NatTrans

📁 Source: Mathlib/CategoryTheory/NatTrans.lean

Statistics

Metric	Count
Definitions NatTrans, app, id, instInhabited, vcomp	5
Theorems ext, ext_iff, id_app', naturality, naturality', naturality_assoc, vcomp_app, congr_app	8
Total	13

CategoryTheory

Definitions

Name	Category	Theorems
NatTrans 📖	CompData	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
congr_app 📖	mathematical	—	NatTrans.app	—	—

CategoryTheory.NatTrans

Definitions

Name	Category	Theorems
app 📖	CompOp	5236 math math: CategoryTheory.Equivalence.adjointify_η_ε_assoc, CategoryTheory.Limits.limMap_π, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₃, CategoryTheory.shiftFunctorZero_inv_app_obj_of_induced, CategoryTheory.Limits.Cones.postcomposeId_hom_app_hom, AlgebraicTopology.DoldKan.natTransPInfty_app, CategoryTheory.Triangulated.SpectralObject.Hom.comm, HomotopyCategory.spectralObjectMappingCone_δ'_app, CategoryTheory.Adjunction.adjToComonadIso_inv_toNatTrans_app, CategoryTheory.MorphismProperty.LeftFraction.map_compatibility, CategoryTheory.Limits.coker.π_app, CategoryTheory.GrothendieckTopology.overMapPullbackId_hom_app_val_app, CategoryTheory.Adjunction.adjunctionOfEquivLeft_counit_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_eq, CategoryTheory.Pseudofunctor.mapComp'_naturality_1_assoc, CategoryTheory.Functor.whiskeringRightObjIdIso_hom_app_app, CategoryTheory.Join.pseudofunctorLeft_mapId_inv_toNatTrans_app, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₁, CategoryTheory.Functor.LeftExtension.coconeAtFunctor_map_hom, CategoryTheory.Functor.functorHomEquiv_apply_app, CategoryTheory.SimplicialObject.id_left_app, CategoryTheory.sum.inrCompInverseAssociator_hom_app, CategoryTheory.Functor.FullyFaithful.homNatIsoMaxRight_inv_app, CategoryTheory.MorphismProperty.exists_isPushout_of_isFiltered, CategoryTheory.prodComonad_ε_app, CategoryTheory.Functor.CommShift.isoAdd_hom_app, CategoryTheory.Adjunction.compUliftCoyonedaIso_hom_app_app_down, CategoryTheory.Monoidal.tensorHom_app, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerLeftIso_inv_app, CategoryTheory.SingleFunctors.postcompPostcompIso_hom_hom_app, CategoryTheory.GrothendieckTopology.Plus.toPlus_mk, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.hπ_assoc, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_hom_app_zero, CategoryTheory.uliftCoyonedaEquiv_apply, CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_app, CategoryTheory.Sum.natTransOfWhiskerLeftInlInr_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitNatIso_inv_app, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.Functor.PushoutObjObj.inr_ι, CategoryTheory.Functor.isoSum_inv_app_inl, CategoryTheory.Equivalence.leftOp_unitIso_hom_app, CategoryTheory.Monad.ForgetCreatesColimits.commuting, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_hom_app_val_app, CategoryTheory.WithTerminal.coneEquiv_unitIso_hom_app_hom_left, CategoryTheory.Functor.mapTriangleIdIso_inv_app_hom₃, CategoryTheory.SimplicialObject.whiskering_obj_map_app, CategoryTheory.Monad.monadMonEquiv_unitIso_inv_app_toNatTrans_app, CategoryTheory.Functor.IsDenseSubsite.instIsIsoSheafAppCounitSheafAdjunctionCocontinuous, CategoryTheory.Join.pseudofunctorRight_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, CategoryTheory.ComposableArrows.opEquivalence_counitIso_inv_app_app, CategoryTheory.mateEquiv_counit_symm, CategoryTheory.Pseudofunctor.DescentData.ofObj_hom, CategoryTheory.MonoidalCategory.DayConvolution.braidingHomCorepresenting_app, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.firstMap₂_app_app_app, CategoryTheory.Functor.coreComp_hom_app_iso_inv, CategoryTheory.ComposableArrows.threeδ₂Toδ₁_app_zero, CategoryTheory.Functor.natTransEquiv_apply_app, CategoryTheory.Functor.mapComposableArrowsObjMk₂Iso_inv_app, CategoryTheory.uliftCoyonedaIsoCoyoneda_hom_app_app, CategoryTheory.Discrete.sumEquiv_counitIso_inv_app, CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc, CategoryTheory.coyonedaEquiv_symm_app_apply, CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_right, HomologicalComplex.singleMapHomologicalComplex_hom_app_ne, CategoryTheory.ComposableArrows.isoMk₁_hom_app, CategoryTheory.StructuredArrow.map_map_right, hcomp_id_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon_map, CategoryTheory.PreGaloisCategory.mulAction_def, CategoryTheory.shiftFunctorAdd'_assoc_inv_app, CategoryTheory.isIso_sheafificationAdjunction_counit, CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair_hom_app, typeToPartialFunIsoPartialFunToPointed_inv_app_toFun, AlgebraicTopology.DoldKan.Compatibility.equivalence₀_unitIso_hom_app, CategoryTheory.ObjectProperty.ColimitOfShape.toCostructuredArrow_obj, CategoryTheory.Idempotents.app_idem_assoc, CategoryTheory.Functor.homObjEquiv_apply_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_left, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app', CategoryTheory.NatIso.mapHomologicalComplex_inv_app_f, 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, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp_inv_app_f, CategoryTheory.evaluationLeftAdjoint_map_app, prod'_app_snd, CategoryTheory.Limits.CategoricalPullback.catCommSq_iso_hom_app, CategoryTheory.Join.inlCompFromSum_hom_app, LightProfinite.Extend.functorOp_obj, AlgebraicGeometry.Scheme.Modules.pushforwardId_inv_app_app, CategoryTheory.Limits.CatCospanTransform.associator_hom_right_app, CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj_map_f, CategoryTheory.DinatTrans.dinaturality_assoc, CategoryTheory.Cat.Hom₂.comp_app, CategoryTheory.Limits.diagramIsoPair_hom_app, CategoryTheory.ihom.coev_naturality, CategoryTheory.obj_ε_app_assoc, CategoryTheory.Monad.id_η_app, CategoryTheory.Functor.mapHomologicalComplexIdIso_hom_app_f, CategoryTheory.Join.mapPairId_hom_app, CategoryTheory.Limits.Bicone.toCocone_ι_app_mk, CategoryTheory.linearCoyoneda_map_app, CategoryTheory.Adjunction.whiskerLeftLCounitIsoOfIsIsoUnit_inv_app, CategoryTheory.Functor.mapMonNatTrans_app_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionHomLeft, CategoryTheory.Limits.WalkingMultispan.functorExt_hom_app, ofOpSequence_app, CategoryTheory.CosimplicialObject.comp_app, CategoryTheory.Core.forgetFunctorToCore_map_app, CategoryTheory.Comma.mapLeftEq_inv_app_right, CategoryTheory.Functor.ι_colimitIsoOfIsLeftKanExtension_inv_assoc, CategoryTheory.Functor.shiftIso_add_inv_app, CategoryTheory.Limits.colimitIsoFlipCompColim_inv_app, CategoryTheory.Functor.Monoidal.μNatIso_inv_app, CategoryTheory.Comma.mapLeftIso_inverse_map_right, CategoryTheory.MonoidalCategory.DayConvolution.unit_naturality, AlgebraicGeometry.PresheafedSpace.stalkMap_germ, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceInverseπ_hom_app, 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.Join.mapWhiskerLeft_app, isIso_app_iff_of_iso, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_map_left, HomologicalComplex.singleMapHomologicalComplex_hom_app_self, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_hom_app, CategoryTheory.Functor.Monoidal.rightUnitor_inv_app, CategoryTheory.GradedObject.ι_mapBifunctorMapMap, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_hom_app_app_down, CategoryTheory.ShortComplex.mapToComposableArrows_app_0, CategoryTheory.Functor.LeftExtension.precomp₂_obj_hom_app, TannakaDuality.FiniteGroup.toRightFDRepComp_in_rightRegular, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_inv_app_val_app, CategoryTheory.Limits.Cotrident.ofCocone_ι, groupHomology.coinfNatTrans_app, CategoryTheory.Limits.colimit.isoColimitCocone_ι_inv, CategoryTheory.Functor.CommShift.isoAdd_inv_app, CategoryTheory.Join.pseudofunctorRight_mapComp_inv_toNatTrans_app, CategoryTheory.Functor.opUnopIso_hom_app, CategoryTheory.Limits.diagramIsoCospan_inv_app, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app_assoc, CategoryTheory.MonoidalOpposite.tensorLeftMopIso_hom_app_unmop, CategoryTheory.Functor.instIsIsoAppCounitRanAdjunctionOfHasPointwiseRightKanExtension, CategoryTheory.Limits.Trident.app_zero, CategoryTheory.Pseudofunctor.map₂_associator_app_assoc, CategoryTheory.Limits.IsColimit.fac, CategoryTheory.shrinkYonedaEquiv_comp, CategoryTheory.Functor.whiskeringRight₂_obj_obj_map_app, naturality_2, CategoryTheory.eval_app, CategoryTheory.Functor.Monoidal.commTensorLeft_hom_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_hom, 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, AlgebraicGeometry.opensCone_pt, CategoryTheory.Adjunction.Localization.ε_app, CategoryTheory.Pseudofunctor.DescentData.pullFunctorCompIso_inv_app_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitNatIso_hom_app, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_isLimit_lift, CategoryTheory.Functor.mapBifunctorHomologicalComplexObj_map_f_f, CategoryTheory.ShortComplex.toCyclesNatTrans_app, CategoryTheory.Functor.mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app_assoc, CategoryTheory.Monad.free_map_f, CategoryTheory.Equivalence.unitIso_hom_app_comp_inverse_map_η_functor_assoc, 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.Functor.Monoidal.whiskerLeft_app_fst_assoc, CategoryTheory.FunctorToTypes.prodMk_fst, CategoryTheory.Limits.Cone.ofTrident_π, CategoryTheory.Functor.mapCommGrpCompIso_inv_app_hom_hom_hom, CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse, CategoryTheory.Sum.functorEquivFunctorCompFstIso_inv_app_app, CategoryTheory.Functor.mapCommMonNatIso_inv_app_hom_hom, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₁, CategoryTheory.CosimplicialObject.id_right_app, CategoryTheory.cocones_map_app_app, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.F_obj, CategoryTheory.Monoidal.leftUnitor_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_app_snd_app, CategoryTheory.Functor.mapTriangleIso_inv_app_hom₁, CategoryTheory.Functor.IsEventuallyConstantFrom.cocone_ι_app, CategoryTheory.Discrete.sumEquiv_unitIso_inv_app, CategoryTheory.Limits.ReflexiveCofork.app_one_eq_π, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_π_app, CategoryTheory.NatIso.cancel_natIso_hom_right, CategoryTheory.Functor.sheafPushforwardContinuousComp'_inv_app_val_app, CategoryTheory.Functor.flip₁₃_map_app_app, CategoryTheory.Limits.isIso_app_coconePt_of_preservesColimit, CategoryTheory.ComposableArrows.isIso_iff₂, CondensedMod.IsSolid.isIso_solidification_map, CategoryTheory.Abelian.LeftResolution.epi_π_app, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_hom_app_app_val, CategoryTheory.FunctorToTypes.functorHomEquiv_symm_apply_app_app, TopCat.Presheaf.Pushforward.id_inv_app, CategoryTheory.MonoidalCategory.tensorRightTensor_hom_app, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₃, CategoryTheory.MonoidalCategory.tensorLeftTensor_inv_app, CategoryTheory.Limits.spanCompIso_inv_app_zero, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_app_assoc, CategoryTheory.WithInitial.opEquiv_unitIso_inv_app, CategoryTheory.Limits.CatCospanTransform.rightUnitor_inv_left_app, CategoryTheory.Limits.Cocone.toOver_ι_app, CategoryTheory.Equivalence.counitIso_inv_app_comp_functor_map_η_inverse, flipApp_app, CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_zero, CategoryTheory.Functor.mapTriangleIso_inv_app_hom₃, SSet.Truncated.mapHomotopyCategory_homMk, TopCat.Presheaf.germ_stalkPullbackHom, CategoryTheory.Under.postComp_inv_app_right, Rep.coindResAdjunction_counit_app, CategoryTheory.Adjunction.map_ε_comp_counit_app_unit_assoc, CategoryTheory.Limits.Multicofork.ofπ_ι_app, AlgebraicGeometry.Scheme.restrictFunctorΓ_inv_app, CategoryTheory.Sheaf.instIsLocallySurjectiveAppArrowILocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, Condensed.hom_ext_iff, CategoryTheory.SimplicialObject.σ_naturality_assoc, partialFunEquivPointed_counitIso_inv_app_toFun, CategoryTheory.Arrow.augmentedCechNerve_hom_app, CategoryTheory.Functor.isoSum_inv_app_inr, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_counit_app_app, CategoryTheory.Limits.cospanIsoMk_inv_app, naturality_apply, CategoryTheory.Functor.mapCocone_ι_app, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₂, CategoryTheory.Comma.map_obj_hom, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_apply, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_incl_app, commBialgCatEquivComonCommAlgCat_unitIso_inv_app, partialFunEquivPointed_unitIso_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_map_snd_app, AlgebraicTopology.DoldKan.MorphComponents.preComp_a, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_app_apply, CategoryTheory.Limits.parallelPairOpIso_inv_app_zero, CategoryTheory.Limits.HasColimit.isoOfEquivalence_inv_π, 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.Adjunction.instIsIsoAppUnitObjOfFaithfulOfFull, CategoryTheory.Arrow.mapCechNerve_app, CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_left, SSet.degenerate_iff_of_mono, CategoryTheory.Idempotents.functorExtension₁CompWhiskeringLeftToKaroubiIso_inv_app_app_f, CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux_fac_assoc, CategoryTheory.Limits.colimit.cocone_ι, CategoryTheory.MorphismProperty.FunctorialFactorizationData.hi, CategoryTheory.sum.inlCompInrCompInverseAssociator_hom_app_down_down, CategoryTheory.Functor.uliftCoyonedaCoreprXIso_hom_app, CategoryTheory.FunctorToTypes.shrinkMap_app, ModuleCat.extendScalarsId_hom_app_one_tmul, CategoryTheory.ComposableArrows.homMk₅_app_five, Profinite.Extend.functorOp_map, CategoryTheory.Functor.Monoidal.tensorHom_app_fst_assoc, CategoryTheory.Iso.core_inv_app_iso_hom, CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_left_app, CategoryTheory.Cat.associator_hom_app, CategoryTheory.Under.forgetMapInitial_inv_app, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.hf, CategoryTheory.Enriched.Functor.whiskerLeft_app_apply, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_hom_app_app, CategoryTheory.Functor.rightDerived_fac_app, CategoryTheory.Limits.HasLimit.isoOfNatIso_inv_π_assoc, PresheafOfModules.restrictScalars_map_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_map_app, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_app_assoc, CommShiftCore.shift_app_comm, CategoryTheory.Functor.map_shiftFunctorComm_hom_app, AlgebraicGeometry.exists_isAffineOpen_preimage_eq, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_hom_app_snd_app, CategoryTheory.Idempotents.functorExtension₂_map_app_f, CategoryTheory.Adjunction.derivedε_fac_app_assoc, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₁, CategoryTheory.Monad.Algebra.unit_assoc, CategoryTheory.PreGaloisCategory.endEquivSectionsFibers_π, CategoryTheory.Paths.liftNatIso_inv_app, CategoryTheory.Functor.sumIsoExt_hom_app_inl, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app, CategoryTheory.Limits.CoconeMorphism.w, CategoryTheory.Equivalence.rightOp_counitIso_inv_app, CategoryTheory.WithInitial.liftToInitialUnique_hom_app, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_right, CategoryTheory.MonadHom.app_μ, CategoryTheory.Functor.curryObjCompIso_hom_app_app, CategoryTheory.Functor.unopOpIso_inv_app, CategoryTheory.Functor.uncurryObjFlip_hom_app, epi_iff_epi_app, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_fst, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id_app, CategoryTheory.Limits.BinaryBicone.toCone_π_app_right, CategoryTheory.yoneda_map_app, CategoryTheory.OplaxFunctor.map₂_associator_app, CategoryTheory.ShortComplex.RightHomologyMapData.natTransApp_φQ, CategoryTheory.Comma.mapLeft_map_left, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIso_inv_app_hom, CategoryTheory.Comonad.comparison_obj_a, CategoryTheory.SmallObject.πObj_ιIteration_app_right, CategoryTheory.NatIso.isIso_app_of_isIso, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_id_fiber, AlgebraicTopology.DoldKan.N₂Γ₂ToKaroubiIso_inv_app, CategoryTheory.MonoidalClosed.ofEquiv_uncurry_def, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_inv_app, CategoryTheory.curryingIso_hom_toFunctor_obj_map, CategoryTheory.CatCommSq.hInv_iso_inv_app, CategoryTheory.GrothendieckTopology.overMapPullbackId_inv_app_val_app, CategoryTheory.Equivalence.leftOp_unitIso_inv_app, CategoryTheory.ShortComplex.leftHomologyπNatTrans_app, CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_cancel_hom_app, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_inl, CategoryTheory.Functor.mapTriangleRotateIso_inv_app_hom₂, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_obj_iso_inv, CategoryTheory.Limits.PushoutCocone.mk_ι_app_zero, CategoryTheory.Functor.whiskeringLeft₃ObjObjObj_obj_map_app_app, CategoryTheory.EnrichedCat.leftUnitor_hom_out_app, CategoryTheory.Functor.shiftIso_hom_app_comp, CategoryTheory.Functor.Monoidal.commTensorRight_inv_app, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom_assoc, CategoryTheory.nerve.functorOfNerveMap_map, StalkSkyscraperPresheafAdjunctionAuxs.counit_app, SSet.opFunctorCompOpFunctorIso_inv_app_app, CategoryTheory.Pretriangulated.shiftFunctorZero_op_inv_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_ι_app, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₂, CategoryTheory.Under.postCongr_inv_app_right, Rep.indCoindNatIso_hom_app, CategoryTheory.Functor.instIsIsoAppRanCounit, CategoryTheory.Join.inclRightCompOpEquivInverse_inv_app_op, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_inv_app_hom, CategoryTheory.NatIso.naturality_1', AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app_assoc, CategoryTheory.Limits.IsLimit.map_π, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerRightIso_hom_app, CategoryTheory.Limits.end_.map_π, CategoryTheory.cosimplicialSimplicialEquiv_counitIso_hom_app_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.comp_snd_app, CategoryTheory.MonoidalCategory.externalProductBifunctor_map_app, CategoryTheory.Adjunction.instIsIsoAppCounitOfFullOfFaithful, CategoryTheory.Adjunction.adjunctionOfEquivRight_counit_app, CategoryTheory.sum.inrCompInrCompInverseAssociator_hom_app_down, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₃, LightCondSet.epi_iff_locallySurjective_on_lightProfinite, CategoryTheory.Monoidal.FunctorCategory.whiskerLeft_app, CategoryTheory.Comonad.ComonadicityInternal.unitFork_pt, CategoryTheory.ComposableArrows.twoδ₁Toδ₀_app_zero, CategoryTheory.Functor.mapTriangleCompIso_inv_app_hom₂, CategoryTheory.Functor.pointwiseRightKanExtension_lift_app, CategoryTheory.Functor.pi'CompEval_hom_app, CategoryTheory.Iso.app_inv, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.leftMapₗ_app, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app, CategoryTheory.Functor.FullyFaithful.homNatIsoMaxRight_hom_app_down, CategoryTheory.Functor.leftOpRightOpEquiv_counitIso_inv_app_app, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp_assoc, CategoryTheory.Adjunction.compCoyonedaIso_inv_app_app, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_unitIso_hom_app_f, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app_assoc, CategoryTheory.Monad.algebraFunctorOfMonadHomId_inv_app_f, CategoryTheory.bifunctorComp₁₂FunctorMap_app_app_app_app, CategoryTheory.Over.forgetMapTerminal_hom_app, CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_inv_app_app, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app, CategoryTheory.Functor.fullyFaithfulCancelRight_inv_app, CategoryTheory.ofTypeMonad_η_app, SSet.Truncated.HomotopyCategory.mkNatTrans_app_mk, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_map_app_app, CategoryTheory.GrothendieckTopology.ι_plusCompIso_hom_assoc, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_inv_app_hom_coe, CategoryTheory.Functor.mapTriangle_obj, CategoryTheory.Functor.leftDerived_fac_app, LightCondensed.isoFinYoneda_inv_app, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_app_assoc, CategoryTheory.BraidedCategory.ofBifunctor.Forward.secondMap₃_app_app_app, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_hom_app, CategoryTheory.ComposableArrows.scMap_τ₁, SSet.nonDegenerate_iff_of_mono, CategoryTheory.Presheaf.imageSieve_app, CategoryTheory.Comonad.ForgetCreatesLimits'.liftedCone_π_app_f, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_one, CondensedMod.isDiscrete_tfae, CategoryTheory.CatCommSq.hId_iso_hom_app, CategoryTheory.Functor.LeftExtension.postcomp₁_map_right_app, TopCat.uliftFunctorCompForgetIso_hom_app, CategoryTheory.Functor.mapComposableArrowsObjMk₁Iso_inv_app, CategoryTheory.Functor.IsEventuallyConstantFrom.isIso_ι_of_isColimit', CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp_app, CategoryTheory.Limits.PullbackCone.π_app_right, CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtension_map_leftKanExtensionObjIsoColimit_hom, AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_hom_app, CategoryTheory.CategoryOfElements.map_map_coe, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃'_map_app_app, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_hom_app, CategoryTheory.Pretriangulated.Triangle.functorHomMk'_app_hom₁, CategoryTheory.simplicialCosimplicialEquiv_counitIso_inv_app_app, CategoryTheory.Limits.PushoutCocone.unop_π_app, CategoryTheory.EnrichedFunctor.forgetComp_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_inv_app, CategoryTheory.MonoidalCategory.DayFunctor.equiv_unitIso_hom_app, CategoryTheory.MonoidalCategory.tensorLeftTensor_hom_app, CategoryTheory.LaxBraidedFunctor.isoOfComponents_inv_hom_hom_app, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app, CategoryTheory.Limits.diagramIsoParallelFamily_inv_app, mapSquare_app_τ₁, SSet.tensorHom_app_apply, CategoryTheory.Functor.mapGrpIdIso_hom_app_hom_hom, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_hom_app_hom_apply, CategoryTheory.SimplicialObject.Augmented.toArrow_map_right, CategoryTheory.Limits.IndObjectPresentation.extend_ι_app_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv, CategoryTheory.Limits.Fork.unop_ι_app_zero, CategoryTheory.ShortComplex.π₁Toπ₂_app, SSet.Edge.map_id, CategoryTheory.Limits.CatCospanTransform.rightUnitor_hom_left_app, CategoryTheory.Adjunction.rightAdjointLaxMonoidal_μ, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_inv_app, CategoryTheory.Functor.inlCompSum'_inv_app, CondensedSet.instEpiTopCatAppCounitTopCatAdjunction, CategoryTheory.Limits.Cocone.ofCotrident_ι, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.unitIso_inv_app_f_f, CochainComplex.mappingCone.homologySequenceδ_triangleh, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_pos_assoc, CategoryTheory.Limits.opCompYonedaSectionsEquiv_symm_apply_coe, CategoryTheory.Yoneda.naturality, CategoryTheory.Adjunction.IsMonoidal.leftAdjoint_μ, CategoryTheory.Cat.Hom₂.id_app, CategoryTheory.Grothendieck.ιNatTrans_app_fiber, CategoryTheory.Functor.closedIhom_obj_map, CategoryTheory.Discrete.natIsoFunctor_hom_app, CategoryTheory.MonoidalCategory.externalProductCompDiagIso_hom_app_app, CondensedSet.hom_naturality_apply, CategoryTheory.Limits.yonedaCompLimIsoCocones_inv_app, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_app_assoc, CategoryTheory.coyonedaEvaluation_map_down, CategoryTheory.Limits.mapPairIso_inv_app, CategoryTheory.nerve.homEquiv_edgeMk_map_nerveMap, CategoryTheory.Limits.LimitPresentation.w, FunctorToFintypeCat.naturality, HomologicalComplex.mapBifunctor₂₃.d₂_eq, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_left_right, CategoryTheory.Functor.shiftIso_zero_inv_app, CategoryTheory.Iso.isoInverseComp_inv_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_hom_app_fst_app, CategoryTheory.Functor.Monoidal.coreMonoidalTransport_εIso_inv, Action.FunctorCategoryEquivalence.counitIso_inv_app_app, Profinite.Extend.cone_π_app, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.g_app, CategoryTheory.Functor.commShift₂_comm, CategoryTheory.WithTerminal.map₂_app, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_obj, CategoryTheory.δ_naturalityₗ_assoc, CategoryTheory.Comma.mapLeftIso_functor_map_left, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.bottomMapₗ_app, CategoryTheory.Iso.map_inv_hom_id_app_assoc, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.secondMap₁_app_app_app, CategoryTheory.Pretriangulated.Triangle.functorHomMk_app_hom₂, CategoryTheory.Functor.Fiber.fiberInclusionCompIsoConst_inv_app, CategoryTheory.MonoidalCategory.associatorNatIso_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_map_app_fst, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_left, CategoryTheory.Limits.reflexivePair.mkNatIso_hom_app, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_inv_app_coe, CategoryTheory.sheafificationNatIso_inv_app_val, CategoryTheory.Limits.colimitCoyonedaHomIsoLimit'_π_apply, CategoryTheory.NatIso.cancel_natIso_inv_right_assoc, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.η_naturality_assoc, CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_eHomWhiskerRight, SSet.Subcomplex.image_obj, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_π_app_left, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_inv_app_hom_apply, CategoryTheory.Functor.cones_map_app, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₃, MonObj.mopEquivCompForgetIso_hom_app_unmop, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_inv_app_app_hom_hom, CategoryTheory.Functor.instIsIsoAppUnitLanAdjunctionOfHasPointwiseLeftKanExtension, CategoryTheory.μ_δ_app_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_inv_app_snd_app, leftOp_app, CategoryTheory.Monoidal.associator_hom_app, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app_apply, CategoryTheory.Join.isoMkFunctor_hom_app, CategoryTheory.Pseudofunctor.mapId'_inv_naturality_assoc, CategoryTheory.Equivalence.leftOp_counitIso_inv_app, CategoryTheory.TransfiniteCompositionOfShape.fac_assoc, CategoryTheory.η_ε_app_assoc, CategoryTheory.Limits.coyonedaCompLimIsoCones_inv_app, CategoryTheory.Limits.Cofork.ofCocone_ι, CategoryTheory.MonoidalClosed.coev_app_comp_pre_app, CategoryTheory.MorphismProperty.Over.pullbackComp_hom_app_left, CategoryTheory.Localization.SmallHom.equiv_equiv_symm, CategoryTheory.Functor.CommShift.isoZero_hom_app, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.isIso_hom_app, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_inv_app_op_zero, AlgebraicTopology.AlternatingFaceMapComplex.ε_app_f_succ, 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, CategoryTheory.Abelian.LeftResolution.karoubi.π_app_toKaroubi_obj, CategoryTheory.Functor.mapCommMonNatTrans_app_hom_hom, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.natTrans_app_uliftYoneda_obj, CategoryTheory.Bicategory.associatorNatIsoLeft_inv_app, CategoryTheory.Equivalence.cancel_unit_right, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one, CategoryTheory.SimplicialObject.Truncated.whiskering_map_app_app, PresheafOfModules.toSheafify_app_apply', CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_right, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app, CategoryTheory.GradedObject.mapBifunctorObjObjSingle₀Iso_hom, CategoryTheory.Functor.Monoidal.whiskerRight_app_fst_assoc, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₂, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_inv_assoc, CategoryTheory.Comma.mapRightEq_hom_app_right, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_inv_app_snd_app, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.secondMap₁_app_app_app, CategoryTheory.yonedaEquiv_apply, CategoryTheory.Monad.beckCoequalizer_desc, Rep.coinvariantsAdjunction_counit_app, CategoryTheory.coprodMonad_μ_app, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app_assoc, CategoryTheory.ComposableArrows.homMk₃_app_three, SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_inv_app, CategoryTheory.Functor.PullbackObjObj.π_fst, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.leftMapᵣ_app, CategoryTheory.Comma.mapRightIso_counitIso_inv_app_right, CategoryTheory.Enriched.FunctorCategory.isLimitConeFunctorEnrichedHom.fac, CategoryTheory.Functor.Monoidal.transport_μ, CategoryTheory.instIsIsoFunctorOppositeValAppSheafCounitSheafificationAdjunction, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_inv_app_app, CategoryTheory.OplaxFunctor.mapComp_assoc_left_app_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_hom_app, CategoryTheory.ShortComplex.rightHomologyιNatTrans_app, CategoryTheory.sum.inlCompInrCompInverseAssociator_inv_app_down_down, CategoryTheory.sheafificationNatIso_hom_app_val, CategoryTheory.StructuredArrow.map₂_map_right, CategoryTheory.Functor.commShiftIso_comp_hom_app, CategoryTheory.Comma.mapLeftEq_hom_app_left, CategoryTheory.Functor.coreId_hom_app_iso_hom, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₂_app, CategoryTheory.Paths.liftNatTrans_app, SSet.Subcomplex.topIso_inv_app_coe, CategoryTheory.Monad.monadMonEquiv_counitIso_hom_app_hom, CategoryTheory.ComposableArrows.homMk₄_app_four, mapSquare_app_τ₂, CategoryTheory.Limits.CatCospanTransform.rightUnitor_inv_base_app, CategoryTheory.constantCommuteCompose_hom_app_val, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.unit_app_ev_app_app_assoc, CategoryTheory.WithTerminal.mapComp_hom_app, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_flip_hom_app, CategoryTheory.Functor.mapTriangleCommShiftIso_inv_app_hom₁, CategoryTheory.Equivalence.cancel_counit_right, CategoryTheory.MonoidalCategory.curriedAssociatorNatIso_hom_app_app_app, CategoryTheory.CosimplicialObject.