategoryTheory.CartesianClosed.homEquiv_symm_apply_eq, zero_obj, homologySequence_exact₂, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom, CategoryTheory.Equivalence.unitInv_naturality_assoc, CategoryTheory.TransfiniteCompositionOfShape.map_isoBot, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_right_as, LightCondensed.isoFinYonedaComponents_inv_comp, CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_π, CategoryTheory.Discrete.sumEquiv_unitIso_hom_app, mapTriangle_map_hom₁, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι, AlgebraicGeometry.Scheme.zeroLocus_iInf_of_nonempty, CategoryTheory.BraidedCategory.ofBifunctor.Forward.secondMap₁_app_app_app, CategoryTheory.LocalizerMorphism.LeftResolution.unop_w, CategoryTheory.SmallObject.objMap_id, CategoryTheory.MonoidalClosed.curry_pre_app, CategoryTheory.MonoOver.image_obj, CategoryTheory.Comma.preRight_map_right, TopologicalSpace.Opens.coe_overEquivalence_functor_obj, CategoryTheory.bijection_symm_apply_id, CategoryTheory.Monoidal.FunctorCategory.tensorHom_app, CategoryTheory.FunctorToTypes.rightAdj_map_app, CoalgCat.MonoidalCategory.inducingFunctorData_μIso, CategoryTheory.Enriched.Functor.associator_hom_apply, CategoryTheory.Comonad.Coalgebra.Hom.h, CategoryTheory.Limits.spanCompIso_app_right, AlgebraicGeometry.Scheme.AffineZariskiSite.generate_presieveOfSections_mem_grothendieckTopology, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_inv_π_π, CategoryTheory.Limits.coker_obj, AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, CategoryTheory.Triangulated.TStructure.isLE_shift, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app, rightDerivedNatTrans_app_assoc, SheafOfModules.pullbackObjFreeIso_hom_naturality_assoc, CategoryTheory.Monad.algebraFunctorOfMonadHomEq_inv_app_f, ModuleCat.FilteredColimits.M.mk_map, CategoryTheory.PreservesImage.hom_comp_map_image_ι, CategoryTheory.NatTrans.CommShiftCore.shift_app, CategoryTheory.sum.inverseAssociator_map_inl, CategoryTheory.Over.μ_pullback_left_fst_snd', toPseudoFunctor_map, CategoryTheory.Limits.PreservesPushout.inl_iso_inv_assoc, CategoryTheory.Limits.FormalCoproduct.Hom.fromIncl_f, SSet.ι₀_snd, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy₂'_homEquiv, relativelyRepresentable.map, CategoryTheory.NatTrans.whiskerLeft_app_tensor_app_assoc, AddMonCat.FilteredColimits.M.map_mk, AlgebraicGeometry.Scheme.basicOpen_pow, CategoryTheory.ProjectiveResolution.instIsIsoFromLeftDerivedZero'Self, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_left, HomologicalComplex₂.flipFunctor_obj, CategoryTheory.Pretriangulated.contractible_distinguished₂, whiskeringLeft₃_obj_obj_obj_obj_obj_obj_obj, CochainComplex.HomComplex.Cochain.leftUnshift_smul, PartOrdEmb.Limits.cocone_ι_app, CategoryTheory.Limits.DiagramOfCocones.mkOfHasColimits_obj, CategoryTheory.Limits.Types.limitCone_π_app, CategoryTheory.CatCommSq.vInv_iso_hom_app, CategoryTheory.Over.mapPullbackAdj_unit_app, ShiftSequence.induced_shiftIso_hom_app_obj, CategoryTheory.eqToHom_map_comp_assoc, CategoryTheory.sheafToPresheaf_δ, CategoryTheory.Limits.lim_ε_π_assoc, AlgebraicGeometry.Scheme.Opens.toSpecΓ_top, Rep.resIndAdjunction_homEquiv_symm_apply, SSet.Truncated.Edge.CompStruct.tensor_simplex_fst, Rep.coinvariantsFunctor_hom_ext_iff, isRepresentedBy_iff, Monoidal.map_associator_inv, CategoryTheory.Localization.homEquiv_comp, CategoryTheory.Sum.natIsoOfWhiskerLeftInlInr_eq, CategoryTheory.PreZeroHypercover.map_X, AlgebraicGeometry.Scheme.Hom.ker_apply, CategoryTheory.quotientPathsTo_obj, SSet.PtSimplex.MulStruct.δ_succ_castSucc_map, ranCompIsoOfPreserves_hom_app, CategoryTheory.lift_comp_preservesLimitIso_hom_assoc, FundamentalGroupoidFunctor.instIsIsoFanGrpdObjTopCatFundamentalGroupoidFunctorPiTopToPiCone, CategoryTheory.Limits.limitUnopIsoUnopColimit_inv_comp_π_assoc, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.hπ, CategoryTheory.Limits.PushoutCocone.condition_zero, CategoryTheory.preservesLimitIso_inv_π, CategoryTheory.Abelian.PreservesImage.iso_hom_ι, CategoryTheory.Subobject.factors_comp_arrow, CategoryTheory.ObjectProperty.ι_obj, TopCat.Sheaf.existsUnique_gluing, CochainComplex.instIsKInjectiveObjIntShiftFunctor, AlgebraicGeometry.Scheme.IdealSheafData.ideal_comap_of_isOpenImmersion, CategoryTheory.Subfunctor.Subpresheaf.mem_equalizer_iff, CategoryTheory.whiskeringRightCompEvaluation_inv_app, associator_inv_app, RightExtension.postcomp₁_obj_left_obj, CochainComplex.mappingConeCompTriangle_mor₃_naturality, CategoryTheory.ShortComplex.mapHomologyIso'_hom_naturality, CategoryTheory.Limits.whiskeringLimYonedaIsoCones_inv_app_app, CategoryTheory.whiskering_linearCoyoneda₂, CategoryTheory.Monad.MonadicityInternal.unitCofork_π, CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp, AlgebraicGeometry.ProjIsoSpecTopComponent.fromSpec_toSpec, homologySequenceδ_comp_assoc, CategoryTheory.LocalizerMorphism.homMap_apply, CategoryTheory.CostructuredArrow.mapNatIso_functor_obj_hom, CategoryTheory.typeEquiv_unitIso_inv_app, functorialityCompPrecompose_hom_app_hom, CategoryTheory.Limits.limit.π_comp_eqToHom_assoc, AlgebraicGeometry.AffineSpace.SpecIso_inv_appTop_coord, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_pt, CategoryTheory.WithTerminal.liftToTerminal_obj, CategoryTheory.Sieve.functorPullback_top, CategoryTheory.Over.mapId_inv_app_left, CategoryTheory.Comma.map_map_left, CategoryTheory.Limits.Cone.equiv_hom_fst, Action.diagonalSuccIsoTensorTrivial_inv_hom_apply, AlgebraicGeometry.AffineSpace.functor_obj_map, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app'_assoc, CategoryTheory.Limits.endFunctor_obj, CochainComplex.HomComplex.Cochain.shiftLinearMap_apply, CategoryTheory.PreGaloisCategory.lt_card_fiber_of_mono_of_notIso, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left_assoc, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id_app, SSet.StrictSegal.spineInjective, CategoryTheory.CostructuredArrow.w_prod_snd, CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_left, CategoryTheory.GrothendieckTopology.Cover.multicospanComp_inv_app, AlgebraicGeometry.germ_stalkClosedPointIso_hom_assoc, CategoryTheory.MorphismProperty.Over.pullbackComp_inv_app_left, CategoryTheory.Comma.mapRightIso_functor_obj_hom, CategoryTheory.shift_equiv_triangle, CategoryTheory.Limits.Cone.toStructuredArrowCone_π_app, CategoryTheory.CosimplicialObject.δ_comp_σ_succ_assoc, CategoryTheory.Limits.imageSubobjectIso_comp_image_map, TwoP.swapEquiv_unitIso_hom_app_hom_toFun, flipping_counitIso_hom_app_app_app, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_inv_app, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_app_comp_π, CategoryTheory.instMonoAppOfFunctor, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_hom_assoc, CategoryTheory.Pseudofunctor.mapComp'_hom_naturality_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_map_snd_app, CategoryTheory.Comma.toIdPUnitEquiv_unitIso_inv_app_right, CategoryTheory.SmallObject.SuccStruct.Iteration.congr_obj, Preorder.hasLimit_iff_hasGLB, CategoryTheory.ProjectiveResolution.of_def, CategoryTheory.Limits.MultispanIndex.multispan_obj_right, CategoryTheory.Pseudofunctor.mapComp'_naturality_2_assoc, CategoryTheory.Limits.kernelComparison_comp_ι_assoc, CategoryTheory.associator_inv, CategoryTheory.Comma.post_map_left, CategoryTheory.Sigma.desc_obj, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_inv_app_app, CategoryTheory.Limits.PreservesPullback.iso_hom_fst, CategoryTheory.Limits.Cones.whiskeringEquivalence_unitIso, LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition', CategoryTheory.ShortComplex.RightHomologyData.map_Q, SSet.degenerate_le_preimage, leftOpRightOpEquiv_functor_obj_obj, CategoryTheory.Limits.colimitCoyonedaHomIsoLimitUnop_π_apply, CommMonCat.hom_forget₂_map, CategoryTheory.shiftFunctorZero_hom_app_obj_of_induced, SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_inv_app, CategoryTheory.Pseudofunctor.ObjectProperty.map_map_hom, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_obj_left, CategoryTheory.Equivalence.map_projective_iff, HomotopicalAlgebra.CofibrantObject.exists_bifibrant_map, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_hom_app, corepresentableByUliftFunctorEquiv_apply_homEquiv, CategoryTheory.Ind.isSeparator_range_yoneda, CategoryTheory.CommaMorphism.w, CategoryTheory.Comma.toPUnitIdEquiv_unitIso_inv_app_left, homologySequence_mono_shift_map_mor₁_iff, CategoryTheory.Equivalence.congrRight_functor, SSet.Subcomplex.mem_nonDegenerate_iff, CondensedSet.topCatAdjunctionUnit_val_app_apply, CategoryTheory.Limits.Fork.hom_comp_ι_assoc, AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality, instFiniteObjOpenNormalSubgroupStabilizerHomSurjectiveAuxFunctor, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_right, Rep.coindMap'_hom, SimplexCategory.toCat.obj_eq_Fin, CategoryTheory.Cokleisli.Adjunction.toCokleisli_obj, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_naturality_app, CategoryTheory.ProjectiveResolution.π'_f_zero_assoc, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceFunctor_obj_fiber, CategoryTheory.Comma.colimitAuxiliaryCocone_pt, CategoryTheory.Subobject.factors_self, AlgebraicGeometry.instIsIsoSchemeMorphismRestrict, instIsEquivalenceLeftExtensionPostcomp₁OfIsIso, Profinite.instEpiAppDiscreteQuotientCarrierToTopTotallyDisconnectedSpaceπAsLimitCone, CategoryTheory.TransfiniteCompositionOfShape.fac, CategoryTheory.Limits.imageSubobject_zero_arrow, CategoryTheory.PreGaloisCategory.exists_lift_of_mono_of_isConnected, isIso_ranAdjunction_unit_app_iff, CategoryTheory.FunctorToTypes.rightAdj_map_app_app, map_sub, CategoryTheory.Localization.Construction.lift_map, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst, CategoryTheory.Join.opEquiv_inverse_obj_right_op, CategoryTheory.LeftExactFunctor.ofExact_map_hom, descColimitType_comp_ι, pointedToTwoPFst_obj_X, CategoryTheory.Join.mkFunctorLeft_hom_app, PreOneHypercoverDenseData.w, CategoryTheory.ProjectiveResolution.π_f_succ, curryingEquiv_apply_obj, OplaxLeftLinear.δₗ_associativity, CategoryTheory.GrothendieckTopology.uliftYonedaCompSheafToPresheaf_inv_app_app, CategoryTheory.CostructuredArrow.CreatesConnected.natTransInCostructuredArrow_app, CategoryTheory.Subfunctor.Subpresheaf.bot_obj, CategoryTheory.Limits.limitRightOpIsoOpColimit_hom_comp_ι, groupHomology.H0π_comp_map_assoc, CategoryTheory.Limits.multispanIndexCoend_snd, CategoryTheory.CatCommSq.iso_hom_naturality, CategoryTheory.Sieve.sieveOfUliftSubfunctor_apply, CategoryTheory.yonedaEquiv_yoneda_map, CategoryTheory.Limits.Cocone.toStructuredArrow_obj, CategoryTheory.Limits.limit.π_comp_eqToHom, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_inv_app_unmop, CategoryTheory.Cat.exp_map, CategoryTheory.Limits.FormalCoproduct.eval_obj_map, CategoryTheory.Equivalence.changeFunctor_counitIso_hom_app, sum'_obj_inl, AddMonCat.equivalence_inverse_obj_coe, AlgebraicGeometry.Scheme.evaluation_eq_zero_iff_notMem_basicOpen, CategoryTheory.Subfunctor.equivalenceMonoOver_inverse_obj, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_pt, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_inverse_obj, CategoryTheory.Localization.Monoidal.map_hexagon_reverse_assoc, CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt_assoc, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_snd_obj, CommMonCat.coyonedaType_obj_obj_coe, LeftExtension.postcompose₂_obj_hom_app, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerLeftIso_hom_app, CategoryTheory.Limits.instPreservesWellOrderContinuousOfShapeFunctorObjEvaluationOfHasIterationOfShape, chosenProd_obj, whiskeringRight₂_obj_obj_obj_obj, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s₀_comp_δ₁_assoc, HomologicalComplex₂.D₁_totalShift₂XIso_hom_assoc, AlgebraicGeometry.Scheme.stalkMap_germ_assoc, CategoryTheory.Pseudofunctor.CoGrothendieck.Hom.congr, CategoryTheory.GlueData.diagramIso_inv_app_left, CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_inv_eq_germ_apply, TopCat.Presheaf.SheafConditionEqualizerProducts.piInters.hom_ext_iff, CategoryTheory.Iso.map_inv_hom_id_app, skyscraperPresheafFunctor_obj, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app_assoc, CategoryTheory.WithInitial.liftFromUnder_obj_obj, SSet.mem_skeleton_obj_iff_of_nonDegenerate, OplaxRightLinear.δᵣ_associativity, LeftLinear.δₗ_comp_μₗ, CategoryTheory.Iso.hom_inv_id_app, CategoryTheory.Subobject.functor_obj, CochainComplex.HomComplex.Cocycle.toSingleMk_coe, CategoryTheory.Iso.app_hom, CategoryTheory.Limits.HasLimit.isoOfEquivalence_hom_π, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_app, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_inv_hom, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_counitIso, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_map_right_right, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π, CategoryTheory.Limits.limitConstTerminal_inv_π, HomologicalComplex₂.shiftFunctor₁XXIso_refl, CategoryTheory.NatIso.naturality_1_assoc, CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_hom, AlgebraicGeometry.instIsOpenImmersionInrScheme, AlgebraicGeometry.SheafedSpace.ofRestrict_hom_c_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_invApp, MulEquiv.toSingleObjEquiv_functor_obj, CategoryTheory.unit_conjugateEquiv_symm, CategoryTheory.CategoryOfElements.comp_val, CategoryTheory.Localization.Preadditive.comp_add'_assoc, CategoryTheory.Localization.Monoidal.μ_natural_left, CategoryTheory.IsPushout.of_isColimit_binaryCofan_of_isInitial, CategoryTheory.preservesLimitNatIso_inv_app, PresheafOfModules.sheafification_map, CategoryTheory.ReflQuiv.forget_obj, CategoryTheory.PreGaloisCategory.evaluation_aut_bijective_of_isGalois, CategoryTheory.Limits.opCompYonedaSectionsEquiv_apply_app, CategoryTheory.Grothendieck.grothendieckTypeToCat_inverse_obj_base, TopCat.Presheaf.whiskerIsoMapGenerateCocone_inv_hom, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app_assoc, CategoryTheory.Pretriangulated.preadditiveYoneda_homologySequenceδ_apply, CategoryTheory.Limits.WalkingParallelPair.inclusionWalkingReflexivePair_obj, CategoryTheory.Grpd.freeForgetAdjunction_homEquiv_symm_apply, AlgebraicTopology.DoldKan.Γ₂_obj_X_map, CategoryTheory.Pretriangulated.Triangle.functorHomMk_app_hom₃, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_obj_right, CategoryTheory.toPresheafToSheafCompComposeAndSheafify_app, CategoryTheory.Iso.map_hom_inv_id, CategoryTheory.Limits.MultispanIndex.ofSigmaCoforkFunctor_obj, CategoryTheory.PreservesImage.inv_comp_image_ι_map, SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁_inv_f_f, RightLinear.δᵣ_comp_μᵣ, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_map_hom, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_naturality_assoc, CategoryTheory.Limits.BinaryBicone.toBiconeFunctor_obj_pt, CategoryTheory.MorphismProperty.instHasPullbackHomDiscretePUnitOfHasPullbacksAlong, CategoryTheory.ChosenPullbacksAlong.iso_pullback_obj, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp_assoc, CategoryTheory.ShortComplex.LeftHomologyData.map_K, CategoryTheory.Limits.BinaryFan.rightUnitor_inv, ι_colimitIsoColimitGrothendieck_hom_assoc, CategoryTheory.forgetEnrichmentOppositeEquivalence_unitIso, AlgebraicGeometry.Scheme.Hom.appIso_inv_app, HomotopicalAlgebra.BifibrantObject.toHoCat_obj_surjective, AlgebraicGeometry.Scheme.Hom.liftCoborder_preimage, InfiniteGalois.proj_adjoin_singleton_val, TopCat.Presheaf.stalk_mono_of_mono, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app_assoc, CategoryTheory.Subfunctor.Subpresheaf.IsGeneratedBy.mem, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id, CategoryTheory.RelCat.graphFunctor_obj, SSet.Truncated.Edge.map_associator_hom, mapMonFunctor_obj, whiskeringLeft₃_obj_obj_map_app_app_app_app, CategoryTheory.subobject_simple_iff_isAtom, CategoryTheory.Triangulated.TStructure.instIsGEObj₃ObjTriangleTriangleLTGE, CategoryTheory.Limits.kernelSubobjectIsoComp_inv_arrow, TopCat.Presheaf.map_germ_eq_Γgerm_assoc, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom, CategoryTheory.unit_conjugateEquiv, HomologicalComplex.instQuasiIsoAtOppositeMapSymmOpFunctorOp, CategoryTheory.MonoidalSingleObj.endMonoidalStarFunctor_obj, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_ι_inv_assoc, TopologicalSpace.Opens.op_map_id_obj, map_commSq, CategoryTheory.NatIso.trans_app, pointedToPartialFun_obj, groupHomology.π_comp_H0Iso_hom_apply, AlgebraicGeometry.Scheme.Hom.opensRange_pullbackFst, CategoryTheory.Limits.PullbackCone.mk_π_app_one, CategoryTheory.isSeparator_iff_faithful_coyoneda_obj, CategoryTheory.Bicategory.precomp_obj, DerivedCategory.left_fac_of_isStrictlyLE_of_isStrictlyGE, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct_assoc, CategoryTheory.GradedObject.mapBifunctorObjSingle₀ObjIso_inv, SSet.degenerate_zero, CategoryTheory.SimplicialObject.δ_comp_σ_of_gt'_assoc, mapGrpNatIso_hom_app_hom_hom, AlgebraicTopology.AlternatingCofaceMapComplex.d_squared, CategoryTheory.SmallObject.ιObj_naturality, CategoryTheory.Limits.BinaryCofan.isColimit_iff_isIso_inl, CategoryTheory.Under.postEquiv_counitIso, CochainComplex.shiftFunctor_map_f', CategoryTheory.Grothendieck.grothendieckTypeToCatFunctor_map_coe, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone_ι_app, whiskeringLeft₃Map_app_app, CategoryTheory.Sieve.uliftNatTransOfLe_comm, CategoryTheory.Bimon.instIsComonHomMonHomEquivMonComonUnitIsoAppX, CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_inv, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionActionOfMonoidalFunctorToEndofunctorIso_hom_app_app, SSet.horn₂₀.sq, CategoryTheory.Subobject.map_bot, AlgebraicGeometry.Scheme.zeroLocus_radical, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_left, CategoryTheory.TransfiniteCompositionOfShape.map_isColimit, CategoryTheory.CosimplicialObject.Augmented.drop_obj, CategoryTheory.uliftYoneda_obj_map, LeibnizAdjunction.adj_counit_app_right, TopCat.Sheaf.interUnionPullbackConeLift_right, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_inv_app_app, LightProfinite.Extend.functor_map, groupCohomology.H1InfRes_X₃, CategoryTheory.IsVanKampenColimit.precompose_isIso, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_ι_assoc, AlgebraicGeometry.Scheme.Cover.sigmaFunctor_obj, CategoryTheory.regularTopology.mapToEqualizer_eq_comp, CategoryTheory.MonoidalClosed.curry_eq, CategoryTheory.Limits.CompleteLattice.limitCone_isLimit_lift, CategoryTheory.Endofunctor.Coalgebra.Terminal.left_inv, CategoryTheory.instIsIsoAppFromLeftDerivedZeroOfProjective, CategoryTheory.Presieve.functorPushforward_overForget, CategoryTheory.ComposableArrows.whiskerLeftFunctor_obj_obj, CategoryTheory.Limits.PushoutCocone.ι_app_left, CategoryTheory.GrothendieckTopology.uliftYonedaCompSheafToPresheaf_hom_app_app, mapTriangleRotateIso_hom_app_hom₂, HomologicalComplex.extend_single_d, CategoryTheory.Equivalence.counitInv_app_comp_functor_map_η_inverse_assoc, CategoryTheory.yoneda_preservesLimitsOfShape, AlgebraicGeometry.affineOpensRestrict_apply_coe_coe, CategoryTheory.Over.conePost_map_hom, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedAction_obj_map, CategoryTheory.Under.postComp_hom_app_right, CategoryTheory.ComposableArrows.opEquivalence_functor_map_app, CategoryTheory.shiftFunctorAdd'_add_zero_inv_app, CategoryTheory.FunctorToTypes.binaryProductIso_hom_comp_snd, CategoryTheory.Equivalence.sheafCongrPrecoherent_inverse_obj_val_obj, MatrixModCat.toModuleCat_obj_carrier, mapGrpFunctor_map_app, CategoryTheory.Preadditive.epi_iff_surjective, mapCommMonCompIso_inv_app_hom_hom, CategoryTheory.GrothendieckTopology.map_yonedaEquiv', Monoidal.μ_of_cartesianMonoidalCategory, CategoryTheory.GrothendieckTopology.W_inverseImage_whiskeringLeft, CategoryTheory.Limits.colimit_obj_ext_iff, Rep.instEpiModuleCatAppActionCoinvariantsMk, CategoryTheory.Classifier.SubobjectRepresentableBy.isPullback, CondensedSet.instUCompactlyGeneratedSpaceCarrierObjTopCatCondensedSetToTopCat, CategoryTheory.Limits.CompleteLattice.finite_colimit_eq_finset_univ_sup, CategoryTheory.FunctorToTypes.shrink_map, CategoryTheory.TwoSquare.instFinalCostructuredArrowObjCostructuredArrowRightwardsOfGuitartExact, map_isZero, AlgebraicGeometry.Scheme.AffineZariskiSite.presieveOfSections_surjective, CategoryTheory.Comonad.cofree_map_f, CategoryTheory.SingleObj.functor_obj, HomologicalComplex.singleObjHomologySelfIso_inv_homologyι_assoc, comp_mapMon_mul, CategoryTheory.FreeMonoidalCategory.tensorFunc_map_app, CategoryTheory.ProjectiveResolution.Hom.hom'_comp_π', CochainComplex.HomComplex.Cochain.rightShift_zero, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceInverse_obj_fiber, CategoryTheory.WithTerminal.mkCommaObject_left_map, CategoryTheory.ShortComplex.quasiIso_map_of_preservesLeftHomology, CategoryTheory.ShortComplex.SnakeInput.functorL₂_obj, rightDerivedZeroIsoSelf_hom_inv_id_app_assoc, CategoryTheory.Comma.preRight_obj_right, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.functor_obj, CategoryTheory.Sieve.natTransOfLe_comm, CompHausLike.instT2SpaceCarrierObjTopCatCompHausLikeToTop, CategoryTheory.Localization.homEquiv_symm_apply, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app, TopologicalSpace.Opens.mapMapIso_unitIso, preservesFiniteColimits_iff_forall_exact_map_and_epi, TopologicalSpace.OpenNhds.map_id_obj_unop, CategoryTheory.Limits.Sigma.ι_isoColimit_hom_assoc, Homotopy.map_nullHomotopicMap, curry₃_obj_obj_obj_map, SSet.stdSimplex.mem_face_iff, CategoryTheory.SimplicialObject.Augmented.rightOp_right_map, AlgebraicGeometry.StructureSheaf.const_one, SSet.Truncated.rightExtensionInclusion_right_as, mapComposableArrowsObjMk₂Iso_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.Presieve.ofArrows_category, CategoryTheory.Limits.PreservesFiniteColimits.underPost, CategoryTheory.LocalizerMorphism.commShift_iso_hom_app_assoc, CategoryTheory.WithInitial.coconeEquiv_functor_map_hom, CategoryTheory.Subobject.factorThru_add_sub_factorThru_right, AlgebraicGeometry.Scheme.Opens.ι_appIso, groupHomology.chainsFunctor_obj, flip₂₃Functor_obj_obj_obj_map, CategoryTheory.Cat.HasLimits.limit_π_homDiagram_eqToHom, CategoryTheory.Monoidal.rightUnitor_inv_app, CategoryTheory.TwoSquare.hId_app, PresheafOfModules.surjective_of_epi, CategoryTheory.Subgroupoid.hom.faithful, CategoryTheory.FinitaryPreExtensive.hasPullbacks_of_is_coproduct, RightExtension.coneAtWhiskerRightIso_inv_hom, PreservesEpimorphisms.preserves, ProfiniteGrp.limit_mul_val, CategoryTheory.CosimplicialObject.δ_comp_σ_succ'_assoc, map_isPullback, CategoryTheory.CosimplicialObject.δ_comp_δ_self'_assoc, liftOfIsRightKanExtension_fac_app_assoc, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_inv_hom₁, Monoidal.map_associator_inv', AlgebraicGeometry.IsAffineOpen.isoSpec_inv_toSpecΓ, FGModuleCat.instFiniteCarrierPiObjModuleCatOfFinite, CategoryTheory.unitCompPartialBijective_natural, HomotopyCategory.instFullFunctorHomologicalComplexObjWhiskeringLeftQuotient, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_right, AlgebraicGeometry.StructureSheaf.globalSectionsIso_hom, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInlIso_hom_app_app, AlgebraicGeometry.disjoint_opensRange_sigmaι, Monoidal.inv_η, CategoryTheory.WithTerminal.ofCommaMorphism_app, CategoryTheory.Adjunction.isIso_unit_app_iff_mem_essImage, CochainComplex.singleFunctor_obj_d, CategoryTheory.Over.lift_obj, CategoryTheory.uliftYoneda_obj_obj, CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence_hom, CategoryTheory.typeEquiv_counitIso_inv_app_val_app, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_inv_app_left, CategoryTheory.OverPresheafAux.counitAuxAux_inv, CategoryTheory.CosimplicialObject.δ_comp_σ_of_le, CategoryTheory.Pretriangulated.Triangle.isZero₂_iff_isIso₃, SimplexCategoryGenRel.toSimplexCategory_obj_mk, pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, LeftExtension.postcomp₁_obj_hom_app, AlgebraicGeometry.instLocallyQuasiFiniteMorphismRestrict, CategoryTheory.ShortComplex.LeftHomologyMapData.quasiIso_map_iff, groupCohomology.functor_obj, groupCohomology.cocyclesMap_comp, CategoryTheory.CosimplicialObject.augmentedCechConerve_obj, mapCommMonIdIso_hom_app_hom_hom, CategoryTheory.Subfunctor.preimage_obj, TopologicalSpace.Opens.overEquivalence_unitIso_hom_app_left, CategoryTheory.MorphismProperty.LeftFraction.map_hom_ofInv_id_assoc, SSet.stdSimplex.coe_edge_down_toOrderHom, CategoryTheory.Preadditive.mono_iff_injective, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_left, CategoryTheory.Iso.inv_hom_id_app_app_app, CategoryTheory.ShortComplex.ShortExact.singleTriangle_obj₂, CategoryTheory.Limits.Multicofork.map_pt, CategoryTheory.Limits.Types.colimit_eq, CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod_fac₂, CategoryTheory.Localization.SmallHom.equiv_mk, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app', AlgebraicGeometry.IsAffineOpen.toSpecΓ_isoSpec_inv, CategoryTheory.ExactFunctor.whiskeringLeft_obj_obj_obj, CategoryTheory.WithTerminal.liftToTerminalUnique_inv_app, CategoryTheory.ComposableArrows.opEquivalence_inverse_obj, flippingEquiv_symm_apply_map_app, AlgebraicGeometry.Scheme.Hom.appIso_inv_naturality, CategoryTheory.Limits.Fork.ofCone_π, CategoryTheory.MonoOver.map_obj_arrow, CategoryTheory.SimplicialObject.δ_comp_δ'_assoc, CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_left, CategoryTheory.ProjectiveResolution.pOpcycles_comp_fromLeftDerivedZero', AlgebraicGeometry.Scheme.IdealSheafData.map_ideal, CategoryTheory.Equivalence.cancel_unitInv_right, AlgebraicTopology.DoldKan.N₂Γ₂_inv_app_f_f, CategoryTheory.Limits.CompleteLattice.finiteLimitCone_isLimit_lift, CategoryTheory.WithTerminal.mapComp_inv_app, SSet.stdSimplex.faceSingletonIso_one_hom_comp_ι_eq_δ, CategoryTheory.Equivalence.invFunIdAssoc_hom_app, CategoryTheory.Comonad.ForgetCreatesColimits'.γ_app, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_X, CategoryTheory.MonoidalClosed.curry_natural_left, CategoryTheory.CategoryOfElements.fromStructuredArrow_obj, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map, CategoryTheory.SimplicialObject.δ_comp_σ_self', LaxMonoidal.right_unitality_inv, CategoryTheory.Limits.π_comp_colimitOpIsoOpLimit_inv_assoc, CategoryTheory.ShortComplex.homologyMap_mapNatTrans, π_tensor_id_preserves_coequalizer_inv_desc, LightCondensed.forget_map_val_app, CategoryTheory.Limits.SingleObj.Types.limitEquivFixedPoints_symm_apply, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.functor_map_hom_app, CategoryTheory.Limits.PushoutCocone.ofCocone_pt, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinset_obj_map, CategoryTheory.Limits.DiagramOfCocones.comp, AlgebraicGeometry.Scheme.basicOpen_add_le, Action.forget_δ, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_right_left_as, CochainComplex.quasiIso_shift_iff, AlgebraicGeometry.Scheme.Hom.comp_app_assoc, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.functorObjObj_comon_counit, CategoryTheory.SmallObject.SuccStruct.iterationFunctor_map_succ_assoc, AlgebraicGeometry.Scheme.comp_app, Action.FunctorCategoryEquivalence.inverse_obj_ρ_apply, CategoryTheory.Square.toArrowArrowFunctor_obj_right_right, CategoryTheory.Limits.pullbackConeEquivBinaryFan_inverse_obj, CategoryTheory.Limits.Cones.postcomposeEquivalence_unitIso, CategoryTheory.shrinkYonedaEquiv_naturality, pointwiseLeftKanExtensionUnit_app, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_unit_app, CategoryTheory.ComonadHom.app_δ_assoc, CategoryTheory.instIsSplitEpiMap, TopologicalSpace.Opens.isOpenEmbedding, AlgebraicGeometry.Scheme.zeroLocus_map, CategoryTheory.Endofunctor.Coalgebra.Terminal.right_inv, AlgebraicGeometry.Scheme.Hom.finite_app, 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, LightCondensed.isoLocallyConstantOfIsColimit_inv, fullyFaithfulCancelRight_hom_app, CategoryTheory.ExactFunctor.whiskeringLeft_obj_map, CochainComplex.HomComplex.Cochain.rightUnshift_v, CategoryTheory.Limits.pullbackConeEquivBinaryFan_functor_obj, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerRightIso_inv_app, AlgebraicGeometry.Scheme.AffineZariskiSite.coequifibered_iff_forall_isLocalizationAway, AlgebraicGeometry.instGeometricallyReducedMorphismRestrict, HomotopyCategory.composableArrowsFunctor_obj, whiskeringLeft₃_obj_map_app_app_app_app_app, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_zeroLocus, HomologicalComplex.singleObjCyclesSelfIso_inv_homologyπ_assoc, AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInfty, CategoryTheory.ComposableArrows.arrowEquiv_symm_apply, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_germ_apply, ContAction.res_obj_obj, CategoryTheory.Center.ofBraided_δ_f, AlgebraicGeometry.Scheme.evaluation_naturality, PreservesEffectiveEpis.preserves, CategoryTheory.Presheaf.imageSieve_apply, Rep.ihom_obj_ρ_apply, CategoryTheory.Iso.compInverseIso_hom_app, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_hom_app_app, CategoryTheory.Limits.KernelFork.IsLimit.isIso_ι, Alexandrov.principals_obj, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_inv_app_fst_app, CategoryTheory.yonedaEquiv_naturality', CategoryTheory.Grothendieck.pre_map_fiber, CategoryTheory.Idempotents.karoubiFunctorCategoryEmbedding_obj, CategoryTheory.isCardinalPresentable_iff_of_isEquivalence, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_hom_app_snd_app, instIsRepresentableObjOppositeTypeYoneda, AlgebraicGeometry.ΓSpec.left_triangle, CategoryTheory.CartesianMonoidalCategory.inv_prodComparison_map_fst_assoc, CategoryTheory.ProjectiveResolution.Hom.hom_f_zero_comp_π_f_zero_assoc, CategoryTheory.ActionCategory.π_obj, CategoryTheory.Subfunctor.Subpresheaf.le_def, mapCommGrpNatIso_inv_app_hom_hom_hom, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app_assoc, CategoryTheory.ReflQuiv.forgetToQuiv_obj, CategoryTheory.Limits.parallelFamily_obj_one, CategoryTheory.sheafBotEquivalence_inverse_obj_val, CategoryTheory.ShortComplex.cyclesFunctor_obj, AlgebraicGeometry.Scheme.Hom.ideal_ker_le, CategoryTheory.Enriched.Functor.whiskerRight_app_apply, AlgebraicGeometry.AffineSpace.comp_homOfVector, CategoryTheory.Limits.colimitIsoSwapCompColim_inv_app, CondensedMod.hom_naturality_apply, CategoryTheory.CartesianMonoidalCategory.prodComparison_comp, CategoryTheory.Localization.full_whiskeringLeft, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_left_as, AlgebraicGeometry.smooth_iff, CategoryTheory.Over.map_obj_hom, CategoryTheory.Limits.Cones.postcomposeEquivalence_counitIso, CategoryTheory.Localization.SmallShiftedHom.equiv_mk, CategoryTheory.isDetector_iff_reflectsIsomorphisms_coyoneda_obj, 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, sum'_obj_inr, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_hom_app_fst_app, SSet.ι₁_snd_assoc, SimplicialObject.Splitting.ofIso_isColimit', PresheafOfModules.toSheaf_map_sheafificationHomEquiv_symm, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₁₃, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₂, LaxLeftLinear.μₗ_unitality_assoc, postcomposeWhiskerLeftMapCone_inv_hom, CategoryTheory.CosimplicialObject.Augmented.toArrow_map_right, SSet.horn.edge_coe, CategoryTheory.Limits.Cofork.π_precompose, OplaxMonoidal.instIsIsoη, PushoutObjObj.isPushout, mapZeroObject_inv, LightCondSet.instEpiTopCatAppCounitTopCatAdjunction, AlgebraicGeometry.Scheme.Hom.appIso_hom', CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_one, cocones_obj, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero, CategoryTheory.Limits.ReflexiveCofork.condition, IsEventuallyConstantTo.coneπApp_eq_id, AlgebraicGeometry.Scheme.zeroLocus_inf, CategoryTheory.Over.associator_hom_left_snd_fst, CategoryTheory.SmallObject.coconeOfLE_pt, CategoryTheory.CostructuredArrow.toOver_map_left, CategoryTheory.Limits.Cones.functorialityEquivalence_unitIso, CategoryTheory.Limits.PreservesLimitPair.iso_inv_snd, CategoryTheory.WithTerminal.opEquiv_functor_obj, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₃, CategoryTheory.Limits.compCoyonedaSectionsEquiv_symm_apply_coe, OplaxMonoidal.whiskeringRight_δ_app, CategoryTheory.Enriched.Functor.functorHom_whiskerLeft_natTransEquiv_symm_app, flippingEquiv_symm_apply_obj_obj, constCompWhiskeringLeftIso_hom_app_app, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply', CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app_assoc, CategoryTheory.Limits.colimit.hom_ext_iff, CategoryTheory.NatTrans.mapElements_map_coe, CategoryTheory.Limits.Types.limitConeIsLimit_lift_coe, CategoryTheory.Adjunction.corepresentableBy_homEquiv, AlgebraicGeometry.Scheme.IdealSheafData.ofIdeals_mono, AlgebraicGeometry.Scheme.instIsOpenImmersionToSpecΓOfIsQuasiAffine, CategoryTheory.Over.postComp_inv_app_left, CategoryTheory.CosimplicialObject.Augmented.const_map_right, CategoryTheory.TwoSquare.whiskerBottom_app, HopfAlgCat.forget₂_bialgebra_obj, AlgebraicGeometry.Scheme.homOfLE_appTop, CochainComplex.shiftFunctorAdd'_inv_app_f', CategoryTheory.Limits.coneOfAdj_pt, CategoryTheory.ShiftedHom.comp_zero, map_inv, Initial.conesEquiv_unitIso, SemilatInfCat.coe_forget_to_partOrd, instTotallyDisconnectedSpaceCarrierToTopTrueObjProfiniteCompHausProfiniteToCompHaus, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counit_app_assoc, ContinuousMap.yonedaPresheaf_obj, CategoryTheory.NatTrans.app_zero, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_app, CategoryTheory.NatTrans.prod'_app_fst, CategoryTheory.Equalizer.Presieve.sheaf_condition, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_cofanPtIsoSelf_inv_assoc, CategoryTheory.cosimplicialSimplicialEquiv_functor_map_app, curryingFlipEquiv_apply_obj, CategoryTheory.Sieve.functorPushforward_inverse, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_right, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_functor_obj_d_f, AlgebraicGeometry.germ_injective_of_isIntegral, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_fst, CategoryTheory.Equivalence.congrFullSubcategory_unitIso, ShiftSequence.induced.shiftIso_hom_app_obj, AlgebraicGeometry.Scheme.isoSpec_inv_naturality_assoc, CategoryTheory.Equivalence.inverseFunctorObjIso_inv, AlgebraicGeometry.StructureSheaf.smul_const, CategoryTheory.Abelian.Ext.hom_comp_singleFunctor_map_shift, TopCat.Presheaf.pushforward_obj_obj, CategoryTheory.Monad.mu_naturality, coreCompInclusionIso_hom_app, CategoryTheory.lift_comp_preservesLimitIso_hom, CategoryTheory.RanIsSheafOfIsCocontinuous.fac', AlgebraicTopology.DoldKan.N₂Γ₂ToKaroubiIso_hom_app, CategoryTheory.AsSmall.up_obj_down, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self, CategoryTheory.Over.toOverSectionsAdj_unit_app, CategoryTheory.Bimon.BimonObjAux_counit, CategoryTheory.Equivalence.changeInverse_counitIso_inv_app, Monoidal.coreMonoidalTransport_μIso_inv, diag_μ, CategoryTheory.SingleFunctors.postcompIsoOfIso_hom_hom_app, CategoryTheory.NatTrans.isIso_iff_isIso_app, toPreimages_map, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_0, commShiftIso_hom_naturality_assoc, CategoryTheory.Limits.IndObjectPresentation.yoneda_isColimit_desc, groupCohomology.resNatTrans_app, TopCat.isOpenEmbedding_of_pullback, PresheafOfModules.injective_of_mono, CategoryTheory.Comma.mapRightEq_inv_app_left, CategoryTheory.Iso.inv_hom_id_app_app_assoc, FullyFaithful.mulEquivEnd_symm_apply, CategoryTheory.Limits.KernelFork.condition, CategoryTheory.flippingIso_inv_toFunctor_map_app_app, SSet.OneTruncation₂.nerveEquiv_symm_apply_map, AlgebraicGeometry.IsOpenImmersion.opensEquiv_apply_coe, AlgebraicGeometry.isClosedImmersion_iff_isAffineHom, CategoryTheory.shiftFunctorAdd'_zero_add_hom_app, comp_mapCommMon_mul, CategoryTheory.whiskering_preadditiveYoneda, CategoryTheory.Comonad.Coalgebra.coassoc, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app, lanCompColimIso_inv_app, CategoryTheory.Limits.opCospan_hom_app, mapTriangleCommShiftIso_hom_app_hom₃, AlgebraicGeometry.PresheafedSpace.restrictTopIso_hom, ModuleCat.free_ε_one, Profinite.exists_isClopen_of_cofiltered, CategoryTheory.Adjunction.comp_counit_app, CategoryTheory.ComposableArrows.mk₁_obj, CategoryTheory.isPullback_initial_to_of_cofan_isVanKampen, mapArrow_map_left, PresheafOfModules.isoMk_inv_app, CategoryTheory.Limits.Bicone.ofColimitCocone_ι, uncurry_obj_obj, AlgebraicGeometry.PresheafedSpace.sheafIsoOfIso_inv, CategoryTheory.Cat.Hom.comp_map, mapBicone_π, CategoryTheory.Limits.FormalCoproduct.incl_obj_obj, flip₁₃Functor_obj_obj_obj_obj, CategoryTheory.SingleFunctors.shiftIso_add_inv_app, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app'_assoc, unopOpIso_hom_app, CategoryTheory.uliftYonedaEquiv_uliftYoneda_map, CategoryTheory.Limits.instIsIsoEqualizerComparison, ShiftSequence.induced_shiftIso_hom_app_obj_assoc, CategoryTheory.Localization.SmallShiftedHom.equiv_shift', AlgebraicGeometry.AffineSpace.hom_ext_iff, CategoryTheory.functorProdToProdFunctor_obj, mapAction_ε_hom, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂'_map_app_app, CategoryTheory.MorphismProperty.over_iso_iff, CategoryTheory.PresheafOfGroups.OneCocycle.ev_symm, CategoryTheory.ShortComplex.mapRightHomologyIso_hom_naturality, CategoryTheory.yoneda_obj_map, CategoryTheory.Limits.WidePullbackShape.wideCospan_obj, CategoryTheory.Subobject.isoOfEq_hom, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.functorToInterchangeIso_hom_app_app, SSet.stdSimplex.isoNerve_hom_app_apply, CategoryTheory.CosimplicialObject.δ_comp_δ_self, CategoryTheory.Cat.opFunctorInvolutive_hom_app_toFunctor_map, OplaxMonoidal.δ_natural_left, mapCommMonFunctor_obj, CategoryTheory.ObjectProperty.isColocal_adj_counit_app, AlgebraicGeometry.ΓSpec.unop_locallyRingedSpaceAdjunction_counit_app', CategoryTheory.CartesianClosed.uncurry_natural_right, SSet.Subcomplex.mem_degenerate_iff, AlgebraicGeometry.LocallyRingedSpace.stalkMap_germ_assoc, CategoryTheory.Limits.PreservesPullback.iso_inv_snd_assoc, CategoryTheory.Mat_.isoBiproductEmbedding_hom, CategoryTheory.Monad.mu_naturality_assoc, mapBiproduct_inv, CategoryTheory.Pseudofunctor.DescentData.ofObj_obj, prod'_obj, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_inv_app_hom, ι_colimitIsoOfIsLeftKanExtension_hom, HomotopyCategory.quotient_obj_surjective, ModuleCat.MonModuleEquivalenceAlgebra.functor_obj_carrier, CategoryTheory.SmallObject.ιFunctorObj_eq, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_functor_map_f, commShiftIso_comp_inv_app, CategoryTheory.MonoidalClosed.curry_pre_app_assoc, TwoP.swapEquiv_counitIso_inv_app_hom_toFun, CategoryTheory.Monoidal.FunctorCategory.whiskerRight_app, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidalObj_obj, AlgebraicGeometry.Scheme.Hom.preimage_basicOpen, CategoryTheory.StructuredArrow.mkPostcomp_comp, CategoryTheory.Adjunction.mkOfHomEquiv_unit_app, mapAction_obj_V, CategoryTheory.Limits.FormalCoproduct.cechFunctor_obj, leftExtensionEquivalenceOfIso₁_inverse_map_right, CategoryTheory.CostructuredArrow.instFaithfulCompObjPost, Monoidal.instIsIsoμ, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocNatIso_inv_app_app_app, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_zero, Monoidal.toUnit_ε, equiv_functor_obj, topCatToSheafCompHausLike_obj, CategoryTheory.Grothendieck.forget_obj, Monoidal.whiskerRight_app_fst, Condensed.epi_iff_locallySurjective_on_compHaus, CategoryTheory.CartesianMonoidalCategory.inv_prodComparison_map_snd_assoc, groupCohomology.mapShortComplexH2_zero, AlgebraicTopology.DoldKan.QInfty_f_naturality_assoc, CategoryTheory.ComposableArrows.whiskerLeft_map, mapComon_obj_comon_comul, CategoryTheory.Cat.opFunctorInvolutive_hom_app_toFunctor_obj, CategoryTheory.MonoidalClosed.comp_eq, CategoryTheory.underToAlgebra_obj_A, CategoryTheory.Limits.spanCompIso_inv_app_right, AlgebraicTopology.DoldKan.MorphComponents.postComp_a, CategoryTheory.GlueData.diagramIso_inv_app_right, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_app_assoc, CategoryTheory.Limits.limit.conePointUniqueUpToIso_hom_comp_assoc, AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app, CategoryTheory.CategoryOfElements.map_obj_fst, CategoryTheory.Limits.Cofan.mk_ι_app, CategoryTheory.Adjunction.instMonoCoeEquivHomObjHomEquivOfReflectsMonomorphisms, imageToKernel_arrow, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_symm_app, CategoryTheory.WithTerminal.inclLiftToTerminal_inv_app, SSet.stdSimplex.faceSingletonComplIso_hom_ι, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app, CategoryTheory.Equivalence.sheafCongr.inverse_obj_val_obj, CategoryTheory.Limits.HasLimit.isoOfNatIso_inv_π, CategoryTheory.Adjunction.leftAdjointCompIso_inv_app, CategoryTheory.Sum.homInduction_left, CochainComplex.mappingCone.map_inr, CategoryTheory.Sheaf.adjunction_counit_app_val, CategoryTheory.CatCommSq.vComp_iso_hom_app, CategoryTheory.Limits.Cones.functoriality_obj_pt, mapCochainComplexShiftIso_inv_app_f, DerivedCategory.HomologySequence.epi_homologyMap_mor₁_iff, CategoryTheory.Under.mapCongr_hom_app, CategoryTheory.LocalizerMorphism.commShift_iso_inv_app_assoc, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_ε, CategoryTheory.LocalizerMorphism.equiv_smallHomMap', map_shiftFunctorCompIsoId_inv_app_assoc, Rep.resIndAdjunction_homEquiv_apply, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id_val_app, CochainComplex.shiftFunctorAdd'_inv_app_f, CategoryTheory.coyonedaEquiv_naturality, CategoryTheory.Limits.BinaryCofan.isColimit_iff_isIso_inr, CategoryTheory.SimplicialObject.δ_comp_δ', AlgebraicGeometry.Scheme.isoSpec_Spec_hom, CategoryTheory.CategoryOfElements.fromCostructuredArrow_obj_snd, CategoryTheory.CartesianMonoidalCategory.map_toUnit_comp_terminalComparison, leftDerivedNatTrans_app_assoc, SSet.ι₁_app_fst, LightCondensed.isLocallySurjective_iff_locallySurjective_on_lightProfinite, SSet.skeleton_succ, CategoryTheory.GrothendieckTopology.yonedaEquiv_comp, HomologicalComplex₂.D₁_totalShift₁XIso_hom_assoc, CategoryTheory.preservesColimitNatIso_hom_app, AlgebraicGeometry.Scheme.basicOpen_res_eq, CategoryTheory.oppositeShiftFunctorZero_inv_app, CategoryTheory.MonoidalCategory.externalProductCompDiagIso_inv_app_app, LeftExtension.postcompose₂_obj_right_obj, prod'CompFst_inv_app, CategoryTheory.Limits.PushoutCocone.mk_ι_app, CategoryTheory.coyonedaEquiv_apply, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom_assoc, whiskeringLeft₂_obj_map_app_app_app, AlgebraicGeometry.IsZariskiLocalAtTarget.coprodMap, SSet.Subcomplex.iSup_ofSimplex_nonDegenerate_eq_top, CategoryTheory.Over.post_comp, mapMonFunctor_map_app_hom, AlgebraicGeometry.IsFinite.instDescScheme, mapTriangleCommShiftIso_inv_app_hom₃, IsEventuallyConstantTo.isIso_map, PresheafOfModules.pushforward_obj_map_apply, CategoryTheory.InjectiveResolution.ι_f_zero_comp_complex_d, AlgebraicGeometry.StructureSheaf.isLocalizedModule_toPushforwardStalkAlgHom, CategoryTheory.CostructuredArrow.mapIso_functor_map_right, CategoryTheory.Comonad.comparisonForget_inv_app, CategoryTheory.Equivalence.changeInverse_unitIso_inv_app, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_hom, AlgebraicGeometry.Scheme.Hom.isAffineOpen_iff_of_isOpenImmersion, CochainComplex.HomComplex.CohomologyClass.equiv_toSmallShiftedHom_mk, CategoryTheory.endofunctorMonoidalCategory_tensorObj_map, CategoryTheory.Limits.compCoyonedaSectionsEquiv_apply_app, CategoryTheory.ShortComplex.quasiIso_map_iff_of_preservesRightHomology, SSet.ι₁_snd, isoSum_hom_app_inl, CochainComplex.truncateAugment_inv_f, CategoryTheory.Limits.Fork.IsLimit.lift_ι, CompHaus.toProfinite_obj', biprodComparison_fst_assoc, CategoryTheory.Over.equivalenceOfIsTerminal_inverse_obj, AlgebraicGeometry.Scheme.Hom.app_invApp', CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_hom_app, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_right, CategoryTheory.Equivalence.rightOp_inverse_obj, TopCat.GlueData.MkCore.t_inv, AlgebraicGeometry.Scheme.Hom.stalkFunctor_toImage_injective, CategoryTheory.Limits.instIsIsoKernelComparison, groupHomology.d₁₀_comp_coinvariantsMk, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompPointIso_inv_app, AlgebraicGeometry.LocallyRingedSpace.Hom.ext_iff, CategoryTheory.WithTerminal.equivComma_functor_obj_hom_app, CategoryTheory.Pretriangulated.op_distinguished, isZero_iff, rightOpLeftOpIso_inv_app, AlgebraicGeometry.isNoetherian_iff_of_finite_iSup_eq_top, mapMon_obj_mon_one, SSet.Truncated.StrictSegal.spineInjective, AlgebraicGeometry.Scheme.image_basicOpen, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso_inv_app_f, CategoryTheory.Enriched.FunctorCategory.enrichedComp_π_assoc, CategoryTheory.Join.inclLeft_obj, IsStronglyCartesian.universal_property', CategoryTheory.Over.toOverSectionsAdj_counit_app, CategoryTheory.Subobject.inf_isPullback, CategoryTheory.Limits.Bicone.toBinaryBiconeFunctor_obj_snd, CategoryTheory.DinatTrans.compNatTrans_app, map.instIsComon_Hom, AlgebraicGeometry.Scheme.Hom.inl_normalizationCoprodIso_hom_fromNormalization_assoc, HomologicalComplex.homologyOp_hom_naturality_assoc, pointedToBipointedCompBipointedToPointedSnd_hom_app_toFun, mapMonIdIso_hom_app_hom, MonCat.adjoinOne_obj_coe, MulEquiv.toSingleObjEquiv_inverse_obj, AlgebraicGeometry.tilde.isIso_toOpen_top, relativelyRepresentable.diag_iff, comp_homologySequenceδ, CategoryTheory.regularTopology.isLocallySurjective_iff, PartialOrder.mem_range_nerve_σ_iff, CategoryTheory.StructuredArrow.toCostructuredArrow_map, CategoryTheory.Limits.ImageMap.factor_map, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_snd, CategoryTheory.Pseudofunctor.DescentData.hom_comp_assoc, mapExactFunctor_smul, CategoryTheory.Mono.cofanInr_of_binaryCoproductDisjoint, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app, CategoryTheory.Join.mapPairComp_inv_app_right, groupHomology.mapCycles₂_comp_apply, DerivedCategory.HomologySequence.mono_homologyMap_mor₂_iff, TopCat.Presheaf.SubmonoidPresheaf.map, CategoryTheory.Abelian.extFunctor_obj, CategoryTheory.Limits.PushoutCocone.ι_app_right, CategoryTheory.CartesianClosed.uncurry_eq, map_shiftFunctorComm_assoc, CategoryTheory.WithInitial.equivComma_inverse_map_app, coconeOfIsLeftKanExtension_ι, CategoryTheory.Limits.coneRightOpOfCocone_π, CategoryTheory.Equalizer.Presieve.Arrows.FirstObj.ext_iff, SimplicialObject.Splitting.πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty, CategoryTheory.Pseudofunctor.Grothendieck.map_obj_fiber, CategoryTheory.Triangulated.TStructure.triangleLTGE_map_hom₃, CategoryTheory.GradedObject.map_obj, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_hom_app_coe, CategoryTheory.Comma.left_hom_inv_right, CochainComplex.HomComplex.Cochain.fromSingleMk_zero, ShiftSequence.induced_isoShiftZero_hom_app_obj_assoc, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompYoneda, CategoryTheory.Limits.comp_lim_obj_ext_iff, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp_assoc, CategoryTheory.forgetAdjToOver_unit_app, OplaxMonoidal.right_unitality_hom, CategoryTheory.Adjunction.adjToComonadIso_hom_toNatTrans_app, CategoryTheory.Limits.LimitPresentation.self_diag, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, CategoryTheory.Cat.FreeRefl.quotientFunctor_map_id, CategoryTheory.Comon.monoidal_whiskerRight_hom, Monoidal.map_associator_inv'_assoc, IsCoverDense.Types.appHom_restrict, CategoryTheory.Limits.DiagramOfCones.conePoints_map, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.e_hom_app, CategoryTheory.OverPresheafAux.counitBackward_counitForward, CochainComplex.mappingCone.inl_v_triangle_mor₃_f_assoc, AlgebraicTopology.DoldKan.map_PInfty_f, CategoryTheory.Arrow.isIso_hom_iff_isIso_of_isIso, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_hom_eq_germ_apply, AddCommGrpCat.Colimits.quotToQuotUlift_ι, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_map_hom_hom, CategoryTheory.Comma.unopFunctor_obj, CategoryTheory.EnrichedFunctor.forget_obj, AlgebraicGeometry.HasRingHomProperty.appTop, Rep.linearization_η_hom_apply, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd, CategoryTheory.Limits.colimitHomIsoLimitYoneda_hom_comp_π_assoc, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_inv_left_app, AlgebraicGeometry.LocallyRingedSpace.basicOpen_zero, functorHom_ext_iff, CategoryTheory.Presheaf.w, CategoryTheory.Subobject.mk_arrow, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_app_assoc, CategoryTheory.Over.iteratedSliceEquivOverMapIso_inv_app_left_left, HomologicalComplex.eval_obj, SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁_hom_app_f_f, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_map, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_functor_map, map_shiftFunctorCompIsoId_hom_app_assoc, CategoryTheory.ShiftMkCore.assoc_inv_app_assoc, ModuleCat.smulNatTrans_apply_app, FGModuleCat.ihom_obj, CategoryTheory.Limits.PullbackCone.π_app_left, TopCat.Sheaf.existsUnique_gluing', CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.NatTrans.sum_app_inl, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₁, CategoryTheory.Over.iteratedSliceEquivOverMapIso_hom_app_left_left, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.functor_obj, CategoryTheory.whiskeringRight_preservesColimitsOfShape, CategoryTheory.Comma.mapLeftComp_inv_app_right, TopCat.isClosed_iff_of_isColimit, CategoryTheory.Retract.map_r, CategoryTheory.CategoryOfElements.ext_iff, CategoryTheory.WithTerminal.isLimitEquiv_symm_apply_lift, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functor_map_app_hom, CategoryTheory.CostructuredArrow.map₂_map_right, CategoryTheory.Comma.coconeOfPreserves_ι_app_right, CategoryTheory.endofunctorMonoidalCategory_rightUnitor_inv_app, CategoryTheory.Comma.toIdPUnitEquiv_unitIso_hom_app_right, CommRingCat.commMon_forget₂_obj_coe, Action.res_obj_V, CategoryTheory.Limits.Wedge.condition, CategoryTheory.Bicategory.leftUnitorNatIso_hom_app, CategoryTheory.Sheaf.ΓObjEquivSections_naturality_symm, isCommMonObj_obj, CategoryTheory.Limits.HasCoequalizersOfHasPushoutsAndBinaryCoproducts.pushoutInl_eq_pushout_inr, map_mono, AlgebraicGeometry.HasAffineProperty.coprodDesc_affineAnd, HomologicalComplex₂.instHasTotalIntObjUpCompShiftFunctor₂ShiftFunctor₁, Braided.braided, CategoryTheory.Limits.CatCospanTransform.rightUnitor_hom_base_app, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_obj_fiber, AddMonCat.FilteredColimits.cocone_naturality, Rep.quotientToInvariantsFunctor_map_hom, CochainComplex.mappingCone.inr_triangleδ_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_map_app_app, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_left, CategoryTheory.Limits.isIso_colimit_cocone_parallelPair_of_eq, AlgebraicGeometry.IsAffineOpen.image_of_isOpenImmersion, CategoryTheory.Grp.forget₂Mon_obj_mul, CategoryTheory.BraidedCategory.ofBifunctor.Forward.firstMap₂_app_app_app, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counitIso_hom_app, groupHomology.chainsMap_id_comp, CategoryTheory.StructuredArrow.toUnder_map_right, CategoryTheory.Iso.unop_hom_inv_id_app, CochainComplex.HomComplex.Cochain.leftShift_zero, CategoryTheory.Coyoneda.naturality, CompHausLike.LocallyConstant.locallyConstantIsoContinuousMap_hom, CategoryTheory.GrothendieckTopology.sheafification_obj, CategoryTheory.ShortComplex.HomologyMapData.map_right, CategoryTheory.PreZeroHypercover.map_f, Condensed.isoLocallyConstantOfIsColimit_inv, CategoryTheory.Mono.cofanInl_of_binaryCoproductDisjoint, CategoryTheory.regularTopology.parallelPair_pullback_initial, AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot, CategoryTheory.WithTerminal.liftFromOver_obj_obj, CategoryTheory.monoidalOpOp_μ, CategoryTheory.MorphismProperty.RightFraction.map_ofInv_hom_id_assoc, CategoryTheory.Join.mapPairLeft_inv_app, CategoryTheory.Sheaf.isLocallyInjective_iff_injective, CategoryTheory.cosimplicialSimplicialEquiv_counitIso_inv_app_app, CategoryTheory.Codiscrete.natIsoFunctor_inv_app, CategoryTheory.Limits.imageSubobject_arrow_comp_apply, commShiftIso_hom_naturality, CategoryTheory.Sieve.functorPushforward_monotone, CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_obj_left, mapBinaryBicone_pt, CategoryTheory.Adjunction.Quadruple.epi_leftTriple_leftToRight_app_iff_mono_rightTriple_rightToLeft_app, CategoryTheory.Comonad.adj_counit, CommShift.comp_commShiftIso_hom_app, AlgebraicGeometry.IsIntegral.component_integral, CategoryTheory.CosimplicialObject.Augmented.toArrow_map_left, CategoryTheory.Over.isRightAdjoint_post, CategoryTheory.Pseudofunctor.isStackFor_iff, AlgebraicGeometry.morphismRestrict_comp, PresheafOfModules.forgetToPresheafModuleCatObjObj_coe, Action.forget_obj, CategoryTheory.Adjunction.homAddEquiv_add, CategoryTheory.Subobject.isoOfEqMk_inv, CategoryTheory.TwoSquare.equivalenceJ_inverse, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatTrans_comp, LightCondSet.instSequentialSpaceCarrierObjTopCatLightCondSetToTopCat, CategoryTheory.Mod_.forget_obj, Bicategory.Opposite.opFunctor_obj, precomposeWhiskerLeftMapCocone_hom_hom, CategoryTheory.ComposableArrows.opEquivalence_unitIso_hom_app, CategoryTheory.Equivalence.congrLeftFunctor_obj, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.firstMap₂_app_app_app, CategoryTheory.ComposableArrows.mapFunctorArrows_app, CategoryTheory.ObjectProperty.