σ_naturality_assoc, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_fac_app_assoc, CategoryTheory.Limits.WidePullbackShape.functorExt_hom_app, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_inv_app_hom₂, CategoryTheory.Functor.flipping_functor_map_app_app, CategoryTheory.Functor.Monoidal.tensorObjComp_hom_app, CategoryTheory.Endofunctor.Algebra.functorOfNatTransId_inv_app_f, CategoryTheory.Functor.flip₂₃_obj_obj_map, CategoryTheory.GradedObject.mapTrifunctor_map_app_app, CategoryTheory.Cat.Hom₂.comp_app_assoc, CategoryTheory.Monad.algebraFunctorOfMonadHomId_hom_app_f, CategoryTheory.Functor.IsEventuallyConstantTo.cone_π_app, CategoryTheory.Functor.IsCoverDense.isoOver_hom_app, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.F_map, AlgebraicGeometry.Scheme.SpecΓIdentity_hom_app, CategoryTheory.Functor.currying₃_unitIso_hom_app_app_app_app, CategoryTheory.Comma.coneOfPreserves_π_app_right, CategoryTheory.Functor.FullyFaithful.compUliftCoyonedaCompWhiskeringLeft_hom_app_app_down, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_unit_app, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_π_app, CategoryTheory.Coyoneda.objOpOp_inv_app, CategoryTheory.toOverPullbackIsoToOver_inv_app_left, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_inv, CategoryTheory.Functor.opComp_inv_app, CategoryTheory.Idempotents.functorExtension_map_app, CategoryTheory.Equivalence.unitInv_naturality, partialFunEquivPointed_unitIso_inv_app, CategoryTheory.FunctorToTypes.binaryProductEquiv_apply, CategoryTheory.Monad.id_μ_app, CategoryTheory.Functor.LeftExtension.precomp_map_right, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₃, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_π_app_walkingParallelPair_one, LightCondMod.isDiscrete_tfae, SSet.opFunctorCompOpFunctorIso_hom_app_app, CategoryTheory.Limits.coprodComparisonNatTrans_app, CategoryTheory.Equivalence.functor_unit_comp, CategoryTheory.FinitaryExtensive.mono_ι, CategoryTheory.Comonad.right_counit_assoc, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app', CategoryTheory.FreeGroupoid.mapComp_hom_app, CategoryTheory.Comonad.ForgetCreatesLimits'.γ_app, CategoryTheory.SimplicialObject.Augmented.w₀, CategoryTheory.BraidedCategory.curriedBraidingNatIso_inv_app_app, CategoryTheory.Functor.RightExtension.coneAt_π_app, SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_hom_app, ModuleCat.restrictScalarsComp'_inv_app, CategoryTheory.Comma.mapRightIso_functor_map_left, CategoryTheory.μ_naturality₂_assoc, CategoryTheory.Equivalence.inv_fun_map, CategoryTheory.ComposableArrows.threeδ₂Toδ₁_app_one, TopCat.Presheaf.pushforwardToOfIso_app, SSet.Subcomplex.toRange_app_val, CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_right, CategoryTheory.Pseudofunctor.CoGrothendieck.map_map_fiber, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_right, groupHomology.coresNatTrans_app, CategoryTheory.Functor.prod'CompSnd_inv_app, CategoryTheory.Idempotents.KaroubiKaroubi.counitIso_inv_app_f_f, CategoryTheory.Presheaf.freeYonedaHomEquiv_comp, PresheafOfModules.free_map_app, CategoryTheory.SimplicialObject.σ_naturality, 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, CategoryTheory.WithInitial.opEquiv_counitIso_hom_app, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_hom_app, CategoryTheory.NatIso.ofComponents_inv_app, CategoryTheory.prodComonad_δ_app, CategoryTheory.uliftCoyonedaIsoCoyoneda_inv_app_app_down, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_hom_app_hom, CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso_hom_app, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.leftMapᵣ_app, CategoryTheory.Quotient.lift.isLift_hom, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_right, HomologicalComplex.natIsoSc'_inv_app_τ₂, CategoryTheory.Limits.Cocone.underPost_ι_app, CategoryTheory.Limits.multicospanIndexEnd_snd, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_hom_app_hom_hom_app, CategoryTheory.Limits.colimitIsoSwapCompColim_hom_app, CategoryTheory.Localization.HasProductsOfShapeAux.adj_counit_app, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_hom_app_val_app, CategoryTheory.Limits.coneOfDiagramTerminal_π_app, CategoryTheory.Functor.mapTriangleCompIso_hom_app_hom₂, CategoryTheory.Adjunction.compYonedaIso_hom_app_app, CommRingCat.coyoneda_map_app, CategoryTheory.Sieve.pullback_functorPushforward_equivalence_eq, CategoryTheory.Functor.currying_counitIso_hom_app_app, CategoryTheory.MorphismProperty.Over.mapCongr_inv_app_left, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app_assoc, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.associator_hom_unit_unit, CategoryTheory.Limits.Cotrident.π_eq_app_one, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.w_app, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_fiber, CategoryTheory.MonoidalCategory.DayFunctor.ν_comp_unitDesc_assoc, CategoryTheory.Functor.RightExtension.postcomp₁_map_right, CategoryTheory.ComposableArrows.threeδ₁Toδ₀_app_zero, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompCoyoneda, CategoryTheory.Limits.colimit.ι_map, CategoryTheory.Functor.prod'CompSnd_hom_app, CategoryTheory.Limits.cospanIsoMk_hom_app, PresheafOfModules.restrictScalarsObj_map, CategoryTheory.Iso.isoInverseComp_hom_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionActionOfMonoidalFunctorToEndofunctorIso_inv_app_app, Profinite.NobelingProof.spanFunctorIsoIndexFunctor_hom_app_hom_hom_apply_coe, CategoryTheory.Limits.piObjIso_hom_comp_π, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_left, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_map_app, CategoryTheory.Over.iteratedSliceForwardIsoPost_inv_app, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.SimplicialObject.Augmented.toArrow_map_left, CategoryTheory.Comma.mapRight_obj_hom, CategoryTheory.NatIso.naturality_1, CategoryTheory.NatIso.inv_map_inv_app, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_map_app, CategoryTheory.Comma.mapRightIso_inverse_map_right, CategoryTheory.Equivalence.core_unitIso_hom_app_iso_inv, CategoryTheory.DifferentialObject.shiftZero_hom_app_f, CategoryTheory.Functor.ranCompLimIso_inv_app, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app, CategoryTheory.MonoidalClosed.uncurry_pre_app_assoc, CategoryTheory.LaxFunctor.mapComp_naturality_left_app_assoc, CategoryTheory.Functor.ShiftSequence.induced.isoZero_hom_app_obj, CategoryTheory.Sum.functorEquiv_unit_app_app_inr, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoColimitUncurryWhiskeringLeft₂_inv_assoc, CategoryTheory.Limits.Cocone.toCostructuredArrow_map, CategoryTheory.Functor.whiskeringLeft₃_map_app_app_app_app_app_app, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε, StalkSkyscraperPresheafAdjunctionAuxs.germ_fromStalk, vcomp_app', CategoryTheory.CostructuredArrow.mapNatIso_unitIso_inv_app_left, CategoryTheory.HasShift.Induced.zero_inv_app_obj, CategoryTheory.Limits.Types.pUnitCocone_ι_app, CategoryTheory.Cat.leftUnitor_hom_app, CategoryTheory.Functor.curry₃_obj_obj_map_app, CategoryTheory.WithTerminal.mkCommaMorphism_left_app, SSet.Truncated.Path.map_arrow, CategoryTheory.ComposableArrows.threeδ₃Toδ₂_app_one, CategoryTheory.shift_shift_neg', SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_quotMk, CategoryTheory.SmallObject.functorialFactorizationData_i_app, CategoryTheory.Limits.parallelPairIsoMk_inv_app, CategoryTheory.Limits.IsColimit.mono_ι_app_of_isFiltered, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.firstMap₃_app_app_app, naturality_2_assoc, CategoryTheory.evaluationAdjunctionLeft_unit_app_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocNatIso_hom_app_app_app, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_inv_app, CategoryTheory.Sum.functorEquiv_unitIso_inv_app_app_inl, CategoryTheory.LocalizerMorphism.commShift_iso_inv_app, CategoryTheory.GradedObject.ιMapBifunctor₁₂BifunctorMapObj_eq_assoc, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality_assoc, CategoryTheory.HasShift.Induced.add_hom_app_obj, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_hom_fac_app, CategoryTheory.Limits.coend.condition, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_eq, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₁_app, CategoryTheory.CatCommSq.hComp_iso_hom_app, CategoryTheory.pullbackShiftFunctorZero_inv_app, CategoryTheory.Functor.mapTriangleRotateIso_inv_app_hom₁, CategoryTheory.Triangulated.TStructure.triangleLTGE_obj_mor₁, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompPointIso_hom_app, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app, groupHomology.π_comp_H0Iso_hom_assoc, CategoryTheory.Discrete.compNatIsoDiscrete_hom_app, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_hom_fac_app, CategoryTheory.CostructuredArrow.mapIso_unitIso_hom_app_left, SSet.Subcomplex.lift_app_coe, CategoryTheory.CatCommSq.iso_inv_naturality, Rep.resCoindAdjunction_unit_app_hom_hom, CategoryTheory.ReflQuiv.adj_unit_app, CategoryTheory.Kleisli.Adjunction.toKleisli_map, mapHomotopyCategory_app, CategoryTheory.coyonedaEquiv_comp, CategoryTheory.uliftYonedaEquiv_symm_apply_app, CategoryTheory.Functor.mapProjectiveResolution_π, CategoryTheory.Adjunction.localization_unit_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₂, app_naturality, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π, CategoryTheory.EnrichedCat.associator_inv_out_app, CategoryTheory.Limits.PushoutCocone.isoMk_inv_hom, CategoryTheory.Limits.colimitYonedaHomIsoLimit'_π_apply, CategoryTheory.Prod.symmetry_hom_app, Condensed.epi_iff_surjective_on_stonean, 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, HomologicalComplex.ι_mapBifunctorAssociatorX_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionActionOfMonoidalFunctorToEndofunctorMopIso_hom_app_unmop_app, CategoryTheory.Functor.IsRepresentedBy.of_natIso, CategoryTheory.CosimplicialObject.augment_hom_app, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_right, CategoryTheory.Limits.Cone.toStructuredArrowCompProj_inv_app, CategoryTheory.Limits.parallelPairOpIso_inv_app_one, CategoryTheory.ε_η_app_assoc, CategoryTheory.Limits.PullbackCone.mk_π_app, CategoryTheory.Join.inrCompFromSum_hom_app, CategoryTheory.Functor.flipping_inverse_obj_obj_map, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app', AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_c_app, CategoryTheory.ε_naturality_assoc, ModuleCat.restrictScalarsComp'_hom_app, LightProfinite.Extend.cocone_ι_app, CategoryTheory.Comma.toPUnitIdEquiv_counitIso_hom_app, CategoryTheory.Functor.sheafAdjunctionCocontinuous_counit_app_val, CategoryTheory.Monad.isSplitMono_iff_isIso_unit, CategoryTheory.coev_expComparison, CategoryTheory.MonoidalCategory.prodCompExternalProduct_inv_app, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.functorToInterchangeIso_inv_app_app, CategoryTheory.Functor.LeftExtension.precomp_obj_hom_app, CategoryTheory.FreeGroupoid.mapId_hom_app, CategoryTheory.Limits.IsColimit.ι_map, CategoryTheory.Functor.mapMatComp_hom_app, CategoryTheory.Limits.Types.binaryCoproductCocone_ι_app, CategoryTheory.Sigma.mapComp_hom_app, CategoryTheory.conjugateEquiv_apply_app, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_left, CategoryTheory.Monad.Algebra.assoc_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_inv_app_app_fst, AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_hom_π, CategoryTheory.LaxBraidedFunctor.isoOfComponents_hom_hom_app, AlgebraicGeometry.PresheafedSpace.componentwiseDiagram_map, AlgebraicGeometry.PresheafedSpace.stalkMap_germ_assoc, CategoryTheory.Adjunction.instIsIsoAppCounitObjOfFaithfulOfFull, CategoryTheory.Idempotents.app_p_comp, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom, CategoryTheory.Limits.compYonedaSectionsEquiv_apply_app, CategoryTheory.exp.coev_ev, CategoryTheory.Endofunctor.Algebra.functorOfNatTransComp_hom_app_f, CategoryTheory.Comma.mapSnd_inv_app, Condensed.lanPresheafExt_inv, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp, HomologicalComplex.forgetEval_hom_app, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.Pretriangulated.Triangle.functorMk_map_hom₃, CategoryTheory.Functor.compConstIso_hom_app_app, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_app_assoc, CategoryTheory.Preadditive.commGrpEquivalence_unitIso_inv_app, commBialgCatEquivComonCommAlgCat_unitIso_hom_app, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app, CategoryTheory.Functor.coreComp_hom_app_iso_hom, CategoryTheory.CatCommSq.vId_iso_hom_app, CategoryTheory.ComposableArrows.fourδ₄Toδ₃_app_two, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_inv_app_snd_app, CategoryTheory.evaluationRightAdjoint_map_app, Rep.coindFunctorIso_hom_app_hom_hom_apply_hom_hom_apply, CategoryTheory.WithTerminal.opEquiv_counitIso_inv_app, CategoryTheory.NatIso.naturality_1'_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.Codiscrete.natIsoFunctor_hom_app, CategoryTheory.Functor.flipping_counitIso_inv_app_app_app, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app, CategoryTheory.FunctorToTypes.coprod.inr_app, CategoryTheory.Under.mapCongr_inv_app, CategoryTheory.Equivalence.congrLeft_counitIso_inv_app, hcomp_app, CategoryTheory.Pseudofunctor.mapComp'_inv_naturality, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_snd, CategoryTheory.Over.postAdjunctionRight_counit_app, CategoryTheory.Over.conePost_obj_π_app, CategoryTheory.Limits.Cocone.w_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁'_map_app_app, CategoryTheory.ofTypeMonad_μ_app, CategoryTheory.Functor.curryObjProdComp_hom_app_app, CategoryTheory.RightExactFunctor.whiskeringLeft_map_app, AlgebraicGeometry.Scheme.Modules.pushforwardComp_inv_app_app, CategoryTheory.oppositeShiftFunctorAdd_inv_app, CategoryTheory.Idempotents.app_p_comm, CategoryTheory.Functor.associator_hom_app, CategoryTheory.Functor.shiftIso_zero_hom_app, CategoryTheory.Limits.inr_comp_pushoutObjIso_hom_assoc, CategoryTheory.LaxMonoidalFunctor.isoOfComponents_inv_hom_app, CategoryTheory.Functor.rightOpComp_hom_app, CategoryTheory.ShortComplex.mapToComposableArrows_app_1, CategoryTheory.obj_zero_map_μ_app_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_map_app_app, CategoryTheory.Functor.isoShift_inv_naturality_assoc, ModuleCat.HasColimit.colimitCocone_ι_app, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality_app, CategoryTheory.EnrichedCat.rightUnitor_hom_out_app, CategoryTheory.Limits.HasColimit.isoOfEquivalence_hom_π, CategoryTheory.Pretriangulated.Triangle.functorMk_map_hom₁, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_app, AlgebraicTopology.DoldKan.PInfty_f_naturality_assoc, CategoryTheory.Adjunction.Triple.adj₁_counit_app_rightToLeft_app, id_app', CategoryTheory.Subfunctor.homOfLe_app_coe, CategoryTheory.Functor.IsCoverDense.Types.appHom_valid_glue, CategoryTheory.Limits.Cofork.unop_π_app_one, AddCommGrpCat.Colimits.colimitCocone_ι_app, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_obj_obj, CategoryTheory.Functor.rightOpLeftOpIso_hom_app, PresheafOfModules.restrictScalarsObj_obj, TopCat.sigmaCofan_ι_app, HomologicalComplex.natIsoSc'_inv_app_τ₃, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap, CategoryTheory.Preadditive.commGrpEquivalence_unitIso_hom_app, AlgebraicGeometry.SheafedSpace.comp_hom_c_app, CategoryTheory.Comonad.ForgetCreatesColimits'.newCocone_ι_app, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.bottomMapₗ_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app, SSet.nonDegenerateEquivOfIso_symm_apply_coe, LightCondSet.topCatAdjunctionUnit_val_app_apply, CategoryTheory.LocalizerMorphism.Derives.isIso, CategoryTheory.Functor.postcompose₃_obj_obj_obj_map_app, CategoryTheory.Limits.piConst_map_app, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_map_hom_app, CategoryTheory.Functor.mapMonCompIso_hom_app_hom, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃'_obj_map_app, CategoryTheory.Limits.Cocone.fromCostructuredArrow_ι_app, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_fiber, CategoryTheory.Limits.Cone.fromStructuredArrow_π_app, CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_right, TopCat.Sheaf.id_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedAction_map_app, CategoryTheory.Comonad.coassoc, SimplicialObject.opFunctor_map_app, CategoryTheory.Functor.RightExtension.precomp_map_left, CategoryTheory.Limits.FormalCoproduct.cochainComplexFunctor_map_f, CategoryTheory.μ_naturalityᵣ_assoc, CategoryTheory.LaxFunctor.mapComp_assoc_right_app, CategoryTheory.Limits.Cocone.toCostructuredArrowCompProj_hom_app, CategoryTheory.Limits.pullbackObjIso_inv_comp_fst_assoc, CategoryTheory.Iso.hom_inv_id_app_app_assoc, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.unit_app_ev_app_app, CategoryTheory.Functor.functorialityCompPostcompose_hom_app_hom, Profinite.exists_locallyConstant_finite_aux, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isIso_of_subset, epi_iff_epi_app', CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app_assoc, CategoryTheory.FunctorToTypes.binaryCoproductEquiv_apply, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_mul_app, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_right_app, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₁, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_μ_unmop_app, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_unit_app, CategoryTheory.Functor.FullyFaithful.homNatIso_inv_app_down, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_symm_apply, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionUnitIso_inv, CategoryTheory.Limits.spanHomMk_app, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_app, CategoryTheory.Functor.ranCounit_app_whiskerLeft_ranAdjunction_unit_app_assoc, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_inv, CategoryTheory.Over.mapCongr_inv_app_left, CategoryTheory.ComonadHom.app_ε, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp, CategoryTheory.Limits.Types.FilteredColimit.colimit_eq_iff_aux, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.id_fst_app, HomologicalComplex.natIsoSc'_hom_app_τ₃, CategoryTheory.Limits.fiberwiseColimitLimitIso_hom_app, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTrans_obj_str, CategoryTheory.RightExactFunctor.whiskeringRight_map_app, SSet.δ_naturality_apply, CategoryTheory.Cat.freeMapIdIso_hom_app, AlgebraicGeometry.PresheafedSpace.comp_c_app, CategoryTheory.Functor.curryingFlipEquiv_symm_apply_map_app, CategoryTheory.MonoidalClosed.uncurry_pre_app, CategoryTheory.Functor.Final.extendCocone_obj_ι_app, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_hom_app_hom₃, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.uliftCoyonedaEquiv_symm_apply_app, CategoryTheory.InjectiveResolution.toRightDerivedZero_eq, CategoryTheory.Pseudofunctor.mapComp'_naturality_1, CategoryTheory.Functor.opId_hom_app, ModuleCat.RestrictionCoextensionAdj.counit'_app, PresheafOfModules.pushforward_map_app_apply', CategoryTheory.Under.lift_obj, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoColimitUncurryWhiskeringLeft₂_inv, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_hom_app_fst_app, CategoryTheory.Over.mapCongr_hom_app_left, CategoryTheory.MonoidalCategory.DayConvolution.unit_naturality_assoc, CategoryTheory.Functor.shift_map_op_assoc, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isColimit_desc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_π_app, CategoryTheory.FunctorToTypes.prodMk_snd, CategoryTheory.Equivalence.funInvIdAssoc_hom_app, CategoryTheory.Limits.ConeMorphism.w, CategoryTheory.Over.postCongr_inv_app_left, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app, CategoryTheory.Functor.opUnopIso_inv_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_η_app, CategoryTheory.ComposableArrows.homMk₂_app_two, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_hom, CategoryTheory.Functor.IsCoverDense.Types.pushforwardFamily_def, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_inv_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_inv_app, SSet.opFunctor_map, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_inv_app, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app', CategoryTheory.ihom.ev_coev_assoc, CategoryTheory.Limits.ι_comp_sigmaObjIso_inv, CategoryTheory.eqToHom_app, CategoryTheory.Monad.instReflectsColimitWalkingParallelPairParallelPairMapAAppCounitObjAOfReflectsColimitOfIsSplitPair, CategoryTheory.Limits.ι_colimitLimitIso_limit_π, CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_hom_app_unmop_unmop, CategoryTheory.WithInitial.inclLift_hom_app, CategoryTheory.OverPresheafAux.counitForward_naturality₁, CategoryTheory.MonoidalCategory.DayConvolution.whiskerLeft_comp_unit_app, CategoryTheory.Over.mapComp_hom_app_left, CategoryTheory.TransfiniteCompositionOfShape.ici_F, CategoryTheory.Monad.instPreservesColimitWalkingParallelPairParallelPairMapAAppCounitObjAOfPreservesColimitOfIsReflexivePair, CategoryTheory.Limits.walkingCospanOpEquiv_counitIso_hom_app, TopologicalSpace.Opens.mapId_hom_app, CategoryTheory.Functor.mapTriangleInvRotateIso_inv_app_hom₃, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_app, CategoryTheory.Limits.prodComparison_natural_of_natTrans_assoc, CategoryTheory.Comma.equivProd_unitIso_hom_app_left, CategoryTheory.FunctorToTypes.binaryCoproductEquiv_symm_apply, TopologicalSpace.Opens.mapComp_hom_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionUnitIso_hom, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app_assoc, CategoryTheory.SimplicialObject.Truncated.rightExtensionInclusion_hom_app, CategoryTheory.Coyoneda.objOpOp_hom_app, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst, CategoryTheory.Functor.PushoutObjObj.mapArrowRight_left, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app, CategoryTheory.Functor.unopId_inv_app, CategoryTheory.Monad.algebraFunctorOfMonadHomEq_hom_app_f, OrderHom.equivalenceFunctor_counitIso_inv_app_app, Action.FunctorCategoryEquivalence.unitIso_inv_app_hom, CategoryTheory.Functor.mapCommGrpCompIso_hom_app_hom_hom_hom, CategoryTheory.Limits.BinaryBicone.toCocone_ι_app_right, CategoryTheory.Subfunctor.nat_trans_naturality, Rep.ihom_ev_app_hom, 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, CategoryTheory.Functor.whiskeringRight₂_obj_obj_obj_map, CategoryTheory.Functor.instIsLeftKanExtensionObjLanAppLanUnit, CategoryTheory.Over.postAdjunctionLeft_unit_app_left, CategoryTheory.Limits.Types.FilteredColimit.isColimit_eq_iff, CategoryTheory.Limits.Cone.extend_π, CategoryTheory.obj_μ_app, Action.FunctorCategoryEquivalence.functor_map_app, CategoryTheory.Idempotents.functorExtension₂CompWhiskeringLeftToKaroubiIso_hom_app_app_f, CategoryTheory.Limits.Multicofork.snd_app_right_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality, CategoryTheory.μ_naturalityₗ, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_tensorHom_app, CategoryTheory.Limits.Bicone.toCone_π_app_mk, CategoryTheory.GradedObject.mapTrifunctorMapFunctorObj_map_app, CategoryTheory.Comonad.counit_naturality, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_counit_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp_val_app, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_inv_app, CompHausLike.LocallyConstant.counitApp_app, CategoryTheory.Monad.ForgetCreatesColimits.γ_app, CategoryTheory.Pseudofunctor.map₂_associator_app, CategoryTheory.GrothendieckTopology.Plus.toPlus_eq_mk, CategoryTheory.BasedNatTrans.isHomLift', CategoryTheory.Limits.spanCompIso_hom_app_zero, CategoryTheory.Functor.homObjEquiv_symm_apply_app, CategoryTheory.Functor.const.opObjUnop_hom_app, AlgebraicGeometry.LocallyRingedSpace.Γ_Spec_left_triangle, CategoryTheory.Adjunction.mkOfHomEquiv_counit_app, ModuleCat.uliftFunctorForgetIso_hom_app, CategoryTheory.Functor.prod'CompFst_hom_app, CategoryTheory.FunctorToTypes.coprod.desc_app, CategoryTheory.Functor.coreId_inv_app_iso_inv, Bipointed.swapEquiv_counitIso_hom_app_toFun, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_inv_app_hom_hom_app, AlgebraicTopology.AlternatingFaceMapComplex.map_f, 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, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, CategoryTheory.flippingIso_inv_toFunctor_obj_map_app, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_tensorDesc_app, CategoryTheory.Functor.sheafPushforwardContinuousNatTrans_app_val, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app_assoc, CategoryTheory.Sheaf.instIsIsoAppCounitConstantSheafAdjOfFaithfulOfFullConstantSheafOfIsConstant, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_iso_inv_app, app_nsmul, CategoryTheory.δ_naturalityᵣ_assoc, CategoryTheory.bifunctorComp₂₃_map_app_app, AddCommMonCat.coyonedaType_map_app, CategoryTheory.ComposableArrows.homMk₅_app_zero, CategoryTheory.LeftExactFunctor.whiskeringRight_map_app, prod_app_fst, CategoryTheory.FreeGroupoid.mapCompLift_inv_app, CategoryTheory.Limits.Fork.ι_postcompose, CategoryTheory.StructuredArrow.map₂_map_left, CategoryTheory.Limits.BinaryBicone.toCone_π_app_left, CategoryTheory.Limits.spanOp_hom_app, CategoryTheory.Limits.limitIsoSwapCompLim_hom_app, AlgebraicTopology.karoubi_alternatingFaceMapComplex_d, 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.Limits.limitIsoFlipCompLim_hom_app, Profinite.Extend.functorOp_obj, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app, CategoryTheory.Limits.coneOfDiagramInitial_π_app, CategoryTheory.Abelian.LeftResolution.π_naturality_assoc, CategoryTheory.Functor.curry₃ObjProdComp_inv_app_app_app, CategoryTheory.Limits.CategoricalPullback.mkNatIso_inv_app_snd, 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.Adjunction.unit_mono_of_L_faithful, CategoryTheory.Limits.limitCompCoyonedaIsoCone_hom_app, CategoryTheory.ComposableArrows.threeδ₂Toδ₁_app_two, CategoryTheory.MonoidalClosed.uncurry_eq, CategoryTheory.Pseudofunctor.mapComp'_inv_naturality_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionAssocIso_inv, CategoryTheory.uliftYonedaEquiv_apply, HomologicalComplex₂.flipEquivalenceUnitIso_hom_app_f_f, CategoryTheory.Limits.WidePullbackShape.mkCone_π_app, CategoryTheory.Functor.sheafPushforwardContinuous_map_val_app, CategoryTheory.Adjunction.leftAdjointUniq_hom_app_counit_assoc, CategoryTheory.Monad.ForgetCreatesLimits.newCone_π_app, CategoryTheory.Limits.spanExt_hom_app_right, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_map, comp_app_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id_app, CategoryTheory.CosimplicialObject.id_app, ModuleCat.binaryProductLimitCone_cone_π_app_right, CochainComplex.shiftFunctorZero_inv_app_f, CategoryTheory.SimplicialObject.hom_ext_iff, CategoryTheory.WithInitial.mkCommaMorphism_right_app, CategoryTheory.Limits.FormalCoproduct.powerBifunctor_map_app, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_app_π_assoc, CategoryTheory.CostructuredArrow.mapIso_functor_map_left, CategoryTheory.HasLiftingProperty.transfiniteComposition.hasLiftingProperty_ι_app_bot, CategoryTheory.shiftFunctorComm_hom_app_comp_shift_shiftFunctorAdd_hom_app, TopCat.Presheaf.comp_app, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObjObj_mon_one, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_left, CategoryTheory.Limits.Types.FilteredColimit.jointly_surjective_of_isColimit₂, CategoryTheory.left_unitality_app_assoc, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_hom_app_hom₁, CategoryTheory.μ_naturality₂, AlgebraicGeometry.Scheme.kerAdjunction_unit_app, CategoryTheory.Sigma.mapComp_inv_app, AlgebraicTopology.alternatingFaceMapComplex_map_f, CategoryTheory.Functor.flip₁₃_obj_map_app, CategoryTheory.Functor.mapCommMonNatIso_hom_app_hom_hom, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_map_left, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.secondMap₂_app_app_app, CategoryTheory.Limits.Cone.toStructuredArrowCompToUnderCompForget_hom_app, CategoryTheory.Comma.equivProd_counitIso_hom_app, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂'_obj_map_app, CategoryTheory.Limits.PullbackCone.combine_π_app, CategoryTheory.Limits.spanCompIso_inv_app_left, topCatToSheafCompHausLike_map_val_app, CategoryTheory.MorphismProperty.colimitsOfShape.of_isColimit, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone_isColimit_desc, CategoryTheory.Localization.homEquiv_eq, CategoryTheory.CategoryOfElements.CreatesLimitsAux.liftedCone_π_app_coe, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_id, CategoryTheory.prodOpEquiv_unitIso_hom_app, CategoryTheory.Adjunction.leftAdjointUniq_trans_app_assoc, LightProfinite.lightToProfinite_map_proj_eq, CategoryTheory.Functor.rightUnitor_hom_app, CategoryTheory.Comma.mapRightId_inv_app_left, CategoryTheory.PreGaloisCategory.toAut_surjective_isGalois_finite_family, vcomp_app, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp_app, CategoryTheory.Functor.FullyFaithful.compUliftYonedaCompWhiskeringLeft_inv_app_app_down, CategoryTheory.GrothendieckTopology.preservesSheafification_iff_of_adjunctions, CategoryTheory.Limits.IsColimit.ι_map_assoc, CategoryTheory.Functor.leftOpId_hom_app, CategoryTheory.Over.mapPullbackAdj_counit_app, CategoryTheory.WithTerminal.opEquiv_unitIso_hom_app, Rep.standardComplex.εToSingle₀_comp_eq, CategoryTheory.Comonad.instPreservesLimitWalkingParallelPairParallelPairMapAAppUnitObjAOfPreservesLimitOfIsCoreflexivePair, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.firstMap₁_app_app_app, CategoryTheory.PreGaloisCategory.toAut_hom_app_apply, CategoryTheory.Functor.isoShift_inv_naturality, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality_apply, CategoryTheory.Equivalence.cancel_counitInv_right, CategoryTheory.Comma.mapLeftId_hom_app_right, CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_exists, CategoryTheory.Over.postCongr_hom_app_left, CategoryTheory.Functor.PushoutObjObj.ofHasPushout_pt, CategoryTheory.Functor.postcompose₃_obj_obj_map_app_app, CategoryTheory.μ_naturalityᵣ, CategoryTheory.Adjunction.compPreadditiveYonedaIso_inv_app_app_apply, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₃, CategoryTheory.Functor.leftOpRightOpEquiv_unitIso_inv_app, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_inv_app_unop, CategoryTheory.Localization.LeftBousfield.W_adj_unit_app, CategoryTheory.GradedObject.singleCompEval_inv_app, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_app, CategoryTheory.Equivalence.changeFunctor_unitIso_hom_app, CategoryTheory.WithTerminal.opEquiv_counitIso_hom_app, CategoryTheory.Monad.instPreservesColimitWalkingParallelPairParallelPairMapAAppCounitObjAOfPreservesColimitOfIsSplitPair, CategoryTheory.ComposableArrows.opEquivalence_unitIso_inv_app, TopCat.Presheaf.pushforward_map_app, AlgebraicGeometry.ΓSpec.adjunction_counit_app', AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_inv_app, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_ihom_ev_app_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_hom_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₃, CategoryTheory.Functor.sectionsFunctor_map_coe, CommGrpCat.coyonedaType_map_app, CategoryTheory.Equivalence.map_η_comp_η, CategoryTheory.Limits.Multiequalizer.multifork_π_app_left, CategoryTheory.Cat.HasLimits.limitCone_π_app, removeLeftOp_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app_assoc, CategoryTheory.MonoidalCategory.DayConvolution.associator_inv_unit_unit, CategoryTheory.Join.pseudofunctorLeft_mapComp_hom_toNatTrans_app, CategoryTheory.Equivalence.counit_naturality_assoc, CategoryTheory.StructuredArrow.mapNatIso_functor_obj_hom, CategoryTheory.CostructuredArrow.mapIso_unitIso_inv_app_left, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObjObj_mon_mul, CategoryTheory.Limits.ConeMorphism.map_w_assoc, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_hom_app, CategoryTheory.Enriched.FunctorCategory.homEquiv_apply_π, HomologicalComplex.cyclesOpNatIso_inv_app, CategoryTheory.preadditiveYonedaMap_app, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app', CategoryTheory.MonoidalCategory.DayFunctor.equiv_counitIso_inv_app, SSet.comp_app_assoc, AddCommGrpCat.coyonedaForget_inv_app_app, CategoryTheory.Adjunction.unit_app_shift_commShiftIso_inv_app, CategoryTheory.Comma.mapRightComp_inv_app_right, CategoryTheory.SmallObject.SuccStruct.restrictionLTOfCoconeIso_inv_app, CategoryTheory.Functor.mapTriangleIso_hom_app_hom₁, CategoryTheory.Monad.left_unit, ModuleCat.restrictScalarsId'_inv_app, CategoryTheory.Pi.closedCounit_app, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_right, CategoryTheory.Functor.compFlipUncurryIso_inv_app, CategoryTheory.Functor.CommShift.ofIso_commShiftIso_hom_app, CategoryTheory.ComposableArrows.homMkSucc_app_zero, 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, CategoryTheory.OplaxFunctor.mapComp_assoc_left_app, CategoryTheory.LeftExactFunctor.whiskeringLeft_map_app, CategoryTheory.Functor.Monoidal.coreMonoidalTransport_μIso_hom, IsMonoidal.unit, CategoryTheory.Functor.lanUnit_app_app_lanAdjunction_counit_app_app, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_snd, CategoryTheory.Adjunction.compUliftCoyonedaIso_inv_app_app_down, CategoryTheory.Pretriangulated.Triangle.functorHomMk'_app_hom₃, AlgebraicTopology.DoldKan.MorphComponents.preComp_b, CategoryTheory.CosimplicialObject.σ_naturality, CategoryTheory.FunctorToTypes.naturality, app_add, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_π_app, AlgebraicTopology.DoldKan.Γ₂_obj_p_app, CategoryTheory.Limits.ι_colimMap, CategoryTheory.Functor.lanUnit_app_whiskerLeft_lanAdjunction_counit_app, CategoryTheory.Localization.Construction.NatTransExtension.app_eq, CategoryTheory.Limits.parallelPairOpIso_hom_app_one, CategoryTheory.Limits.walkingCospanOpEquiv_counitIso_inv_app, CategoryTheory.Functor.mapTriangleInvRotateIso_hom_app_hom₃, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_assoc, HomologicalComplex.natTransHomologyπ_app, groupCohomology.infNatTrans_app, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso_inv_app_f, CategoryTheory.WithInitial.mapId_inv_app, CategoryTheory.Functor.ι_colimitIsoOfIsLeftKanExtension_inv, AlgebraicGeometry.isBasis_preimage_isAffineOpen, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc, CategoryTheory.Limits.PullbackCone.op_ι_app, CategoryTheory.Functor.whiskeringLeft₃ObjObjMap_app, CategoryTheory.Functor.Monoidal.coreMonoidalTransport_εIso_hom, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_hom_app, CategoryTheory.Functor.constComp_inv_app, Rep.invariantsAdjunction_unit_app, Bipointed.swapEquiv_unitIso_inv_app_toFun, CategoryTheory.ComposableArrows.homMk₄_app_three, TopCat.Presheaf.pushforwardEq_hom_app, CategoryTheory.GradedObject.mapBifunctorRightUnitorCofan_inj, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality_app, CategoryTheory.Comonad.delta_naturality_assoc, CategoryTheory.FunctorToTypes.inv_hom_id_app_apply, CategoryTheory.ShiftMkCore.add_zero_hom_app, CategoryTheory.Idempotents.DoldKan.N₂_map_isoΓ₀_hom_app_f, CategoryTheory.Functor.liftOfIsRightKanExtension_fac_app, CategoryTheory.Sum.swapCompInl_hom_app, CategoryTheory.StructuredArrow.mapNatIso_functor_map_right, CategoryTheory.Cat.associator_inv_app, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counitIso_hom_app_tensor_assoc, CategoryTheory.Limits.MultispanIndex.multispanMapIso_inv_app, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.ι_toBase, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_hom_app_f, CategoryTheory.Bicategory.precomposing_map_app, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_apply, CategoryTheory.LocalizerMorphism.functorialRightResolutions.Φ_functor_map_ι_app, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_snd, AlgebraicGeometry.PresheafedSpace.Γ_map_op, CategoryTheory.Limits.diagramIsoCospan_hom_app, CategoryTheory.Comonad.isSplitEpi_iff_isIso_counit, AddCommGrpCat.coyonedaForget_hom_app_app_hom, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_unitIso_hom_app_f_f, CategoryTheory.Monad.comparisonForget_hom_app, CategoryTheory.Grothendieck.ιNatTrans_app_base, CategoryTheory.MonoidalOpposite.tensorIso_hom_app_unmop, CategoryTheory.Monad.algebraFunctorOfMonadHomComp_hom_app_f, CategoryTheory.Cat.rightUnitor_hom_app, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_right_app, CategoryTheory.Limits.Fork.unop_ι_app_one, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app_apply, CategoryTheory.evaluation_obj_map, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_apply_f, CategoryTheory.yonedaMon_naturality_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_map_app_app, CategoryTheory.TwistShiftData.shiftFunctorZero_hom_app, SheafOfModules.pushforwardComp_inv_app_val_app, CategoryTheory.Pi.closedUnit_app, CategoryTheory.Functor.Monoidal.transport_ε, CategoryTheory.Limits.pointwiseCocone_ι_app_app, CategoryTheory.endofunctorMonoidalCategory_associator_inv_app, app_homology, SSet.id_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_app_fst_app, CategoryTheory.Functor.currying_counitIso_inv_app_app, CategoryTheory.Functor.ihom_ev_app, CategoryTheory.Limits.Types.Colimit.ι_desc_apply', CategoryTheory.WithTerminal.inclLift_hom_app, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_unit_app, CategoryTheory.Equivalence.sheafCongrPreregular_functor_map_val_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality_assoc, CategoryTheory.Limits.FormalCoproduct.eval_map_app, CategoryTheory.LaxFunctor.mapComp_naturality_right_app_assoc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_inv_app_hom, CategoryTheory.instIsIsoAppToRightDerivedZeroOfInjective, CategoryTheory.Limits.opHomCompWhiskeringLimYonedaIsoCocones_hom_app_app_app, CategoryTheory.Functor.curry₃_obj_map_app_app, CategoryTheory.Functor.coreId_inv_app_iso_hom, CategoryTheory.Grothendieck.map_map, CategoryTheory.Functor.isoShift_hom_naturality, CategoryTheory.Adjunction.map_restrictFullyFaithful_unit_app_assoc, CategoryTheory.GradedObject.ι_mapTrifunctorMapMap_assoc, CategoryTheory.conjugateEquiv_counit_symm, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_base, CategoryTheory.GrothendieckTopology.toSheafification_app, CategoryTheory.Functor.CommShift.isoZero'_inv_app, CategoryTheory.Grothendieck.ιCompMap_inv_app_fiber, typeToPartialFunIsoPartialFunToPointed_hom_app_toFun, TopCat.Sheaf.extend_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_shift, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₁, CategoryTheory.id_app, CategoryTheory.Limits.ker.ι_app, CategoryTheory.Limits.opParallelPairIso_hom_app_zero, PartOrdEmb.Limits.CoconePt.fac_apply, HomologicalComplex.singleMapHomologicalComplex_inv_app_self, CategoryTheory.PreGaloisCategory.autIsoFibers_inv_app, CategoryTheory.Functor.Initial.extendCone_obj_π_app', CategoryTheory.Enriched.FunctorCategory.coneFunctorEnrichedHom_π_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_map_left, CategoryTheory.evaluationAdjunctionRight_counit_app_app, groupHomology.coinvariantsMk_comp_H0Iso_inv, CategoryTheory.Functor.coreprW_hom_app, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.bottomMapᵣ_app, CategoryTheory.Pseudofunctor.ObjectProperty.mapId_inv_app, CategoryTheory.Monad.comparison_obj_a, CategoryTheory.Limits.Cocone.toCostructuredArrowCompToOverCompForget_inv_app, CategoryTheory.Limits.CatCospanTransform.rightUnitor_inv_right_app, AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTrans, SSet.Subcomplex.toImage_app_coe, CategoryTheory.Limits.Cowedge.condition_assoc, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_left, CategoryTheory.Functor.natTransEquiv_symm_apply_app, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_1, CategoryTheory.CatCommSq.hId_iso_inv_app, CategoryTheory.δ_μ_app, CategoryTheory.WithTerminal.equivComma_functor_map_right, CategoryTheory.Join.mkNatTrans_app_right, 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.ComposableArrows.homMk₄_app_zero, CategoryTheory.Coyoneda.colimitCocone_ι_app, CategoryTheory.Functor.whiskeringLeft₂_obj_obj_obj_map_app, SheafOfModules.pushforwardNatTrans_id, CategoryTheory.LaxFunctor.map₂_associator_app_assoc, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_unit, CategoryTheory.Monoidal.whiskerRight_app, CategoryTheory.Functor.commShiftOfLocalization_iso_inv_app, CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id_app, CategoryTheory.Limits.ι_colimMap_assoc, CategoryTheory.Functor.uncurry_map_app, CategoryTheory.Adjunction.map_restrictFullyFaithful_counit_app, CategoryTheory.Over.forgetAdjStar_counit_app, CategoryTheory.Limits.diagramIsoParallelPair_hom_app, CommMonCat.coyonedaForget_inv_app_app, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₁, CategoryTheory.ComposableArrows.twoδ₂Toδ₁_app_zero, CategoryTheory.WithInitial.coconeEquiv_counitIso_inv_app_hom, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₃, AlgebraicGeometry.PresheafedSpace.colimitCocone_ι_app_base, removeUnop_app, CategoryTheory.Functor.commShiftOfLocalization.iso_inv_app, CategoryTheory.flipCompEvaluation_hom_app, AlgebraicGeometry.SheafedSpace.comp_c_app, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.topMapₗ_app, HomotopicalAlgebra.FibrantObject.instWeakEquivalenceHoCatAppιCompResolutionNatTrans, CategoryTheory.Functor.instIsIsoAppLanUnit, CategoryTheory.WithInitial.mkCommaMorphism_left, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_inv_assoc, CategoryTheory.coev_app_comp_pre_app, CategoryTheory.Arrow.leftToRight_app, AlgebraicGeometry.ExistsHomHomCompEqCompAux.exists_index, Action.resId_inv_app_hom, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_whiskerLeft_app, CategoryTheory.simplicialCosimplicialEquiv_unitIso_hom_app, CategoryTheory.Adjunction.leftAdjointUniq_hom_app_counit, CategoryTheory.Functor.LeftExtension.postcompose₂ObjMkIso_inv_right_app, CategoryTheory.Functor.CommShift.comp_commShiftIso_inv_app, CategoryTheory.Equivalence.counitInv_functor_comp, CategoryTheory.Limits.CompleteLattice.finiteColimitCocone_cocone_ι_app, AlgebraicTopology.DoldKan.N₁Γ₀_hom_app_f_f, CategoryTheory.Functor.sheafPushforwardContinuousCompSheafToPresheafIso_inv_app_app, CategoryTheory.yonedaMon_naturality, SSet.hom_ext_iff, CategoryTheory.MorphismProperty.Over.mapId_inv_app_left, CategoryTheory.Limits.colimitYonedaHomIsoLimit_π_apply, CategoryTheory.Functor.Monoidal.transport_δ, CategoryTheory.CosimplicialObject.Augmented.whiskering_map_app_left, AlgebraicGeometry.SheafedSpace.id_hom_c_app, CategoryTheory.Functor.inlCompSum'_hom_app, CategoryTheory.Equivalence.sheafCongrPreregular_inverse_map_val_app, CategoryTheory.GradedObject.ι_mapBifunctorRightUnitor_hom_apply, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_app, Rep.coinvariantsTensorIndNatIso_inv_app, CategoryTheory.Limits.walkingCospanOpEquiv_unitIso_inv_app, CategoryTheory.Join.mapPairComp_hom_app_right, CategoryTheory.bifunctorComp₁₂_map_app_app, CategoryTheory.Functor.sumIsoExt_inv_app_inr, AddCommGrpCat.binaryProductLimitCone_cone_π_app_left, CategoryTheory.GrothendieckTopology.W_adj_unit_app, CategoryTheory.Limits.CoconeMorphism.w_assoc, CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan_inj, CategoryTheory.Functor.instIsSplitMonoApp, CategoryTheory.Limits.coneOfCoconeLeftOp_π_app, CategoryTheory.Comonad.ComonadicityInternal.unitFork_ι, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app, CategoryTheory.SmallObject.SuccStruct.extendToSuccRestrictionLEIso_hom_app, AlgebraicGeometry.ΓSpec.adjunction_counit_app, CategoryTheory.ComonadHom.app_ε_assoc, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app_assoc, PresheafOfModules.limitCone_π_app_app, CategoryTheory.Adjunction.IsMonoidal.leftAdjoint_ε, CategoryTheory.WithInitial.liftStar_lift_map, CategoryTheory.Under.mapPushoutAdj_unit_app, CategoryTheory.MonoidalCategory.tensoringRight_δ, CategoryTheory.nerveMap_app_mk₁, CategoryTheory.OverPresheafAux.yonedaCollectionPresheafToA_app, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.secondMap₂_app_app_app, CategoryTheory.Limits.Types.isLimitEquivSections_apply, CategoryTheory.Functor.leftOpRightOpIso_hom_app, CategoryTheory.Functor.ranCompIsoOfPreserves_inv_app, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one_assoc, CategoryTheory.Comma.mapLeftComp_inv_app_left, CategoryTheory.shiftFunctorComm_hom_app_comp_shift_shiftFunctorAdd_hom_app_assoc, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_star, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv_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.Join.mapWhiskerRight_app, CategoryTheory.TwoSquare.isIso_lanBaseChange_app, CategoryTheory.Limits.CompleteLattice.colimitCocone_cocone_ι_app, CategoryTheory.ProjectiveResolution.extMk_hom, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_neg_assoc, CategoryTheory.Adjunction.isIso_counit_app_of_iso, CategoryTheory.MonoidalClosed.curry_id_eq_coev, CategoryTheory.Functor.shiftIso_add_hom_app, CategoryTheory.Functor.mapMonNatIso_hom_app_hom, CategoryTheory.presheafHom_map_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_app_fst_app, CategoryTheory.shiftFunctorAdd_inv_app_obj_of_induced, CategoryTheory.Functor.mapTriangleIso_hom_app_hom₂, CondensedMod.epi_iff_surjective_on_stonean, CategoryTheory.Limits.opParallelPairIso_hom_app_one, CategoryTheory.typeEquiv_unitIso_hom_app, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_hom_assoc, CategoryTheory.Limits.cospanCompIso_inv_app_left, CategoryTheory.Limits.CatCospanTransform.associator_hom_left_app, CategoryTheory.Functor.mapTriangleCompIso_inv_app_hom₃, CategoryTheory.OverPresheafAux.MakesOverArrow.map₁, CategoryTheory.Functor.rightOpId_inv_app, CategoryTheory.WithInitial.inclLiftToInitial_inv_app, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_unit_app_left, CategoryTheory.Limits.yonedaCompLimIsoCocones_hom_app_app, CategoryTheory.Over.starPullbackIsoStar_hom_app_left, CategoryTheory.Over.postEquiv_inverse, AlgebraicTopology.DoldKan.Γ₂N₂ToKaroubiIso_hom_app, CategoryTheory.StructuredArrow.mapNatIso_unitIso_hom_app_right, CategoryTheory.Limits.coend.condition_assoc, CategoryTheory.Adjunction.functorialityUnit_app_hom, CategoryTheory.Abelian.Ext.mapExactFunctor_hom, CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_hom_apply, CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_hom_apply, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_app, CategoryTheory.Monad.adj_unit, CategoryTheory.Comma.natTrans_app, CategoryTheory.simplicialCosimplicialEquiv_counitIso_hom_app_app, CategoryTheory.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCocone_π_app_eq_sum, CategoryTheory.Functor.mapTriangleCompIso_hom_app_hom₃, Rep.coindResAdjunction_unit_app, CategoryTheory.Limits.coneOfIsSplitMono_π_app, CategoryTheory.Limits.ι_comp_sigmaObjIso_hom, CategoryTheory.Limits.parallelPairIsoMk_hom_app, CategoryTheory.GradedObject.mapBifunctorObjSingle₀ObjIso_hom, 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, CategoryTheory.linearYoneda_map_app, CategoryTheory.Join.isoMkFunctor_inv_app, CategoryTheory.SimplicialObject.δ_naturality, 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, CategoryTheory.Limits.end_.condition, CategoryTheory.WithTerminal.coneEquiv_functor_obj_π_app_of, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_map_app_snd, CategoryTheory.Paths.liftNatIso_hom_app, CategoryTheory.WithInitial.coconeEquiv_unitIso_hom_app_hom_right, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_right, CategoryTheory.Sheaf.instMonoAppArrowPLocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, CategoryTheory.Localization.lift₂_iso_hom_app_app₂, CategoryTheory.Over.forgetMapTerminal_inv_app, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_hom_app, CategoryTheory.Limits.Concrete.isColimit_exists_rep, CategoryTheory.MorphismProperty.Over.mapCongr_hom_app_left, CategoryTheory.Functor.shiftIso_add'_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app, CategoryTheory.Functor.Monoidal.transport_μ_assoc, CategoryTheory.endofunctorMonoidalCategory_whiskerRight_app, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app, CategoryTheory.Limits.spanExt_hom_app_zero, CategoryTheory.sectionsFunctorNatIsoCoyoneda_inv_app_coe, ModuleCat.directLimitIsColimit_desc, CategoryTheory.BraidedCategory.ofBifunctor.Forward.secondMap₂_app_app_app, CondensedSet.epi_iff_surjective_on_stonean, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app, CategoryTheory.Comonad.instPreservesLimitWalkingParallelPairParallelPairMapAAppUnitObjAOfPreservesLimitOfIsCosplitPair, CategoryTheory.LaxBraidedFunctor.isoOfComponents_hom_hom_hom_app, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_inv_app_app, CategoryTheory.Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_one_app, SSet.leftUnitor_inv_app_apply, naturality_app_app_assoc, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₁, CategoryTheory.Adjunction.Triple.leftToRight_app_obj, CategoryTheory.Equivalence.sheafCongrPrecoherent_inverse_map_val_app, CategoryTheory.Preadditive.commGrpEquivalenceAux_hom_app_hom_hom_hom, CategoryTheory.Presheaf.restrictedULiftYoneda_map_app, CategoryTheory.Abelian.LeftResolution.instEpiKaroubiAppπ', CategoryTheory.Adjunction.instIsIsoAppUnitOfFullOfFaithful, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan_inv_app_app_apply_eq_id, CategoryTheory.Discrete.functorComp_hom_app, CategoryTheory.Limits.spanOp_inv_app, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom, CategoryTheory.right_unitality_app_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app_assoc, CategoryTheory.Limits.Types.Limit.map_π_apply', LightCondensed.isColimitLocallyConstantPresheafDiagram_desc_apply, CategoryTheory.Equivalence.rightOp_unitIso_hom_app, CategoryTheory.Over.conePostIso_hom_app_hom, CategoryTheory.EnrichedCat.rightUnitor_inv_out_app, CategoryTheory.Join.pseudofunctorLeft_mapComp_inv_toNatTrans_app, CategoryTheory.Limits.Cones.functoriality_obj_π_app, SSet.OneTruncation₂.ofNerve₂.natIso_hom_app_obj, CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_cancel_hom_app, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descAddMonoidHom_quotMk, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom, CategoryTheory.Limits.reflexivePair.compRightIso_hom_app, CategoryTheory.Functor.shiftIso_inv_naturality, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.secondMap₃_app_app_app, CategoryTheory.η_app_obj, CategoryTheory.MonoidalCategory.endofunctorMonoidalCategory.evaluationRightAction_actionHomRight, CategoryTheory.Functor.whiskerLeft_app, TopCat.nonempty_isLimit_iff_eq_induced, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_whiskerRight_app, CategoryTheory.MonoidalCategory.DayFunctor.equiv_counitIso_hom_app, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInrIso_inv_app_app, CategoryTheory.NatIso.mapHomologicalComplex_hom_app_f, CategoryTheory.isIso_iff_isIso_yoneda_map, CategoryTheory.Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor_assoc, CategoryTheory.Functor.whiskeringLeft₃ObjMap_app, CategoryTheory.Functor.essImage.liftFunctorCompIso_hom_app, CategoryTheory.Sheaf.natTransΓRes_app, CategoryTheory.shiftFunctorAdd'_zero_add_inv_app, CategoryTheory.ShortComplex.RightHomologyMapData.natTransApp_φH, CategoryTheory.Functor.essImage.counit_isIso, CategoryTheory.Limits.Multicofork.π_eq_app_right, CategoryTheory.MonoidalClosed.uncurry_pre, CategoryTheory.Functor.curry₃ObjProdComp_hom_app_app_app, CategoryTheory.Functor.whiskeringLeftObjIdIso_hom_app_app, CategoryTheory.BraidedCategory.curriedBraidingNatIso_hom_app_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided_map_hom_hom_app, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.secondMap_app_app_app, CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_snd_apply, CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_hom_app, CategoryTheory.Functor.mapMonNatIso_inv_app_hom, CategoryTheory.Adjunction.shift_counit_app, CategoryTheory.SimplicialObject.isoCoskOfIsCoskeletal_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_hom_app_hom_hom_app, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom, CategoryTheory.Functor.map_shift_unop, CategoryTheory.PreGaloisCategory.toAut_surjective_isGalois, CategoryTheory.CosimplicialObject.δ_naturality_assoc, CategoryTheory.Functor.IsCoverDense.presheafIso_hom_app, AlgebraicGeometry.exists_appTop_π_eq_of_isAffine_of_isLimit, CategoryTheory.TwoSquare.whiskerVertical_app, CategoryTheory.Limits.ConeMorphism.map_w, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₂, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_base, CategoryTheory.SmallObject.ε_app, CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_inv_app, SSet.Truncated.id_app, CategoryTheory.curryingIso_inv_toFunctor_obj_map_app, CategoryTheory.Functor.mapCommMonFunctor_map_app, CategoryTheory.Monad.assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_app, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_app, CategoryTheory.Adjunction.map_restrictFullyFaithful_counit_app_assoc, CategoryTheory.Iso.inv_hom_id_app_app, CategoryTheory.endofunctorMonoidalCategory_tensorMap_app, CategoryTheory.Discrete.productEquiv_counitIso_hom_app, CategoryTheory.Presheaf.app_localPreimage, CategoryTheory.Limits.limit.isoLimitCone_hom_π, CategoryTheory.Functor.LeftExtension.postcompose₂_map_right_app, SSet.RelativeMorphism.map_eq_of_mem, SSet.whiskerRight_app_apply, CategoryTheory.δ_app, CategoryTheory.Limits.pullbackConeOfRightIso_π_app_right, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_map_app_app, CategoryTheory.Join.mapIsoWhiskerRight_hom_app, CategoryTheory.ExponentiableMorphism.ev_coev, Rep.indResAdjunction_counit_app_hom_hom, CategoryTheory.Idempotents.app_p_comp_assoc, CategoryTheory.Adjunction.counit_naturality, CategoryTheory.Limits.Fork.ofι_π_app, CategoryTheory.Functor.Monoidal.whiskeringLeft_ε_app, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_iso_inv_app, CategoryTheory.ULift.equivalence_counitIso_hom_app, CategoryTheory.Functor.op_commShiftIso_hom_app_assoc, CategoryTheory.WithInitial.mkCommaObject_hom_app, CategoryTheory.Functor.FullyFaithful.compYonedaCompWhiskeringLeftMaxRight_inv_app_app, SSet.StrictSegal.spineToSimplex_map, CategoryTheory.CartesianClosed.curry_eq, SSet.rightUnitor_inv_app_apply, IsMonoidal.tensor, CategoryTheory.pullbackShiftFunctorZero'_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_inv_app, CategoryTheory.uliftYonedaEquiv_comp, CategoryTheory.CostructuredArrow.map_map_right, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app_assoc, CategoryTheory.Limits.IsLimit.hom_lift, SheafOfModules.pushforwardCongr_hom_app_val_app, CategoryTheory.Limits.coconePointwiseProduct_ι_app, CategoryTheory.ExactFunctor.whiskeringLeft_map_app, CategoryTheory.μ_naturality, CategoryTheory.Comonad.left_counit, CategoryTheory.Limits.PullbackCone.mk_π_app_right, CategoryTheory.Limits.Cofork.op_π_app_zero, ModuleCat.restrictScalarsCongr_hom_app, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.instIsIsoAppIncl, AlgebraicGeometry.Scheme.kerAdjunction_counit_app, CategoryTheory.pullbackShiftFunctorZero_hom_app, AlgebraicGeometry.opensDiagramι_app, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.inverseObj_comon_counit_app, CategoryTheory.ComposableArrows.fourδ₄Toδ₃_app_one, CategoryTheory.Monad.unit_naturality, TopologicalSpace.Opens.mapIso_inv_app, CategoryTheory.Limits.opSpan_hom_app, groupHomology.isoShortComplexH1_hom, CategoryTheory.MonoidalClosed.pre_comm_ihom_map, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃'_obj_map_app, CategoryTheory.obj_zero_map_μ_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionActionOfMonoidalFunctorToEndofunctorMopIso_inv_app_unmop_app, CategoryTheory.Iso.compInverseIso_inv_app, CategoryTheory.Adjunction.restrictFullyFaithful_homEquiv_apply, CategoryTheory.Limits.piObjIso_inv_comp_π, CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id_app, CategoryTheory.Limits.ColimitPresentation.Total.Hom.w, CategoryTheory.Limits.coneOfConeCurry_π_app, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app_assoc, AlgebraicTopology.AlternatingFaceMapComplex.ε_app_f_zero, CategoryTheory.Functor.Monoidal.whiskeringLeft_μ_app, CategoryTheory.Limits.limMap_π_assoc, 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, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom, CategoryTheory.Equivalence.unitInv_naturality_assoc, CategoryTheory.Discrete.sumEquiv_unitIso_hom_app, CategoryTheory.Functor.mapTriangle_map_hom₁, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι, CategoryTheory.BraidedCategory.ofBifunctor.Forward.secondMap₁_app_app_app, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.inverse_map_app, CategoryTheory.MonoidalClosed.curry_pre_app, CategoryTheory.Monoidal.FunctorCategory.tensorHom_app, CategoryTheory.FunctorToTypes.rightAdj_map_app, AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app, CategoryTheory.Functor.rightDerivedNatTrans_app_assoc, AlgebraicGeometry.