ι_δ, mapHomotopy_hom, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_zero, CategoryTheory.ProjectiveResolution.Hom.hom'_comp_π'_assoc, MonObj.mopEquiv_inverse_obj_X, CategoryTheory.StructuredArrow.IsUniversal.hom_desc, CategoryTheory.bifunctorComp₁₂_obj, HomologicalComplex.singleObjOpcyclesSelfIso_inv_naturality, AlgebraicGeometry.StructureSheaf.const_zero, CategoryTheory.TwoSquare.hComp_app, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_left_right_as, initial_const_of_isInitial, CategoryTheory.Comma.mapRightIso_inverse_obj_right, mapExtAddHom_apply, Rep.quotientToCoinvariantsFunctor_map_hom, CategoryTheory.toSkeleton_fromSkeleton_obj, CategoryTheory.Subfunctor.equivalenceMonoOver_functor_obj, CategoryTheory.Pretriangulated.mem_distTriang_op_iff, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right_assoc, AlgebraicGeometry.IsProper.instMorphismRestrict, CategoryTheory.Subfunctor.min_obj, CategoryTheory.Limits.colimit.w_apply, SemiNormedGrp.completion.map_normNoninc, CategoryTheory.NatTrans.whiskerRight_app_tensor_app, mapComposableArrowsObjMk₁Iso_hom_app, CategoryTheory.Limits.Multifork.app_left_eq_ι, CategoryTheory.Limits.Cocone.fromStructuredArrow_obj_pt, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_left_app, CategoryTheory.η_naturality, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_app_app_germToPullbackStalk_assoc, AlgebraicGeometry.Scheme.isPullback_toSpecΓ_toSpecΓ, CategoryTheory.MonoidalClosed.curry'_comp, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetObj_map, CategoryTheory.Limits.BinaryBicones.functoriality_faithful, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerRight, HomologicalComplex.cyclesOpIso_inv_naturality, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverse_map_hom_app, AlgebraicGeometry.IsZariskiLocalAtTarget.iff_of_iSup_eq_top, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_map_bijective, CategoryTheory.yonedaGrp_naturality_assoc, CategoryTheory.Abelian.LeftResolution.karoubi_F, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_hom_app_app_hom_hom, AlgebraicGeometry.Scheme.instSubsingletonCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensBot, CategoryTheory.Pretriangulated.contractibleTriangleFunctor_obj, CategoryTheory.Limits.CategoricalPullback.Hom.w_assoc, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_hom_eq_germ_apply, CategoryTheory.Sheaf.ΓRes_map_assoc, isoCopyObj_inv_app, instIsCardinalAccessibleObjConst, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_snd_assoc, mapComposableArrows_obj_map, AlgebraicTopology.DoldKan.N₂Γ₂_compatible_with_N₁Γ₀, prod'_δ_fst, AlgebraicGeometry.Scheme.ΓSpecIso_naturality, CategoryTheory.Grp.δ_def, CategoryTheory.CostructuredArrow.pre_obj_right, SSet.whiskerLeft_app_apply, prod'_μ_snd, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon_obj, CategoryTheory.Bimon.ofMonComon_toMonComon_obj_counit, CategoryTheory.Limits.coconeOfConeRightOp_ι, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorEquivalence_unitIso, lightDiagramToProfinite_obj, relativelyRepresentable.isPullback, CategoryTheory.Limits.Fork.op_π, CategoryTheory.PresheafOfGroups.OneCochain.mul_ev, CategoryTheory.Limits.pointwiseProduct_map, CategoryTheory.Limits.piObjIso_hom_comp_π_assoc, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_fst_assoc, AlgebraicGeometry.Scheme.restrictFunctorΓ_hom_app, TopologicalSpace.Opens.set_range_inclusion', CategoryTheory.Pseudofunctor.bijective_toDescentData_map_iff, CategoryTheory.Limits.inv_prodComparison_map_fst, CategoryTheory.Limits.limit.conePointUniqueUpToIso_inv_comp_assoc, uncurryObjFlip_inv_app, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_inv_app_hom, CategoryTheory.Groupoid.CategoryTheory.Functor.mapVertexGroup_apply, Elements.initialOfCorepresentableBy_snd, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_hom_app_app, CategoryTheory.PreGaloisCategory.continuousSMul_aut_fiber, HomologicalComplex.shortComplexFunctor'_obj_X₂, CategoryTheory.CatCommSq.iso_inv_naturality_assoc, colimitTypePrecomp_ιColimitType, CategoryTheory.Limits.CatCospanTransform.leftUnitor_inv_right_app, CategoryTheory.Under.liftCone_π_app, ModuleCat.ExtendRestrictScalarsAdj.homEquiv_symm_apply, CategoryTheory.ShiftedHom.comp_neg, CategoryTheory.Square.fromArrowArrowFunctor_obj_X₁, CategoryTheory.Limits.Cocone.ofCofork_ι, CategoryTheory.TwoSquare.isIso_lanBaseChange_app_iff, HomologicalComplex.opcyclesOpIso_hom_naturality, CategoryTheory.TwoSquare.instIsIsoFunctorLanBaseChangeOfGuitartExact, CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_hom_assoc, CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_left, CategoryTheory.Limits.kernelSubobject_arrow_comp_apply, CategoryTheory.isoCartesianComon_hom_hom, ProfiniteAddGrp.limit_add_val, CategoryTheory.Square.map_X₁, CategoryTheory.Over.pullback_map_left, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.functorObjObj_X, sheafPushforwardContinuous_obj_val_map, AlgebraicGeometry.instIsIsoSchemeAppUnitOppositeCommRingCatAdjunctionOfIsAffine, CategoryTheory.tensoringLeft_linear, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id, CategoryTheory.SmallObject.instIsIsoRightAppArrowMapToTypeOrdFunctorIterationFunctor, groupHomology.mapShortComplexH1_id_comp, MonCat.uliftFunctor_obj_coe, CategoryTheory.Pairwise.cocone_ι_app, TopCat.Presheaf.stalkSpecializes_stalkFunctor_map_assoc, TopCat.Sheaf.comp_app, CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_inv_assoc, 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, smoothSheafCommRing.ι_forgetStalk_inv_apply, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_left, CategoryTheory.PreOneHypercover.multicospanIndex_left, CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod_fac₁, PresheafOfModules.unitHomEquiv_apply_coe, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.F_map, 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.sum.associator_obj_inl_inl, CategoryTheory.Join.pseudofunctorRight_mapId_hom_toNatTrans_app, CategoryTheory.Limits.FormalCoproduct.cochainComplexFunctor_obj_d, CategoryTheory.Equivalence.symmEquivInverse_obj_functor, Rep.coindResAdjunction_homEquiv_apply, CochainComplex.mappingCone.inr_f_triangle_mor₃_f, CategoryTheory.Limits.SingleObj.colimitTypeRelEquivOrbitRelQuotient_apply, CategoryTheory.Limits.WidePullbackShape.equivalenceOfEquiv_functor_obj_some, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_map_fiber, CochainComplex.HomComplex.Cocycle.fromSingleMk_coe, pointedToTwoPSnd_obj_X, CategoryTheory.Limits.widePushoutShapeOp_obj, AlgebraicGeometry.SheafedSpace.Γ_map, ModuleCat.FreeMonoidal.εIso_inv_freeMk, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_hom_π, RightLinear.inv_μᵣ, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_pt, CategoryTheory.Limits.colimCompFlipIsoWhiskerColim_hom_app_app, AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id, mapHomologicalComplexIdIso_inv_app_f, CategoryTheory.Discrete.sumEquiv_counitIso_hom_app, CategoryTheory.Limits.DiagramOfCocones.mkOfHasColimits_map_hom, CategoryTheory.StrictPseudofunctor.toFunctor_obj, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_fst, CategoryTheory.Comma.mapRightIso_functor_map_right, leftKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.Sieve.functorInclusion_app, CategoryTheory.sum.inverseAssociator_obj_inr_inr, CategoryTheory.Pretriangulated.shiftFunctorZero_op_hom_app, CategoryTheory.Subobject.isoOfMkEq_inv, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_app_apply, DerivedCategory.isLE_Q_obj_iff, SSet.comp_app, AlgebraicGeometry.Scheme.Modules.pushforwardComp_hom_app_app, CategoryTheory.Equivalence.cancel_counitInv_right_assoc, CategoryTheory.CommMon.mkIso_inv_hom_hom, Rep.Tor_map, CategoryTheory.Mon.limitCone_π_app_hom, CategoryTheory.Comma.limitAuxiliaryCone_π_app, CategoryTheory.OverPresheafAux.yonedaCollectionPresheaf_obj, Rep.ofModuleMonoidAlgebra_obj_ρ, CategoryTheory.Subobject.underlyingIso_arrow, CategoryTheory.StructuredArrow.isEquivalence_post, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι_assoc, CategoryTheory.Limits.coequalizerComparison_map_desc, CategoryTheory.SimplicialObject.δ_comp_σ_succ', CategoryTheory.Pseudofunctor.presheafHom_map, CategoryTheory.Limits.limit.post_π_assoc, AlgebraicTopology.AlternatingFaceMapComplex.obj_d_eq, CategoryTheory.FreeMonoidalCategory.inclusion_map, CategoryTheory.MorphismProperty.costructuredArrow_iso_iff, CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj_obj_X, PresheafOfModules.freeObj_obj, TwoP.swapEquiv_functor_obj_X, CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_map_left, postcompose₃_map_app_app_app_app, CategoryTheory.Sheaf.ΓObjEquivHom_naturality_symm, AlgebraicGeometry.Scheme.Hom.inl_normalizationCoprodIso_hom_fromNormalization, AlgebraicGeometry.germ_stalkClosedPointIso_hom, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_iso_hom_app, CategoryTheory.WithInitial.equivComma_functor_map_right_app, CategoryTheory.Join.opEquiv_inverse_map_inclLeft_op, TopCat.Presheaf.isLocallySurjective_iff, CategoryTheory.frobeniusMorphism_iso_of_preserves_binary_products, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply, SSet.Augmented.stdSimplex_obj_right, CategoryTheory.Grothendieck.toTransport_fiber, CategoryTheory.DifferentialObject.shiftFunctorAdd_hom_app_f, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_hom, CategoryTheory.Over.postEquiv_counitIso, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_ι_app_right, CategoryTheory.Limits.multispanIndexCoend_left, AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv, CategoryTheory.ι_colimitCompWhiskeringRightIsoColimitComp_hom, IsEventuallyConstantFrom.isoMap_inv_hom_id, AlgebraicGeometry.IsFinite.instHasAffinePropertyAndIsAffineFiniteCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTopHomAppTop, AlgebraicTopology.normalizedMooreComplex_objD, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_hom_app_hom_left, CategoryTheory.Subobject.ofLE_comp_ofLE_assoc, ranObjObjIsoLimit_inv_π_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_hom_app_app, mapBicone_pt, CategoryTheory.OplaxFunctor.mapComp_assoc_right_app_assoc, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π_assoc, precomposeWhiskerLeftMapCocone_inv_hom, CategoryTheory.Subobject.instMonoOfLEMk, SheafOfModules.pushforwardCongr_inv_app_val_app, CategoryTheory.Cat.HasLimits.id_def, PullbackObjObj.ofHasPullback_π, CategoryTheory.ComposableArrows.mkOfObjOfMapSucc_obj, CategoryTheory.Over.sections_obj, HomologicalComplex.instHasHomologyOppositeObjSymmOpFunctorOp, CategoryTheory.Limits.instIsIsoProdComparison, CategoryTheory.Abelian.Ext.homAddEquiv_apply, FullyFaithful.whiskeringRight_preimage_app, CategoryTheory.Grp.mkIso'_hom_hom_hom, SheafOfModules.freeFunctor_obj, Rep.resIndAdjunction_counit_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_map_right, ContAction.resComp_hom, RightExtension.precomp_obj_right, CategoryTheory.preservesLimits_preadditiveYoneda_obj, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_assoc, comp_mapCommGrp_mul, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_inv_π_assoc, SSet.StrictSegal.spineToSimplex_spine, SSet.Subcomplex.prod_obj, mapCoconePrecomposeEquivalenceFunctor_hom_hom, SimplicialObject.Split.cofan_inj_naturality_symm_assoc, CochainComplex.shiftFunctorZero'_hom_app_f, CategoryTheory.InjectiveResolution.self_cocomplex, CategoryTheory.whiskeringLeft_preservesLimits, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatIso_hom, IsCoverDense.Types.appIso_inv, CategoryTheory.MorphismProperty.Comma.ext_iff, TwoP.swapEquiv_functor_obj_toTwoPointing_toProd, HomologicalComplex₂.flipEquivalenceUnitIso_inv_app_f_f, CategoryTheory.CosimplicialObject.Truncated.whiskering_obj_map_app, CategoryTheory.ProjectiveResolution.lift_commutes_zero, SimplicialObject.Splitting.ofIso_ι, HomotopicalAlgebra.FibrantObject.instIsFibrantObjι, CategoryTheory.Comma.toIdPUnitEquiv_inverse_obj_left_as, PresheafOfModules.Sheafify.smul_add, AlgebraicGeometry.opensDiagram_obj, CategoryTheory.isCodetector_iff_reflectsIsomorphisms_yoneda_obj, DerivedCategory.triangleOfSES_obj₁, CategoryTheory.MonadHom.app_η_assoc, PushoutObjObj.ι_iso_of_iso_right_hom, 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.Equivalence.sheafCongr.unitIso_hom_app_val_app, CategoryTheory.monoidalOpOp_η, CategoryTheory.Comon.monoidal_associator_hom_hom, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.isoAux_hom_app, CategoryTheory.Subfunctor.map, Monoidal.tensorObjComp_inv_app, CategoryTheory.MonoidalCategory.DayFunctor.equiv_functor_obj, SSet.Truncated.Edge.map_whiskerLeft, CategoryTheory.Adjunction.functorialityCounit_app_hom, CategoryTheory.Iso.map_hom_inv_id_app, op_commShiftIso_inv_app_assoc, FinBoolAlg.hasForgetToFinPartOrd_forget₂_obj_carrier, OplaxMonoidal.ofBifunctor.topMapᵣ_app, StalkSkyscraperPresheafAdjunctionAuxs.unit_app, Profinite.Extend.functor_obj, ModuleCat.RestrictionCoextensionAdj.unit'_app, CategoryTheory.CostructuredArrow.toStructuredArrow'_map, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₂, CategoryTheory.ShortComplex.mapRightHomologyIso_inv_naturality_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_id, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_hom_app_snd_app, CategoryTheory.Abelian.LeftResolution.instEpiKaroubiAppπObjToKaroubi, CategoryTheory.prod.prodFunctorToFunctorProdAssociator_inv_app_app, mapGrpCompIso_hom_app_hom_hom, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_map_mkHom_homMk_id, CategoryTheory.Localization.SmallShiftedHom.equiv_chgUniv, AddCommGrpCat.μ_forget_apply, map_shiftFunctorCompIsoId_hom_app, CategoryTheory.additive_coyonedaObj', CategoryTheory.CategoryOfElements.map_obj_snd, LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom_assoc, CategoryTheory.sum.inverseAssociator_obj_inl, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocNatIso_inv_app_app_app, CategoryTheory.Subfunctor.range_eq_ofSection', SimplicialObject.opFunctor_obj_δ, mapTriangleInvRotateIso_inv_app_hom₂, CategoryTheory.Pretriangulated.Triangle.functorHomMk_app_hom₁, FullyFaithful.homNatIso'_hom_app_down, CategoryTheory.SimplicialObject.Augmented.const_map_right, CategoryTheory.Limits.sigmaConst_obj_map, Bipointed.swap_obj_toProd, leftExtensionEquivalenceOfIso₁_inverse_obj_right, HomotopyCategory.instFaithfulFunctorHomologicalComplexObjWhiskeringLeftQuotient, CategoryTheory.Abelian.coim_obj, CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence_inv, CategoryTheory.Over.star_obj_left, PreOneHypercoverDenseData.multicospanMap_app, Initial.extendCone_map_hom, mapArrow_map_right, CategoryTheory.Limits.Bicones.functoriality_full, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_obj, CommRingCat.forgetToRingCat_obj, CommRingCat.Colimits.cocone_naturality_components, CategoryTheory.SimplicialObject.σ_comp_σ, CategoryTheory.Comonad.comparisonForget_hom_app, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_obj_X₁, SheafOfModules.conjugateEquiv_pullbackComp_inv, CategoryTheory.NatTrans.CommShiftCore.shift_app_assoc, AlgebraicGeometry.Spec.sheafedSpaceMap_hom_c_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_inv_app_snd_app, AlgCat.free_obj, CategoryTheory.typeEquiv_functor_obj_val_map, TopCat.Presheaf.Pushforward.comp_inv_app, CategoryTheory.Sieve.functorPushforward_comp, CategoryTheory.Discrete.functor_obj_eq_as, CategoryTheory.WithTerminal.liftFromOverComp_hom_app, AlgebraicGeometry.morphismRestrict_app', AlgebraicGeometry.SheafedSpace.restrictTopIso_inv, CategoryTheory.regularTopology.isSheaf_yoneda_obj, coe_mapAddHom, mapIso_trans, CategoryTheory.ShiftedHom.comp_smul, CategoryTheory.equivToOverUnit_counitIso, whiskeringLeft₃Obj_obj, LaxMonoidal.tensorHom_ε_comp_μ_assoc, CategoryTheory.Limits.colimit.map_post, CategoryTheory.Join.homInduction_left, corepresentableByUliftFunctorEquiv_symm_apply_homEquiv, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_of, CategoryTheory.MorphismProperty.overObj_iff, AlgebraicGeometry.Scheme.evaluation_naturality_apply, homologySequence_exact₃, IsFreeGroupoid.SpanningTree.functorOfMonoidHom_obj, AlgebraicGeometry.instIsOpenImmersionMapScheme, instIsSplitEpiBiprodComparison, AlgebraicGeometry.Spec.toSheafedSpace_obj, RepresentableBy.equivUliftYonedaIso_symm_apply_homEquiv, CategoryTheory.Idempotents.functorExtension₂_obj_obj_X, CategoryTheory.Limits.BinaryFan.π_app_right, CategoryTheory.shiftFunctorCompIsoId_add'_hom_app, ModuleCat.free_η_freeMk, AlgebraicGeometry.sigmaι_eq_iff, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_comp, CategoryTheory.ProjectiveResolution.leftDerived_app_eq, CategoryTheory.MonadHom.app_μ_assoc, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_apply, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_iso_hom_app, AlgebraicGeometry.opensCone_π_app, CategoryTheory.Over.tensorHom_left, CategoryTheory.CostructuredArrow.w, AlgebraicGeometry.Scheme.toSpecΓ_appTop, CategoryTheory.Limits.colimitFlipIsoCompColim_hom_app, CategoryTheory.Dial.Hom.le, CategoryTheory.Equivalence.invFunIdAssoc_inv_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_inv_app_snd_app, HomologicalComplex₂.ι_totalShift₁Iso_inv_f_assoc, CategoryTheory.Limits.coendFunctor_obj, CategoryTheory.Limits.colimit.isoColimitCocone_ι_inv_assoc, CategoryTheory.Monad.Algebra.assoc, CategoryTheory.ObjectProperty.ihom_obj, SSet.Truncated.Edge.map_snd, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.leftUnitor_hom_unit_app, CategoryTheory.Cokleisli.Adjunction.fromCokleisli_map, CategoryTheory.SimplicialObject.instIsIsoAppUnitTruncatedCoskAdj, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_app_app, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_right_as, CochainComplex.HomComplex.Cocycle.leftUnshift_coe, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_obj, AlgebraicGeometry.Scheme.Hom.appIso_inv_naturality_assoc, CategoryTheory.Cat.free_obj, CategoryTheory.Limits.BinaryCofan.ι_app_right, AlgebraicTopology.DoldKan.MorphComponents.id_φ, CategoryTheory.MorphismProperty.Over.mapComp_hom_app_left, SSet.stdSimplex.instFiniteObjOppositeSimplexCategory, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₂, CategoryTheory.GrothendieckTopology.sheafToPresheaf_map_sheafComposeNatTrans_eq_sheafifyCompIso_inv, AlgebraicGeometry.IsOpenImmersion.opensEquiv_symm_apply, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_two, CategoryTheory.SimplicialObject.δ_comp_δ'', CategoryTheory.Idempotents.app_p_comm_assoc, CategoryTheory.toOverIteratedSliceForwardIsoPullback_hom_app_left, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.unitIso_hom_app_hom_app, CategoryTheory.Triangulated.TStructure.le_shift, PrincipalSeg.cocone_pt, CategoryTheory.StructuredArrow.homMk'_id, CommShift₂.comm, HomologicalComplex.shortComplexFunctor_obj_f, CategoryTheory.Limits.Fork.π_comp_hom_assoc, IsEventuallyConstantFrom.isoMap_hom, MonObj.mopEquiv_counitIso_hom_app_hom_unmop, CategoryTheory.pullbackShiftFunctorAdd'_hom_app, CategoryTheory.Limits.IsColimit.homEquiv_symm_naturality, Accessible.Limits.isColimitMapCocone.surjective, CategoryTheory.Monoidal.transportStruct_whiskerRight, imageToKernel_epi_of_zero_of_mono, limitIsoOfIsRightKanExtension_hom_π_assoc, PresheafOfModules.freeAdjunctionUnit_app, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₂₃, CategoryTheory.ε_naturality, smoothSheaf.obj_eq, CategoryTheory.Presieve.FamilyOfElements.singletonEquiv_symm_apply, RightExtension.IsPointwiseRightKanExtension.isIso_hom, RightExtension.mk_right_as, LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv_assoc, CategoryTheory.ProjectiveResolution.lift_commutes, CategoryTheory.prod.leftInverseUnitor_obj, CategoryTheory.MonoidalCategory.curriedTensorPreFunctor_obj, coconeTypesEquiv_symm_apply_ι, TopologicalSpace.Opens.mapId_inv_app, CategoryTheory.StructuredArrow.w_prod_snd, CategoryTheory.Localization.Monoidal.μ_inv_natural_left_assoc, CategoryTheory.NatTrans.mono_iff_mono_app, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_inv_app, leftExtensionEquivalenceOfIso₁_counitIso_inv_app_right_app, flip₁₃Functor_obj_map_app_app, CategoryTheory.MorphismProperty.PreIndSpreads.exists_isPushout, unop_obj, CategoryTheory.Bimon.ofMon_Comon_toMon_Comon_obj_comul, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_pt, Monoidal.μIso_hom, AlgebraicGeometry.PresheafedSpace.comp_c_app_assoc, CategoryTheory.ExponentiableMorphism.ev_coev_assoc, CategoryTheory.Limits.reflexiveCoforkEquivCofork_functor_obj_pt, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_map_left_app, isIso_ranAdjunction_homEquiv_iff, CategoryTheory.Limits.lim_obj, CategoryTheory.Localization.instHasSmallLocalizedHomObjShiftFunctor, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_hom, CategoryTheory.SmallObject.SuccStruct.Iteration.obj_succ, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_right_right, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_left_hom, CategoryTheory.WithInitial.mkCommaObject_right_map, CategoryTheory.shiftFunctorZero_inv_app_shift, mapAction_μ_hom, CategoryTheory.Presheaf.isSheaf_iff_isLimit, CategoryTheory.Bimon.equivMonComonUnitIsoAppXAux_inv, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.map_f', CategoryTheory.Under.opEquivOpOver_functor_obj, HomotopicalAlgebra.instWeakEquivalenceMapFullSubcategoryι, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_right_left_as, CategoryTheory.WithInitial.equivComma_functor_obj_hom_app, CategoryTheory.PreGaloisCategory.FiberFunctor.isPretransitive_of_isConnected, SSet.Subcomplex.preimage_obj, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_hom_c_app, Representation.coind'_apply_apply, CategoryTheory.Monoidal.InducingFunctorData.tensorHom_eq, AlgebraicGeometry.IsAffineOpen.iSup_basicOpen_eq_self_iff, essImage.unit_isIso, CategoryTheory.Limits.WalkingMultispan.functorExt_inv_app, CategoryTheory.ComposableArrows.naturality', AlgebraicGeometry.Scheme.Hom.comp_appIso, CategoryTheory.Adjunction.commShiftIso_inv_app_counit_app_assoc, CategoryTheory.Comma.toIdPUnitEquiv_functor_obj, CategoryTheory.Limits.Multicofork.map_ι_app, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_map, CategoryTheory.Enriched.Functor.natTransEquiv_symm_app_app_apply, AlgebraicGeometry.Scheme.basicOpen_one, CategoryTheory.CostructuredArrow.prodEquivalence_unitIso, CategoryTheory.Limits.Cones.whiskeringEquivalence_counitIso, CategoryTheory.Limits.CatCospanTransform.associator_inv_left_app, CategoryTheory.Grothendieck.pre_obj_base, CommShift.id_commShiftIso_inv_app, CategoryTheory.Limits.instIsIsoCoprodComparison, CategoryTheory.Tor_obj, CochainComplex.quasiIsoAt_shift_iff, LaxMonoidal.ε_tensorHom_comp_μ_assoc, curryingFlipEquiv_symm_apply_obj_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_app_snd_app, chosenProd_map, CategoryTheory.TransfiniteCompositionOfShape.ici_isoBot, LocallyCoverDense.functorPushforward_functorPullback_mem, CategoryTheory.Limits.limit.post_post, CategoryTheory.StructuredArrow.mapNatIso_inverse_obj_hom, CategoryTheory.Over.associator_inv_left_fst_snd, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_apply, CategoryTheory.CommGrp.mkIso'_inv_hom_hom_hom, CategoryTheory.Kleisli.Adjunction.toKleisli_obj, CochainComplex.instIsKProjectiveObjIntShiftFunctor, commShiftIso_inv_naturality_assoc, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₃, SSet.Truncated.HomotopyCategory.descOfTruncation_map_homMk, AlgebraicGeometry.instSurjectiveDescI₀SchemeF, CategoryTheory.Endofunctor.Algebra.functorOfNatTransEq_inv_app_f, PresheafOfModules.presheaf_obj_coe, CategoryTheory.Discrete.addMonoidalFunctor_obj, CategoryTheory.Limits.CatCospanTransform.leftUnitor_hom_left_app, OneHypercoverDenseData.SieveStruct.fac, CategoryTheory.GrothendieckTopology.uliftYonedaIsoYoneda_hom_app_val_app, CategoryTheory.Pseudofunctor.DescentData.pullFunctorObj_obj, TopCat.coinduced_of_isColimit, CategoryTheory.NatTrans.op_app, AlgebraicTopology.DoldKan.Γ₀_map_app, CategoryTheory.Limits.Cocone.toCostructuredArrowCocone_ι_app, pushforward_cover_iff_cover_pullback, whiskeringLeft₃ObjObjObj_obj_obj_obj_obj, CategoryTheory.uliftYoneda_obj_map_down, obj.ε_def, CategoryTheory.SimplicialObject.comp_left_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_right, CategoryTheory.Limits.PushoutCocone.op_π_app, CategoryTheory.ObjectProperty.leftOrthogonal.map_bijective_of_isTriangulated, CategoryTheory.Equivalence.congrLeft_unitIso_inv_app, CategoryTheory.shiftFunctorAdd'_assoc_inv_app_assoc, LeftExtension.postcompose₂ObjMkIso_hom_right_app, ModuleCat.ExtendScalars.smul_tmul, LightCondensed.free_internallyProjective_iff_tensor_condition', curry₃_map_app_app_app, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp, CategoryTheory.Square.toArrowArrowFunctor_obj_hom_left, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_map_mkHom_homMk_homMk, CategoryTheory.Comonad.ForgetCreatesLimits'.newCone_π, sheafPushforwardContinuousComp_inv_app_val_app, CategoryTheory.Iso.map_inv_hom_id, CategoryTheory.exp.ev_coev, CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois_apply, CategoryTheory.Monad.comparison_obj_A, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap_assoc, CategoryTheory.Limits.limit.lift_π_app, CategoryTheory.Limits.limit_obj_ext_iff, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionRight_obj, AlgebraicGeometry.Scheme.Modules.Hom.id_app, CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_π_assoc, HomologicalComplex.shortComplexFunctor'_obj_X₃, CategoryTheory.Limits.Cone.equiv_inv_π, CategoryTheory.biconeMk_map, CategoryTheory.Comonad.map_counit_app, IsDenseSubsite.functorPushforward_mem_iff, isZero_leftDerived_obj_projective_succ, CategoryTheory.Idempotents.DoldKan.N_obj, CategoryTheory.MonoOver.forget_obj_left, CategoryTheory.WithInitial.commaFromUnder_obj_hom_app, CategoryTheory.Equivalence.cancel_unit_right_assoc, AlgebraicGeometry.targetAffineLocally_affineAnd_iff, CategoryTheory.Limits.CategoricalPullback.Hom.w', CompHausLike.LocallyConstant.adjunction_left_triangle, ranCounit_app_app_ranAdjunction_unit_app_app_assoc, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app, AlgebraicGeometry.StructureSheaf.algebraMap_obj_top_bijective, AlgebraicTopology.DoldKan.toKaroubiCompN₂IsoN₁_hom_app, CategoryTheory.extensiveTopology.isLocallySurjective_iff, CategoryTheory.any_functor_const_on_obj, mapTriangleInvRotateIso_inv_app_hom₁, CochainComplex.HomComplex.Cochain.rightShift_smul, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight_symm_apply, CategoryTheory.Limits.Cocone.isColimit_iff_isIso_colimMap_ι, TopologicalSpace.Opens.inclusion'_map_eq_top, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_left, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_hom_app_app_snd, CategoryTheory.Adjunction.ε_comp_map_ε, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_assoc, CategoryTheory.Subfunctor.le_def, LaxRightLinear.μᵣ_naturality_right, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIso_hom_app_hom, HomologicalComplex.complexOfFunctorsToFunctorToComplex_map_app_f, CategoryTheory.Limits.coprodComparison_inr_assoc, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map_assoc, CochainComplex.HomComplex.Cochain.map_comp, CategoryTheory.Adjunction.counit_epi_of_R_faithful, CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero, CategoryTheory.Limits.π_comp_colimitOpIsoOpLimit_inv, curryingEquiv_symm_apply_map_app, CategoryTheory.Equivalence.functorFunctor_obj, TopCat.Sheaf.pushforward_obj_val, CategoryTheory.SimplicialObject.Truncated.trunc_obj_map, CategoryTheory.Free.lift_obj, CategoryTheory.PreGaloisCategory.aut_discreteTopology, HomologicalComplex.opInverse_obj, CategoryTheory.Iso.isoFunctorOfIsoInverse_inv_app, CategoryTheory.SmallObject.SuccStruct.extendToSucc.obj_eq, CategoryTheory.Cat.opFunctorInvolutive_inv_app_toFunctor_map, CategoryTheory.ProjectiveResolution.Hom.hom_comp_π, CategoryTheory.CostructuredArrow.mapNatIso_inverse_obj_hom, CategoryTheory.Presheaf.isSheaf_iff_multiequalizer, CategoryTheory.Monad.map_unit_app, hasBiproduct_of_preserves, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_comp_π_assoc, Final.extendCocone_obj_ι_app', OrderIso.equivalence_counitIso, CategoryTheory.ShortComplex.quasiIso_map_iff_of_preservesLeftHomology, CategoryTheory.Presheaf.uliftYonedaAdjunction_homEquiv_app, CategoryTheory.Sheaf.isLocallyInjective_forget, CategoryTheory.WithInitial.commaFromUnder_obj_right, CategoryTheory.Adjunction.leftAdjointUniq_trans_app, CategoryTheory.Equivalence.counitInv_app_comp_functor_map_η_inverse, CategoryTheory.flippingIso_hom_toFunctor_obj_obj_map, CategoryTheory.forget_obj, groupHomology.map_id_comp_H0Iso_hom_assoc, HomologicalComplex.mkHomToSingle_f, CategoryTheory.TransfiniteCompositionOfShape.iic_F, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_inverse_obj_X_X, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w, CategoryTheory.Limits.Bicones.functoriality_obj_pt, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_self, CategoryTheory.Sieve.uliftNatTransOfLe_app_down_coe, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIso_inv_app_hom, CategoryTheory.SmallObject.SuccStruct.restrictionLTOfCoconeIso_hom_app, CategoryTheory.WithInitial.equivComma_inverse_obj_map, SimplicialObject.Split.Hom.comm, CategoryTheory.Over.forget_obj, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_hom_app_val_app, mapBiproduct_hom, CategoryTheory.Limits.lim_ε_π, CategoryTheory.fromSkeleton_obj, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerRight_assoc, CategoryTheory.instEpiMap'KernelCokernelCompSequenceOfNatNat, CategoryTheory.CartesianClosed.uncurry_id_eq_ev, leftKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, CoreMonoidal.associativity, CategoryTheory.CostructuredArrow.grothendieckProj_map, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq, CategoryTheory.SimplicialObject.whiskering_map_app_app, CategoryTheory.MorphismProperty.Over.w_assoc, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst_assoc, SheafOfModules.restrictScalars_map_val, CategoryTheory.PreGaloisCategory.nhds_one_has_basis_stabilizers, CategoryTheory.SimplicialObject.Augmented.rightOp_right_obj, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_mon, CategoryTheory.toOverPullbackIsoToOver_hom_app_left, ModuleCat.restrictScalarsComp'App_hom_naturality, SSet.Truncated.hoFunctor₂_naturality, flip₁₃_obj_obj_map, CategoryTheory.Over.star_obj_hom, CategoryTheory.Monad.beckCofork_pt, CochainComplex.homotopyOp_hom_eq, CategoryTheory.Abelian.PreservesImage.iso_inv_ι_assoc, RightExtension.postcomp₁_map_left_app, CategoryTheory.cones_obj_map_app, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π_assoc, AlgebraicGeometry.Scheme.zeroLocus_eq_univ_iff_subset_nilradical_of_isCompact, QuadraticModuleCat.forget₂_obj, CochainComplex.HomComplex.Cochain.map_sub, CategoryTheory.shiftFunctorAdd'_add_zero_hom_app, CategoryTheory.Limits.Types.Small.limitCone_π_app, CategoryTheory.PreGaloisCategory.fiberBinaryProductEquiv_symm_snd_apply, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, AlgebraicTopology.DoldKan.QInfty_f_naturality, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.instIsIsoCommRingCatInvApp, CategoryTheory.NatTrans.removeRightOp_app, CategoryTheory.shiftComm', CategoryTheory.Limits.PushoutCocone.coequalizer_ext, CategoryTheory.SmallObject.πObj_ιIteration_app_right_assoc, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_apply, CategoryTheory.MonoidalCategory.curriedTensor_obj_map, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_μIso_inv, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_X_obj, HomologicalComplex.shortComplexFunctor'_obj_g, TopCat.Presheaf.stalkFunctor_map_germ_apply, CategoryTheory.Limits.PreservesInitial.iso_hom, HomologicalComplex.natIsoSc'_hom_app_τ₂, TopCat.Presheaf.germ_res_apply', CategoryTheory.LocalizerMorphism.homMap_apply_assoc, CategoryTheory.Subobject.ofMkLE_comp_ofLEMk, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_right_assoc, pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.WithTerminal.ofCommaObject_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_obj_iso_inv, LaxMonoidal.associativity_inv, CategoryTheory.ShortComplex.SnakeInput.functorL₃_obj, CategoryTheory.Limits.Cocones.functoriality_obj_ι_app, CategoryTheory.Limits.coprodComparison_inr, CategoryTheory.Limits.opCospan_inv_app, RightLinear.instIsIsoμᵣ, CategoryTheory.PreGaloisCategory.card_hom_le_card_fiber_of_connected, CategoryTheory.Equivalence.congrLeft_unitIso_hom_app, CategoryTheory.coalgebraToOver_obj, SSet.Truncated.HomotopyCategory.mkNatIso_inv_app_mk, CategoryTheory.Grothendieck.grothendieckTypeToCatFunctor_obj_fst, CategoryTheory.Over.associator_hom_left_snd_snd_assoc, CategoryTheory.preservesColimitIso_inv_comp_desc_assoc, CategoryTheory.Limits.Cone.overPost_pt, CategoryTheory.Comma.mapRightComp_hom_app_left, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_left, CategoryTheory.BinaryCofan.mono_inr_of_isVanKampen, CategoryTheory.Limits.limitRightOpIsoOpColimit_hom_comp_ι_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_inv_app_snd_app, CategoryTheory.ActionCategory.back_coe, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_app, CategoryTheory.MonoidalClosed.id_tensor_pre_app_comp_ev_assoc, CategoryTheory.Monoidal.leftUnitor_inv_app, CategoryTheory.sum.inlCompAssociator_hom_app, groupCohomology.mapShortComplexH2_id_comp_assoc, CategoryTheory.Limits.instIsIsoCokernelComparison, 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, mapTriangleRotateIso_hom_app_hom₃, groupHomology.mapCycles₂_id_comp_assoc, AlgebraicGeometry.Scheme.Modules.Hom.isIso_iff_isIso_app, CategoryTheory.Adjunction.homEquiv_naturality_right_square_iff, CategoryTheory.conjugateEquiv_counit, CategoryTheory.NatTrans.CommShiftCore.shift_app_comm_assoc, AlgebraicGeometry.Scheme.Hom.inr_normalizationCoprodIso_hom_fromNormalization_assoc, CategoryTheory.SimplicialObject.Truncated.rightExtensionInclusion_right_as, CategoryTheory.StructuredArrow.post_map, CochainComplex.IsKProjective.Qh_map_bijective, Condensed.isoFinYonedaComponents_inv_comp, CategoryTheory.whiskerRight_ι_colimitCompWhiskeringRightIsoColimitComp_inv_assoc, Bicategory.Opposite.unopFunctor_obj, CategoryTheory.LocalizerMorphism.smallHomMap'_mk, imageToKernel_comp_left, Rep.coindIso_inv_hom_hom, Initial.limit_cone_comp_aux, mapCommMon_id_mul, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_left, partialFunEquivPointed_inverse_obj, CategoryTheory.Sheaf.coneΓ_pt, FullyFaithful.monObj_one, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂'_map_app_app, AlgebraicGeometry.Spec_zeroLocus_eq_zeroLocus, SSet.face_le_horn, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_whiskerLeft, LaxMonoidal.ofBifunctor.topMapᵣ_app, CochainComplex.homOfDegreewiseSplit_f, PullbackObjObj.mapArrowRight_comp, flippingEquiv_symm_apply_obj_map, prod_map, CategoryTheory.Bimon.instIsMonHomHomEquivMonComonUnitIsoAppXAux, CategoryTheory.Equivalence.unitInv_app_inverse, instIsEquivalenceObjWhiskeringLeft, LeftExtension.postcomp₁_obj_right_map, CategoryTheory.Equivalence.sheafCongr.functor_map_val_app, AlgebraicGeometry.Scheme.Opens.ι_appTop, CategoryTheory.SmallObject.SuccStruct.arrowι_def, CategoryTheory.Adjunction.rightAdjointUniq_trans_app_assoc, AlgebraicGeometry.Scheme.Modules.Hom.comp_app, CategoryTheory.Limits.pointwiseProductCompEvaluation_inv_app, AlgebraicGeometry.Scheme.Hom.map_mem_image_iff, groupHomology.mapShortComplexH2_comp, CategoryTheory.bifunctorComp₁₂Obj_obj_map, CategoryTheory.Limits.CompleteLattice.finite_limit_eq_finset_univ_inf, ranges_directed, CategoryTheory.Monad.instHasCoequalizerMapAAppCounitObjAOfHasCoequalizerOfIsSplitPair, ranObjObjIsoLimit_hom_π_assoc, sheafPushforwardContinuousComp_hom_app_val_app, HomologicalComplex.cyclesOpIso_hom_naturality_assoc, CategoryTheory.ExactFunctor.whiskeringRight_obj_obj_obj, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatTrans_id, flip₂₃Functor_obj_obj_map_app, CategoryTheory.Limits.isLimitConeOfAdj_lift, toOplaxFunctor_mapComp, CochainComplex.shiftFunctorAdd_inv_app_f, CategoryTheory.RetractArrow.map_r_left, CategoryTheory.Adjunction.compPreadditiveYonedaIso_hom_app_app_apply, CategoryTheory.Limits.ι_colimitLimitIso_limit_π_assoc, CategoryTheory.Limits.IndObjectPresentation.yoneda_ι_app, CategoryTheory.Arrow.mapCechConerve_app, CategoryTheory.Triangulated.Octahedron.map_m₁, CategoryTheory.uncurry_pre, LaxMonoidal.tensorUnit_whiskerLeft_comp_leftUnitor_hom, CategoryTheory.Limits.colimIsoFlipCompWhiskerColim_hom_app_app, CategoryTheory.AdditiveFunctor.ofLeftExact_obj_fst, Monoidal.whiskerRight_app_snd_assoc, DerivedCategory.isGE_Q_obj_iff, ModuleCat.forget_obj, ModuleCat.directLimitDiagram_obj_isAddCommGroup, CategoryTheory.Limits.Types.Limit.lift_π_apply, CategoryTheory.Limits.preserves_cokernel_iso_comp_cokernel_map, CategoryTheory.SimplicialObject.δ_comp_δ_self, CategoryTheory.Abelian.Ext.add_hom, CategoryTheory.sum.inrCompInlCompAssociator_inv_app_down_down, CategoryTheory.Comma.toPUnitIdEquiv_inverse_map_left, PreservesPointwiseLeftKanExtensionAt.preserves, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.functor_obj, CategoryTheory.Under.equivalenceOfIsInitial_unitIso, AddCommGrpCat.coyonedaType_obj_map, CategoryTheory.Limits.Cofork.condition, CategoryTheory.Square.opFunctor_obj, OplaxRightLinear.δᵣ_unitality_hom, CategoryTheory.Limits.Bicone.toBinaryBiconeFunctor_obj_pt, 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, CategoryTheory.Limits.BinaryFan.braiding_inv_fst_assoc, partialLeftAdjointHomEquiv_map_comp, CategoryTheory.Limits.im_obj, CategoryTheory.NatTrans.mapHomologicalComplex_naturality, ChainComplex.augmentTruncate_hom_f_succ, CategoryTheory.Limits.PreservesPushout.inl_iso_hom_assoc, CategoryTheory.Under.isLeftAdjoint_post, flip₂₃Functor_map_app_app_app, PullbackObjObj.π_iso_of_iso_right_inv, CategoryTheory.Limits.Cone.equiv_hom_snd, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₁, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₂, CategoryTheory.Adjunction.homAddEquiv_symm_zero, CategoryTheory.ConcreteCategory.forget₂_comp_apply, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_obj, CategoryTheory.instIsIsoAppUnitReflectorAdjunctionObjEssImage, CategoryTheory.ihom.coev_naturality_assoc, CategoryTheory.Limits.end_.hom_ext_iff, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst, CategoryTheory.CartesianMonoidalCategory.terminalComparison_isIso_of_preservesLimits, PresheafOfModules.toPresheaf_map_app_apply, RepresentableBy.homEquiv_comp, CategoryTheory.Equivalence.symmEquivInverse_obj_counitIso_inv, CategoryTheory.yonedaCommGrpGrp_obj, CategoryTheory.Limits.ConeMorphism.w_assoc, CategoryTheory.Monad.free_obj_a, MonCat.FilteredColimits.cocone_naturality, AlgebraicGeometry.Scheme.map_basicOpen, CategoryTheory.ShortComplex.FunctorEquivalence.functor_obj_map, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₁, CategoryTheory.Subfunctor.Subpresheaf.iInf_obj, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_inv_π, CategoryTheory.Limits.FormalCoproduct.Hom.fromIncl_φ, CategoryTheory.endofunctorMonoidalCategory_whiskerLeft_app, AlgebraicGeometry.IsOpenImmersion.affineOpensEquiv_apply_coe_coe, CategoryTheory.Subfunctor.Subpresheaf.top_obj, CategoryTheory.LocalizerMorphism.equiv_smallShiftedHomMap, AddCommGrpCat.coyonedaType_obj_obj_coe, CategoryTheory.FreeGroupoid.mapComp_inv_app, CategoryTheory.ForgetEnrichment.equivInverse_obj, CondensedSet.continuous_coinducingCoprod, CategoryTheory.SmallObject.restrictionLE_map, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₁, CategoryTheory.Adjunction.unit_app_shift_commShiftIso_inv_app_assoc, TopologicalSpace.Opens.adjunction_counit_map_functor, AlgebraicGeometry.coprodSpec_coprodMk, groupCohomology.map_id_comp_H0Iso_hom, CategoryTheory.Adjunction.unit_isSplitEpi_of_L_full, commShiftOfLocalization.iso_inv_app_assoc, CategoryTheory.OrthogonalReflection.iteration_map_succ_assoc, CategoryTheory.Sieve.sieveOfSubfunctor_apply, CategoryTheory.Limits.PullbackCone.unop_ι_app, CategoryTheory.Triangulated.SpectralObject.Hom.comm_assoc, TopCat.Presheaf.generateEquivalenceOpensLe_functor, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_inv_app_hom, AlgebraicGeometry.Scheme.IdealSheafData.opensRange_subschemeCover_map, Monoidal.whiskeringLeft_η_app, CategoryTheory.Sieve.functorPullback_monotone, CoalgCat.comonEquivalence_unitIso, AlgebraicGeometry.Proj.zero_apply, Fiber.instIsHomLiftIdMapFiberInclusion, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality_assoc, PresheafOfModules.Derivation'.d_app, CategoryTheory.CategoryOfElements.π_map, PresheafOfModules.neg_app, RightLinear.instIsIsoδᵣ, CategoryTheory.Idempotents.functorExtension₂_obj_obj_p, CategoryTheory.exp.ev_coev_assoc, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_hom_right_app, sheafPushforwardContinuous_obj_val_obj, CategoryTheory.Localization.Monoidal.μ_inv_natural_right_assoc, CategoryTheory.Limits.FormalCoproduct.evalOp_map_app, instReflectsIsomorphismsDiscreteObjWhiskeringLeftIncl, prod_ε_fst, CategoryTheory.CommMon.forget₂Mon_obj_mul, CategoryTheory.SmallObject.SuccStruct.arrowMap_ofCocone_to_top, CategoryTheory.Limits.Multifork.toPiFork_π_app_one, CategoryTheory.Bimon.equivMonComonCounitIsoAppX_hom_hom, AlgebraicGeometry.PresheafedSpace.GlueData.componentwise_diagram_π_isIso, CategoryTheory.SmallObject.SuccStruct.Iteration.mapObj_trans_assoc, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_inv_app, AlgebraicGeometry.Scheme.Hom.preimageIso_hom_ι, LaxMonoidal.id_μ, CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_none, CategoryTheory.ComposableArrows.mk₀_obj, CategoryTheory.Pretriangulated.mem_distTriang_op_iff', CategoryTheory.ShortComplex.LeftHomologyData.mapLeftHomologyIso_eq, CategoryTheory.Comma.mapRightIso_functor_obj_left, OrderHom.equivalenceFunctor_functor_obj_obj, mapShortComplex_obj, FullyFaithful.comp_preimage, groupHomology.mapCycles₁_id_comp, StalkSkyscraperPresheafAdjunctionAuxs.germ_fromStalk_assoc, AlgebraicGeometry.affinePreimage, AddCommGrpCat.Colimits.toCocone_ι_app, CategoryTheory.Over.μ_pullback_left_fst_fst', CategoryTheory.Limits.coconeOfDiagramTerminal_ι_app, RepresentableBy.isRepresentedBy, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₂, Rep.trivialFunctor_obj_V, LaxMonoidal.μ_natural_left_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_map_fst_app, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_pullback_obj, CategoryTheory.Limits.pullbackObjIso_hom_comp_fst, LaxMonoidal.ofBifunctor.firstMap₁_app_app_app, AddCommGrpCat.Colimits.Quot.ι_desc, CategoryTheory.ProjectiveResolution.π'_f_zero, CategoryTheory.CosimplicialObject.δ_comp_σ_succ', CategoryTheory.IsVanKampenColimit.precompose_isIso_iff, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_map_right, CategoryTheory.Limits.π_comp_cokernelComparison_assoc, CategoryTheory.Limits.cospanOp_hom_app, CategoryTheory.Sheaf.isConstant_iff_isIso_counit_app', CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w_apply, CategoryTheory.CartesianClosed.uncurry_natural_left_assoc, AlgebraicGeometry.Scheme.isoSpec_inv_naturality, CategoryTheory.shiftFunctorZero_hom_app_shift, CategoryTheory.whiskeringLeft_preservesColimit, ProfiniteAddGrp.limit_ext_iff, AlgebraicGeometry.IsAffineOpen.toSpecΓ_fromSpec_assoc, Types.monoOverEquivalenceSet_functor_map, CategoryTheory.Presieve.map_monotone, CategoryTheory.Limits.asEmptyCocone_ι_app, CategoryTheory.MonadHom.app_η, CategoryTheory.Limits.MultispanIndex.map_left, CategoryTheory.Over.μ_pullback_left_fst_snd, CategoryTheory.Over.whiskerRight_left, CategoryTheory.coherentTopology.isSheaf_yoneda_obj, CategoryTheory.Subobject.eq_of_comp_arrow_eq_iff, ModuleCat.homEquiv_extendScalarsComp, CategoryTheory.CosimplicialObject.Augmented.toArrow_obj_left, CategoryTheory.Equivalence.changeFunctor_unitIso_inv_app, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_hom_inv_id_assoc, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_apply_snd, CategoryTheory.Limits.CategoricalPullback.π₁_obj, TopCat.Sheaf.objSupIsoProdEqLocus_inv_snd, CategoryTheory.CostructuredArrow.homMk'_left, CategoryTheory.Over.monObjMkPullbackSnd_one, AlgebraicTopology.DoldKan.P_f_naturality_assoc, CategoryTheory.unitOfTensorIsoUnit_inv_app, CategoryTheory.Limits.imageSubobjectCompIso_inv_arrow_assoc, CategoryTheory.Limits.Concrete.to_product_injective_of_isLimit, TopologicalSpace.Opens.overEquivalence_unitIso_inv_app_left, AlgebraicGeometry.StructureSheaf.const_algebraMap, AlgebraicGeometry.instMonoObjWalkingSpanCompSchemeSpanForgetNoneWalkingPairSomeMapInitOfIsOpenImmersion, CategoryTheory.StructuredArrow.homMk'_right, LaxMonoidal.associativity_inv_assoc, HomologicalComplex.forget_obj, Profinite.lift_lifts_assoc, AddCommMonCat.equivalence_inverse_obj_coe, QuasiIsoAt.quasiIso, CategoryTheory.Regular.instIsRegularEpiFrobeniusMorphism, CategoryTheory.NatTrans.naturality_app, CategoryTheory.ComposableArrows.twoδ₁Toδ₀_app_one, AddCommGrpCat.Colimits.Quot.map_ι, AlgebraicGeometry.Scheme.Hom.id_appIso, CategoryTheory.InjectiveResolution.desc_commutes, CategoryTheory.Abelian.coimageImageComparisonFunctor_obj, CategoryTheory.Limits.isIso_limit_cone_parallelPair_of_eq, ModuleCat.ExtendScalars.map_tmul, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₁₃, biprodComparison'_comp_biprodComparison, CategoryTheory.Sieve.uliftFunctorInclusion_app, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_counitIso, CategoryTheory.ShiftedHom.comp_map, smoothSheafCommRing.ι_forgetStalk_inv_assoc, CategoryTheory.Monoidal.transportStruct_leftUnitor, CategoryTheory.Limits.reflexiveCoforkEquivCofork_functor_obj_π, skyscraperPresheafCocone_ι_app, ModuleCat.FilteredColimits.colimit_add_mk_eq', CategoryTheory.Sum.swap_obj_inl, CategoryTheory.Adjunction.CommShift.compatibilityCounit_left, AlgebraicGeometry.Scheme.Hom.preimageIso_inv_ι_assoc, CategoryTheory.MorphismProperty.Comma.forget_obj, LeftExtension.coconeAtFunctor_obj, AlgebraicTopology.DoldKan.map_P, flipping_unitIso_hom_app_app_app, CategoryTheory.MonoidalCategory.externalProductBifunctorCurried_map_app_app_app, CategoryTheory.Equivalence.inverseFunctorObj'_hom_app, CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_obj_hom, CategoryTheory.StructuredArrow.pre_map_left, CategoryTheory.Join.pseudofunctorRight_mapId_inv_toNatTrans_app, op_commShiftIso_inv_app, AlgebraicGeometry.instQuasiSeparatedToSpecΓOfQuasiSeparatedSpaceCarrierCarrierCommRingCat, PresheafOfModules.map_comp, AlgebraicGeometry.IsAffineOpen.basicOpenSectionsToAffine_isIso, AlgebraicGeometry.isAffineHom_iff, CategoryTheory.cocones_obj_map_app, CategoryTheory.Core.functorToCore_map_iso_hom, LaxRightLinear.μᵣ_associativity_assoc, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_tensorDesc_app_assoc, Monoidal.map_associator', CategoryTheory.LaxBraidedFunctor.forget_obj, CategoryTheory.ObjectProperty.ColimitOfShape.prop_diag_obj, CategoryTheory.obj_η_app_assoc, CategoryTheory.coyonedaPreservesLimitsOfShape, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃'_map_app_app, CategoryTheory.Sieve.mem_functorPushforward_inverse, CategoryTheory.Comma.inv_left_hom_right, CategoryTheory.Monoidal.transportStruct_rightUnitor, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right, map_braiding_assoc, instIsRightKanExtensionObjRanAppRanCounit, AlgebraicGeometry.Scheme.IdealSheafData.subschemeFunctor_obj, CategoryTheory.ShiftedHom.opEquiv'_symm_apply, CategoryTheory.Limits.imageSubobjectMap_arrow, CategoryTheory.Comonad.coassoc_assoc, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_ihom_ev_app, AlgebraicGeometry.PresheafedSpace.map_id_c_app, inducedTopology_sieves, CategoryTheory.ExponentiableMorphism.ev_naturality_assoc, CategoryTheory.Limits.inv_piComparison_comp_map_π, CategoryTheory.Limits.colimitPointwiseProductToProductColimit_app, mapCone_pt, TopCat.Presheaf.germ_exist, CategoryTheory.Idempotents.DoldKan.η_inv_app_f, AlgebraicGeometry.exists_smooth_of_formallySmooth_stalk, AlgebraicGeometry.Scheme.comp_appTop_assoc, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_right_as, CochainComplex.HomComplex.Cocycle.fromSingleMk_neg, CategoryTheory.Limits.imageSubobjectMap_arrow_assoc, mapTriangleIdIso_hom_app_hom₃, AddCommGrpCat.kernelIsoKer_inv_comp_ι, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, CategoryTheory.Adjunction.Triple.adj₁_counit_app_rightToLeft_app_assoc, CategoryTheory.Limits.limit.map_post, CategoryTheory.GrothendieckTopology.diagramPullback_app, rightDerivedZeroIsoSelf_inv_hom_id_app_assoc, CategoryTheory.IsFinitelyPresentable.exists_hom_of_isColimit, CategoryTheory.Limits.colim_obj, CategoryTheory.Over.opEquivOpUnder_counitIso, CategoryTheory.Limits.widePullbackShapeOp_obj, TopCat.Presheaf.SheafConditionEqualizerProducts.res_π, CategoryTheory.Limits.map_lift_kernelComparison, CategoryTheory.NatTrans.mono_iff_mono_app', CategoryTheory.SimplicialObject.Augmented.whiskering_map_app_left, SSet.PtSimplex.MulStruct.δ_map_of_lt, AlgebraicGeometry.Scheme.local_affine, TopCat.Presheaf.germ_res, mapCone₂_pt, CategoryTheory.CostructuredArrow.prodFunctor_obj, AddCommGrpCat.HasLimit.productLimitCone_cone_π, CategoryTheory.Comma.coconeOfPreserves_ι_app_left, closedUnit_app_app, CategoryTheory.ProdPreservesConnectedLimits.forgetCone_pt, CategoryTheory.SmallObject.SuccStruct.iterationFunctor_map_succ, ModuleCat.restrictScalarsComp'App_inv_naturality, AlgebraicGeometry.PresheafedSpace.GlueData.f_invApp_f_app, OplaxMonoidal.δ_comp_whiskerLeft_δ, CategoryTheory.CommGrp.forget₂Grp_obj_one, LeftExtension.coconeAtWhiskerRightIso_hom_hom, CategoryTheory.Comma.equivProd_inverse_map_right, CategoryTheory.OverPresheafAux.counitAux_hom, SheafOfModules.pushforward_map_val, RightExtension.IsPointwiseRightKanExtensionAt.isIso_hom_app, ModuleCat.free_μ_freeMk_tmul_freeMk, CategoryTheory.instPreservesFilteredColimitsOfSizeObjOppositeFunctorTypeCoyonedaOpOfIsFinitelyPresentable, ModuleCat.forget₂_obj_moduleCat_of, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_hom_app_left, CategoryTheory.Subfunctor.isSheaf_iff, CategoryTheory.plusPlusAdjunction_counit_app_val, CategoryTheory.SmallObject.SuccStruct.extendToSuccRestrictionLEIso_inv_app, AlgebraicGeometry.Scheme.IdealSheafData.ideal_top, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_left, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_σ, CategoryTheory.InjectiveResolution.desc_commutes_assoc, HomologicalComplex.single_map_f_self_assoc, CategoryTheory.Subfunctor.sInf_obj, instIsEquivalenceLeftExtensionCompPrecomp, commAlgCatEquivUnder_inverse_obj_carrier, equiv_unitIso, CategoryTheory.Limits.PreservesLimit₂.nonempty_isLimit_mapCone₂, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_symm_apply, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_comp_π, CommAlgCat.forget₂_algCat_obj, TopologicalSpace.Opens.adjunction_counit_app_self, TopCat.Presheaf.instIsLocalizationCarrierObjOppositeOpensCarrierCommRingCatObjLocalizationPresheaf, CategoryTheory.Limits.ImageFactorisation.ofArrowIso_F, CategoryTheory.Subfunctor.mem_equalizer_iff, CategoryTheory.Mat_.embedding_obj_fintype, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_app, CategoryTheory.map_functorial_obj, TopologicalSpace.Opens.mem_map, mapHomologicalComplex_commShiftIso_inv_app_f, CategoryTheory.uncurry_expComparison, leftExtensionEquivalenceOfIso₁_inverse_obj_hom_app, CategoryTheory.CategoryOfElements.fromCostructuredArrow_map_coe, SSet.stdSimplex.instHasDimensionLEObjSimplexCategoryMk, AlgebraicGeometry.instIsAffineObjOppositeCommRingCatSchemeSpec, CategoryTheory.GradedObject.mapBifunctor_map_app, CategoryTheory.Adjunction.adjToMonadIso_inv_toNatTrans_app, CategoryTheory.Pretriangulated.binaryProductTriangle_mor₃, CategoryTheory.Equivalence.leftOp_inverse_map, PresheafOfModules.evaluation_preservesColimitsOfSize, CategoryTheory.forget₂_comp_apply, CategoryTheory.Limits.limit.isoLimitCone_inv_π_assoc, CategoryTheory.CartesianClosed.uncurry_natural_left, whiskeringLeft₃_obj_obj_obj_map_app_app_app, CategoryTheory.Limits.BinaryFan.braiding_hom_fst, CategoryTheory.Equivalence.inverseFunctorMapIso_symm_eq_isoInverseOfIsoFunctor, SSet.stdSimplex.monotone_apply, prod_μ_fst, AddGrpCat.