ΓSpec.adjunction_unit_app, CategoryTheory.Monad.algebraFunctorOfMonadHomEq_inv_app_f, CommShiftCore.shift_app, CategoryTheory.Functor.homObjFunctor_map_app, whiskerLeft_app_tensor_app_assoc, PartOrdEmb.Limits.cocone_ι_app, CategoryTheory.Limits.Types.limitCone_π_app, CategoryTheory.CatCommSq.vInv_iso_hom_app, CategoryTheory.Over.mapPullbackAdj_unit_app, CategoryTheory.Functor.ShiftSequence.induced_shiftIso_hom_app_obj, Rep.coinvariantsFunctor_hom_ext_iff, CategoryTheory.Functor.ranCompIsoOfPreserves_hom_app, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.hπ, CategoryTheory.Limits.PushoutCocone.condition_zero, CategoryTheory.Subfunctor.Subpresheaf.mem_equalizer_iff, CategoryTheory.whiskeringRightCompEvaluation_inv_app, CategoryTheory.Functor.associator_inv_app, CochainComplex.mappingConeCompTriangle_mor₃_naturality, CategoryTheory.Limits.whiskeringLimYonedaIsoCones_inv_app_app, CategoryTheory.Monad.MonadicityInternal.unitCofork_π, CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp, CategoryTheory.LocalizerMorphism.homMap_apply, CategoryTheory.CostructuredArrow.mapNatIso_functor_obj_hom, CategoryTheory.typeEquiv_unitIso_inv_app, CategoryTheory.Functor.functorialityCompPrecompose_hom_app_hom, CategoryTheory.Over.mapId_inv_app_left, CategoryTheory.Comma.map_map_left, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app'_assoc, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id_app, CategoryTheory.GrothendieckTopology.Cover.multicospanComp_inv_app, CategoryTheory.MorphismProperty.Over.pullbackComp_inv_app_left, CategoryTheory.Comma.mapRightIso_functor_obj_hom, CategoryTheory.Limits.Cone.toStructuredArrowCone_π_app, TwoP.swapEquiv_unitIso_hom_app_hom_toFun, CategoryTheory.Functor.flipping_counitIso_hom_app_app_app, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_inv_app, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_app_comp_π, CategoryTheory.instMonoAppOfFunctor, CategoryTheory.Pseudofunctor.mapComp'_hom_naturality_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_map_snd_app, CategoryTheory.Comma.toIdPUnitEquiv_unitIso_inv_app_right, CategoryTheory.Pseudofunctor.mapComp'_naturality_2_assoc, CategoryTheory.Pseudofunctor.Grothendieck.categoryStruct_id_fiber, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_inv_app_app, SSet.degenerate_le_preimage, CategoryTheory.Limits.colimitCoyonedaHomIsoLimitUnop_π_apply, CategoryTheory.shiftFunctorZero_hom_app_obj_of_induced, SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_inv_app, CompHausLike.LocallyConstant.functorToPresheaves_map_app, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_hom_app, CategoryTheory.Comma.toPUnitIdEquiv_unitIso_inv_app_left, CondensedSet.topCatAdjunctionUnit_val_app_apply, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_right, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_naturality_app, Profinite.instEpiAppDiscreteQuotientCarrierToTopTotallyDisconnectedSpaceπAsLimitCone, CategoryTheory.TransfiniteCompositionOfShape.fac, CategoryTheory.Functor.isIso_ranAdjunction_unit_app_iff, CategoryTheory.FunctorToTypes.rightAdj_map_app_app, CategoryTheory.Join.mkFunctorLeft_hom_app, Rep.normNatTrans_app, CategoryTheory.GrothendieckTopology.uliftYonedaCompSheafToPresheaf_inv_app_app, CategoryTheory.CostructuredArrow.CreatesConnected.natTransInCostructuredArrow_app, CategoryTheory.CatCommSq.iso_hom_naturality, CategoryTheory.Sieve.sieveOfUliftSubfunctor_apply, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_inv_app_unmop, CategoryTheory.Equivalence.changeFunctor_counitIso_hom_app, CategoryTheory.Functor.LeftExtension.postcompose₂_obj_hom_app, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerLeftIso_hom_app, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s₀_comp_δ₁_assoc, CategoryTheory.GlueData.diagramIso_inv_app_left, CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc, CategoryTheory.Iso.map_inv_hom_id_app, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app_assoc, CategoryTheory.Iso.hom_inv_id_app, CategoryTheory.Iso.app_hom, CategoryTheory.Limits.HasLimit.isoOfEquivalence_hom_π, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_app, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π, CategoryTheory.NatIso.naturality_1_assoc, AlgebraicGeometry.SheafedSpace.ofRestrict_hom_c_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_invApp, CategoryTheory.unit_conjugateEquiv_symm, AlgebraicTopology.inclusionOfMooreComplex_app, CategoryTheory.preservesLimitNatIso_inv_app, CategoryTheory.Limits.opCompYonedaSectionsEquiv_apply_app, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app_assoc, CategoryTheory.Pretriangulated.preadditiveYoneda_homologySequenceδ_apply, CategoryTheory.Pretriangulated.Triangle.functorHomMk_app_hom₃, CategoryTheory.toPresheafToSheafCompComposeAndSheafify_app, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_map_hom, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app_assoc, CategoryTheory.Limits.Types.Colimit.ι_map_apply', CategoryTheory.Functor.whiskeringLeft₃_obj_obj_map_app_app_app_app, CategoryTheory.unit_conjugateEquiv, CategoryTheory.SimplicialObject.augment_hom_zero, CategoryTheory.Limits.PullbackCone.mk_π_app_one, CategoryTheory.GradedObject.mapBifunctorObjSingle₀ObjIso_inv, CategoryTheory.Functor.mapGrpNatIso_hom_app_hom_hom, CategoryTheory.Under.postEquiv_counitIso, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone_ι_app, CategoryTheory.Functor.whiskeringLeft₃Map_app_app, TopCat.Presheaf.app_surjective_of_stalkFunctor_map_bijective, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionActionOfMonoidalFunctorToEndofunctorIso_hom_app_app, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_right, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_inv_app_app, LightProfinite.Extend.functor_map, CategoryTheory.MonoidalClosed.curry_eq, CategoryTheory.instIsIsoAppFromLeftDerivedZeroOfProjective, CategoryTheory.Limits.PushoutCocone.ι_app_left, CategoryTheory.GrothendieckTopology.uliftYonedaCompSheafToPresheaf_hom_app_app, CategoryTheory.Functor.mapTriangleRotateIso_hom_app_hom₂, CategoryTheory.Equivalence.counitInv_app_comp_functor_map_η_inverse_assoc, CategoryTheory.GradedObject.mapTrifunctorMap_map_app_app, CategoryTheory.Over.conePost_map_hom, CategoryTheory.Under.postComp_hom_app_right, CategoryTheory.ComposableArrows.opEquivalence_functor_map_app, CategoryTheory.shiftFunctorAdd'_add_zero_inv_app, CategoryTheory.Functor.mapGrpFunctor_map_app, CategoryTheory.Functor.mapCommMonCompIso_inv_app_hom_hom, CategoryTheory.GrothendieckTopology.map_yonedaEquiv', CategoryTheory.Limits.colimit_obj_ext_iff, Rep.instEpiModuleCatAppActionCoinvariantsMk, CategoryTheory.Comonad.cofree_map_f, CategoryTheory.FreeMonoidalCategory.tensorFunc_map_app, CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id_app_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app, CategoryTheory.Functor.mapComposableArrowsObjMk₂Iso_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.LocalizerMorphism.commShift_iso_hom_app_assoc, CategoryTheory.WithInitial.coconeEquiv_functor_map_hom, CategoryTheory.Functor.flip₂₃Functor_obj_obj_obj_map, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₃, CategoryTheory.Monoidal.rightUnitor_inv_app, CategoryTheory.TwoSquare.hId_app, CategoryTheory.FinitaryPreExtensive.hasPullbacks_of_is_coproduct, CategoryTheory.eHomFunctor_map_app, CategoryTheory.Functor.liftOfIsRightKanExtension_fac_app_assoc, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_right, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInlIso_hom_app_app, CategoryTheory.WithTerminal.ofCommaMorphism_app, CategoryTheory.Adjunction.isIso_unit_app_iff_mem_essImage, CategoryTheory.Over.lift_obj, CategoryTheory.typeEquiv_counitIso_inv_app_val_app, CategoryTheory.Comonad.id_δ_app, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_inv_app_left, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, CategoryTheory.Functor.LeftExtension.postcomp₁_obj_hom_app, CategoryTheory.Functor.mapCommMonIdIso_hom_app_hom_hom, CategoryTheory.Subfunctor.preimage_obj, TopologicalSpace.Opens.overEquivalence_unitIso_hom_app_left, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_left, CategoryTheory.Iso.inv_hom_id_app_app_app, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app', CategoryTheory.WithTerminal.liftToTerminalUnique_inv_app, CategoryTheory.Functor.flippingEquiv_symm_apply_map_app, CategoryTheory.LaxMonoidalFunctor.isoOfComponents_hom_hom_app, CategoryTheory.Limits.Fork.ofCone_π, CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_left, 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, CategoryTheory.ShortComplex.homologyMap_mapNatTrans, CategoryTheory.WithTerminal.mkCommaMorphism_right, LightCondensed.forget_map_val_app, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.functor_map_hom_app, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.functorObjObj_comon_counit, CategoryTheory.yonedaMon_map_app, CategoryTheory.Functor.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, CategoryTheory.Functor.fullyFaithfulCancelRight_hom_app, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerRightIso_inv_app, AlgebraicGeometry.Scheme.AffineZariskiSite.coequifibered_iff_forall_isLocalizationAway, CategoryTheory.Functor.whiskeringLeft₃_obj_map_app_app_app_app_app, AlgebraicGeometry.exists_preimage_eq, CategoryTheory.Presheaf.imageSieve_apply, CategoryTheory.Limits.coprod.functor_map_app, CategoryTheory.Iso.compInverseIso_hom_app, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_hom_app_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_inv_app_fst_app, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_hom_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_hom_app_snd_app, pi'_app, CategoryTheory.WithInitial.equivComma_functor_map_left, AlgebraicGeometry.ΓSpec.left_triangle, CategoryTheory.Functor.mapCommGrpNatIso_inv_app_hom_hom_hom, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app_assoc, CategoryTheory.Enriched.Functor.whiskerRight_app_apply, CategoryTheory.Limits.colimitIsoSwapCompColim_inv_app, CondensedMod.hom_naturality_apply, SimplexCategory.revCompRevIso_inv_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app, CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj_inv_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_hom_app_fst_app, SimplicialObject.Splitting.ofIso_isColimit', CochainComplex.shiftShortComplexFunctor'_hom_app_τ₂, CategoryTheory.Limits.walkingSpanOpEquiv_counitIso_hom_app, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_inv_hom, CategoryTheory.CosimplicialObject.Augmented.toArrow_map_right, CategoryTheory.Limits.Types.Colimit.ι_map_apply, CategoryTheory.Functor.map₂HomologicalComplex_map_app, TopCat.uliftFunctorCompForgetIso_inv_app, CategoryTheory.Limits.Cofork.π_precompose, CategoryTheory.Functor.PushoutObjObj.isPushout, LightCondSet.instEpiTopCatAppCounitTopCatAdjunction, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₃, CategoryTheory.Limits.compCoyonedaSectionsEquiv_symm_apply_coe, CategoryTheory.Functor.OplaxMonoidal.whiskeringRight_δ_app, CategoryTheory.Enriched.Functor.functorHom_whiskerLeft_natTransEquiv_symm_app, CategoryTheory.Functor.constCompWhiskeringLeftIso_hom_app_app, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply', CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app_assoc, mapElements_map_coe, CategoryTheory.Limits.Types.limitConeIsLimit_lift_coe, CategoryTheory.Over.postComp_inv_app_left, CategoryTheory.TwoSquare.whiskerBottom_app, CategoryTheory.Pretriangulated.Triangle.π₁Toπ₂_app, CochainComplex.shiftFunctorAdd'_inv_app_f', CategoryTheory.Sigma.natTrans_app, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counit_app_assoc, CategoryTheory.Pretriangulated.Triangle.π₂Toπ₃_app, app_zero, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_app, prod'_app_fst, CategoryTheory.cosimplicialSimplicialEquiv_functor_map_app, CategoryTheory.Sieve.functorPushforward_inverse, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_right, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_fst, CategoryTheory.Functor.mapBifunctorHomologicalComplex_map_app_f_f, CategoryTheory.Functor.ShiftSequence.induced.shiftIso_hom_app_obj, CategoryTheory.Monad.mu_naturality, CategoryTheory.Functor.coreCompInclusionIso_hom_app, CategoryTheory.RanIsSheafOfIsCocontinuous.fac', AlgebraicTopology.DoldKan.N₂Γ₂ToKaroubiIso_hom_app, CategoryTheory.Over.toOverSectionsAdj_unit_app, CategoryTheory.Equivalence.changeInverse_counitIso_inv_app, CategoryTheory.Functor.Monoidal.coreMonoidalTransport_μIso_inv, CategoryTheory.SingleFunctors.postcompIsoOfIso_hom_hom_app, isIso_iff_isIso_app, CategoryTheory.Functor.commShiftIso_hom_naturality_assoc, CategoryTheory.Limits.IndObjectPresentation.yoneda_isColimit_desc, groupCohomology.resNatTrans_app, CategoryTheory.Comma.mapRightEq_inv_app_left, CategoryTheory.Iso.inv_hom_id_app_app_assoc, CategoryTheory.flippingIso_inv_toFunctor_map_app_app, CategoryTheory.shiftFunctorAdd'_zero_add_hom_app, CategoryTheory.Comonad.Coalgebra.coassoc, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app, CategoryTheory.Functor.lanCompColimIso_inv_app, CategoryTheory.Limits.opCospan_hom_app, CategoryTheory.Functor.mapTriangleCommShiftIso_hom_app_hom₃, Profinite.exists_isClopen_of_cofiltered, CategoryTheory.Adjunction.comp_counit_app, CategoryTheory.isPullback_initial_to_of_cofan_isVanKampen, CategoryTheory.Limits.Bicone.ofColimitCocone_ι, CategoryTheory.SingleFunctors.shiftIso_add_inv_app, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app'_assoc, CategoryTheory.Functor.unopOpIso_hom_app, CategoryTheory.Functor.ShiftSequence.induced_shiftIso_hom_app_obj_assoc, CategoryTheory.Localization.SmallShiftedHom.equiv_shift', CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂'_map_app_app, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.functorToInterchangeIso_hom_app_app, SSet.stdSimplex.isoNerve_hom_app_apply, CategoryTheory.ComposableArrows.homMk₅_app_two, CategoryTheory.Cat.opFunctorInvolutive_hom_app_toFunctor_map, CategoryTheory.ObjectProperty.isColocal_adj_counit_app, AlgebraicGeometry.ΓSpec.unop_locallyRingedSpaceAdjunction_counit_app', AlgebraicGeometry.LocallyRingedSpace.stalkMap_germ_assoc, TopCat.Presheaf.app_bijective_of_stalkFunctor_map_bijective, CategoryTheory.Monad.mu_naturality_assoc, CategoryTheory.functorProdFunctorEquivUnitIso_hom_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_inv_app_hom, CategoryTheory.Functor.ι_colimitIsoOfIsLeftKanExtension_hom, CategoryTheory.Functor.commShiftIso_comp_inv_app, CategoryTheory.MonoidalClosed.curry_pre_app_assoc, TwoP.swapEquiv_counitIso_inv_app_hom_toFun, CategoryTheory.Monoidal.FunctorCategory.whiskerRight_app, CategoryTheory.Adjunction.mkOfHomEquiv_unit_app, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_map_right, CategoryTheory.Functor.sumIsoExt_hom_app_inr, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocNatIso_inv_app_app_app, CategoryTheory.Functor.Monoidal.whiskerRight_app_fst, Condensed.epi_iff_locallySurjective_on_compHaus, AlgebraicTopology.DoldKan.QInfty_f_naturality_assoc, 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.Limits.limit.conePointUniqueUpToIso_hom_comp_assoc, CategoryTheory.Limits.Cofan.mk_ι_app, CategoryTheory.EnrichedFunctor.forgetId_inv_app, CategoryTheory.WithTerminal.lift_map_liftStar, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_symm_app, CategoryTheory.WithTerminal.inclLiftToTerminal_inv_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app, CategoryTheory.Limits.HasLimit.isoOfNatIso_inv_π, CategoryTheory.Adjunction.leftAdjointCompIso_inv_app, CategoryTheory.Sheaf.adjunction_counit_app_val, CategoryTheory.CatCommSq.vComp_iso_hom_app, CategoryTheory.Functor.mapCochainComplexShiftIso_inv_app_f, CategoryTheory.Under.mapCongr_hom_app, CategoryTheory.LocalizerMorphism.commShift_iso_inv_app_assoc, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_ε, CategoryTheory.LocalizerMorphism.equiv_smallHomMap', CategoryTheory.Functor.map_shiftFunctorCompIsoId_inv_app_assoc, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id_val_app, CochainComplex.shiftFunctorAdd'_inv_app_f, CategoryTheory.MonadHom.ext_iff, CategoryTheory.Functor.leftDerivedNatTrans_app_assoc, SSet.ι₁_app_fst, CategoryTheory.Sigma.descUniq_inv_app, LightCondensed.isLocallySurjective_iff_locallySurjective_on_lightProfinite, CategoryTheory.GrothendieckTopology.yonedaEquiv_comp, CategoryTheory.preservesColimitNatIso_hom_app, CategoryTheory.oppositeShiftFunctorZero_inv_app, CategoryTheory.MonoidalCategory.externalProductCompDiagIso_inv_app_app, CategoryTheory.Functor.prod'CompFst_inv_app, CategoryTheory.Limits.PushoutCocone.mk_ι_app, CategoryTheory.coyonedaEquiv_apply, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom_assoc, CategoryTheory.Functor.whiskeringLeft₂_obj_map_app_app_app, CategoryTheory.Functor.mapMonFunctor_map_app_hom, CategoryTheory.Functor.mapTriangleCommShiftIso_inv_app_hom₃, CategoryTheory.CostructuredArrow.mapIso_functor_map_right, CategoryTheory.Comonad.comparisonForget_inv_app, CategoryTheory.Equivalence.changeInverse_unitIso_inv_app, CategoryTheory.Limits.compCoyonedaSectionsEquiv_apply_app, CategoryTheory.Functor.isoSum_hom_app_inl, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_hom_app, groupHomology.d₁₀_comp_coinvariantsMk, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompPointIso_inv_app, CategoryTheory.WithTerminal.equivComma_functor_obj_hom_app, CategoryTheory.Functor.rightOpLeftOpIso_inv_app, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso_inv_app_f, CategoryTheory.Over.toOverSectionsAdj_counit_app, CategoryTheory.DinatTrans.compNatTrans_app, pointedToBipointedCompBipointedToPointedSnd_hom_app_toFun, CategoryTheory.Functor.mapMonIdIso_hom_app_hom, CategoryTheory.regularTopology.isLocallySurjective_iff, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app, CategoryTheory.Join.mapPairComp_inv_app_right, CategoryTheory.Limits.PushoutCocone.ι_app_right, CategoryTheory.CartesianClosed.uncurry_eq, CategoryTheory.Functor.map_shiftFunctorComm_assoc, CategoryTheory.WithInitial.equivComma_inverse_map_app, CategoryTheory.Triangulated.TStructure.triangleLTGE_map_hom₃, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_hom_app_coe, CategoryTheory.Functor.ShiftSequence.induced_isoShiftZero_hom_app_obj_assoc, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompYoneda, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp_assoc, CategoryTheory.forgetAdjToOver_unit_app, CategoryTheory.Adjunction.adjToComonadIso_hom_toNatTrans_app, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, CategoryTheory.Functor.IsCoverDense.Types.appHom_restrict, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.e_hom_app, CategoryTheory.EnrichedCat.associator_hom_out_app, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd, CategoryTheory.Limits.Types.binaryProductFunctor_map_app, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_inv_left_app, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_app_assoc, CategoryTheory.Over.iteratedSliceEquivOverMapIso_inv_app_left_left, SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁_hom_app_f_f, CategoryTheory.Functor.map_shiftFunctorCompIsoId_hom_app_assoc, CategoryTheory.ShiftMkCore.assoc_inv_app_assoc, ModuleCat.smulNatTrans_apply_app, CategoryTheory.Limits.PullbackCone.π_app_left, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_left, sum_app_inl, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₁, CategoryTheory.Over.iteratedSliceEquivOverMapIso_hom_app_left_left, CategoryTheory.Comma.mapLeftComp_inv_app_right, SSet.Path.map_arrow, TopCat.isClosed_iff_of_isColimit, CategoryTheory.Comma.equivProd_counitIso_inv_app, 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, CategoryTheory.Limits.Wedge.condition, CategoryTheory.Bicategory.leftUnitorNatIso_hom_app, CategoryTheory.Limits.CatCospanTransform.rightUnitor_hom_base_app, CategoryTheory.Limits.spanExt_inv_app_zero, CategoryTheory.Abelian.extFunctor_map_app, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_map_app_app, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_left, CategoryTheory.BraidedCategory.ofBifunctor.Forward.firstMap₂_app_app_app, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counitIso_hom_app, CategoryTheory.Iso.unop_hom_inv_id_app, CategoryTheory.Coyoneda.naturality, CategoryTheory.Join.mapPairLeft_inv_app, CategoryTheory.Sheaf.isLocallyInjective_iff_injective, CategoryTheory.cosimplicialSimplicialEquiv_counitIso_inv_app_app, CategoryTheory.Codiscrete.natIsoFunctor_inv_app, CategoryTheory.Functor.commShiftIso_hom_naturality, ModuleCat.uliftFunctorForgetIso_inv_app, CategoryTheory.Adjunction.Quadruple.epi_leftTriple_leftToRight_app_iff_mono_rightTriple_rightToLeft_app, CategoryTheory.Comonad.adj_counit, CategoryTheory.Functor.CommShift.comp_commShiftIso_hom_app, CategoryTheory.CosimplicialObject.Augmented.toArrow_map_left, HomologicalComplex.ι_mapBifunctorAssociatorX_hom_assoc, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_hom_hom, CategoryTheory.ComposableArrows.opEquivalence_unitIso_hom_app, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.firstMap₂_app_app_app, CategoryTheory.ComposableArrows.mapFunctorArrows_app, CategoryTheory.SimplicialObject.augment_hom_app, HomologicalComplex.ιOrZero_mapBifunctorAssociatorX_hom, CategoryTheory.TwoSquare.hComp_app, CategoryTheory.Adjunction.adjunctionOfEquivRight_unit_app, whiskerRight_app_tensor_app, CategoryTheory.Functor.mapComposableArrowsObjMk₁Iso_hom_app, CategoryTheory.Limits.Multifork.app_left_eq_ι, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_left_app, CategoryTheory.η_naturality, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_app_app_germToPullbackStalk_assoc, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverse_map_hom_app, CategoryTheory.yonedaGrp_naturality_assoc, AddCommMonCat.coyoneda_map_app, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_hom_app_app_hom_hom, CategoryTheory.Functor.isoCopyObj_inv_app, AlgebraicTopology.DoldKan.N₂Γ₂_compatible_with_N₁Γ₀, SSet.whiskerLeft_app_apply, CategoryTheory.Limits.piObjIso_hom_comp_π_assoc, AlgebraicGeometry.Scheme.restrictFunctorΓ_hom_app, CategoryTheory.Limits.limit.conePointUniqueUpToIso_inv_comp_assoc, CategoryTheory.Functor.uncurryObjFlip_inv_app, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_inv_app_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedAction_map_app, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_hom_app_app, CategoryTheory.CatCommSq.iso_inv_naturality_assoc, CategoryTheory.Limits.CatCospanTransform.leftUnitor_inv_right_app, CategoryTheory.Under.liftCone_π_app, CategoryTheory.Limits.Cocone.ofCofork_ι, CategoryTheory.TwoSquare.isIso_lanBaseChange_app_iff, CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_left, AlgebraicGeometry.instIsIsoSchemeAppUnitOppositeCommRingCatAdjunctionOfIsAffine, CategoryTheory.SmallObject.instIsIsoRightAppArrowMapToTypeOrdFunctorIterationFunctor, CategoryTheory.Pairwise.cocone_ι_app, TopCat.Sheaf.comp_app, CategoryTheory.Localization.liftNatTrans_app, naturality_app_assoc, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_inv_app_app, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_left, 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.Join.pseudofunctorRight_mapId_hom_toNatTrans_app, CategoryTheory.Under.forgetMapInitial_hom_app, Condensed.lanPresheafNatIso_hom_app, CategoryTheory.Limits.fiberwiseColim_map_app, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_map_fiber, CategoryTheory.sum.inrCompInrCompInverseAssociator_inv_app_down, AlgebraicGeometry.SheafedSpace.Γ_map, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_hom_π, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_pt, CategoryTheory.Limits.colimCompFlipIsoWhiskerColim_hom_app_app, CategoryTheory.Functor.mapHomologicalComplexIdIso_inv_app_f, CategoryTheory.Discrete.sumEquiv_counitIso_hom_app, CategoryTheory.Comma.mapRightIso_functor_map_right, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.Sieve.functorInclusion_app, CategoryTheory.Pretriangulated.shiftFunctorZero_op_hom_app, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_app_apply, SSet.comp_app, AlgebraicGeometry.Scheme.Modules.pushforwardComp_hom_app_app, CategoryTheory.Equivalence.cancel_counitInv_right_assoc, CategoryTheory.Mon.limitCone_π_app_hom, CategoryTheory.Comma.limitAuxiliaryCone_π_app, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι_assoc, CategoryTheory.prodOpEquiv_unitIso_inv_app, CategoryTheory.Functor.postcompose₃_map_app_app_app_app, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_iso_hom_app, CategoryTheory.WithInitial.equivComma_functor_map_right_app, TopCat.Presheaf.isLocallySurjective_iff, CategoryTheory.GradedObject.mapBifunctorRightUnitor_inv_apply, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply, CategoryTheory.DifferentialObject.shiftFunctorAdd_hom_app_f, 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.Over.ConstructProducts.conesEquivCounitIso_hom_app_hom_left, CategoryTheory.Functor.ranObjObjIsoLimit_inv_π_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_hom_app_app, CategoryTheory.OplaxFunctor.mapComp_assoc_right_app_assoc, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π_assoc, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_inv_hom, SheafOfModules.pushforwardCongr_inv_app_val_app, CategoryTheory.Functor.PullbackObjObj.ofHasPullback_π, CategoryTheory.Functor.FullyFaithful.whiskeringRight_preimage_app, Rep.resIndAdjunction_counit_app, AlgebraicGeometry.Scheme.Modules.mapPresheaf_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_map_right, SimplicialObject.Split.cofan_inj_naturality_symm_assoc, CochainComplex.shiftFunctorZero'_hom_app_f, CategoryTheory.Limits.fiberwiseColimitLimitIso_inv_app, CategoryTheory.MonoidalOpposite.tensorRightUnmopIso_inv_app, HomologicalComplex₂.flipEquivalenceUnitIso_inv_app_f_f, CategoryTheory.CosimplicialObject.Truncated.whiskering_obj_map_app, SimplicialObject.Splitting.ofIso_ι, CategoryTheory.MonadHom.app_η_assoc, CategoryTheory.Idempotents.whiskeringLeft_obj_preimage_app, AlgebraicGeometry.PresheafedSpace.GlueData.f_invApp_f_app_assoc, 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, CategoryTheory.Functor.Monoidal.tensorObjComp_inv_app, SSet.Truncated.Edge.map_whiskerLeft, CategoryTheory.Adjunction.functorialityCounit_app_hom, CategoryTheory.Iso.map_hom_inv_id_app, CategoryTheory.Functor.op_commShiftIso_inv_app_assoc, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.topMapᵣ_app, StalkSkyscraperPresheafAdjunctionAuxs.unit_app, Profinite.Extend.functor_obj, ModuleCat.RestrictionCoextensionAdj.unit'_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₂, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_hom_app_snd_app, CategoryTheory.Abelian.LeftResolution.instEpiKaroubiAppπObjToKaroubi, CategoryTheory.prod.prodFunctorToFunctorProdAssociator_inv_app_app, CategoryTheory.Functor.mapGrpCompIso_hom_app_hom_hom, CategoryTheory.Functor.map_shiftFunctorCompIsoId_hom_app, CategoryTheory.CategoryOfElements.map_obj_snd, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocNatIso_inv_app_app_app, CategoryTheory.Functor.mapTriangleInvRotateIso_inv_app_hom₂, CategoryTheory.Pretriangulated.Triangle.functorHomMk_app_hom₁, CategoryTheory.Functor.FullyFaithful.homNatIso'_hom_app_down, CategoryTheory.Limits.parallelPairHomMk_app, CategoryTheory.Functor.leftOpId_inv_app, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanMap_app, CategoryTheory.Functor.Initial.extendCone_map_hom, CategoryTheory.Comonad.comparisonForget_hom_app, CommShiftCore.shift_app_assoc, AlgebraicGeometry.Spec.sheafedSpaceMap_hom_c_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_inv_app_snd_app, SSet.const_app, CategoryTheory.EnrichedCat.leftUnitor_inv_out_app, CategoryTheory.ShortComplex.LeftHomologyMapData.natTransApp_φK, TopCat.Presheaf.Pushforward.comp_inv_app, CategoryTheory.WithTerminal.liftFromOverComp_hom_app, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_of, CategoryTheory.Limits.BinaryFan.π_app_right, CategoryTheory.shiftFunctorCompIsoId_add'_hom_app, CategoryTheory.ProjectiveResolution.leftDerived_app_eq, CategoryTheory.MonadHom.app_μ_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_iso_hom_app, AlgebraicGeometry.opensCone_π_app, CategoryTheory.Limits.colimitFlipIsoCompColim_hom_app, CategoryTheory.Equivalence.invFunIdAssoc_inv_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_inv_app_snd_app, CategoryTheory.Limits.colimit.isoColimitCocone_ι_inv_assoc, CategoryTheory.Monad.Algebra.assoc, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.leftUnitor_hom_unit_app, CategoryTheory.Cokleisli.Adjunction.fromCokleisli_map, CategoryTheory.SimplicialObject.instIsIsoAppUnitTruncatedCoskAdj, CategoryTheory.Limits.BinaryCofan.ι_app_right, 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.Idempotents.app_p_comm_assoc, CategoryTheory.toOverIteratedSliceForwardIsoPullback_hom_app_left, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.unitIso_hom_app_hom_app, CategoryTheory.Functor.CommShift₂.comm, MonObj.mopEquiv_counitIso_hom_app_hom_unmop, CategoryTheory.pullbackShiftFunctorAdd'_hom_app, CategoryTheory.Functor.Accessible.Limits.isColimitMapCocone.surjective, CategoryTheory.Functor.limitIsoOfIsRightKanExtension_hom_π_assoc, PresheafOfModules.freeAdjunctionUnit_app, CategoryTheory.GrothendieckTopology.toPlusNatTrans_app, CategoryTheory.ε_naturality, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv_assoc, CategoryTheory.Functor.coconeTypesEquiv_symm_apply_ι, TopologicalSpace.Opens.mapId_inv_app, mono_iff_mono_app, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_inv_app, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_counitIso_inv_app_right_app, CategoryTheory.Functor.flip₁₃Functor_obj_map_app_app, CategoryTheory.MorphismProperty.PreIndSpreads.exists_isPushout, CategoryTheory.ShortComplex.mapToComposableArrows_app_2, AlgebraicGeometry.PresheafedSpace.comp_c_app_assoc, CategoryTheory.ExponentiableMorphism.ev_coev_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_map_left_app, SSet.degenerate_app_apply, CategoryTheory.shiftFunctorZero_inv_app_shift, CategoryTheory.WithInitial.equivComma_functor_obj_hom_app, SSet.Subcomplex.preimage_obj, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_hom_c_app, CategoryTheory.Functor.essImage.unit_isIso, CategoryTheory.Limits.WalkingMultispan.functorExt_inv_app, CategoryTheory.Adjunction.commShiftIso_inv_app_counit_app_assoc, CategoryTheory.Limits.Multicofork.map_ι_app, CategoryTheory.Enriched.Functor.natTransEquiv_symm_app_app_apply, CategoryTheory.Limits.CatCospanTransform.associator_inv_left_app, CategoryTheory.Functor.CommShift.id_commShiftIso_inv_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_app_snd_app, CategoryTheory.TransfiniteCompositionOfShape.ici_isoBot, CategoryTheory.StructuredArrow.mapNatIso_inverse_obj_hom, SheafOfModules.pushforwardPushforwardAdj_unit_app_val_app, CategoryTheory.Functor.commShiftIso_inv_naturality_assoc, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₃, SSet.Truncated.HomotopyCategory.descOfTruncation_map_homMk, CategoryTheory.Endofunctor.Algebra.functorOfNatTransEq_inv_app_f, CategoryTheory.Limits.CatCospanTransform.leftUnitor_hom_left_app, CategoryTheory.GrothendieckTopology.uliftYonedaIsoYoneda_hom_app_val_app, TopCat.coinduced_of_isColimit, op_app, AlgebraicTopology.DoldKan.Γ₀_map_app, CategoryTheory.Limits.Cocone.toCostructuredArrowCocone_ι_app, CategoryTheory.SimplicialObject.comp_left_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_right, CategoryTheory.Limits.PushoutCocone.op_π_app, CategoryTheory.Equivalence.congrLeft_unitIso_inv_app, CategoryTheory.Limits.Cofork.coequalizer_ext, CategoryTheory.shiftFunctorAdd'_assoc_inv_app_assoc, CategoryTheory.Functor.LeftExtension.postcompose₂ObjMkIso_hom_right_app, CategoryTheory.Functor.curry₃_map_app_app_app, CategoryTheory.MonoidalOpposite.unmopEquiv_counitIso_hom_app, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp, CategoryTheory.Functor.sheafPushforwardContinuousComp_inv_app_val_app, CategoryTheory.exp.ev_coev, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap_assoc, SSet.Truncated.Edge.map_id, CategoryTheory.Limits.limit.lift_π_app, CategoryTheory.Limits.limit_obj_ext_iff, CategoryTheory.biconeMk_map, CategoryTheory.Comonad.map_counit_app, CategoryTheory.WithInitial.commaFromUnder_obj_hom_app, CategoryTheory.Equivalence.cancel_unit_right_assoc, CompHausLike.LocallyConstant.adjunction_left_triangle, CategoryTheory.Functor.ranCounit_app_app_ranAdjunction_unit_app_app_assoc, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app, AlgebraicTopology.DoldKan.toKaroubiCompN₂IsoN₁_hom_app, CategoryTheory.extensiveTopology.isLocallySurjective_iff, CategoryTheory.Functor.mapTriangleInvRotateIso_inv_app_hom₁, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_hom_app_app_snd, CategoryTheory.Adjunction.ε_comp_map_ε, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIso_hom_app_hom, HomologicalComplex.complexOfFunctorsToFunctorToComplex_map_app_f, CategoryTheory.Adjunction.counit_epi_of_R_faithful, CategoryTheory.Functor.curryingEquiv_symm_apply_map_app, CategoryTheory.WithTerminal.inclLift_inv_app, CategoryTheory.Join.InclLeftCompRightOpOpEquivFunctor_hom_app, CategoryTheory.Iso.isoFunctorOfIsoInverse_inv_app, CategoryTheory.Cat.opFunctorInvolutive_inv_app_toFunctor_map, CategoryTheory.Functor.leftOpRightOpEquiv_unitIso_hom_app, CategoryTheory.CostructuredArrow.mapNatIso_inverse_obj_hom, CategoryTheory.Monad.map_unit_app, CategoryTheory.Functor.Final.extendCocone_obj_ι_app', CategoryTheory.Presheaf.uliftYonedaAdjunction_homEquiv_app, CategoryTheory.Adjunction.leftAdjointUniq_trans_app, CategoryTheory.Equivalence.counitInv_app_comp_functor_map_η_inverse, CategoryTheory.flippingIso_hom_toFunctor_obj_obj_map, CategoryTheory.Limits.parallelPair.ext_hom_app, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w, 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.Equivalence.sheafCongrPreregular_counitIso_hom_app_val_app, CategoryTheory.CartesianClosed.uncurry_id_eq_ev, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, CategoryTheory.SimplicialObject.whiskering_map_app_app, CategoryTheory.Limits.reflexivePair.mkNatIso_inv_app, CategoryTheory.toOverPullbackIsoToOver_hom_app_left, CategoryTheory.Functor.flip₁₃_obj_obj_map, CategoryTheory.Monad.beckCofork_pt, CategoryTheory.Functor.RightExtension.postcomp₁_map_left_app, CategoryTheory.cones_obj_map_app, CategoryTheory.ComposableArrows.sc'Map_τ₁, CategoryTheory.shiftFunctorAdd'_add_zero_hom_app, CategoryTheory.Limits.Types.Small.limitCone_π_app, CategoryTheory.Limits.sigmaConst_map_app, CategoryTheory.Comma.toIdPUnitEquiv_counitIso_hom_app, AlgebraicTopology.DoldKan.QInfty_f_naturality, CategoryTheory.Limits.walkingSpanOpEquiv_unitIso_inv_app, removeRightOp_app, CategoryTheory.Limits.PushoutCocone.coequalizer_ext, CategoryTheory.SmallObject.πObj_ιIteration_app_right_assoc, ComplexShape.Embedding.ιTruncLENatTrans_app, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_apply, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_μIso_inv, TopCat.Presheaf.stalkFunctor_map_germ_apply, HomologicalComplex.natIsoSc'_hom_app_τ₂, CategoryTheory.LocalizerMorphism.homMap_apply_assoc, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_right_assoc, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.WithTerminal.ofCommaObject_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_obj_iso_inv, CategoryTheory.Limits.Cocones.functoriality_obj_ι_app, CategoryTheory.Limits.opCospan_inv_app, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_hom, CategoryTheory.Equivalence.congrLeft_unitIso_hom_app, SSet.Truncated.HomotopyCategory.mkNatIso_inv_app_mk, CategoryTheory.Limits.Cone.overPost_pt, CategoryTheory.Comma.mapRightComp_hom_app_left, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_left, 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.Monoidal.leftUnitor_inv_app, CategoryTheory.sum.inlCompAssociator_hom_app, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₂, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_inv_app_val_app, CategoryTheory.Functor.mapTriangleRotateIso_hom_app_hom₃, CategoryTheory.conjugateEquiv_counit, CommShiftCore.shift_app_comm_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_ε_app, CategoryTheory.Functor.Initial.limit_cone_comp_aux, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂'_map_app_app, CategoryTheory.Grpd.freeForgetAdjunction_counit_app, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.topMapᵣ_app, CategoryTheory.Functor.flippingEquiv_symm_apply_obj_map, CategoryTheory.Equivalence.unitInv_app_inverse, CategoryTheory.Equivalence.sheafCongr.functor_map_val_app, CategoryTheory.Adjunction.rightAdjointUniq_trans_app_assoc, CategoryTheory.Limits.pointwiseProductCompEvaluation_inv_app, CategoryTheory.Monad.instHasCoequalizerMapAAppCounitObjAOfHasCoequalizerOfIsSplitPair, CategoryTheory.Functor.ranObjObjIsoLimit_hom_π_assoc, CategoryTheory.Functor.sheafPushforwardContinuousComp_hom_app_val_app, CategoryTheory.Functor.flip₂₃Functor_obj_obj_map_app, congr_app, CategoryTheory.Limits.natTransIntoForgetCompFiberwiseColimit_app, CochainComplex.shiftFunctorAdd_inv_app_f, CategoryTheory.Adjunction.compPreadditiveYonedaIso_hom_app_app_apply, CategoryTheory.Limits.ι_colimitLimitIso_limit_π_assoc, CategoryTheory.Limits.IndObjectPresentation.yoneda_ι_app, TopologicalSpace.Opens.overEquivalence_counitIso_inv_app, CategoryTheory.Arrow.mapCechConerve_app, CategoryTheory.Triangulated.Octahedron.map_m₁, CategoryTheory.uncurry_pre, CategoryTheory.Limits.colimIsoFlipCompWhiskerColim_hom_app_app, CategoryTheory.Functor.Monoidal.whiskerRight_app_snd_assoc, CategoryTheory.ReflQuiv.adj_counit_app, CategoryTheory.Limits.Types.Limit.lift_π_apply, CategoryTheory.sum.inrCompInlCompAssociator_inv_app_down_down, CategoryTheory.whiskeringRightCompEvaluation_hom_app, CategoryTheory.shiftFunctorAdd_assoc_hom_app_assoc, CategoryTheory.Limits.cospanExt_inv_app_one, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_right, mapHomologicalComplex_naturality, CategoryTheory.Functor.flip₂₃Functor_map_app_app_app, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₁, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₂, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_obj, CategoryTheory.instIsIsoAppUnitReflectorAdjunctionObjEssImage, CategoryTheory.ihom.coev_naturality_assoc, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst, PresheafOfModules.toPresheaf_map_app_apply, CategoryTheory.Limits.ConeMorphism.w_assoc, CategoryTheory.Monad.free_obj_a, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₁, CategoryTheory.Limits.FormalCoproduct.cechFunctor_map_app, CategoryTheory.endofunctorMonoidalCategory_whiskerLeft_app, 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, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_inv_app, CategoryTheory.Adjunction.unit_isSplitEpi_of_L_full, CategoryTheory.Functor.commShiftOfLocalization.iso_inv_app_assoc, CategoryTheory.Sieve.sieveOfSubfunctor_apply, CategoryTheory.Limits.PullbackCone.unop_ι_app, CategoryTheory.Triangulated.SpectralObject.Hom.comm_assoc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_inv_app_hom, CategoryTheory.Functor.Monoidal.whiskeringLeft_η_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality_assoc, PresheafOfModules.Derivation'.d_app, CategoryTheory.exp.ev_coev_assoc, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_hom_right_app, CategoryTheory.Limits.FormalCoproduct.evalOp_map_app, CategoryTheory.SmallObject.SuccStruct.arrowMap_ofCocone_to_top, CategoryTheory.Limits.Multifork.toPiFork_π_app_one, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_inv_app, CategoryTheory.Functor.IsCoverDense.Types.presheafIso_inv_app, CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_none, CategoryTheory.cosimplicialSimplicialEquiv_unitIso_hom_app, CategoryTheory.Join.inclRightCompOpEquivInverse_hom_app_op, StalkSkyscraperPresheafAdjunctionAuxs.germ_fromStalk_assoc, AddCommGrpCat.Colimits.toCocone_ι_app, CategoryTheory.Limits.coconeOfDiagramTerminal_ι_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_map_fst_app, CategoryTheory.Limits.pullbackObjIso_hom_comp_fst, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.firstMap₁_app_app_app, AddCommGrpCat.Colimits.Quot.ι_desc, Preorder.coconeOfUpperBound_ι_app, CategoryTheory.Limits.cospanOp_hom_app, CategoryTheory.Sheaf.isConstant_iff_isIso_counit_app', CategoryTheory.shiftFunctorZero_hom_app_shift, CategoryTheory.Limits.asEmptyCocone_ι_app, CategoryTheory.MonadHom.app_η, ModuleCat.homEquiv_extendScalarsComp, CategoryTheory.Equivalence.changeFunctor_unitIso_inv_app, AlgebraicTopology.DoldKan.P_f_naturality_assoc, CategoryTheory.unitOfTensorIsoUnit_inv_app, CategoryTheory.Limits.Concrete.to_product_injective_of_isLimit, TopologicalSpace.Opens.overEquivalence_unitIso_inv_app_left, naturality_app, CategoryTheory.ComposableArrows.twoδ₁Toδ₀_app_one, CategoryTheory.sum.inlCompInlCompAssociator_inv_app_down, CategoryTheory.Sieve.uliftFunctorInclusion_app, skyscraperPresheafCocone_ι_app, CategoryTheory.Adjunction.CommShift.compatibilityCounit_left, CategoryTheory.Functor.flipping_unitIso_hom_app_app_app, CategoryTheory.MonoidalCategory.externalProductBifunctorCurried_map_app_app_app, CategoryTheory.Equivalence.inverseFunctorObj'_hom_app, CategoryTheory.ComposableArrows.homMkSucc_app_succ, CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_obj_hom, CategoryTheory.Join.pseudofunctorRight_mapId_inv_toNatTrans_app, CategoryTheory.Functor.op_commShiftIso_inv_app, CategoryTheory.Comma.unopFunctorCompSnd_inv_app, PresheafOfModules.map_comp, CategoryTheory.cocones_obj_map_app, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_tensorDesc_app_assoc, CategoryTheory.obj_η_app_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃'_map_app_app, CategoryTheory.Sieve.mem_functorPushforward_inverse, HomologicalComplex.mapBifunctor₂₃.d₁_eq, CategoryTheory.Functor.instIsRightKanExtensionObjRanAppRanCounit, CategoryTheory.ShiftedHom.opEquiv'_symm_apply, CategoryTheory.Comonad.coassoc_assoc, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_ihom_ev_app, AlgebraicGeometry.PresheafedSpace.map_id_c_app, CategoryTheory.ExponentiableMorphism.ev_naturality_assoc, CategoryTheory.Limits.colimitPointwiseProductToProductColimit_app, CategoryTheory.Idempotents.DoldKan.η_inv_app_f, CategoryTheory.Functor.mapTriangleIdIso_hom_app_hom₃, CategoryTheory.typeEquiv_inverse_map, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, CategoryTheory.Adjunction.Triple.adj₁_counit_app_rightToLeft_app_assoc, CategoryTheory.GrothendieckTopology.diagramPullback_app, CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id_app_assoc, CategoryTheory.IsFinitelyPresentable.exists_hom_of_isColimit, mono_iff_mono_app', CategoryTheory.SimplicialObject.Augmented.whiskering_map_app_left, CategoryTheory.Comma.coconeOfPreserves_ι_app_left, CategoryTheory.Functor.closedUnit_app_app, AlgebraicGeometry.PresheafedSpace.GlueData.f_invApp_f_app, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isIso_hom_app, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_hom_app_left, CategoryTheory.plusPlusAdjunction_counit_app_val, CategoryTheory.SmallObject.SuccStruct.extendToSuccRestrictionLEIso_inv_app, CategoryTheory.Functor.equiv_unitIso, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_symm_apply, TopologicalSpace.Opens.adjunction_counit_app_self, CategoryTheory.Subfunctor.mem_equalizer_iff, CategoryTheory.Limits.coconeOfDiagramInitial_ι_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_app, HomologicalComplex.ι_mapBifunctorMap_assoc, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_inv_app_f, CategoryTheory.uncurry_expComparison, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_obj_hom_app, CategoryTheory.GradedObject.mapBifunctor_map_app, CategoryTheory.Adjunction.adjToMonadIso_inv_toNatTrans_app, CategoryTheory.Limits.coconeFiberwiseColimitOfCocone_ι_app, CategoryTheory.Limits.limit.isoLimitCone_inv_π_assoc, CategoryTheory.Functor.whiskeringLeft₃_obj_obj_obj_map_app_app_app, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_inv_apply, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_μIso_hom, CategoryTheory.Idempotents.KaroubiUniversal₁.counitIso_hom_app_app_f, CategoryTheory.Functor.CommShift.id_commShiftIso_hom_app, groupHomology.isoShortComplexH1_inv, CategoryTheory.Limits.CatCospanTransform.associator_inv_base_app, 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, CategoryTheory.extensiveTopology.presheafIsLocallySurjective_iff, CategoryTheory.Triangulated.TStructure.triangleLTGE_map_hom₂, CategoryTheory.Coreflective.instIsIsoAppCounitCoreflectorAdjunctionA, prod_app_snd, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.coequalizer_π_app_isLocalHom, CategoryTheory.Functor.Monoidal.transport_η_assoc, CategoryTheory.Limits.ColimitPresentation.w_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_app_assoc, SheafOfModules.pushforwardComp_hom_app_val_app, CategoryTheory.Functor.flipping_functor_obj_map_app, CategoryTheory.Bicategory.postcomposing_map_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_inv_app, CategoryTheory.ComposableArrows.threeδ₁Toδ₀_app_two, CategoryTheory.Adjunction.functorialityUnit'_app_hom, AlgebraicTopology.DoldKan.toKaroubiCompN₂IsoN₁_inv_app, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_unitIso_inv_app_f, CategoryTheory.Pseudofunctor.mapComp'_hom_naturality, CategoryTheory.Idempotents.KaroubiUniversal₁.counitIso_inv_app_app_f, CategoryTheory.Functor.LaxMonoidal.whiskeringRight_μ_app, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app, CategoryTheory.StructuredArrow.map_map_left, CategoryTheory.GradedObject.mapBifunctorObjObjSingle₀Iso_inv, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_left, TopCat.Presheaf.Pushforward.id_hom_app, CategoryTheory.MonoidalClosed.uncurry_ihom_map, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_hom_app_hom₂, CategoryTheory.Grothendieck.map_obj_fiber, TopCat.Presheaf.pullback_obj_obj_ext_iff, CategoryTheory.Endofunctor.Algebra.functorOfNatTrans_map_f, CategoryTheory.Bicategory.rightUnitorNatIso_inv_app, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd, CategoryTheory.Functor.flipIsoCurrySwapUncurry_hom_app_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso_hom_app_app, CategoryTheory.Limits.CategoricalPullback.mkNatIso_hom_app_snd, CategoryTheory.SingleFunctors.postcomp_shiftIso_inv_app, CategoryTheory.shiftFunctorAdd_assoc_inv_app_assoc, CategoryTheory.Functor.mapCone₂_π_app, AlgebraicGeometry.Scheme.ofRestrict_toLRSHom_c_app, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc, CategoryTheory.Limits.Cones.functoriality_map_hom, CategoryTheory.FreeGroupoid.mapId_inv_app, CategoryTheory.Limits.limitFlipIsoCompLim_inv_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_hom_app, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_app_hom, CategoryTheory.toOverIsoToOverUnit_hom_app_left, LightCondMod.LocallyConstant.instIsIsoLightCondSetMapForgetAppLightCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, CategoryTheory.Adjunction.compYonedaIso_inv_app_app, CategoryTheory.MonoidalClosed.uncurry_id_eq_ev, CategoryTheory.Equivalence.changeInverse_counitIso_hom_app, CategoryTheory.Functor.leftUnitor_inv_app, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₃, CategoryTheory.Limits.HasLimit.isoOfNatIso_hom_π_assoc, CategoryTheory.Functor.mapTriangleRotateIso_hom_app_hom₁, CategoryTheory.Functor.coreCompInclusionIso_inv_app, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_obj_map_app, SSet.Subcomplex.image_ofSimplex, CategoryTheory.BraidedCategory.tensorLeftIsoTensorRight_hom_app, CategoryTheory.Sheaf.adjunction_unit_app_val, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.sq, SSet.Truncated.HomotopyCategory.homToNerveMk_app_one, CategoryTheory.FreeGroupoid.liftNatIso_inv_app, CategoryTheory.Coyoneda.colimitCoconeIsColimit_desc, CategoryTheory.Comma.mapLeftEq_hom_app_right, TopCat.Presheaf.app_injective_of_stalkFunctor_map_injective, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_pos, CategoryTheory.Functor.const_map_app, CategoryTheory.Endofunctor.Algebra.functorOfNatTransId_hom_app_f, CategoryTheory.GradedObject.ι_mapBifunctorMapMap_assoc, CategoryTheory.Functor.opInv_map, CategoryTheory.Equivalence.fun_inv_map, CategoryTheory.StructuredArrow.mapIso_unitIso_inv_app_right, CategoryTheory.Functor.whiskeringRight₂_map_app_app_app, CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_left, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π_assoc, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app_assoc, CategoryTheory.Functor.mapTriangleIso_hom_app_hom₃, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_π_app, CategoryTheory.MonoidalOpposite.tensorLeftUnmopIso_hom_app, CategoryTheory.MonoidalCategory.DayConvolution.braidingInvCorepresenting_app, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.flipFunctorToInterchange_inv_app_app, CategoryTheory.Limits.spanCompIso_hom_app_right, SimplicialObject.Splitting.cofan_inj_comp_app, CategoryTheory.Functor.lanUnit_app_whiskerLeft_lanAdjunction_counit_app_assoc, whiskerLeft_app_tensor_app, Rep.invariantsAdjunction_counit_app_hom, CategoryTheory.Triangulated.TStructure.triangleLTGE_obj_mor₃, CategoryTheory.Functor.ihom_coev_app, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₁, CategoryTheory.comp_app, LightProfinite.Extend.functorOp_map, CategoryTheory.Presieve.FamilyOfElements.map_apply, CategoryTheory.Monoidal.Reflective.instIsIsoAppUnitObjIhom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality_assoc, CategoryTheory.Functor.const.opObjOp_hom_app, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₂, MonObj.mopEquivCompForgetIso_inv_app_unmop, CategoryTheory.CosimplicialObject.augment_hom_zero, CategoryTheory.Functor.rightDerivedNatTrans_app, tensor_naturality_assoc, CategoryTheory.Functor.sumIsoExt_inv_app_inl, CategoryTheory.MonoidalCategory.externalProductFlip_hom_app_app_app_app, retractArrowApp_r, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s₀_comp_δ₁, CategoryTheory.toSheafification_app, SSet.nonDegenerate_iff_of_isIso, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_hom_app_fst_app, CategoryTheory.TransfiniteCompositionOfShape.ici_isColimit, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app_assoc, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality, CategoryTheory.Limits.colimit.ι_desc_apply, Alexandrov.lowerCone_π_app, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_fst, AlgebraicTopology.DoldKan.Γ₀.map_app, AlgebraicGeometry.PresheafedSpace.stalkMap_germ_apply, CategoryTheory.extendCofan_ι_app, CategoryTheory.MonoidalCategory.externalProductBifunctorCurried_obj_obj_map_app, CategoryTheory.Comma.opFunctorCompSnd_hom_app, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π, CategoryTheory.Localization.SmallShiftedHom.equiv_shift, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map_d, CategoryTheory.Functor.shiftIso_hom_naturality_assoc, CategoryTheory.WithInitial.opEquiv_counitIso_inv_app, CategoryTheory.ShiftMkCore.add_zero_inv_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_obj, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.leftMapₗ_app, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_snd_coe, CategoryTheory.HasShift.Induced.zero_hom_app_obj, Bipointed.swapEquiv_counitIso_inv_app_toFun, CategoryTheory.Functor.Monoidal.tensorHom_app_fst, CategoryTheory.Limits.coneLeftOpOfCocone_π_app, AlgebraicTopology.DoldKan.natTransP_app, CategoryTheory.CosimplicialObject.Augmented.toArrow_obj_hom, CategoryTheory.StructuredArrow.mapIso_functor_map_left, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.e_inv_app, CategoryTheory.Functor.sheafPushforwardContinuousId_hom_app_val_app, ModuleCat.binaryProductLimitCone_cone_π_app_left, CategoryTheory.Functor.flipping_unitIso_inv_app_app_app, SSet.Truncated.comp_app_assoc, CategoryTheory.liftedLimitMapsToOriginal_inv_map_π, CategoryTheory.Subfunctor.Subpresheaf.IsGeneratedBy.image, SSet.Truncated.Edge.map_tensorHom, PresheafOfModules.pushforward_obj_obj, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_inv_app_one, CategoryTheory.Adjunction.shift_unit_app, CategoryTheory.Join.inclLeftCompOpEquivInverse_inv_app_op, CategoryTheory.Adjunction.map_η_comp_η_assoc, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app_assoc, 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', TopCat.continuous_iff_of_isColimit, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.secondMap₂_app_app_app, CategoryTheory.Sigma.inclCompMap_hom_app, CategoryTheory.Limits.KernelFork.app_one, CondensedSet.topCatAdjunctionUnit_val_app, CategoryTheory.Functor.sheafPushforwardContinuousId'_inv_app_val_app, CategoryTheory.instEpiAppOfFunctor, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso_hom_app_f, CategoryTheory.NatIso.hom_app_isIso, LightCondensed.hom_ext_iff, CategoryTheory.CostructuredArrow.preFunctor_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app_assoc, CategoryTheory.Limits.Fork.app_zero_eq_ι, CategoryTheory.uliftYoneda_map_app, CategoryTheory.Limits.Cones.postcomposeComp_inv_app_hom, CategoryTheory.Preadditive.commGrpEquivalenceAux_inv_app_hom_hom_hom, CategoryTheory.Limits.limit.cone_π, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_obj_hom_app, CategoryTheory.Comma.mapLeftIso_inverse_obj_hom, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_hom_app_val_app_apply, CategoryTheory.Functor.Monoidal.whiskerLeft_app_snd, CategoryTheory.Limits.Types.Colimit.ι_desc_apply, CategoryTheory.Functor.uliftYonedaReprXIso_hom_app, CategoryTheory.Functor.whiskeringLeft₂_map_app_app_app_app, naturality_1_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app, CategoryTheory.Limits.limit.lift_π_apply, CategoryTheory.Adjunction.inv_counit_map, pointedToBipointedCompBipointedToPointedSnd_inv_app_toFun, CategoryTheory.equivYoneda_hom_app, CategoryTheory.Monad.FreeCoequalizer.bottomMap_f, CategoryTheory.Functor.HomObj.map_app, CategoryTheory.Limits.parallelPairHom_app_one, TopCat.Presheaf.presheafEquivOfIso_unitIso_inv_app_app, CategoryTheory.unit_mateEquiv_symm, CategoryTheory.Enriched.FunctorCategory.functorEnrichedComp_app, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁'_obj_map_app, CategoryTheory.Comma.mapLeftId_hom_app_left, CategoryTheory.Presieve.FamilyOfElements.IsAmalgamation.compPresheafMap, CategoryTheory.Limits.pullbackConeOfRightIso_π_app_left, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_left_assoc, CategoryTheory.MonoidalOpposite.mopMopEquivalence_counitIso_inv_app, ProfiniteGrp.cone_π_app, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd, CategoryTheory.ComposableArrows.fourδ₂Toδ₁_app_three, CategoryTheory.Limits.Cone.toStructuredArrowCompProj_hom_app, CategoryTheory.Limits.Trident.ofCone_π, CategoryTheory.Triangulated.SpectralObject.distinguished', CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop_assoc, CategoryTheory.Functor.curryingEquiv_apply_map, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₂, CategoryTheory.Limits.Cocone.w, app_sum, CategoryTheory.Functor.flip₁₃Functor_obj_obj_map_app, CategoryTheory.Functor.Monoidal.commTensorLeft_inv_app, CategoryTheory.Limits.Types.Small.limitConeIsLimit_lift, CategoryTheory.Adjunction.Triple.epi_rightToLeft_app_iff, CategoryTheory.Join.mapPairId_inv_app, CategoryTheory.Functor.const.opObjOp_inv_app, CategoryTheory.Pseudofunctor.map₂_left_unitor_app, CategoryTheory.Limits.prodComparison_natural_of_natTrans, CategoryTheory.MonoidalCategory.Functor.curriedTensorPreIsoPost_hom_app_app, CategoryTheory.Iso.core_hom_app_iso_inv, 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, CategoryTheory.Functor.commShiftOfLocalization.iso_hom_app, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_right, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_map_fst_app, CategoryTheory.Comonad.delta_naturality, SSet.Subcomplex.homOfLE_app_val, CategoryTheory.Functor.mapMonIdIso_inv_app_hom, CategoryTheory.Functor.fun_inv_map, CategoryTheory.Iso.isoCompInverse_inv_app, app_shift_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality, CategoryTheory.Functor.postcompose₂_obj_map_app_app, CategoryTheory.Tor'_obj_map, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_app_assoc, CategoryTheory.GradedObject.comapEq_hom_app, CategoryTheory.sum.inrCompAssociator_hom_app_down_down, CategoryTheory.Limits.limit.conePointUniqueUpToIso_hom_comp, CategoryTheory.SingleObj.natTrans_app, CategoryTheory.cosimplicialSimplicialEquiv_unitIso_inv_app, AlgebraicTopology.DoldKan.Q_f_naturality_assoc, CategoryTheory.Limits.pullbackObjIso_hom_comp_fst_assoc, CategoryTheory.Functor.mapCone_π_app, CategoryTheory.yonedaMap_app_apply, CategoryTheory.ε_app_obj, CategoryTheory.Functor.toSheafify_pullbackSheafificationCompatibility, AlgebraicGeometry.SheafedSpace.comp_hom_c_app', CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_right_assoc, SimplexCategory.revCompRevIso_hom_app, CategoryTheory.Functor.IsCoverDense.Types.naturality_apply, CategoryTheory.Iso.hom_inv_id_app_assoc, CategoryTheory.MonoidalOpposite.tensorRightIso_hom_app_unmop, SimplicialObject.opFunctorCompOpFunctorIso_hom_app_app, CategoryTheory.Limits.WidePushoutShape.mkCocone_ι_app, MonObj.mopEquiv_unitIso_hom_app_hom, CategoryTheory.Pseudofunctor.ObjectProperty.mapId_hom_app, pointedToBipointedCompBipointedToPointedFst_inv_app_toFun, CategoryTheory.Iso.isoInverseOfIsoFunctor_inv_app, CategoryTheory.Comonad.comparison_map_f, CategoryTheory.SmallObject.SuccStruct.ofCocone_map_to_top, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_π_app, CategoryTheory.Pretriangulated.Triangle.π₃Toπ₁_app, CategoryTheory.Functor.commShiftIso_id_hom_app, CategoryTheory.Grothendieck.