μ_forget_apply, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_μIso_hom, CochainComplex.exists_iso_single, CategoryTheory.Idempotents.KaroubiUniversal₁.counitIso_hom_app_app_f, CommShift.id_commShiftIso_hom_app, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_whiskerLeft, CategoryTheory.Limits.CatCospanTransform.associator_inv_base_app, SSet.horn.faceι_ι, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_tensorHom_hom_eq_tensorHom, CochainComplex.HomComplex.Cocycle.rightShiftAddEquiv_symm_apply, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₃, CategoryTheory.Adjunction.commShiftIso_hom_app_counit_app_shift_assoc, CategoryTheory.SingleFunctors.hom_inv_id_hom_app_assoc, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_ε_assoc, HomotopicalAlgebra.BifibrantObject.HoCat.ιFibrantObject_obj, AlgebraicTopology.DoldKan.degeneracy_comp_PInfty_assoc, CategoryTheory.extensiveTopology.presheafIsLocallySurjective_iff, CategoryTheory.TwoSquare.GuitartExact.isConnected_rightwards, CategoryTheory.Triangulated.TStructure.triangleLTGE_map_hom₂, CochainComplex.HomComplex.Cochain.shift_units_smul, FullyFaithful.homMulEquiv_symm_apply, mapBiprod_hom, CategoryTheory.Coreflective.instIsIsoAppCounitCoreflectorAdjunctionA, CategoryTheory.NatTrans.prod_app_snd, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.coequalizer_π_app_isLocalHom, CategoryTheory.LocalizerMorphism.homMap_comp, CategoryTheory.Join.homInduction_right, 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.Discrete.equivOfEquivalence_apply, flipping_functor_obj_map_app, AlgebraicGeometry.Scheme.isoSpec_Spec, CategoryTheory.Limits.kernelSubobject_arrow, projective_obj_of_projective, CategoryTheory.Limits.Cones.postcompose_obj_π, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_inv_app, CategoryTheory.ComposableArrows.threeδ₁Toδ₀_app_two, CategoryTheory.Adjunction.functorialityUnit'_app_hom, CategoryTheory.Limits.colimit.ι_post_assoc, AddGrpCat.FilteredColimits.colimit_add_mk_eq', AlgebraicTopology.DoldKan.toKaroubiCompN₂IsoN₁_inv_app, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_unitIso_inv_app_f, CategoryTheory.MorphismProperty.shift, CategoryTheory.Paths.lift_cons, OplaxMonoidal.comp_η, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_isIso, CategoryTheory.Pseudofunctor.mapComp'_hom_naturality, AlgebraicGeometry.PresheafedSpace.c_isIso_of_iso, CategoryTheory.Idempotents.KaroubiUniversal₁.counitIso_inv_app_app_f, LaxMonoidal.whiskeringRight_μ_app, AlgebraicGeometry.instLocallyOfFiniteTypeMorphismRestrict, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app, CategoryTheory.StructuredArrow.map_map_left, eventualRange_mapsTo, CategoryTheory.GradedObject.mapBifunctorObjObjSingle₀Iso_inv, CategoryTheory.GrothendieckTopology.Point.instIsIsoMapFunctorOppositePresheafFiberToSheafify, PullbackObjObj.mapArrowLeft_left, CategoryTheory.yonedaGrpObj_map, CategoryTheory.Iso.map_hom_inv_id_eval_assoc, unop_map, CategoryTheory.Limits.Types.isPushout_of_bicartSq, CategoryTheory.eHomFunctor_obj_map, TopCat.Presheaf.Pushforward.id_hom_app, CategoryTheory.MonoidalClosed.uncurry_ihom_map, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_hom_app_hom₂, CategoryTheory.Square.flipFunctor_obj, CategoryTheory.ObjectProperty.strictMap_iff, SSet.S.equivElements_apply_fst, instPreservesLimitOfIsCoreflexivePairDiscreteObjWhiskeringLeftIncl, CategoryTheory.Localization.Monoidal.isInvertedBy₂, AlgebraicGeometry.IsIntegralHom.instMorphismRestrict, CategoryTheory.Grothendieck.map_obj_fiber, TopCat.Presheaf.pullback_obj_obj_ext_iff, SSet.Subcomplex.ofSimplex_le_iff, CategoryTheory.Join.inclRight_obj, CategoryTheory.forgetEnrichmentOppositeEquivalence_counitIso, CategoryTheory.Limits.IsZero.map, CategoryTheory.cosimplicialToSimplicialAugmented_obj, CategoryTheory.Endofunctor.Algebra.functorOfNatTrans_map_f, CategoryTheory.Limits.PreservesPushout.inr_iso_hom, CategoryTheory.Bicategory.rightUnitorNatIso_inv_app, Rep.linearization_obj_ρ, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd, RepresentableBy.homEquiv_unop_comp, flipIsoCurrySwapUncurry_hom_app_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso_hom_app_app, AlgebraicGeometry.Scheme.IdealSheafData.isLocalization_away, CategoryTheory.Limits.CategoricalPullback.mkNatIso_hom_app_snd, TopCat.Opens.coverDense_iff_isBasis, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_map_left_right, CategoryTheory.SingleFunctors.postcomp_shiftIso_inv_app, CategoryTheory.shiftFunctorAdd_assoc_inv_app_assoc, CategoryTheory.Subobject.ofLE_refl, mapCone₂_π_app, AlgebraicGeometry.Scheme.ofRestrict_toLRSHom_c_app, CategoryTheory.yonedaGrpObjIsoOfRepresentableBy_hom, CategoryTheory.Limits.PreservesLimitPair.iso_inv_snd_assoc, CategoryTheory.Regular.frobeniusStrongEpiMonoFactorisation_e, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.functor_obj, CategoryTheory.Limits.parallelPair_obj_one, DerivedCategory.instFaithfulFunctorHomotopyCategoryIntUpObjWhiskeringLeftQh, CategoryTheory.Limits.Cones.functoriality_map_hom, CategoryTheory.StructuredArrow.mkPostcomp_right, ModuleCat.restrictScalarsComp'App_inv_naturality_assoc, CategoryTheory.MonoidalClosed.uncurry_injective, CochainComplex.HomComplex.Cochain.leftShiftLinearEquiv_symm_apply, CategoryTheory.Limits.cokernel_map_comp_cokernelComparison, CategoryTheory.OverPresheafAux.unitBackward_unitForward, OplaxMonoidal.δ_comp_η_tensorHom, AlgebraicGeometry.Scheme.Hom.preimage_sup, CategoryTheory.ShortComplex.ShortExact.injective_f, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_map_left_left, GrpCat.forget₂_map, LeftExtension.precomp_obj_right, obj.μ_def, CategoryTheory.Limits.limitFlipIsoCompLim_inv_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_hom_app, CategoryTheory.regularTopology.equalizerCondition_iff_isIso_lift, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_app_hom, CategoryTheory.toOverIsoToOverUnit_hom_app_left, CategoryTheory.rightAdjointOfCostructuredArrowTerminalsAux_apply, CategoryTheory.Limits.cokernelComparison_map_desc, LightCondMod.LocallyConstant.instIsIsoLightCondSetMapForgetAppLightCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, CategoryTheory.Adjunction.compYonedaIso_inv_app_app, PartialOrder.mem_nerve_nonDegenerate_iff_strictMono, CategoryTheory.GrothendieckTopology.preservesSheafification_iff_of_adjunctions_of_hasSheafCompose, CategoryTheory.yonedaGrpObjIsoOfRepresentableBy_inv, CoconeTypes.IsColimitCore.fac, CategoryTheory.Limits.parallelPair_functor_obj, CategoryTheory.ComposableArrows.isComplex₂_iff, FullyFaithful.map_surjective, CategoryTheory.prod.rightUnitor_obj, CategoryTheory.MonoidalClosed.uncurry_id_eq_ev, CategoryTheory.Comon.Comon_EquivMon_OpOp_unitIso, PresheafOfModules.evaluation_preservesFiniteLimits, CategoryTheory.Equivalence.changeInverse_counitIso_hom_app, CategoryTheory.Over.w, leftUnitor_inv_app, CategoryTheory.Limits.HasLimit.isoOfNatIso_hom_π_assoc, CategoryTheory.ShiftedHom.mk₀_add, AlgebraicGeometry.IsClosedImmersion.hasAffineProperty, mapTriangleRotateIso_hom_app_hom₁, SheafOfModules.Presentation.map_relations_I, HomologicalComplex₂.D₁_totalShift₁XIso_hom, CategoryTheory.MorphismProperty.CostructuredArrow.toOver_map, CategoryTheory.SimplicialObject.Augmented.drop_obj, coreCompInclusionIso_inv_app, CategoryTheory.Join.opEquiv_functor_obj_op_left, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_obj_map_app, TopCat.Presheaf.Pushforward.id_eq, CategoryTheory.Equalizer.Presieve.Arrows.sheaf_condition, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_inv, hom_obj, CategoryTheory.Sheaf.adjunction_unit_app_val, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.sq, CategoryTheory.StructuredArrow.mapIso_functor_obj_right, AlgebraicGeometry.Scheme.preimage_opensRange_toSpecΓ, CategoryTheory.Limits.sigmaComparison_map_desc_assoc, CategoryTheory.GrothendieckTopology.OneHypercover.map_toPreOneHypercover, AlgebraicGeometry.instIsOpenImmersionMorphismRestrict, SSet.Truncated.HomotopyCategory.homToNerveMk_app_one, shiftMap_zero, groupHomology.lsingle_comp_chainsMap_f, ι_biproductComparison', HomologicalComplex₂.D₂_totalShift₁XIso_hom, CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_unitor, CategoryTheory.Coyoneda.colimitCoconeIsColimit_desc, CategoryTheory.ObjectProperty.ihom_map, CategoryTheory.Comma.mapLeftEq_hom_app_right, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceFunctor_obj_base, ModuleCat.FreeMonoidal.μIso_hom_freeMk_tmul_freeMk, CategoryTheory.Join.opEquiv_inverse_obj_left_op, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_pullback_map, CategoryTheory.SimplicialObject.equivalenceRightToLeft_right, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_apply, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_pos, CategoryTheory.Endofunctor.Algebra.functorOfNatTransId_hom_app_f, PullbackObjObj.mapArrowLeft_comp_assoc, opInv_map, CategoryTheory.Limits.isIndObject_yoneda, CategoryTheory.PreGaloisCategory.isPretransitive_of_surjective, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_functor_obj_X_p, AddMonCat.FilteredColimits.colimit_add_mk_eq', TopCat.Presheaf.generateEquivalenceOpensLe_counitIso, 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, whiskeringRight₂_map_app_app_app, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_m, CategoryTheory.StructuredArrow.prodFunctor_obj, CategoryTheory.Cat.ihom_map, SSet.prodStdSimplex.objEquiv_map_apply, CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_left, DerivedCategory.isGE_iff, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π_assoc, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app_assoc, SSet.Subcomplex.le_iff_of_hasDimensionLT, CategoryTheory.GrothendieckTopology.OneHypercover.IsPreservedBy.mem₀, mapTriangleIso_hom_app_hom₃, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_π_app, topCatOpToFrm_obj_coe, CategoryTheory.MonoidalCategory.DayConvolution.braidingInvCorepresenting_app, HomotopicalAlgebra.CofibrantObject.HoCat.bifibrantResolution_map, id_tensor_π_preserves_coequalizer_inv_desc, AlgebraicGeometry.ProjectiveSpectrum.Proj.mk_mem_toSpec_base_apply, CategoryTheory.Limits.DiagramOfCones.mkOfHasLimits_obj, Bipointed.swapEquiv_functor_obj_X, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.flipFunctorToInterchange_inv_app_app, CategoryTheory.Limits.PreservesPullback.iso_hom_snd_assoc, CategoryTheory.Monad.free_obj_A, CategoryTheory.Limits.spanCompIso_hom_app_right, CategoryTheory.Limits.cospan_right, SSet.stdSimplex.objEquiv_symm_mem_nonDegenerate_iff_mono, CategoryTheory.Abelian.PreservesCoimage.iso_inv_π, CommAlgCat.forget_obj, SimplicialObject.Splitting.cofan_inj_comp_app, lanUnit_app_whiskerLeft_lanAdjunction_counit_app_assoc, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_three, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatIso_inv, CategoryTheory.Presheaf.instIsLeftKanExtensionOppositeObjFunctorTypeYonedaYonedaMap, SimplexCategory.rev_obj, CategoryTheory.NatTrans.whiskerLeft_app_tensor_app, Rep.invariantsAdjunction_counit_app_hom, AlgebraicGeometry.Scheme.eq_zeroLocus_of_isClosed_of_isAffine, CategoryTheory.Limits.prodComparison_snd, CategoryTheory.Limits.limitOpIsoOpColimit_inv_comp_π_assoc, CategoryTheory.Triangulated.TStructure.triangleLTGE_obj_mor₃, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_hom_π_π_assoc, CategoryTheory.Subobject.ofLEMk_comp_ofMkLEMk_assoc, CategoryTheory.Comma.mapLeft_obj_right, CategoryTheory.comp_app, LightProfinite.Extend.functorOp_map, PresheafOfModules.sub_app, TopCat.Sheaf.interUnionPullbackConeLift_left, PushoutObjObj.ι_iso_of_iso_left_inv, CategoryTheory.Monoidal.Reflective.instIsIsoAppUnitObjIhom, AlgebraicTopology.NormalizedMooreComplex.d_squared, AlgebraicGeometry.Scheme.Opens.ι_preimage_self, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality_assoc, const.opObjOp_hom_app, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₂, groupHomology.cyclesMap_comp_cyclesIso₀_hom, MonObj.mopEquivCompForgetIso_inv_app_unmop, LeftExtension.postcompose₂_obj_left, relativelyRepresentable.w_assoc, CategoryTheory.Sieve.yonedaFamily_fromCocone_compatible, isIso_lanAdjunction_homEquiv_symm_iff, CategoryTheory.subterminalsEquivMonoOverTerminal_inverse_obj_obj, rightDerivedNatTrans_app, CategoryTheory.GradedObject.single_map_singleObjApplyIsoOfEq_hom, CategoryTheory.NatTrans.tensor_naturality_assoc, mapCommGrp_id_one, CategoryTheory.MorphismProperty.RightFraction.op_map, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_fst_assoc, CategoryTheory.MonoidalCategory.externalProductFlip_hom_app_app_app_app, CategoryTheory.NatTrans.retractArrowApp_r, CategoryTheory.Subfunctor.bot_obj, CategoryTheory.CosimplicialObject.Augmented.toArrow_obj_right, CategoryTheory.RightExactFunctor.ofExact_map, groupCohomology.cochainsMap_f, AlgebraicGeometry.Scheme.toSpecΓ_image_zeroLocus, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s₀_comp_δ₁, AlgebraicGeometry.Scheme.monObjAsOverPullback_mul, CategoryTheory.LeftExactFunctor.ofExact_obj, CategoryTheory.Iso.map_inv_hom_id_assoc, CategoryTheory.coalgebraEquivOver_counitIso, mapCommMon_map_hom_hom, AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c, SSet.nonDegenerate_iff_of_isIso, AlgebraicGeometry.instQuasiSeparatedMorphismRestrict, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_hom_app_fst_app, CategoryTheory.TransfiniteCompositionOfShape.ici_isColimit, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app_assoc, AlgebraicGeometry.HasAffineProperty.iff_of_iSup_eq_top, AlgebraicGeometry.Scheme.Hom.image_iSup, CategoryTheory.ComposableArrows.δlastFunctor_obj_obj, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality, CategoryTheory.SimplicialObject.cechNerve_obj, CategoryTheory.Limits.colimit.ι_desc_apply, Alexandrov.lowerCone_π_app, CategoryTheory.Limits.Bicones.functoriality_obj_ι, CategoryTheory.SmallObject.SuccStruct.Iteration.arrowSucc_eq, CategoryTheory.SimplicialObject.δ_comp_σ_of_le, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_fst, AlgebraicTopology.DoldKan.Γ₀.map_app, CategoryTheory.Abelian.Ext.zero_hom, AlgebraicGeometry.PresheafedSpace.stalkMap_germ_apply, CategoryTheory.extendCofan_ι_app, Rep.coind'_ext_iff, CategoryTheory.Limits.colimitLimitToLimitColimitCone_iso, FullyFaithful.mapCommMon_preimage, CategoryTheory.MonoidalCategory.externalProductBifunctorCurried_obj_obj_map_app, CategoryTheory.Limits.ι_comp_colimitRightOpIsoUnopLimit_hom, CategoryTheory.Limits.reflexiveCoforkEquivCofork_inverse_obj_pt, LeftExtension.IsPointwiseLeftKanExtension.isIso_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionObj, HeytAlg.hasForgetToLat_forget₂_obj_isBoundedOrder, RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π, CategoryTheory.Localization.SmallShiftedHom.equiv_shift, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map_d, CategoryTheory.Limits.kernelComparison_comp_kernel_map, LeftExtension.precomp_obj_left, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.inverse_obj_map, topToLocale_map, OplaxMonoidal.left_unitality_hom, LaxLeftLinear.μₗ_associativity, CategoryTheory.Abelian.isoModSerre_kernel_eq_leftBousfield_W_of_rightAdjoint, CategoryTheory.TransportEnrichment.eComp_eq, shiftIso_hom_naturality_assoc, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_right, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac', CategoryTheory.ShiftMkCore.add_zero_inv_app, imageSubobjectIso_imageToKernel', CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_obj, DerivedCategory.instIsLEObjSingleFunctor, OplaxMonoidal.ofBifunctor.leftMapₗ_app, CategoryTheory.Endofunctor.Coalgebra.Terminal.str_isIso, Monoidal.inv_ε, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_snd_coe, CategoryTheory.Limits.Fork.condition, sectionsEquivHom_naturality_symm, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id_assoc, CategoryTheory.Arrow.mk_eq, CategoryTheory.hoFunctor.isIso_prodComparison_stdSimplex, CategoryTheory.MorphismProperty.CostructuredArrow.toOver_obj, CategoryTheory.HasShift.Induced.zero_hom_app_obj, Types.monoOverEquivalenceSet_functor_obj, Bipointed.swapEquiv_counitIso_inv_app_toFun, groupHomology.chainsMap_comp, TopCat.Presheaf.stalkSpecializes_stalkFunctor_map, IsEventuallyConstantFrom.coconeιApp_eq, AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv_assoc, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_two_assoc, CategoryTheory.Equalizer.Presieve.w, CategoryTheory.Limits.imageSubobject_arrow, Monoidal.tensorHom_app_fst, CategoryTheory.MorphismProperty.Under.w, CategoryTheory.Limits.coneLeftOpOfCocone_π_app, AlgebraicGeometry.Scheme.homOfLE_app, AlgebraicGeometry.SheafedSpace.Γ_obj_op, map_finite_effectiveEpiFamily, CategoryTheory.InjectiveResolution.Hom.ι_f_zero_comp_hom_f_zero, CategoryTheory.CosimplicialObject.Augmented.toArrow_obj_hom, DerivedCategory.instIsGEObjCochainComplexIntQOfIsGE, PresheafOfModules.Elements.fromFreeYoneda_app_apply, CategoryTheory.StructuredArrow.mapIso_functor_map_left, CategoryTheory.Monad.FreeCoequalizer.π_f, CategoryTheory.Limits.imageSubobject_comp_le_epi_of_epi, IsLocallyFaithful.functorPushforward_equalizer_mem, CategoryTheory.Localization.Monoidal.lifting₂CurriedTensorPost_iso, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.e_inv_app, sheafPushforwardContinuousId_hom_app_val_app, AlgebraicGeometry.PresheafedSpace.sheafIsoOfIso_hom, CategoryTheory.ShiftedHom.add_comp, ModuleCat.binaryProductLimitCone_cone_π_app_left, CategoryTheory.Equalizer.Presieve.Arrows.compatible_iff_of_small, flipping_unitIso_inv_app_app_app, CategoryTheory.isIso_iff_of_reflects_iso, HomologicalComplex.homologyπ_singleObjHomologySelfIso_hom, CategoryTheory.Equivalence.core_functor_obj_of, SSet.Truncated.comp_app_assoc, CategoryTheory.Coyoneda.colimitCocone_pt, AlgebraicGeometry.Scheme.Hom.comp_preimage, CategoryTheory.liftedLimitMapsToOriginal_inv_map_π, CategoryTheory.Adjunction.homAddEquiv_symm_neg, CategoryTheory.Bimon.equivMonComonUnitIsoApp_inv_hom_hom, ModuleCat.HasColimit.coconePointSMul_apply, SSet.Truncated.Edge.map_tensorHom, SheafOfModules.ιFree_mapFree_inv, CategoryTheory.Bimon.ofMon_Comon_toMon_Comon_obj_counit, PresheafOfModules.pushforward_obj_obj, AlgebraicGeometry.Scheme.kerFunctor_map, CategoryTheory.PreGaloisCategory.functorToAction_map, obj.ι_def, CategoryTheory.Comonad.Coalgebra.Hom.h_assoc, CategoryTheory.Adjunction.shift_unit_app, CategoryTheory.IsPullback.map_iff, mapHomotopyEquiv_homotopyInvHomId, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_fst_obj, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃'_obj_obj_obj, CategoryTheory.TwoSquare.hasPointwiseLeftKanExtensionAt_iff, CategoryTheory.MorphismProperty.Comma.prop, AlgebraicGeometry.Scheme.Modules.instIsIsoAbApp, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.instIsIsoMapF, CategoryTheory.Adjunction.map_η_comp_η_assoc, AlgebraicGeometry.Scheme.Hom.naturality_assoc, CategoryTheory.Sieve.functorPullback_pullback, PushoutObjObj.inl_ι_assoc, SSet.horn.edge₃_coe_down, SheafOfModules.Presentation.mapRelations_mapGenerators, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app_assoc, AlgebraicGeometry.Scheme.IdealSheafData.opensRange_glueDataObjMap, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self_apply, CategoryTheory.CostructuredArrow.instEssSurjCompObjPostOfFull, SimplicialObject.Split.nondegComplexFunctor_obj, HomologicalComplex.cyclesOpIso_hom_naturality, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_map_hom_hom_app, CategoryTheory.Comonad.Coalgebra.coassoc_assoc, CategoryTheory.Adjunction.unit_app_commShiftIso_hom_app_assoc, TopCat.Presheaf.pushforward_map_app', CategoryTheory.MonoOver.congr_functor, TopCat.continuous_iff_of_isColimit, LaxMonoidal.ofBifunctor.secondMap₂_app_app_app, CochainComplex.mappingConeCompHomotopyEquiv_comm₂, AlgebraicTopology.DoldKan.N₁_obj_X, AlgebraicGeometry.Scheme.Hom.iInf_ker_openCover_map_comp_apply, skyscraperPresheaf_eq_pushforward, CategoryTheory.Abelian.PreservesImage.iso_hom_ι_assoc, OplaxLeftLinear.δₗ_unitality_hom, SSet.Truncated.rightExtensionInclusion_left, FundamentalGroupoid.punitEquivDiscretePUnit_unitIso, CategoryTheory.Pseudofunctor.IsStack.essSurj_of_sieve, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₂₃_assoc, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.sheafCondition_iff_bijective_toPullbackObj, CategoryTheory.Subobject.imageFactorisation_F_I, SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero_assoc, CategoryTheory.Limits.KernelFork.app_one, RepresentableBy.uniqueUpToIso_hom, CondensedSet.topCatAdjunctionUnit_val_app, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac'_assoc, AlgebraicGeometry.eq_zero_of_basicOpen_eq_bot, AlgebraicTopology.map_alternatingFaceMapComplex, hasPointwiseLeftDerivedFunctorAt_iff, CategoryTheory.SimplicialObject.δ_comp_σ_self, CategoryTheory.CostructuredArrow.homMk'_mk_comp, sheafPushforwardContinuousId'_inv_app_val_app, preservesFilteredColimits_coyoneda, CategoryTheory.instEpiAppOfFunctor, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso_hom_app_f, CategoryTheory.NatIso.hom_app_isIso, coneOfIsRightKanExtension_π, CategoryTheory.Over.associator_inv_left_fst_fst, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app_assoc, Final.exists_coeq, CategoryTheory.Limits.Fork.app_zero_eq_ι, CategoryTheory.uliftYoneda_map_app, AlgebraicGeometry.Scheme.Hom.normalizationCoprodIso_inv_coprodDesc_fromNormalization, CategoryTheory.Limits.Cones.postcomposeComp_inv_app_hom, CategoryTheory.SmallObject.SuccStruct.ofCocone_obj_eq_pt, IsEventuallyConstantTo.isoMap_hom_inv_id, prod'_η_snd, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_carrier, CategoryTheory.Preadditive.commGrpEquivalenceAux_inv_app_hom_hom_hom, CategoryTheory.Limits.limit.cone_π, leftExtensionEquivalenceOfIso₁_functor_obj_hom_app, CategoryTheory.Presieve.isSheafFor_over_map_op_comp_ofArrows_iff, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_map_right_right, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_pt, CategoryTheory.Comma.mapLeftIso_inverse_obj_hom, CategoryTheory.Localization.SmallHom.equiv_chgUniv, CategoryTheory.Limits.IsLimit.isIso_limMap_π, map_opShiftFunctorEquivalence_counitIso_hom_app_unop, DerivedCategory.exists_iso_singleFunctor_obj_of_isGE_of_isLE, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_hom_app_val_app_apply, CategoryTheory.SingleFunctors.postcompFunctor_obj, CategoryTheory.Subobject.inf_map, Monoidal.whiskerLeft_app_snd, relativelyRepresentable.of_diag, CategoryTheory.Limits.Types.Colimit.ι_desc_apply, mapGrp_map_hom_hom, FundamentalGroupoid.map_eq, mapConePostcomposeEquivalenceFunctor_inv_hom, SSet.stdSimplex.const_down_toOrderHom, uliftYonedaReprXIso_hom_app, TopCat.Presheaf.pushforward_obj_map, CategoryTheory.Sum.homInduction_right, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_unitIso, CategoryTheory.Limits.Sigma.ι_isoColimit_hom, AlgCat.forget₂_module_obj, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_isoBot, CategoryTheory.Limits.map_π_preserves_coequalizer_inv_assoc, AlgebraicGeometry.Scheme.inv_appTop, whiskeringLeft₂_map_app_app_app_app, CategoryTheory.NatTrans.naturality_1_assoc, CategoryTheory.ComposableArrows.opEquivalence_functor_obj_obj, HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac_assoc, CategoryTheory.Limits.FormalCoproduct.cochainComplexFunctor_obj_X, CategoryTheory.Pretriangulated.TriangleMorphism.comm₃_assoc, AddCommGrpCat.leftExactFunctorForgetEquivalence.instPreservesFiniteLimitsObjLeftExactFunctorTypeFunctorInverseAux, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app, CategoryTheory.Limits.limit.lift_π_apply, CategoryTheory.Limits.DiagramOfCones.conePoints_obj, CategoryTheory.Adjunction.inv_counit_map, CategoryTheory.Limits.SingleObj.colimitTypeRel_iff_orbitRel, pointedToBipointedCompBipointedToPointedSnd_inv_app_toFun, AlgebraicGeometry.isLocalization_away_of_isAffine, CategoryTheory.Presieve.isSheafFor_over_map_op_comp_iff, AlgebraicGeometry.Scheme.Hom.isIso_app, CategoryTheory.equivYoneda_hom_app, CategoryTheory.Monad.FreeCoequalizer.bottomMap_f, CategoryTheory.CartesianMonoidalCategory.preservesTerminalIso_hom, CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse_obj_right_as, CategoryTheory.Limits.ColimitPresentation.Total.Hom.comp_hom, Monoidal.μ_comp, CochainComplex.HomComplex.Cochain.δ_toSingleMk, CategoryTheory.Presheaf.instIsCardinalPresentableFunctorOppositeTypeObjUliftYonedaOfHasColimitsOfSize, AlgebraicGeometry.IsAffineOpen.ι_basicOpen_preimage, groupCohomology.map_id_comp_assoc, mapTriangleOpCompTriangleOpEquivalenceFunctorApp_hom_hom₃, CommMonCat.uliftFunctor_obj_coe, TopologicalSpace.Opens.map_iSup, TopCat.Presheaf.presheafEquivOfIso_unitIso_inv_app_app, SSet.horn₂₁.isPushout, CategoryTheory.unit_mateEquiv_symm, prod'_map, CategoryTheory.CommGrp.forget₂Grp_map_hom, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_right, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁'_obj_map_app, CategoryTheory.Comma.mapLeftId_hom_app_left, CategoryTheory.Limits.isKernelCompMono_lift, CategoryTheory.Limits.pullbackConeOfRightIso_π_app_left, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_left_assoc, CategoryTheory.Comma.post_obj_left, CategoryTheory.Equivalence.core_functor_map_iso_inv, SheafOfModules.relationsOfIsCokernelFree_I, ProfiniteGrp.cone_π_app, CategoryTheory.Over.snd_left, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_map_left_left, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd, CategoryTheory.SimplicialObject.δ_comp_σ_of_gt_assoc, CochainComplex.HomComplex.CohomologyClass.toHom_bijective, CategoryTheory.ComposableArrows.fourδ₂Toδ₁_app_three, Monoidal.whiskerRight_μ_δ, CategoryTheory.Limits.Trident.ofCone_π, CategoryTheory.Triangulated.SpectralObject.distinguished', AlgebraicGeometry.instIsOpenImmersionInlScheme, CategoryTheory.Equivalence.symmEquiv_counitIso, map_opShiftFunctorEquivalence_counitIso_inv_app_unop_assoc, CategoryTheory.Limits.ImageMap.map_ι, curryingEquiv_apply_map, CategoryTheory.Bifunctor.diagonal, partialFunEquivPointed_functor_obj_X, CompHausLike.pullback.cone_π, CategoryTheory.Sieve.functorPushforward_pullback_le, CategoryTheory.Limits.Cocone.w, CategoryTheory.NatTrans.app_sum, CategoryTheory.MonoOver.congr_inverse, flip₁₃Functor_obj_obj_map_app, CategoryTheory.Limits.PreservesEqualizer.iso_inv_ι, Monoidal.commTensorLeft_inv_app, CategoryTheory.CostructuredArrow.prodInverse_map, Rep.linearizationTrivialIso_inv_hom, Rep.isZero_Tor_succ_of_projective, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_fst_assoc, CategoryTheory.Limits.Types.Small.limitConeIsLimit_lift, initial_iff_of_isCofiltered, AddCommMonCat.coe_forget₂_obj, CategoryTheory.Adjunction.Triple.epi_rightToLeft_app_iff, leibnizPushout_obj_obj, CategoryTheory.Join.mapPairId_inv_app, const.opObjOp_inv_app, CategoryTheory.Pseudofunctor.map₂_left_unitor_app, CategoryTheory.tensoringLeft_additive, CategoryTheory.LocalizerMorphism.RightResolution.Hom.comm, AlgebraicGeometry.structureSheafInType.add_apply, LaxMonoidal.tensorUnit_whiskerLeft_comp_leftUnitor_hom_assoc, CategoryTheory.Limits.prodComparison_natural_of_natTrans, CategoryTheory.MonoidalCategory.Functor.curriedTensorPreIsoPost_hom_app_app, CorepresentableBy.equivUliftCoyonedaIso_symm_apply_homEquiv, instMonoImageToKernel, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ_assoc, CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj, CategoryTheory.Iso.core_hom_app_iso_inv, map_comp_assoc, groupHomology.chainsMap_f_0_comp_chainsIso₀_assoc, AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap, CategoryTheory.ObjectProperty.IsDetecting.isIso_iff_of_mono, SSet.Subcomplex.fromPreimage_app_coe, CategoryTheory.Equivalence.cancel_unit_right_assoc', CategoryTheory.FunctorToTypes.functorHomEquiv_apply_app, AlgebraicTopology.DoldKan.MorphComponents.preComp_φ, CategoryTheory.Comma.mapLeftId_inv_app_left, SSet.horn_eq_iSup, AlgebraicGeometry.morphismRestrict_appTop, commShiftOfLocalization.iso_hom_app, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_right, AlgebraicGeometry.Scheme.Hom.exists_mem_and_isIso_morphismRestrict_toNormalization, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_map_fst_app, splitMonoBiproductComparison'_retraction, AlgebraicGeometry.Scheme.IdealSheafData.ofIdealTop_ideal, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_self_assoc, CategoryTheory.Comonad.delta_naturality, SSet.Subcomplex.homOfLE_app_val, mapMonIdIso_inv_app_hom, CategoryTheory.monoidalOfHasFiniteProducts.instIsIsoδ, Rep.quotientToInvariantsFunctor_obj_V, fun_inv_map, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π, CategoryTheory.Limits.piConst_obj_obj, AlgebraicTopology.DoldKan.Γ₀_obj_obj, CategoryTheory.Iso.isoCompInverse_inv_app, CategoryTheory.NatTrans.app_shift_assoc, CochainComplex.HomComplex.Cochain.fromSingleMk_precomp, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality, CategoryTheory.Monoidal.FunctorCategory.tensorObj_obj, postcompose₂_obj_map_app_app, instIsCommMonObjOppositeCommAlgCatXUnopMonObjCommBialgCatFunctorCommBialgCatEquivComonCommAlgCatOfIsCocommCarrier, CategoryTheory.Arrow.isIso_hom_iff_isIso_hom_of_isIso, CategoryTheory.Tor'_obj_map, LightCondensed.underlying_obj, CategoryTheory.Presieve.IsSheafFor.functorInclusion_comp_extend, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_app_assoc, CategoryTheory.Limits.evaluation_preservesColimits, CategoryTheory.GradedObject.comapEq_hom_app, mapConePostcomposeEquivalenceFunctor_hom_hom, CategoryTheory.Triangulated.TStructure.triangleLTGE_obj_obj₁, CategoryTheory.sum.inrCompAssociator_hom_app_down_down, CategoryTheory.Limits.limit.conePointUniqueUpToIso_hom_comp, AlgebraicTopology.DoldKan.Q_f_naturality_assoc, CategoryTheory.Limits.pullbackObjIso_hom_comp_fst_assoc, CategoryTheory.CommGrp.forget₂CommMon_obj_mul, CategoryTheory.Comma.fromProd_map_right, CategoryTheory.MonoidalCategory.curriedTensor_obj_obj, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_limit_map, CategoryTheory.Limits.ι_comp_coequalizerComparison_assoc, TopCat.Presheaf.stalkPushforward_germ, CategoryTheory.Limits.Cocones.functorialityEquivalence_counitIso, CategoryTheory.ActionCategory.curry_apply_left, mapCone_π_app, CategoryTheory.yonedaMap_app_apply, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceFunctor_map_base, CategoryTheory.ε_app_obj, commAlgCatEquivUnder_unitIso, toSheafify_pullbackSheafificationCompatibility, HomologicalComplex.singleObjCyclesSelfIso_inv_iCycles_assoc, CochainComplex.HomComplex.Cochain.leftUnshift_add, CategoryTheory.WithTerminal.widePullbackShapeEquiv_inverse_obj, CategoryTheory.Over.tensorHom_left_fst, CategoryTheory.Sheaf.ΓHomEquiv_naturality_right_symm, AlgebraicGeometry.SheafedSpace.comp_hom_c_app', CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_obj, CategoryTheory.Comma.equivProd_inverse_obj_right, map_units_smul, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_right_assoc, CategoryTheory.Square.fromArrowArrowFunctor_obj_X₄, IsCoverDense.Types.naturality_apply, SSet.stdSimplex.obj₀Equiv_symm_mem_face_iff, 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, AlgebraicGeometry.Scheme.Hom.preimage_opensRange, CategoryTheory.Equivalence.induced_unitIso, CategoryTheory.Equivalence.sheafCongr.functor_obj_val_map, CategoryTheory.Limits.limit_map_limitObjIsoLimitCompEvaluation_hom_assoc, CategoryTheory.AdditiveFunctor.ofRightExact_obj_fst, CategoryTheory.ShortComplex.ShortExact.singleTriangle_obj₁, 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.Over.whiskerRight_left_snd, TopCat.Presheaf.stalkPushforward.id, germ_skyscraperPresheafStalkOfSpecializes_hom_assoc, CategoryTheory.Under.instIsEquivalenceObjPost, pointedToBipointedCompBipointedToPointedFst_inv_app_toFun, CategoryTheory.Iso.isoInverseOfIsoFunctor_inv_app, CategoryTheory.Comonad.comparison_map_f, CategoryTheory.SmallObject.SuccStruct.ofCocone_map_to_top, FinBoolAlg.hasForgetToFinPartOrd_forget₂_obj_isFintype, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_apply, CategoryTheory.DifferentialObject.shiftFunctor_map_f, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_π_app, commShiftIso_id_hom_app, SSet.Subcomplex.PairingCore.nonDegenerate₂, CategoryTheory.Grothendieck.ιCompMap_inv_app_base, lanAdjunction_unit, CategoryTheory.ComposableArrows.whiskerLeftFunctor_map_app, CategoryTheory.Over.conePostIso_inv_app_hom, CategoryTheory.Limits.Types.binaryProductFunctor_obj_obj, CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair_inv_app, leftDerivedZeroIsoSelf_inv_hom_id_app, CategoryTheory.PreGaloisCategory.fiber_in_connected_component, CategoryTheory.instSmallHomDerivedCategoryObjSingleFunctorOfHasExt, PreservesPointwiseRightKanExtensionAt.preserves, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_mapPullbackAdj_unit_app, PresheafOfModules.restrictScalars_obj, shiftIso_hom_app_comp_assoc, CategoryTheory.algebraEquivUnder_unitIso, CategoryTheory.Sheaf.coneΓ_π_app, CategoryTheory.SimplicialObject.Truncated.trunc_map_app, SSet.prodStdSimplex.instFiniteTensorObjObjSimplexCategoryStdSimplexMk, LaxLeftLinear.μₗ_naturality_left, CategoryTheory.Comonad.ComonadicityInternal.main_pair_coreflexive, AlgebraicGeometry.isOpenImmersion_sigmaDesc, CategoryTheory.WithInitial.map_map, CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_hom_π_π, CategoryTheory.ShortComplex.ShortExact.surjective_g, CategoryTheory.Limits.Fork.equivOfIsos_inverse_obj_ι, CategoryTheory.MorphismProperty.structuredArrowObj_iff, SSet.stdSimplex.objEquiv_symm_comp, CategoryTheory.SimplicialObject.Augmented.w₀_assoc, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃_assoc, OneHypercoverDenseData.essSurj.presheafObj_condition, curryObjCompIso_inv_app_app, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen, CategoryTheory.Adjunction.Triple.leftToRight_app_map_adj₁_unit_app_assoc, CategoryTheory.Equivalence.core_counitIso_hom_app_iso_hom, CategoryTheory.Subfunctor.range_obj, CategoryTheory.Limits.instIsIsoSigmaComparison, TopCat.Presheaf.germ_stalkPullbackHom_assoc, CategoryTheory.Equivalence.inv_fun_map_assoc, CategoryTheory.PresheafOfGroups.OneCochain.ev_precomp, CategoryTheory.Limits.pullbackComparison_comp_snd_assoc, biprodComparison_snd, CategoryTheory.Square.fromArrowArrowFunctor'_obj_X₄, CategoryTheory.Limits.FormalCoproduct.instPreservesLimitOppositeDiscreteFunctorCompOpObjFunctorEvalOp, TopCat.Presheaf.whiskerIsoMapGenerateCocone_hom_hom, AlgebraicGeometry.LocallyRingedSpace.Γ_map, CategoryTheory.Discrete.natIso_hom_app, CategoryTheory.Subobject.factorThru_ofLE, AlgebraicGeometry.coprodSpec_inr_assoc, CategoryTheory.Equivalence.inverse_counitInv_comp_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd_assoc, CategoryTheory.Limits.PreservesKernel.iso_hom, CategoryTheory.GrothendieckTopology.Cover.multicospanComp_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_snd_map, mapCommGrpIdIso_hom_app_hom_hom_hom, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_inv_app_val_app, ModuleCat.ihom_map_apply, AlgebraicGeometry.isCompactOpen_iff_eq_basicOpen_union, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd, CategoryTheory.Equivalence.induced_inverse_obj, HomotopicalAlgebra.CofibrantObject.HoCat.adjCounitIso_inv_app, TopCat.Presheaf.presheafEquivOfIso_functor_obj_obj, CategoryTheory.CategoryOfElements.π_obj, CategoryTheory.ShortComplex.zero_apply, CategoryTheory.WithTerminal.commaFromOver_obj_hom_app, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransEq_hom_app_f, AlgebraicGeometry.PresheafedSpace.componentwiseDiagram_obj, AlgebraicGeometry.AffineSpace.functor_obj_obj, CategoryTheory.Sieve.arrows_generate_map_eq_functorPushforward, CategoryTheory.Sheaf.ΓObjEquivHom_naturality, CategoryTheory.obj_μ_inv_app, ModuleCat.ihom_coev_app, CategoryTheory.Idempotents.Karoubi.retract_i_f, CategoryTheory.StructuredArrow.map_obj_left, HomologicalComplex.HomologySequence.snakeInput_L₀, CategoryTheory.Limits.colimit.ι_desc, CategoryTheory.NatTrans.appHom_apply, CategoryTheory.Limits.coneOfConeUncurry_π_app, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_left_symm, CategoryTheory.SimplicialObject.whiskering_obj_obj_obj, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app, IsRepresentedBy.uliftYonedaIso_hom, SemiNormedGrp.completion_obj_str, CategoryTheory.MorphismProperty.mem_toSet_iff, Elements.initialOfCorepresentableBy_fst, OplaxMonoidal.associativity_inv, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_σ_assoc, CategoryTheory.NatTrans.mapElements_obj, CategoryTheory.Sheaf.ΓRes_map, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_self, CategoryTheory.Equivalence.core_inverse_map_iso_inv, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv, PreOneHypercoverDenseData.multicospanIndex_right, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinset_map_app, SheafOfModules.pushforwardCongr_symm, mapCommMon_obj_mon_one, Monoidal.μ_fst, CategoryTheory.Idempotents.DoldKan.Γ_obj_map, RightExtension.IsPointwiseRightKanExtension.isRightKanExtension, const.unop_functor_op_obj_map, leftOpComp_inv_app, CategoryTheory.Limits.MonoCoprod.mono_inl_iff, CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj_obj_p, CategoryTheory.NatTrans.tensor_naturality, instIsCorepresentableCompObjOppositeTypeCoyonedaOpObjLeftAdjointObjIsDefined, CategoryTheory.Iso.op2_unop_inv_unop2, Rep.coinvariantsTensorIndNatIso_hom_app, CommShift.ofIso_commShiftIso_inv_app, CategoryTheory.CartesianMonoidalCategory.preservesTerminalIso_comp, CategoryTheory.MonObj.ofRepresentableBy_mul, CategoryTheory.Limits.Cones.forget_obj, CategoryTheory.Preadditive.toCommGrp_obj_grp, CategoryTheory.ComposableArrows.fourδ₂Toδ₁_app_zero, CategoryTheory.Limits.Types.jointly_surjective_of_isColimit, CategoryTheory.Limits.evaluation_preservesColimitsOfShape, CategoryTheory.LocalizerMorphism.homMap_comp_assoc, PresheafOfModules.instAdditiveModuleCatCarrierObjOppositeRingCatEvaluation, CategoryTheory.evaluationRightAdjoint_obj_obj, CategoryTheory.Over.iteratedSliceEquiv_unitIso, CategoryTheory.Localization.homEquiv_refl, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_π_assoc, groupHomology.congr, SSet.Truncated.mapHomotopyCategory_obj, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMop_map_unmop_app, CategoryTheory.Localization.instHasSmallLocalizedHomObjShiftFunctor_3, CategoryTheory.InjectiveResolution.ι'_f_zero_assoc, CategoryTheory.MorphismProperty.IsStableUnderTransfiniteCompositionOfShape.of_isStableUnderColimitsOfShape.mem_map_bot_le, CategoryTheory.underToAlgebra_obj_a, Rep.standardComplex.quasiIso_forget₂_εToSingle₀, SimplexCategoryGenRel.simplicialEvalσ_of_isAdmissible, CategoryTheory.Comma.toPUnitIdEquiv_unitIso_hom_app_left, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit_assoc, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₃, AlgebraicGeometry.LocallyRingedSpace.stalkMap_germ_apply, CategoryTheory.CatCommSq.vInv_iso_inv_app, LaxMonoidal.whiskeringRight_ε_app, CategoryTheory.regularTopology.equalizerCondition_w', CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_naturality₂, CategoryTheory.Localization.homEquiv_trans, CategoryTheory.CommSq.of_arrow, CochainComplex.shiftFunctorZero'_inv_app_f, CategoryTheory.Comonad.CofreeEqualizer.ι_f, CategoryTheory.Prod.sectR_obj, CategoryTheory.Presieve.image_mem_functorPushforward, CategoryTheory.Limits.ι_colimitOfIsReflexivePairIsoCoequalizer_hom, CategoryTheory.Limits.Multicofork.fst_app_right, FullyFaithful.autMulEquivOfFullyFaithful_symm_apply_inv, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse_assoc, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_cofanPtIsoSelf_inv, CategoryTheory.Limits.BinaryBicones.functoriality_obj_fst, SSet.ι₀_comp_assoc, AlgebraicGeometry.instIsOpenImmersionMapWalkingSpanSchemeSpan, CommGrpCat.coyonedaForget_hom_app_app_hom, HomotopicalAlgebra.CofibrantObject.HoCat.adjUnit_app, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv', constCompEvaluationObj_inv_app, TopCat.GlueData.MkCore.t_id, CategoryTheory.oppositeShiftFunctorZero_hom_app, mapSquare_obj, CategoryTheory.Comma.mapRightIso_unitIso_hom_app_left, AlgebraicGeometry.HasAffineProperty.affineAnd_iff, CategoryTheory.Limits.limitCompYonedaIsoCocone_inv, HomologicalComplex.singleMapHomologicalComplex_inv_app_ne, AddMonCat.adjoinZero_obj_coe, PresheafOfModules.Hom.naturality_assoc, CategoryTheory.WithInitial.equivComma_unitIso_inv_app_app, CategoryTheory.MonoidalOpposite.tensorRightIso_inv_app_unmop, CategoryTheory.Limits.asEmptyCone_π_app, CategoryTheory.FunctorToTypes.coprod.inl_app, CategoryTheory.Limits.CompleteLattice.finiteLimitCone_cone_pt, LaxRightLinear.μᵣ_unitality, CategoryTheory.nerve_map, CochainComplex.HomComplex.Cochain.rightShift_units_smul, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_functor_obj_V, AlgebraicGeometry.IsOpenImmersion.app_eq_appIso_inv_app_of_comp_eq, CategoryTheory.Limits.Fork.op_ι_app, CategoryTheory.ShortComplex.hasLeftHomology_of_preserves', AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.c_iso, instIsEquivalenceObjWhiskeringRight, CategoryTheory.Comma.fromProd_map_left, LaxMonoidal.μ_whiskerRight_comp_μ_assoc, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_obj_f, CategoryTheory.Idempotents.Karoubi.decompId_i_toKaroubi, CategoryTheory.SimplicialObject.cechNerveEquiv_symm_apply, AlgebraicGeometry.Scheme.IdealSheafData.ker_subschemeι_app, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counitIso_hom_app_assoc, CategoryTheory.ProjectiveResolution.self_complex, CategoryTheory.ObjectProperty.isColocal_iff_isIso_map, Preorder.isLUB_of_isColimit, AlgebraicGeometry.IsOpenImmersion.ΓIso_inv, CategoryTheory.SimplicialObject.Augmented.const_obj_left, AlgebraicGeometry.Scheme.Modules.Hom.sub_app, CategoryTheory.functorProdFunctorEquivCounitIso_inv_app_app, CategoryTheory.ShortComplex.mapCyclesIso_hom_naturality_assoc, CategoryTheory.ι_preservesColimitIso_hom, AlgebraicTopology.alternatingCofaceMapComplex_obj, CategoryTheory.instHasSmallLocalizedShiftedHomHomologicalComplexIntUpQuasiIsoObjCochainComplexCompSingleFunctorOfNatOfHasExt, Monoidal.tensorHom_app_snd, prod_δ_snd, BddLat.coe_forget_to_lat, HomologicalComplex.dgoToHomologicalComplex_map_f, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.iso_hom_naturality_assoc, AlgebraicGeometry.IsOpenImmersion.range_pullback_snd_of_left, AlgebraicGeometry.LocallyRingedSpace.restrict_presheaf_map, CategoryTheory.algebraToUnder_obj, sum'_map_inl, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_incl, IsEventuallyConstantTo.isIso_π_of_isLimit, CategoryTheory.MonoidalClosed.curry_natural_left_assoc, CategoryTheory.ObjectProperty.ι_μ, OplaxMonoidal.ofBifunctor.bottomMapᵣ_app, CategoryTheory.associativity_app_assoc, CategoryTheory.Limits.equalizerSubobject_arrow, CategoryTheory.WithInitial.commaFromUnder_map_right, CategoryTheory.PreGaloisCategory.instIsPretransitiveCarrierObjFintypeCatOfIsConnected, CategoryTheory.coyonedaEquiv_coyoneda_map, CategoryTheory.Limits.ColimitPresentation.Total.Hom.w_assoc, CategoryTheory.Pretriangulated.Triangle.rotate_obj₃, DerivedCategory.exists_iso_Q_obj_of_isGE_of_isLE, CategoryTheory.TwoSquare.whiskerLeft_app, pointwiseRightKanExtensionCounit_app, CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_cancel_inv_app, ChainComplex.truncateAugment_hom_f, CategoryTheory.IsPreconnected.iso_constant, CategoryTheory.endofunctorMonoidalCategory_leftUnitor_hom_app, CategoryTheory.ShortComplex.homologyFunctor_obj, CategoryTheory.evaluationIsLeftAdjoint, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₁, CategoryTheory.Limits.Bicone.toCocone_ι_app, mapTriangleOpCompTriangleOpEquivalenceFunctorApp_inv_hom₂, CategoryTheory.CatEnriched.comp_eq, AlgebraicGeometry.ΓSpec.adjunction_homEquiv_apply, lanCompIsoOfPreserves_inv_app, CategoryTheory.WithInitial.equivComma_functor_obj_left, CategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_fst, IsEventuallyConstantTo.cone_pt, CategoryTheory.Equivalence.rightOp_functor_obj, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_app, CategoryTheory.Limits.Trident.ofι_π_app, AlgebraicGeometry.Proj.add_apply, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_inv_comp_π, AlgebraicGeometry.PresheafedSpace.Γ_obj, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_hom, CategoryTheory.Subfunctor.toFunctor_map_coe, CategoryTheory.CartesianClosed.uncurry_natural_right_assoc, CategoryTheory.Limits.map_lift_piComparison_assoc, CategoryTheory.Limits.coneOfSectionCompYoneda_π, CategoryTheory.Subobject.instMonoOfMkLE, CategoryTheory.CosimplicialObject.σ_comp_σ, CategoryTheory.Equivalence.map_η_comp_η_assoc, HomotopyCategory.mem_quasiIso_iff, OplaxMonoidal.δ_fst, CategoryTheory.Limits.imageSubobject_arrow_comp_assoc, CategoryTheory.shiftZero', CategoryTheory.Limits.coend.ι_map, CochainComplex.HomComplex.Cochain.rightUnshift_smul, CategoryTheory.Limits.cospan_map_id, Topology.IsOpenEmbedding.functor_obj_injective, CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_hom, AlgebraicGeometry.Scheme.Opens.isoOfLE_inv_ι, mapActionCongr_inv, CategoryTheory.CostructuredArrow.toStructuredArrow_obj, AlgebraicGeometry.Scheme.Hom.ι_toNormalization_assoc, CategoryTheory.Monoidal.InducingFunctorData.whiskerRight_eq, CoalgCat.forget₂_obj, HomotopyCategory.composableArrowsFunctor_map, HomotopicalAlgebra.CofibrantObject.instWeakEquivalenceIBifibrantResolutionObj, OneHypercoverDenseData.isSheaf_iff.fac_assoc, CategoryTheory.Pseudofunctor.toDescentData_obj, CategoryTheory.Limits.isIso_kernelSubobject_zero_arrow, CategoryTheory.Limits.ι_comp_sigmaObjIso_hom_assoc, flip_obj_map, CommRingCat.equalizer_ι_isLocalHom', CategoryTheory.Mat_.ι_additiveObjIsoBiproduct_inv, CategoryTheory.Limits.diagramIsoParallelFamily_hom_app, coreId_hom_app_iso_inv, instIsMonHomε, CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_hom, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.forgetToPresheafedSpacePreservesOpenImmersion, CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ, CategoryTheory.ParametrizedAdjunction.unit_whiskerRight_map_assoc, CategoryTheory.Over.star_map_left, CategoryTheory.SimplicialObject.δ_naturality_assoc, mapTriangleCompIso_inv_app_hom₁, CategoryTheory.simplicialCosimplicialEquiv_inverse_obj, AlgebraicGeometry.PresheafedSpace.toRestrictTop_c, CategoryTheory.Comma.preRight_obj_hom, SSet.ι₀_comp, CategoryTheory.Limits.colimit.post_post, CategoryTheory.Comma.unopFunctor_map, CategoryTheory.ShrinkHoms.equivalence_counitIso, CategoryTheory.Arrow.isIso_of_isIso, AlgebraicGeometry.IsLocalAtTarget.restrict, CategoryTheory.Arrow.rightFunc_obj, CategoryTheory.Limits.walkingCospanOpEquiv_functor_obj, CategoryTheory.Over.tensorHom_left_fst_assoc, Topology.IsInducing.map_functorObj, pi'CompEval_inv_app, 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, groupCohomology.H1InfRes_g, CategoryTheory.Monad.algebraFunctorOfMonadHom_obj_a, CategoryTheory.Enriched.FunctorCategory.functorEnrichedHom_obj, CategoryTheory.forgetAdjToOver.homEquiv_symm, CategoryTheory.nerve.δ_obj, AlgebraicTopology.DoldKan.natTransPInfty_f_app, map_inv_hom_assoc, toEventualRanges_map, CategoryTheory.Bicategory.associatorNatIsoMiddle_hom_app, CategoryTheory.preservesLimitIso_hom_π_assoc, CondensedSet.isDiscrete_tfae, CategoryTheory.Idempotents.DoldKan.Γ_obj_obj, CategoryTheory.linearCoyoneda_obj_map, CategoryTheory.Equivalence.symmEquiv_unitIso, CategoryTheory.Under.postMap_app, pointedToBipointedCompBipointedToPointedFst_hom_app_toFun, HomologicalComplex.single_map_f_self, AlgebraicGeometry.Scheme.Hom.fromNormalization_app_assoc, Profinite.exists_locallyConstant, CategoryTheory.Limits.instIsIsoPullbackComparison, AlgebraicGeometry.Scheme.isoSpec_inv_toSpecΓ_assoc, GrpCat.FilteredColimits.colimit_mul_mk_eq, CategoryTheory.simplicialCosimplicialEquiv_functor_map_app, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.functor_map_app_hom, ChainComplex.fromSingle₀Equiv_symm_apply_f_zero, leftOpRightOpEquiv_counitIso_hom_app_app, CochainComplex.HomComplex.Cocycle.equivHomShift'_apply, CategoryTheory.MorphismProperty.LeftFraction.map_ofInv_hom_id_assoc, CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder_obj, CochainComplex.instQuasiIsoIntMapHomologicalComplexUpShiftFunctor, CategoryTheory.CatCommSq.hComp_iso_inv_app, PreOneHypercoverDenseData.toPreOneHypercover_X, CategoryTheory.OverPresheafAux.restrictedYonedaObj_obj, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_pt, AlgebraicGeometry.ProjectiveSpectrum.Proj.isIso_toSpec, CategoryTheory.OverPresheafAux.MakesOverArrow.app, CategoryTheory.Pseudofunctor.map₂_whisker_right_app_assoc, ContinuousMap.piComparison_fac, MonObj.mopEquiv_functor_obj_X_unmop, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app_apply, AlgebraicGeometry.Scheme.IdealSheafData.ideal_iInf, CategoryTheory.InjectiveResolution.Hom.ι'_comp_hom'_assoc, Monoidal.ε_of_cartesianMonoidalCategory, AlgebraicGeometry.IsAffineOpen.primeIdealOf_eq_map_closedPoint, AlgebraicGeometry.Scheme.Hom.isoImage_inv_ι, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_inr, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_hom, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_π_app, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp, Fiber.fiberInclusion_obj_inj, CategoryTheory.ExactFunctor.whiskeringRight_map_app, CategoryTheory.DifferentialObject.shiftFunctorAdd_inv_app_f, CommGrpTypeEquivalenceCommGrp.inverse_obj_inv, CategoryTheory.shiftFunctorAdd_add_zero_inv_app, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_unitIso, CategoryTheory.SimplicialObject.δ_comp_σ_succ, PresheafOfModules.comp_toPresheaf_map_sheafifyHomEquiv'_symm_hom, CategoryTheory.Pretriangulated.binaryBiproductTriangle_mor₃, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃_assoc, CategoryTheory.Monad.beckCofork_π, SSet.IsStrictSegal.segal, CategoryTheory.extendFan_π_app, CategoryTheory.Discrete.equivalence_counitIso, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInrIso_hom_app_app, CategoryTheory.Over.prodLeftIsoPullback_inv_fst_assoc, CategoryTheory.Limits.lim_μ_π_assoc, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_inv_right, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_μ_app, CategoryTheory.Limits.kernel_map_comp_preserves_kernel_iso_inv, CategoryTheory.Abelian.im_obj, currying_unitIso_inv_app_app_app, CategoryTheory.MonoidalClosed.curry_natural_right_assoc, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_hom_left, CategoryTheory.PreGaloisCategory.exists_hom_from_galois_of_fiber, CategoryTheory.coreFunctor_map_app_iso_inv, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_hom_app_hom, CategoryTheory.Subobject.le_inf, CategoryTheory.OverPresheafAux.OverArrows.app_val, AlgebraicGeometry.Scheme.stalkMap_germ_apply, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι, coconeTypesEquiv_apply_ι_app, CategoryTheory.Subobject.bot_arrow, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map_val_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_δ_unmop_app, CategoryTheory.IsDetecting.isIso_iff_of_mono, CategoryTheory.Pretriangulated.Triangle.functorMk_map_hom₂, opHom_obj, AlgebraicGeometry.Scheme.Hom.isoImage_inv_ι_assoc, Rep.ihom_obj_V_isAddCommGroup, AlgebraicTopology.NormalizedMooreComplex.map_f, Monoidal.map_μ_δ, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_add, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_obj_obj_map, AlgebraicGeometry.Scheme.Hom.instIsIsoCommRingCatAppObjOpensOpensFunctor, CategoryTheory.instIsIsoAppToRightDerivedZero, currying_unitIso_hom_app_app_app, CategoryTheory.Limits.PreservesCoequalizer.iso_hom, CategoryTheory.yonedaCommGrpGrpObj_obj_coe, CategoryTheory.Discrete.sumEquiv_functor_obj, CategoryTheory.Subfunctor.range_eq_ofSection, CategoryTheory.evaluationUncurried_map, CategoryTheory.coprodMonad_η_app, CategoryTheory.linearYoneda_obj_additive, CategoryTheory.Equivalence.counitIso_inv_app_comp_functor_map_η_inverse_assoc, CategoryTheory.CosimplicialObject.Augmented.const_map_left, CategoryTheory.Join.pseudofunctorRight_mapComp_hom_toNatTrans_app, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_whiskerRight_assoc, CategoryTheory.MonoidalCategory.curriedAssociatorNatIso_inv_app_app_app, CategoryTheory.Pseudofunctor.CoGrothendieck.forget_obj, AlgebraicGeometry.Scheme.ker_morphismRestrict_ideal, CategoryTheory.Iso.unop_hom_inv_id_app_assoc, CategoryTheory.CosimplicialObject.