ιCompMap_inv_app_base, CategoryTheory.ComposableArrows.whiskerLeftFunctor_map_app, CategoryTheory.Over.conePostIso_inv_app_hom, CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair_inv_app, CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id_app, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_mapPullbackAdj_unit_app, CategoryTheory.Functor.shiftIso_hom_app_comp_assoc, CategoryTheory.Sheaf.coneΓ_π_app, CategoryTheory.SimplicialObject.Truncated.trunc_map_app, CategoryTheory.Comonad.ComonadicityInternal.main_pair_coreflexive, SSet.stdSimplex.objEquiv_symm_comp, CategoryTheory.SimplicialObject.Augmented.w₀_assoc, CategoryTheory.Functor.Fiber.inducedFunctorCompIsoSelf_hom_app, CategoryTheory.Functor.curryObjCompIso_inv_app_app, CategoryTheory.Adjunction.Triple.leftToRight_app_map_adj₁_unit_app_assoc, CategoryTheory.Equivalence.core_counitIso_hom_app_iso_hom, CategoryTheory.Subfunctor.range_obj, TopCat.Presheaf.germ_stalkPullbackHom_assoc, CategoryTheory.Equivalence.inv_fun_map_assoc, CategoryTheory.GradedObject.mapBifunctorMap_map_app, AlgebraicGeometry.LocallyRingedSpace.Γ_map, CategoryTheory.Discrete.natIso_hom_app, CategoryTheory.Equivalence.inverse_counitInv_comp_assoc, CategoryTheory.GrothendieckTopology.Cover.multicospanComp_hom_app, CategoryTheory.Functor.mapCommGrpIdIso_hom_app_hom_hom_hom, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_inv_app_val_app, CategoryTheory.LaxBraidedFunctor.isoOfComponents_inv_hom_app, HomotopicalAlgebra.CofibrantObject.HoCat.adjCounitIso_inv_app, CategoryTheory.ComposableArrows.scMap_τ₃, HomologicalComplex.natTransOpCyclesToCycles_app, CategoryTheory.WithTerminal.commaFromOver_obj_hom_app, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransEq_hom_app_f, CategoryTheory.obj_μ_inv_app, ModuleCat.ihom_coev_app, CategoryTheory.Limits.colimit.ι_desc, appHom_apply, CategoryTheory.Limits.coneOfConeUncurry_π_app, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app, mapElements_obj, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinset_map_app, CategoryTheory.Functor.leftOpComp_inv_app, CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj_obj_p, tensor_naturality, Rep.coinvariantsTensorIndNatIso_hom_app, CategoryTheory.Functor.CommShift.ofIso_commShiftIso_inv_app, CategoryTheory.Comma.opFunctorCompFst_hom_app, CategoryTheory.ComposableArrows.fourδ₂Toδ₁_app_zero, CategoryTheory.Limits.Types.jointly_surjective_of_isColimit, LightCondSet.hom_naturality_apply, CategoryTheory.ComposableArrows.δlastFunctor_map_app, SSet.Truncated.mapHomotopyCategory_obj, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMop_map_unmop_app, CategoryTheory.Comma.toPUnitIdEquiv_unitIso_hom_app_left, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₃, AlgebraicGeometry.LocallyRingedSpace.stalkMap_germ_apply, CategoryTheory.CatCommSq.vInv_iso_inv_app, CategoryTheory.Functor.LaxMonoidal.whiskeringRight_ε_app, CochainComplex.shiftFunctorZero'_inv_app_f, CategoryTheory.Limits.Multicofork.fst_app_right, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse_assoc, CommGrpCat.coyonedaForget_hom_app_app_hom, HomotopicalAlgebra.CofibrantObject.HoCat.adjUnit_app, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv', CategoryTheory.Functor.constCompEvaluationObj_inv_app, CategoryTheory.oppositeShiftFunctorZero_hom_app, CategoryTheory.Comma.mapRightIso_unitIso_hom_app_left, HomologicalComplex.singleMapHomologicalComplex_inv_app_ne, 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.fiberwiseColimCompEvaluationIso_hom_app, CategoryTheory.Limits.Fork.op_ι_app, AlgebraicGeometry.AffineSpace.functor_map_app, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.c_iso, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counitIso_hom_app_assoc, CategoryTheory.functorProdFunctorEquivCounitIso_inv_app_app, SSet.Truncated.Edge.map_edge, CategoryTheory.Functor.Monoidal.tensorHom_app_snd, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.iso_hom_naturality_assoc, CategoryTheory.Functor.IsEventuallyConstantTo.isIso_π_of_isLimit, CategoryTheory.Join.mkNatTrans_app_left, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.bottomMapᵣ_app, CategoryTheory.associativity_app_assoc, CategoryTheory.Limits.ColimitPresentation.Total.Hom.w_assoc, CategoryTheory.TwoSquare.whiskerLeft_app, CategoryTheory.Functor.pointwiseRightKanExtensionCounit_app, CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_cancel_inv_app, CategoryTheory.endofunctorMonoidalCategory_leftUnitor_hom_app, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₁, CategoryTheory.Limits.Bicone.toCocone_ι_app, CategoryTheory.Functor.lanCompIsoOfPreserves_inv_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_app, CategoryTheory.Limits.Trident.ofι_π_app, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_inv_comp_π, CategoryTheory.Equivalence.map_η_comp_η_assoc, CategoryTheory.Comma.opFunctorCompFst_inv_app, CategoryTheory.Limits.cospanExt_hom_app_one, CategoryTheory.Limits.coend.ι_map, CategoryTheory.WithInitial.inclLift_inv_app, HomotopyCategory.composableArrowsFunctor_map, CategoryTheory.Limits.ι_comp_sigmaObjIso_hom_assoc, CategoryTheory.Functor.flip_obj_map, CategoryTheory.Limits.diagramIsoParallelFamily_hom_app, CategoryTheory.Functor.coreId_hom_app_iso_inv, CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ, CategoryTheory.SimplicialObject.δ_naturality_assoc, CategoryTheory.Functor.mapTriangleCompIso_inv_app_hom₁, CategoryTheory.Limits.Concrete.surjective_π_app_zero_of_surjective_map, CategoryTheory.Functor.pi'CompEval_inv_app, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_app_assoc, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc, CategoryTheory.Monad.algebraFunctorOfMonadHom_obj_a, CategoryTheory.ComposableArrows.sc'Map_τ₃, AlgebraicTopology.DoldKan.natTransPInfty_f_app, CategoryTheory.Bicategory.associatorNatIsoMiddle_hom_app, CondensedSet.isDiscrete_tfae, CategoryTheory.Under.postMap_app, pointedToBipointedCompBipointedToPointedFst_hom_app_toFun, Profinite.exists_locallyConstant, CategoryTheory.simplicialCosimplicialEquiv_functor_map_app, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.functor_map_app_hom, CategoryTheory.Functor.leftOpRightOpEquiv_counitIso_hom_app_app, CategoryTheory.CatCommSq.hComp_iso_inv_app, CategoryTheory.Limits.Trident.equalizer_ext, CategoryTheory.OverPresheafAux.MakesOverArrow.app, CategoryTheory.Pseudofunctor.map₂_whisker_right_app_assoc, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app_apply, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_inr, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_π_app, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp, CategoryTheory.ExactFunctor.whiskeringRight_map_app, CategoryTheory.DifferentialObject.shiftFunctorAdd_inv_app_f, CategoryTheory.shiftFunctorAdd_add_zero_inv_app, CategoryTheory.Monad.beckCofork_π, CategoryTheory.extendFan_π_app, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInrIso_hom_app_app, CategoryTheory.ShortComplex.rightHomologyFunctorOpNatIso_hom_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_μ_app, CategoryTheory.Functor.currying_unitIso_inv_app_app_app, CategoryTheory.coreFunctor_map_app_iso_inv, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_hom_app_hom, Rep.coinvariantsMk_app_hom, CategoryTheory.OverPresheafAux.OverArrows.app_val, CategoryTheory.Functor.coconeTypesEquiv_apply_ι_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map_val_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_δ_unmop_app, CategoryTheory.Pretriangulated.Triangle.functorMk_map_hom₂, AlgebraicTopology.NormalizedMooreComplex.map_f, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc, CategoryTheory.instIsIsoAppToRightDerivedZero, CategoryTheory.Functor.currying_unitIso_hom_app_app_app, CategoryTheory.evaluationUncurried_map, CategoryTheory.coprodMonad_η_app, CategoryTheory.Discrete.productEquiv_counitIso_inv_app, CategoryTheory.Equivalence.counitIso_inv_app_comp_functor_map_η_inverse_assoc, Rep.indCoindNatIso_inv_app, CategoryTheory.Join.pseudofunctorRight_mapComp_hom_toNatTrans_app, CategoryTheory.MonoidalCategory.curriedAssociatorNatIso_inv_app_app_app, CategoryTheory.Iso.unop_hom_inv_id_app_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_assoc, CategoryTheory.Limits.Cocone.w_apply, AlgebraicGeometry.Scheme.Modules.pushforwardId_hom_app_app, pi_app, CategoryTheory.Limits.BinaryBicone.ofLimitCone_snd, CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id_app, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app, CategoryTheory.WithInitial.inclLiftToInitial_hom_app, PresheafOfModules.restriction_app, CategoryTheory.η_app, CategoryTheory.ShiftedHom.opEquiv_symm_apply_comp, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_obj_map_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app, AlgebraicGeometry.ExistsHomHomCompEqCompAux.ha, AlgebraicTopology.DoldKan.Γ₂N₂ToKaroubiIso_inv_app, CategoryTheory.LiftLeftAdjoint.instIsReflexivePairMapAppCounitOtherMap, CategoryTheory.Sigma.inclCompMap_inv_app, SSet.Augmented.stdSimplex_obj_hom_app, CategoryTheory.ComposableArrows.homMk₄_app_one, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_π, CategoryTheory.Functor.rightOpComp_inv_app, 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, CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_inv_apply, 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, CategoryTheory.Over.conePost_obj_pt, CategoryTheory.Functor.FullyFaithful.hasShift.map_add_hom_app, CategoryTheory.uliftYoneda_map_app_down, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_inv_app_app, CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_none, CategoryTheory.Join.mapPairComp_hom_app_left, CategoryTheory.Functor.opId_inv_app, CategoryTheory.unit_mateEquiv, CategoryTheory.Functor.mapTriangle_map_hom₃, CategoryTheory.Limits.limitConeOfUnique_isLimit_lift, CategoryTheory.Functor.mapDifferentialObject_obj_d, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app, CategoryTheory.coherentTopology.epi_π_app_zero_of_epi, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₃, CategoryTheory.sum.inrCompInlCompAssociator_hom_app_down_down, CategoryTheory.OverPresheafAux.restrictedYonedaObjMap₁_app, CategoryTheory.Limits.spanCompIso_hom_app_left, OrderHom.equivalenceFunctor_counitIso_hom_app_app, CategoryTheory.Sheaf.instIsLocallyInjectiveAppArrowPLocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, CategoryTheory.Limits.FormalCoproduct.evalOpCompInlIsoId_hom_app_app, CategoryTheory.Comonad.cofree_obj_a, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_right, CategoryTheory.endofunctorMonoidalCategory_associator_hom_app, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom, CategoryTheory.Equivalence.counitInv_app_functor, CategoryTheory.ComposableArrows.homMk₅_app_three, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_inv_app_app_snd, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_hom_assoc, CategoryTheory.Functor.const.opObjUnop_inv_app, CategoryTheory.Over.postComp_hom_app_left, CategoryTheory.Functor.flipping_inverse_obj_map_app, groupHomology.isoShortComplexH2_hom, CategoryTheory.Subfunctor.Subpresheaf.nat_trans_naturality, HomologicalComplex.singleCompEvalIsoSelf_inv_app, CategoryTheory.Equivalence.rightOp_counitIso_hom_app, CategoryTheory.FunctorToTypes.colimit.map_ι_apply, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_obj, CategoryTheory.Limits.Trident.ι_eq_app_zero, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_unit_app_app, CategoryTheory.Functor.Monoidal.whiskerLeft_app_fst, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinset_map_app, HomologicalComplex.asFunctor_obj_d, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_app_assoc, CategoryTheory.yonedaPairingExt_iff, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply, CategoryTheory.Idempotents.app_comp_p, CategoryTheory.OverPresheafAux.app_unitForward, CategoryTheory.Limits.limIsoFlipCompWhiskerLim_hom_app_app, CategoryTheory.Limits.MultispanIndex.multispanMapIso_hom_app, SSet.Truncated.liftOfStrictSegal_app_0, CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtensionObjIsoColimit_hom, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_counit_app, CategoryTheory.SmallObject.πFunctorObj_eq, CategoryTheory.μ_δ_app, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_hom_app_unmop, CategoryTheory.StructuredArrow.mapNatIso_counitIso_hom_app_right, HasCardinalLT.Set.cocone_ι_app, CategoryTheory.expComparison_ev, 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.Limits.Fork.op_ι_app_one, CategoryTheory.Under.postEquiv_inverse, CategoryTheory.Limits.colimIsoFlipCompWhiskerColim_inv_app_app, CategoryTheory.LaxFunctor.mapComp_assoc_left_app, CategoryTheory.Comma.mapRightId_hom_app_right, CategoryTheory.Adjunction.unit_naturality, CategoryTheory.Limits.Cone.w, CategoryTheory.Presheaf.uliftYonedaAdjunction_unit_app_app, CategoryTheory.ComposableArrows.homMk₃_app_two, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_flip_inv_app, SSet.Truncated.HomotopyCategory.BinaryProduct.associativity'Iso_hom_app, CategoryTheory.Sum.functorEquiv_unitIso_inv_app_app_inr, CategoryTheory.left_unitality_app, CategoryTheory.Functor.FullyFaithful.compYonedaCompWhiskeringLeftMaxRight_hom_app_app_down, CategoryTheory.Cat.rightUnitor_inv_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app_assoc, TopCat.Presheaf.SubmonoidPresheaf.toLocalizationPresheaf_app, ModuleCat.restrictScalarsId'_hom_app, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₃, CategoryTheory.Limits.inl_comp_pushoutObjIso_inv, CategoryTheory.Equivalence.counitInv_functor_comp_assoc, CategoryTheory.Functor.LeftExtension.postcompose₂_map_left, CategoryTheory.Limits.pullbackObjIso_inv_comp_fst, CategoryTheory.Functor.uncurry_obj_map, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_app_assoc, id_hcomp_app, CategoryTheory.shift_shiftFunctorCompIsoId_inv_app, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_counit_app_left, CategoryTheory.Join.inclLeftCompOpEquivInverse_hom_app_op, CategoryTheory.Presheaf.coconeOfRepresentable_naturality, CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_left, PresheafOfModules.Derivation.d_app, CategoryTheory.Functor.Monoidal.snd_app, app_naturality_assoc, CategoryTheory.Adjunction.map_μ_comp_counit_app_tensor, rightOp_app, CategoryTheory.Grothendieck.map_obj, CategoryTheory.Functor.Monoidal.fst_app, CategoryTheory.Enriched.Functor.natTransEquiv_symm_whiskerRight_functorHom_app, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counit_app, CategoryTheory.Adjunction.compCoyonedaIso_hom_app_app, CategoryTheory.Kleisli.Adjunction.fromKleisli_map, CategoryTheory.Functor.currying₃_unitIso_inv_app_app_app_app, CategoryTheory.Equivalence.fun_inv_map_assoc, CategoryTheory.Functor.closedIhom_map_app, CategoryTheory.Functor.instIsSplitEpiApp, CategoryTheory.Functor.whiskeringLeftObjIdIso_inv_app_app, 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, HomotopicalAlgebra.FibrantObject.HoCat.ιCompResolutionNatTrans_app, LightCondMod.hom_naturality_apply, OrderHom.equivalenceFunctor_unitIso_hom_app, AlgebraicGeometry.ExistsHomHomCompEqCompAux.hab, CategoryTheory.Functor.Monoidal.transport_η, CategoryTheory.MonoidalCategory.associatorNatIso_inv_app, CategoryTheory.Equivalence.ε_comp_map_ε, CategoryTheory.Functor.mapCocone₂_ι_app, CategoryTheory.Functor.RightExtension.postcompose₂_obj_hom_app, CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv', CategoryTheory.ObjectProperty.ColimitOfShape.toCostructuredArrow_map, SheafOfModules.unitToPushforwardObjUnit_val_app_apply, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_left, CategoryTheory.Limits.Cofork.unop_π_app_zero, Action.resComp_inv_app_hom, CategoryTheory.WithInitial.equivComma_unitIso_hom_app_app, CategoryTheory.Functor.RightExtension.precomp_obj_hom_app, CategoryTheory.Localization.lift₃NatTrans_app_app_app, CategoryTheory.ShiftedHom.opEquiv'_zero_add_symm, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_right_right, groupHomology.pOpcycles_comp_opcyclesIso_hom, CategoryTheory.Functor.ranCounit_app_app_ranAdjunction_unit_app_app, CategoryTheory.Comma.mapRightId_hom_app_left, CategoryTheory.Limits.IsColimit.hom_desc, CategoryTheory.Functor.Final.colimit_cocone_comp_aux, CategoryTheory.ShiftedHom.opEquiv'_symm_op_opShiftFunctorEquivalence_counitIso_inv_app_op_shift, CategoryTheory.Functor.RightExtension.precomp_map_right, CategoryTheory.Monad.MonadicityInternal.unitCofork_pt, SSet.rightUnitor_hom_app_apply, CategoryTheory.ShortComplex.mapNatTrans_τ₁, CategoryTheory.ProjectiveResolution.leftDerivedToHomotopyCategory_app_eq, CategoryTheory.FunctorToTypes.jointly_surjective, CategoryTheory.Under.postCongr_hom_app_right, CategoryTheory.Over.mapId_hom_app_left, CategoryTheory.Comma.mapLeftEq_inv_app_left, AddCommMonCat.coyonedaForget_inv_app_app, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_right, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_hom_app_unop_assoc, AlgebraicGeometry.Scheme.AffineZariskiSite.opensRange_relativeGluingData_map, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_apply, naturality, CategoryTheory.WithInitial.map₂_app, HomologicalComplex.coconeOfHasColimitEval_ι_app_f, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp_assoc, CategoryTheory.Limits.Cone.toStructuredArrow_obj, CategoryTheory.Functor.essImage.liftFunctorCompIso_inv_app, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.c_iso', CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_right, CategoryTheory.Limits.Cotrident.app_one, CategoryTheory.Monoidal.rightUnitor_hom_app, ComplexShape.Embedding.πTruncGENatTrans_app, CategoryTheory.CostructuredArrow.map_map_left, CategoryTheory.Limits.CategoricalPullback.mkNatIso_inv_app_fst, CategoryTheory.sectionsFunctorNatIsoCoyoneda_hom_app_app, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_hom_app_app_down, CategoryTheory.CostructuredArrow.map₂_map_left, CategoryTheory.Functor.PullbackObjObj.ofHasPullback_snd, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε_assoc, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_presheafHom_uliftYoneda_obj, CategoryTheory.Subfunctor.toRange_app_val, CategoryTheory.Functor.shift_map_op, CategoryTheory.Limits.limitIsoSwapCompLim_inv_app, CategoryTheory.Functor.mapTriangleCommShiftIso_inv_app_hom₂, CategoryTheory.ε_η_app, CategoryTheory.CosimplicialObject.whiskering_obj_map_app, Action.FunctorCategoryEquivalence.unitIso_hom_app_hom, CategoryTheory.LocalizerMorphism.isIso_iff_of_hasRightResolutions, CategoryTheory.Sum.swapCompInl_inv_app, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_inv_app_fst_app, CategoryTheory.EnrichedFunctor.forgetId_hom_app, CategoryTheory.Adjunction.comp_unit_app_assoc, CategoryTheory.InjectiveResolution.extMk_hom, CategoryTheory.Limits.inr_comp_pushoutObjIso_inv, CategoryTheory.Limits.IsLimit.fac_assoc, groupCohomology.isoShortComplexH1_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy_homEquiv_apply_app, CategoryTheory.Pretriangulated.shiftFunctor_op_map, CategoryTheory.Idempotents.functorExtension₂CompWhiskeringLeftToKaroubiIso_inv_app_app_f, AlgebraicTopology.DoldKan.PInfty_f_naturality, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map, CategoryTheory.Limits.cospanCompIso_hom_app_left, CategoryTheory.Adjunction.rightAdjointUniq_trans_app, CategoryTheory.SimplicialObject.equivalenceRightToLeft_left, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceFunctorProj_hom_app, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₁, HomologicalComplex.homologyFunctorSingleIso_inv_app, CategoryTheory.exp.coev_ev_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_app_assoc, CategoryTheory.Functor.RightExtension.postcompose₂ObjMkIso_inv_left_app, SimplicialObject.opFunctorCompOpFunctorIso_inv_app_app, CategoryTheory.prod_map_pre_app_comp_ev, CategoryTheory.Limits.spanExt_hom_app_left, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app_assoc, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app_assoc, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app, CategoryTheory.Equivalence.unit_naturality_assoc, ofSequence_app, CategoryTheory.Endofunctor.Algebra.functorOfNatTransEq_hom_app_f, CategoryTheory.ShortComplex.LeftHomologyMapData.natTransApp_φH, CategoryTheory.Equivalence.unit_app_tensor_comp_inverse_map_δ_functor_assoc, shift_app_assoc, AlgebraicTopology.DoldKan.Compatibility.υ_hom_app, CategoryTheory.ComposableArrows.threeδ₃Toδ₂_app_two, CategoryTheory.FunctorToTypes.jointly_surjective', CategoryTheory.NatIso.cancel_natIso_inv_right, CategoryTheory.Limits.CatCospanTransform.leftUnitor_inv_left_app, CategoryTheory.GradedObject.ι_mapBifunctorLeftUnitor_hom_apply, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, SSet.iSup_range_eq_top_of_isColimit, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_inv_app_eq, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp_app, CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_inv_app_unmop_unmop, CategoryTheory.Functor.IsCoverDense.sheafCoyonedaHom_app, CategoryTheory.NatIso.naturality_2'_assoc, AlgebraicGeometry.instIsOpenImmersionAppOverSchemeOpensDiagramι, CategoryTheory.Functor.inrCompSum'_inv_app, CategoryTheory.Functor.constComp_hom_app, CategoryTheory.Adjunction.derivedη_fac_app, CategoryTheory.DinatTrans.precompNatTrans_app, AlgebraicGeometry.Scheme.SpecΓIdentity_inv_app, SSet.const_comp, CategoryTheory.Abelian.LeftResolution.instEpiKaroubiAppπ, CategoryTheory.Adjunction.rightAdjointUniq_hom_app_counit, CategoryTheory.simplicialCosimplicialEquiv_unitIso_inv_app, CategoryTheory.Adjunction.derivedη_fac_app_assoc, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_inv_comp_π_assoc, CategoryTheory.Functor.RightExtension.postcompose₂_map_left_app, CategoryTheory.Equivalence.unit_naturality, CategoryTheory.ComposableArrows.isoMk₀_inv_app, CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_two, 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, ModuleCat.FilteredColimits.ι_colimitDesc, CategoryTheory.Equivalence.functor_unitIso_comp, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_apply, 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.uliftYonedaIsoYoneda_hom_app_app, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv_assoc, CategoryTheory.MonoidalClosed.curry'_whiskerRight_comp_assoc, CategoryTheory.Limits.CategoricalPullback.mkNatIso_hom_app_fst, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app, CommShiftCore.app_shift, CategoryTheory.Functor.FullyFaithful.compUliftYonedaCompWhiskeringLeft_hom_app_app_down, CategoryTheory.Pseudofunctor.map₂_whisker_left_app_assoc, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.trans_app_left, CategoryTheory.Functor.whiskeringRightObjCompIso_hom_app_app, CategoryTheory.ComposableArrows.fourδ₂Toδ₁_app_one, SSet.Edge.map_edge, CategoryTheory.equivYoneda_inv_app, CategoryTheory.Functor.PushoutObjObj.ofHasPushout_inl, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_obj, SSet.Edge.CompStruct.map_simplex, SSet.Truncated.HomotopyCategory.mkNatIso_hom_app_mk, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app, CategoryTheory.presheafToSheafCompComposeAndSheafifyIso_inv_app, CategoryTheory.Iso.map_hom_inv_id_eval_app_assoc, CategoryTheory.Comma.mapLeft_map_right, CommMonCat.coyoneda_map_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_right, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_symm_apply_f, appLinearMap_apply, SSet.Truncated.Path.map_vertex, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app, CategoryTheory.Adjunction.localization_counit_app, CategoryTheory.Functor.mapGrpIdIso_inv_app_hom_hom, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₂, CategoryTheory.Comma.unopFunctorCompFst_inv_app, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_hom_hom, CategoryTheory.Limits.inl_comp_pushoutObjIso_inv_assoc, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIso_hom_app_hom, CategoryTheory.Limits.Cotrident.coequalizer_ext, CategoryTheory.Pseudofunctor.mapComp'_naturality_2, CategoryTheory.ComposableArrows.homMk₂_app_zero, CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id_app_assoc, CategoryTheory.Limits.IndObjectPresentation.extend_isColimit_desc_app, CategoryTheory.ShortComplex.leftHomologyFunctorOpNatIso_hom_app, TopCat.coneOfConeForget_π_app, CategoryTheory.FreeMonoidalCategory.normalizeIsoAux_hom_app, CategoryTheory.ComposableArrows.scMap_τ₂, CategoryTheory.Limits.pullbackObjIso_hom_comp_snd_assoc, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_apply, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon_map, CategoryTheory.Adjunction.instIsIsoMapAppUnitOfFaithfulOfFull, CategoryTheory.Limits.colimitIsoFlipCompColim_hom_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_inv_app_app, CategoryTheory.Monad.algebraFunctorOfMonadHomComp_inv_app_f, CategoryTheory.Sieve.functorPushforward_functor, CategoryTheory.Functor.FullyFaithful.compUliftCoyonedaCompWhiskeringLeft_inv_app_app_down, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_obj_iso_hom, CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_fst_apply, CategoryTheory.Functor.whiskerRight_app, LightCondensed.lanPresheafNatIso_hom_app, CategoryTheory.ComposableArrows.isIso_iff₀, CategoryTheory.Limits.Bicone.ofLimitCone_π, CategoryTheory.Limits.CatCospanTransform.associator_inv_right_app, CategoryTheory.Limits.ι_comp_sigmaObjIso_inv_assoc, CategoryTheory.Limits.colimit.ι_coconeMorphism, CategoryTheory.Comma.equivProd_unitIso_inv_app_right, CategoryTheory.LocalizerMorphism.equiv_smallHomMap, CategoryTheory.ShortComplex.π₂Toπ₃_app, CategoryTheory.Monad.beckAlgebraCofork_ι_app, CategoryTheory.Functor.Monoidal.tensorHom_app_snd_assoc, CategoryTheory.plusPlusAdjunction_unit_app, CategoryTheory.Adjunction.CommShift.compatibilityUnit_right, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_inv_app_fst_app, CategoryTheory.Functor.Monoidal.associator_inv_app, CategoryTheory.Functor.CommShift.isoAdd'_hom_app, CategoryTheory.flippingIso_hom_toFunctor_obj_map_app, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_app, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app_assoc, CategoryTheory.WithTerminal.mapId_hom_app, CategoryTheory.Functor.IsCoverDense.homOver_app, CategoryTheory.NatIso.naturality_2', CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_inv_app_app, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_mon_mul, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app, CategoryTheory.Limits.Cone.ofFork_π, CategoryTheory.Limits.colimit.ι_map_assoc, CategoryTheory.Limits.fiberwiseColimCompColimIso_hom_app, CategoryTheory.Functor.mapTriangleCompIso_hom_app_hom₁, CategoryTheory.ComonadHom.app_δ, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_iso_inv_app, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_hom_app_f, CategoryTheory.Adjunction.Triple.map_rightToLeft_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app_assoc, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_comp, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_app, CategoryTheory.Localization.lift₂NatTrans_app_app, HomotopicalAlgebra.CofibrantObject.instIsIsoHoCatAppAdjCounit', CategoryTheory.MonoidalOpposite.tensorRightMopIso_inv_app_unmop, CategoryTheory.Adjunction.eq_unit_comp_map_iff, mapHomologicalComplex_naturality_assoc, CategoryTheory.Equivalence.core_counitIso_hom_app_iso_inv, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_hom_app_val_app, CategoryTheory.Functor.constCompEvaluationObj_hom_app, CategoryTheory.Limits.WalkingMulticospan.functorExt_hom_app, CategoryTheory.Functor.leftKanExtensionIsoFiberwiseColimit_hom_app, CategoryTheory.Monad.comparisonForget_inv_app, CategoryTheory.CosimplicialObject.equivalenceRightToLeft_right_app, CategoryTheory.shiftFunctorAdd_add_zero_hom_app, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, CategoryTheory.StructuredArrow.mapIso_unitIso_hom_app_right, CategoryTheory.Equivalence.cancel_counitInv_right_assoc', CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_fst, CategoryTheory.piEquivalenceFunctorDiscrete_inverse_map, TopCat.induced_of_isLimit, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_hom, groupHomology.pOpcycles_comp_opcyclesIso_hom_assoc, CategoryTheory.TransfiniteCompositionOfShape.iic_incl_app, CategoryTheory.Functor.curryingFlipEquiv_apply_map, CategoryTheory.Limits.Types.surjective_π_app_zero_of_surjective_map, Rep.indResAdjunction_unit_app_hom_hom, CategoryTheory.Functor.IsCoverDense.Types.presheafIso_hom_app, CategoryTheory.Limits.coconeLeftOpOfCone_ι_app, CategoryTheory.EnrichedFunctor.forgetComp_hom_app, CategoryTheory.CosimplicialObject.hom_ext_iff, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_fac_app, CategoryTheory.Functor.constCompWhiskeringLeftIso_inv_app_app, CategoryTheory.Functor.RightExtension.postcompose₂_map_right, AlgebraicTopology.DoldKan.N₂_obj_p_f, AlgebraicGeometry.exists_mem_of_isClosed_of_nonempty', CategoryTheory.Functor.leftOpComp_hom_app, CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit_assoc, CategoryTheory.Limits.cospanCompIso_hom_app_one, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv, CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero, CategoryTheory.Subfunctor.ofSection_image, CategoryTheory.Idempotents.app_comp_p_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_app_snd_app, CategoryTheory.coreFunctor_map_app_iso_hom, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_hom_comp_map_π, CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatTrans_app, CategoryTheory.Limits.CatCospanTransform.associator_hom_base_app, CategoryTheory.Functor.CommShift.isoZero_inv_app, CategoryTheory.TwoSquare.whiskerTop_app, CategoryTheory.WithTerminal.inclLiftToTerminal_hom_app, CategoryTheory.Functor.sheafPushforwardContinuousCompSheafToPresheafIso_hom_app_app, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π_assoc, CommRingCat.coyonedaUnique_inv_app_hom_apply, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_counitIso_hom_app_f, LightCondMod.epi_iff_locallySurjective_on_lightProfinite, CategoryTheory.Functor.commShiftIso_inv_naturality, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_app, CategoryTheory.Functor.HomObj.ofNatTrans_app, CategoryTheory.Limits.colimit.ι_desc_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_app_fst_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app_assoc, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.secondMap₃_app_app_app, AlgebraicTopology.DoldKan.Compatibility.τ₁_hom_app, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj, CategoryTheory.Functor.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, LightCondensed.ihom_map_val_app, CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_cancel_inv_app, CategoryTheory.LaxFunctor.map₂_rightUnitor_app_assoc, 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.Iso.map_hom_inv_id_app_assoc, HomotopyCategory.homologyFunctor_shiftMap_assoc, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_hom_app_left, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_app_assoc, Action.FunctorCategoryEquivalence.inverse_map_hom, AlgebraicGeometry.PresheafedSpace.Γ_map, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.unitIso_hom_app_f_f, SSet.mem_skeletonOfMono_obj_iff_of_nonDegenerate, AlgebraicGeometry.ΓSpec.right_triangle, CategoryTheory.Limits.colimit.ι_desc_app_assoc, CategoryTheory.TwoSquare.whiskerRight_app, CategoryTheory.Limits.Cocone.toCostructuredArrow_obj, CategoryTheory.Idempotents.KaroubiKaroubi.unitIso_hom_app_f, CategoryTheory.Adjunction.homEquiv_symm_id, AlgebraicGeometry.SheafedSpace.id_c_app, TopCat.Presheaf.app_isIso_of_stalkFunctor_map_iso, CategoryTheory.TwistShiftData.shiftFunctorAdd'_inv_app, CategoryTheory.Limits.PullbackCone.combine_pt_map, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₃, CochainComplex.shiftFunctorZero_hom_app_f, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counit_app_tensor_assoc, CategoryTheory.Join.mapPairComp_inv_app_left, CategoryTheory.WithInitial.coconeEquiv_inverse_map_hom_right, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_inv_app_hom_coe', CategoryTheory.Sigma.mapId_hom_app, CategoryTheory.Functor.limitIsoOfIsRightKanExtension_inv_π_assoc, Condensed.isColimitLocallyConstantPresheafDiagram_desc_apply, CategoryTheory.instIsIsoAppFromLeftDerivedZero, CategoryTheory.Comonad.counit_naturality_assoc, CategoryTheory.Functor.unopComp_inv_app, CategoryTheory.δ_naturality_assoc, CategoryTheory.CatCommSq.vComp_iso_inv_app, CategoryTheory.Limits.Types.jointly_surjective, CategoryTheory.Limits.PullbackCone.equalizer_ext, CategoryTheory.Join.pseudofunctorLeft_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, CategoryTheory.Equivalence.core_unitIso_hom_app_iso_hom, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd_assoc, SimplicialObject.Split.Hom.comm_assoc, CategoryTheory.Over.liftCocone_ι_app, SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_hom_app, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm, CategoryTheory.Idempotents.DoldKan.isoN₁_hom_app_f, Preorder.coneOfLowerBound_π_app, AlgebraicTopology.DoldKan.N₁Γ₀_hom_app, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_εIso_inv, IsMonoidal.unit_assoc, CategoryTheory.Limits.Types.Limit.map_π_apply, HomologicalComplex.mapBifunctorMapHomotopy.comm₁_aux, CategoryTheory.Functor.mapMonCompIso_inv_app_hom, CategoryTheory.NatIso.naturality_2, CategoryTheory.Functor.opComp_hom_app, CategoryTheory.ExponentiableMorphism.coev_naturality_assoc, CategoryTheory.Functor.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.Functor.PushoutObjObj.mapArrowLeft_left, CategoryTheory.StructuredArrow.mapNatIso_unitIso_inv_app_right, CategoryTheory.Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone_ι_app, CategoryTheory.Limits.wideCoequalizer.cotrident_ι_app_one, CategoryTheory.Limits.limit.lift_π_assoc, CategoryTheory.Functor.ranObjObjIsoLimit_hom_π, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_mapPullbackAdj_counit_app, CategoryTheory.Codiscrete.adj_unit_app, CategoryTheory.Equivalence.rightOp_unitIso_inv_app, CategoryTheory.Functor.mapTriangleCommShiftIso_hom_app_hom₁, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_map_app_fst, ModuleCat.ExtendRestrictScalarsAdj.counit_app, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.secondMap₁_app_app_app, ModuleCat.directLimitCocone_ι_app, CategoryTheory.curryingIso_inv_toFunctor_map_app_app, CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso_hom_app, AlgebraicGeometry.Scheme.Hom.ι_fromNormalization_assoc, CategoryTheory.Idempotents.natTrans_eq, CategoryTheory.Functor.FullyFaithful.homNatIso'_inv_app_down, CategoryTheory.ReflQuiv.adj.counit.comp_app_eq, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.inverseObj_comon_comul_app, CategoryTheory.Limits.IsColimit.ι_smul, CategoryTheory.Functor.isoShift_hom_naturality_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitNatIso_hom_app, CategoryTheory.ComposableArrows.twoδ₂Toδ₁_app_one, AlgebraicGeometry.Scheme.emptyTo_c_app, CategoryTheory.SingleFunctors.inv_hom_id_hom_app_assoc, CategoryTheory.MonoidalClosed.whiskerLeft_curry_ihom_ev_app, SSet.Truncated.HomotopyCategory.homToNerveMk_app_edge, CompHausLike.LocallyConstant.counit_app_val, CategoryTheory.ComonadHom.ext_iff, CategoryTheory.Bicategory.associatorNatIsoRight_hom_app, CategoryTheory.Join.InclLeftCompRightOpOpEquivFunctor_inv_app, CategoryTheory.ULift.equivalence_counitIso_inv_app, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.functorObjObj_comon_comul, CategoryTheory.GrothendieckTopology.diagramNatTrans_app, CategoryTheory.Sum.swapCompInr_hom_app, CategoryTheory.SimplicialObject.Augmented.rightOp_hom_app, CategoryTheory.Over.postEquiv_unitIso, naturality', SSet.Truncated.hom_ext_iff, CategoryTheory.Adjunction.homEquiv_apply, CategoryTheory.ComposableArrows.fourδ₃Toδ₂_app_one, SheafOfModules.pushforwardNatTrans_app_val_app, AddCommGrpCat.HasLimit.lift_hom_apply, CategoryTheory.Limits.PullbackCone.combine_pt_obj, Profinite.Extend.cocone_ι_app, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_left, CategoryTheory.MonadHom.ext'_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.whiskeringLimYonedaIsoCones_hom_app_app_app, CategoryTheory.Iso.isoCompInverse_hom_app, CategoryTheory.Limits.BinaryCofan.ι_app_left, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app_assoc, CategoryTheory.Comonad.Coalgebra.counit_assoc, CategoryTheory.Iso.isoInverseOfIsoFunctor_hom_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app_assoc, CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app, CategoryTheory.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCone_π_app, CategoryTheory.Endofunctor.Algebra.functorOfNatTrans_obj_str, CategoryTheory.NatIso.inv_app_isIso, CategoryTheory.δ_naturality, CategoryTheory.Limits.BinaryBicone.toCocone_ι_app_left, CondensedMod.epi_iff_locallySurjective_on_compHaus, CategoryTheory.Functor.mapGrpNatTrans_app_hom_hom, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_map, CategoryTheory.Comonad.right_counit, CategoryTheory.typeEquiv_functor_map_val_app, CategoryTheory.Limits.WidePullbackShape.functorExt_inv_app, CochainComplex.shiftFunctorAdd'_hom_app_f', CategoryTheory.Comma.mapRight_map_left, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_inv, CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_counit_app, CategoryTheory.Limits.Multifork.ofPiFork_π_app_right, CategoryTheory.Iso.map_inv_hom_id_eval_app, CategoryTheory.Limits.PushoutCocone.mk_ι_app_right, CategoryTheory.Limits.Multicofork.snd_app_right, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_inv_right_app, CategoryTheory.Comma.mapRightId_inv_app_right, CategoryTheory.Functor.LeftExtension.postcomp₁_map_left, CategoryTheory.Functor.equiv_functor_map, LightCondensed.epi_π_app_zero_of_epi, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_π_app_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_app, CategoryTheory.Functor.RightExtension.coneAtFunctor_map_hom, TopologicalSpace.Opens.mapComp_inv_app, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_symm_apply, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_hom_app_hom_hom_hom, CategoryTheory.Limits.spanIsoMk_hom_app, CategoryTheory.Functor.map_shift_unop_assoc, naturality_app_app, CategoryTheory.Functor.IsCoverDense.Types.presheafHom_app, CategoryTheory.ShiftMkCore.zero_add_hom_app, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₁, HomologicalComplex.mapBifunctor.d₁_eq', 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.Functor.mapCommGrpIdIso_inv_app_hom_hom_hom, id_app, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app, CategoryTheory.yonedaCommGrpGrp_map_app, CategoryTheory.EnrichedCat.whiskerLeft_out_app, CategoryTheory.Functor.whiskeringRightObjIdIso_inv_app_app, CategoryTheory.Functor.inv_fun_map, CategoryTheory.Iso.core_inv_app_iso_inv, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_assoc, CategoryTheory.ihom.ev_naturality, HomologicalComplex.singleCompEvalIsoSelf_hom_app, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_hom_comp_map_π_assoc, AlgebraicGeometry.exists_appTop_π_eq_of_isLimit, SSet.nonDegenerateEquivOfIso_apply_coe, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_app_assoc, TopCat.Presheaf.isGluing_iff_pairwise, CategoryTheory.CosimplicialObject.whiskering_map_app_app, CategoryTheory.Monoidal.associator_inv_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_assoc, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_obj_pt, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_cone_π_app, CategoryTheory.Bicategory.associatorNatIsoLeft_hom_app, CategoryTheory.Limits.colimit.isoColimitCocone_ι_hom_assoc, CategoryTheory.Limits.pullbackConeOfRightIso_π_app_none, CategoryTheory.Adjunction.rightAdjointUniq_hom_app_counit_assoc, HomotopicalAlgebra.CofibrantObject.instWeakEquivalenceHoCatAppAdjUnit, CategoryTheory.Functor.flipping_inverse_map_app_app, CategoryTheory.Comma.mapRightIso_inverse_obj_hom, CategoryTheory.TwistShiftData.shiftFunctorAdd'_hom_app, CategoryTheory.Functor.flip₁₃Functor_map_app_app_app, Action.FunctorCategoryEquivalence.counitIso_hom_app_app, CategoryTheory.Subfunctor.image_obj, CategoryTheory.GradedObject.mapTrifunctorObj_map_app, CategoryTheory.MonoOver.commSqOfHasStrongEpiMonoFactorisation, CategoryTheory.MonoidalCategory.externalProductSwap_inv_app_app, CategoryTheory.Functor.mapArrowFunctor_map_app_right, 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, CategoryTheory.Limits.inl_comp_pushoutObjIso_hom_assoc, PresheafOfModules.map_id, CommGrpCat.coyonedaForget_inv_app_app, CategoryTheory.Sieve.natTransOfLe_app_coe, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv, CategoryTheory.StructuredArrow.mapIso_inverse_map_right, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app_assoc, CategoryTheory.Limits.fiberwiseColimCompColimIso_inv_app, CategoryTheory.sum.inlCompInverseAssociator_inv_app_down_down, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoColimitUncurryWhiskeringLeft₂_hom_assoc, CategoryTheory.Functor.shiftIso_hom_app_comp_shiftMap, 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.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.ComonadHom.ext'_iff, CategoryTheory.Functor.shiftIso_add'_inv_app, CategoryTheory.Limits.Cocones.functoriality_map_hom, CategoryTheory.Limits.WalkingMulticospan.functorExt_inv_app, CategoryTheory.Functor.PushoutObjObj.mapArrowLeft_right, ModuleCat.HasLimit.lift_hom_apply, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, CategoryTheory.Under.mapPushoutAdj_counit_app, CategoryTheory.Limits.combineCocones_ι_app_app, CategoryTheory.FunctorToTypes.binaryProductCone_π_app, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right, ModuleCat.binaryProductLimitCone_isLimit_lift, CategoryTheory.Comonad.beckEqualizer_lift, CategoryTheory.Subfunctor.Subpresheaf.toRange_app_val, CategoryTheory.Comonad.id_ε_app, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom_assoc, CategoryTheory.Adjunction.Triple.map_adj₂_counit_app_leftToRight_app, CategoryTheory.Adjunction.Triple.map_rightToLeft_app_assoc, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_hom_app_app, CategoryTheory.GrothendieckTopology.Plus.inj_of_sep, CategoryTheory.EnrichedFunctor.hom_ext_iff, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_assoc, CategoryTheory.Functor.leftDerived_fac_app_assoc, CategoryTheory.Functor.mapTriangleIso_inv_app_hom₂, CategoryTheory.OverPresheafAux.OverArrows.map₁_val, CategoryTheory.evaluationAdjunctionRight_unit_app, CategoryTheory.MonoidalCategory.DayConvolution.whiskerLeft_comp_unit_app_assoc, CategoryTheory.Adjunction.unit_app_tensor_comp_map_δ, CategoryTheory.ComposableArrows.homMk₃_app_one, CategoryTheory.WithTerminal.coneEquiv_unitIso_inv_app_hom_left, CategoryTheory.Limits.Multifork.ofι_π_app, Profinite.NobelingProof.spanFunctorIsoIndexFunctor_inv_app, AlgebraicGeometry.LocallyRingedSpace.preimage_basicOpen, CategoryTheory.Pi.sum_map_app, CategoryTheory.Functor.mapMatId_hom_app, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_app, CategoryTheory.counit_obj_eq_map_counit, CategoryTheory.Join.InclRightCompRightOpOpEquivFunctor_inv_app, CategoryTheory.Subfunctor.toRangeSheafify_app_coe, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_hom_app_f, TopCat.nonempty_isColimit_iff_eq_coinduced, CategoryTheory.Limits.limit.isoLimitCone_inv_π, CategoryTheory.SimplicialObject.Augmented.toArrow_obj_hom, CategoryTheory.Functor.FullyFaithful.hasShift.map_add_inv_app, CategoryTheory.Limits.Bicone.toCone_π_app, CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj_hom_app, SSet.Truncated.liftOfStrictSegal_app_1, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_left, CategoryTheory.Functor.IsCoverDense.isoOver_inv_app, CategoryTheory.Comonad.beckFork_ι, CategoryTheory.WithTerminal.equivComma_functor_map_left_app, CategoryTheory.Adjunction.whiskerLeftRUnitIsoOfIsIsoCounit_hom_app, groupHomology.H0π_comp_H0Iso_hom, CategoryTheory.Limits.cospanExt_inv_app_left, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_δ_app, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_app_assoc, CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app_assoc, CategoryTheory.Functor.flipping_functor_obj_obj_map, CommMonCat.coyonedaForget_hom_app_app_hom, CategoryTheory.MonoidalCategory.DayConvolution.associator_inv_unit_unit_assoc, TopologicalSpace.Opens.mapIso_hom_app, HomologicalComplex.coneOfHasLimitEval_π_app_f, CategoryTheory.Functor.isoSum_hom_app_inr, CategoryTheory.Functor.postcompose₂_obj_obj_map_app, CategoryTheory.CosimplicialObject.Augmented.whiskering_map_app_right, CategoryTheory.Monad.ForgetCreatesColimits.liftedCocone_ι_app_f, SSet.associator_hom_app_apply, ModuleCat.extendScalarsComp_hom_app_one_tmul, CategoryTheory.Subobject.leInfCone_π_app_none, CategoryTheory.Limits.fiberwiseColimCompEvaluationIso_inv_app, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π, CategoryTheory.WithInitial.liftFromUnderComp_hom_app, CategoryTheory.Equivalence.counitInv_naturality, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom_assoc, CategoryTheory.Functor.CommShift.OfComp.map_iso_hom_app_assoc, CategoryTheory.yonedaEvaluation_map_down, ComplexShape.Embedding.restrictionToTruncGE'NatTrans_app, CochainComplex.ι_mapBifunctorShift₁Iso_hom_f_assoc, groupCohomology.isoShortComplexH2_hom, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity, CategoryTheory.PresheafHom.IsSheafFor.app_cond, CategoryTheory.Monad.monadMonEquiv_counitIso_inv_app_hom, TopCat.Presheaf.Pushforward.comp_hom_app, CategoryTheory.Limits.FormalCoproduct.evalCompInclIsoId_inv_app_app, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w_assoc, CategoryTheory.Limits.PullbackCone.condition_one, MonObj.mopEquiv_counitIso_inv_app_hom_unmop, app_smul, CategoryTheory.MonoidalCategory.curriedTensor_map_app, CategoryTheory.GrothendieckTopology.coneCompEvaluationOfConeCompDiagramFunctorCompEvaluation_π_app, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_inv_app_hom_app, CategoryTheory.FunctorToTypes.binaryCoproductCocone_ι_app, AddCommGrpCat.coyoneda_map_app, CategoryTheory.Functor.sectionsEquivHom_apply_app, mapSquare_app_τ₄, CategoryTheory.Grothendieck.functorFrom_map, CategoryTheory.Monad.ForgetCreatesLimits.γ_app, CategoryTheory.Equivalence.unit_inverse_comp, CategoryTheory.Limits.BinaryBicone.ofLimitCone_fst, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app, CategoryTheory.sheafificationAdjunction_counit_app_val, 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.ShortComplex.rightHomologyFunctorOpNatIso_inv_app, CategoryTheory.ihom.ev_naturality_assoc, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_hom_app_hom_coe, LightCondensed.lanPresheafExt_inv, CategoryTheory.Limits.Cone.toUnder_π_app, CategoryTheory.isIso_iff_isIso_coyoneda_map, SSet.image_degenerate_le, Condensed.lanPresheafExt_hom, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id_app, CategoryTheory.Limits.colimitCoyonedaHomIsoLimit_π_apply, AlgebraicTopology.DoldKan.karoubi_PInfty_f, CategoryTheory.Adjunction.unit_app_commShiftIso_hom_app, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counitIso_hom_app_tensor, CategoryTheory.Under.postAdjunctionLeft_counit_app, CategoryTheory.Functor.functorialityCompPrecompose_inv_app_hom, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₃, CategoryTheory.Comonad.beckFork_pt, CategoryTheory.Functor.flip₂₃_obj_map_app, CategoryTheory.flippingIso_inv_toFunctor_obj_obj_map, CategoryTheory.Functor.commShiftIso_id_inv_app, CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso_inv_app, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp_assoc, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_hom_π_assoc, CategoryTheory.Functor.mapGrpNatIso_inv_app_hom_hom, CategoryTheory.Functor.rightOpId_hom_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_inv_app_hom_hom_app, CategoryTheory.CostructuredArrow.mapNatIso_functor_map_left, CategoryTheory.Adjunction.whiskerLeft_unit_app_app, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_comp, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app_assoc, CategoryTheory.Subfunctor.ι_app, CategoryTheory.Limits.CoconeMorphism.map_w_assoc, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_hom_app_hom, ext_iff, CategoryTheory.IsCardinalPresentable.exists_hom_of_isColimit, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_left, HomotopyCategory.homologyShiftIso_hom_app, CategoryTheory.Limits.limCompFlipIsoWhiskerLim_hom_app_app, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app, CochainComplex.shiftFunctorAdd_hom_app_f, AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_comp, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_apply, SheafOfModules.pushforwardPushforwardEquivalence_unit_app_val_app, CategoryTheory.WithInitial.liftFromUnder_map_app, CategoryTheory.obj_μ_app_assoc, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_left, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIdIso_inv_app_hom, CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_hom_app, CategoryTheory.ShortComplex.mapNatTrans_τ₂, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_counit_app, CategoryTheory.Functor.Monoidal.whiskerRight_app_snd, CategoryTheory.GrothendieckTopology.overMapPullbackComp_hom_app_val_app, CategoryTheory.Quotient.lift.isLift_inv, CategoryTheory.Limits.IsColimit.isIso_ι_app_of_isTerminal, CategoryTheory.Sigma.mapId_inv_app, CategoryTheory.Limits.limitCompYonedaIsoCocone_hom_app, CategoryTheory.ComposableArrows.homMk₅_app_one, CategoryTheory.Functor.lanCompIsoOfPreserves_hom_app, CategoryTheory.Adjunction.isIso_unit_app_of_iso, CategoryTheory.Functor.flip₂₃_map_app_app, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.F_obj, CategoryTheory.Iso.inverseCompIso_inv_app, CategoryTheory.ShortComplex.iCyclesNatTrans_app, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_obj_map, CategoryTheory.Functor.postcompose₃_obj_map_app_app_app, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_right, CategoryTheory.Limits.coconeOfConeLeftOp_ι_app, CategoryTheory.Functor.Monoidal.μNatIso_hom_app, AlgebraicGeometry.PresheafedSpace.congr_app, CategoryTheory.OverPresheafAux.unitAuxAux_hom_app, CategoryTheory.pullbackShiftFunctorZero'_inv_app, CategoryTheory.Limits.limit.coneMorphism_π, CategoryTheory.Functor.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, CategoryTheory.Functor.whiskeringLeft₃ObjObjObj_obj_obj_map_app, TopCat.Presheaf.presheafEquivOfIso_counitIso_hom_app_app, CategoryTheory.Abelian.FunctorCategory.imageObjIso_hom, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv, CategoryTheory.Join.mkFunctorRight_inv_app, CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.map_eq_pullHom_assoc, CategoryTheory.Idempotents.DoldKan.Γ_map_app, CategoryTheory.endofunctorMonoidalCategory_rightUnitor_hom_app, Rep.resIndAdjunction_unit_app, CategoryTheory.NatIso.isIso_inv_app, CategoryTheory.Pseudofunctor.map₂_whisker_left_app, CategoryTheory.Limits.coend.ι_map_assoc, CategoryTheory.Functor.PushoutObjObj.ofHasPushout_inr, CategoryTheory.Enriched.FunctorCategory.homEquiv_apply_π_assoc, CategoryTheory.MorphismProperty.Over.mapComp_inv_app_left, CategoryTheory.Limits.colimitYonedaHomIsoLimitOp_π_apply, congr, CategoryTheory.MonoidalCategory.tensorRightTensor_inv_app, CategoryTheory.Limits.epi_of_isColimit_parallelFamily, CategoryTheory.LocalizerMorphism.Derives.isRightDerivedFunctor_iff_isIso, AlgebraicTopology.DoldKan.Γ₂N₁.natTrans_app_f_app, CategoryTheory.NatIso.naturality_2_assoc, CategoryTheory.shiftFunctorComm_hom_app_of_add_eq_zero, CategoryTheory.Limits.PushoutCocone.isoMk_hom_hom, CategoryTheory.MonoidalClosed.compTranspose_eq, CategoryTheory.Iso.isoFunctorOfIsoInverse_hom_app, CategoryTheory.SimplicialObject.instIsLeftKanExtensionOppositeTruncatedSimplexCategoryObjSkAppTruncatedUnitSkAdjTruncation, CategoryTheory.bifunctorComp₂₃FunctorMap_app_app_app_app, CategoryTheory.ShiftedHom.opEquiv_symm_apply, CategoryTheory.prodOpEquiv_counitIso_hom_app, CategoryTheory.Over.starPullbackIsoStar_inv_app_left, CategoryTheory.LocalizerMorphism.isIso_iff_of_isRightDerivabilityStructure, CategoryTheory.Comma.mapSnd_hom_app, AlgebraicGeometry.exists_mem_of_isClosed_of_nonempty, 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, CategoryTheory.Functor.descOfIsLeftKanExtension_fac_app_assoc, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_snd, CategoryTheory.Limits.end_.map_π_assoc, HomologicalComplex₂.flipEquivalenceCounitIso_inv_app_f_f, CategoryTheory.Functor.mapTriangleIdIso_inv_app_hom₁, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left, HomologicalComplex.natTransHomologyι_app, HomologicalComplex.homologyFunctorIso_hom_app, CategoryTheory.Subfunctor.Subpresheaf.ofSection_image, CategoryTheory.Limits.coconeOfCoconeUncurry_ι_app, CategoryTheory.Functor.postcompose₂_map_app_app_app, CategoryTheory.Functor.mapGrpCompIso_inv_app_hom_hom, CategoryTheory.Limits.cospanOp_inv_app, CategoryTheory.bifunctorComp₁₂FunctorObj_map_app_app_app, CategoryTheory.Presheaf.freeYonedaHomEquiv_comp_assoc, CategoryTheory.Adjunction.homEquiv_counit, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_hom_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionUnitIso_hom, CategoryTheory.Limits.cospanCompIso_hom_app_right, AlgebraicGeometry.PresheafedSpace.id_c_app, CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_none, CategoryTheory.Functor.mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app, CategoryTheory.Presheaf.tautologicalCocone_ι_app, CategoryTheory.Equivalence.unit_app_comp_inverse_map_η_functor_assoc, CategoryTheory.Limits.zero_app, CategoryTheory.Pseudofunctor.CoGrothendieck.compIso_inv_app, Rep.ihom_coev_app_hom, CategoryTheory.CosimplicialObject.Augmented.leftOp_hom_app, HomologicalComplex.asFunctor_map_f, AlgebraicGeometry.Scheme.exists_π_app_comp_eq_of_locallyOfFinitePresentation, CategoryTheory.ShiftedHom.opEquiv'_apply, CategoryTheory.Limits.CatCospanTransform.leftUnitor_inv_base_app, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₁_assoc, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app_assoc, CategoryTheory.Cat.HasLimits.limitConeLift_toFunctor, CategoryTheory.Pretriangulated.Triangle.functorHomMk'_app_hom₂, 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.Limits.Trident.app_zero_assoc, CategoryTheory.constantSheafAdj_counit_w, CategoryTheory.OverPresheafAux.yonedaCollectionPresheafMap₁_app, CategoryTheory.oppositeShiftFunctorAdd'_hom_app, CategoryTheory.ComposableArrows.isoMk₁_inv_app, ComplexShape.Embedding.truncLE'ToRestrictionNatTrans_app, CategoryTheory.Presheaf.tautologicalCocone'_ι_app, PresheafOfModules.pushforward_obj_map_apply', CategoryTheory.sum.inlCompInlCompAssociator_hom_app_down, CategoryTheory.Limits.PushoutCocone.mk_ι_app_left, CategoryTheory.Functor.curry_obj_map_app, CategoryTheory.Comma.toPUnitIdEquiv_counitIso_inv_app, CategoryTheory.mono_of_cofan_isVanKampen, CategoryTheory.MonoidalCategory.leftUnitorNatIso_inv_app, CategoryTheory.Functor.closedCounit_app_app, CategoryTheory.toOverIteratedSliceForwardIsoPullback_inv_app_left, CategoryTheory.Presheaf.coconeOfRepresentable_ι_app, CategoryTheory.ComposableArrows.threeδ₁Toδ₀_app_one, CategoryTheory.Limits.coconeOfCoconeFiberwiseColimit_ι_app, CompHausLike.LocallyConstant.unit_app, CategoryTheory.MonoidalCategory.Functor.curriedTensorPreIsoPost_inv_app_app, CategoryTheory.PresheafIsGeneratedBy.of_epi, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₂, 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.Pseudofunctor.DescentData.pullFunctorIdIso_hom_app_hom, CochainComplex.shiftFunctorAdd'_hom_app_f, CategoryTheory.Limits.Cofork.op_π_app_one, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_right_app, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₁, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceInverseπ_inv_app, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp_assoc, CategoryTheory.ComposableArrows.threeδ₃Toδ₂_app_zero, CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm_assoc, CategoryTheory.Quotient.LiftCommShift.iso_inv_app, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app, Action.resId_hom_app_hom, CategoryTheory.Functor.mapCommGrpNatIso_hom_app_hom_hom_hom, CategoryTheory.Limits.limit.conePointUniqueUpToIso_inv_comp, CategoryTheory.Limits.IsLimit.map_π_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_obj_iso_hom, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_unitIso_inv_app_f_f, CategoryTheory.ProdPreservesConnectedLimits.γ₁_app, CategoryTheory.Comonad.Coalgebra.counit, CategoryTheory.conjugateEquiv_adjunction_id_symm, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_symm_apply, CategoryTheory.Monad.right_unit, CategoryTheory.ComposableArrows.fourδ₂Toδ₁_app_two, CategoryTheory.Limits.ColimitPresentation.w, CategoryTheory.Subfunctor.IsGeneratedBy.image, CategoryTheory.Functor.OplaxMonoidal.whiskeringRight_η_app, groupHomology.isoShortComplexH2_inv, 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.SingleFunctors.inv_hom_id_hom_app, CategoryTheory.Equivalence.core_counitIso_inv_app_iso_hom, CategoryTheory.Limits.piObjIso_inv_comp_π_assoc, LightCondSet.isDiscrete_tfae, CategoryTheory.Iso.unop_inv_hom_id_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_hom_toNatTrans_app_val_app, AlgebraicTopology.DoldKan.N₁Γ₀_inv_app, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₂, CategoryTheory.Coyoneda.fullyFaithful_preimage, CategoryTheory.Functor.ranObjObjIsoLimit_inv_π, SSet.yonedaEquiv_comp, LightCondSet.topCatAdjunctionUnit_val_app, AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_inv_ι_app, CategoryTheory.MonoidalOpposite.tensorLeftIso_hom_app_unmop, CategoryTheory.Iso.inverseCompIso_hom_app, CategoryTheory.Equivalence.congrLeft_counitIso_hom_app, CategoryTheory.Adjunction.leftAdjointUniq_inv_app, CategoryTheory.Sigma.descUniq_hom_app, CategoryTheory.coherentTopology.isLocallySurjective_π_app_zero_of_isLocallySurjective_map, CategoryTheory.Limits.cospanHomMk_app, CategoryTheory.Limits.Cocone.toCostructuredArrowCompProj_inv_app, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_app_apply, CategoryTheory.Limits.Types.Pushout.cocone_ι_app, CategoryTheory.EnrichedCat.whiskerRight_out_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_map_app_snd, CategoryTheory.flipFunctor_map_app_app, CategoryTheory.GrothendieckTopology.