δ_comp_δ'', CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_assoc, mapCoconeWhisker_inv_hom, HomotopicalAlgebra.BifibrantObject.instIsFibrantObjCofibrantObjectsObjCofibrantObjectιCofibrantObject, CategoryTheory.Limits.Cocone.w_apply, DerivedCategory.HomologySequence.exact₁, CategoryTheory.SmallObject.SuccStruct.Iteration.subsingleton.MapEq.src, CategoryTheory.Limits.colimit.pre_map', AlgebraicGeometry.Scheme.Modules.pushforwardId_hom_app_app, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_ι, CategoryTheory.Limits.BinaryBicone.ofLimitCone_snd, rightDerivedZeroIsoSelf_inv_hom_id_app, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app, CategoryTheory.WithInitial.inclLiftToInitial_hom_app, CategoryTheory.Limits.coprodComparison_inv_natural_assoc, AlgebraicGeometry.Scheme.Hom.germ_stalkMap, mapCocone₂_pt, CategoryTheory.Pi.sum_obj_map, CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt'_assoc, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_inv_assoc, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.fromBiprod_biprodIsoProd_inv_apply, HomologicalComplex.HomologySequence.snakeInput_L₂, PresheafOfModules.restriction_app, CategoryTheory.η_app, CategoryTheory.ShiftedHom.opEquiv_symm_apply_comp, CategoryTheory.yonedaPairing_map, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_obj_map_app, preservesFiniteLimits_iff_forall_exact_map_and_mono, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst, CategoryTheory.Localization.isoOfHom_hom_inv_id, CategoryTheory.ShortComplex.RightHomologyData.mapRightHomologyIso_eq, CategoryTheory.Over.η_pullback_left, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_hom_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app, CochainComplex.isSplitMono_from_singleFunctor_obj_of_injective, toOplaxFunctor_map, CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt, AlgebraicGeometry.ExistsHomHomCompEqCompAux.ha, AlgebraicTopology.DoldKan.Γ₂N₂ToKaroubiIso_inv_app, AlgebraicGeometry.Scheme.toOpen_eq, alexDiscEquivPreord_unitIso, groupCohomology.mapShortComplexH1_id_comp, HomotopicalAlgebra.CofibrantObject.HoCat.bifibrantResolution_obj, AlgebraicTopology.DoldKan.instMonoChainComplexNatInclusionOfMooreComplexMap, PresheafOfModules.ι_fromFreeYonedaCoproduct_apply, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_rightUnitor_hom_eq_rightUnitor_hom, CategoryTheory.LiftLeftAdjoint.instIsReflexivePairMapAppCounitOtherMap, CategoryTheory.Presieve.CoverByImageStructure.fac_assoc, CategoryTheory.BasedFunctor.w_obj, CategoryTheory.Limits.splitEpiOfIdempotentOfIsColimitCofork_section_, RightExtension.mk_left, closedIhom_obj_obj, SSet.Augmented.stdSimplex_obj_hom_app, CategoryTheory.MonoidalClosed.comp_id_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_map_fst, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_π, rightOpComp_inv_app, CategoryTheory.Limits.CategoricalPullback.Hom.w, CategoryTheory.Limits.cospanCompIso_inv_app_one, CategoryTheory.bifunctorComp₂₃FunctorObj_map_app_app_app, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_apply, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₁, TopCat.Presheaf.map_restrict, AlgebraicGeometry.Scheme.Modules.restrict_obj, CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_inv_apply, CategoryTheory.ExponentiableMorphism.coev_ev_assoc, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_inv_app_hom_hom_hom, CategoryTheory.Bimon.ofMonComon_obj, CategoryTheory.SimplicialObject.whiskering_obj_obj_map, CategoryTheory.Over.postAdjunctionRight_unit_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_inv_app_fst_app, IsTriangulated.map_distinguished, CategoryTheory.Over.conePost_obj_pt, FullyFaithful.hasShift.map_add_hom_app, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_g, SSet.horn.faceι_ι_assoc, CategoryTheory.SmallObject.SuccStruct.prop_iterationFunctor_map_succ, CategoryTheory.Square.evaluation₄_obj, HomologicalComplex.cyclesFunctor_obj, partialLeftAdjoint_obj, groupCohomology.cocyclesMap_comp_assoc, CategoryTheory.CostructuredArrow.mapNatIso_functor_obj_left, CategoryTheory.uliftYoneda_map_app_down, CategoryTheory.orderDualEquivalence_functor_obj, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_inv_app_app, Monoidal.μIso_inv, CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_none, CategoryTheory.Join.mapPairComp_hom_app_left, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_assoc, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_hom_left, CategoryTheory.unit_mateEquiv, CategoryTheory.Grp.forget₂Mon_obj_X, CategoryTheory.LocalizerMorphism.LeftResolution.hw, SimplicialObject.Splitting.decomposition_id, OplaxRightLinear.δᵣ_associativity_inv_assoc, CategoryTheory.Idempotents.FunctorExtension₁.obj_map_f, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.isPushoutAddCommGrpFreeSheaf, CategoryTheory.PreGaloisCategory.surjective_on_fiber_of_epi, mapTriangle_map_hom₃, CochainComplex.HomComplex.Cochain.δ_shift, CategoryTheory.Limits.limitConeOfUnique_isLimit_lift, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₃, CategoryTheory.sum.inrCompInlCompAssociator_hom_app_down_down, CategoryTheory.Limits.spanCompIso_hom_app_left, OrderHom.equivalenceFunctor_counitIso_hom_app_app, CategoryTheory.Sheaf.instIsLocallyInjectiveAppArrowPLocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, CategoryTheory.Limits.FormalCoproduct.evalOpCompInlIsoId_hom_app_app, whiskeringLeft_obj_map, CategoryTheory.Arrow.iso_w, CategoryTheory.Comonad.cofree_obj_a, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_right, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_pullback_obj, ModuleCat.mkOfSMul_smul, CategoryTheory.endofunctorMonoidalCategory_associator_hom_app, PresheafOfModules.free_obj, CategoryTheory.Limits.widePullbackShapeUnop_obj, RepresentableBy.ext_iff, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom, CategoryTheory.GrothendieckTopology.yoneda_obj_val, CategoryTheory.Equivalence.counitInv_app_functor, CochainComplex.HomComplex.Cochain.fromSingleMk_sub, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_inv_app_app_snd, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturality, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_hom_assoc, const.opObjUnop_inv_app, CategoryTheory.Limits.walkingParallelPairOp_zero, CategoryTheory.Over.postComp_hom_app_left, CochainComplex.toSingle₀Equiv_symm_apply_f_succ, CategoryTheory.Limits.FormalCoproduct.powerFunctor_obj, CategoryTheory.Abelian.PreservesImage.iso_inv_ι, CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_π_0, flipping_inverse_obj_map_app, CategoryTheory.Cat.Hom.id_obj, CategoryTheory.MorphismProperty.LeftFraction.Localization.instIsIsoQinv, SSet.RelativeMorphism.Homotopy.h₁_assoc, Rep.coindResAdjunction_homEquiv_symm_apply, CochainComplex.IsKProjective.leftOrthogonal, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver_map, CategoryTheory.Subfunctor.Subpresheaf.nat_trans_naturality, HomologicalComplex.singleCompEvalIsoSelf_inv_app, AlgebraicGeometry.Scheme.Hom.preimage_iSup_eq_top, CategoryTheory.Equivalence.rightOp_counitIso_hom_app, TopologicalSpace.Opens.functor_map_eq_inf, CategoryTheory.FunctorToTypes.colimit.map_ι_apply, Monoidal.map_tensor_assoc, CategoryTheory.curryingIso_inv_toFunctor_obj_obj_obj, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_obj, Profinite.lift_lifts, CategoryTheory.Limits.Trident.ι_eq_app_zero, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_unit_app_app, Monoidal.whiskerLeft_app_fst, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinset_map_app, RightExtension.postcomp₁_obj_right, OplaxMonoidal.oplax_left_unitality, CategoryTheory.Adjunction.homAddEquiv_zero, HomologicalComplex.asFunctor_obj_d, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_app_assoc, CategoryTheory.Limits.Cones.functorialityEquivalence_counitIso, CategoryTheory.yonedaPairingExt_iff, CategoryTheory.Over.whiskerLeft_left_fst, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply, CategoryTheory.Iso.op2_unop_hom_unop2, CategoryTheory.Idempotents.app_comp_p, CategoryTheory.CostructuredArrow.ofCommaFstEquivalence_counitIso, mapComon_obj_comon_counit, CategoryTheory.Discrete.functor_ext_iff, ChainComplex.augmentTruncate_hom_f_zero, DerivedCategory.from_singleFunctor_obj_eq_zero_of_projective, AlgebraicGeometry.IsLocalAtTarget.iff_of_iSup_eq_top, CategoryTheory.ProjectiveResolution.lift_commutes_assoc, CategoryTheory.evaluationLeftAdjoint_obj_obj, ModuleCat.restrictScalars.smul_def, CategoryTheory.Limits.limIsoFlipCompWhiskerLim_hom_app_app, AlgebraicGeometry.StructureSheaf.comapₗ_const, HomologicalComplex.shortComplexFunctor_obj_X₁, CategoryTheory.Endofunctor.Coalgebra.Hom.h, CategoryTheory.Limits.MultispanIndex.multispanMapIso_hom_app, leftKanExtensionUnit_leftKanExtensionObjIsoColimit_hom, CategoryTheory.isCoseparator_iff_faithful_yoneda_obj, AlgebraicTopology.DoldKan.MorphComponents.postComp_b, CategoryTheory.instPresheafIsFiniteObjFunctorOppositeTypeYoneda, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_counit_app, CategoryTheory.SmallObject.πFunctorObj_eq, AlgebraicGeometry.isCompl_opensRange_inl_inr, CategoryTheory.μ_δ_app, TopCat.Presheaf.restrictOpenCommRingCat_apply, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality_assoc, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_iff_epi₂, CategoryTheory.Comma.opEquiv_unitIso, CategoryTheory.Pretriangulated.unop_distinguished, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_hom_app_unmop, pointwiseRightKanExtension_obj, AlgebraicGeometry.Scheme.Hom.isIntegral_app, HasFibers.inducedMap_comp_assoc, CategoryTheory.StructuredArrow.mapNatIso_counitIso_hom_app_right, HasCardinalLT.Set.cocone_ι_app, HomotopyCategory.quotient_obj_as, CategoryTheory.expComparison_ev, HomologicalComplex₂.totalShift₁Iso_trans_totalShift₂Iso, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality, CategoryTheory.MonoOver.inf_map_app, AlgebraicGeometry.Scheme.Hom.app_eq_appLE, CategoryTheory.SingleFunctors.postcompPostcompIso_inv_hom_app, IsCoveringMap.monodromyFunctor_obj, CategoryTheory.PreGaloisCategory.IsFundamentalGroup.continuous_smul, CategoryTheory.Sum.functorEquivFunctorCompSndIso_inv_app_app, CategoryTheory.MorphismProperty.LeftFraction.map_hom_ofInv_id, CategoryTheory.typeEquiv_counitIso_hom_app_val_app, CategoryTheory.Discrete.compNatIsoDiscrete_inv_app, flipping_functor_obj_obj_obj, CategoryTheory.WithTerminal.map_obj, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_aux_one, prod_η_fst, CategoryTheory.Limits.Fork.op_ι_app_one, CategoryTheory.Under.postEquiv_inverse, CategoryTheory.equivOfTensorIsoUnit_functor, Monoidal.inv_δ, CategoryTheory.CategoryOfElements.toCostructuredArrow_obj, CategoryTheory.Limits.colimIsoFlipCompWhiskerColim_inv_app_app, DerivedCategory.exists_iso_Q_obj_of_isGE, CategoryTheory.ShortComplex.mapCyclesIso_inv_naturality_assoc, CategoryTheory.LaxFunctor.mapComp_assoc_left_app, CategoryTheory.Comma.mapRightId_hom_app_right, SemiNormedGrp.completion.lift_comp_incl, CategoryTheory.Adjunction.unit_naturality, CategoryTheory.preadditiveYonedaObj_obj_isAddCommGroup, CategoryTheory.Limits.Cone.w, IsDenseSubsite.mapPreimage_comp_map_assoc, CategoryTheory.Presheaf.uliftYonedaAdjunction_unit_app_app, CategoryTheory.Triangulated.TStructure.instIsGEObjTruncGE, CategoryTheory.ShiftedHom.opEquiv'_symm_add, AlgebraicGeometry.ΓSpecIso_inv_ΓSpec_adjunction_homEquiv, CategoryTheory.SmallObject.SuccStruct.ofCocone_obj_eq, SSet.Truncated.HomotopyCategory.BinaryProduct.associativity'Iso_hom_app, CategoryTheory.Grothendieck.transportIso_inv_fiber, CategoryTheory.GradedObject.single_map_singleObjApplyIso_hom, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObjObj_X, CategoryTheory.Sum.functorEquiv_unitIso_inv_app_app_inr, CategoryTheory.Limits.mono_of_isLimit_fork, SSet.Subcomplex.le_iff_contains_nonDegenerate, CategoryTheory.SmallObject.objMap_comp, CategoryTheory.left_unitality_app, CategoryTheory.Limits.pullback_factors, AlgebraicGeometry.RingedSpace.zeroLocus_empty_eq_univ, FullyFaithful.compYonedaCompWhiskeringLeftMaxRight_hom_app_app_down, CategoryTheory.Cat.rightUnitor_inv_app, CategoryTheory.ProjectiveResolution.extAddEquivCohomologyClass_apply, map_id, CategoryTheory.Limits.PullbackCone.ofCone_π, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_left, CategoryTheory.Sieve.functorPushforward_union, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app_assoc, AlgebraicGeometry.StructureSheaf.algebraMap_germ_assoc, Monoidal.whiskerLeft_δ_μ, TopCat.Presheaf.SubmonoidPresheaf.toLocalizationPresheaf_app, ModuleCat.restrictScalarsId'_hom_app, HomotopicalAlgebra.CofibrantObject.instWeakEquivalenceWWeakEquivalences, Rep.coindVEquiv_apply_hom, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₃, groupCohomology.mapShortComplexH1_comp, Final.ι_colimitIso_inv_assoc, CategoryTheory.Pseudofunctor.Grothendieck.Hom.ext_iff, HasPointwiseRightDerivedFunctorAt.hasColimit, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.isConnected, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_pt, TwoP.swapEquiv_inverse_obj_toTwoPointing_toProd, HasFibers.Fib.isoMk_inv, CategoryTheory.Limits.inl_comp_pushoutObjIso_inv, CategoryTheory.Equivalence.counitInv_functor_comp_assoc, LeftExtension.postcompose₂_map_left, CategoryTheory.Limits.pullbackObjIso_inv_comp_fst, OplaxLeftLinear.δₗ_naturality_right, uncurry_obj_map, CategoryTheory.CosimplicialObject.Augmented.const_obj_hom, CategoryTheory.MonoidalCategory.externalProductBifunctorCurried_obj_obj_obj_obj, CategoryTheory.bifunctorComp₁₂FunctorObj_obj, CategoryTheory.CartesianMonoidalCategory.inv_prodComparison_map_snd, mapPresheaf_map_c, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_app_assoc, AlgebraicGeometry.Scheme.Modules.Hom.add_app, CategoryTheory.Limits.BinaryFan.isLimit_iff_isIso_fst, CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc_assoc, CategoryTheory.Limits.LimitPresentation.map_π, Monoidal.whiskerLeft_ε_η, CategoryTheory.NatTrans.id_hcomp_app, SSet.stdSimplex.yonedaEquiv_map, CategoryTheory.shift_shiftFunctorCompIsoId_inv_app, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_counit_app_left, CategoryTheory.Presheaf.coconeOfRepresentable_naturality, OplaxLeftLinear.δₗ_associativity_assoc, postcompose₂_obj_obj_obj_obj, CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_left, PresheafOfModules.Derivation.d_app, CategoryTheory.Over.post_obj, CategoryTheory.Subobject.ofLE_comp_ofLEMk, Monoidal.snd_app, LeftExtension.postcomp₁_obj_right_obj, CategoryTheory.NatTrans.app_naturality_assoc, TopCat.instDiscreteTopologyCarrierObjDiscrete, Action.FunctorCategoryEquivalence.inverse_obj_V, SemiNormedGrp.completion.map_zero, CategoryTheory.Adjunction.map_μ_comp_counit_app_tensor, CategoryTheory.NatTrans.rightOp_app, CategoryTheory.Grothendieck.map_obj, Monoidal.fst_app, SSet.RelativeMorphism.Homotopy.ofEq_h, CategoryTheory.Arrow.inv_left_hom_right, CategoryTheory.Enriched.Functor.natTransEquiv_symm_whiskerRight_functorHom_app, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counit_app, FintypeCat.Skeleton.incl_mk_nat_card, CategoryTheory.Adjunction.compCoyonedaIso_hom_app_app, CategoryTheory.Kleisli.Adjunction.fromKleisli_map, CategoryTheory.ComposableArrows.Exact.cokerIsoKer_hom_fac_assoc, SSet.horn_obj_zero, currying₃_unitIso_inv_app_app_app_app, AlgebraicGeometry.instIsOpenImmersionSigmaSpec, mapConeWhisker_hom_hom, AlexDisc.coe_forgetToTop, CategoryTheory.Equivalence.fun_inv_map_assoc, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.sigma_ι_isOpenImmersion_aux, InfiniteGalois.toAlgEquivAux_eq_liftNormal, closedIhom_map_app, instIsSplitEpiApp, TopologicalSpace.OpenNhds.isOpenEmbedding, AlgebraicTopology.DoldKan.hσ'_eq, whiskeringLeftObjIdIso_inv_app_app, CategoryTheory.ShortComplex.RightHomologyData.exact_map_iff, HomotopicalAlgebra.FibrantObject.instWeakEquivalenceWWeakEquivalences, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_inv_app_app, CategoryTheory.Cat.opFunctorInvolutive_inv_app_toFunctor_obj, CategoryTheory.Limits.Cocone.toCostructuredArrowCompToOverCompForget_hom_app, CategoryTheory.Comma.toPUnitIdEquiv_inverse_obj_right_as, CategoryTheory.WithTerminal.mkCommaObject_hom_app, CoconeTypes.precomp_ι, HomotopicalAlgebra.FibrantObject.HoCat.ιCompResolutionNatTrans_app, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural, LightCondMod.hom_naturality_apply, AlgebraicGeometry.ExistsHomHomCompEqCompAux.hab, Monoidal.transport_η, CategoryTheory.SimplicialObject.eqToIso_refl, ChainComplex.toSingle₀Equiv_symm_apply_f_zero, TopModuleCat.forget₂_TopCat_obj, CategoryTheory.Equivalence.ε_comp_map_ε, CategoryTheory.WithTerminal.mkCommaObject_left_obj, mapCocone₂_ι_app, CategoryTheory.StructuredArrow.toUnder_obj_hom, AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv, PresheafOfModules.forgetToPresheafModuleCat_obj, CategoryTheory.MonoidalCategory.endofunctorMonoidalCategory.evaluationRightAction_actionObj, SSet.mem_skeleton, RightExtension.postcompose₂_obj_hom_app, CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv', CategoryTheory.ObjectProperty.ColimitOfShape.toCostructuredArrow_map, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv, SheafOfModules.unitToPushforwardObjUnit_val_app_apply, CategoryTheory.Limits.limitCompCoyonedaIsoCone_inv, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_left, CategoryTheory.Limits.Cofork.unop_π_app_zero, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_inv_ι_assoc, CategoryTheory.Subobject.factorThru_add_sub_factorThru_left, Action.resComp_inv_app_hom, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓUnitOpensCarrierCarrierCommRingCatRingCatSheaf, CategoryTheory.Regular.exists_inf_pullback_eq_exists_inf, CategoryTheory.Subobject.inf_def, CategoryTheory.WithInitial.equivComma_unitIso_hom_app_app, AlgebraicTopology.DoldKan.MorphComponents.id_a, CategoryTheory.Bicategory.precomposing_obj, PresheafOfModules.forgetToPresheafModuleCatObj_obj, RightExtension.precomp_obj_hom_app, CategoryTheory.Localization.lift₃NatTrans_app_app_app, CategoryTheory.ShiftedHom.opEquiv'_zero_add_symm, CategoryTheory.CostructuredArrow.mapNatIso_functor_obj_right, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_right_right, CategoryTheory.MonoidalClosed.uncurry_natural_left, groupHomology.pOpcycles_comp_opcyclesIso_hom, CategoryTheory.ObjectProperty.prop_ι_obj, SheafOfModules.pullback_assoc, toPseudoFunctor_mapId, ranCounit_app_app_ranAdjunction_unit_app_app, CategoryTheory.Subobject.isoOfMkEq_hom, AlgebraicGeometry.RingedSpace.basicOpen_mul, CategoryTheory.Limits.instIsIsoInitialComparison, CategoryTheory.Comma.mapRightId_hom_app_left, BialgCat.MonoidalCategory.inducingFunctorData_μIso, CategoryTheory.Pseudofunctor.isPrestackFor_iff, CategoryTheory.Limits.IsColimit.hom_desc, Final.colimit_cocone_comp_aux, SSet.horn.spineId_vertex_coe, AlgebraicGeometry.Scheme.Hom.inv_appTop, CategoryTheory.ShiftedHom.opEquiv'_symm_op_opShiftFunctorEquivalence_counitIso_inv_app_op_shift, CategoryTheory.algebraEquivUnder_counitIso, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_map_left, RightExtension.precomp_map_right, CategoryTheory.Equivalence.core_inverse_obj_of, CategoryTheory.CosimplicialObject.δ_comp_δ'_assoc, CategoryTheory.Monad.MonadicityInternal.unitCofork_pt, CategoryTheory.ChosenPullbacksAlong.Over.lift_left, SSet.rightUnitor_hom_app_apply, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₁₂, CategoryTheory.MonoidalClosed.homEquiv_symm_apply_eq, CategoryTheory.ShortComplex.opFunctor_obj, CategoryTheory.ProjectiveResolution.leftDerivedToHomotopyCategory_app_eq, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_leftUnitor_hom_eq_leftUnitor_hom, CategoryTheory.Under.postCongr_hom_app_right, CategoryTheory.StructuredArrow.map_mk, CategoryTheory.Over.mapId_hom_app_left, CategoryTheory.Comma.mapLeftEq_inv_app_left, CategoryTheory.Limits.PreservesLimitsOfSize.overPost, ChainComplex.instHasHomologyNatObjAlternatingConst, AddCommMonCat.coyonedaForget_inv_app_app, CategoryTheory.ShortComplex.gFunctor_obj, CategoryTheory.ObjectProperty.IsMonoidalClosed.prop_ihom, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_right, map_opShiftFunctorEquivalence_unitIso_hom_app_unop_assoc, CategoryTheory.Limits.Cofork.IsColimit.existsUnique, CategoryTheory.ShortComplex.π₃_obj, CategoryTheory.instIsIsoPost_1, AlgebraicGeometry.Scheme.AffineZariskiSite.opensRange_relativeGluingData_map, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_apply, CategoryTheory.NatTrans.naturality, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_hom_π_π_assoc, CategoryTheory.CompatiblePreserving.apply_map, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv, groupHomology.cyclesIso₀_inv_comp_cyclesMap_assoc, CategoryTheory.WithInitial.map₂_app, CategoryTheory.Limits.combineCocones_pt_obj, HomologicalComplex.coconeOfHasColimitEval_ι_app_f, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp_assoc, CategoryTheory.Subobject.pullback_map_self, CategoryTheory.LocalizerMorphism.homMap_homMap, CategoryTheory.Limits.Cone.toStructuredArrow_obj, CategoryTheory.Center.ofBraided_μ_f, CategoryTheory.Limits.imageSubobject_arrow'_assoc, CochainComplex.HomComplex.Cocycle.toSingleMk_sub, CategoryTheory.Subobject.factorThru_arrow, AlgebraicGeometry.Scheme.Hom.toNormalization_inr_normalizationCoprodIso_hom_assoc, CategoryTheory.WithTerminal.commaFromOver_map_right, IsRepresentedBy.map_bijective, CommRingCat.coproductCoconeIsColimit_desc, CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_right, CategoryTheory.Limits.Cotrident.app_one, CategoryTheory.Triangulated.TStructure.instIsLEObj₁ObjTriangleTriangleLTGEHSubIntOfNat, CategoryTheory.Monoidal.rightUnitor_hom_app, AlgebraicGeometry.isIntegralHom_iff, CategoryTheory.Limits.hasPullback_of_preservesPullback, CategoryTheory.CostructuredArrow.map_map_left, CategoryTheory.Limits.CategoricalPullback.mkNatIso_inv_app_fst, CategoryTheory.sectionsFunctorNatIsoCoyoneda_hom_app_app, CategoryTheory.RetractArrow.map_i_left, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_hom_app_app_down, TopCat.GlueData.ofOpenSubsets_toGlueData_V, CategoryTheory.Limits.instHasBinaryProductObjOfPreservesLimitDiscreteWalkingPairPair, mapIso_symm, CategoryTheory.Endofunctor.Algebra.Hom.h, mapEnd_apply, CategoryTheory.Pretriangulated.Triangle.π₁_obj, CochainComplex.isKProjective_iff_leftOrthogonal, CategoryTheory.CostructuredArrow.map₂_map_left, PullbackObjObj.ofHasPullback_snd, CategoryTheory.evaluationUncurried_obj, CategoryTheory.bifunctorComp₂₃Functor_obj, HomologicalComplex.quasiIsoAt_iff_evaluation, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε_assoc, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_presheafHom_uliftYoneda_obj, CommGrpCat.coyoneda_obj_obj_coe, CategoryTheory.Subobject.inf_arrow_factors_left, CategoryTheory.WithInitial.equivComma_inverse_obj_obj, CategoryTheory.Subfunctor.toRange_app_val, CategoryTheory.Pretriangulated.Triangle.mono₃, representableByUliftFunctorEquiv_apply_homEquiv, shift_map_op, CategoryTheory.Square.fromArrowArrowFunctor'_obj_X₁, CategoryTheory.Limits.limitIsoSwapCompLim_inv_app, mapTriangleCommShiftIso_inv_app_hom₂, CategoryTheory.PreGaloisCategory.isGalois_iff_pretransitive, CategoryTheory.Bimon.toMonComon_obj, LaxRightLinear.μᵣ_naturality_left_assoc, LaxLeftLinear.μₗ_associativity_inv, CategoryTheory.ε_η_app, CategoryTheory.Over.isPullback_of_binaryFan_isLimit, CategoryTheory.CosimplicialObject.whiskering_obj_map_app, AlgebraicGeometry.RingedSpace.basicOpen_res_eq, Action.FunctorCategoryEquivalence.unitIso_hom_app_hom, CategoryTheory.Limits.colimit.pre_map, LightCondensed.ihomPoints_symm_apply, CategoryTheory.sheafificationIso_hom_val, CategoryTheory.LocalizerMorphism.isIso_iff_of_hasRightResolutions, AlgebraicGeometry.Spec_zeroLocus, CategoryTheory.MorphismProperty.commaObj_iff, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_map_right_right, CategoryTheory.Pseudofunctor.IsStackFor.isEquivalence, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv, CategoryTheory.Limits.SingleObj.Types.limitEquivFixedPoints_apply_coe, HomologicalComplex.truncGE.rightHomologyMapData_φH, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_inv_app_fst_app, CorepresentableBy.equivUliftCoyonedaIso_apply, LaxLeftLinear.μₗ_unitality_inv, CategoryTheory.Adjunction.comp_unit_app_assoc, CategoryTheory.nerve_obj, AlgebraicGeometry.Scheme.basicOpen_mul, LightCondensed.discrete_obj, CategoryTheory.Limits.ι_comp_colimitOpIsoOpLimit_hom, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp_assoc, SSet.Truncated.tensor_map_apply_fst, CategoryTheory.InjectiveResolution.extMk_hom, CategoryTheory.Limits.inr_comp_pushoutObjIso_inv, AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality, CategoryTheory.Localization.isoOfHom_hom_inv_id_assoc, CategoryTheory.Subobject.isoOfEq_inv, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_obj_obj_obj, SimplexCategory.rev_map_rev_map, CategoryTheory.Limits.IsLimit.fac_assoc, CategoryTheory.Limits.MultispanIndex.map_right, AlgebraicGeometry.Scheme.IdealSheafData.coe_support_eq_eq_iInter_zeroLocus, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy_homEquiv_apply_app, PresheafOfModules.Monoidal.tensorHom_app, SSet.Truncated.HomotopyCategory.BinaryProduct.functor_obj, CategoryTheory.Pretriangulated.shiftFunctor_op_map, CategoryTheory.Idempotents.functorExtension₂CompWhiskeringLeftToKaroubiIso_inv_app_app_f, CategoryTheory.Limits.CokernelCofork.condition_assoc, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_inv_comp_π, AlgebraicTopology.DoldKan.PInfty_f_naturality, Monoidal.whiskerRight_δ_μ, CategoryTheory.Localization.hasSmallLocalizedHom_iff, AlgebraicGeometry.exists_of_res_eq_of_qcqs_of_top, CategoryTheory.Center.forget_obj, CategoryTheory.Limits.pushoutComparison_map_desc_assoc, CategoryTheory.Limits.BinaryFan.braiding_inv_fst, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map, SSet.horn.multicoequalizerDiagram, AddCommGrpCat.uliftFunctor_obj, quasiIsoAt_iff', CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_whiskerRight, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_right, currying_functor_obj_obj, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_map_snd, CategoryTheory.Limits.cospanCompIso_hom_app_left, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand, CategoryTheory.Sieve.uliftFunctorInclusion_is_mono, groupCohomology.map_id_comp, CategoryTheory.Limits.BinaryFan.assoc_snd, CategoryTheory.Adjunction.rightAdjointUniq_trans_app, instPreservesZeroMorphismsObjFlip, SSet.horn.spineId_arrow_coe, CategoryTheory.SimplicialObject.equivalenceRightToLeft_left, CategoryTheory.rightDualFunctor_obj, CategoryTheory.ShortComplex.LeftHomologyData.mapCyclesIso_eq, SSet.skeletonOfMono_obj_eq_top, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₁, MonCat.Colimits.cocone_naturality_components, CategoryTheory.uliftCoyonedaEquiv_naturality, CochainComplex.HomComplex.Cocycle.fromSingleMk_sub, HomologicalComplex.homologyFunctorSingleIso_inv_app, AlgebraicTopology.DoldKan.HigherFacesVanish.of_comp, CategoryTheory.exp.coev_ev_assoc, CategoryTheory.Over.whiskerLeft_left_fst_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_app_assoc, CategoryTheory.Subobject.mapIsoToOrderIso_symm_apply, RightExtension.postcompose₂ObjMkIso_inv_left_app, SimplicialObject.opFunctorCompOpFunctorIso_inv_app_app, mapMon_map_hom, CategoryTheory.prod_map_pre_app_comp_ev, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMop_obj_unmop_obj, CategoryTheory.Limits.Pi.cone_pt, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app_assoc, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π_assoc, CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.arrowMap_functor, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app, CategoryTheory.Equivalence.unit_naturality_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_snd_obj, CategoryTheory.shiftComm_hom_comp, FullyFaithful.mapCommGrp_preimage, CategoryTheory.Endofunctor.Algebra.functorOfNatTransEq_hom_app_f, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_left_left, CategoryTheory.Cat.Hom.comp_obj, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_X_map, CategoryTheory.FunctorToTypes.prod_ext_iff, CategoryTheory.Limits.BinaryBicones.functoriality_obj_inr, TopCat.GlueData.ofOpenSubsets_toGlueData_f, CategoryTheory.Equivalence.unit_app_tensor_comp_inverse_map_δ_functor_assoc, CategoryTheory.NatTrans.shift_app_assoc, Action.tensorHom_hom, CategoryTheory.MonoOver.pullback_obj_left, CategoryTheory.Sheaf.isLocallyInjective_sheafToPresheaf_map_iff, PresheafOfModules.pullbackObjIsDefined_free_yoneda, CategoryTheory.Subobject.factorThru_add, AlgebraicTopology.DoldKan.Compatibility.υ_hom_app, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_left_left, CategoryTheory.Limits.MultispanIndex.toSigmaCoforkFunctor_obj, CategoryTheory.NatIso.cancel_natIso_inv_right, CategoryTheory.Limits.CatCospanTransform.leftUnitor_inv_left_app, ComplexShape.Embedding.truncLE'Functor_obj, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, AlgebraicGeometry.Scheme.zeroLocus_biInf_of_nonempty, SSet.iSup_range_eq_top_of_isColimit, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_inv_app_eq, Rep.coinvariantsTensor_hom_ext_iff, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp_app, CategoryTheory.Under.pushout_obj, Action.associator_hom_hom, CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_inv_app_unmop_unmop, IsCoverDense.sheafCoyonedaHom_app, SSet.stdSimplex.objEquiv_toOrderHom_apply, CategoryTheory.Localization.SmallHom.equiv_comp, CategoryTheory.NatIso.naturality_2'_assoc, AlgCat.instSmallSubtypeForallCarrierObjMemSubalgebraSectionsSubalgebra, AlgebraicGeometry.instIsOpenImmersionAppOverSchemeOpensDiagramι, inrCompSum'_inv_app, CategoryTheory.CartesianMonoidalCategory.inv_prodComparison_map_fst, CategoryTheory.SmallObject.SuccStruct.Iteration.obj_limit, constComp_hom_app, CategoryTheory.MorphismProperty.Over.w, CategoryTheory.Adjunction.derivedη_fac_app, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_left, ModuleCat.free_δ_freeMk, mapIso_inv, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.map_mem, CategoryTheory.Square.toArrowArrowFunctor_obj_right_hom, CategoryTheory.Pseudofunctor.Grothendieck.Hom.congr, CategoryTheory.Grpd.freeForgetAdjunction_homEquiv_apply, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom_assoc, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.inverse_obj_obj, CategoryTheory.DinatTrans.precompNatTrans_app, TopCat.Presheaf.isSheaf_on_punit_iff_isTerminal, CategoryTheory.equivOfTensorIsoUnit_inverse, CategoryTheory.Over.instFaithfulObjPost, obj.μ_def_assoc, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ₀, AlgebraicGeometry.Scheme.SpecΓIdentity_inv_app, CategoryTheory.Pretriangulated.productTriangle_mor₃, SSet.ι₁_fst, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_zero, CategoryTheory.Square.toArrowArrowFunctor_obj_right_left, PresheafOfModules.instMonoModuleCatCarrierObjOppositeRingCatApp, CategoryTheory.SmallObject.SuccStruct.extendToSucc_map, CategoryTheory.Abelian.LeftResolution.instEpiKaroubiAppπ, CategoryTheory.Adjunction.rightAdjointUniq_hom_app_counit, CategoryTheory.Limits.imageSubobjectCompIso_hom_arrow_assoc, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.const_s, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_base, Action.res_obj_ρ, reflective, CategoryTheory.Adjunction.derivedη_fac_app_assoc, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_inv_comp_π_assoc, CategoryTheory.Regular.frobeniusMorphism_isPullback, whiskeringRight_obj_map, RightExtension.postcompose₂_map_left_app, CategoryTheory.CosimplicialObject.σ_comp_σ_assoc, CategoryTheory.Equivalence.unit_naturality, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_snd_map, CategoryTheory.ComposableArrows.isoMk₀_inv_app, CategoryTheory.Sieve.generate_map_eq_functorPushforward, CategoryTheory.Limits.limit.homIso_hom, CategoryTheory.Limits.colimitConstInitial_inv, prod'_ε_snd, CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_two, CategoryTheory.actionAsFunctor_obj, 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, CategoryTheory.CoverPreserving.cover_preserve, imageToKernel_arrow_apply, CochainComplex.HomComplex.Cochain.δ_rightUnshift, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom, ModuleCat.FilteredColimits.ι_colimitDesc, LaxMonoidal.right_unitality_assoc, CategoryTheory.Equivalence.functor_unitIso_comp, CategoryTheory.PrelaxFunctor.mapFunctor_obj, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_apply, CategoryTheory.Bimon.equivMonComonCounitIsoAppX_inv_hom, CategoryTheory.Comma.mapFst_hom_app, curry_obj_obj_map, CategoryTheory.Limits.sigmaConst_obj_obj, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_val_map, CategoryTheory.Over.coprodObj_obj, 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, TopologicalSpace.OpenNhds.inclusion_obj, PresheafOfModules.Derivation'.app_apply, CategoryTheory.uliftYonedaIsoYoneda_hom_app_app, CategoryTheory.IsCodetecting.isIso_iff_of_epi, flip_obj_obj, CategoryTheory.prodFunctor_obj, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv_assoc, IsEventuallyConstantFrom.coconeιApp_eq_id, CategoryTheory.MonoidalClosed.curry'_whiskerRight_comp_assoc, CategoryTheory.Limits.CategoricalPullback.mkNatIso_hom_app_fst, CategoryTheory.Limits.SingleObj.colimitTypeRelEquivOrbitRelQuotient_symm_apply, CategoryTheory.Limits.limit.map_pre', CategoryTheory.Limits.ColimitPresentation.reindex_ι, Monoidal.map_whiskerRight_assoc, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_hom, CategoryTheory.Sieve.functorPushforward_bot, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app, Monoidal.tensorObj_obj, CategoryTheory.NatTrans.CommShiftCore.app_shift, lightProfiniteToLightDiagram_obj, CategoryTheory.Limits.FormalCoproduct.instPreservesColimitsOfShapeDiscreteObjFunctorEval, FullyFaithful.compUliftYonedaCompWhiskeringLeft_hom_app_app_down, CategoryTheory.Pseudofunctor.map₂_whisker_left_app_assoc, SSet.Truncated.Edge.tensor_edge, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.trans_app_left, LaxRightLinear.μᵣ_associativity, whiskeringRightObjCompIso_hom_app_app, Monoidal.map_leftUnitor, AlgebraicGeometry.isLocallyNoetherian_iff_of_iSup_eq_top, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_neg, CategoryTheory.Sheaf.isConstant_iff_of_equivalence, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst, RightExtension.postcompose₂_obj_left_obj, CategoryTheory.IsSplitCoequalizer.map_leftSection, CategoryTheory.equivYoneda_inv_app, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_pullback_obj, PushoutObjObj.ofHasPushout_inl, CategoryTheory.uliftCoyonedaEquiv_symm_map_assoc, Rep.unit_iso_comm, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_obj, HasCardinalLT.Set.functor_map_coe, SSet.Truncated.HomotopyCategory.mkNatIso_hom_app_mk, CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor_obj_left_right_as, ChainComplex.truncate_obj_d, CategoryTheory.StructuredArrow.preEquivalenceInverse_map_right_right, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app, CategoryTheory.presheafToSheafCompComposeAndSheafifyIso_inv_app, CategoryTheory.Iso.map_hom_inv_id_eval_app_assoc, CategoryTheory.PreGaloisCategory.comp_autMap_apply, CategoryTheory.Comma.mapLeft_map_right, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_right, CategoryTheory.enrichedFunctorTypeEquivFunctor_apply_obj, CategoryTheory.Comma.mapLeft_obj_left, CategoryTheory.Adjunction.homAddEquiv_symm_apply, Faithful.map_injective, CategoryTheory.Presheaf.coherentExtensiveEquivalence_functor_obj_val, CategoryTheory.Presieve.mem_comap_jointlySurjectivePrecoverage_iff, AlgebraicGeometry.basicOpen_eq_of_affine', CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_symm_apply_f, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceInverse_obj_base, CategoryTheory.NatTrans.appLinearMap_apply, AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex_homotopyInvHomId, CategoryTheory.CostructuredArrow.IsUniversal.fac, CategoryTheory.Subfunctor.equivalenceMonoOver_unitIso, CategoryTheory.MonoidalClosed.curry_injective, CategoryTheory.Quotient.lift_obj_functor_obj, Monoidal.map_ε_η, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₄, CategoryTheory.Limits.reflexivePair_obj_zero, CochainComplex.HomComplex.Cochain.leftUnshift_units_smul, CategoryTheory.ObjectProperty.isLocal_iff_isIso_map, CategoryTheory.Localization.Construction.liftToPathCategory_map, CategoryTheory.Limits.Trident.IsLimit.homIso_symm_apply, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app, AlgebraicGeometry.Scheme.Hom.coe_image, CategoryTheory.ActionCategory.comp_val, CategoryTheory.Adjunction.localization_counit_app, AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom_appTop, AlgebraicGeometry.Scheme.Hom.coe_preimage, CategoryTheory.PreGaloisCategory.not_initial_iff_fiber_nonempty, mapGrpIdIso_inv_app_hom_hom, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₂, postcomposeWhiskerLeftMapCone_hom_hom, CategoryTheory.Limits.inl_comp_pushoutObjIso_inv_assoc, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIso_hom_app_hom, CategoryTheory.Over.prodComparisonIso_pullback_Spec_inv_left_fst_fst', OneHypercoverDenseData.essSurj.presheafMap_restriction, CategoryTheory.Limits.parallelPair_obj_zero, id_obj, CochainComplex.quasiIsoAt₀_iff, CategoryTheory.ShortComplex.exact_iff_epi_imageToKernel, AlgebraicGeometry.coprodSpec_inl_assoc, AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem_toSpecΓ, CategoryTheory.shift_zero_eq_zero, Rep.FiniteCyclicGroup.resolution_complex, SSet.PtSimplex.MulStruct.δ_castSucc_castSucc_map_assoc, CategoryTheory.CostructuredArrow.map_mk, CategoryTheory.yoneda'_obj_val, CochainComplex.HomComplex.Cochain.rightShiftLinearEquiv_apply, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_hom, CategoryTheory.Pseudofunctor.mapComp'_naturality_2, ModuleCat.directLimitDiagram_obj_carrier, leftDerivedZeroIsoSelf_inv_hom_id_app_assoc, CategoryTheory.Limits.IndObjectPresentation.extend_isColimit_desc_app, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_IsMon_Hom, HomologicalComplex.singleObjHomologySelfIso_hom_naturality, mapActionCongr_hom, AlgebraicGeometry.Scheme.Opens.toScheme_presheaf_map, CategoryTheory.Bimon.toMonComonObj_mon_one_hom, HomologicalComplex.gradedHomologyFunctor_obj, AddCommMonCat.coyonedaType_obj_obj_coe, TopCat.coneOfConeForget_π_app, CategoryTheory.FreeMonoidalCategory.normalizeIsoAux_hom_app, CategoryTheory.ObjectProperty.rightOrthogonal.map_bijective_of_isTriangulated, CategoryTheory.Limits.pullbackObjIso_hom_comp_snd_assoc, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_apply, CategoryTheory.GradedObject.mapTrifunctorObj_obj_map, CochainComplex.HomComplex.Cocycle.shift_coe, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon_map, homologySequence_exact₁, CategoryTheory.Adjunction.instIsIsoMapAppUnitOfFaithfulOfFull, HomotopicalAlgebra.FibrantObject.toHoCat_obj_surjective, PushoutObjObj.ι_iso_of_iso_right_inv, CategoryTheory.Limits.colimitIsoFlipCompColim_hom_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_inv_app_app, CategoryTheory.toSkeletonFunctor_map_hom, CategoryTheory.Monad.algebraFunctorOfMonadHomComp_inv_app_f, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_obj_base, CorepresentableBy.homEquiv_comp, CategoryTheory.Limits.BinaryFan.braiding_inv_snd_assoc, AlgebraicGeometry.instIsDominantToSpecΓOfCompactSpaceCarrierCarrierCommRingCat, CategoryTheory.MonoOver.subobjectMk_le_mk_of_hom, CategoryTheory.Sieve.functorPushforward_functor, FullyFaithful.compUliftCoyonedaCompWhiskeringLeft_inv_app_app_down, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_obj_iso_hom, CategoryTheory.Adjunction.homAddEquiv_symm_add, CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_fst_apply, whiskerRight_app, CategoryTheory.Triangulated.TStructure.triangleLTGE_distinguished, AlgebraicGeometry.Scheme.preimage_eq_top_of_closedPoint_mem, CategoryTheory.ComposableArrows.isIso_iff₀, CategoryTheory.Limits.Bicone.ofLimitCone_π, CategoryTheory.Limits.PreservesLimitPair.iso_inv_fst, SSet.mem_nonDegenerate_iff_notMem_degenerate, CategoryTheory.Limits.CatCospanTransform.associator_inv_right_app, CategoryTheory.Limits.ι_comp_sigmaObjIso_inv_assoc, CategoryTheory.Subfunctor.mem_ofSection_obj, CategoryTheory.Limits.colimit.ι_coconeMorphism, CategoryTheory.Comma.equivProd_unitIso_inv_app_right, smoothSheafCommRing.ι_forgetStalk_hom_apply, CategoryTheory.Over.whiskerLeft_left_snd_assoc, CategoryTheory.LocalizerMorphism.equiv_smallHomMap, TopologicalSpace.OpenNhds.map_id_obj', CategoryTheory.Monad.beckAlgebraCofork_ι_app, IsDenseSubsite.mapPreimage_comp, TopCat.Sheaf.objSupIsoProdEqLocus_hom_snd, Monoidal.tensorHom_app_snd_assoc, CategoryTheory.Sheaf.instIsLocallySurjectiveHomMapTypeSheafComposeForget, CategoryTheory.ShiftedHom.map_smul, AlgebraicGeometry.stalkToFiberRingHom_germ, CategoryTheory.Adjunction.CommShift.compatibilityUnit_right, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_inv_app_fst_app, CategoryTheory.WithInitial.commaFromUnder_obj_left, CategoryTheory.CartesianMonoidalCategory.prodComparisonIso_comp, Monoidal.associator_inv_app, CommShift.isoAdd'_hom_app, CategoryTheory.flippingIso_hom_toFunctor_obj_map_app, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_app, AlgebraicGeometry.StructureSheaf.const_mul_cancel', CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app_assoc, CategoryTheory.ShortComplex.π₁_obj, CategoryTheory.Limits.IsColimit.pushoutCoconeEquivBinaryCofanFunctor_desc_right, AlgebraicGeometry.Scheme.isoSpec_Spec_inv, IsCoverDense.homOver_app, CategoryTheory.Groupoid.invEquivalence_functor_obj, CategoryTheory.NatIso.naturality_2', CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal_δ_unmop_unmop, AlgebraicGeometry.Scheme.IdealSheafData.supportSet_subset_zeroLocus, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_inv_app_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w_assoc, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_mon_mul, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app, CategoryTheory.Limits.equalizerSubobject_arrow', CategoryTheory.shiftComm_symm, CategoryTheory.MorphismProperty.LeftFraction.map_comp_map_eq_map, CategoryTheory.MorphismProperty.ind_underObj_pushout, CategoryTheory.Limits.Cone.ofFork_π, CorepresentableBy.uniqueUpToIso_hom, CategoryTheory.Limits.colimit.ι_map_assoc, SSet.Subcomplex.mem_ofSimplex_obj, CategoryTheory.SplitEpi.map_section_, HomologicalComplex.HomologySequence.snakeInput_L₃, CategoryTheory.OverPresheafAux.unitForward_unitBackward, mapTriangleCompIso_hom_app_hom₁, CategoryTheory.ComonadHom.app_δ, AlgebraicGeometry.Proj.awayι_preimage_basicOpen, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_iso_inv_app, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left_assoc, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_hom_app_f, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorEquivalence_counitIso, Topology.IsInducing.functorNhds_obj_coe, CategoryTheory.CostructuredArrow.grothendieckProj_obj, HomotopyCategory.mem_subcategoryAcyclic_iff, CategoryTheory.FunctorToTypes.rightAdj_obj_map_app, CategoryTheory.CosimplicialObject.δ_comp_σ_self, CochainComplex.isStrictlyLE_shift, CategoryTheory.SimplicialObject.δ_comp_σ_of_gt', CategoryTheory.Subfunctor.Subpresheaf.sInf_obj, CategoryTheory.Adjunction.Triple.map_rightToLeft_app, CategoryTheory.Localization.Preadditive.add'_comp, CategoryTheory.Grothendieck.map_obj_base, TopCat.Sheaf.objSupIsoProdEqLocus_inv_eq_iff, AlgebraicGeometry.IsFinite.finite_app, FundamentalGroupoidFunctor.piToPiTop_obj_as, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_associator, HomologicalComplex.instQuasiIsoOppositeMapSymmOpFunctorOp, CategoryTheory.Limits.limitUnopIsoUnopColimit_hom_comp_ι_assoc, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_isoBot, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app_assoc, CategoryTheory.Subobject.underlying_arrow_assoc, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_comp, groupHomology.chainsMap_f_hom, CategoryTheory.Limits.colimit_ι_zero_cokernel_desc, pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_app, CategoryTheory.Over.equivalenceOfIsTerminal_unitIso, CategoryTheory.PreGaloisCategory.autEmbedding_apply, CategoryTheory.Localization.lift₂NatTrans_app_app, HomotopicalAlgebra.CofibrantObject.instIsIsoHoCatAppAdjCounit', CategoryTheory.Equivalence.sheafCongrPrecoherent_inverse_obj_val_map, CategoryTheory.Limits.CokernelCofork.map_condition, CategoryTheory.Square.toArrowArrowFunctor_obj_left_right, CategoryTheory.TwoSquare.EquivalenceJ.functor_obj, AlgebraicGeometry.sigmaOpenCover_I₀, CategoryTheory.MonoidalOpposite.tensorRightMopIso_inv_app_unmop, CategoryTheory.Adjunction.eq_unit_comp_map_iff, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₃₁_assoc, HomologicalComplex.singleObjHomologySelfIso_hom_naturality_assoc, TopologicalSpace.Opens.coe_overEquivalence_inverse_obj_left, lightCondSetToTopCat_obj_carrier, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_id, CompHaus.presentation.epi_π, CategoryTheory.Comma.toPUnitIdEquiv_inverse_obj_left, AlgebraicTopology.DoldKan.map_Q, CategoryTheory.NatTrans.mapHomologicalComplex_naturality_assoc, HomologicalComplex.singleObjHomologySelfIso_inv_naturality_assoc, CategoryTheory.Equivalence.core_counitIso_hom_app_iso_inv, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_hom_app_val_app, Topology.IsInducing.functor_obj, AlgebraicGeometry.instSubsingletonCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensOfIsEmpty, AlgebraicGeometry.exists_eq_pow_mul_of_isAffineOpen, CategoryTheory.Over.iteratedSliceEquiv_counitIso, CategoryTheory.SimplicialObject.Truncated.whiskering_obj_obj_map, constCompEvaluationObj_hom_app, CategoryTheory.Limits.WalkingMulticospan.functorExt_hom_app, leftKanExtensionIsoFiberwiseColimit_hom_app, CategoryTheory.Monad.comparisonForget_inv_app, CategoryTheory.Limits.colimitQuotientCoproduct_epi, OrderHom.equivalenceFunctor_inverse_obj, smoothSheafCommRing.ι_forgetStalk_hom_assoc, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.evalAt_apply, CategoryTheory.CosimplicialObject.equivalenceRightToLeft_right_app, LaxMonoidal.comp_ε, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_assoc, CategoryTheory.ULiftHom.up_obj, CategoryTheory.shiftFunctorAdd_add_zero_hom_app, AlgebraicGeometry.Proj.awayMap_awayToSection, CategoryTheory.LocalizerMorphism.RightResolution.hw, CategoryTheory.Groupoid.invEquivalence_counitIso, CategoryTheory.TwoSquare.isConnected_rightwards_iff_downwards, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, CategoryTheory.Limits.π_comp_cokernelComparison, CategoryTheory.StructuredArrow.mapIso_unitIso_hom_app_right, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_app_app, CategoryTheory.Equivalence.cancel_counitInv_right_assoc', CategoryTheory.ShortComplex.SnakeInput.functorL₂'_obj, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_fst, CochainComplex.HomComplex.Cochain.δ_rightShift, AlgebraicGeometry.finite_appTop_of_universallyClosed, CategoryTheory.Free.lift_map_single, DerivedCategory.right_fac_of_isStrictlyLE, CategoryTheory.Abelian.Ext.mapExactFunctor_add, CategoryTheory.Presheaf.map_comp_uliftYonedaEquiv_down_assoc, CategoryTheory.Endofunctor.Adjunction.Coalgebra.toAlgebraOf_obj_a, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_obj, CategoryTheory.Sieve.functor_galoisConnection, TopCat.induced_of_isLimit, HomologicalComplex₂.ι_totalShift₂Iso_inv_f, CategoryTheory.Subobject.pullback_obj_mk, AlgebraicGeometry.IsLocallyNoetherian.component_noetherian, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_hom, CategoryTheory.ShortComplex.FunctorEquivalence.functor_obj_obj, id_mapMon_mul, CategoryTheory.StructuredArrow.w, SheafOfModules.forget_obj, groupHomology.pOpcycles_comp_opcyclesIso_hom_assoc, CategoryTheory.Coyoneda.instHasColimitObjOppositeFunctorTypeCoyoneda, CategoryTheory.TransfiniteCompositionOfShape.iic_incl_app, curryingFlipEquiv_apply_map, Rep.indResAdjunction_unit_app_hom_hom, CategoryTheory.Limits.coconeLeftOpOfCone_ι_app, CategoryTheory.Limits.π_comp_colimitRightOpIsoUnopLimit_inv, CategoryTheory.Limits.ι_comp_colimitUnopIsoOpLimit_hom_assoc, CategoryTheory.MonoidalCategory.DayFunctor.ι_obj, CoreMonoidal.μIso_hom_natural_right, CategoryTheory.yonedaGrpObj_obj_coe, CategoryTheory.LocalizerMorphism.RightResolution.unop_w, HasPointwiseLeftDerivedFunctorAt.hasLimit, mapAddHom_apply, CategoryTheory.GrothendieckTopology.diagramFunctor_obj, pointwiseLeftKanExtensionCompIsoOfPreserves_fac_app, constCompWhiskeringLeftIso_inv_app_app, RightExtension.postcompose₂_map_right, groupHomology.map_id_comp_H0Iso_hom_apply, CategoryTheory.Limits.BinaryBicones.functoriality_obj_snd, AlgebraicTopology.DoldKan.N₂_obj_p_f, CategoryTheory.Limits.map_lift_kernelComparison_assoc, leftOpComp_hom_app, CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit_assoc, SSet.Truncated.HomotopyCategory.BinaryProduct.square, CategoryTheory.Limits.cospanCompIso_hom_app_one, CategoryTheory.Limits.ι_comp_coequalizerComparison, AlgebraicGeometry.IsIntegralHom.integral_app, CategoryTheory.Limits.Cone.fromCostructuredArrow_obj_pt, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv, OneHypercoverDenseData.SieveStruct.fac_assoc, CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero, CategoryTheory.Cat.FreeRefl.lift'_obj, CategoryTheory.Idempotents.app_comp_p_assoc, CategoryTheory.FreeGroupoid.of_obj_bijective, CategoryTheory.Subobject.ofLE_comp_ofLE, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_app_snd_app, RepresentableBy.uniqueUpToIso_inv, CategoryTheory.coreFunctor_map_app_iso_hom, instNonemptyObjOpenNormalSubgroupStabilizerHomSurjectiveAuxFunctor, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_hom_comp_map_π, Monotone.functor_obj, CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatTrans_app, CategoryTheory.Limits.CatCospanTransform.associator_hom_base_app, Initial.exists_eq, CommShift.isoZero_inv_app, CategoryTheory.instPreservesFiniteLimitsFunctorObjWhiskeringLeftOfHasFiniteLimits, CategoryTheory.TwoSquare.whiskerTop_app, CochainComplex.HomComplex.Cochain.leftShift_v, AlgebraicGeometry.isIso_SpecMap_stakMap_localization, CategoryTheory.Limits.coend.hom_ext_iff, MonCat.FilteredColimits.colimit_one_eq, CategoryTheory.WithTerminal.inclLiftToTerminal_hom_app, sheafPushforwardContinuousCompSheafToPresheafIso_hom_app_app, Monoidal.instIsIsoε, RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π_assoc, CategoryTheory.Sum.swap_obj_inr, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left, CategoryTheory.Limits.equalizerSubobject_arrow_comp_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_obj_snd, CommMonCat.coyoneda_obj_obj_coe, instIsCorepresentableObjOppositeTypeCoyoneda, groupHomology.H1CoresCoinfOfTrivial_f, CommRingCat.coyonedaUnique_inv_app_hom_apply, LightProfinite.Extend.cocone_pt, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_counitIso_hom_app_f, CategoryTheory.Limits.Cone.isLimit_iff_isIso_limMap_π, LightCondMod.epi_iff_locallySurjective_on_lightProfinite, CategoryTheory.Subobject.ofMkLE_comp_ofLE, commShiftIso_inv_naturality, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_pt, CategoryTheory.Limits.kernelSubobject_arrow'_assoc, CategoryTheory.CommMon.mkIso_hom_hom_hom, CategoryTheory.Cat.freeRefl_obj, CategoryTheory.expComparison_iso_of_frobeniusMorphism_iso, CategoryTheory.Limits.limitIsoLimitCurryCompLim_inv_π, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_app, AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit_map, SSet.horn₂₀.isPushout, CategoryTheory.Limits.colimit.ι_desc_assoc, CategoryTheory.IsPushout.of_is_coproduct, SSet.stdSimplex.ofSimplex_yonedaEquiv_δ, CochainComplex.HomComplex.Cochain.rightUnshift_add, CategoryTheory.ActionCategory.uncurry_obj, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_app_fst_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app_assoc, CategoryTheory.Under.forget_obj, CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_inv, imageToKernel_zero_right, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.secondMap₃_app_app_app, CategoryTheory.Sieve.forallYonedaIsSheaf_iff_colimit, CategoryTheory.Pretriangulated.Triangle.epi₃, PullbackObjObj.mapArrowRight_id, AlgebraicTopology.DoldKan.σ_comp_PInfty, CategoryTheory.Bimon.toMonComon_ofMonComon_obj_mul, CategoryTheory.Discrete.productEquiv_inverse_obj_as, CategoryTheory.WithTerminal.liftFromOver_obj_map, CochainComplex.HomComplex.Cochain.toSingleMk_zero, ProfiniteGrp.instCompactSpaceSubtypeForallCarrierToTopTotallyDisconnectedSpaceToProfiniteObjMemSubgroupLimitConePtAux, AlgebraicTopology.DoldKan.Compatibility.τ₁_hom_app, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj, Rep.coindFunctor'_obj, TopCat.Presheaf.SheafConditionEqualizerProducts.w_apply, LeftExtension.precomp_map_left, CategoryTheory.Comma.mapLeftIso_functor_obj_hom, CategoryTheory.Equivalence.unit_app_comp_inverse_map_η_functor, CategoryTheory.Pseudofunctor.DescentData.pullFunctorObjHom_eq_assoc, AlgebraicGeometry.specTargetImageFactorization_app_injective, LightCondensed.ihom_map_val_app, AlgebraicGeometry.Scheme.IsGermInjectiveAt.cond, mapGrp_obj_grp_mul, CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_cancel_inv_app, CategoryTheory.LaxFunctor.map₂_rightUnitor_app_assoc, LaxLeftLinear.μₗ_unitality, CategoryTheory.Abelian.Pseudoelement.pseudoZero_aux, mapCommpGrp_id_mul, SheafOfModules.map_ιFree_mapFree_hom, CategoryTheory.CommGrp.forget₂CommMon_obj_one, CategoryTheory.ShortComplex.SnakeInput.composableArrowsFunctor_obj, CategoryTheory.sheafToPresheaf_η, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_right, preordToCat_obj, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_hom_app_app_hom, TopCat.Presheaf.presheafEquivOfIso_counitIso_inv_app_app, AlgebraicGeometry.Scheme.IdealSheafData.zeroLocus_inter_subset_supportSet, CategoryTheory.Iso.map_hom_inv_id_app_assoc, HomotopyCategory.homologyFunctor_shiftMap_assoc, CochainComplex.augmentTruncate_inv_f_succ, PreservesMonomorphisms.preserves, AlgebraicGeometry.ι_sigmaSpec_assoc, CategoryTheory.Subobject.underlyingIso_inv_top_arrow_assoc, AlgebraicGeometry.IsAffineOpen.preimage_of_isIso, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_hom_app_left, CategoryTheory.ι_colimitCompWhiskeringRightIsoColimitComp_hom_assoc, HomologicalComplex₂.totalShift₂Iso_hom_naturality, CategoryTheory.Subobject.isPullback, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_app_assoc, CategoryTheory.DifferentialObject.Hom.comm, Action.FunctorCategoryEquivalence.inverse_map_hom, AlgebraicGeometry.PresheafedSpace.Γ_map, CategoryTheory.Idempotents.KaroubiKaroubi.inverse_obj_p, CategoryTheory.Limits.coconeRightOpOfCone_ι, AlgebraicGeometry.instIsClosedImmersionMorphismRestrict, CategoryTheory.Pretriangulated.contractibleTriangle_mor₃, CategoryTheory.Limits.MonoFactorisation.ofArrowIso_I, CategoryTheory.Mat_.lift_map, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.unitIso_hom_app_f_f, CategoryTheory.Adjunction.homAddEquiv_neg, AlgebraicGeometry.Scheme.Hom.preimage_inf, MonObj.mopEquiv_functor_obj_mon_mul_unmop, CategoryTheory.MorphismProperty.comma_iso_iff, AlgebraicGeometry.SheafedSpace.id_hom_c, AlgebraicTopology.NormalizedMooreComplex.obj_X, mapHomotopyCategory_map, SSet.mem_skeletonOfMono_obj_iff_of_nonDegenerate, CategoryTheory.StructuredArrow.pre_map_right, FundamentalGroupoidFunctor.piIso_inv, AlgebraicGeometry.ΓSpec.right_triangle, CategoryTheory.Limits.colimit.ι_desc_app_assoc, CategoryTheory.TwoSquare.whiskerRight_app, ModuleCat.FreeMonoidal.μIso_inv_freeMk, CategoryTheory.PreGaloisCategory.stabilizer_normal_of_isGalois, CoreMonoidal.right_unitality, CategoryTheory.Limits.Cocone.toCostructuredArrow_obj, TopologicalSpace.Opens.op_map_comp_obj, CategoryTheory.Idempotents.KaroubiKaroubi.unitIso_hom_app_f, CategoryTheory.Adjunction.homEquiv_symm_id, AlgebraicGeometry.SheafedSpace.id_c_app, AlgebraicGeometry.isPullback_morphismRestrict, CochainComplex.shiftFunctor_obj_X', elementsFunctor_obj, Rep.linearization_δ_hom, CategoryTheory.TwistShiftData.shiftFunctorAdd'_inv_app, CategoryTheory.Limits.PullbackCone.combine_pt_map, CategoryTheory.SmallObject.SuccStruct.extendToSucc_obj_succ_eq, CategoryTheory.Limits.equalizerSubobject_arrow_assoc, OplaxRightLinear.δᵣ_naturality_left_assoc, CategoryTheory.Quotient.full_whiskeringLeft_functor, CategoryTheory.Limits.Fork.IsLimit.lift_ι_assoc, mapBiprod_inv, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal', CochainComplex.HomComplex.Cochain.shift_v, CompHausLike.LocallyConstant.instIsIsoFunctorTypeUnitSheafCoherentTopologyAdjunction, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₃, CategoryTheory.Kleisli.Adjunction.fromKleisli_obj, CategoryTheory.CartesianMonoidalCategory.prodComparison_fst_assoc, AlgebraicGeometry.StructureSheaf.toOpenₗ_top_bijective, CochainComplex.shiftFunctorZero_hom_app_f, CategoryTheory.Bimon.BimonObjAux_comul, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counit_app_tensor_assoc, CategoryTheory.Join.mapPairComp_inv_app_left, AlgebraicGeometry.isPullback_inr_inr_coprodMap, CategoryTheory.StructuredArrow.w_prod_fst_assoc, CategoryTheory.WithInitial.coconeEquiv_inverse_map_hom_right, AlgebraicGeometry.StructureSheaf.comap_id_eq_map, AlgebraicGeometry.Scheme.Hom.appIso_hom, CategoryTheory.Quotient.faithful_whiskeringLeft_functor, CategoryTheory.Limits.colimit.eqToHom_comp_ι, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_inv_app_hom_coe', CategoryTheory.Presieve.isSheafFor_arrows_iff_pullbacks, isMittagLeffler_iff_subset_range_comp, CategoryTheory.Subobject.isIso_arrow_iff_eq_top, ContAction.resCongr_inv, CategoryTheory.Endofunctor.Coalgebra.forget_obj, Monoidal.map_whiskerLeft, limitIsoOfIsRightKanExtension_inv_π_assoc, CategoryTheory.Square.fromArrowArrowFunctor_obj_f₂₄, CategoryTheory.ProjectiveResolution.Hom.hom_f_zero_comp_π_f_zero, Condensed.isColimitLocallyConstantPresheafDiagram_desc_apply, CategoryTheory.instIsIsoAppFromLeftDerivedZero, CategoryTheory.Comonad.counit_naturality_assoc, HomologicalComplex.pOpcycles_singleObjOpcyclesSelfIso_inv_assoc, SSet.S.equivElements_apply_snd, CategoryTheory.SimplicialObject.δ_comp_σ_self_assoc, CategoryTheory.ShiftedHom.opEquiv'_symm_comp, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀, CategoryTheory.Subfunctor.orderIsoSubobject_symm_apply, unopComp_inv_app, CategoryTheory.δ_naturality_assoc, CategoryTheory.CatCommSq.vComp_iso_inv_app, CategoryTheory.Limits.Types.jointly_surjective, AlgebraicTopology.NormalizedMooreComplex.objX_add_one, CategoryTheory.Limits.PullbackCone.equalizer_ext, CategoryTheory.Limits.CokernelCofork.map_π, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, AlgebraicTopology.DoldKan.N₂_obj_X_X, CategoryTheory.Limits.multicospanIndexEnd_left, Action.whiskerLeft_hom, CategoryTheory.Limits.limit.hom_ext_iff, mapMat__obj_fintype, CategoryTheory.Equivalence.core_unitIso_hom_app_iso_hom, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_X_isAddCommGroup, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd_assoc, SimplicialObject.Split.Hom.comm_assoc, CategoryTheory.Over.liftCocone_ι_app, SSet.HasDimensionLT.degenerate_eq_top, CategoryTheory.Sieve.functorInclusion_top_isIso, CategoryTheory.Adjunction.homEquiv_naturality_left_square_iff, CategoryTheory.Subobject.ofLE_mk_le_mk_of_comm, groupCohomology.mapCocycles₁_comp_i_apply, SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_hom_app, final_const_terminal, LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm, CategoryTheory.Limits.inr_comp_pushoutComparison_assoc, CategoryTheory.Idempotents.DoldKan.isoN₁_hom_app_f, CategoryTheory.Limits.PreservesCoproduct.inv_hom, CategoryTheory.Iso.map_inv_hom_id_eval, CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_π_succ, CategoryTheory.simplicialToCosimplicialAugmented_obj, AlgebraicTopology.DoldKan.N₁Γ₀_hom_app, CategoryTheory.Pretriangulated.Triangle.π₂_obj, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_εIso_inv, CategoryTheory.NatTrans.IsMonoidal.unit_assoc, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_apply, preimageIso_inv, HomologicalComplex.HomologySequence.instMonoMap'ComposableArrows₃OfNatNat, LeftExtension.precomp₂_obj_right, PullbackObjObj.π_snd_assoc, CategoryTheory.Adjunction.homEquiv_naturality_right_symm, InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj, LaxMonoidal.μ_natural_left, mapMonCompIso_inv_app_hom, SSet.prodStdSimplex.nonDegenerate_iff_injective_objEquiv, groupHomology.mapCycles₂_id_comp_apply, CategoryTheory.NatIso.naturality_2, CategoryTheory.MonoidalClosed.internalHom_obj, CategoryTheory.Pretriangulated.Triangle.π₃_obj, opComp_hom_app, CategoryTheory.ExponentiableMorphism.coev_naturality_assoc, CategoryTheory.FreeGroupoid.map_obj_mk, rightDerived_fac_app_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_left, Rep.standardComplex.instQuasiIsoNatεToSingle₀, CategoryTheory.Limits.CategoricalPullback.catCommSq_iso_inv_app, AlgebraicGeometry.Scheme.IdealSheafData.ideal_sup, CategoryTheory.Monad.comparison_map_f, CategoryTheory.StructuredArrow.mapIso_functor_obj_hom, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_fst, PushoutObjObj.mapArrowLeft_left, CategoryTheory.StructuredArrow.mapNatIso_unitIso_inv_app_right, BddLat.coe_forget_to_semilatSup, CategoryTheory.Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone_ι_app, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_functor_obj_d_f, CategoryTheory.Abelian.Ext.neg_hom, CategoryTheory.FinCategory.objAsTypeToAsType_obj, CategoryTheory.ShortComplex.mapCyclesIso_hom_iCycles, CategoryTheory.Limits.wideCoequalizer.cotrident_ι_app_one, CategoryTheory.Limits.limit.lift_π_assoc, CategoryTheory.Equivalence.sheafCongrPreregular_inverse_obj_val_obj, ranObjObjIsoLimit_hom_π, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_mapPullbackAdj_counit_app, AlgebraicGeometry.Scheme.evaluation_naturality_assoc, CategoryTheory.WithTerminal.isLimitEquiv_apply_lift_left, CategoryTheory.Limits.Fork.IsLimit.lift_ι', AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom, CategoryTheory.overToCoalgebra_obj_A, CategoryTheory.Equivalence.rightOp_unitIso_inv_app, mapTriangleCommShiftIso_hom_app_hom₁, LaxLeftLinear.μₗ_unitality_inv_assoc, OplaxLeftLinear.δₗ_unitality_inv_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_map_app_fst, OplaxMonoidal.ofBifunctor.secondMap₁_app_app_app, SSet.Quasicategory.hornFilling, CommMonCat.units_obj_coe, ModuleCat.directLimitCocone_ι_app, CategoryTheory.Mat_.isoBiproductEmbedding_inv, AlgebraicGeometry.tilde.toOpen_res, Alexandrov.projSup_obj, AlgebraicGeometry.tilde.toOpen_res_assoc, CategoryTheory.PreservesImage.hom_comp_map_image_ι_assoc, CategoryTheory.curryingIso_inv_toFunctor_map_app_app, AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap_assoc, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv_assoc, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_extMk, SSet.stdSimplex.instFiniteObjSimplexCategory, CompHausLike.isIsoSigmaComparison, CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso_hom_app, AlgebraicGeometry.Scheme.Hom.ι_fromNormalization_assoc, CochainComplex.HomComplex.Cochain.shiftAddHom_apply, CategoryTheory.Idempotents.natTrans_eq, FullyFaithful.homNatIso'_inv_app_down, CategoryTheory.ReflQuiv.adj.counit.comp_app_eq, SSet.stdSimplex.objMk_apply, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.inverseObj_comon_comul_app, isoShift_hom_naturality_assoc, CategoryTheory.ShortComplex.quasiIso_iff_evaluation, Monoidal.map_δ_μ, CategoryTheory.Comonad.forget_obj, CategoryTheory.Limits.CategoricalPullback.Hom.w'_assoc, CommRingCat.equalizer_ι_isLocalHom, Rep.MonoidalClosed.linearHomEquiv_hom, AlgebraicGeometry.Scheme.emptyTo_c_app, TopCat.presheafToType_obj, CategoryTheory.SingleFunctors.inv_hom_id_hom_app_assoc, Rep.invariantsAdjunction_homEquiv_apply_hom, CategoryTheory.MonoidalClosed.whiskerLeft_curry_ihom_ev_app, IsRepresentedBy.iff_isIso_uliftYonedaEquiv, CategoryTheory.InjectiveResolution.instQuasiIsoIntι', CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_hom_comp_π, SSet.Truncated.HomotopyCategory.homToNerveMk_app_edge, CompHausLike.LocallyConstant.counit_app_val, CategoryTheory.exists_simple_subobject, OneHypercoverDenseData.essSurj.presheafObj_hom_ext_iff, CategoryTheory.NatIso.isIso_map_iff, CategoryTheory.Bicategory.associatorNatIsoRight_hom_app, CategoryTheory.ULift.equivalence_counitIso_inv_app, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.functorObjObj_comon_comul, CategoryTheory.GrothendieckTopology.diagramNatTrans_app, SSet.Subcomplex.PairingCore.notMem₁, CategoryTheory.whiskeringLeft_preservesColimitsOfShape, CategoryTheory.Limits.prodComparison_natural, AlgebraicGeometry.Scheme.Opens.mem_basicOpen_toScheme, isZero_Ext_succ_of_projective, CategoryTheory.Meq.mk_apply, AlgebraicGeometry.affineAnd_apply, AlgebraicTopology.DoldKan.MorphComponents.postComp_φ, CategoryTheory.SimplicialObject.Augmented.rightOp_hom_app, CategoryTheory.Over.postEquiv_unitIso, AlgebraicGeometry.IsAffineOpen.preimage_of_isOpenImmersion, CategoryTheory.Square.evaluation₂_obj, LeftExtension.coconeAt_pt, CategoryTheory.NatTrans.naturality', CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂'_obj_obj_obj, CategoryTheory.yonedaEquiv_naturality, CategoryTheory.prodOpEquiv_inverse_obj, AlgebraicGeometry.tilde.isUnit_algebraMap_end_basicOpen, SimplicialObject.Splitting.πSummand_comp_cofan_inj_id_comp_PInfty_eq_PInfty_assoc, FundamentalGroupoidFunctor.prodIso_inv, CategoryTheory.Adjunction.homEquiv_apply, CategoryTheory.Abelian.preadditiveCoyonedaObj_map_surjective, SheafOfModules.instIsIsoPullbackObjUnitToUnitOfFinal, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_symm_apply, CochainComplex.HomComplex.Cochain.δ_leftUnshift, CategoryTheory.coalgebraToOver_map, SSet.N.mk_surjective, AlgebraicGeometry.coprodSpec_inl, CategoryTheory.ComposableArrows.fourδ₃Toδ₂_app_one, CategoryTheory.Limits.limit.lift_map, CategoryTheory.Grp.mkIso_inv_hom_hom, SheafOfModules.pushforwardNatTrans_app_val_app, AddCommGrpCat.HasLimit.lift_hom_apply, CategoryTheory.Under.instFullObjPostOfFaithful, CategoryTheory.Limits.PullbackCone.combine_pt_obj, mapPresheaf_obj_X, Profinite.Extend.cocone_ι_app, CategoryTheory.GrothendieckTopology.W_iff, AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE_locally, CategoryTheory.Idempotents.functorExtension_obj_map, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceInverse_map_fiber, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_left, CategoryTheory.StructuredArrow.functor_obj, CategoryTheory.PreGaloisCategory.evaluation_aut_surjective_of_isGalois, CategoryTheory.SimplicialObject.Augmented.point_obj, SimplicialObject.Split.natTransCofanInj_app, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_map_app_app, preservesColimit_coyoneda_of_finitePresentation, AlgebraicGeometry.Scheme.Hom.image_le_opensRange, CochainComplex.HomComplex.Cocycle.toSingleMk_neg, CategoryTheory.Limits.ImageFactorisation.ofArrowIso_isImage, CategoryTheory.Endofunctor.Algebra.functorOfNatTransComp_inv_app_f, PresheafOfModules.Sheafify.one_smul, CategoryTheory.Equivalence.unit_app_inverse, CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence_hom, CategoryTheory.Limits.whiskeringLimYonedaIsoCones_hom_app_app_app, CategoryTheory.Iso.isoCompInverse_hom_app, CategoryTheory.Limits.BinaryCofan.ι_app_left, CategoryTheory.ObjectProperty.inverseImage_trW_iff, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app_assoc, CategoryTheory.Limits.FormalCoproduct.cosimplicialObjectFunctor_obj_map, CategoryTheory.Comonad.Coalgebra.counit_assoc, ChainComplex.fromSingle₀Equiv_apply, CategoryTheory.Iso.isoInverseOfIsoFunctor_hom_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app_assoc, CategoryTheory.Limits.ColimitPresentation.ofIso_ι, CategoryTheory.Bimon.equivMonComonCounitIsoApp_hom_hom_hom, AlgebraicGeometry.targetAffineLocally_affineAnd_iff', CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app, CategoryTheory.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCone_π_app, CategoryTheory.Endofunctor.Algebra.functorOfNatTrans_obj_str, AlgebraicGeometry.AffineSpace.reindex_appTop_coord, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv_assoc, CategoryTheory.Pseudofunctor.IsStackFor.essSurj, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_inv_hom, CategoryTheory.Limits.colimit.map_desc_assoc, CategoryTheory.NatIso.inv_app_isIso, AlgebraicGeometry.smoothOfRelativeDimension_iff, CategoryTheory.InjectiveResolution.desc_commutes_zero, CategoryTheory.δ_naturality, CategoryTheory.enrichedNatTransYoneda_obj, topToPreord_obj_coe, CategoryTheory.Limits.BinaryBicone.toCocone_ι_app_left, CondensedMod.epi_iff_locallySurjective_on_compHaus, mapGrpNatTrans_app_hom_hom, AlgebraicGeometry.quasiCompact_iff_forall_isAffineOpen, FundamentalGroupoid.map_obj_as, CategoryTheory.LocalizerMorphism.LeftResolution.op_w, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_map, CategoryTheory.Idempotents.karoubiUniversal₁_unitIso, Rep.FiniteCyclicGroup.resolution_quasiIso, ModuleCat.uliftFunctor_obj, CategoryTheory.ComposableArrows.Exact.cokerIsoKer_hom_fac, HomologicalComplex.singleObjCyclesSelfIso_hom_assoc, CategoryTheory.Comonad.right_counit, AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE, CategoryTheory.Bimon.ofMonComon_toMonComon_obj_comul, MonCat.FilteredColimits.colimit_mul_mk_eq, comp_mapCommGrp_one, CategoryTheory.Limits.π_reflexiveCoequalizerIsoCoequalizer_inv, CategoryTheory.typeEquiv_functor_map_val_app, CategoryTheory.Subobject.underlyingIso_inv_top_arrow, CategoryTheory.SimplicialObject.δ_comp_δ_self', CategoryTheory.Limits.WidePullbackShape.functorExt_inv_app, toPseudoFunctor'_mapId, CochainComplex.shiftFunctorAdd'_hom_app_f', splitMonoBiprodComparison'_retraction, AlgebraicGeometry.ΓSpec.adjunction_homEquiv_symm_apply, CategoryTheory.Over.associator_inv_left_fst_snd_assoc, CategoryTheory.Comon.monoidal_leftUnitor_inv_hom, IsEventuallyConstantFrom.isoMap_hom_inv_id_assoc, CategoryTheory.CosimplicialObject.Augmented.leftOp_left_obj, AlgebraicGeometry.instSmoothMorphismRestrict, CategoryTheory.Comma.mapRight_map_left, mapHomotopyCategory_obj, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_inv, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_counit_app, CategoryTheory.Limits.Multifork.ofPiFork_π_app_right, CategoryTheory.Iso.op2_inv_unop2, SSet.RelativeMorphism.Homotopy.h₀, CategoryTheory.Monoidal.InducingFunctorData.whiskerLeft_eq, CochainComplex.HomComplex.Cochain.leftShift_add, pointwiseRightKanExtension_map, CategoryTheory.Iso.map_inv_hom_id_eval_app, CategoryTheory.Limits.PushoutCocone.mk_ι_app_right, BoolAlg.hasForgetToHeytAlg_forget₂_obj_coe, AlgebraicGeometry.Spec_Γ_naturality_assoc, AlgebraicGeometry.Scheme.IdealSheafData.ideal_mono, CategoryTheory.Abelian.PreservesCoimage.hom_coimageImageComparison, AlgebraicGeometry.RingedSpace.isUnit_res_basicOpen, AlgebraicGeometry.Scheme.empty_presheaf, CategoryTheory.Limits.Multicofork.snd_app_right, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_apply, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_inv_right_app, CategoryTheory.Comma.mapRightId_inv_app_right, CategoryTheory.SmallObject.SuccStruct.Iteration.congr_map, LeftExtension.postcomp₁_map_left, TopCat.Presheaf.germ_res'_assoc, TopModuleCat.free_obj, AlgebraicGeometry.Scheme.Opens.ι_app_self, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₂, CategoryTheory.ShortComplex.mapCyclesIso_inv_naturality, CategoryTheory.Grp.forget₂Mon_obj_one, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_π_app_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_app, RightExtension.coneAtFunctor_map_hom, CategoryTheory.GradedObject.eval_obj, CategoryTheory.Iso.map_hom_inv_id_eval, mapConeOp_inv_hom, CategoryTheory.prodFunctorToFunctorProd_obj, CategoryTheory.Limits.ι_reflexiveCoequalizerIsoCoequalizer_hom, TopologicalSpace.Opens.mapComp_inv_app, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_symm_apply, CategoryTheory.Limits.Cotrident.condition, CategoryTheory.Limits.reflexiveCoforkEquivCofork_inverse_obj_π, AlgebraicGeometry.ΓSpec.toSpecΓ_of, CochainComplex.HomComplex.Cochain.leftShift_comp_zero_cochain, HomologicalComplex.singleObjCyclesSelfIso_inv_naturality, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_hom_app_hom_hom_hom, CategoryTheory.MonoOver.forget_obj_hom, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_inv, TopCat.toSheafCompHausLike_val_map, map_shift_unop_assoc, CategoryTheory.toQuotientPaths_obj_as, AlgebraicGeometry.Scheme.zeroLocus_span, CategoryTheory.NatTrans.naturality_app_app, mapComposableArrows_obj_obj, CategoryTheory.ActionCategory.id_val, CategoryTheory.ShiftMkCore.zero_add_hom_app, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_comp, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₁, AlgebraicGeometry.StructureSheaf.toOpen_germ, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality, CategoryTheory.Over.rightUnitor_hom_left, AlgebraicGeometry.Scheme.IdealSheafData.ideal_iSup, CategoryTheory.Square.isPullback_iff_map_coyoneda_isPullback, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₃_assoc, CategoryTheory.monoidalUnopUnop_μ, Monoidal.whiskerRight_ε_η, CategoryTheory.Triangulated.Octahedron.comm₂, AlgebraicGeometry.Scheme.Hom.naturality, CochainComplex.augmentTruncate_hom_f_succ, CategoryTheory.MorphismProperty.Over.pullback_map_left, groupCohomology.cochainsMap_f_hom, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₁_app, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_snd_map, CategoryTheory.Comma.mapRightComp_hom_app_right, diag_η, HomotopicalAlgebra.CofibrantObject.instWeakEquivalenceHoCatAppιCompResolutionNatTrans, mapCommGrpIdIso_inv_app_hom_hom_hom, CategoryTheory.NatTrans.id_app, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app, CategoryTheory.ShortComplex.mapLeftHomologyIso_hom_naturality_assoc, CategoryTheory.Limits.Multifork.ofPiFork_π_app_left, AlgebraicGeometry.Scheme.Hom.image_injective, CategoryTheory.regularTopology.equalizerCondition_w, mapConePostcompose_hom_hom, HasFibers.Fib.isoMk_hom, whiskeringRightObjIdIso_inv_app_app, inv_fun_map, CategoryTheory.CostructuredArrow.instFullCompObjPostOfFaithful, CategoryTheory.Limits.pullbackComparison_comp_fst, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₁, CategoryTheory.Subobject.inf_le_right, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.pullback_to_base_isOpenImmersion, CategoryTheory.RightExactFunctor.ofExact_obj, CategoryTheory.sum.associator_map_inl_inr, CategoryTheory.Iso.core_inv_app_iso_inv, whiskeringLeft₂_obj_obj_obj_obj_map, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_assoc, CategoryTheory.Grothendieck.grothendieckTypeToCat_inverse_obj_fiber_as, partialRightAdjointHomEquiv_symm_comp_assoc, CategoryTheory.ihom.ev_naturality, CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence_inv, HomologicalComplex.singleCompEvalIsoSelf_hom_app, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app, 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, SSet.nonDegenerateEquivOfIso_apply_coe, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_app_assoc, Final.coconesEquiv_counitIso, CategoryTheory.CatEnriched.id_eq, LaxMonoidal.associativity, HomologicalComplex.homologicalComplexToDGO_obj_d, CategoryTheory.Equivalence.sheafCongr.inverse_obj_val_map, AlgebraicGeometry.Proj.stalkIso'_germ, TopCat.Presheaf.isGluing_iff_pairwise, SSet.modelCategoryQuillen.boundary_ι_mem_I, SimplexCategory.toCat_obj, flip₁₃_obj_obj_obj, CategoryTheory.CosimplicialObject.whiskering_map_app_app, CategoryTheory.Subobject.underlyingIso_top_hom, CategoryTheory.OrthogonalReflection.D₁.ι_comp_t, CategoryTheory.Limits.span_left, CategoryTheory.Sigma.incl_obj, CategoryTheory.Limits.HasImageMaps.has_image_map, AlgebraicGeometry.exists_isFinite_morphismRestrict_of_finite_preimage_singleton, CategoryTheory.Monoidal.associator_inv_app, SSet.Augmented.stdSimplex_map_left, CategoryTheory.FunctorToTypes.rightAdj_obj_obj, groupHomology.H1CoresCoinfOfTrivial_g, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_assoc, AlgebraicGeometry.IsAffine.affine, AlgebraicGeometry.IsAffineOpen.instAwayCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecPresheafOpOpensBasicOpen, map_isIso, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_obj_pt, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_cone_π_app, AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal.to_basicOpen, CategoryTheory.Bicategory.associatorNatIsoLeft_hom_app, AlgebraicGeometry.SheafedSpace.Γ_obj, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π_assoc, CategoryTheory.Limits.colimit.isoColimitCocone_ι_hom_assoc, CategoryTheory.Over.sections_map, CochainComplex.HomComplex.Cocycle.equivHomShift_comp, CategoryTheory.isCardinalPresentable_iff_isCardinalAccessible_coyoneda_obj, CategoryTheory.MorphismProperty.inverseImage_iff, CategoryTheory.Limits.pullbackConeOfRightIso_π_app_none, CategoryTheory.ShortComplex.SnakeInput.naturality_φ₂, CategoryTheory.Limits.pullbackComparison_comp_snd, CategoryTheory.Adjunction.rightAdjointUniq_hom_app_counit_assoc, CategoryTheory.SingleObj.differenceFunctor_obj, CategoryTheory.ChosenPullbacksAlong.fst'_left, HomotopicalAlgebra.CofibrantObject.instWeakEquivalenceHoCatAppAdjUnit, RightExtension.coneAtWhiskerRightIso_hom_hom, flipping_inverse_map_app_app, CategoryTheory.Monoidal.InducingFunctorData.leftUnitor_eq, SSet.Truncated.trunc_spine, HomologicalComplex.singleObjOpcyclesSelfIso_inv_naturality_assoc, CategoryTheory.ShortComplex.toComposableArrows_obj, CategoryTheory.sheafification_obj, CategoryTheory.Comma.mapRightIso_inverse_obj_hom, CommBialgCat.forget_obj, SSet.stdSimplex.faceSingletonComplIso_hom_ι_assoc, CategoryTheory.TwistShiftData.shiftFunctorAdd'_hom_app, AlgebraicGeometry.Scheme.restrict_presheaf_map, flip₁₃Functor_map_app_app_app, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_right, CategoryTheory.Cat.HasLimits.comp_def, Action.FunctorCategoryEquivalence.counitIso_hom_app_app, CategoryTheory.Sheaf.ΓHomEquiv_naturality_right, CategoryTheory.CosimplicialObject.equivalenceLeftToRight_left, CategoryTheory.Subfunctor.image_obj, SSet.RelativeMorphism.Homotopy.precomp_h, CategoryTheory.CartesianMonoidalCategory.prodComparisonIso_id, CategoryTheory.GradedObject.mapTrifunctorObj_map_app, HomologicalComplex.quasiIso_opFunctor_map_iff, CategoryTheory.MonoOver.commSqOfHasStrongEpiMonoFactorisation, CategoryTheory.Limits.cokernel_map_comp_cokernelComparison_assoc, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_inv_assoc, CategoryTheory.Subobject.ofMkLE_comp_ofLE_assoc, CategoryTheory.MonoidalCategory.externalProductSwap_inv_app_app, CategoryTheory.MonoidalClosed.curryHomEquiv'_symm_apply, mapArrowFunctor_map_app_right, FundamentalGroupoidFunctor.projRight_map, CategoryTheory.evaluation_obj_obj, CategoryTheory.PreGaloisCategory.PointedGaloisObject.Hom.comp, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_hom_app_app, CategoryTheory.ExponentiableMorphism.coev_naturality, CategoryTheory.Triangulated.TStructure.triangleLTGE_obj_mor₂, CategoryTheory.map_yonedaEquiv, groupHomology.π_comp_H0Iso_hom, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.ofRestrict_invApp, CategoryTheory.Limits.coequalizerComparison_map_desc_assoc, AlgebraicGeometry.formallyUnramified_iff, TopCat.adj₂_counit, CategoryTheory.Subfunctor.range_subobjectMk_ι, CategoryTheory.ComposableArrows.IsComplex.epi_cokerToKer', CategoryTheory.rightAdjointOfCostructuredArrowTerminalsAux_symm_apply, CategoryTheory.Limits.inl_comp_pushoutObjIso_hom_assoc, TopologicalSpace.Opens.map_comp_obj, PresheafOfModules.map_id, CommGrpCat.coyonedaForget_inv_app_app, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv, CategoryTheory.StructuredArrow.mapIso_inverse_map_right, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_obj_obj_obj, AlgebraicGeometry.Scheme.mem_basicOpen_top, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app_assoc, CategoryTheory.sum.inlCompInverseAssociator_inv_app_down_down, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoColimitUncurryWhiskeringLeft₂_hom_assoc, shiftIso_hom_app_comp_shiftMap, CochainComplex.shiftFunctor_obj_d', CategoryTheory.MonoidalClosed.enrichedCategorySelf_hom, CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois_symm_fiber, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_hom, CategoryTheory.GrothendieckTopology.uliftYonedaIsoYoneda_inv_app_val_app_down, CommRingCat.coyonedaUnique_hom_app_hom_apply, Condensed.isoFinYoneda_hom_app, CategoryTheory.Over.μ_pullback_left_snd, groupCohomology.mapShortComplexH1_id_comp_assoc, partialLeftAdjointHomEquiv_symm_comp_assoc, CategoryTheory.ULift.downFunctor_obj, CategoryTheory.Ind.isSeparating_range_yoneda, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.inverse_obj, CategoryTheory.ShortComplex.LeftHomologyData.mapHomologyIso_eq, CategoryTheory.instIsCardinalPresentableObjFullSubcategoryIsCardinalPresentableι, CategoryTheory.Limits.BinaryCofan.IsColimit.desc'_coe, AlgebraicGeometry.IsAffineOpen.range_fromSpec, shiftIso_add'_inv_app, CategoryTheory.Limits.Cocones.functoriality_map_hom, CategoryTheory.Join.mapPair_obj_left, CategoryTheory.Limits.ι_colimitLimitToLimitColimit_π_apply, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_naturality₂, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionHomRight, CategoryTheory.Limits.WalkingMulticospan.functorExt_inv_app, PushoutObjObj.mapArrowLeft_right, AlgebraicGeometry.IsOpenImmersion.image_preimage_eq_preimage_image_of_isPullback, ModuleCat.HasLimit.lift_hom_apply, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, groupCohomology.mapShortComplexH1_zero, SheafOfModules.pullbackPushforwardAdjunction_homEquiv_symm_unitToPushforwardObjUnit, biprodComparison_fst, CategoryTheory.Under.mapPushoutAdj_counit_app, CategoryTheory.Limits.combineCocones_ι_app_app, CategoryTheory.WithInitial.map_obj, CategoryTheory.FunctorToTypes.binaryProductCone_π_app, CategoryTheory.Over.iteratedSliceBackward_obj, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right, ModuleCat.binaryProductLimitCone_isLimit_lift, AlgebraicTopology.NormalizedMooreComplex.objX_zero, CategoryTheory.sum.associator_obj_inl_inr, CategoryTheory.Comonad.beckEqualizer_lift, instAdditiveObjEvaluation, CategoryTheory.Subfunctor.Subpresheaf.toRange_app_val, FullyFaithful.isoEquiv_symm_apply, SSet.ι₀_fst, CategoryTheory.Limits.DiagramOfCocones.coconePoints_obj, SimplexCategory.skeletalFunctor_obj, CategoryTheory.PreGaloisCategory.autEmbedding_range, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom_assoc, CategoryTheory.subterminalsEquivMonoOverTerminal_counitIso, HomologicalComplex.singleObjHomologySelfIso_inv_naturality, CategoryTheory.SmallObject.SuccStruct.arrowSucc_extendToSucc, CategoryTheory.CostructuredArrow.homMk'_comp, CategoryTheory.Adjunction.Triple.map_adj₂_counit_app_leftToRight_app, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen', CategoryTheory.Adjunction.Triple.map_rightToLeft_app_assoc, CategoryTheory.Regular.frobeniusStrongEpiMonoFactorisation_m, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_hom_app_app, CategoryTheory.GrothendieckTopology.Plus.inj_of_sep, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_assoc, CategoryTheory.Triangulated.TStructure.ge_shift, CategoryTheory.Comonad.comparison_obj_A, CategoryTheory.Idempotents.karoubiUniversal₁_inverse, CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_iff_epi₃, CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctor_obj, Profinite.Extend.cone_pt, leftDerived_fac_app_assoc, CategoryTheory.TwoSquare.structuredArrowDownwards_map, mapTriangleIso_inv_app_hom₂, CategoryTheory.Discrete.sumEquiv_inverse_obj, CategoryTheory.SmallObject.SuccStruct.arrowMap_ofCocone, CategoryTheory.evaluationAdjunctionRight_unit_app, AlgebraicTopology.DoldKan.N₂_obj_X_d, CategoryTheory.Limits.FormalCoproduct.evalOp_obj_map, CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse_map_left, CategoryTheory.MonoidalCategory.DayConvolution.whiskerLeft_comp_unit_app_assoc, CategoryTheory.Adjunction.unit_app_tensor_comp_map_δ, CategoryTheory.whiskeringRight_preservesLimitsOfShape, CategoryTheory.Over.mapFunctor_obj, groupCohomology.mapShortComplexH1_comp_assoc, Rep.coinvariantsTensorMk_apply, CategoryTheory.WithTerminal.coneEquiv_unitIso_inv_app_hom_left, CategoryTheory.Limits.Multifork.ofι_π_app, groupHomology.cyclesIso₀_inv_comp_cyclesMap, AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit_obj, CategoryTheory.Comon.monoidal_rightUnitor_hom_hom, Profinite.NobelingProof.spanFunctorIsoIndexFunctor_inv_app, whiskeringLeft₃ObjObjObj_obj_obj_obj_map, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_π, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_obj_obj_map, AlgebraicGeometry.LocallyRingedSpace.preimage_basicOpen, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_f, CategoryTheory.Pi.sum_map_app, CategoryTheory.Localization.structuredArrowEquiv_symm_apply, CategoryTheory.Over.map_obj_left, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionLeft_obj, CategoryTheory.BasedFunctor.instIsHomLiftObjPIdObj, AlgebraicGeometry.ProjectiveSpectrum.Proj.stalkMap_toSpec, mapMatId_hom_app, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_app, CategoryTheory.Triangulated.instNonemptyOctahedron, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_toSpecΓ_assoc, CategoryTheory.Equivalence.congrRightFunctor_obj, CategoryTheory.counit_obj_eq_map_counit, ModuleCat.localizedModule_functor_obj, CategoryTheory.ObjectProperty.strictMap_ofObj, Types.monoOverEquivalenceSet_inverse_obj, CategoryTheory.Subfunctor.toRangeSheafify_app_coe, mapHomologicalComplex_commShiftIso_hom_app_f, OplaxLeftLinear.δₗ_naturality_left, CategoryTheory.ShiftedHom.map_mk₀, CategoryTheory.RanIsSheafOfIsCocontinuous.fac, AlgebraicGeometry.Scheme.Hom.normalizationCoprodIso_inv_coprodDesc_fromNormalization_assoc, TopCat.nonempty_isColimit_iff_eq_coinduced, CategoryTheory.Limits.limit.isoLimitCone_inv_π, LeftExtension.mk_right, AlgebraicGeometry.AffineSpace.homOverEquiv_apply, CategoryTheory.SimplicialObject.Augmented.toArrow_obj_hom, FullyFaithful.hasShift.map_add_inv_app, SimpleGraph.componentComplFunctor_finite, CategoryTheory.Limits.Bicone.toCone_π_app, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_inv_hom₂, Monoidal.μ_snd, AlgebraicGeometry.pullbackRestrictIsoRestrict_inv_fst_assoc, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberDesc_assoc, CategoryTheory.ComposableArrows.δ₀Functor_obj_obj, CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj_hom_app, ModuleCat.instProjectiveObjFree, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_left, IsCoverDense.isoOver_inv_app, CategoryTheory.Comonad.beckFork_ι, Fin.castSuccFunctor_obj, partialFunToPointed_obj, CategoryTheory.WithTerminal.equivComma_functor_map_left_app, CategoryTheory.Adjunction.whiskerLeftRUnitIsoOfIsIsoCounit_hom_app, OplaxMonoidal.δ_comp_tensorHom_η_assoc, ContinuousCohomology.I_obj_V_topologicalSpace, groupHomology.H0π_comp_H0Iso_hom, FullyFaithful.grpObj_mul, CategoryTheory.Comma.preLeft_map_left, CategoryTheory.Subfunctor.ofSection_le_iff, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_δ_app, CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.functor_obj, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_app_assoc, CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app_assoc, CategoryTheory.Prod.swap_obj, flipping_functor_obj_obj_map, AlgebraicGeometry.Scheme.basicOpen_res, CommMonCat.coyonedaForget_hom_app_app_hom, CategoryTheory.Subfunctor.Subpresheaf.sSup_obj, CategoryTheory.MonoidalCategory.endofunctorMonoidalCategory.evaluationRightAction_actionAssocIso, CategoryTheory.MonoidalCategory.DayConvolution.associator_inv_unit_unit_assoc, CategoryTheory.Limits.limitOpIsoOpColimit_inv_comp_π, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_fst, CategoryTheory.Localization.Monoidal.triangle_aux₂, Rep.homEquiv_symm_apply_hom, AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem_toSpecΓ_assoc, AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp, CategoryTheory.Subobject.arrow_congr, TopologicalSpace.Opens.mapIso_hom_app, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.map_toTransfiniteCompositionOfShape, TopCat.Sheaf.objSupIsoProdEqLocus_inv_fst, CategoryTheory.instIsConstantObjSheafSheafCompose, CategoryTheory.Limits.equalizerComparison_comp_π_assoc, smoothSheaf.ι_evalHom, HomologicalComplex.coneOfHasLimitEval_π_app_f, CategoryTheory.linearYoneda_obj_obj_isModule, isoSum_hom_app_inr, postcompose₂_obj_obj_map_app, CategoryTheory.Limits.isIso_π_of_isInitial, CategoryTheory.toThinSkeleton_obj, CategoryTheory.Core.inclusion_obj, OplaxMonoidal.id_η, CategoryTheory.GlueData.ι_gluedIso_hom, CategoryTheory.CosimplicialObject.Augmented.whiskering_map_app_right, CategoryTheory.Monad.ForgetCreatesColimits.liftedCocone_ι_app_f, CategoryTheory.Localization.Preadditive.comp_add', AlgebraicGeometry.Smooth.exists_isStandardSmooth, SSet.associator_hom_app_apply, CategoryTheory.instIsIsoFunctorOppositeSheafToPresheafToSheafCompComposeAndSheafify, ModuleCat.FilteredColimits.M.mk_surjective, FDRep.forget₂_ρ, ModuleCat.extendScalarsComp_hom_app_one_tmul, CategoryTheory.Subobject.leInfCone_π_app_none, AlgebraicGeometry.Scheme.comp_appTop, RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π, CategoryTheory.WithInitial.liftFromUnderComp_hom_app, smoothSheafCommRing.ι_evalHom_assoc, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.forgetMapIsOpenImmersion, CategoryTheory.Equivalence.counitInv_naturality, CategoryTheory.ShortComplex.opcyclesFunctor_obj, groupHomology.map_id_comp_H0Iso_hom, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom_assoc, CommShift.OfComp.map_iso_hom_app_assoc, CategoryTheory.SimplicialObject.σ_comp_σ_assoc, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_obj_left, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTrans_obj_V, CategoryTheory.Limits.BinaryBicone.toBiconeFunctor_obj_ι, CategoryTheory.yonedaEvaluation_map_down, CategoryTheory.yoneda_preservesLimits, CochainComplex.HomComplex.Cocycle.fromSingleMk_precomp, CategoryTheory.Limits.DiagramOfCones.comp, CategoryTheory.CartesianClosed.uncurry_injective, CategoryTheory.Subfunctor.iInf_obj, AlgebraicGeometry.Scheme.IdealSheafData.radical_ideal, CategoryTheory.MonoidalCategory.DayConvolutionUnit.corepresentableByLeft_homEquiv, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_hom, AlgebraicGeometry.sigmaOpenCover_f, CategoryTheory.PresheafHom.IsSheafFor.app_cond, CategoryTheory.RetractArrow.map_i_right, CategoryTheory.Monad.monadMonEquiv_counitIso_inv_app_hom, Monoidal.map_η_ε_assoc, TopCat.Presheaf.Pushforward.comp_hom_app, CategoryTheory.Arrow.cechConerve_map, CategoryTheory.Limits.FormalCoproduct.evalCompInclIsoId_inv_app_app, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w_assoc, LaxMonoidal.whiskerRight_tensorUnit_comp_rightUnitor_hom, PushoutObjObj.mapArrowLeft_comp_assoc, mapCoconeOp_hom_hom, CategoryTheory.PreGaloisCategory.surjective_of_nonempty_fiber_of_isConnected, 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.NatTrans.app_smul, CategoryTheory.GrothendieckTopology.coneCompEvaluationOfConeCompDiagramFunctorCompEvaluation_π_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_right, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_inv_app_hom_app, CategoryTheory.FunctorToTypes.binaryCoproductCocone_ι_app, CategoryTheory.ULiftHom.down_obj, CategoryTheory.Limits.Sigma.cocone_ι, AlgebraicGeometry.IsClosedImmersion.isAffine_surjective_of_isAffine, sectionsEquivHom_apply_app, toPseudoFunctor'_mapComp, CategoryTheory.ProjectiveResolution.exact₀, CategoryTheory.Limits.limitIsoLimitCurryCompLim_inv_π_assoc, CategoryTheory.Subobject.inf_comp_left_assoc, CategoryTheory.bifunctorComp₂₃FunctorObj_obj, CategoryTheory.NatTrans.mapSquare_app_τ₄, CategoryTheory.ExactFunctor.forget_obj_of, CategoryTheory.ComposableArrows.map'_self, CommRingCat.instIsRightAdjointOppositeObjFunctorTypeYoneda, CategoryTheory.TwoSquare.structuredArrowDownwards_obj, CategoryTheory.ComposableArrows.Exact.isIso_cokerToKer', AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_germ, CategoryTheory.Monad.ForgetCreatesLimits.γ_app, CategoryTheory.ForgetEnrichment.equiv_counitIso, CategoryTheory.JointlyReflectIsomorphisms.isIso_iff, CategoryTheory.Presieve.piComparison_fac, CategoryTheory.Equivalence.unit_inverse_comp, CochainComplex.mappingCone.mapHomologicalComplexXIso'_hom, CategoryTheory.CostructuredArrow.mapNatIso_inverse_obj_right, SSet.OneTruncation₂.nerveEquiv_symm_apply_obj, AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp_assoc, map_comp, AlgebraicGeometry.Spec.toPresheafedSpace_obj_op, AlgebraicGeometry.StructureSheaf.toOpenₗ_eq_const, CategoryTheory.PreGaloisCategory.mulAction_naturality, CategoryTheory.Limits.BinaryBicone.ofLimitCone_fst, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst, CategoryTheory.Localization.Construction.objEquiv_apply, CategoryTheory.Localization.Monoidal.β_hom_app, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app, CategoryTheory.sheafificationAdjunction_counit_app_val, CategoryTheory.Square.map_X₂, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_inv_app_app, CategoryTheory.Adjunction.right_triangle_components, CategoryTheory.Limits.pullbackObjIso_inv_comp_snd_assoc, CategoryTheory.WithInitial.coconeEquiv_counitIso_hom_app_hom, CategoryTheory.ihom.ev_naturality_assoc, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_hom_whiskerLeft_π_assoc, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_hom_app_hom_coe, Action.FunctorCategoryEquivalence.functor_μ, CategoryTheory.Limits.Cone.toUnder_π_app, CategoryTheory.isIso_iff_isIso_coyoneda_map, SSet.image_degenerate_le, AlgebraicGeometry.Scheme.fromSpecStalk_app, Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eq, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id_app, CategoryTheory.Limits.colimitCoyonedaHomIsoLimit_π_apply, copyObj_obj, CategoryTheory.Enriched.FunctorCategory.diagram_obj_map, AlgebraicGeometry.IsAffineOpen.isLocalization_stalk, AlgebraicTopology.DoldKan.karoubi_PInfty_f, CategoryTheory.ParametrizedAdjunction.unit_whiskerRight_map, CategoryTheory.Adjunction.unit_app_commShiftIso_hom_app, CategoryTheory.CommMon.forget_obj, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counitIso_hom_app_tensor, CategoryTheory.Under.postAdjunctionLeft_counit_app, CategoryTheory.Endofunctor.Adjunction.Algebra.toCoalgebraOf_obj_V, CategoryTheory.Limits.Cones.equivalenceOfReindexing_unitIso, CategoryTheory.CartesianMonoidalCategory.isLeftAdjoint_prod_functor, functorialityCompPrecompose_inv_app_hom, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₃, TopCat.GlueData.MkCore.t_inter, CategoryTheory.Over.instFullObjPostOfFaithful, prod'_η_fst, CategoryTheory.ShortComplex.mapOpcyclesIso_inv_naturality_assoc, CategoryTheory.Limits.FormalCoproduct.instPreservesColimitDiscreteFunctorObjFunctorEval, CategoryTheory.MonoidalClosed.homEquiv_apply_eq, CategoryTheory.Comonad.beckFork_pt, CategoryTheory.Limits.coneOfSectionCompCoyoneda_π, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isColimit, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_comp, flip₂₃_obj_map_app, CategoryTheory.ActionCategory.stabilizerIsoEnd_apply, CochainComplex.fromSingle₀Equiv_symm_apply_f_zero, HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_symm_apply, CategoryTheory.flippingIso_inv_toFunctor_obj_obj_map, HomologicalComplex.homologicalComplexToDGO_obj_obj, AddCommMonCat.equivalence_functor_obj_coe, CategoryTheory.Subobject.pullback_top, CochainComplex.HomComplex.Cochain.leftShift_units_smul, CategoryTheory.CommSq.map, commShiftIso_id_inv_app, CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso_inv_app, CategoryTheory.Limits.DiagramOfCocones.id, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp_assoc, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_hom_π_assoc, mapGrpNatIso_inv_app_hom_hom, AlgebraicGeometry.isField_of_universallyClosed, commBialgCatEquivComonCommAlgCat_inverse_obj, ModuleCat.preservesFiniteLimits_tensorLeft_of_ringHomFlat, Monoidal.μ_snd_assoc, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_base_apply, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_inv_app_hom_hom_app, CategoryTheory.Over.instEssSurjObjPostOfFull, Monoidal.map_η_ε, CategoryTheory.CostructuredArrow.mapNatIso_functor_map_left, CategoryTheory.Adjunction.whiskerLeft_unit_app_app, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_comp, CategoryTheory.Limits.MulticospanIndex.parallelPairDiagramOfIsLimit_obj, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app_assoc, HomObj.naturality_assoc, CategoryTheory.Subfunctor.ι_app, CategoryTheory.Limits.CoconeMorphism.map_w_assoc, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_hom_app_hom, Monoidal.map_tensor, CategoryTheory.IsCardinalPresentable.exists_hom_of_isColimit, CategoryTheory.hoFunctor.instIsIsoCatProdComparisonSSetHoFunctorNerve, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_left, CategoryTheory.Over.braiding_hom_left, CategoryTheory.MorphismProperty.LeftFraction.map_comp_map_s, CategoryTheory.MonoOver.instMonoHomDiscretePUnitObjOverForget, CategoryTheory.Presieve.IsSheafFor.functorInclusion_comp_extend_assoc, HomotopyCategory.homologyShiftIso_hom_app, AlgebraicGeometry.Scheme.IdealSheafData.ideal_inf, CategoryTheory.Presheaf.map_comp_uliftYonedaEquiv_down, CategoryTheory.Abelian.LeftResolution.instPreservesZeroMorphismsKaroubiFKaroubi, CategoryTheory.Limits.limCompFlipIsoWhiskerLim_hom_app_app, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_eq_zero_iff_notMem_basicOpen, CategoryTheory.Free.lift_map, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq_comap, SSet.boundary_eq_iSup, CategoryTheory.Limits.limitIsoLimitCurryCompLim_hom_π_π, CategoryTheory.Limits.instHasCokernelMapOfPreservesColimitWalkingParallelPairParallelPairOfNatHom, ChainComplex.augmentTruncate_inv_f_zero, CategoryTheory.Limits.prodComparison_natural_assoc, CategoryTheory.ShiftedHom.map_add, CategoryTheory.Subpresheaf.isSheaf_iff, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app, CochainComplex.shiftFunctorAdd_hom_app_f, CategoryTheory.GrothendieckTopology.Cover.index_right, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_apply, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_obj_hom, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv_assoc, CategoryTheory.Limits.hasLimitCompEvaluation, CategoryTheory.WithInitial.liftFromUnder_map_app, CategoryTheory.obj_μ_app_assoc, groupCohomology.mapShortComplexH2_id_comp, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_left, CategoryTheory.SingleFunctors.evaluation_obj, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIdIso_inv_app_hom, CategoryTheory.Limits.instIsIsoCoequalizerComparison, SSet.RelativeMorphism.Homotopy.h₁, whiskeringRight_obj_obj, CategoryTheory.Discrete.monoidalFunctor_obj, CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_hom_app, CoreMonoidal.toLaxMonoidal_ε, CategoryTheory.HasLiftingProperty.transfiniteComposition.sqFunctor_obj, Stonean.instProjectiveCompHausCompHaus, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_counit_app, CochainComplex.truncateAugment_hom_f, Monoidal.whiskerRight_app_snd, smoothSheafCommRing.ι_forgetStalk_hom, CategoryTheory.MorphismProperty.Over.pullback_obj_hom, CategoryTheory.Sieve.functorInclusion_is_mono, CategoryTheory.GrothendieckTopology.overMapPullbackComp_hom_app_val_app, CategoryTheory.CommGrp.forget_obj, SimplicialObject.Splitting.comp_PInfty_eq_zero_iff, CategoryTheory.Quotient.lift.isLift_inv, CategoryTheory.Limits.IsColimit.isIso_ι_app_of_isTerminal, PreservesProjectiveObjects.projective_obj, CategoryTheory.Injective.injective_iff_preservesEpimorphisms_yoneda_obj, InfiniteGalois.mk_toAlgEquivAux, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_germ, SSet.stdSimplex.spineId_vertex, CategoryTheory.Limits.limitCompYonedaIsoCocone_hom_app, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_inv, lanCompIsoOfPreserves_hom_app, CategoryTheory.Adjunction.isIso_unit_app_of_iso, AlgebraicGeometry.instGeometricallyIntegralMorphismRestrict, flip₂₃_map_app_app, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.F_obj, CategoryTheory.Iso.inverseCompIso_inv_app, AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app_surjective, AlgebraicGeometry.Scheme.preimage_zeroLocus, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_obj_map, CategoryTheory.SimplicialObject.cechNerveEquiv_apply, mono_map_iff_mono, postcompose₃_obj_map_app_app_app, LeibnizAdjunction.adj_unit_app_right, CategoryTheory.Limits.coconeOfConeLeftOp_ι_app, CategoryTheory.Comma.equivProd_inverse_obj_left, CategoryTheory.StructuredArrow.projectSubobject_factors, OplaxMonoidal.δ_natural, GrpCat.toAddGrp_obj_coe, LaxLeftLinear.μₗ_naturality_left_assoc, CategoryTheory.Limits.coconeEquivalenceOpConeOp_inverse_obj, AlgebraicGeometry.PresheafedSpace.congr_app, DerivedCategory.Qh_obj_singleFunctors_obj, CategoryTheory.pullbackShiftFunctorZero'_inv_app, CategoryTheory.Limits.limit.coneMorphism_π, leftExtensionEquivalenceOfIso₁_unitIso_hom_app_right_app, CategoryTheory.simplicialCosimplicialEquiv_functor_obj_obj, CategoryTheory.Idempotents.KaroubiKaroubi.counitIso_hom_app_f_f, CategoryTheory.Subfunctor.Subpresheaf.ofSection_le_iff, CategoryTheory.ObjectProperty.isLocal_adj_unit_app, AlgebraicGeometry.Scheme.AffineZariskiSite.cocone_ι_app, CategoryTheory.Subfunctor.top_obj, whiskeringLeft₃ObjObjObj_obj_obj_map_app, TopCat.Presheaf.presheafEquivOfIso_counitIso_hom_app_app, CategoryTheory.TwoSquare.guitartExact_iff_isConnected_rightwards, CategoryTheory.Abelian.FunctorCategory.imageObjIso_hom, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv, CategoryTheory.Limits.MultispanIndex.multispan_obj_left, CategoryTheory.Join.mkFunctorRight_inv_app, CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.map_eq_pullHom_assoc, map_neg, CategoryTheory.Idempotents.DoldKan.Γ_map_app, CategoryTheory.PresheafOfGroups.OneCocycle.ev_refl, CategoryTheory.Subobject.underlyingIso_hom_comp_eq_mk, CategoryTheory.Limits.ι_colimitPointwiseProductToProductColimit_π_assoc, OplaxMonoidal.δ_natural_right, CategoryTheory.Limits.Cocone.op_π, CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_snd, CategoryTheory.endofunctorMonoidalCategory_rightUnitor_hom_app, AlgebraicGeometry.Scheme.forgetToLocallyRingedSpace_obj, Rep.resIndAdjunction_unit_app, CategoryTheory.Subobject.pullback_comp, homMonoidHom_apply, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd, CategoryTheory.NatIso.isIso_inv_app, CategoryTheory.Limits.KernelFork.map_condition, CategoryTheory.Monad.ofMon_obj, CategoryTheory.Sieve.functorPushforward_top, HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_apply, CategoryTheory.Pseudofunctor.map₂_whisker_left_app, CategoryTheory.Limits.coend.ι_map_assoc, CategoryTheory.overToCoalgebra_obj_a, CochainComplex.HomComplex.δ_map, CategoryTheory.Limits.PreservesPullback.iso_hom_fst_assoc, PushoutObjObj.ofHasPushout_inr, CategoryTheory.Endofunctor.Adjunction.Algebra.toCoalgebraOf_map_f, CategoryTheory.Limits.coconeOfConeUnop_ι, CategoryTheory.Adjunction.homEquiv_naturality_left_symm, CategoryTheory.Enriched.FunctorCategory.homEquiv_apply_π_assoc, CategoryTheory.MorphismProperty.Over.mapComp_inv_app_left, AlgebraicGeometry.Scheme.IdealSheafData.coe_support_inter, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_obj_right_as, CategoryTheory.FunctorToTypes.mem_fromOverSubfunctor_iff, CategoryTheory.Limits.colimitYonedaHomIsoLimitOp_π_apply, HomologicalComplex₂.totalShift₁Iso_hom_naturality_assoc, CategoryTheory.coyoneda_preservesLimit, CategoryTheory.Limits.imageSubobjectCompIso_inv_arrow, CategoryTheory.NatTrans.congr, CategoryTheory.Pseudofunctor.CoGrothendieck.comp_const, CategoryTheory.Limits.epi_of_isColimit_parallelFamily, CategoryTheory.LocalizerMorphism.Derives.isRightDerivedFunctor_iff_isIso, AlgebraicTopology.DoldKan.Γ₂N₁.natTrans_app_f_app, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_inv_π, QuadraticModuleCat.cliffordAlgebra_obj_carrier, CategoryTheory.IsPushout.map, CategoryTheory.flip_comp_evaluation, CategoryTheory.Square.map_X₃, HomologicalComplex.unopInverse_obj, CompHausLike.isoOfHomeo_inv_hom_hom_apply, OplaxRightLinear.δᵣ_associativity_assoc, CategoryTheory.Limits.Types.FilteredColimit.eqvGen_colimitTypeRel_of_rel, CategoryTheory.NatIso.naturality_2_assoc, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_inverse_obj_X_X, SSet.degenerate_eq_iUnion_range_σ, CategoryTheory.shiftFunctorComm_hom_app_of_add_eq_zero, AlgebraicGeometry.IsAffineOpen.fromSpec_top, CategoryTheory.nerve.functorOfNerveMap_nerveFunctor₂_map, CategoryTheory.Limits.PushoutCocone.isoMk_hom_hom, CategoryTheory.Over.μ_pullback_left_fst_fst, CategoryTheory.Limits.coconeOfCoconeUncurry_pt, CategoryTheory.MonoidalClosed.compTranspose_eq, CategoryTheory.PreGaloisCategory.IsNaturalSMul.naturality, CategoryTheory.Iso.isoFunctorOfIsoInverse_hom_app, CategoryTheory.WithInitial.opEquiv_functor_obj, SheafOfModules.relationsOfIsCokernelFree_s, CategoryTheory.Discrete.opposite_inverse_obj, CategoryTheory.SimplicialObject.instIsLeftKanExtensionOppositeTruncatedSimplexCategoryObjSkAppTruncatedUnitSkAdjTruncation, CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse_obj_left_as, CategoryTheory.bifunctorComp₂₃FunctorMap_app_app_app_app, CategoryTheory.ShiftedHom.opEquiv_symm_apply, CategoryTheory.Over.starPullbackIsoStar_inv_app_left, CategoryTheory.LocalizerMorphism.isIso_iff_of_isRightDerivabilityStructure, CategoryTheory.Comma.mapSnd_hom_app, CategoryTheory.IsHomLift.domain_eq, SSet.RelativeMorphism.Homotopy.postcomp_h, AddCommGrpCat.kernelIsoKer_hom_comp_subtype, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_functor_obj_str, CategoryTheory.Limits.FintypeCat.jointly_surjective, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_map_snd_app, CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero_assoc, CategoryTheory.Limits.Fork.op_ι_app_zero, descOfIsLeftKanExtension_fac_app_assoc, CategoryTheory.Over.iteratedSliceForward_map, CategoryTheory.ActionCategory.homOfPair.val, CategoryTheory.Comonad.CofreeEqualizer.condition, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_snd, CategoryTheory.prodOpEquiv_functor_obj, CategoryTheory.Sieve.functorPullback_pushforward_le, CategoryTheory.Limits.end_.map_π_assoc, HomologicalComplex.opcyclesFunctor_obj, HomologicalComplex₂.flipEquivalenceCounitIso_inv_app_f_f, mapTriangleIdIso_inv_app_hom₁, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left, CategoryTheory.Limits.coconeOfCoconeUncurry_ι_app, AlgebraicTopology.DoldKan.degeneracy_comp_PInfty, postcompose₂_map_app_app_app, CategoryTheory.Adjunction.rightAdjointLaxMonoidal_ε, CategoryTheory.Limits.kernelSubobject_arrow_comp_assoc, CategoryTheory.Pretriangulated.rotate_obj, FullyFaithful.preimage_comp_assoc, mapGrpCompIso_inv_app_hom_hom, AlgebraicGeometry.Scheme.map_basicOpen_map, CategoryTheory.Limits.cospanOp_inv_app, CategoryTheory.Grothendieck.transport_fiber, CategoryTheory.bifunctorComp₁₂FunctorObj_map_app_app_app, MatrixModCat.toModuleCat_obj_isAddCommGroup, CochainComplex.HomComplex.Cochain.toSingleMk_postcomp, CategoryTheory.Presheaf.freeYonedaHomEquiv_comp_assoc, CategoryTheory.Sieve.functorPushforward_le_iff_le_functorPullback, Final.exists_coeq_of_locally_small, CategoryTheory.ShortComplex.mapRightHomologyIso_hom_naturality_assoc, AlgebraicGeometry.affineOpensRestrict_symm_apply_coe, CategoryTheory.coyonedaPairing_map, CategoryTheory.Subobject.pullback_self, CategoryTheory.Adjunction.homEquiv_counit, CategoryTheory.MorphismProperty.underObj_iff, CategoryTheory.Limits.MonoCoprod.mono_binaryCofanSum_inr, CategoryTheory.Localization.Monoidal.μ_natural_right_assoc, CategoryTheory.ExponentialIdeal.exp_closed, CategoryTheory.CosimplicialObject.whiskering_obj_obj_map, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_hom_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionUnitIso_hom, CategoryTheory.Limits.cospanCompIso_hom_app_right, CategoryTheory.MonoOver.inf_obj, AlgebraicGeometry.PresheafedSpace.id_c_app, CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_none, ComplexShape.Embedding.restrictionFunctor_obj, mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app, LaxRightLinear.μᵣ_unitality_assoc, CategoryTheory.Presheaf.tautologicalCocone_ι_app, CategoryTheory.CostructuredArrow.pre_map_right, CategoryTheory.Equivalence.unit_app_comp_inverse_map_η_functor_assoc, PreOneHypercoverDenseData.multicospanIndex_left, LaxMonoidal.ε_tensorHom_comp_μ, Rep.coinvariantsTensorIndHom_mk_tmul_indVMk, CategoryTheory.Limits.zero_app, CategoryTheory.Sum.inr__obj, map_injective, CategoryTheory.Pseudofunctor.CoGrothendieck.map_obj_base, CategoryTheory.Pseudofunctor.CoGrothendieck.compIso_inv_app, AlgebraicGeometry.Scheme.Hom.comp_appTop, Rep.ihom_coev_app_hom, CategoryTheory.CosimplicialObject.Augmented.leftOp_hom_app, HomologicalComplex.asFunctor_map_f, CategoryTheory.Pretriangulated.instIsHomologicalAddCommGrpCatObjOppositeFunctorPreadditiveCoyoneda, ChainComplex.alternatingConst_exactAt, CategoryTheory.ShiftedHom.opEquiv'_apply, CategoryTheory.Limits.CatCospanTransform.leftUnitor_inv_base_app, SSet.S.equivElements_symm_apply_simplex, CategoryTheory.Square.fromArrowArrowFunctor'_map_τ₁, CategoryTheory.Presheaf.equalizerSieve_apply, CochainComplex.toSingle₀Equiv_apply, SSet.stdSimplex.face_inter_face, CategoryTheory.WithInitial.mkCommaObject_left, core_map_iso_hom, CategoryTheory.Limits.colimit.post_desc, LaxMonoidal.whiskerLeft_μ_comp_μ, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app_assoc, RepresentableBy.equivUliftYonedaIso_apply, core_map_iso_inv, AlgebraicGeometry.IsOpenImmersion.opensRange_pullback_snd_of_left, CategoryTheory.Cat.HasLimits.limitConeLift_toFunctor, CategoryTheory.StructuredArrow.mapNatIso_functor_obj_left, CategoryTheory.Pretriangulated.Triangle.functorHomMk'_app_hom₂, leftOp_map, toOplaxFunctor_mapId, CategoryTheory.nerveFunctor_obj, AlgebraicGeometry.IsIntegralHom.hasAffineProperty, CategoryTheory.CatCommSq.iso_hom_naturality_assoc, AlgebraicGeometry.Scheme.Hom.preimage_mono, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_left, CategoryTheory.Adjunction.counit_naturality_assoc, CategoryTheory.Equivalence.leftOp_counitIso_hom_app, obj.ι_def_assoc, CategoryTheory.Limits.Trident.app_zero_assoc, CategoryTheory.MorphismProperty.Under.w_assoc, CategoryTheory.Arrow.square_to_iso_invert, CategoryTheory.constantSheafAdj_counit_w, CategoryTheory.Limits.colimit_map_colimitObjIsoColimitCompEvaluation_hom, HomologicalComplex.singleObjCyclesSelfIso_hom_naturality_assoc, CategoryTheory.Limits.instIsIsoPiComparison, SSet.stdSimplex.mem_nonDegenerate_iff_mono, CategoryTheory.Endofunctor.Adjunction.Algebra.toCoalgebraOf_obj_str, CategoryTheory.oppositeShiftFunctorAdd'_hom_app, MonCat.units_obj_coe, SheafOfModules.bijective_pushforwardSections, ModuleCat.restrictScalars.smul_def', SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero, CategoryTheory.Presheaf.tautologicalCocone'_ι_app, PresheafOfModules.pushforward_obj_map_apply', CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.presheafHom_naturality_assoc, CategoryTheory.Limits.PushoutCocone.mk_ι_app_left, curry_obj_map_app, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_comp_assoc, CategoryTheory.Limits.cospanCompIso_app_one, CategoryTheory.mono_of_cofan_isVanKampen, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec, CategoryTheory.Limits.walkingSpanOpEquiv_functor_obj, CategoryTheory.ProjectiveResolution.instQuasiIsoIntπ', groupHomology.chainsMap_zero, closedCounit_app_app, CategoryTheory.StructuredArrow.preEquivalenceFunctor_map_right, CategoryTheory.Subfunctor.IsGeneratedBy.mem, CategoryTheory.toOverIteratedSliceForwardIsoPullback_inv_app_left, mapCoconePrecompose_hom_hom, CategoryTheory.ShortComplex.ShortExact.singleTriangle_obj₃, PullbackObjObj.π_snd, CategoryTheory.Presheaf.coconeOfRepresentable_ι_app, CategoryTheory.ComposableArrows.threeδ₁Toδ₀_app_one, TwoP.swap_obj_X, CompHausLike.LocallyConstant.sigmaComparison_comp_sigmaIso, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂'_obj_obj_map, CategoryTheory.Limits.combineCones_pt_map, CompHausLike.LocallyConstant.unit_app, HomologicalComplex.mkHomFromSingle_f, AlgebraicGeometry.Scheme.basicOpen_zero, InfiniteGalois.proj_of_le, CategoryTheory.LocalizerMorphism.LeftResolution.Hom.comm_assoc, CategoryTheory.MonoidalCategory.Functor.curriedTensorPreIsoPost_inv_app_app, DerivedCategory.exists_iso_Q_obj_of_isLE, CategoryTheory.nerve.ext_of_isThin_iff, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counit_app_tensor, CategoryTheory.Adjunction.Triple.leftToRight_app, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₃, CategoryTheory.Limits.PreservesPushout.inl_iso_hom, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIdIso_hom_app_hom, CategoryTheory.Mon.limit_mon_one, CategoryTheory.PreGaloisCategory.exists_lift_of_mono, CochainComplex.shiftFunctorAdd'_hom_app_f, CategoryTheory.Limits.Cofork.op_π_app_one, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_right_app, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₁, AlgebraicGeometry.Scheme.IdealSheafData.ideal_ofIdeals_le, CategoryTheory.Limits.PreservesCokernel.π_iso_hom, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp_assoc, CategoryTheory.Limits.Types.FilteredColimit.rel_eq_eqvGen_colimitTypeRel, CategoryTheory.ComposableArrows.threeδ₃Toδ₂_app_zero, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.sigma_ι_isOpenEmbedding, CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm_assoc, CategoryTheory.Quotient.LiftCommShift.iso_inv_app, Stonean.instProjectiveProfiniteObjToProfinite, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_hom_right, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app, Action.resId_hom_app_hom, CommRingCat.monoidAlgebra_obj, DerivedCategory.instFullFunctorHomotopyCategoryIntUpObjWhiskeringLeftQh, PullbackObjObj.mapArrowRight_left, pi_obj, mapCommGrpNatIso_hom_app_hom_hom_hom, CategoryTheory.Limits.MulticospanIndex.multicospan_obj, CategoryTheory.Limits.limit.conePointUniqueUpToIso_inv_comp, CategoryTheory.prod.leftUnitor_obj, SSet.N.nonDegenerate, CategoryTheory.Arrow.cechConerve_obj, AlgebraicGeometry.Scheme.SpecMap_presheaf_map_eqToHom, CategoryTheory.Limits.IsLimit.map_π_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_obj_iso_hom, curryingFlipEquiv_symm_apply_obj_obj, AlgebraicGeometry.IsAffineOpen.fromSpec_image_basicOpen, uncurry_obj_curry_obj_flip_flip', CategoryTheory.Idempotents.karoubiChainComplexEquivalence_unitIso_inv_app_f_f, CategoryTheory.ProdPreservesConnectedLimits.γ₁_app, CochainComplex.mappingCone.inr_f_triangle_mor₃_f_assoc, PresheafOfModules.Hom.naturality, CategoryTheory.ChosenPullbacksAlong.iso_pullback_map, CategoryTheory.Pi.eval_obj, CategoryTheory.Comonad.Coalgebra.counit, AlgebraicGeometry.instHasAffinePropertyIsomorphismsSchemeAndIsAffineIsIsoCommRingCatAppTop, CategoryTheory.conjugateEquiv_adjunction_id_symm, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_morphismRestrict, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_symm_apply, CategoryTheory.Monad.right_unit, groupHomology.mapShortComplexH2_id_comp, CategoryTheory.SmallObject.restrictionLT_obj, OplaxMonoidal.δ_natural_assoc, CategoryTheory.ShortComplex.mapHomologyIso_inv_naturality, isStrongGenerator_of_isDense, CategoryTheory.hasExt_iff, HomologicalComplex.shortComplexFunctor_obj_g, CategoryTheory.ComposableArrows.fourδ₂Toδ₁_app_two, CategoryTheory.Limits.ColimitPresentation.w, LaxMonoidal.right_unitality_inv_assoc, CategoryTheory.Limits.Cofork.IsColimit.π_desc, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_add, mapBinaryBicone_fst, OplaxMonoidal.whiskeringRight_η_app, CategoryTheory.CategoryOfElements.id_val, CategoryTheory.Limits.image_map_comp_imageSubobjectIso_inv, SSet.Truncated.Path.mk₂_vertex, CategoryTheory.Grothendieck.map_map_fiber, skyscraperPresheafCoconeOfSpecializes_ι_app, SSet.horn₂₂.isPushout, CategoryTheory.Under.opEquivOpOver_inverse_obj, BddLat.coe_forget_to_bddOrd, AddCommMonCat.uliftFunctor_obj_coe, CategoryTheory.PresheafHom.IsSheafFor.exists_app, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompCoyoneda, CategoryTheory.Over.ConstructProducts.conesEquivInverse_obj, Action.rightUnitor_hom_hom, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_app, TopCat.isOpen_iff_of_isColimit_cofork, CategoryTheory.SingleFunctors.inv_hom_id_hom_app, AlgebraicGeometry.IsAffineOpen.basicOpen_union_eq_self_iff, MonObj.mopEquiv_inverse_obj_mon_one, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_map_injective, CategoryTheory.Limits.BinaryFan.leftUnitor_inv, AlgebraicGeometry.SheafedSpace.id_c, CategoryTheory.Equivalence.core_counitIso_inv_app_iso_hom, CategoryTheory.Limits.piObjIso_inv_comp_π_assoc, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_hom_eq_germ_assoc, LightCondSet.isDiscrete_tfae, Action.forget_μ, CategoryTheory.Iso.unop_inv_hom_id_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_hom_toNatTrans_app_val_app, AlgebraicGeometry.isFinite_iff, TopCat.Presheaf.presheafEquivOfIso_inverse_obj_obj, HomologicalComplex₂.ι_totalShift₂Iso_hom_f, AlgebraicTopology.DoldKan.N₁Γ₀_inv_app, HomologicalComplex.exactAt_single_obj, CategoryTheory.typeToCat_obj, CategoryTheory.BasedFunctor.isHomLift_iff, SSet.prodStdSimplex.nonDegenerate_iff_strictMono_objEquiv, AlgebraicGeometry.Scheme.Hom.inl_toNormalization_normalizationCoprodIso_inv_assoc, Types.monoOverEquivalenceSet_unitIso, SheafOfModules.forgetToSheafModuleCat_map_val, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₂, CategoryTheory.Coyoneda.fullyFaithful_preimage, SheafOfModules.pullbackObjFreeIso_hom_naturality, ranObjObjIsoLimit_inv_π, SSet.yonedaEquiv_comp, LightCondSet.topCatAdjunctionUnit_val_app, AlgebraicGeometry.etale_iff, CategoryTheory.CostructuredArrow.ofCommaFstEquivalence_unitIso, CategoryTheory.IsSplitCoequalizer.map_rightSection, AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_inv_ι_app, BddLat.coe_forget_to_semilatInf, CategoryTheory.MonoidalOpposite.tensorLeftIso_hom_app_unmop, SSet.Truncated.IsStrictSegal.spine_bijective, Profinite.presentation.epi_π, CategoryTheory.Limits.colimit_map_colimitObjIsoColimitCompEvaluation_hom_assoc, SSet.op_map, CategoryTheory.Limits.pair_obj_left, HomologicalComplex₂.instHasTotalIntObjUpShiftFunctor₁, CategoryTheory.Iso.inverseCompIso_hom_app, CategoryTheory.TwoSquare.EquivalenceJ.functor_map, IsMittagLeffler.eq_image_eventualRange, CommGrpCat.coyonedaType_obj_map, CategoryTheory.Equivalence.congrLeft_counitIso_hom_app, mapConeOp_hom_hom, OplaxMonoidal.left_unitality_assoc, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.inverse_obj, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_app_apply, CategoryTheory.Limits.Types.Pushout.cocone_ι_app, CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument.preservesColimit, SSet.stdSimplex.spineId_arrow_apply_one, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_obj_fst, CategoryTheory.StructuredArrow.mapIso_inverse_obj_left, AlgebraicGeometry.Scheme.germ_residue_assoc, prod_μ_snd, CategoryTheory.Limits.colimit.w_assoc, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq, IsEventuallyConstantTo.isoMap_hom_inv_id_assoc, CategoryTheory.Sieve.mem_functorPushforward_iff_of_full_of_faithful, ModuleCat.free_map_apply, SemiRingCat.forget_obj, TopCat.isQuotientMap_of_isColimit_cofork, CategoryTheory.InjectiveResolution.Hom.ι_f_zero_comp_hom_f_zero_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_map_app_snd, CategoryTheory.Limits.KernelFork.map_ι, SSet.Quasicategory.hornFilling', CategoryTheory.flipFunctor_map_app_app, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_obj_obj_left, CategoryTheory.GrothendieckTopology.ι_plusCompIso_hom, CategoryTheory.MorphismProperty.instHasPullbackSndHomDiscretePUnitOfHasPullbacksAlongOfIsStableUnderBaseChangeAlong, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionUnitIso_inv, leftDerivedNatTrans_app, AlgebraicGeometry.instIsIsoSchemeCoprodSpec, CategoryTheory.PreGaloisCategory.functorToContAction_obj_obj, CategoryTheory.Localization.hasSmallLocalizedShiftedHom_iff, AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.opensRange_map, CategoryTheory.obj_μ_zero_app, AlgebraicTopology.DoldKan.Compatibility.τ₀_hom_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_right_map, mapTriangleIdIso_inv_app_hom₂, AlgebraicGeometry.Scheme.kerFunctor_obj, flippingEquiv_apply_obj_map, CommGrpTypeEquivalenceCommGrp.inverse_obj_mul, CategoryTheory.BasedFunctor.preserves_isHomLift, CochainComplex.HomComplex.Cochain.map_ofHom, PresheafOfModules.freeAdjunction_unit_app, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst_assoc, CategoryTheory.ExponentiableMorphism.ev_naturality, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver_obj, CategoryTheory.SmallObject.restrictionLE_obj, CategoryTheory.Comma.mapRightEq_hom_app_left, SSet.OneTruncation₂.nerveHomEquiv_apply, CategoryTheory.Pretriangulated.complete_distinguished_triangle_morphism, CategoryTheory.frobeniusMorphism_iso_of_expComparison_iso, CategoryTheory.Over.forgetCocone_ι_app, CategoryTheory.Grothendieck.map_map_base, CategoryTheory.SmallObject.functor_obj, CochainComplex.HomComplex.CohomologyClass.toHom_mk_eq_zero_iff, AlgebraicGeometry.Scheme.Opens.ι_image_le, CategoryTheory.Limits.Pi.isoLimit_hom_π, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_ι_inv, FintypeCat.uSwitchEquiv_symm_naturality, TopCat.Presheaf.Γgerm_res_apply, groupHomology.mapCycles₂_comp_i_apply, commShiftOfLocalization_iso_hom_app, CategoryTheory.Pretriangulated.Triangle.isZero₃_iff, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_left, CategoryTheory.Join.fromSum_obj, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₂, CategoryTheory.Discrete.equivOfEquivalence_symm_apply, CategoryTheory.Limits.limit_π_isIso_of_is_strict_terminal, DerivedCategory.triangleOfSES_obj₂, CategoryTheory.PreGaloisCategory.FiberFunctor.isPretransitive_of_isGalois, LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv, CategoryTheory.CosimplicialObject.equivalenceRightToLeft_left, CategoryTheory.evaluationIsRightAdjoint, OplaxRightLinear.δᵣ_unitality_inv_assoc, CategoryTheory.WithTerminal.liftFromOverComp_inv_app, OplaxLeftLinear.δₗ_naturality_right_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_right, CategoryTheory.WithInitial.liftToInitial_map, Initial.limitConeOfComp_cone, CategoryTheory.Limits.hasLimit_const_of_isConnected, CategoryTheory.Comma.mapRightEq_inv_app_right, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_jointly_surjective₂, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_map_app_assoc, CategoryTheory.isCardinalPresentable_iff_isCardinalAccessible_uliftCoyoneda_obj, AlgebraicGeometry.StructureSheaf.comap_basicOpen, CategoryTheory.StructuredArrow.mapIso_functor_map_right, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_hom_assoc, CategoryTheory.Limits.ι_colimitConstInitial_hom, CategoryTheory.Bifunctor.diagonal', AlgebraicGeometry.LocallyRingedSpace.forgetToTop_obj, CategoryTheory.Limits.π_comp_colimitRightOpIsoUnopLimit_inv_assoc, Condensed.underlying_obj, AlgebraicGeometry.IsOpenImmersion.opensRange_pullback_fst_of_right, CategoryTheory.Adjunction.map_restrictFullyFaithful_unit_app, CategoryTheory.Limits.reflexivePair.compRightIso_inv_app, CategoryTheory.Limits.equalizer.fork_π_app_zero, partialFunEquivPointed_counitIso_hom_app_toFun, CategoryTheory.Sheaf.sheafifyCocone_ι_app_val_assoc, commBialgCatEquivComonCommAlgCat_inverse_map_unop_hom, CategoryTheory.prod.rightInverseUnitor_obj, CategoryTheory.Core.forgetFunctorToCore_obj_map, AlgebraicGeometry.tilde.functor_obj, curryObjProdComp_inv_app_app, TwoP.swapEquiv_counitIso_hom_app_hom_toFun, CategoryTheory.coalgebraEquivOver_unitIso, CategoryTheory.Sheaf.Hom.add_app, structuredArrowMapCone_pt, CategoryTheory.Under.costar_map_left, AlgebraicGeometry.Scheme.mem_basicOpen'', Monoidal.associator_hom_app, CategoryTheory.Grothendieck.ι_obj, CategoryTheory.PreGaloisCategory.endEquivAutGalois_π, CategoryTheory.ActionCategory.π_map, CategoryTheory.Limits.coneOfConeUncurry_pt, CategoryTheory.Triangulated.SpectralObject.triangle_obj₃, CategoryTheory.Monad.unit_naturality_assoc, LaxMonoidal.ofBifunctor.firstMap_app_app_app, CategoryTheory.NatTrans.app_units_zsmul, CategoryTheory.Limits.Cocone.extend_ι, CategoryTheory.Limits.splitMonoOfIdempotentOfIsLimitFork_retraction, CategoryTheory.Presieve.extension_iff_amalgamation, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_whiskerRight, CategoryTheory.Limits.prod.functor_obj_obj, HomologicalComplex.quasiIso_unopFunctor_map_iff, HomotopicalAlgebra.CofibrantObject.HoCat.ιCompResolutionNatTrans_app, CategoryTheory.Triangulated.TStructure.triangleLTGE_map_hom₁, CategoryTheory.OplaxFunctor.map₂_rightUnitor_app, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_X_carrier, CategoryTheory.ShortComplex.mapHomologyIso'_hom_naturality_assoc, SimpleGraph.componentComplFunctor_nonempty_of_infinite, CategoryTheory.Limits.prodComparisonNatTrans_app, CochainComplex.shiftFunctorComm_hom_app_f, CategoryTheory.Idempotents.KaroubiKaroubi.inverse_obj_X, CategoryTheory.Over.whiskerRight_left_fst_assoc, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.SheafCondition.bijective_toPullbackObj, CategoryTheory.CartesianClosed.curry_natural_left, LaxMonoidal.tensorHom_ε_comp_μ, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_app, CategoryTheory.Comma.post_map_right, CategoryTheory.StructuredArrow.pre_obj_hom, const_obj_obj, CategoryTheory.map_is_split_pair, ProfiniteGrp.toLimitFun_continuous, CategoryTheory.Limits.CompleteLattice.limit_eq_iInf, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_left_map, CategoryTheory.LaxFunctor.mapComp_naturality_right_app, CategoryTheory.Localization.SmallShiftedHom.equiv_mk₀Inv, CategoryTheory.WithTerminal.equivComma_inverse_map_app, CategoryTheory.Idempotents.KaroubiKaroubi.unitIso_inv_app_f, CategoryTheory.Limits.cospanCompIso_app_left, CategoryTheory.TwoSquare.vComp_app, Action.isContinuous_def, CategoryTheory.Sum.functorEquiv_unit_app_app_inl, LaxMonoidal.comp_μ, CategoryTheory.Join.mkFunctorLeft_inv_app, AlgebraicGeometry.isEmpty_pullback_sigmaι_of_ne, CategoryTheory.CostructuredArrow.mapIso_functor_obj_right, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₃, SSet.RelativeMorphism.Homotopy.rel, CategoryTheory.MonoidalClosed.curryHomEquiv'_apply, mapCommGrp_map_hom_hom_hom, AlgebraicGeometry.Scheme.Spec_obj, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.preimage_toBase_eq_range_ι, CategoryTheory.Limits.Cone.w_apply, TopCat.isOpen_iff_of_isColimit, AlgebraicGeometry.tilde.toOpen_map_app_assoc, CategoryTheory.Limits.LimitPresentation.map_diag, SheafOfModules.Presentation.map_generators_I, CategoryTheory.Equivalence.sheafCongr.inverse_map_val_app, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d_1_0, LeftLinear.inv_δₗ, faithful_whiskeringRight_obj, CategoryTheory.Limits.limitFlipIsoCompLim_hom_app, CategoryTheory.shiftFunctorAdd_assoc_hom_app, CategoryTheory.ShortComplex.FunctorEquivalence.functor_map_app, SSet.horn.primitiveEdge_coe_down, CategoryTheory.toSkeletonFunctor_obj, CategoryTheory.CategoryOfElements.fromCostructuredArrow_obj_mk, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_hom_π_π, PullbackObjObj.mapArrowLeft_right, mapGrp_obj_grp_inv, CategoryTheory.Limits.limIsoFlipCompWhiskerLim_inv_app_app, CategoryTheory.sum.associator_map_inl_inl, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_unitIso, TopCat.adj₂_unit, CategoryTheory.Over.tensorHom_left_snd, CategoryTheory.WithInitial.ofCommaObject_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_rightUnitor, mapExtAddHom_coe, CategoryTheory.Abelian.DoldKan.comparisonN_hom_app_f, CategoryTheory.Subobject.inf_comp_right, CategoryTheory.TwoSquare.equivalenceJ_functor, IsEventuallyConstantFrom.isIso_map, CategoryTheory.MonoidalOpposite.tensorRightMopIso_hom_app_unmop, CategoryTheory.Limits.Cone.overPost_π_app, CategoryTheory.Under.opEquivOpOver_counitIso, mapTriangleRotateIso_inv_app_hom₃, CategoryTheory.ShortComplex.leftHomologyFunctor_obj, mapAction_map_hom, LaxMonoidal.whiskerRight_tensorUnit_comp_rightUnitor_hom_assoc, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_f, AlgebraicGeometry.basicOpen_eq_of_affine, CategoryTheory.StructuredArrow.toUnder_map_left, AlgebraicGeometry.LocallyRingedSpace.Γ_map_op, CategoryTheory.StructuredArrow.w_prod_snd_assoc, CategoryTheory.Grp.η_def, HasFibers.proj_eq, AlgebraicGeometry.IsIntegralHom.instDescScheme, 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.ObjectProperty.ιOfLE_obj_obj, CategoryTheory.StructuredArrow.prodInverse_obj, CochainComplex.HomComplex.Cochain.leftShiftAddEquiv_symm_apply, CategoryTheory.Limits.FormalCoproduct.homOfPiHom_f, CategoryTheory.Adjunction.Triple.mono_leftToRight_app_iff_mono_adj₂_unit_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_inv_app_app, toEssImageCompι_inv_app, CategoryTheory.Adjunction.Triple.epi_rightToLeft_app_iff_epi_map_adj₂_counit_app, TopologicalSpace.OpenNhds.map_id_obj, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition'_assoc, CategoryTheory.ofTypeFunctor_obj, ProfiniteGrp.diagram_map, Final.extendCocone_obj_pt, CategoryTheory.DifferentialObject.d_squared_assoc, CategoryTheory.conjugateEquiv_adjunction_id, CategoryTheory.Yoneda.fullyFaithful_preimage, AlgebraicGeometry.AffineScheme.forgetToScheme_obj, CategoryTheory.Pi.ihom_obj, CategoryTheory.Limits.prodComparison_fst_assoc, CategoryTheory.Limits.Concrete.colimit_exists_rep, OneHypercoverDenseData.essSurj.presheafMap_π, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_incl_app, CategoryTheory.Subfunctor.iSup_obj, CochainComplex.HomComplex.Cochain.rightShift_neg, CategoryTheory.CosimplicialObject.Augmented.whiskering_obj, SSet.stdSimplex.faceSingletonIso_one_hom_comp_ι_eq_δ_assoc, CategoryTheory.Limits.WidePushoutShape.wideSpan_obj, CategoryTheory.Subobject.ofLEMk_comp_ofMkLE_assoc, CategoryTheory.Limits.Cone.toStructuredArrow_map, AlgebraicGeometry.Scheme.ΓSpecIso_naturality_assoc, CategoryTheory.SmallObject.restrictionLT_map, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_fst_obj, mapArrowFunctor_map_app_left, final_iff_of_isFiltered, AlgebraicGeometry.ExistsHomHomCompEqCompAux.hb, CategoryTheory.coyonedaEquiv_symm_map, HomologicalComplex₂.totalShift₁Iso_hom_naturality, leftDerivedZeroIsoSelf_hom_inv_id_app_assoc, groupCohomology.cocyclesMap_id_comp, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ_assoc, CategoryTheory.GradedObject.mapTrifunctor_obj, opHom_map_app, Rep.res_obj_ρ, CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_hom_assoc, HasPointwiseRightDerivedFunctorAt.hasColimit', CategoryTheory.Comon.monoidal_associator_inv_hom, AlgebraicGeometry.Scheme.Hom.comp_image, CategoryTheory.Abelian.FunctorCategory.functor_category_isIso_coimageImageComparison, FullyFaithful.mulEquivEnd_apply, Action.associator_inv_hom, CategoryTheory.SmallObject.SuccStruct.ofCocone_map, AlgebraicGeometry.IsOpenImmersion.range_pullbackFst, cocones_map_app, CategoryTheory.CostructuredArrow.preEquivalence.functor_map_left, CategoryTheory.StructuredArrow.preEquivalence_counitIso, AlgebraicGeometry.IsAffineOpen.fromSpec_image_zeroLocus, CategoryTheory.Limits.coprod.functor_obj_map, CategoryTheory.ShiftMkCore.assoc_hom_app, Monoidal.map_leftUnitor_assoc, CochainComplex.mappingConeCompTriangle_mor₃_naturality_assoc, RightExtension.postcomp₁_obj_hom_app, map_opShiftFunctorEquivalence_counitIso_inv_app_unop, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_map, CategoryTheory.equivYoneda'_hom_val, AlgebraicGeometry.Scheme.IdealSheafData.mem_supportSet_iff_of_mem, HomotopyCategory.quotient_obj_singleFunctors_obj, AddMonCat.uliftFunctor_obj_coe, CategoryTheory.Limits.Multicoequalizer.multicofork_ι_app_right, AlgebraicGeometry.PresheafedSpace.toRestrictTop_base, AlgebraicGeometry.LocallyRingedSpace.isUnit_res_toΓSpecMapBasicOpen, AlgebraicGeometry.Scheme.affineBasisCover_map_range, CategoryTheory.Limits.colimit.w, OplaxMonoidal.right_unitality_assoc, CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.map_eq_pullHom, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app, CategoryTheory.Adjunction.adjToMonadIso_hom_toNatTrans_app, diag_obj, SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁_inv_app_f_f, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_obj₂, flip₂₃Functor_obj_map_app_app, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_hom_app_val_app, CategoryTheory.FunctorToTypes.prod.lift_app, InfiniteGalois.algEquivToLimit_continuous, CategoryTheory.RightExactFunctor.whiskeringLeft_obj_obj_obj, TopCat.Presheaf.germ_stalkSpecializes, CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.arrowMap_functor_to_top, CategoryTheory.Subobject.representative_coe, FullyFaithful.grpObj_one, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃'_obj_obj_map, CategoryTheory.Equivalence.core_functor_map_iso_hom, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₂, commShiftOfLocalization.iso_hom_app_assoc, ι_leftKanExtensionObjIsoColimit_hom, CategoryTheory.Limits.SequentialProduct.cone_π_app, biproductComparison_π, PresheafOfModules.freeYonedaEquiv_comp, AlgebraicGeometry.ΓSpec_adjunction_homEquiv_eq, CategoryTheory.PresheafOfGroups.OneCochain.inv_ev, AddCommMonCat.coyoneda_obj_map, ranAdjunction_counit, PresheafOfModules.Sheafify.zero_smul, CategoryTheory.endofunctorMonoidalCategory_leftUnitor_inv_app, AlgebraicGeometry.Scheme.Opens.ι_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMop_obj_unmop_map, CategoryTheory.WithInitial.liftFromUnder_obj_map, CategoryTheory.ShortComplex.π₂_obj, CategoryTheory.flippingIso_hom_toFunctor_obj_obj_obj, CategoryTheory.InjectiveResolution.instMonoFNatι, SSet.StrictSegal.spine_spineToSimplex, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₃, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₂, CategoryTheory.Limits.limit.lift_π_app_assoc, CategoryTheory.Square.toArrowArrowFunctor'_obj_hom_right, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_inv_app_app, CategoryTheory.NatTrans.app_shift, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv_assoc, CategoryTheory.Limits.limitRightOpIsoOpColimit_inv_comp_π_assoc, mapConnectedComponents_mk, whiskeringLeft₃_obj_obj_obj_obj_obj_map_app, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_mul_app, ι_colimitIsoOfIsLeftKanExtension_hom_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app_assoc, homologySequenceδ_naturality_assoc, ofSequence_obj, AlgebraicGeometry.Scheme.IdealSheafData.supportSet_inter, CategoryTheory.NatTrans.comp_app, AlgebraicGeometry.locallyOfFinitePresentation_iff, CategoryTheory.Subgroupoid.hom.inj_on_objects, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_left_right_as, instIsIsoAppLanUnit_1, CategoryTheory.Limits.Cone.w_assoc, CategoryTheory.LaxFunctor.mapComp_naturality_left_app, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right_assoc, CategoryTheory.ComposableArrows.fourδ₃Toδ₂_app_three, AlgebraicGeometry.Scheme.Hom.isoImage_hom_ι, SSet.Truncated.HomotopyCategory.homToNerveMk_app_zero, AlgebraicGeometry.IsAffineOpen.isOpenImmersion_fromSpec, CategoryTheory.Limits.limitIsoFlipCompLim_inv_app, CategoryTheory.Join.mapPairLeft_hom_app, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransId_hom_app_f, CategoryTheory.ShiftedHom.map_zero, flipIsoCurrySwapUncurry_inv_app_app, CategoryTheory.cones_map_app_app, Rep.ihom_obj_V_isModule, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_hom_comp_ι_assoc, CategoryTheory.SmallObject.SuccStruct.iterationFunctor_obj, CochainComplex.HomComplex.Cochain.fromSingleMk_v_eq_zero, CommGrpCat.coyoneda_obj_map, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.firstMap₃_app_app_app, CategoryTheory.nat_trans_from_is_connected, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_app_snd_app, CategoryTheory.Limits.BinaryBicones.functoriality_obj_inl, CategoryTheory.WithTerminal.liftFromOver_map_app, CompHausLike.LocallyConstant.incl_comap, CategoryTheory.Abelian.LeftResolution.karoubi.F'_obj_X, CategoryTheory.MonoidalClosed.coev_app_comp_pre_app_assoc, CategoryTheory.whiskerRight_ι_colimitCompWhiskeringRightIsoColimitComp_inv, CategoryTheory.Limits.kernelSubobject_arrow_apply, SSet.Truncated.Edge.map_whiskerRight, CategoryTheory.StructuredArrow.preEquivalenceInverse_obj_left_as, CategoryTheory.Triangulated.TStructure.isGE_shift, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_of_mono₁, ModuleCat.FreeMonoidal.εIso_hom_one, relativelyRepresentable.w, AlgebraicGeometry.Scheme.Hom.isCompact_preimage, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₂, CategoryTheory.Pretriangulated.complete_distinguished_triangle_morphism₁, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_map_right_app, CategoryTheory.preadditiveCoyonedaObj_obj_carrier, SSet.Truncated.comp_app, sheafPushforwardContinuousId_inv_app_val_app, LightProfinite.Extend.functor_obj, LightCondensed.isoFinYoneda_hom_app, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app_assoc, AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id_assoc, CategoryTheory.coyonedaPairingExt_iff, CategoryTheory.Pseudofunctor.DescentData.pullFunctorCompIso_hom_app_hom, AlgebraicGeometry.instUniversallyClosedMorphismRestrict, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₂, CategoryTheory.associativity_app, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_precomp, CategoryTheory.Pretriangulated.preadditiveYoneda_shiftMap_apply, CategoryTheory.SmallObject.prop_iterationFunctor_map_succ, AlgebraicGeometry.SheafedSpace.congr_hom_app, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_right, AlgebraicGeometry.Scheme.Hom.instIsIsoCommRingCatApp, AlgebraicGeometry.IsOpenImmersion.instIsOpenImmersionMapSchemeLocallyRingedSpaceForgetToLocallyRingedSpace, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformPrecomposeObjSquare_iso_hom_comp, CategoryTheory.Limits.parallelPair.eqOfHomEq_hom_app, CategoryTheory.MorphismProperty.IsCompatibleWithTriangulation.compatible_with_triangulation, CategoryTheory.Limits.limit.map_pre, CategoryTheory.WithTerminal.coneEquiv_inverse_map_hom_left, HomotopicalAlgebra.FibrantObject.instIsFibrantObjFunctorWeakEquivalencesLocalizerMorphism, CategoryTheory.Iso.inv_hom_id_app_app_app_assoc, FundamentalGroupoid.punitEquivDiscretePUnit_counitIso, mapCochainComplexShiftIso_hom_app_f, LaxMonoidal.μ_whiskerRight_comp_μ, CategoryTheory.NatTrans.IsMonoidal.tensor_assoc, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_preimage_basicOpen, CategoryTheory.evalEquiv_symm_apply, map_opShiftFunctorEquivalence_unitIso_inv_app_unop_assoc, OplaxMonoidal.δ_comp_δ_whiskerRight, sum_map_inr, CategoryTheory.Iso.inv_hom_id_app, CategoryTheory.SingleFunctors.shiftIso_add_hom_app, CategoryTheory.flippingIso_hom_toFunctor_map_app_app, AlgebraicGeometry.Scheme.Hom.toNormalization_inl_normalizationCoprodIso_hom, CategoryTheory.Arrow.left_hom_inv_right, CategoryTheory.Idempotents.Karoubi.decompId_p_toKaroubi, CategoryTheory.ShortComplex.exact_iff_of_forks, CategoryTheory.cosimplicialSimplicialEquiv_inverse_map, bifunctorComp₁₂Iso_inv_app_app_app, PresheafOfModules.sheafificationAdjunction_homEquiv_apply, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_inv_app, CategoryTheory.Adjunction.representableBy_homEquiv, CategoryTheory.shiftFunctorCompIsoId_zero_zero_hom_app, AlgebraicGeometry.Scheme.Hom.inv_image, LeftLinear.μₗ_comp_δₗ, PushoutObjObj.inr_ι_assoc, Elements.initialOfRepresentableBy_snd, CategoryTheory.Equivalence.inverseFunctorObjIso_hom, TopCat.colimit_isOpen_iff, CategoryTheory.MonoidalCategory.externalProductBifunctorCurried_obj_map_app_app, CategoryTheory.Limits.coequalizer.cofork_ι_app_one, CategoryTheory.wideInducedFunctor_obj, CategoryTheory.CommComon.forget₂Comon_obj_comon, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one, CategoryTheory.SimplicialObject.δ_comp_σ_of_le_assoc, CategoryTheory.SimplicialObject.δ_comp_δ, CategoryTheory.obj_μ_inv_app_assoc, CorepresentableBy.ext_iff, CategoryTheory.Subobject.inf_eq_map_pullback, CategoryTheory.IsPullback.map, CategoryTheory.Over.postMap_app, toEssImageCompι_hom_app, CategoryTheory.Equivalence.toOrderIso_symm_apply, CategoryTheory.Limits.imageSubobject_arrow_comp, CategoryTheory.Pseudofunctor.DescentData.pullFunctorObjHom_eq, CorepresentableBy.homEquiv_symm_comp, CategoryTheory.GrothendieckTopology.W_eq_isLocal_range_sheafToPresheaf_obj, whiskeringLeft₃_obj_obj_obj_obj_obj_obj_map, CategoryTheory.δ_naturalityₗ, AlgebraicGeometry.Scheme.Hom.inr_toNormalization_normalizationCoprodIso_inv_assoc, AlgebraicGeometry.Scheme.germ_residue, CategoryTheory.InjectiveResolution.toRightDerivedZero'_comp_iCycles_assoc, CategoryTheory.Limits.ColimitPresentation.comp_hom, CategoryTheory.StructuredArrow.preEquivalenceFunctor_obj_right, CategoryTheory.GrothendieckTopology.instIsIsoSheafAppFunctorOppositeSheafComposeNatTransPlusPlusAdjunction, CategoryTheory.Monad.ForgetCreatesLimits.liftedCone_π_app_f, CategoryTheory.Square.toArrowArrowFunctor'_obj_left_left, whiskeringRight_obj_comp, CategoryTheory.isCardinalPresentable_of_equivalence, PushoutObjObj.hom_ext_iff, CategoryTheory.Limits.combineCones_pt_obj, PushoutObjObj.mapArrowRight_comp, TopologicalSpace.Opens.map_top, CategoryTheory.TwoSquare.vComp'_app, CategoryTheory.Equivalence.congrLeft_inverse, CategoryTheory.ShiftedHom.mk₀_neg, AlgebraicGeometry.IsPreimmersion.instMorphismRestrict, CategoryTheory.Join.mapIsoWhiskerLeft_inv_app, 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, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_right_as, CategoryTheory.CategoryOfElements.CreatesLimitsAux.liftedCone_pt_snd, CategoryTheory.Preadditive.commGrpEquivalence_inverse_map, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_left, TopCat.Presheaf.presheafEquivOfIso_functor_map_app, SSet.stdSimplex.face_le_face_iff, CategoryTheory.Equivalence.inverseFunctorObj'_inv_app, CategoryTheory.Enriched.FunctorCategory.enrichedComp_π, LightProfinite.proj_surjective, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_X₂, rightUnitor_inv_app, CategoryTheory.Comonad.ComonadicityInternal.main_pair_F_cosplit, CategoryTheory.Subfunctor.Subpresheaf.subobjectMk_range_arrow, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_map_surjective, CategoryTheory.Join.mkFunctor_obj_right, leftUnitor_hom_app, AlgebraicGeometry.Scheme.Hom.opensRange_comp, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_map_right, CategoryTheory.Limits.Types.FilteredColimit.rel_equiv, CategoryTheory.extensiveTopology.surjective_of_isLocallySurjective_sheaf_of_types, flippingEquiv_apply_map_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality, CategoryTheory.Grothendieck.ιCompMap_hom_app_base, CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ι_assoc, AlgebraicTopology.DoldKan.Γ₂_obj_X_obj, SSet.RelativeMorphism.Homotopy.refl_h, Topology.IsInducing.le_functorObj_iff, AlgebraicGeometry.Scheme.Hom.ι_fromNormalization, CategoryTheory.Under.equivalenceOfIsInitial_inverse_obj, toPreimages_obj, CategoryTheory.Iso.core_hom_app_iso_hom, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_zeroLocus_eq, CategoryTheory.Over.ConstructProducts.conesEquivInverseObj_π_app, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_inv, CategoryTheory.MonoidalOpposite.mopMopEquivalence_inverse_obj_unmop_unmop, CategoryTheory.GradedObject.comapEq_inv_app, SSet.truncation_spine, mapConeMapCone_inv_hom, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_inv_eq_germ, CategoryTheory.GrothendieckTopology.liftToPlusObjLimitObj_fac, AlgebraicGeometry.exists_finite_imageι_comp_morphismRestrict_of_finite_image_preimage, CategoryTheory.Adjunction.right_triangle_components_assoc, CategoryTheory.Limits.CatCospanTransform.leftUnitor_hom_base_app, ModuleCat.extendRestrictScalarsAdj_unit_app_apply, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_hom_app, CategoryTheory.TransfiniteCompositionOfShape.map_incl, CategoryTheory.GradedObject.mapBifunctor_obj_map, SheafOfModules.map_ιFree_mapFree_hom_assoc, homEquivOfIsRightKanExtension_apply_app, CategoryTheory.Subfunctor.Subpresheaf.toPresheaf_map_coe, CategoryTheory.Limits.CompleteLattice.limitCone_cone_π_app, CategoryTheory.ParametrizedAdjunction.homEquiv_eq, CategoryTheory.Endofunctor.Adjunction.Coalgebra.toAlgebraOf_obj_str, CategoryTheory.Equivalence.symmEquivInverse_obj_unitIso_inv, CategoryTheory.ShortComplex.RightHomologyMapData.map_φH, CategoryTheory.Limits.combineCocones_pt_map, CategoryTheory.Limits.IsLimit.homEquiv_symm_naturality, CategoryTheory.MonoidalCategory.curriedTensorPreFunctor_map_app_app, TopologicalSpace.Opens.overEquivalence_inverse_obj_right_as, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₁, CategoryTheory.Limits.pointwiseProductCompEvaluation_hom_app, CategoryTheory.decomposedTo_obj, CategoryTheory.StructuredArrow.proj_obj, AlgebraicGeometry.instIsQuasicoherentOpensCarrierCarrierCommRingCatSpecTilde, TopCat.adj₁_counit, CategoryTheory.Pseudofunctor.mapId'_hom_naturality, CategoryTheory.Pseudofunctor.DescentData.hom_self, imageToKernel_zero_left, HomotopyCategory.quotient_obj_mem_subcategoryAcyclic_iff_acyclic, CategoryTheory.coprodComparison_tensorLeft_braiding_hom, HomotopicalAlgebra.CofibrantObject.exists_bifibrant, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_hom, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceInverse_map_base, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_app, ranCounit_app_whiskerLeft_ranAdjunction_unit_app, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_app, CategoryTheory.Limits.Cotrident.ofπ_ι_app, CategoryTheory.Monad.MonadicityInternal.main_pair_G_split, alexDiscEquivPreord_counitIso, CategoryTheory.Under.costar_obj_hom, shiftIso_inv_naturality_assoc, SSet.PtSimplex.RelStruct.δ_succ_map, CategoryTheory.DifferentialObject.objEqToHom_d_assoc, CategoryTheory.Adjunction.homAddEquiv_apply, IsEventuallyConstantTo.isIso_π_of_isLimit', PullbackObjObj.ofHasPullback_pt, CategoryTheory.Triangulated.SpectralObject.triangle_obj₁, linear_iff, CategoryTheory.Iso.unop_inv_hom_id_app_assoc, CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ι, CategoryTheory.CosimplicialObject.Truncated.whiskering_obj_obj_map, LeftExtension.coconeAt_ι_app, CategoryTheory.Pseudofunctor.ObjectProperty.map_obj_obj, AlgebraicGeometry.Scheme.Γevaluation_naturality, CategoryTheory.Limits.coconeOfIsSplitEpi_ι_app, CategoryTheory.CosimplicialObject.δ_naturality, CategoryTheory.Adjunction.unit_app_unit_comp_map_η_assoc, CategoryTheory.Presheaf.isLimit_iff_isSheafFor, SheafOfModules.Presentation.IsFinite.finite_relations, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_one_app, LightProfinite.proj_comp_transitionMapLE, LightProfinite.instEpiAppOppositeNatπAsLimitCone, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst_assoc, CategoryTheory.FunctorToTypes.binaryProductCone_pt_map, CategoryTheory.Limits.π_comp_colimitUnopIsoOpLimit_inv_assoc, mapCommGrpNatTrans_app_hom_hom_hom, CategoryTheory.Localization.isoOfHom_inv_hom_id_assoc, AlgebraicGeometry.IsSeparated.instMorphismRestrict, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_left_as, mapTriangleCommShiftIso_hom_app_hom₂, Rep.coinvariantsAdjunction_unit_app_hom, CategoryTheory.PreGaloisCategory.exists_lift_of_quotient_openSubgroup, CategoryTheory.Adjunction.leftAdjointCompIso_hom_app, CategoryTheory.RightExactFunctor.forget_obj_of, CategoryTheory.NatTrans.shift_app_comm_assoc, CochainComplex.HomComplex.Cocycle.rightShiftAddEquiv_apply, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₂, AlgebraicGeometry.basicOpen_eq_bot_iff, CategoryTheory.Comonad.instHasEqualizerMapAAppUnitObjAOfHasEqualizerOfIsCosplitPair, CategoryTheory.Over.lift_left, toOplaxFunctor'_mapComp, CategoryTheory.CosimplicialObject.cechConerve_obj, CategoryTheory.TwoSquare.guitartExact_iff_final, CategoryTheory.Limits.CompleteLattice.finiteColimitCocone_cocone_pt, AlgebraicGeometry.Scheme.IdealSheafData.ker_glueDataObjι_appTop, SheafOfModules.pushforwardNatTrans_app_val_app_apply, CategoryTheory.Limits.PreservesColimitsOfShape.underPost, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_obj_snd, CategoryTheory.Equivalence.congrRight_inverse, CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_iff_mono₃, flip₁₃Functor_obj_obj_obj_map, CategoryTheory.Sieve.uliftFunctorInclusion_top_isIso, CategoryTheory.Limits.ColimitPresentation.id_hom, CategoryTheory.Limits.walkingParallelPairOp_one, AlgebraicGeometry.Spec.germ_stalkMapIso_hom, CategoryTheory.Monad.MonadicityInternal.counitCofork_pt, TopologicalSpace.Opens.mapMapIso_counitIso, CategoryTheory.GrothendieckTopology.Point.toPresheafFiberNatTrans_app, AlgebraicTopology.DoldKan.Γ₂_map_f_app, CategoryTheory.Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone_ι_app_eq_sum, Monoidal.whiskeringLeft_δ_app, CategoryTheory.MonoidalOpposite.unmopFunctor_η, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_apply, CategoryTheory.NatTrans.shift_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app, CategoryTheory.DifferentialObject.d_squared_apply_assoc, CategoryTheory.whiskering_linearYoneda₂, SSet.Truncated.HomotopyCategory.homToNerveMk_comp, SSet.Truncated.HomotopyCategory.BinaryProduct.functor_map, CochainComplex.HomComplex.Cocycle.fromSingleMk_mem_coboundaries_iff, CategoryTheory.Abelian.LeftResolution.π_naturality, CategoryTheory.Under.postAdjunctionRight_counit_app_right, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_counitIso, CategoryTheory.Limits.inr_comp_pushoutObjIso_inv_assoc, ShiftSequence.induced_shiftMap, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_app_assoc, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_comp_fiber, LeftExtension.mk_left_as, groupHomology.d₁₀_comp_coinvariantsMk_assoc, CategoryTheory.Limits.CokernelCofork.map_condition_assoc, GrpCat.FilteredColimits.colimit_mul_mk_eq', CategoryTheory.SmallObject.coconeOfLE_ι_app, SimplexCategory.skeletalFunctor.coe_map, AddCommMonCat.coyonedaForget_hom_app_app_hom, CategoryTheory.unitCompPartialBijectiveAux_symm_apply, CategoryTheory.Limits.inr_comp_pushoutObjIso_hom, AlgebraicTopology.DoldKan.decomposition_Q, CategoryTheory.Limits.colimitCoconeOfUnique_cocone_ι, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, CategoryTheory.Sum.functorEquiv_inverse_obj, PresheafOfModules.Finite.evaluation_preservesFiniteColimits, CategoryTheory.μ_naturality_assoc, CategoryTheory.TwoSquare.EquivalenceJ.inverse_obj, mapCommMonIdIso_inv_app_hom_hom, quasiIsoAt_iff, CategoryTheory.Pseudofunctor.mapId'_hom_naturality_assoc, AlgebraicGeometry.Scheme.restrictFunctor_obj_left, CategoryTheory.Limits.Pi.isoLimit_hom_π_assoc, CategoryTheory.Limits.BinaryFan.assocInv_snd, CategoryTheory.shiftFunctorAdd_hom_app_obj_of_induced, CategoryTheory.InjectiveResolution.exact₀, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_succ_succ, CategoryTheory.Comma.mapLeftIso_inverse_map_left, HomologicalComplex.quasiIsoAt_map_of_preservesHomology, CategoryTheory.Limits.biprod.mapBiprod_inv_map_desc, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₂, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left_assoc, CategoryTheory.LocalizerMorphism.RightResolution.op_w, map_shiftFunctorComm, CategoryTheory.MonoOver.congr_counitIso, CategoryTheory.OplaxFunctor.mapComp_naturality_right_app_assoc, CategoryTheory.instEffectiveEpiFamilyObjMapOfIsEquivalence, LaxRightLinear.μᵣ_naturality_left, CategoryTheory.ShortComplex.SnakeInput.naturality_φ₂_assoc, LaxMonoidal.ofBifunctor.firstMap₂_app_app_app, TopologicalSpace.Opens.toTopCat_map, op_commShiftIso_hom_app, CategoryTheory.Limits.biproduct.mapBiproduct_hom_desc, CategoryTheory.Localization.SmallShiftedHom.equiv_mk₀, flipping_inverse_obj_obj_obj, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_app_fst_app, CategoryTheory.instSmallHomFunctorOppositeTypeColimitCompYoneda, CategoryTheory.StructuredArrow.map_obj_hom, CategoryTheory.CostructuredArrow.preEquivalence.inverse_map_left_left, AlgebraicTopology.DoldKan.σ_comp_P_eq_zero, CategoryTheory.Groupoid.invEquivalence_unitIso, CategoryTheory.Limits.BinaryBicones.functoriality_full, CategoryTheory.Limits.FormalCoproduct.eval_obj_obj, AlgebraicGeometry.Spec.fromSpecStalk_eq, AlgebraicGeometry.quasiCompact_iff_forall_affine, CategoryTheory.RightExactFunctor.whiskeringLeft_obj_map, PushoutObjObj.inl_ι, CategoryTheory.Comma.preLeft_obj_left, CategoryTheory.Idempotents.FunctorExtension₁.map_app_f, CategoryTheory.SmallObject.functorialFactorizationData_p_app, HomologicalComplex.shortComplexFunctor'_obj_f, CochainComplex.HomComplex.Cocycle.equivHomShift_comp_shift, HomotopyCategory.homologyFunctor_shiftMap, CategoryTheory.Adjunction.whiskerRight_counit_app_app, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over, CategoryTheory.instPreservesColimitFunctorOppositeTypeObjCoyonedaOpYoneda, bifunctorComp₁₂Iso_hom_app_app_app, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_inv_hom_id, CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm, CategoryTheory.Over.opEquivOpUnder_functor_map, CategoryTheory.Limits.prodComparison_inv_natural_assoc, CategoryTheory.Comma.mapRight_obj_right, CategoryTheory.Limits.PullbackCone.isoMk_hom_hom, SSet.S.IsUniquelyCodimOneFace.existsUnique_δ_cast_simplex, HasFibers.inducedFunctor_map_coe, CategoryTheory.Subobject.inf_pullback, descOfIsLeftKanExtension_fac_app, hasPointwiseRightDerivedFunctorAt_iff, CategoryTheory.Limits.CatCospanTransform.leftUnitor_hom_right_app, CochainComplex.HomComplex.Cochain.rightShiftLinearEquiv_symm_apply, CategoryTheory.CatCommSq.hInv_iso_hom_app, CategoryTheory.CartesianMonoidalCategory.preservesTerminalIso_id, CategoryTheory.SimplicialObject.isCoskeletal_iff_isIso, CategoryTheory.Comma.mapLeftComp_hom_app_left, CategoryTheory.Comonad.ForgetCreatesLimits'.commuting, HomologicalComplex.HomologySequence.composableArrows₃Functor_obj, CategoryTheory.Presieve.in_coverByImage, AlgebraicGeometry.instLocallyOfFinitePresentationMorphismRestrict, AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_π, LeftLinear.instIsIsoμₗ, CategoryTheory.MonoidalCategory.DayFunctor.ν_comp_unitDesc, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_functor_obj, CategoryTheory.TransfiniteCompositionOfShape.map_F, CategoryTheory.IsCoseparator.of_equivalence, CategoryTheory.δ_naturalityᵣ, TopCat.Presheaf.stalkFunctor_map_germ, CategoryTheory.Limits.SequentialProduct.functorMap_commSq_succ, CategoryTheory.ComposableArrows.mkOfObjOfMapSucc_exists, CategoryTheory.ShortComplex.mapHomologyIso_inv_naturality_assoc, PreOneHypercoverDenseData.toPreOneHypercover_Y, CategoryTheory.ComposableArrows.isoMk₀_hom_app, AlgebraicGeometry.Scheme.IdealSheafData.ideal_biInf, CategoryTheory.preadditiveCoyonedaObj_obj_isModule, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, CoreMonoidal.μIso_hom_natural_right_assoc, CategoryTheory.Monad.MonadicityInternal.counitCofork_ι_app, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app, CategoryTheory.Limits.Multifork.ofPiFork_ι, bifunctorComp₂₃Iso_hom_app_app_app, AlgebraicTopology.DoldKan.Γ₀.obj_obj, CategoryTheory.Limits.Cofork.IsColimit.homIso_symm_apply, CategoryTheory.Adjunction.Triple.rightToLeft_app_adj₂_unit_app, PresheafOfModules.toPresheaf_map_sheafificationAdjunction_unit_app, typeToPointed_obj_X, PushoutObjObj.mapArrowRight_right, CategoryTheory.ShortComplex.mapOpcyclesIso_hom_naturality, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality, PullbackObjObj.π_fst_assoc, CategoryTheory.Pretriangulated.Triangle.isZero₁_iff, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen', CochainComplex.shiftShortComplexFunctor'_inv_app_τ₁, Initial.extendCone_obj_π_app, MonObj.mopEquiv_unitIso_inv_app_hom, CondensedSet.toTopCatMap_hom_apply, CategoryTheory.NatIso.cancel_natIso_hom_right_assoc, CategoryTheory.Limits.isIso_π_initial, CategoryTheory.Localization.SmallHom.equiv_shift, CategoryTheory.ComposableArrows.functorArrows_map, CategoryTheory.Limits.SingleObj.Types.sections.equivFixedPoints_symm_apply_coe, CategoryTheory.Subobject.inf_comp_right_assoc, CategoryTheory.Limits.Fork.condition_assoc, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₃, CategoryTheory.Limits.Cofork.IsColimit.π_desc', CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp, AlgebraicGeometry.structurePresheafInCommRingCat_obj_carrier, CategoryTheory.nerveMap_app, CategoryTheory.Presieve.isSheaf_yoneda', TopCat.Presheaf.germToPullbackStalk_stalkPullbackHom_assoc, CategoryTheory.CartesianClosed.curry_injective, CategoryTheory.Prod.snd_obj, groupHomology.H0π_comp_H0Iso_hom_assoc, CategoryTheory.SimplicialObject.augmentedCechNerve_obj_right, CochainComplex.shiftShortComplexFunctorIso_zero_add_hom_app, CategoryTheory.Grothendieck.pre_obj_fiber, CategoryTheory.Limits.ι_comp_colimitLeftOpIsoUnopLimit_hom_assoc, CategoryTheory.Under.postEquiv_functor, AlgebraicGeometry.IsAffineOpen.app_basicOpen_eq_away_map, AlgebraicGeometry.LocallyRingedSpace.toΓSpecMapBasicOpen_eq, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv_assoc, CategoryTheory.uliftYonedaMap_app_apply, CategoryTheory.Limits.diagramIsoSpan_inv_app, inrCompSum'_hom_app, WellOrderInductionData.Extension.map_limit, CategoryTheory.FunctorToTypes.shrink_obj, CochainComplex.isKProjective_shift_iff, whiskeringLeftObjCompIso_hom_app_app, mapTriangleInvRotateIso_hom_app_hom₁, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.rightUnitor_hom_unit_app, functorialityCompPostcompose_inv_app_hom, LeftExtension.precomp₂_map_left, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_inv_app_assoc, InfiniteGalois.limitToAlgEquiv_symm_apply, Action.Iso.conj_ρ, CategoryTheory.Limits.HasLimit.isoOfNatIso_hom_π, CategoryTheory.MonoidalClosed.curry'_whiskerRight_comp, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_inv_app_hom_hom, CategoryTheory.Localization.Construction.liftToPathCategory_obj, CategoryTheory.Limits.HasBiproductsOfShape.colimIsoLim_hom_app, CategoryTheory.OverPresheafAux.counitForward_counitBackward, CategoryTheory.Abelian.LeftResolution.karoubi.π'_app_f, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_obj_map_app, CategoryTheory.Under.lift_map, CategoryTheory.Limits.Wedge.condition_assoc, CategoryTheory.Bicategory.LeftLift.whiskering_obj, CategoryTheory.Mat.equivalenceSingleObjInverse_obj_str, groupHomology.cyclesMap_comp, CategoryTheory.Limits.inv_prodComparison_map_snd_assoc, IsCoverDense.Types.appIso_hom, CategoryTheory.Comonad.id_obj, CategoryTheory.Monad.MonadicityInternal.main_pair_reflexive, AddGrpCat.FilteredColimits.colimit_zero_eq, LightCondensed.internallyProjective_iff_tensor_condition', AlgebraicGeometry.StructureSheaf.instAwayObjOppositeOpensCarrierTopValStructureSheafInTypeOpBasicOpen, CategoryTheory.Limits.WidePullbackShape.equivalenceOfEquiv_functor_obj_none, LaxLeftLinear.μₗ_associativity_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionAssocIso_inv, AlgebraicGeometry.Scheme.preimage_basicOpen, CategoryTheory.Limits.CokernelCofork.π_eq_zero, CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac_assoc, CategoryTheory.OverPresheafAux.costructuredArrowPresheafToOver_obj, CategoryTheory.PreservesImage.iso_inv, Final.extendCocone_map_hom, CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso_inv_app, CategoryTheory.GrothendieckTopology.Point.presheafFiber_hom_ext_iff, CategoryTheory.ObjectProperty.LimitOfShape.toStructuredArrow_obj, AlgebraicGeometry.instMonoObjWalkingSpanCompOverSchemeTopMorphismPropertySpanOverForgetForgetForgetNoneWalkingPairSomeMapInitOfIsOpenImmersionLeftDiscretePUnit, AlgebraicGeometry.Scheme.Opens.instIsIsoCommRingCatAppLEιTopToScheme, CategoryTheory.Grothendieck.grothendieckTypeToCatInverse_obj_base, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_map_fst_app, CategoryTheory.CommMon.forget₂Mon_obj_X, CategoryTheory.orderDualEquivalence_inverse_obj, CategoryTheory.Subfunctor.Subpresheaf.range_subobjectMk_ι, CategoryTheory.Sieve.equalizer_eq_equalizerSieve, CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_one, CochainComplex.instIsStrictlyLEObjIntSingleFunctor, SSet.Truncated.rightExtensionInclusion_hom_app, AlgebraicGeometry.IsAffineHom.isAffine_preimage, CategoryTheory.Equivalence.leftOp_inverse_obj, HomotopicalAlgebra.CofibrantObject.instWeakEquivalenceHoCatAppUnitHoCatAdj, CategoryTheory.MonoidalClosed.ofEquiv_curry_def, CategoryTheory.Limits.isIso_colimit_cocone_parallelPair_of_self, CategoryTheory.StructuredArrow.prodEquivalence_counitIso, CategoryTheory.Limits.multispanIndexCoend_fst, CategoryTheory.Idempotents.app_idem, TopCat.Presheaf.toPushforwardOfIso_app, CategoryTheory.OrthogonalReflection.iteration_map_succ_surjectivity, Monoidal.leftUnitor_hom_app, AlgebraicGeometry.Scheme.monObjAsOverPullback_one, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_obj_map_app, CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_left_assoc, AlgebraicGeometry.IsAffineOpen.ΓSpecIso_hom_fromSpec_app, CochainComplex.instIsStrictlyGEObjIntSingleFunctor, CategoryTheory.Equivalence.changeInverse_unitIso_hom_app, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso_hom_app_f, CategoryTheory.Comma.mapLeftIso_functor_obj_right, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_inv_app_val_app_hom_hom, CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_tensor, CategoryTheory.Adjunction.homEquiv_symm_rightAdjointUniq_hom_app, CategoryTheory.Pseudofunctor.map₂_whisker_right_app, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₁, CategoryTheory.Limits.instPreservesFiniteColimitsFunctorObjEvaluationOfHasFiniteColimits, CategoryTheory.Limits.coconeUnopOfCone_ι, CategoryTheory.curryingIso_inv_toFunctor_obj_obj_map, AlgebraicGeometry.Scheme.exists_le_and_germ_injective, CoreMonoidal.toLaxMonoidal_μ, CategoryTheory.Abelian.PreservesCoimage.iso_inv_π_assoc, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₃, Action.rightUnitor_inv_hom, TannakaDuality.FiniteGroup.map_mul_toRightFDRepComp, CategoryTheory.unitOfTensorIsoUnit_hom_app, CategoryTheory.StructuredArrow.mapIso_inverse_map_left, CategoryTheory.preservesLimitNatIso_hom_app, CategoryTheory.cones_obj_obj, mapCocone_pt, Rep.indResHomEquiv_apply_hom, Bipointed.swapEquiv_unitIso_hom_app_toFun, CategoryTheory.Limits.MonoCoprod.mono_binaryCofanSum_inl, CategoryTheory.Limits.whiskerLeft_ι_colimitCompWhiskeringLeftIsoCompColimit_inv, FullyFaithful.homNatIso_hom_app_down, CategoryTheory.Comma.mapLeft_obj_hom, Final.ι_colimitIso_hom, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_obj_g, CategoryTheory.Limits.coprodComparison_natural_assoc, CategoryTheory.AdditiveFunctor.ofExact_map_hom, CategoryTheory.Adjunction.commShiftIso_inv_app_counit_app, CategoryTheory.FunctorToTypes.prod.fst_app, LaxMonoidal.μ_natural_assoc, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₁, CategoryTheory.Limits.IndizationClosedUnderFilteredColimitsAux.exists_nonempty_limit_obj_of_colimit, CategoryTheory.Monad.monadMonEquiv_unitIso_hom_app_toNatTrans_app, AlgebraicTopology.AlternatingFaceMapComplex.obj_X, PresheafOfModules.instIsLocallyInjectiveToSheafify, CompHausLike.instCompactSpaceCarrierObjTopCatCompHausLikeToTop, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_mul, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_X_isModule, CategoryTheory.nerve.functorOfNerveMap_obj, CategoryTheory.Adjunction.homAddEquiv_symm_sub, HomotopicalAlgebra.BifibrantObject.instIsCofibrantObjι, CategoryTheory.GrothendieckTopology.W_eq_W_range_sheafToPresheaf_obj, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d_1_0_assoc, CategoryTheory.Endofunctor.Adjunction.Coalgebra.homEquiv_naturality_str_symm, AlgebraicGeometry.Scheme.affineOpenCover_X, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompYoneda, AlgebraicGeometry.Scheme.comp_app_assoc, pointedToTwoPSnd_obj_toTwoPointing_toProd, TopCat.Presheaf.generateEquivalenceOpensLe_functor'_map, CategoryTheory.Limits.BinaryFan.assocInv_fst, HomologicalComplex₂.D₁_totalShift₂XIso_hom, CategoryTheory.MorphismProperty.LeftFraction.Localization.Q_obj, CategoryTheory.Comonad.instReflectsLimitWalkingParallelPairParallelPairMapAAppUnitObjAOfReflectsLimitOfIsCosplitPair, mapMatId_inv_app, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_hom_app, CategoryTheory.Limits.Fork.isoForkOfι_inv_hom, Monoidal.lift_μ, CategoryTheory.Comonad.CofreeEqualizer.bottomMap_f, groupHomology.mapShortComplexH1_τ₃, CategoryTheory.Sieve.functorPullback_apply, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionObj, CategoryTheory.MonoidalCategory.externalProductSwap_hom_app_app, coreflective', CategoryTheory.Adjunction.Triple.leftToRight_app_obj_assoc, CategoryTheory.Limits.PreservesPullback.iso_hom_snd, CategoryTheory.Limits.map_inl_inv_coprodComparison, CompHausLike.isoOfHomeo_hom_hom_hom_apply, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocNatIso_hom_app_app_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionHomRight, CategoryTheory.Limits.span_zero, CategoryTheory.CostructuredArrow.pre_map_left, CategoryTheory.subterminalInclusion_obj, CategoryTheory.shiftFunctorAdd'_assoc_hom_app_assoc, CategoryTheory.Limits.BinaryFan.π_app_left, IsEventuallyConstantFrom.isIso_ι_of_isColimit, AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_fac, CategoryTheory.Monoidal.tensorObj_map, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp_assoc, CategoryTheory.Limits.Cofork.ofπ_ι_app, AlgebraicGeometry.instQuasiCompactToSpecΓOfCompactSpaceCarrierCarrierCommRingCat, CategoryTheory.Equivalence.congrRight_unitIso_hom_app, CategoryTheory.NatTrans.shift_app_comm, CategoryTheory.Join.mapPairRight_hom_app, partialFunEquivPointed_functor_obj_point, shiftMap_comp_assoc, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_whiskerLeft_assoc, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon_obj, SkyscraperPresheafFunctor.map'_app, limitIsoOfIsRightKanExtension_hom_π, CategoryTheory.Subobject.functor_map, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_assoc, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_hom_app_hom, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂'_obj_obj_map, AlgebraicGeometry.morphismRestrict_app, PullbackObjObj.hom_ext_iff, CategoryTheory.Grp.forget_obj, CommGrpCat.toAddCommGrp_obj_coe, ProfiniteGrp.profiniteCompletion_obj, CategoryTheory.Equivalence.sheafCongrPrecoherent_functor_map_val_app, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, currying_functor_obj_map, preimageIso_hom, CategoryTheory.SimplicialObject.augmentedCechNerve_obj_left_map, AlgebraicGeometry.AffineSpace.comp_homOfVector_assoc, leftOpRightOpEquiv_functor_map_app, CategoryTheory.Limits.prodComparison_inv_natural, CochainComplex.HomComplex.Cochain.rightShift_v, mapConeWhisker_inv_hom, CochainComplex.HomComplex.Cochain.rightUnshift_zero, CategoryTheory.yonedaGrp_map_app, CommRingCat.forgetToRingCat_map_hom, Monoidal.leftUnitor_inv_app, PresheafOfModules.germ_ringCat_smul, groupHomology.cyclesMap_comp_cyclesIso₀_hom_assoc, CochainComplex.mappingConeCompTriangleh_comm₁, ShiftSequence.induced_isoShiftZero_hom_app_obj, AlgebraicTopology.DoldKan.Q_f_naturality, SSet.ι₁_fst_assoc, CategoryTheory.Equalizer.FirstObj.ext_iff, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_extMk, Monoidal.εIso_inv, AlgebraicGeometry.LocallyRingedSpace.toStalk_stalkMap_toΓSpec, CochainComplex.HomComplex.Cocycle.toSingleMk_postcomp, CategoryTheory.Limits.Sigma.ι_isoColimit_inv_assoc, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.functor_map, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app_assoc, CochainComplex.HomComplex.Cocycle.leftShift_coe, CategoryTheory.Limits.map_lift_pullbackComparison, SemiRingCat.forget₂_monCat_map, groupHomology.lsingle_comp_chainsMap_f_assoc, CategoryTheory.Monoidal.transportStruct_whiskerLeft, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality, CategoryTheory.InjectiveResolution.homotopyEquiv_inv_ι_assoc, AlgebraicGeometry.Scheme.Opens.ι_image_top, AlgebraicGeometry.Scheme.Hom.toImage_app, CategoryTheory.ObjectProperty.prop_ihom, HomologicalComplex₂.D₂_totalShift₂XIso_hom, Rep.linearizationTrivialIso_hom_hom, CategoryTheory.MorphismProperty.map_mem_map, isoCopyObj_hom_app, CategoryTheory.PreOneHypercover.map_Y, CategoryTheory.Grpd.freeForgetAdjunction_unit_app, CategoryTheory.Discrete.productEquiv_functor_obj, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_hom, CategoryTheory.SingleFunctors.shiftIso_zero_hom_app, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_fst, CategoryTheory.MonoidalClosed.curry_natural_right, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_hom_app_app, TopCat.Sheaf.eq_of_locally_eq_iff, flip_map_app, partialLeftAdjointHomEquiv_comp, CategoryTheory.Localization.homEquiv_map, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app_assoc, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_inv_comp_π_assoc, CategoryTheory.Pseudofunctor.map₂_left_unitor_app_assoc, CategoryTheory.Limits.preserves_cokernel_iso_comp_cokernel_map_assoc, CategoryTheory.equivEssImageOfReflective_counitIso, splitEpiBiprodComparison_section_, CategoryTheory.Idempotents.toKaroubi_obj_X, HomotopicalAlgebra.CofibrantObject.weakEquivalence_toHoCat_map_iff, imageToKernel_epi_of_epi_of_zero, CategoryTheory.Adjunction.leftAdjointIdIso_inv_app, CategoryTheory.Bifunctor.map_comp_id, PresheafOfModules.naturality_apply, MonCat.Colimits.cocone_naturality, CategoryTheory.Limits.ι_colimitLimitToLimitColimit_π_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.id_snd_app, map_shiftFunctorCompIsoId_inv_app, CategoryTheory.Equivalence.ε_comp_map_ε_assoc, HomologicalComplex.instHasBinaryBiproductObjEval, AlgebraicGeometry.IsAffineOpen.isoSpec_hom, mapIso_hom, CategoryTheory.Limits.FintypeCat.instFiniteObjCompFintypeCatIncl, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_η_unmop_app, CategoryTheory.Pseudofunctor.map₂_right_unitor_app_assoc, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv_def, CategoryTheory.Pseudofunctor.map₂_right_unitor_app, CategoryTheory.Equivalence.core_unitIso_inv_app_iso_hom, AlgebraicGeometry.Scheme.Modules.Hom.app_smul, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_obj, AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id, ChainComplex.truncate_obj_X, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_naturality_app, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.pushouts_ofLE_le_largerSubobject, CategoryTheory.PreOneHypercover.map_f, CategoryTheory.regularTopology.EqualizerCondition.bijective_mapToEqualizer_pullback, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_unitIso, CategoryTheory.ChosenPullbacksAlong.Over.fst_eq_fst', CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.flipFunctorToInterchange_hom_app_app, CategoryTheory.Limits.Cofork.unop_ι, CategoryTheory.Cokleisli.Adjunction.fromCokleisli_obj, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec, CategoryTheory.Limits.Cone.toStructuredArrowCompToUnderCompForget_inv_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_hom_app_app_fst, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_iff_mono₁, AlgebraicTopology.DoldKan.identity_N₂_objectwise, FundamentalGroupoid.punitEquivDiscretePUnit_inverse, AlgebraicGeometry.Scheme.Γ_obj_op, CochainComplex.single₀_obj_zero, CategoryTheory.Iso.hom_inv_id_app_app_app_assoc, CategoryTheory.ComposableArrows.naturality'_assoc, CategoryTheory.StructuredArrow.map_id, CategoryTheory.Localization.Monoidal.μ_inv_natural_left, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_π_app_walkingParallelPair_zero, CategoryTheory.Abelian.Ext.homLinearEquiv_symm_apply, typeToPointed_obj_point, CategoryTheory.PreGaloisCategory.isPretransitive_of_isGalois, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_iso_hom_app, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_invApp, CochainComplex.HomComplex.Cochain.shift_v', CategoryTheory.map_shrinkYonedaEquiv, CategoryTheory.GrothendieckTopology.Point.sheafFiberCompIso_hom_app, CategoryTheory.NatTrans.app_zsmul, CategoryTheory.Equivalence.sheafCongr.functor_obj_val_obj, 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, AlgebraicGeometry.PresheafedSpace.comp_c, CategoryTheory.WithTerminal.coneEquiv_functor_obj_pt, CategoryTheory.ObjectProperty.LimitOfShape.toStructuredArrow_map, HomObj.naturality, CategoryTheory.Under.opEquivOpOver_functor_map, BialgCat.forget₂_algebra_obj, LightCondMod.isDiscrete_iff_isDiscrete_forget, CategoryTheory.ι_preservesColimitIso_inv, mapCommMon_id_one, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_ε_unmop_app, CategoryTheory.Limits.biproduct.map_lift_mapBiprod, TopCat.Presheaf.IsSheaf.isSheafUniqueGluing, CategoryTheory.MonoidalOpposite.tensorLeftMopIso_inv_app_unmop, CategoryTheory.Limits.Cocone.ofPushoutCocone_pt, CategoryTheory.Bimon.equivMonComonCounitIsoAppXAux_hom, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₃, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_inv_app_val_app, SSet.Subcomplex.PairingCore.notMem₂, CategoryTheory.CommGrp.mkIso'_hom_hom_hom_hom, CategoryTheory.Subobject.finset_inf_arrow_factors, CategoryTheory.Limits.diagramIsoPair_inv_app, CategoryTheory.Adjunction.homEquiv_apply_eq, FintypeCat.incl_obj, AlgebraicTopology.inclusionOfMooreComplexMap_f, CategoryTheory.Limits.coprod.functor_obj_obj, CategoryTheory.yonedaEquiv_symm_map, CategoryTheory.Limits.ι_reflexiveCoequalizerIsoCoequalizer_hom_assoc, AlgebraicGeometry.Scheme.image_zeroLocus, AlgebraicGeometry.Scheme.Pullback.forget_comparison_surjective, CategoryTheory.Limits.IsLimit.homIso_hom, CategoryTheory.Square.toArrowArrowFunctor'_obj_hom_left, CategoryTheory.MonoidalCategory.rightAssocTensor_obj, CategoryTheory.NatTrans.whiskerRight_app_tensor_app_assoc, map_nsmul, CategoryTheory.obj_ε_app, ModuleCat.FilteredColimits.ι_colimitDesc_assoc, AlgebraicGeometry.Scheme.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, leftKanExtensionUnit_leftKanExtensionObjIsoColimit_hom_assoc, DerivedCategory.HomologySequence.δ_comp_assoc, UniformSpaceCat.extensionHom_val, AlgebraicGeometry.HasRingHomProperty.iff_of_source_openCover, IsOpenMap.coe_functor_obj, AlgebraicGeometry.Scheme.Hom.isoImage_hom_ι_assoc, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCBasicOpens_app, ModuleCat.extendScalarsId_inv_app_apply, CategoryTheory.Subgroupoid.inclusion_faithful, CategoryTheory.Limits.PullbackCone.ofCone_pt, AlgebraicGeometry.LocallyRingedSpace.evaluation_eq_zero_iff_notMem_basicOpen, CategoryTheory.Adjunction.comp_counit_app_assoc, OplaxMonoidal.ofBifunctor.firstMap₃_app_app_app, CategoryTheory.liftedLimitMapsToOriginal_hom_π, ModuleCat.semilinearMapAddEquiv_symm_apply_apply, AlgebraicGeometry.isIso_toSpecΓ, FinBoolAlg.hasForgetToFinPartOrd_forget₂_obj_str, CategoryTheory.Center.forget_δ, CategoryTheory.SimplicialObject.augmentedCechNerve_obj_left_obj, SSet.Edge.toTruncated_id, SSet.horn.ι_ι_assoc, CategoryTheory.MorphismProperty.LeftFraction.map_ofInv_hom_id, LaxBraided.braided_assoc, IsDenseSubsite.isIso_ranCounit_app_of_isDenseSubsite, CategoryTheory.CostructuredArrow.mapIso_inverse_obj_hom, CategoryTheory.Limits.opParallelPairIso_inv_app_zero, Monoidal.rightUnitor_hom_app, AlgebraicGeometry.Proj.res_apply, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_unitIso_inv_app_f_f, CategoryTheory.Comonad.left_counit_assoc, CategoryTheory.Under.postEquiv_unitIso, CategoryTheory.ShrinkHoms.functor_obj, Rep.coinvariantsAdjunction_homEquiv_apply_hom, CategoryTheory.CostructuredArrow.projectQuotient_factors, Monoidal.commTensorRight_hom_app, TopCat.Presheaf.app_injective_iff_stalkFunctor_map_injective, AlgebraicGeometry.StructureSheaf.comapₗ_eq_localRingHom, CategoryTheory.Sieve.toFunctor_app_coe, CategoryTheory.NatTrans.naturality_1, AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.preimage_basicOpen, CategoryTheory.isFinitelyPresentable_iff_preservesFilteredColimits, CategoryTheory.Limits.PullbackCone.mk_π_app_left, CategoryTheory.constantPresheafAdj_counit_app_app, CategoryTheory.CategoryOfElements.CreatesLimitsAux.map_lift_mapCone, DerivedCategory.HomologySequence.δ_comp, CategoryTheory.Equivalence.sheafCongr.unitIso_inv_app_val_app, CategoryTheory.Sum.functorEquivFunctorCompSndIso_hom_app_app, SheafOfModules.pushforwardSections_coe, AlgebraicGeometry.Scheme.Opens.topIso_hom, CategoryTheory.Join.mapIsoWhiskerLeft_hom_app, AlgebraicTopology.DoldKan.N₁Γ₀_inv_app_f_f, CategoryTheory.Limits.ι_comp_colimitLeftOpIsoUnopLimit_hom, CategoryTheory.MonoidalClosed.comp_id, CategoryTheory.GrothendieckTopology.map_yonedaEquiv, CategoryTheory.Limits.kernelSubobject_arrow_comp, SimplexCategory.toCat_map, AlgebraicGeometry.IsLocalAtSource.sigmaDesc, CategoryTheory.CostructuredArrow.mkPrecomp_comp, ComplexShape.Embedding.extendFunctor_obj, CategoryTheory.Sigma.map_obj, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_hom_app_fst_app, AlgebraicTopology.alternatingFaceMapComplex_obj_X, essImage_overPost, mapCommGrp_obj_grp_mul, CategoryTheory.WithTerminal.commaFromOver_obj_left, PresheafOfModules.Sheafify.smul_zero, PresheafOfModules.fromFreeYonedaCoproduct_app_mk, CategoryTheory.Cat.HasLimits.homDiagram_obj, reprW_hom_app, CategoryTheory.FreeGroupoid.mapCompLift_hom_app, PresheafOfModules.Sheafify.map_smul, CategoryTheory.ComposableArrows.opEquivalence_counitIso_hom_app_app, CategoryTheory.uliftCoyonedaEquiv_symm_map, CategoryTheory.Over.fst_left, groupHomology.H1CoresCoinf_f, CategoryTheory.Over.prodLeftIsoPullback_hom_fst, CategoryTheory.Limits.CompleteLattice.colimitCocone_isColimit_desc, OplaxMonoidal.comp_δ, AlgebraicGeometry.StructureSheaf.toOpen_res, CategoryTheory.Comonad.ComonadicityInternal.counitFork_pt, curry_map_app_app, CategoryTheory.Limits.Pi.isoLimit_inv_π_assoc, CategoryTheory.Precoverage.ZeroHypercover.map_toPreZeroHypercover, CategoryTheory.Over.associator_hom_left_fst_assoc, CategoryTheory.Limits.opParallelPairIso_inv_app_one, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_hom_eq_germ_assoc, CategoryTheory.TwoSquare.lanBaseChange_app, CategoryTheory.NatTrans.mapSquare_app_τ₃, hcongr_hom, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π, CategoryTheory.Sum.functorEquivFunctorCompFstIso_hom_app_app, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.tensorHom_eq, CategoryTheory.whiskeringLeftCompEvaluation_inv_app, CategoryTheory.Limits.CompleteLattice.finiteColimitCocone_isColimit_desc, AlgebraicGeometry.Scheme.ofRestrict_app, AlgebraicGeometry.structurePresheafInModuleCat_obj_carrier, DerivedCategory.mem_distTriang_iff, CategoryTheory.CatCommSq.vId_iso_inv_app, Monoidal.map_rightUnitor, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec_assoc, AlgebraicGeometry.SheafedSpace.congr_app, CategoryTheory.Comma.equivProd_unitIso_inv_app_left, CategoryTheory.Limits.map_lift_pullbackComparison_assoc, AlgebraicGeometry.Scheme.OpenCover.restrict_X, CategoryTheory.yonedaYonedaColimit_app_inv, CategoryTheory.Sheaf.ΓObjEquivSections_naturality, CategoryTheory.Limits.Cone.extensions_app, CategoryTheory.Grothendieck.grothendieckTypeToCatInverse_map_base, CategoryTheory.yonedaEquiv_symm_naturality_left, CategoryTheory.Limits.pullbackConeEquivBinaryFan_unitIso, CategoryTheory.ShortComplex.RightHomologyData.map_opcyclesMap', CategoryTheory.ShrinkHoms.equivalence_unitIso, PresheafOfModules.germ_smul, CategoryTheory.OplaxFunctor.mapComp_naturality_left_app_assoc, CategoryTheory.Adjunction.left_triangle_components_assoc, RightLinear.δᵣ_comp_μᵣ_assoc, AlgebraicGeometry.Scheme.zeroLocus_univ, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_symm_apply, CategoryTheory.CosimplicialObject.equivalenceLeftToRight_right, HomotopicalAlgebra.BifibrantObject.HoCat.ιCofibrantObject_map_toHoCat_map, CategoryTheory.Equalizer.Presieve.Arrows.SecondObj.ext_iff, SSet.leftUnitor_hom_app_apply, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_spec, CategoryTheory.PreGaloisCategory.exists_galois_representative, CategoryTheory.SmallObject.preservesColimit, SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁_hom_f_f, CategoryTheory.Limits.PreservesPullback.iso_hom, CategoryTheory.Over.isMonHom_pullbackFst_id_right, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionLeft_obj, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_inv_π, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand', Monoidal.whiskerRight_δ_μ_assoc, FundamentalGroupoidFunctor.prodToProdTop_map, SemilatInfCat.dual_obj_isSemilatticeSup, CategoryTheory.Limits.coneUnopOfCocone_π, CategoryTheory.Limits.cokernelComparison_map_desc_assoc, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransEq_inv_app_f, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionAssocIso_hom, OplaxMonoidal.lift_δ_assoc, CategoryTheory.ObjectProperty.IsCodetecting.isIso_iff_of_epi, CategoryTheory.Endofunctor.Coalgebra.Terminal.right_inv', CategoryTheory.Over.pullback_obj_hom, AlgebraicGeometry.Scheme.Hom.image_le_image_iff, CategoryTheory.Pretriangulated.Opposite.complete_distinguished_triangle_morphism, CategoryTheory.Cat.whiskerRight_app, CategoryTheory.Limits.pullbackComparison_comp_fst_assoc, CategoryTheory.Limits.Cotrident.app_one_assoc, mapSkeleton_injective, LightCondSet.toTopCatMap_hom_apply, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.isIso_post, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_left, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_hom_comp_ι, CategoryTheory.δ_μ_app_assoc, CategoryTheory.ComposableArrows.functorArrows_obj, CategoryTheory.Over.forgetAdjStar_unit_app_left, CoreMonoidal.left_unitality_assoc, AlgebraicGeometry.Scheme.Hom.comp_appTop_assoc, map_opShiftFunctorEquivalence_counitIso_hom_app_unop_assoc, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObj_obj, CategoryTheory.Equivalence.leftOp_functor_map, GrpCat.FilteredColimits.colimit_one_eq, CategoryTheory.TwoSquare.guitartExact_iff_isConnected_downwards, AlgebraicGeometry.IsAffineOpen.fromSpec_app_of_le, Rep.ihom_obj_ρ, shiftIso_hom_app_comp_shiftMap_of_add_eq_zero, CategoryTheory.IsSplitEqualizer.map_rightRetraction, CategoryTheory.Limits.ι_comp_sigmaComparison_assoc, toEssImage_obj_obj, CategoryTheory.mateEquiv_counit, AlgebraicGeometry.StructureSheaf.const_mul, AlgebraicGeometry.AffineSpace.map_appTop_coord, CategoryTheory.Limits.HasLimit.isoOfEquivalence_inv_π, CommShift.OfComp.map_iso_inv_app, CochainComplex.isKInjective_iff_rightOrthogonal, rightKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, CategoryTheory.Pretriangulated.preadditiveYoneda_map_distinguished, CategoryTheory.Limits.coconeOfDiagramTerminal_pt, CategoryTheory.Limits.hasColimit_const_of_isConnected, whiskeringLeft_obj_obj, CategoryTheory.Subobject.map_obj_injective, CategoryTheory.LaxFunctor.map₂_associator_app, AlgebraicGeometry.Scheme.toSpecΓ_preimage_basicOpen, CategoryTheory.Limits.coconeOfCoconeCurry_ι_app, CategoryTheory.Bicategory.LeftExtension.whiskering_obj, CategoryTheory.Presheaf.coherentExtensiveEquivalence_inverse_obj_val, map_dite, CategoryTheory.Adjunction.whiskerLeftRUnitIsoOfIsIsoCounit_inv_app, flippingEquiv_apply_obj_obj, Fin.succFunctor_obj, CategoryTheory.Presieve.map_singleton, CategoryTheory.ObjectProperty.trW.shift, CategoryTheory.yonedaEquiv_symm_naturality_right, SheafOfModules.pushforwardSections_unitHomEquiv, CategoryTheory.PreGaloisCategory.PointedGaloisObject.cocone_app, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app, CochainComplex.HomComplex.Cochain.rightShift_add, CochainComplex.ShiftSequence.shiftIso_inv_app, CategoryTheory.Limits.FormalCoproduct.cech_obj, CategoryTheory.Comma.preLeft_map_right, compConstIso_inv_app_app, ranCompLimIso_hom_app, mapTriangleInvRotateIso_hom_app_hom₂, CategoryTheory.constantSheafAdj_counit_app, CategoryTheory.Grothendieck.congr, PresheafOfModules.toSheafify_app_apply, CategoryTheory.Equalizer.Sieve.SecondObj.ext_iff, leibnizPullback_map_app, CategoryTheory.Abelian.LeftResolution.karoubi.F_obj_X, CategoryTheory.ProjectiveResolution.instEpiFNatπ, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₂_app, TopCat.Presheaf.isIso_iff_stalkFunctor_map_iso, AlgebraicGeometry.Scheme.Hom.app_appIso_inv, TopCat.limit_topology, Action.resComp_hom_app_hom, AlgebraicGeometry.isIso_fromTildeΓ_iff, CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero_assoc, Monoidal.δ_μ_assoc, groupCohomology.cochainsMap_id_comp_assoc, CategoryTheory.Equivalence.funInvIdAssoc_inv_app, CategoryTheory.MorphismProperty.FunctorialFactorizationData.hp, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_functor_obj_X_X, CategoryTheory.MorphismProperty.LeftFraction.map_comp_map_s_assoc, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_inv_app_f, CategoryTheory.Grothendieck.grothendieckTypeToCat_functor_map_coe, TopCat.Sheaf.interUnionPullbackCone_pt, CategoryTheory.Localization.SmallShiftedHom.equiv_apply, CategoryTheory.Triangulated.TStructure.triangleLTGE_obj_obj₂, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_inv, Profinite.exists_locallyConstant_finite_nonempty, CategoryTheory.Limits.BinaryFan.assoc_fst, CategoryTheory.CommMon.mkIso'_hom_hom_hom, CategoryTheory.sheafSectionsNatIsoEvaluation_hom_app, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_app_assoc, CategoryTheory.Limits.factorThruKernelSubobject_comp_kernelSubobjectIso, HomologicalComplex.homologyOp_hom_naturality, CategoryTheory.Limits.MulticospanIndex.multiforkOfParallelHomsEquivFork_functor_obj_ι, CategoryTheory.Enriched.FunctorCategory.enrichedId_π, CategoryTheory.StructuredArrow.toCostructuredArrow'_map, CategoryTheory.Adjunction.map_η_comp_η, TopCat.Presheaf.stalkSpecializes_stalkPushforward_assoc, DerivedCategory.instIsLEObjCochainComplexIntQOfIsLE, map_isPushout, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberCompIso_hom_app_assoc, OplaxMonoidal.right_unitality, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_assoc, leftKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.ComposableArrows.fourδ₄Toδ₃_app_zero, AlgebraicGeometry.PresheafedSpace.restrictTopIso_inv, CategoryTheory.Limits.colimCompFlipIsoWhiskerColim_inv_app_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_obj_fst, partialLeftAdjointHomEquiv_comp_symm, TopCat.Presheaf.stalkPushforward.comp, CategoryTheory.Limits.parallelPair.eqOfHomEq_inv_app, CategoryTheory.Limits.FormalCoproduct.cosimplicialObjectFunctor_map_app, groupCohomology.map_H0Iso_hom_f_assoc, CategoryTheory.Triangulated.Octahedron.comm₄, CategoryTheory.sum.inlCompAssociator_inv_app, CategoryTheory.ExactFunctor.whiskeringRight_obj_map, AlgebraicGeometry.Scheme.Hom.normalizationObjIso_hom_val, AlgebraicGeometry.Scheme.openCoverBasicOpenTop_f, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_inverse_obj_X_d, CategoryTheory.Limits.IndObjectPresentation.yoneda_I, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.sheafCondition_iff_comp_coyoneda, CategoryTheory.Over.tensorObj_left, OplaxRightLinear.δᵣ_naturality_right, CategoryTheory.IsPushout.map_iff, IsCoverDense.functorPullback_pushforward_covering, HomologicalComplex₂.flipEquivalenceCounitIso_hom_app_f_f, SSet.stdSimplex.objEquiv_symm_apply, commShift₂_comm_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_inv_app_snd_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionHomLeft, CategoryTheory.Limits.CompleteLattice.finiteLimitCone_cone_π_app, CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac, CategoryTheory.FinitaryExtensive.isPullback_initial_to, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinset_obj_obj, SSet.StrictSegal.instIsStrictSegalObjTruncatedHAddNatOfNatTruncationOfIsStrictSegal, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_left_right_as, CategoryTheory.WithInitial.liftToInitialUnique_inv_app, CategoryTheory.instIsReflexivePairMapAppCounitObj, CategoryTheory.Limits.limit.lift_map_assoc, CategoryTheory.WithInitial.mapComp_inv_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_aux_mul, CategoryTheory.Localization.HasSmallLocalizedHom.small, injective_obj, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_hom_c_app, CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_right, mem_inducedTopology_sieves_iff, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv_assoc, CategoryTheory.Localization.instHasSmallLocalizedHomObjShiftFunctor_2, CategoryTheory.Limits.Types.Limit.lift_π_apply', CategoryTheory.Localization.Preadditive.map_add, CochainComplex.HomComplex.Cochain.toSingleEquiv_toSingleMk, CategoryTheory.OverPresheafAux.OverArrows.map_val, AddCommGrpCat.binaryProductLimitCone_cone_π_app_right, CategoryTheory.sum.inverseAssociator_map_inr_inl, AlgebraicGeometry.Scheme.Hom.appLE_eq_app, sheafAdjunctionCocontinuous_homEquiv_apply_val, CochainComplex.isGE_shift, CategoryTheory.Iso.inv_hom_id_app_assoc, limitIsoOfIsRightKanExtension_inv_π, Types.monoOverEquivalenceSet_counitIso, CategoryTheory.PreOneHypercover.forkOfIsColimit_ι_map_inj, CategoryTheory.Equivalence.symmEquivInverse_obj_inverse, SemilatSupCat.coe_forget_to_partOrd, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one_assoc, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, CategoryTheory.StructuredArrow.post_obj, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_hom_app_snd_app, CategoryTheory.PreservesFiniteLimitsOfFlat.fac, AlgebraicGeometry.Scheme.OpenCover.instIsOpenImmersionMapI₀FunctorOfLocallyDirected, PresheafOfModules.pushforward₀_obj_obj_isModule, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app_assoc, CategoryTheory.CostructuredArrow.unop_left_comp_underlyingIso_hom_unop, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_yonedaULift_map, DerivedCategory.HomologySequence.exact₃, AlgebraicTopology.DoldKan.map_hσ', FullyFaithful.hasShift.map_zero_inv_app, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_snd, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_inverse_map_f, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec.image_basicOpen_eq_basicOpen, AlgebraicTopology.DoldKan.N₂_map_f_f, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app_assoc, CochainComplex.truncate_obj_d, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinset_obj_obj, curry_obj_comp_flip, CategoryTheory.Adjunction.leftAdjointIdIso_hom_app, CategoryTheory.InjectiveResolution.rightDerivedToHomotopyCategory_app_eq, CategoryTheory.CategoryOfElements.CreatesLimitsAux.map_π_liftedConeElement, CategoryTheory.Comonad.ForgetCreatesColimits'.liftedCocone_ι_app_f, SSet.Subcomplex.PairingCore.nonDegenerate₁, AlgebraicGeometry.Scheme.Cover.functorOfLocallyDirectedHomBase_app, CategoryTheory.CostructuredArrow.mapIso_inverse_map_right, CategoryTheory.GrothendieckTopology.uliftYoneda_obj_val_obj, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₂, CategoryTheory.MonoidalClosed.leftDistrib_inv, CategoryTheory.Injective.injective_iff_preservesEpimorphisms_preadditiveYoneda_obj, CategoryTheory.uliftYonedaIsoYoneda_inv_app_app_down, CategoryTheory.Monad.forget_obj, AlgebraicGeometry.IsOpenImmersion.app_eq_invApp_app_of_comp_eq_aux, AlgebraicGeometry.isField_of_isIntegral_of_subsingleton, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_fst, CategoryTheory.Subobject.underlyingIso_arrow_apply, HomotopicalAlgebra.CofibrantObject.instWeakEquivalenceHomFullSubcategoryCofibrantObjectsIBifibrantResolutionObj, SSet.KanComplex.hornFilling, CategoryTheory.Localization.lift₂_iso_hom_app_app₁, CategoryTheory.Limits.Cocones.precompose_map_hom, CategoryTheory.uliftYonedaEquiv_symm_map_assoc, CategoryTheory.Sieve.image_mem_functorPushforward, CategoryTheory.Adjunction.instIsIsoMapAppCounitOfFaithfulOfFull, CategoryTheory.Limits.constCone_π, Monoidal.transport_ε_assoc, CategoryTheory.StructuredArrow.toCostructuredArrow'_obj, ModuleCat.restrictScalarsCongr_inv_app, PushoutObjObj.mapArrowLeft_comp, CategoryTheory.Abelian.app_hom, CategoryTheory.MonoidalSingleObj.endMonoidalStarFunctorEquivalence_inverse_obj, CategoryTheory.Adjunction.strongEpi_map_of_isEquivalence, AlgebraicGeometry.exists_of_res_eq_of_qcqs, Monoidal.transport_δ_assoc, AlgebraicGeometry.PresheafedSpace.map_comp_c_app, CategoryTheory.IsSplitEqualizer.map_leftRetraction, CategoryTheory.Iso.map_inv_hom_id_eval_assoc, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_left_as, CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_left_left, SSet.PtSimplex.RelStruct.δ_map_of_gt, curryingEquiv_symm_apply_obj_map, CategoryTheory.Limits.opSpan_inv_app, HomologicalComplex.singleObjCyclesSelfIso_hom, CategoryTheory.LeftExactFunctor.whiskeringLeft_obj_map, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_neg, CategoryTheory.Comma.post_obj_hom, leftExtensionEquivalenceOfIso₁_counitIso_hom_app_right_app, HomObj.id_app, CategoryTheory.SingleFunctors.shiftIso_add'_inv_app, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right_assoc, IsEventuallyConstantTo.isoMap_inv_hom_id_assoc, CategoryTheory.IsPullback.of_isLimit_cone, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_snd', CategoryTheory.Limits.coyonedaCompLimIsoCones_hom_app_app, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoColimitUncurryWhiskeringLeft₂_hom, LaxMonoidal.μ_natural, CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_right, CategoryTheory.Limits.whiskerLeft_ι_colimitCompWhiskeringLeftIsoCompColimit_inv_assoc, CategoryTheory.Limits.colimitCoconeOfUnique_isColimit_desc, CategoryTheory.Pretriangulated.contractible_distinguished₁, CategoryTheory.toOverUnitPullback_hom_app_left, CategoryTheory.Limits.mapPairIso_hom_app, sheafPushforwardContinuousId'_hom_app_val_app, TopCat.subpresheafToTypes_obj, CategoryTheory.Center.ofBraided_obj, TopCat.Presheaf.submonoidPresheafOfStalk_obj, CochainComplex.HomComplex.Cocycle.fromSingleMk_postcomp, CategoryTheory.Monad.left_unit_assoc, Condensed.isoFinYoneda_inv_app, HomologicalComplex.quasiIsoAt_opFunctor_map_iff, CategoryTheory.Limits.pullbackObjIso_inv_comp_snd, CategoryTheory.Limits.FormalCoproduct.evalOp_obj_obj, CategoryTheory.ExponentiableMorphism.coev_ev, CategoryTheory.Preadditive.toCommGrp_obj_X, CategoryTheory.Limits.limit.lift_π, CategoryTheory.Limits.Cofork.IsColimit.π_desc'_assoc, CategoryTheory.subterminalsEquivMonoOverTerminal_functor_obj_obj, HomotopyCategory.quotient_obj_mem_subcategoryAcyclic_iff_exactAt, SSet.nondegenerate_zero, CochainComplex.HomComplex.Cocycle.rightUnshift_coe, CategoryTheory.Limits.IsColimit.fac_assoc, AlgebraicGeometry.SheafedSpace.isColimit_exists_rep, CategoryTheory.LocalizerMorphism.RightResolution.Hom.comm_assoc, CategoryTheory.Limits.colimit.toCostructuredArrow_obj, CategoryTheory.tensoringRight_additive, AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_inv_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso_inv_app_app, CategoryTheory.Subfunctor.equalizer_obj, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι, CategoryTheory.compEvaluation_inv_app, leftAdjointObjIsDefined_iff, FundamentalGroupoidFunctor.proj_map, TopCat.Presheaf.stalkFunctor_map_germ_apply', CategoryTheory.Comonad.adj_unit, CategoryTheory.MorphismProperty.IsCompatibleWithShift.iff, AlgebraicGeometry.StructureSheaf.algebraMap_pushforward_stalk, AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.colimitDesc_preimage, CategoryTheory.Cat.FreeRefl.lift_obj, CategoryTheory.Adjunction.map_ε_comp_counit_app_unit, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_app, CategoryTheory.SmallObject.πObj_naturality, mem_eventualRange_iff, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₂, CategoryTheory.SingleFunctors.hom_inv_id_hom_app, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, PullbackObjObj.π_iso_of_iso_left_hom, DerivedCategory.HomologySequence.epi_homologyMap_mor₂_iff, AlgebraicTopology.DoldKan.P_f_naturality, fintypeToFinBoolAlgOp_obj, CategoryTheory.Limits.map_π_epi, CategoryTheory.SmallObject.SuccStruct.Iteration.prop_map_succ, CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_right, PresheafOfModules.freeAdjunction_homEquiv, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_val_app, SSet.Truncated.HomotopyCategory.descOfTruncation_obj_mk, SSet.S.IsUniquelyCodimOneFace.iff, CategoryTheory.ObjectProperty.ιOfLE_η, leftOpRightOpEquiv_inverse_obj, AlexDisc.forgetToTop_of, mapHomotopyEquiv_hom, Action.FunctorCategoryEquivalence.functor_obj_map, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimIso_aux, CategoryTheory.Limits.wideEqualizer.trident_π_app_zero, AlgebraicTopology.DoldKan.MorphComponents.id_b, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_invApp, CategoryTheory.Grp.mkIso'_inv_hom_hom, CategoryTheory.Limits.BinaryFan.isLimit_iff_isIso_snd, AlgebraicGeometry.isLocalization_basicOpen_of_qcqs, AlgebraicGeometry.Scheme.IdealSheafData.strictMono_ideal, MatrixModCat.toModuleCat_obj_isModule, CategoryTheory.TransfiniteCompositionOfShape.ici_incl, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₃, TopCat.GlueData.MkCore.cocycle, SimplicialObject.Split.cofan_inj_naturality_symm, CategoryTheory.MonoidalOpposite.tensorLeftIso_inv_app_unmop, CategoryTheory.Limits.LimitPresentation.w_assoc, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃, CategoryTheory.uliftFunctor_obj, CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_three, CategoryTheory.cocones_obj_obj, const_obj_map, CategoryTheory.Comon.monoidal_tensorHom_hom, commBialgCatEquivComonCommAlgCat_functor_map_unop_hom, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_hom, CategoryTheory.Pseudofunctor.Grothendieck.forget_obj, CategoryTheory.Limits.colimitYonedaHomIsoLimitRightOp_π_apply, CategoryTheory.CostructuredArrow.map_id, CategoryTheory.obj_η_app, CategoryTheory.Over.ε_pullback_left, RepresentableBy.ofIsoObj_homEquiv, CategoryTheory.Monad.instIsReflexivePairAlgebraTopMapBottomMap, AlgebraicGeometry.LocallyRingedSpace.forgetToSheafedSpace_obj, CategoryTheory.Limits.FormalCoproduct.evalCompInclIsoId_hom_app_app, id_mapMon_one, DeltaGenerated.topToDeltaGenerated_obj_toTop_carrier, TopologicalSpace.OpenNhds.inclusionMapIso_inv_app, CategoryTheory.Sheaf.isConstant_iff_isIso_counit_app, CategoryTheory.ComposableArrows.IsComplex.zero, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_rightUnitor, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_functor, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_map, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.mem_map, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_map_snd_app, CategoryTheory.Over.coprod_map_app, CorepresentableBy.coyoneda_homEquiv, SheafOfModules.forgetToSheafModuleCat_obj_val, ProfiniteGrp.limit_ext_iff, CategoryTheory.yoneda'_map_val, RightLinear.inv_δᵣ, CategoryTheory.Adjunction.homEquiv_leftAdjointUniq_hom_app, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_apply, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_hom_app_hom_hom, AlgebraicTopology.DoldKan.factors_normalizedMooreComplex_PInfty, CategoryTheory.Bicategory.associatorNatIsoMiddle_inv_app, CochainComplex.HomComplex.Cochain.δ_leftShift, ι_leftKanExtensionObjIsoColimit_hom_assoc, SimplexCategory.II_obj, CategoryTheory.ComposableArrows.IsComplex.cokerToKer_fac, LaxRightLinear.μᵣ_unitality_inv, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ, DerivedCategory.isIso_Q_map_iff_quasiIso, CategoryTheory.isoCartesianComon_inv_hom, CategoryTheory.Limits.map_π_preserves_coequalizer_inv, CategoryTheory.ShiftMkCore.zero_add_inv_app, CategoryTheory.Limits.map_lift_equalizerComparison_assoc, Rep.coindFunctor_obj, SSet.associator_inv_app_apply, AlgebraicGeometry.map_injective_of_isIntegral, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.functor_obj, comp_map, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_unitIso_hom_app_f_f, CategoryTheory.Limits.colimit.isoColimitCocone_ι_hom, CategoryTheory.CostructuredArrow.mapIso_inverse_map_left, CategoryTheory.Adjunction.whiskerRight_unit_app_app, UniformSpaceCat.extension_comp_hom, CategoryTheory.Subobject.underlying_arrow, DerivedCategory.isIso_Qh_map_iff, AlgebraicGeometry.exists_eq_pow_mul_of_isCompact_of_isQuasiSeparated, AlgebraicGeometry.AffineSpace.homOfVector_appTop_coord, CategoryTheory.GrothendieckTopology.uliftYoneda_obj_val_map_down, SSet.stdSimplex.nonDegenerateEquiv_symm_apply_coe, AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex_hom, CategoryTheory.Limits.inv_prodComparison_map_snd, CategoryTheory.Quotient.natTransLift_app, ranAdjunction_unit_app, AlgebraicGeometry.sourceAffineLocally_morphismRestrict, CategoryTheory.Limits.Types.FilteredColimit.isColimit_eq_iff', CategoryTheory.prod_preservesConnectedLimits, CategoryTheory.pullbackShiftFunctorAdd'_inv_app, PresheafOfModules.evaluation_obj, CategoryTheory.StructuredArrow.IsUniversal.fac_assoc, CategoryTheory.OverPresheafAux.map_mkPrecomp_eqToHom, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_app_π, CategoryTheory.Limits.end_.condition_assoc, CategoryTheory.Limits.map_inl_inv_coprodComparison_assoc, Profinite.exists_locallyConstant_fin_two, CategoryTheory.Arrow.equivSigma_apply_snd_fst, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_obj_obj_obj, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_limit_map_assoc, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor, shiftIso_hom_naturality, AlgebraicGeometry.Scheme.IsQuasiAffine.isBasis_basicOpen, AlgebraicGeometry.Scheme.pullbackComparison_forget_surjective, AlgebraicGeometry.Proj.stalkIso'_symm_mk, CategoryTheory.WithInitial.ofCommaMorphism_app, SSet.horn.ι_ι, CategoryTheory.Limits.Cocone.fromStructuredArrow_obj_ι, CategoryTheory.Sheaf.ΓRes_naturality, CategoryTheory.Monad.Algebra.unit, coreComp_inv_app_iso_hom, mapSkeleton_surjective, CategoryTheory.CostructuredArrow.map₂_obj_hom, CategoryTheory.Bimon.toMon_Comon_ofMon_Comon_obj_mul, CategoryTheory.GrothendieckTopology.pullback_obj, SimplicialObject.Splitting.cofan_inj_comp_app_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_eq, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTrans_map_f, CategoryTheory.AdditiveFunctor.ofLeftExact_map_hom, GrpCat.μ_forget_apply, ModuleCat.HasLimit.productLimitCone_isLimit_lift, CategoryTheory.Grothendieck.isoMk_hom_fiber, SheafOfModules.pushforwardNatIso_hom, AlgebraicGeometry.structureSheafInType.smul_apply, isZero_rightDerived_obj_injective_succ, Monoidal.ε_η_assoc, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app_assoc, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_obj₁, CategoryTheory.TwistShiftData.shiftFunctor_map, CategoryTheory.Comonad.beckCoalgebraFork_π_app, CategoryTheory.Grothendieck.grothendieckTypeToCat_functor_obj_snd, CochainComplex.HomComplex.Cocycle.toSingleMk_precomp, CategoryTheory.MonoidalOpposite.tensorIso_inv_app_unmop, CategoryTheory.ObjectProperty.ιOfLE_μ, HomologicalComplex.extendSingleIso_hom_f, AlgebraicGeometry.Etale.instMorphismRestrict, TopCat.Presheaf.stalkPushforward.stalkPushforward_iso_of_isInducing, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_app_assoc, map_distinguished, CochainComplex.HomComplex.CohomologyClass.toHom_mk, RingCat.forget_obj, CategoryTheory.TwistShiftData.shiftFunctorZero_inv_app, AlgebraicTopology.DoldKan.N₁Γ₀_app, AlgebraicGeometry.Scheme.isoSpec_image_zeroLocus, CategoryTheory.bifunctorComp₂₃Obj_map_app, CategoryTheory.Equivalence.core_unitIso_inv_app_iso_inv, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp_hom_app_f, CategoryTheory.Limits.colimitLimitToLimitColimit_injective, CategoryTheory.Adjunction.homEquiv_naturality_right, CategoryTheory.Equalizer.Presieve.isSheafFor_singleton_iff_of_hasPullback, lanAdjunction_counit_app, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst_assoc, CategoryTheory.GradedObject.single_map_singleObjApplyIso_hom_assoc, CategoryTheory.Adjunction.unit_comp_map_eq_iff, CategoryTheory.CosimplicialObject.Augmented.const_obj_left, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_map, Monoidal.map_rightUnitor_inv_assoc, IsRepresentedBy.iff_exists_representableBy, AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_eq_id, CategoryTheory.ShortComplex.LeftHomologyData.map_H, CategoryTheory.Pseudofunctor.DescentData.pullFunctor_obj, CategoryTheory.Subfunctor.sieveOfSection_apply, CategoryTheory.ShortComplex.RightHomologyMapData.map_φQ, PushoutObjObj.ι_iso_of_iso_left_hom, RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π_assoc, CategoryTheory.coreFunctor_obj_map_iso_hom, CategoryTheory.ObjectProperty.prop_inverseImage_iff, Rep.linearization_map_hom_single, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_obj_map_app, CategoryTheory.FunctorToTypes.binaryCoproductCocone_pt_obj, CategoryTheory.CosimplicialObject.cechConerveEquiv_apply, OplaxMonoidal.δ_natural_right_assoc, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_map, CategoryTheory.hoFunctor.isIso_prodComparison, rightOp_map_unop, isIso_lanAdjunction_counit_app_iff, LaxMonoidal.ofBifunctor.secondMap₃_app_app_app, AlgebraicGeometry.Scheme.IdealSheafData.ideal_map_of_isAffineHom, CategoryTheory.CostructuredArrow.map₂_obj_left, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_val_app, AlgebraicGeometry.isCompact_and_isOpen_iff_finite_and_eq_biUnion_basicOpen, CategoryTheory.Adjunction.isIso_counit_app_iff_mem_essImage, CategoryTheory.shiftFunctorCompIsoId_zero_zero_inv_app, CategoryTheory.Limits.instHasLimitProdObjFunctorUncurryWhiskeringLeft₂OfPreservesLimit₂, CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_inv_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_inv_app'_assoc, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_inv, LightProfinite.proj_comp_transitionMap', CochainComplex.HomComplex.Cocycle.leftShiftAddEquiv_apply, HomotopyCategory.quotient_map_mem_quasiIso_iff, CategoryTheory.monoidalUnopUnop_η, CategoryTheory.preadditiveCoyoneda_obj, CategoryTheory.CostructuredArrow.commaToGrothendieckPrecompFunctor_obj_base, CategoryTheory.WithTerminal.equivComma_unitIso_hom_app_app, CategoryTheory.Limits.map_lift_equalizerComparison, CategoryTheory.cosimplicialSimplicialEquiv_functor_obj_map, CategoryTheory.prod.prodFunctorToFunctorProdAssociator_hom_app_app, CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse_assoc, CategoryTheory.GlueData.ι_gluedIso_hom_assoc, DeltaGenerated.deltaGeneratedToTop_obj, CategoryTheory.DinatTrans.dinaturality, AlgebraicGeometry.IsAffineOpen.toSpecΓ_isoSpec_inv_assoc, CategoryTheory.TwoSquare.costructuredArrowRightwards_obj, AlgebraicGeometry.PresheafedSpace.restrict_top_presheaf, CochainComplex.toSingle₀Equiv_symm_apply_f_zero, TopCat.piFan_π_app, DerivedCategory.left_fac_of_isStrictlyGE, LaxMonoidal.left_unitality_inv, CochainComplex.mappingConeHomOfDegreewiseSplitIso_hom_f, coreComp_inv_app_iso_inv, CategoryTheory.Adjunction.shift_unit_app_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionHom, mapCoconeMapCocone_inv_hom, CochainComplex.augmentTruncate_hom_f_zero, CategoryTheory.SmallObject.instIsIsoRightAppArrowιIteration, CategoryTheory.oppositeShiftFunctorAdd_hom_app, Rep.ihom_obj_ρ_def, TopCat.coconeOfCoconeForget_ι_app, CategoryTheory.ComposableArrows.homMk₀_app, AlgebraicGeometry.Scheme.Modules.pushforward_map_app, CategoryTheory.Equivalence.counitInv_naturality_assoc, CategoryTheory.Comma.toIdPUnitEquiv_inverse_obj_right, Rep.ihom_obj_V_carrier, CategoryTheory.Comma.colimitAuxiliaryCocone_ι_app, CategoryTheory.Prod.fst_obj, CategoryTheory.Limits.Fan.mk_π_app, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map_assoc, ContinuousCohomology.const_app_hom, ModuleCat.semilinearMapAddEquiv_apply, CategoryTheory.FunctorToTypes.prod.snd_app, CategoryTheory.Square.toArrowArrowFunctor'_obj_right_left, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂, CategoryTheory.curryingIso_hom_toFunctor_map_app, ModuleCat.CoextendScalars.map'_hom_apply_apply, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_fst, CategoryTheory.Center.forget_μ, ContAction.resComp_inv, CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatTrans_comp, mapZeroObject_hom, leftOpRightOpIso_inv_app, mapTriangleIdIso_hom_app_hom₁, Rep.coindIso_hom_hom_hom, HomotopicalAlgebra.CofibrantObject.HoCat.adjCounit'_app, CategoryTheory.Meq.condition, AlgebraicGeometry.Scheme.AffineZariskiSite.presieveOfSections_eq_ofArrows, CategoryTheory.Sheaf.sheafifyCocone_ι_app_val, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatTrans_app, CategoryTheory.Localization.Monoidal.rightUnitor_hom_app, CategoryTheory.MorphismProperty.Over.mapId_hom_app_left, CategoryTheory.Bimon.toMonComonObj_X, CategoryTheory.Idempotents.DoldKan.N_map, ModuleCat.RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply, ι_colimitIsoColimitGrothendieck_inv, ChainComplex.single₀_obj_zero, CategoryTheory.Endofunctor.Algebra.Initial.left_inv', AlgebraicGeometry.Spec.toTop_obj_carrier, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_map_of_preserves, ModuleCat.freeHomEquiv_symm_apply, CategoryTheory.SimplicialObject.δ_comp_σ_succ_assoc, AlgebraicGeometry.Scheme.Hom.inv_app, SSet.RelativeMorphism.map_coe, coreflective, CategoryTheory.Comma.mapRightIso_inverse_obj_left, CategoryTheory.StructuredArrow.instFullObjCompPostOfFaithful, homologySequenceδ_comp, CategoryTheory.Under.postAdjunctionLeft_unit_app, CategoryTheory.StructuredArrow.IsUniversal.fac, CategoryTheory.Limits.evaluation_preservesLimitsOfShape, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app', CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_hom_app_hom_app, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_app, CategoryTheory.preadditiveCoyonedaObj_obj_isAddCommGroup, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₂₄, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_inv_app, mapTriangleIdIso_hom_app_hom₂, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop, CategoryTheory.SingleFunctors.postcompIsoOfIso_inv_hom_app, AlgebraicGeometry.Scheme.restrictFunctor_obj_hom, ShiftSequence.induced_shiftMap_assoc, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom, CategoryTheory.Limits.map_ι_comp_inv_sigmaComparison, relativelyRepresentable.toPullbackTerminal, ιColimitType_eq_iff, CategoryTheory.LocalizerMorphism.isIso_iff_of_hasLeftResolutions, pushforwardContinuousSheafificationCompatibility_hom_app_val, AlgebraicGeometry.Scheme.Hom.isQuasiSeparated_preimage, CategoryTheory.InjectiveResolution.quasiIso, AlgebraicGeometry.RingedSpace.mem_basicOpen, CategoryTheory.Limits.diagramIsoParallelPair_inv_app, CategoryTheory.MonoidalCategory.DayConvolution.whiskerRight_comp_unit_app, ChainComplex.fromSingle₀Equiv_symm_apply_f_succ, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_obj, CategoryTheory.StructuredArrow.ofDiagEquivalence.functor_obj_left_as, CategoryTheory.Adjunction.commShiftIso_hom_app_counit_app_shift, AlgebraicGeometry.Scheme.Hom.app_injective, CategoryTheory.MorphismProperty.Over.pullbackComp_left_fst_fst, mapPresheaf_obj_presheaf, Profinite.Extend.functor_map, CategoryTheory.LaxFunctor.mapComp_assoc_right_app_assoc, CategoryTheory.GlueData.mapGlueData_t', CategoryTheory.OverPresheafAux.counitAuxAux_hom, ContAction.res_map, CategoryTheory.Limits.inv_prodComparison_map_fst_assoc, CategoryTheory.Discrete.natIsoFunctor_inv_app, CategoryTheory.NatTrans.removeOp_app, CategoryTheory.Bicategory.associatorNatIsoRight_inv_app, groupHomology.H0π_comp_H0Iso_hom_apply, SSet.Subcomplex.N.notMem, CategoryTheory.Comma.ext_iff, CategoryTheory.Limits.lim_μ_π, CategoryTheory.Limits.colimitCoyonedaHomIsoLimitLeftOp_π_apply, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_obj_hom, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.convolutionUnitApp_eq, CategoryTheory.Subobject.representative_arrow, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app, CategoryTheory.ExponentiableMorphism.homEquiv_apply_eq, ModuleCat.freeDesc_apply, CategoryTheory.StructuredArrow.toUnder_obj_right, TopCat.Presheaf.mono_iff_stalk_mono, CategoryTheory.Limits.kernelSubobjectMap_arrow, CategoryTheory.Center.ofBraided_η_f, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_inv_π_assoc, AlgebraicGeometry.Scheme.Modules.inv_app, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂'_obj_map_app, CategoryTheory.Over.associator_hom_left_snd_snd, AlgebraicGeometry.IsOpenImmersion.hasLimit_cospan_forget_of_left', CategoryTheory.instIsIsoSSetProdComparisonCatCompNerveFunctorHoFunctorOf, SSet.PtSimplex.MulStruct.δ_succ_castSucc_map_assoc, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom_assoc, CategoryTheory.Grothendieck.grothendieckTypeToCatInverse_obj_fiber_as, CategoryTheory.Over.associator_inv_left_snd_assoc, CategoryTheory.Limits.MultispanIndex.parallelPairDiagramOfIsColimit_obj, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₁_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_map, inr_biprodComparison'_assoc, Elements.initialOfRepresentableBy_fst, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π_assoc, mem_mapTriangle_essImage_of_distinguished, CategoryTheory.PreGaloisCategory.endMulEquivAutGalois_pi, CategoryTheory.Bimon.toMon_Comon_ofMon_Comon_obj_one, Condensed.locallyConstantIsoFinYoneda_hom_app, CategoryTheory.Localization.homEquiv_isoOfHom_inv, CategoryTheory.Over.coprodObj_map, map_braiding, AlgebraicTopology.DoldKan.hσ'_naturality, CategoryTheory.Localization.homEquiv_id, CategoryTheory.NatTrans.app_sub, CategoryTheory.MorphismProperty.arrow_iso_iff, AlgebraicGeometry.Scheme.Opens.toSpecΓ_preimage_zeroLocus, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_two_assoc, leibnizPullback_obj_obj, AlgebraicTopology.DoldKan.P_add_Q_f, CategoryTheory.Limits.sigmaComparison_map_desc, CategoryTheory.NatTrans.naturality_assoc, CategoryTheory.Limits.isIso_limit_cone_parallelPair_of_self, CategoryTheory.ShiftedHom.smul_comp, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_left_right, PresheafOfModules.evaluation_map, CategoryTheory.linearCoyoneda_obj_obj_isModule, CategoryTheory.GlueData.diagramIso_hom_app_right, ModuleCat.homEquiv_extendScalarsId, SSet.horn.const_val_apply, 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.NatTrans.app_neg, CategoryTheory.toOverUnitPullback_inv_app_left, CategoryTheory.NatIso.cancel_natIso_hom_left, CategoryTheory.Comma.mapRightIso_inverse_map_left, sheafPushforwardContinuousComp'_hom_app_val_app, ModuleCat.ExtendScalars.hom_ext_iff, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app_assoc, mapBinaryBicone_inr, RightLinear.μᵣ_comp_δᵣ_assoc, OplaxMonoidal.ofBifunctor.firstMap_app_app_app, OneHypercoverDenseData.isSheaf_iff.lift_map, HomRel.IsCompatibleWithShift.condition, CategoryTheory.RightExactFunctor.forget_obj, AlgebraicTopology.DoldKan.hσ'_eq', CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv, CategoryTheory.Limits.Cofork.app_one_eq_π, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_inv_app_val_app, CategoryTheory.Limits.constCocone_ι, CategoryTheory.Equivalence.counit_app_functor, CategoryTheory.MonoidalClosed.id_comp, CochainComplex.HomComplex.Cochain.leftShift_neg, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_apply, CategoryTheory.Join.fromSum_map_inl, OrderIso.equivalence_unitIso, LaxMonoidal.left_unitality_inv_assoc, CategoryTheory.GrothendieckTopology.Plus.toPlus_apply, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.Limits.limitUnopIsoUnopColimit_inv_comp_π, CategoryTheory.Limits.instHasKernelMapOfPreservesLimitWalkingParallelPairParallelPairOfNatHom, CategoryTheory.Subfunctor.Subpresheaf.ofSection_eq_range, ProfiniteAddGrp.instCompactSpaceSubtypeForallCarrierToTopTotallyDisconnectedSpaceToProfiniteObjMemAddSubgroupLimitConePtAux, CategoryTheory.Presheaf.isLocallyInjective_iff_injective_of_separated, CategoryTheory.piEquivalenceFunctorDiscrete_counitIso, CategoryTheory.isZero_Tor_succ_of_projective, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst, CategoryTheory.SingleFunctors.shiftIso_add'_hom_app, CategoryTheory.Under.w_assoc, whiskeringLeft₃_obj_obj_obj_obj_map_app_app, CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_hom, CategoryTheory.Limits.image.factor_map, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc, CategoryTheory.Limits.instHasColimitProdObjFunctorUncurryWhiskeringLeft₂OfPreservesColimit₂, CommRingCat.preservesFilteredColimits_coyoneda, CategoryTheory.Comma.mapLeftId_inv_app_right, CategoryTheory.StructuredArrow.w_assoc, AlgebraicGeometry.coprodMk_inr, CategoryTheory.Equivalence.sheafCongr.counitIso_inv_app_val_app, mapMatComp_inv_app, HomologicalComplex.singleObjHomologySelfIso_inv_homologyι, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_bijective, groupHomology.coinvariantsMk_comp_H0Iso_inv_assoc, HomologicalComplex.homologyFunctor_obj, SSet.Truncated.IsStrictSegal.segal, CommGrpCat.forget₂_map, ModuleCat.toKernelSubobject_arrow, AlgebraicTopology.DoldKan.HigherFacesVanish.induction, CategoryTheory.Sieve.functorPushforward_equivalence_eq_pullback, CategoryTheory.Limits.opHomCompWhiskeringLimYonedaIsoCocones_inv_app_app, AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInfty, PresheafOfModules.freeObjDesc_app, CategoryTheory.StructuredArrow.mapNatIso_functor_map_left, CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp_assoc, AlgebraicGeometry.LocallyRingedSpace.comp_c_app, CategoryTheory.sheafSectionsNatIsoEvaluation_inv_app, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_isAddCommGroup, instIsAccessibleObjConst, CategoryTheory.Precoverage.mem_comap_iff, CategoryTheory.nerveMap_app_mk₀, CategoryTheory.Limits.imageSubobject_arrow', CategoryTheory.OverPresheafAux.YonedaCollection.map₂_fst, CategoryTheory.Tor_map, CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal_μ_unmop_unmop, HomotopyCategory.isoOfHomotopyEquiv_inv, CategoryTheory.Limits.Types.colimitEquivColimitType_symm_apply, CategoryTheory.Subobject.factorThru_zero, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd_assoc, CategoryTheory.FunctorToTypes.prod_ext'_iff, TopCat.Presheaf.presheafEquivOfIso_functor_obj_map, CategoryTheory.inducedFunctor_obj, CategoryTheory.Limits.Sigma.cocone_pt, CategoryTheory.NatTrans.unop_app, CategoryTheory.SmallObject.SuccStruct.Iteration.mapObj_trans, CategoryTheory.Square.toArrowArrowFunctor'_obj_right_hom, mapDerivedCategoryFactorsh_hom_app, CategoryTheory.OplaxFunctor.mapComp_naturality_right_app, SSet.horn₂₁.sq, CategoryTheory.Limits.colimit.ι_inv_pre_assoc, Rep.linearization_ε_hom, CochainComplex.HomComplex.Cochain.toSingleMk_sub, CategoryTheory.Adjunction.Localization.η_app, AlgebraicTopology.isZero_singularHomologyFunctor_of_totallyDisconnectedSpace, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_basicOpen_eq, CategoryTheory.Limits.CategoricalPullback.mkNatIso_eq, SemiNormedGrp.completion_obj_carrier, CategoryTheory.StructuredArrow.map₂_obj_hom, CategoryTheory.sum.inlCompInverseAssociator_hom_app_down_down, CategoryTheory.Limits.Bicone.toBinaryBiconeFunctor_obj_fst, AlgebraicGeometry.StructureSheaf.algebraMap_germ_apply, sheafAdjunctionCocontinuous_unit_app_val, CategoryTheory.Limits.HasBiproductsOfShape.colimIsoLim_inv_app, CategoryTheory.StructuredArrow.mapNatIso_counitIso_inv_app_right, CategoryTheory.MonoidalOpposite.mopMopEquivalenceInverseMonoidal_η_unmop_unmop, CategoryTheory.Under.isRightAdjoint_post, map_opShiftFunctorEquivalence_unitIso_hom_app_unop, CategoryTheory.Sieve.toUliftFunctor_app_down_coe, homObjFunctor_obj, CategoryTheory.NatIso.cancel_natIso_inv_left, op_obj, AlgebraicGeometry.Scheme.stalkMap_germ, Condensed.instAB4CondensedMod, CategoryTheory.WithInitial.coconeEquiv_unitIso_inv_app_hom_right, CategoryTheory.ShiftedHom.mk₀_smul, OneHypercoverDenseData.isSheaf_iff.lift_map_assoc, CategoryTheory.Preadditive.commGrpEquivalence_inverse_obj, CategoryTheory.Tor'_map_app, groupHomology.chainsMap_f_1_comp_chainsIso₁_apply, Monoidal.whiskerLeft_η_ε_assoc, CategoryTheory.Presieve.isSheafFor_ofArrows_iff_bijective_toCompabible, CategoryTheory.ProjectiveResolution.fromLeftDerivedZero_eq, SheafOfModules.pushforward_obj_val, CategoryTheory.InjectiveResolution.Hom.ι_comp_hom, AlgebraicGeometry.Scheme.AffineZariskiSite.mem_grothendieckTopology_iff_sectionsOfPresieve, CategoryTheory.CosimplicialObject.Augmented.point_obj, CategoryTheory.oppositeShiftFunctorAdd'_inv_app, CategoryTheory.Pseudofunctor.Grothendieck.map_obj_base, CategoryTheory.Equivalence.symmEquivInverse_obj_unitIso_hom, CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit, whiskeringRight_map_app_app, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_ι, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_inv_assoc, CategoryTheory.LocalizerMorphism.smallShiftedHomMap_mk₀, CategoryTheory.Bimon.equivMonComonCounitIsoApp_inv_hom_hom, CategoryTheory.Under.opEquivOpOver_inverse_map, CategoryTheory.Limits.Cones.whiskering_obj, lanUnit_app_app_lanAdjunction_counit_app_app_assoc, Rep.Tor_obj, CategoryTheory.IsHomLift.instIsHomLiftIdObj, GrpCat.uliftFunctor_obj, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_right, SimplicialObject.Splitting.cofan_inj_eq_assoc, imageToKernel_comp_mono, PresheafOfModules.Sheafify.mul_smul, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_appTop, CategoryTheory.Cat.FreeRefl.quotientFunctor_map_cons, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_germ_assoc, leftExtensionEquivalenceOfIso₁_functor_map_right, CategoryTheory.Subobject.isoOfEqMk_hom, CategoryTheory.GrothendieckTopology.Point.sheafFiberCompIso_inv_app, Action.resCongr_hom, CategoryTheory.GrothendieckTopology.uliftYoneda_map_val_app_down, CategoryTheory.Limits.Cocone.underPost_pt, CategoryTheory.ε_app, CategoryTheory.Limits.FormalCoproduct.evalOpCompInlIsoId_inv_app_app, CategoryTheory.Abelian.DoldKan.comparisonN_inv_app_f, whiskeringLeft₂_obj_obj_map_app_app, HomologicalComplex.homologyFunctorSingleIso_hom_app, LeftLinear.δₗ_comp_μₗ_assoc, CochainComplex.HomComplex.Cocycle.equivHomShift_apply, CategoryTheory.Limits.Cofork.op_ι, CategoryTheory.right_unitality_app, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal_basicOpen, CategoryTheory.Abelian.FunctorCategory.imageObjIso_inv, CommGrpCat.coyonedaType_obj_obj_coe, CategoryTheory.CommMon.forget₂Mon_map_hom, AlgebraicGeometry.Scheme.AffineZariskiSite.toOpensFunctor_obj, CategoryTheory.Adjunction.homEquiv_id, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_inv_app_fst_app, instIsIsoAppRanCounit_1, CategoryTheory.Limits.Cones.postcomposeComp_hom_app_hom, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_hom_app, CommRingCat.coproductCocone_ι, SSet.Truncated.HomotopyCategory.homToNerveMk_comp_assoc, CategoryTheory.PreGaloisCategory.instIsPretransitiveAutCarrierVFintypeCatFunctorObjActionFunctorToActionOfIsGalois, TopCat.Presheaf.presheafEquivOfIso_inverse_map_app, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓFreeOpensCarrierCarrierCommRingCat, CategoryTheory.Equivalence.adjointify_η_ε, AlgebraicGeometry.RingedSpace.zeroLocus_singleton, TopCat.Presheaf.stalkFunctor_map_germ_assoc, CategoryTheory.Limits.Cocone.extensions_app, CategoryTheory.Localization.LeftBousfield.isLocalization, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_map_app, CategoryTheory.Limits.IndObjectPresentation.yoneda_F, CategoryTheory.MonoidalCategory.externalProductFlip_inv_app_app_app_app, CategoryTheory.LaxFunctor.mapComp_assoc_left_app_assoc, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₁, CategoryTheory.Retract.map_i, CommRingCat.preservesColimit_coyoneda_of_finitePresentation, CategoryTheory.Adjunction.homEquiv_naturality_left, HomologicalComplex.singleObjOpcyclesSelfIso_hom_assoc, CategoryTheory.Comon.monoidal_tensorObj_comon_counit, CategoryTheory.Under.forgetCone_π_app, CategoryTheory.Equivalence.inverse_counitInv_comp, CategoryTheory.MorphismProperty.LeftFraction.Localization.Q_map_comp_Qinv, PullbackObjObj.ofHasPullback_fst, OplaxMonoidal.left_unitality_hom_assoc, IsRepresentedBy.representableBy_homEquiv_apply, CategoryTheory.WithTerminal.liftToTerminalUnique_hom_app, CategoryTheory.Limits.diagramIsoSpan_hom_app, CoconeTypes.IsColimit.fac, CategoryTheory.Limits.limit.w_apply, TopologicalSpace.OpenNhds.inclusionMapIso_hom_app, Monoidal.whiskerLeft_app_snd_assoc, CategoryTheory.flipCompEvaluation_inv_app, ChainComplex.single₀_map_f_zero, CategoryTheory.Over.iteratedSliceForward_obj, FullyFaithful.hasShift.map_zero_hom_app, map_one, ChainComplex.alternatingConst_obj, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality'_assoc, CategoryTheory.Limits.kernelSubobject_arrow', Fiber.fiberInclusionCompIsoConst_hom_app, CochainComplex.HomComplex.Cochain.leftUnshift_neg, CategoryTheory.Cat.leftUnitor_inv_app, CategoryTheory.η_ε_app, leftKanExtensionIsoFiberwiseColimit_inv_app, CategoryTheory.GradedObject.mapTrifunctorMapNatTrans_app_app_app, toPseudoFunctor_obj, CategoryTheory.shiftFunctorAdd_assoc_inv_app, CategoryTheory.Limits.PreservesBiproduct.preserves, CategoryTheory.Over.postEquiv_functor, SSet.horn.primitiveTriangle_coe, CategoryTheory.Comon.forget_obj, HomologicalComplex.singleObjHomologySelfIso_hom_singleObjHomologySelfIso_inv, CategoryTheory.ShortComplex.quasiIso_map_of_preservesRightHomology, CategoryTheory.LaxFunctor.map₂_leftUnitor_app, CategoryTheory.Limits.Cones.postcompose_map_hom, CategoryTheory.Adjunction.left_triangle_components, CompHausLike.LocallyConstant.functorToPresheaves_obj_map, CategoryTheory.Subfunctor.lift_app_coe, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj, AlgebraicGeometry.PresheafedSpace.colimitCocone_ι_app_c, CategoryTheory.sheafCompose_obj_val, CochainComplex.isLE_shift, CategoryTheory.Equivalence.core_counitIso_inv_app_iso_inv, FundamentalGroupoidFunctor.coneDiscreteComp_obj_mapCone, CategoryTheory.PreGaloisCategory.evaluation_aut_injective_of_isConnected, CategoryTheory.ComposableArrows.fourδ₃Toδ₂_app_zero, groupHomology.mapCycles₁_quotientGroupMk'_epi, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_right_hom, CategoryTheory.Equivalence.unit_app_tensor_comp_inverse_map_δ_functor, PresheafOfModules.zero_app, CategoryTheory.Join.mapPairRight_inv_app, RightExtension.postcompose₂ObjMkIso_hom_left_app, sum_obj_inr, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂_assoc, CategoryTheory.Limits.IsLimit.isIso_π_app_of_isInitial, CategoryTheory.Limits.Cotrident.IsColimit.homIso_apply_coe, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₁, CategoryTheory.ActionCategory.stabilizerIsoEnd_symm_apply, CategoryTheory.Over.coreHomEquivToOverSections_homEquiv, CategoryTheory.PreOneHypercover.map_p₂, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_inv_app_f, AlgebraicGeometry.Scheme.Hom.fromNormalization_app, mapTriangleOpCompTriangleOpEquivalenceFunctorApp_hom_hom₂, groupHomology.H0π_comp_map_apply, equiv_counitIso, CategoryTheory.WithTerminal.equivComma_unitIso_inv_app_app, 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.monoidalOfHasFiniteProducts.instIsIsoη, CategoryTheory.ShrinkHoms.inverse_obj, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma_obj_hom, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'_assoc, CategoryTheory.Idempotents.functorExtension₁_obj, CategoryTheory.NatTrans.CommShiftCore.app_shift_assoc, AlgebraicGeometry.Scheme.presheaf_map_eqToHom_op, SemimoduleCat.forget₂_obj, CategoryTheory.ObjectProperty.ιOfLE_δ, PresheafOfModules.map_comp_assoc, CategoryTheory.CostructuredArrow.preEquivalence.functor_obj_left, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app, Monoidal.μ_δ, CategoryTheory.Limits.Cocones.functorialityEquivalence_unitIso, homologySequence_mono_shift_map_mor₂_iff, CategoryTheory.Equalizer.Presieve.Arrows.w, Bicategory.Opposite.bicategory_rightUnitor_hom_unop2, CategoryTheory.Comma.mapLeftComp_hom_app_right, ModuleCat.restrictScalarsId'App_inv_apply, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_μ_assoc, CategoryTheory.Endofunctor.Adjunction.Coalgebra.toAlgebraOf_map_f, CategoryTheory.Quiv.forget_obj, AlgebraicGeometry.Scheme.Hom.eqToHom_app, obj.Δ_def, HomologicalComplex.singleObjOpcyclesSelfIso_hom_naturality, CategoryTheory.Limits.ι_colimitOfIsReflexivePairIsoCoequalizer_hom_assoc, prod_δ_fst, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedAction_obj_obj, whiskeringRight₂_obj_map_app_app, CategoryTheory.shiftFunctorAdd'_assoc_hom_app, CategoryTheory.CostructuredArrow.toStructuredArrow_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.iso_hom_naturality, biproductComparison'_comp_biproductComparison_assoc, CategoryTheory.Over.whiskerLeft_left_snd, groupCohomology.mapShortComplexH1_τ₁, CategoryTheory.yonedaMon_obj, CategoryTheory.NatTrans.retractArrowApp_i, TopCat.presheafToTypes_obj, unopComp_hom_app, TopCat.Presheaf.stalkSpecializes_stalkPushforward_apply, CategoryTheory.Core.functorToCore_obj_of, OplaxMonoidal.right_unitality_hom_assoc, leibnizPushout_map_app, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor_obj_hom, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberCompIso_hom_app, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₁, CategoryTheory.μ_naturalityₗ_assoc, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_inv_π_π_assoc, AlgebraicTopology.DoldKan.Compatibility.υ_inv_app, compFlipUncurryIso_hom_app, CategoryTheory.Grothendieck.transportIso_hom_fiber, CategoryTheory.Localization.LeftBousfield.W_iff_isIso_map, TopCat.Presheaf.isSheaf_iff_isTerminal_of_indiscrete, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_right_obj, CategoryTheory.Over.w_assoc, CategoryTheory.Endofunctor.Algebra.forget_obj, CategoryTheory.Comma.mapRight_map_right, CochainComplex.mappingCone.mapHomologicalComplexXIso'_inv, CategoryTheory.Discrete.natIso_inv_app, IsCoverDense.Types.pushforwardFamily_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_yoneda_map, CategoryTheory.SingleFunctors.postcomp_shiftIso_hom_app, CategoryTheory.Limits.CoconeMorphism.map_w, HomologicalComplexUpToQuasiIso.isIso_Q_map_iff_mem_quasiIso, CategoryTheory.Pseudofunctor.CoGrothendieck.compIso_hom_app, AlgebraicGeometry.Scheme.id_app, CategoryTheory.whiskeringLeftCompEvaluation_hom_app, CategoryTheory.Square.toArrowArrowFunctor'_obj_left_right, CategoryTheory.Pseudofunctor.DescentData.hom_comp, CategoryTheory.unit_obj_eq_map_unit, HomotopicalAlgebra.CofibrantObject.instCofibrationHomFullSubcategoryCofibrantObjectsIBifibrantResolutionObj, CategoryTheory.Pretriangulated.Triangle.functorMk_obj, leftExtensionEquivalenceOfIso₁_unitIso_inv_app_right_app, CategoryTheory.StructuredArrow.homMk'_mk_id, CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.map_app_f, whiskeringRightObjCompIso_inv_app_app, PreservesZeroMorphisms.map_zero, CategoryTheory.Limits.instEpiFactorThruImageSubobjectOfHasEqualizers, CategoryTheory.CostructuredArrow.IsUniversal.fac_assoc, CategoryTheory.CategoryOfElements.CreatesLimitsAux.liftedCone_pt_fst, CategoryTheory.CommComon.forget₂Comon_obj_X, CategoryTheory.Equivalence.unit_inverse_comp_assoc, CategoryTheory.Pseudofunctor.IsPrestackFor.nonempty_fullyFaithful, CategoryTheory.Join.mkFunctorRight_hom_app, Rep.FiniteCyclicGroup.resolution.π_f, CategoryTheory.Comma.mapFst_inv_app, CategoryTheory.Limits.Cones.postcomposeId_inv_app_hom, CoalgCat.toComon_obj, CategoryTheory.Pretriangulated.invRotate_obj, CategoryTheory.FunctorToTypes.binaryProductIso_hom_comp_fst, HomologicalComplex.natIsoSc'_inv_app_τ₁, CategoryTheory.PreOneHypercover.map_I₁, AlgebraicGeometry.flat_iff, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.comp_fst_app, CategoryTheory.LocalizerMorphism.isIso_α_iff_of_isRightDerivabilityStructure, CategoryTheory.SimplicialObject.equivalenceLeftToRight_left_app, CategoryTheory.Limits.Fork.unop_π, inl_biprodComparison'_assoc, CategoryTheory.Over.liftCocone_pt, CategoryTheory.MonoidalCategory.DayConvolutionUnit.corepresentableByRight_homEquiv, eventualRange_eq_iff, comp_homologySequenceδ_assoc, TopCat.Presheaf.SheafConditionEqualizerProducts.res_π_apply, CategoryTheory.Subfunctor.equivalenceMonoOver_counitIso, CategoryTheory.Limits.cospan_one, AlgebraicGeometry.Scheme.zeroLocus_map_of_eq, CategoryTheory.Square.toArrowArrowFunctor_obj_left_hom, CategoryTheory.PreGaloisCategory.instContinuousSMulAutFintypeCatObjCarrier, CategoryTheory.toOver_map, PresheafOfModules.forgetToPresheafModuleCat_map, AlgebraicGeometry.IsAffineOpen.toSpecΓ_fromSpec, CategoryTheory.WithTerminal.coneEquiv_counitIso_hom_app_hom, CategoryTheory.ObjectProperty.ihom_map_hom, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv, groupCohomology.cochainsFunctor_obj, AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.isOpenImmersion, CategoryTheory.Core.functorToCore_map_iso_inv, OplaxLeftLinear.δₗ_associativity_inv_assoc, CategoryTheory.Grothendieck.pre_map_base, Condensed.lanPresheafIso_hom, CategoryTheory.InjectiveResolution.rightDerived_app_eq, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_app_app_germToPullbackStalk, SSet.degenerate_iff_of_isIso, HomologicalComplex.instHasHomologyObjOppositeSymmUnopFunctorOp, Condensed.discrete_obj, CategoryTheory.coprodMonad_obj, CategoryTheory.Limits.diagonal_pullback_fst, CategoryTheory.Cat.whiskerLeft_app, ModuleCat.restrictScalarsComp'App_inv_apply, CategoryTheory.InjectiveResolution.Hom.ι'_comp_hom', AlgebraicGeometry.IsAffineOpen.fromSpec_primeIdealOf, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_comp, CategoryTheory.CostructuredArrow.isEquivalence_post, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_inv_app, CategoryTheory.Over.isLeftAdjoint_post, CategoryTheory.Pseudofunctor.ObjectProperty.map₂_app_hom, CategoryTheory.Limits.IndObjectPresentation.yoneda_ℐ, CategoryTheory.PreservesImage.inv_comp_image_ι_map_assoc, CategoryTheory.whiskeringRight_comp_evaluation, CategoryTheory.ShortComplex.mapLeftHomologyIso_inv_naturality, SSet.Truncated.liftOfStrictSegal.spineEquiv_f₂_arrow_one, SSet.stdSimplex.face_singleton_compl, partialRightAdjointHomEquiv_map_comp, CategoryTheory.CategoryOfElements.fromCostructuredArrow_obj_fst, SSet.ι₀_app_fst, CommShift.isoAdd'_inv_app, CategoryTheory.Limits.constCocone_pt, CategoryTheory.Adjunction.derivedε_fac_app, CategoryTheory.ComposableArrows.isIso_iff₁, CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt', CategoryTheory.instIsIsoPost, CategoryTheory.Localization.associator_hom_app_app_app, OplaxMonoidal.ofBifunctor.topMapₗ_app, CategoryTheory.Limits.instHasLimitObjFunctorConstTerminal, SSet.Truncated.spine_injective, CategoryTheory.StructuredArrow.pre_obj_left, CommShift.OfComp.map_iso_hom_app, CategoryTheory.ofTypeMonad_obj, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_ι_inv_assoc, CategoryTheory.Limits.factorThruImageSubobject_comp_self, Rep.linearization_map_hom, CommShift.OfComp.map_iso_inv_app_assoc, CommShift.isoZero'_hom_app, CategoryTheory.Bicategory.leftUnitorNatIso_inv_app, CategoryTheory.InjectiveResolution.extAddEquivCohomologyClass_symm_apply, CategoryTheory.Equivalence.congrRight_counitIso_inv_app, CategoryTheory.Under.w, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst_assoc, CategoryTheory.Equivalence.counit_naturality, CategoryTheory.Pseudofunctor.CoGrothendieck.Hom.ext_iff, CategoryTheory.IsPullback.of_is_product, CategoryTheory.Localization.Monoidal.map_hexagon_forward_assoc, CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_fst, CategoryTheory.BinaryCofan.isPullback_initial_to_of_isVanKampen, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.unitIso_inv_app_hom_app, CategoryTheory.Limits.colimit.ι_desc_app, SheafOfModules.Presentation.map_π_eq, CategoryTheory.Limits.Cocones.precomposeEquivalence_counitIso, CategoryTheory.instPreservesFiniteColimitsFunctorObjWhiskeringLeftOfHasFiniteColimits, CategoryTheory.MonoidalCategory.externalProductBifunctor_obj_map, CoconeTypes.ι_naturality, CategoryTheory.MorphismProperty.LeftFraction.map_eq, CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.inverse_map, AlgebraicGeometry.IsOpenImmersion.lift_app, CategoryTheory.sum.inrCompInverseAssociator_inv_app, CategoryTheory.JointlyReflectEpimorphisms.epi_iff, comp_mapMon_one, CategoryTheory.Endofunctor.Algebra.functorOfNatTrans_obj_a, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_mon_one, CategoryTheory.sheafComposeNatTrans_fac, CategoryTheory.nerve.δ₂_two, HomotopyCategory.Pretriangulated.shift_distinguished_triangle, CochainComplex.shiftFunctor_obj_d, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_left_left_as, CategoryTheory.Limits.IsLimit.fac, CategoryTheory.Limits.limitOpIsoOpColimit_hom_comp_ι, CategoryTheory.PreGaloisCategory.autGaloisSystem_map_surjective, CategoryTheory.Mat_.additiveObjIsoBiproduct_hom_π_assoc, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_app_comp_π_assoc, OplaxMonoidal.associativity_inv_assoc, CategoryTheory.CostructuredArrow.mapIso_counitIso_inv_app_left, preimage_id, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₁, CategoryTheory.GrothendieckTopology.yonedaEquiv_apply, CategoryTheory.SimplicialObject.Truncated.whiskering_obj_map_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_left_obj, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst_assoc, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₁₂, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_map_app_hom_hom, CategoryTheory.MonoOver.mono_obj_hom, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_ι_assoc, germ_skyscraperPresheafStalkOfSpecializes_hom, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_obj_π_app, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_obj_obj_map, CategoryTheory.OplaxFunctor.map₂_rightUnitor_app_assoc, CategoryTheory.GradedObject.shiftFunctor_obj_apply, CategoryTheory.Localization.isoOfHom_id_inv, AlgebraicGeometry.HasRingHomProperty.iff_of_isAffine, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.toBiprod_apply, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_obj_obj_obj, SheafOfModules.Finite.evaluationPreservesFiniteLimits, CategoryTheory.shrinkYonedaEquiv_symm_map, TopModuleCat.hom_forget₂_TopCat_map, CategoryTheory.ComposableArrows.IsComplex.zero', CategoryTheory.IsPushout.of_isColimit_cocone, CochainComplex.HomComplex.Cochain.toSingleMk_precomp, CategoryTheory.Sieve.overEquiv_iff, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_snd, CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_assoc, CategoryTheory.Adjunction.map_μ_comp_counit_app_tensor_assoc, ModuleCat.exteriorPower.functor_obj, CategoryTheory.ObjectProperty.isLocal_eq_inverseImage_isomorphisms, CategoryTheory.Comma.mapLeftIso_functor_map_right, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.epi_f, CategoryTheory.SimplicialObject.augmentedCechNerve_obj_hom_app, CochainComplex.HomComplex.Cocycle.rightShift_coe, isMittagLeffler_iff_eventualRange, CategoryTheory.MonoidalCategory.DayFunctor.ι_comp_isoPointwiseLeftKanExtension_inv, currying_functor_map_app, SimplicialObject.Splitting.cofan_inj_epi_naturality, CategoryTheory.map_coyonedaEquiv, CategoryTheory.toUnit_comp_curryRightUnitorHom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_map_fst, CategoryTheory.shiftFunctorAdd_zero_add_inv_app, CategoryTheory.Adjunction.homEquiv_symm_apply, CategoryTheory.StructuredArrow.mkPostcomp_id, CategoryTheory.Limits.limit.w, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_inv_app_hom₁, CategoryTheory.Iso.hom_inv_id_app_app_app, Action.leftUnitor_hom_hom, CategoryTheory.Limits.inv_piComparison_comp_map_π_assoc, CategoryTheory.shiftFunctorComm_hom_app_of_add_eq_zero_assoc, Initial.limitConeOfComp_isLimit, CategoryTheory.Limits.combineCones_π_app_app, CategoryTheory.Idempotents.toKaroubi_obj_p, CochainComplex.single₀ObjXSelf, AlgebraicGeometry.Scheme.IdealSheafData.le_def, CategoryTheory.Limits.isCokernelEpiComp_desc, CategoryTheory.Over.opEquivOpUnder_functor_obj, CategoryTheory.Adjunction.counit_isSplitMono_of_R_full, AlgebraicGeometry.SheafedSpace.restrictTopIso_hom, SSet.Edge.toTruncated_edge, bifunctorComp₂₃Iso_inv_app_app_app, CategoryTheory.instIsCardinalAccessibleObjOppositeFunctorTypeUliftCoyonedaOpOfIsCardinalPresentable, CategoryTheory.CommMon.forget₂Mon_obj_one, SimplexCategoryGenRel.isSplitMono_toSimplexCategory_map_of_P_δ, CategoryTheory.ihom.ev_coev, CategoryTheory.Limits.isIso_limit_cocone_parallelPair_of_epi, mem_homologicalKernel_trW_iff, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_snd, ModuleCat.ihom_ev_app, Bicategory.Opposite.bicategory_rightUnitor_inv_unop2, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_inv_app_hom₃, CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_snd, Action.FunctorCategoryEquivalence.functor_η, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_hom_app_hom, CategoryTheory.Yoneda.obj_map_id, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι, CategoryTheory.MonoidalClosed.whiskerLeft_curry_ihom_ev_app_assoc, CategoryTheory.Limits.prodComparison_snd_assoc, CategoryTheory.Limits.limit.pre_π, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.w_app_assoc, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_inv_app, isSplitEpi_iff, CategoryTheory.ShortComplex.RightHomologyData.mapHomologyIso'_eq, CategoryTheory.Pseudofunctor.Grothendieck.map_map_base, CategoryTheory.Groupoid.invFunctor_obj, CategoryTheory.Monoidal.whiskerLeft_app, Preorder.isGLB_of_isLimit, CategoryTheory.Adjunction.inv_map_unit, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app_val_app, AlgebraicGeometry.ΓSpec.toSpecΓ_unop, CategoryTheory.map_yonedaEquiv', HomologicalComplex.natIsoSc'_hom_app_τ₁, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionHom, CategoryTheory.WithTerminal.widePullbackShapeEquiv_functor_obj, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_right_right, CategoryTheory.PreGaloisCategory.autGaloisSystem_obj_coe, CategoryTheory.bifunctorComp₂₃Obj_obj_map, CategoryTheory.StructuredArrow.mapIso_counitIso_hom_app_right, AlgebraicGeometry.isClosedImmersion_diagonal_restrict_diagonalCoverDiagonalRange, CategoryTheory.Limits.Cowedge.condition, mapGrp_obj_X, CochainComplex.HomComplex.Cochain.leftUnshift_zero, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.instIsOpenImmersionMapI₀Functor, costructuredArrowMapCocone_ι_app, SSet.range_eq_iSup_of_isColimit, CategoryTheory.AdditiveFunctor.ofRightExact_map_hom, CategoryTheory.Over.iteratedSliceForwardIsoPost_hom_app, CategoryTheory.Meq.pullback_apply, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_fst_map, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.isPullback_natTrans_ι_toBase, map_sum, CategoryTheory.Cokleisli.Adjunction.toCokleisli_map, CategoryTheory.Limits.map_lift_piComparison, Rep.indResHomEquiv_symm_apply_hom, ComplexShape.Embedding.stupidTruncFunctor_obj, CategoryTheory.SmallObject.SuccStruct.Iteration.arrow_mk_mapObj, LaxMonoidal.ofBifunctor.secondMap_app_app_app, CategoryTheory.evaluation_map_app, CategoryTheory.Subfunctor.subobjectMk_range_arrow, CategoryTheory.CategoryOfElements.toCostructuredArrow_map, mapTriangle_map_hom₂, toOplaxFunctor'_mapId, CategoryTheory.Comma.equivProd_functor_obj, CategoryTheory.evaluationLeftAdjoint_obj_map, CoreMonoidal.toOplaxMonoidal_η, comp_mapCommMon_one, CategoryTheory.Equivalence.congrRight_counitIso_hom_app, CategoryTheory.Square.evaluation₃_obj, CategoryTheory.Adjunction.functorialityCounit'_app_hom, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop_assoc, homEquivOfIsLeftKanExtension_apply_app, CategoryTheory.BasedNatTrans.app_isHomLift, CategoryTheory.Iso.map_inv_hom_id_eval_app_assoc, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_hom_whiskerLeft_π, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_right_app, ModuleCat.FilteredColimits.colimit_add_mk_eq, DerivedCategory.left_fac, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_right_as, ModuleCat.free_hom_ext_iff, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality, CategoryTheory.Sum.functorEquiv_counitIso, CategoryTheory.WithInitial.mapComp_hom_app, CategoryTheory.Idempotents.DoldKan.η_hom_app_f, groupHomology.chainsMap_f_0_comp_chainsIso₀, AlgebraicTopology.normalizedMooreComplex_obj, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_right, CategoryTheory.Dial.tensorObj_rel, CompHausLike.LocallyConstant.adjunction_unit, CategoryTheory.simplicialCosimplicialEquiv_functor_obj_map, CategoryTheory.Over.lift_map, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_left, lanCompColimIso_hom_app, 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.Pretriangulated.preadditiveCoyoneda_homologySequenceδ_apply, CategoryTheory.PreGaloisCategory.autEmbedding_isClosedEmbedding, Profinite.exists_hom, AlgebraicGeometry.tilde.instIsLocalizedModuleCarrierCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecModuleCatPresheafModulesSheafModulesSpecToSheafOpBasicOpenPowersHomToOpen, CategoryTheory.StructuredArrow.toCostructuredArrow_obj, AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot_of_isCompact, CategoryTheory.CosimplicialObject.δ_comp_σ_self'_assoc, classifyingSpaceUniversalCover_obj, SSet.ι₁_comp_assoc, LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm_assoc, CategoryTheory.Limits.isIso_ι_of_isTerminal, CategoryTheory.Comma.map_obj_left, CategoryTheory.CartesianMonoidalCategory.isIso_prodComparison_of_preservesLimit_pair, CategoryTheory.μ_app, CategoryTheory.Monad.Algebra.Hom.h_assoc, CategoryTheory.Adjunction.Triple.leftToRight_app_map_adj₁_unit_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedAction_obj_map, CategoryTheory.Sigma.inclDesc_hom_app, CategoryTheory.toOverUnit_obj_hom, CategoryTheory.Over.postAdjunctionLeft_counit_app_left, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.instIsIsoInvApp, CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_inv_apply, CochainComplex.HomComplex.Cochain.map_neg, SSet.skeletonOfMono_succ, CategoryTheory.Limits.ι_colimitConstInitial_hom_assoc, CategoryTheory.Arrow.augmentedCechConerve_hom_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_hom_app_app, CategoryTheory.SimplicialObject.δ_comp_δ_self'_assoc, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_symm_apply, CategoryTheory.CostructuredArrow.preEquivalence.inverse_obj_left_hom, CategoryTheory.LaxFunctor.map₂_leftUnitor_app_assoc, HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac'_assoc, CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_hom, CategoryTheory.Comma.mapRightComp_inv_app_left, CategoryTheory.Subobject.map_id, CategoryTheory.Limits.cospanCompIso_app_right, CategoryTheory.Cat.eqToHom_app, CategoryTheory.Limits.pullbackConeEquivBinaryFan_inverse_map_hom, CategoryTheory.StructuredArrow.mapNatIso_inverse_obj_right, CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_right, CategoryTheory.StructuredArrow.preEquivalenceFunctor_obj_hom, CategoryTheory.StructuredArrow.mapIso_counitIso_inv_app_right, TopCat.Presheaf.generateEquivalenceOpensLe_inverse, AlgebraicGeometry.Scheme.IdealSheafData.supportSet_eq_iInter_zeroLocus, CategoryTheory.ShiftMkCore.assoc_hom_app_assoc, CategoryTheory.Equivalence.changeFunctor_counitIso_inv_app, CategoryTheory.Reflective.instIsIsoAppUnitReflectorAdjunctionA, CategoryTheory.MonoidalOpposite.unmopEquiv_functor_obj, CategoryTheory.Endofunctor.Algebra.Initial.left_inv, CategoryTheory.Sum.functorEquiv_functor_obj, AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_app, AlgebraicGeometry.Scheme.Hom.inl_toNormalization_normalizationCoprodIso_inv, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_three_assoc, CategoryTheory.Limits.BinaryBicones.functoriality_obj_pt, StalkSkyscraperPresheafAdjunctionAuxs.toSkyscraperPresheaf_app, AlgebraicGeometry.Scheme.Hom.inr_normalizationCoprodIso_hom_fromNormalization, mapCommGrp_obj_grp_inv, CategoryTheory.Limits.Types.colimitEquivColimitType_apply, SSet.PtSimplex.RelStruct.δ_succ_map_assoc, CategoryTheory.ShortComplex.mapHomologyIso'_inv_naturality_assoc, CategoryTheory.Limits.kernelSubobjectMap_arrow_apply, whiskeringLeft₃ObjObjObj_map_app_app_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply_assoc, 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.Limits.HasLimit.lift_isoOfNatIso_inv_assoc, CategoryTheory.PresheafOfGroups.Cochain₀.mul_apply, AlgebraicGeometry.RingedSpace.mem_basicOpen', CategoryTheory.SimplicialObject.equivalenceLeftToRight_right, CochainComplex.HomComplex.CohomologyClass.homAddEquiv_apply, TwoP.swapEquiv_unitIso_inv_app_hom_toFun, CategoryTheory.Equivalence.congrRight_unitIso_inv_app, CategoryTheory.Limits.WalkingReflexivePair.map_reflexion_comp_map_right_assoc, CategoryTheory.NatIso.inv_inv_app, CategoryTheory.Limits.ker_map, CategoryTheory.Presheaf.isLocallySurjective_presheafToSheaf_map_iff, CategoryTheory.Adjunction.shift_counit_app_assoc, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_right, whiskeringLeft₃ObjObj_obj, CategoryTheory.shift_neg_shift', CategoryTheory.Monoidal.Reflective.instIsIsoMapTensorHomAppUnit, CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerLeft, CategoryTheory.LeftExactFunctor.whiskeringRight_obj_obj_obj, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality_assoc, CategoryTheory.CategoryOfElements.CreatesLimitsAux.π_liftedConeElement', CategoryTheory.Grothendieck.ι_map, CategoryTheory.ihom.coev_ev_assoc, SheafOfModules.pushforwardNatTrans_comp, CategoryTheory.RightExactFunctor.whiskeringRight_obj_map, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_hom_whiskerRight_π, mapLinearMap_apply, CategoryTheory.shrinkYonedaEquiv_shrinkYoneda_map, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_counit, CategoryTheory.Bimon.toComon_obj_comon_comul, CategoryTheory.NatTrans.CommShift₂.commShift_app, CategoryTheory.Adjunction.map_projective, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂'_obj_obj_obj, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_obj_obj_map, CategoryTheory.Equivalence.functor_unit_comp_assoc, AlgebraicGeometry.Scheme.mem_basicOpen, CategoryTheory.InjectiveResolution.extAddEquivCohomologyClass_apply, comp_mapGrp_one, CategoryTheory.enrichedNatTransYoneda_map_app, CategoryTheory.yonedaGrp_naturality, instIsSplitMonoBiproductComparison', LeftExtension.mk_hom, homologySequence_epi_shift_map_mor₂_iff, AlgebraicGeometry.IsOpenImmersion.affineOpensEquiv_symm_apply_coe, CategoryTheory.Sheaf.instEpiAppArrowILocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, CategoryTheory.Adjunction.unit_naturality_assoc, currying_inverse_map_app_app, FullyFaithful.preimage_id, Final.colimitCoconeOfComp_cocone, PullbackObjObj.isPullback, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_inv_app_fst_app, ChainComplex.map_chain_complex_of, CategoryTheory.ShiftMkCore.assoc_inv_app, Subobject.presheaf_map, CategoryTheory.constantPresheafAdj_unit_app, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app_assoc, CategoryTheory.Limits.limitRightOpIsoOpColimit_inv_comp_π, IsLeftKanExtension.nonempty_isUniversal, CategoryTheory.MorphismProperty.quotient_iff, CategoryTheory.Presheaf.freeYoneda_obj, CategoryTheory.Limits.limit_map_limitObjIsoLimitCompEvaluation_hom, CategoryTheory.Equivalence.symmEquivInverse_map_app, HomologicalComplex₂.ι_totalShift₁Iso_hom_f, AlgebraicGeometry.SheafedSpace.comp_c_app', CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app_assoc, CategoryTheory.Square.fromArrowArrowFunctor'_obj_f₃₄, CategoryTheory.Limits.instEpiDescι, CategoryTheory.ShiftedHom.opEquiv'_add_symm, CategoryTheory.MorphismProperty.costructuredArrowObj_iff, CategoryTheory.Sigma.inclDesc_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_hom_app, functorHomEquiv_symm_apply_app_app, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.mem_incl_app, CategoryTheory.MorphismProperty.Over.map_obj_hom, CategoryTheory.Pretriangulated.Triangle.yoneda_exact₃, CategoryTheory.Bicategory.rightUnitorNatIso_hom_app, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_hom, PushoutObjObj.ofHasPushout_ι, CategoryTheory.CostructuredArrow.IsUniversal.hom_desc, CategoryTheory.Adjunction.Triple.mono_leftToRight_app_iff, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app, OplaxMonoidal.instIsIsoδ, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst_assoc, MonCat.FilteredColimits.M.mk_surjective, SSet.stdSimplex.isoNerve_inv_app_apply, CategoryTheory.Limits.coprodComparison_natural, SemiRingCat.forget₂_addCommMonCat_map, CategoryTheory.ShortComplex.LeftHomologyMapData.map_φK, CategoryTheory.colimitYonedaHomEquiv_π_apply, CategoryTheory.Equivalence.induced_counitIso, CategoryTheory.Enriched.FunctorCategory.diagram_obj_obj, CategoryTheory.Presheaf.instIsLeftKanExtensionOppositeObjFunctorTypeUliftYonedaUliftYonedaMap, CategoryTheory.Adjunction.comp_unit_app, CategoryTheory.CommGrp.forget_map, CategoryTheory.Sieve.functorPullback_union, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_inv_ι, AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ_assoc, CategoryTheory.comonEquiv_counitIso, CategoryTheory.ParametrizedAdjunction.whiskerLeft_map_counit_assoc, CategoryTheory.StructuredArrow.pre_obj_right, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_apply, Monoidal.μ_δ_assoc, AlgebraicGeometry.PresheafedSpace.ofRestrict_c_app, whiskeringLeft_map_app_app, CategoryTheory.LeftExactFunctor.forget_obj_of, SSet.Truncated.liftOfStrictSegal.spineEquiv_f₂_arrow_zero, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd_assoc, CategoryTheory.Limits.SequentialProduct.functorMap_commSq, CategoryTheory.Limits.MonoCoprod.binaryCofan_inr, HomotopicalAlgebra.BifibrantObject.HoCat.ιFibrantObject_map_toHoCat_map, CategoryTheory.Adjunction.whiskerLeft_counit_app_app, CategoryTheory.Sheaf.isSheaf_yoneda_obj, π_tensor_id_preserves_coequalizer_inv_colimMap_desc, CategoryTheory.BasedNatTrans.forgetful_obj, CategoryTheory.instIsIsoFromLeftDerivedZero', CategoryTheory.Grothendieck.faithful_ι, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_iff, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.ofRestrict_invApp_apply, CategoryTheory.Limits.Types.isLimitEquivSections_symm_apply, AlgebraicGeometry.IsAffineOpen.preimage, CategoryTheory.Limits.pullbackObjIso_hom_comp_snd, CategoryTheory.Comma.preLeft_obj_hom, CategoryTheory.ComposableArrows.IsComplex.cokerToKer_fac_assoc, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_obj₃, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_obj_obj_obj, OneHypercoverDenseData.isSheaf_iff.fac, CategoryTheory.FreeMonoidalCategory.tensorFunc_obj_map, Rep.linearization_μ_hom, CategoryTheory.Comon.monoidal_tensorObj_comon_comul, CategoryTheory.uliftCoyonedaEquiv_comp, CategoryTheory.IsHomLift.fac, CategoryTheory.Localization.whiskeringLeftFunctor'_obj, ContinuousMap.Homotopy.eq_diag_path, IsCoverDense.Types.naturality_assoc, CategoryTheory.Abelian.PreservesCoimage.iso_hom_π, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetObj_map, CategoryTheory.BraidedCategory.ofBifunctor.Forward.firstMap₃_app_app_app, CompHausLike.LocallyConstant.functorToPresheaves_obj_obj, AlgebraicGeometry.LocallyRingedSpace.comp_c, CategoryTheory.Limits.Cone.op_ι, AlgebraicGeometry.Scheme.Opens.isoOfLE_inv_ι_assoc, CategoryTheory.Limits.colimitFlipIsoCompColim_inv_app, CategoryTheory.yonedaEquiv_symm_app_apply, CategoryTheory.Adjunction.leftAdjointCompNatTrans_app, CategoryTheory.Limits.PreservesPushout.iso_hom, AlgebraicGeometry.LocallyRingedSpace.Γ_obj, map_inv_hom, RightExtension.precomp_obj_left, CategoryTheory.TwoSquare.vId_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_snd_map, ModuleCat.ExtendRestrictScalarsAdj.unit_app, CategoryTheory.Limits.colimitLimitToLimitColimit_surjective, instIsEquivalenceRightExtensionCompPrecomp, CategoryTheory.ComposableArrows.δlastFunctor_obj_map, AlgebraicGeometry.Spec.map_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_hom_app, mapCommMonCompIso_hom_app_hom_hom, CategoryTheory.GlueData.mapGlueData_V, CategoryTheory.associator_hom, CategoryTheory.Limits.inr_comp_pushoutComparison, CategoryTheory.preservesColimitsOfShape_of_isCardinalPresentable, CategoryTheory.evaluationAdjunctionLeft_counit_app, ComplexShape.Embedding.truncGEFunctor_obj, CategoryTheory.WithTerminal.coneEquiv_functor_map_hom, SSet.PtSimplex.MulStruct.δ_castSucc_castSucc_map, TopCat.isEmbedding_of_pullback, CategoryTheory.Join.mapIsoWhiskerRight_inv_app, CategoryTheory.Limits.ι_comp_colimitUnopIsoOpLimit_hom, CategoryTheory.Limits.epi_of_isColimit_cofork, CategoryTheory.Pseudofunctor.mapId'_inv_naturality, map_surjective, CategoryTheory.Monad.algebraFunctorOfMonadHom_map_f, ModuleCat.CoextendScalars.map_apply, AlgebraicGeometry.Scheme.Spec_fromSpecStalk, op_map, CategoryTheory.functorProdFunctorEquivCounitIso_hom_app_app, PresheafOfModules.pushforward₀_obj_map, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_right_assoc, CategoryTheory.Limits.PreservesColimit₂.nonempty_isColimit_mapCocone₂, mapExtLinearMap_apply, CategoryTheory.Limits.pullback_equalizer, groupHomology.chainsMap_f, ProfiniteGrp.diagram_obj, SSet.RelativeMorphism.Homotopy.rel_assoc, Rep.quotientToCoinvariantsFunctor_obj_V, MonObj.mopEquiv_inverse_obj_mon_mul, leftExtensionEquivalenceOfIso₁_functor_obj_right, HomologicalComplex.shortComplexFunctor_obj_X₃, Monoidal.η_ε, CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left, CategoryTheory.NatIso.ofComponents_hom_app, SheafOfModules.unitHomEquiv_apply_coe, CategoryTheory.Monad.right_unit_assoc, CategoryTheory.Square.fromArrowArrowFunctor_map_τ₄, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_app_assoc, CochainComplex.ShiftSequence.shiftIso_hom_app, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInlIso_inv_app_app, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁'_obj_obj_map, AlgebraicGeometry.IsAffineOpen.ideal_ext_iff, CategoryTheory.MonoidalCategory.tensoringRight_μ, CategoryTheory.Presheaf.isSheaf_iff_isLimit_pretopology, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_app, CategoryTheory.PreGaloisCategory.autEmbedding_range_isClosed, CategoryTheory.Limits.Bicones.functoriality_obj_π, groupHomology.chainsMap_f_2_comp_chainsIso₂_apply, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_shift, CategoryTheory.MonoidalClosed.id_comp_assoc, topToCompHaus_obj, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_assoc, CategoryTheory.Monad.FreeCoequalizer.topMap_f, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π, CategoryTheory.Limits.CatCospanTransform.rightUnitor_hom_right_app, AlgebraicGeometry.morphismRestrict_id, CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse_map_left_right, structuredArrowMapCone_π_app, whiskeringLeftObjCompIso_inv_app_app, CategoryTheory.Presieve.functorPushforward_comp, groupCohomology.map_comp_assoc, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_neg, CategoryTheory.Limits.IsLimit.homEquiv_apply, CategoryTheory.whiskering_preadditiveCoyoneda, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_fst_obj, typeToBoolAlgOp_obj, uncurry_obj_curry_obj_flip_flip, CategoryTheory.ShortComplex.mapHomologyIso'_inv_naturality, CategoryTheory.CostructuredArrow.mapIso_inverse_obj_left, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_inv_app_fst_app, CategoryTheory.ShortComplex.mapCyclesIso_hom_naturality, DerivedCategory.instIsGEObjSingleFunctor, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_app, CategoryTheory.Square.isPushout_iff_op_map_yoneda_isPullback, CategoryTheory.NatTrans.sum_app_inr, CategoryTheory.Limits.CompleteLattice.limitCone_cone_pt, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_map_app_app_app, CategoryTheory.Triangulated.Octahedron.comm₂_assoc, CategoryTheory.Pseudofunctor.DescentData.Hom.comm, pi'_obj, AlgebraicGeometry.tilde.toOpen_map_app, CategoryTheory.Limits.compYonedaSectionsEquiv_symm_apply_coe, CategoryTheory.Limits.KernelFork.map_condition_assoc, CategoryTheory.yonedaEquiv_comp, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app_assoc, HomotopicalAlgebra.BifibrantObject.instIsFibrantObjι, CategoryTheory.Adjunction.Quadruple.epi_leftTriple_rightToLeft_app_iff_mono_rightTriple_leftToRight_app, CategoryTheory.Limits.ColimitPresentation.self_ι, CategoryTheory.Comma.coneOfPreserves_π_app_left, Monoidal.whiskerLeft_δ_μ_assoc, CochainComplex.mappingCone.map_δ, CategoryTheory.unitCompPartialBijective_symm_apply, AddCommGrpCat.coyoneda_obj_map, CategoryTheory.Abelian.Ext.comp_hom, CategoryTheory.ihom.coev_ev, SemiNormedGrp.completion_completeSpace, CategoryTheory.bifunctorComp₁₂Obj_map_app, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_εIso_hom, AlgebraicGeometry.IsAffineOpen.primeIdealOf_genericPoint, ChainComplex.linearYonedaObj_X, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map, CategoryTheory.Monad.ForgetCreatesColimits.newCocone_ι, currying_inverse_obj_map_app, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right, CategoryTheory.Limits.parallelPairOpIso_hom_app_zero, IsCoverDense.Types.naturality, CategoryTheory.Localization.structuredArrowEquiv_apply, CategoryTheory.LiftRightAdjoint.instIsCoreflexivePairMapAppUnitOtherMap, AlgebraicGeometry.LocallyRingedSpace.stalkMap_germ, CategoryTheory.Limits.kernelSubobjectMap_id, ModuleCat.toMatrixModCat_obj_isModule, HomologicalComplex.quasiIsoAt_map_iff_of_preservesHomology, CategoryTheory.CosimplicialObject.δ_comp_σ_of_le_assoc, mapComposableArrows_map_app, AlgebraicGeometry.Scheme.Hom.id_image, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_hom, AlgebraicGeometry.IsAffineOpen.mem_ideal_iff, AlgebraicGeometry.Scheme.toSpecΓ_base, AlgebraicGeometry.Smooth.iff_forall_exists_isStandardSmooth
toPrefunctor 📖	CompOp	14 math math: CategoryTheory.Quiv.pathsOf_pathComposition_toPrefunctor, toPrefunctor_map, CategoryTheory.PrelaxFunctor.mkOfHomFunctors_toPrelaxFunctorStruct, toPrefunctor_obj, CategoryTheory.ReflQuiv.adj.unit.map_app_eq, Quiver.FreeGroupoid.lift_spec, toPrefunctor_comp, CategoryTheory.Quiv.forget_map, toReflPrefunctor_toPrefunctor, CategoryTheory.Paths.lift_spec, CategoryTheory.Quiv.pathComposition_naturality, CategoryTheory.functorMapReverse, CategoryTheory.Quiv.pathsOf_freeMap_toPrefunctor, Quiver.FreeGroupoid.of_eq

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
comp_id 📖	mathematical	—	comp id	—	—
comp_map 📖	mathematical	—	map comp obj	—	—
comp_obj 📖	mathematical	—	obj comp	—	—
congr_map 📖	mathematical	—	map	—	—
id_comp 📖	mathematical	—	comp id	—	—
id_map 📖	mathematical	—	map id	—	—
id_obj 📖	mathematical	—	obj id	—	—
map_comp 📖	mathematical	—	map CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct obj	—	—
map_comp_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct obj map	—	—
map_dite 📖	mathematical	—	map Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct obj	—	—
map_id 📖	mathematical	—	map CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct obj	—	—
toPrefunctor_comp 📖	mathematical	—	Prefunctor.comp CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct toPrefunctor comp	—	—
toPrefunctor_injective 📖	—	toPrefunctor	—	—	—
toPrefunctor_map 📖	mathematical	—	Prefunctor.map CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct toPrefunctor map	—	—
toPrefunctor_obj 📖	mathematical	—	Prefunctor.obj CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct toPrefunctor obj	—	—

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