ι_plusCompIso_hom, CategoryTheory.WithTerminal.mapId_inv_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionUnitIso_inv, CategoryTheory.Functor.leftDerivedNatTrans_app, AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.opensRange_map, CategoryTheory.obj_μ_zero_app, AlgebraicTopology.DoldKan.Compatibility.τ₀_hom_app, CategoryTheory.Functor.mapTriangleIdIso_inv_app_hom₂, CategoryTheory.Functor.flippingEquiv_apply_obj_map, PresheafOfModules.freeAdjunction_unit_app, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst_assoc, CategoryTheory.ExponentiableMorphism.ev_naturality, CategoryTheory.Comma.mapRightEq_hom_app_left, CategoryTheory.Over.forgetCocone_ι_app, CategoryTheory.Grothendieck.map_map_base, CategoryTheory.Functor.commShiftOfLocalization_iso_hom_app, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_left, CategoryTheory.Limits.reflexivePair.mkNatTrans_app_zero, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₂, CategoryTheory.Join.inrCompFromSum_inv_app, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv, CategoryTheory.WithTerminal.liftFromOverComp_inv_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_right, CategoryTheory.Comma.mapRightEq_inv_app_right, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_map_app_assoc, CategoryTheory.StructuredArrow.mapIso_functor_map_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, CategoryTheory.Functor.curryObjProdComp_inv_app_app, TwoP.swapEquiv_counitIso_hom_app_hom_toFun, SheafOfModules.pushforwardPushforwardAdj_counit_app_val_app, CategoryTheory.Sheaf.Hom.add_app, CategoryTheory.Functor.Monoidal.associator_hom_app, CategoryTheory.PresheafIsGeneratedBy.range, CategoryTheory.PreGaloisCategory.endEquivAutGalois_π, CategoryTheory.Monad.unit_naturality_assoc, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.firstMap_app_app_app, app_units_zsmul, CategoryTheory.Limits.Cocone.extend_ι, HomotopicalAlgebra.CofibrantObject.HoCat.ιCompResolutionNatTrans_app, CategoryTheory.Triangulated.TStructure.triangleLTGE_map_hom₁, CategoryTheory.OplaxFunctor.map₂_rightUnitor_app, CategoryTheory.Limits.prodComparisonNatTrans_app, CochainComplex.shiftFunctorComm_hom_app_f, ext'_iff, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_app, CategoryTheory.ShortComplex.fromOpcyclesNatTrans_app, CategoryTheory.LaxFunctor.mapComp_naturality_right_app, CategoryTheory.WithTerminal.equivComma_inverse_map_app, CategoryTheory.Idempotents.KaroubiKaroubi.unitIso_inv_app_f, CategoryTheory.TwoSquare.vComp_app, CategoryTheory.Sum.functorEquiv_unit_app_app_inl, CategoryTheory.Join.mkFunctorLeft_inv_app, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₃, CategoryTheory.Limits.Cone.w_apply, TopCat.isOpen_iff_of_isColimit, AlgebraicGeometry.tilde.toOpen_map_app_assoc, 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.ShortComplex.FunctorEquivalence.functor_map_app, CategoryTheory.ComposableArrows.homMk₄_app_two, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_right, CategoryTheory.Limits.limIsoFlipCompWhiskerLim_inv_app_app, CategoryTheory.WithInitial.ofCommaObject_map, CategoryTheory.Abelian.DoldKan.comparisonN_hom_app_f, CategoryTheory.MonoidalOpposite.tensorRightMopIso_hom_app_unmop, CategoryTheory.Limits.Cone.overPost_π_app, CategoryTheory.Functor.mapTriangleRotateIso_inv_app_hom₃, CategoryTheory.ComposableArrows.fourδ₃Toδ₂_app_two, AlgebraicGeometry.LocallyRingedSpace.Γ_map_op, 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.Functor.toEssImageCompι_inv_app, CategoryTheory.Adjunction.Triple.epi_rightToLeft_app_iff_epi_map_adj₂_counit_app, CategoryTheory.conjugateEquiv_adjunction_id, CategoryTheory.Yoneda.fullyFaithful_preimage, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_incl_app, CategoryTheory.Limits.Cone.toStructuredArrow_map, CategoryTheory.Functor.mapArrowFunctor_map_app_left, AlgebraicGeometry.ExistsHomHomCompEqCompAux.hb, CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id_app_assoc, CategoryTheory.Functor.opHom_map_app, CategoryTheory.Comma.toIdPUnitEquiv_counitIso_inv_app, CategoryTheory.Functor.cocones_map_app, CategoryTheory.MonoidalCategory.DayFunctor.equiv_unitIso_inv_app, CategoryTheory.ShiftMkCore.assoc_hom_app, CochainComplex.mappingConeCompTriangle_mor₃_naturality_assoc, CategoryTheory.Functor.RightExtension.postcomp₁_obj_hom_app, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop, CategoryTheory.Limits.Multicoequalizer.multicofork_ι_app_right, CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.map_eq_pullHom, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app, CategoryTheory.functorProdFunctorEquivUnitIso_inv_app, CategoryTheory.Adjunction.adjToMonadIso_hom_toNatTrans_app, SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁_inv_app_f_f, CategoryTheory.Functor.flip₂₃Functor_obj_map_app_app, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_hom_app_val_app, CategoryTheory.FunctorToTypes.prod.lift_app, CategoryTheory.Functor.commShiftOfLocalization.iso_hom_app_assoc, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_hom, CategoryTheory.Limits.SequentialProduct.cone_π_app, CategoryTheory.endofunctorMonoidalCategory_leftUnitor_inv_app, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₂, CategoryTheory.Limits.limit.lift_π_app_assoc, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_inv_app_app, app_shift, CategoryTheory.Functor.whiskeringLeft₃_obj_obj_obj_obj_obj_map_app, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_mul_app, CategoryTheory.Functor.ι_colimitIsoOfIsLeftKanExtension_hom_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app_assoc, comp_app, CategoryTheory.Functor.instIsIsoAppLanUnit_1, CategoryTheory.Limits.Cone.w_assoc, CategoryTheory.LaxFunctor.mapComp_naturality_left_app, CategoryTheory.ComposableArrows.fourδ₃Toδ₂_app_three, SSet.Truncated.HomotopyCategory.homToNerveMk_app_zero, CategoryTheory.Limits.limitIsoFlipCompLim_inv_app, CategoryTheory.Join.mapPairLeft_hom_app, groupHomology.shortComplexH0_g, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransId_hom_app_f, CategoryTheory.Functor.flipIsoCurrySwapUncurry_inv_app_app, CategoryTheory.cones_map_app_app, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.firstMap₃_app_app_app, CategoryTheory.nat_trans_from_is_connected, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_app_snd_app, CategoryTheory.WithTerminal.liftFromOver_map_app, CategoryTheory.MonoidalClosed.coev_app_comp_pre_app_assoc, SSet.Truncated.Edge.map_whiskerRight, AlgebraicGeometry.isAffineHom_π_app, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₂, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_map_right_app, CategoryTheory.GradedObject.ιMapBifunctor₁₂BifunctorMapObj_eq, SSet.Truncated.comp_app, CategoryTheory.Functor.sheafPushforwardContinuousId_inv_app_val_app, LightProfinite.Extend.functor_obj, LightCondensed.isoFinYoneda_hom_app, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app_assoc, CategoryTheory.coyonedaPairingExt_iff, CategoryTheory.Pseudofunctor.DescentData.pullFunctorCompIso_hom_app_hom, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₂, CategoryTheory.associativity_app, AlgebraicGeometry.SheafedSpace.congr_hom_app, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_right, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app, CategoryTheory.Limits.parallelPair.eqOfHomEq_hom_app, CategoryTheory.WithTerminal.coneEquiv_inverse_map_hom_left, CategoryTheory.Iso.inv_hom_id_app_app_app_assoc, CategoryTheory.Functor.mapCochainComplexShiftIso_hom_app_f, IsMonoidal.tensor_assoc, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_inv_app_unop_assoc, CategoryTheory.Iso.inv_hom_id_app, CategoryTheory.SingleFunctors.shiftIso_add_hom_app, CategoryTheory.flippingIso_hom_toFunctor_map_app_app, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_apply_app, CategoryTheory.cosimplicialSimplicialEquiv_inverse_map, CategoryTheory.Functor.bifunctorComp₁₂Iso_inv_app_app_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_inv_app, CategoryTheory.shiftFunctorCompIsoId_zero_zero_hom_app, CategoryTheory.Functor.PushoutObjObj.inr_ι_assoc, CategoryTheory.MonoidalCategory.externalProductBifunctorCurried_obj_map_app_app, CategoryTheory.Limits.coequalizer.cofork_ι_app_one, CategoryTheory.ComposableArrows.homMk_app, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one, CategoryTheory.obj_μ_inv_app_assoc, CategoryTheory.Limits.prod.functor_map_app, SSet.Path.map_vertex, CategoryTheory.Over.postMap_app, CategoryTheory.Functor.toEssImageCompι_hom_app, SSet.Truncated.Edge.CompStruct.map_simplex, CategoryTheory.Pseudofunctor.DescentData.pullFunctorObjHom_eq, CategoryTheory.δ_naturalityₗ, CochainComplex.shiftEval_inv_app, CategoryTheory.GrothendieckTopology.instIsIsoSheafAppFunctorOppositeSheafComposeNatTransPlusPlusAdjunction, CategoryTheory.Monad.ForgetCreatesLimits.liftedCone_π_app_f, CategoryTheory.FunctorToTypes.hom_inv_id_app_apply, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitNatIso_inv_app, sum'_app_inr, CategoryTheory.TwoSquare.vComp'_app, CategoryTheory.Limits.walkingSpanOpEquiv_unitIso_hom_app, CategoryTheory.Join.mapIsoWhiskerLeft_inv_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_inv_app', CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app_assoc, CategoryTheory.Presieve.FamilyOfElements.IsAmalgamation.map, TopCat.Presheaf.presheafEquivOfIso_functor_map_app, CategoryTheory.Equivalence.inverseFunctorObj'_inv_app, CategoryTheory.Functor.rightUnitor_inv_app, CategoryTheory.Comonad.ComonadicityInternal.main_pair_F_cosplit, CategoryTheory.Functor.leftUnitor_hom_app, CategoryTheory.extensiveTopology.surjective_of_isLocallySurjective_sheaf_of_types, CategoryTheory.Functor.flippingEquiv_apply_map_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality, CategoryTheory.Grothendieck.ιCompMap_hom_app_base, AlgebraicGeometry.Scheme.Hom.ι_fromNormalization, CategoryTheory.Iso.core_hom_app_iso_hom, CategoryTheory.Over.ConstructProducts.conesEquivInverseObj_π_app, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_inv, CategoryTheory.GradedObject.comapEq_inv_app, CategoryTheory.GrothendieckTopology.liftToPlusObjLimitObj_fac, CategoryTheory.Adjunction.right_triangle_components_assoc, CategoryTheory.Limits.CatCospanTransform.leftUnitor_hom_base_app, ModuleCat.extendRestrictScalarsAdj_unit_app_apply, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_hom_app, CategoryTheory.Functor.homEquivOfIsRightKanExtension_apply_app, CategoryTheory.Limits.CompleteLattice.limitCone_cone_π_app, CategoryTheory.MonoidalCategory.curriedTensorPreFunctor_map_app_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₁, CategoryTheory.Limits.pointwiseProductCompEvaluation_hom_app, CategoryTheory.Pseudofunctor.mapId'_hom_naturality, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_app, CategoryTheory.Functor.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, CategoryTheory.Functor.shiftIso_inv_naturality_assoc, CategoryTheory.Functor.IsEventuallyConstantTo.isIso_π_of_isLimit', CategoryTheory.Functor.PullbackObjObj.ofHasPullback_pt, CategoryTheory.Iso.unop_inv_hom_id_app_assoc, CategoryTheory.Functor.LeftExtension.coconeAt_ι_app, CategoryTheory.Limits.coconeOfIsSplitEpi_ι_app, CategoryTheory.CosimplicialObject.δ_naturality, CategoryTheory.Adjunction.unit_app_unit_comp_map_η_assoc, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_one_app, LightProfinite.instEpiAppOppositeNatπAsLimitCone, SSet.OneTruncation₂.map_obj, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst_assoc, CategoryTheory.Functor.mapCommGrpNatTrans_app_hom_hom_hom, CategoryTheory.ComposableArrows.homMk₂_app_one, CategoryTheory.Functor.mapTriangleCommShiftIso_hom_app_hom₂, Rep.coinvariantsAdjunction_unit_app_hom, CategoryTheory.Adjunction.leftAdjointCompIso_hom_app, shift_app_comm_assoc, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₂, CategoryTheory.ComposableArrows.δ₀Functor_map_app, SSet.σ_naturality_apply, CategoryTheory.Comonad.instHasEqualizerMapAAppUnitObjAOfHasEqualizerOfIsCosplitPair, SheafOfModules.pushforwardNatTrans_app_val_app_apply, CategoryTheory.Functor.flip₁₃Functor_obj_obj_obj_map, PresheafOfModules.colimitCocone_ι_app_app, CategoryTheory.Monad.MonadicityInternal.counitCofork_pt, CategoryTheory.GrothendieckTopology.Point.toPresheafFiberNatTrans_app, AlgebraicTopology.DoldKan.Γ₂_map_f_app, CategoryTheory.Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone_ι_app_eq_sum, CategoryTheory.Functor.Monoidal.whiskeringLeft_δ_app, CategoryTheory.Limits.reflexivePair.mkNatTrans_app_one, shift_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app, CategoryTheory.Abelian.LeftResolution.π_naturality, CategoryTheory.Under.postAdjunctionRight_counit_app_right, CategoryTheory.Limits.inr_comp_pushoutObjIso_inv_assoc, CategoryTheory.Functor.ShiftSequence.induced_shiftMap, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_app_assoc, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_comp_fiber, groupHomology.d₁₀_comp_coinvariantsMk_assoc, CategoryTheory.SmallObject.coconeOfLE_ι_app, AddCommMonCat.coyonedaForget_hom_app_app_hom, CategoryTheory.unitCompPartialBijectiveAux_symm_apply, CategoryTheory.Limits.inr_comp_pushoutObjIso_hom, CategoryTheory.μ_naturality_assoc, CategoryTheory.Functor.mapCommMonIdIso_inv_app_hom_hom, CategoryTheory.Pseudofunctor.mapId'_hom_naturality_assoc, CategoryTheory.ShortComplex.leftHomologyFunctorOpNatIso_inv_app, CategoryTheory.shiftFunctorAdd_hom_app_obj_of_induced, CategoryTheory.Comma.mapLeftIso_inverse_map_left, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₂, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left_assoc, CategoryTheory.Functor.map_shiftFunctorComm, CategoryTheory.OplaxFunctor.mapComp_naturality_right_app_assoc, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.firstMap₂_app_app_app, CategoryTheory.Functor.op_commShiftIso_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_app_fst_app, CategoryTheory.ComposableArrows.homMk₅_app_four, HomologicalComplex.mapBifunctor₁₂.ι_eq, CategoryTheory.Idempotents.FunctorExtension₁.map_app_f, CategoryTheory.SmallObject.functorialFactorizationData_p_app, HomotopyCategory.homologyFunctor_shiftMap, CategoryTheory.Adjunction.whiskerRight_counit_app_app, CategoryTheory.Functor.bifunctorComp₁₂Iso_hom_app_app_app, CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm, CategoryTheory.Functor.Fiber.inducedFunctorCompIsoSelf_inv_app, CategoryTheory.Limits.PullbackCone.isoMk_hom_hom, CategoryTheory.Functor.descOfIsLeftKanExtension_fac_app, CategoryTheory.Limits.CatCospanTransform.leftUnitor_hom_right_app, CategoryTheory.CatCommSq.hInv_iso_hom_app, CategoryTheory.SimplicialObject.isCoskeletal_iff_isIso, CategoryTheory.Limits.mapPair_right, CategoryTheory.Comma.mapLeftComp_hom_app_left, CategoryTheory.Comonad.ForgetCreatesLimits'.commuting, CategoryTheory.MonoidalCategory.DayFunctor.ν_comp_unitDesc, CategoryTheory.δ_naturalityᵣ, TopCat.Presheaf.stalkFunctor_map_germ, CategoryTheory.ComposableArrows.sc'Map_τ₂, CategoryTheory.PresheafHom.isAmalgamation_iff, CategoryTheory.ComposableArrows.isoMk₀_hom_app, CategoryTheory.Monad.MonadicityInternal.counitCofork_ι_app, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app, CategoryTheory.Functor.bifunctorComp₂₃Iso_hom_app_app_app, CategoryTheory.Adjunction.Triple.rightToLeft_app_adj₂_unit_app, PresheafOfModules.toPresheaf_map_sheafificationAdjunction_unit_app, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality, CategoryTheory.Functor.PullbackObjObj.π_fst_assoc, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₁, CategoryTheory.Functor.Initial.extendCone_obj_π_app, MonObj.mopEquiv_unitIso_inv_app_hom, CondensedSet.toTopCatMap_hom_apply, CategoryTheory.NatIso.cancel_natIso_hom_right_assoc, CategoryTheory.Localization.SmallHom.equiv_shift, CategoryTheory.ComposableArrows.functorArrows_map, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₃, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp, CategoryTheory.nerveMap_app, CategoryTheory.FunctorToTypes.comp, groupHomology.H0π_comp_H0Iso_hom_assoc, CochainComplex.shiftShortComplexFunctorIso_zero_add_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv_assoc, CategoryTheory.uliftYonedaMap_app_apply, CategoryTheory.Limits.diagramIsoSpan_inv_app, CategoryTheory.Functor.inrCompSum'_hom_app, CategoryTheory.Functor.whiskeringLeftObjCompIso_hom_app_app, CategoryTheory.Functor.mapTriangleInvRotateIso_hom_app_hom₁, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.rightUnitor_hom_unit_app, CategoryTheory.Functor.functorialityCompPostcompose_inv_app_hom, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_inv_app_assoc, CategoryTheory.Limits.HasLimit.isoOfNatIso_hom_π, CategoryTheory.MonoidalClosed.curry'_whiskerRight_comp, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_inv_app_hom_hom, CategoryTheory.Limits.HasBiproductsOfShape.colimIsoLim_hom_app, CategoryTheory.Abelian.LeftResolution.karoubi.π'_app_f, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_obj_map_app, CategoryTheory.Under.lift_map, CategoryTheory.Limits.Wedge.condition_assoc, CategoryTheory.Monad.MonadicityInternal.main_pair_reflexive, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionAssocIso_inv, CategoryTheory.Limits.CokernelCofork.π_eq_zero, CategoryTheory.MonoidalCategory.rightUnitorNatIso_inv_app, CategoryTheory.Functor.Final.extendCocone_map_hom, CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso_inv_app, CategoryTheory.ObjectProperty.LimitOfShape.toStructuredArrow_obj, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_map_fst_app, CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_one, SSet.Truncated.rightExtensionInclusion_hom_app, HomotopicalAlgebra.CofibrantObject.instWeakEquivalenceHoCatAppUnitHoCatAdj, CategoryTheory.MonoidalClosed.ofEquiv_curry_def, CategoryTheory.Limits.multispanIndexCoend_fst, CategoryTheory.Idempotents.app_idem, TopCat.Presheaf.toPushforwardOfIso_app, CategoryTheory.Functor.Monoidal.leftUnitor_hom_app, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_obj_map_app, 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, sum'_app_inl, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₃, TannakaDuality.FiniteGroup.map_mul_toRightFDRepComp, CategoryTheory.unitOfTensorIsoUnit_hom_app, CategoryTheory.StructuredArrow.mapIso_inverse_map_left, CategoryTheory.preservesLimitNatIso_hom_app, Bipointed.swapEquiv_unitIso_hom_app_toFun, CategoryTheory.Functor.FullyFaithful.homNatIso_hom_app_down, CategoryTheory.Comma.mapLeft_obj_hom, CategoryTheory.Adjunction.commShiftIso_inv_app_counit_app, CategoryTheory.FunctorToTypes.prod.fst_app, CategoryTheory.SimplicialObject.augmentedCechNerve_map_left_app, CategoryTheory.Monad.monadMonEquiv_unitIso_hom_app_toNatTrans_app, CategoryTheory.nerve.functorOfNerveMap_obj, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d_1_0_assoc, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompYoneda, CategoryTheory.Comonad.instReflectsLimitWalkingParallelPairParallelPairMapAAppUnitObjAOfReflectsLimitOfIsCosplitPair, CategoryTheory.Functor.mapMatId_inv_app, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_hom_app, CategoryTheory.Comonad.CofreeEqualizer.bottomMap_f, CategoryTheory.MonoidalCategory.externalProductSwap_hom_app_app, CategoryTheory.Adjunction.Triple.leftToRight_app_obj_assoc, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_inv_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocNatIso_hom_app_app_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionHomRight, CategoryTheory.shiftFunctorAdd'_assoc_hom_app_assoc, CategoryTheory.Limits.BinaryFan.π_app_left, CategoryTheory.Functor.IsEventuallyConstantFrom.isIso_ι_of_isColimit, AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_fac, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp_assoc, CategoryTheory.Limits.Cofork.ofπ_ι_app, CategoryTheory.Equivalence.congrRight_unitIso_hom_app, shift_app_comm, CategoryTheory.Join.mapPairRight_hom_app, SkyscraperPresheafFunctor.map'_app, CategoryTheory.Functor.limitIsoOfIsRightKanExtension_hom_π, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_assoc, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_hom_app_hom, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_hom_app_one, CategoryTheory.Equivalence.sheafCongrPrecoherent_functor_map_val_app, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, CategoryTheory.Functor.currying_functor_obj_map, CategoryTheory.Functor.leftOpRightOpEquiv_functor_map_app, CategoryTheory.yonedaGrp_map_app, CategoryTheory.Functor.Monoidal.leftUnitor_inv_app, CategoryTheory.Functor.ShiftSequence.induced_isoShiftZero_hom_app_obj, AlgebraicTopology.DoldKan.Q_f_naturality, HomologicalComplex.mapBifunctor₁₂.d₁_eq, CategoryTheory.Limits.walkingSpanOpEquiv_counitIso_inv_app, OrderHom.equivalenceFunctor_unitIso_inv_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app_assoc, CategoryTheory.Functor.isoCopyObj_hom_app, CategoryTheory.Grpd.freeForgetAdjunction_unit_app, CategoryTheory.SingleFunctors.shiftIso_zero_hom_app, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_fst, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_hom_app_app, CategoryTheory.Functor.flip_map_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app_assoc, CategoryTheory.Pseudofunctor.map₂_left_unitor_app_assoc, CategoryTheory.equivEssImageOfReflective_counitIso, LightCondensed.underlying_map, CategoryTheory.Adjunction.leftAdjointIdIso_inv_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.id_snd_app, CategoryTheory.Functor.map_shiftFunctorCompIsoId_inv_app, CategoryTheory.Equivalence.ε_comp_map_ε_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_η_unmop_app, CategoryTheory.Pseudofunctor.map₂_right_unitor_app_assoc, CategoryTheory.Pseudofunctor.map₂_right_unitor_app, CategoryTheory.Equivalence.core_unitIso_inv_app_iso_hom, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_naturality_app, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.flipFunctorToInterchange_hom_app_app, groupCohomology.isoShortComplexH1_inv, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec, CategoryTheory.Limits.Cone.toStructuredArrowCompToUnderCompForget_inv_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_hom_app_app_fst, AlgebraicTopology.DoldKan.identity_N₂_objectwise, CategoryTheory.Iso.hom_inv_id_app_app_app_assoc, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_π_app_walkingParallelPair_zero, CategoryTheory.MonoidalOpposite.tensorRightUnmopIso_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_iso_hom_app, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_invApp, CategoryTheory.map_shrinkYonedaEquiv, CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan_inj_assoc, CategoryTheory.GrothendieckTopology.Point.sheafFiberCompIso_hom_app, Condensed.underlying_map, app_zsmul, CategoryTheory.OverPresheafAux.YonedaCollection.map₁_snd, CategoryTheory.CostructuredArrow.mapNatIso_functor_map_right, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.hf, CategoryTheory.congr_app, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_obj_map_app, CategoryTheory.Functor.mapBifunctorHomologicalComplex_obj_map_f_f, CategoryTheory.ObjectProperty.LimitOfShape.toStructuredArrow_map, CategoryTheory.Functor.IsRepresentedBy.iff_natIso, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_ε_unmop_app, CategoryTheory.MonoidalOpposite.tensorLeftMopIso_inv_app_unmop, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₃, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_inv_app_val_app, CategoryTheory.Limits.diagramIsoPair_inv_app, whiskerRight_app_tensor_app_assoc, CategoryTheory.obj_ε_app, ModuleCat.FilteredColimits.ι_colimitDesc_assoc, CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtensionObjIsoColimit_hom_assoc, CategoryTheory.Localization.Construction.natTransExtension_app, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCBasicOpens_app, ModuleCat.extendScalarsId_inv_app_apply, CategoryTheory.Adjunction.comp_counit_app_assoc, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.firstMap₃_app_app_app, CategoryTheory.liftedLimitMapsToOriginal_hom_π, CategoryTheory.Functor.IsDenseSubsite.isIso_ranCounit_app_of_isDenseSubsite, CategoryTheory.Limits.opParallelPairIso_inv_app_zero, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_inv, CategoryTheory.Functor.Monoidal.rightUnitor_hom_app, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_unitIso_inv_app_f_f, CategoryTheory.Comonad.left_counit_assoc, CategoryTheory.Under.postEquiv_unitIso, Rep.coinvariantsAdjunction_homEquiv_apply_hom, CategoryTheory.Functor.Monoidal.commTensorRight_hom_app, TopCat.Presheaf.app_injective_iff_stalkFunctor_map_injective, CategoryTheory.Sieve.toFunctor_app_coe, naturality_1, CategoryTheory.Limits.PullbackCone.mk_π_app_left, CategoryTheory.constantPresheafAdj_counit_app_app, CategoryTheory.Equivalence.sheafCongr.unitIso_inv_app_val_app, CategoryTheory.Sum.functorEquivFunctorCompSndIso_hom_app_app, CategoryTheory.Join.mapIsoWhiskerLeft_hom_app, AlgebraicTopology.DoldKan.N₁Γ₀_inv_app_f_f, CategoryTheory.GrothendieckTopology.map_yonedaEquiv, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_hom_app_fst_app, TopologicalSpace.Opens.overEquivalence_counitIso_hom_app, CategoryTheory.Functor.reprW_hom_app, CategoryTheory.FreeGroupoid.mapCompLift_hom_app, CategoryTheory.ComposableArrows.opEquivalence_counitIso_hom_app_app, CategoryTheory.Comonad.ComonadicityInternal.counitFork_pt, CategoryTheory.Functor.curry_map_app_app, CategoryTheory.Limits.opParallelPairIso_inv_app_one, CategoryTheory.TwoSquare.lanBaseChange_app, mapSquare_app_τ₃, CategoryTheory.Sum.functorEquivFunctorCompFstIso_hom_app_app, CategoryTheory.Linear.toCatCenter_apply_app, CategoryTheory.whiskeringLeftCompEvaluation_inv_app, AlgebraicGeometry.Scheme.ofRestrict_app, CategoryTheory.CatCommSq.vId_iso_inv_app, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec_assoc, AlgebraicGeometry.SheafedSpace.congr_app, CategoryTheory.Comma.equivProd_unitIso_inv_app_left, CategoryTheory.Limits.Cone.extensions_app, CategoryTheory.OplaxFunctor.mapComp_naturality_left_app_assoc, CategoryTheory.Adjunction.left_triangle_components_assoc, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_symm_apply, CategoryTheory.CosimplicialObject.equivalenceLeftToRight_right, SSet.leftUnitor_hom_app_apply, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransEq_inv_app_f, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionAssocIso_hom, CategoryTheory.Cat.whiskerRight_app, CategoryTheory.Limits.Cotrident.app_one_assoc, LightCondSet.toTopCatMap_hom_apply, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_left, CategoryTheory.δ_μ_app_assoc, CategoryTheory.Over.forgetAdjStar_unit_app_left, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop_assoc, CategoryTheory.Discrete.functorComp_inv_app, CategoryTheory.Functor.mapBifunctorHomologicalComplexObj_obj_d_f, CondensedSet.epi_iff_locallySurjective_on_compHaus, CategoryTheory.Functor.shiftIso_hom_app_comp_shiftMap_of_add_eq_zero, CategoryTheory.mateEquiv_counit, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₁, CategoryTheory.Limits.HasLimit.isoOfEquivalence_inv_π, CategoryTheory.ComposableArrows.homMk₂_app_two', CategoryTheory.Comma.unopFunctorCompSnd_hom_app, CategoryTheory.Functor.CommShift.OfComp.map_iso_inv_app, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, CategoryTheory.LaxFunctor.map₂_associator_app, CategoryTheory.Limits.coconeOfCoconeCurry_ι_app, CategoryTheory.Adjunction.whiskerLeftRUnitIsoOfIsIsoCounit_inv_app, LightCondensed.lanPresheafExt_hom, CategoryTheory.yonedaEquiv_symm_naturality_right, CategoryTheory.PreGaloisCategory.PointedGaloisObject.cocone_app, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app, CochainComplex.ShiftSequence.shiftIso_inv_app, CategoryTheory.Functor.compConstIso_inv_app_app, CategoryTheory.Functor.ranCompLimIso_hom_app, CategoryTheory.Functor.mapTriangleInvRotateIso_hom_app_hom₂, CategoryTheory.constantSheafAdj_counit_app, PresheafOfModules.toSheafify_app_apply, CategoryTheory.Functor.leibnizPullback_map_app, CategoryTheory.GradedObject.ι_mapBifunctorRightUnitor_hom_apply_assoc, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₂_app, Action.resComp_hom_app_hom, CategoryTheory.Equivalence.funInvIdAssoc_inv_app, CategoryTheory.MorphismProperty.FunctorialFactorizationData.hp, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_inv_app_f, Profinite.exists_locallyConstant_finite_nonempty, CategoryTheory.sheafSectionsNatIsoEvaluation_hom_app, CategoryTheory.Limits.MonoFactorisation.fac_apply, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_app_assoc, CategoryTheory.Adjunction.map_η_comp_η, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberCompIso_hom_app_assoc, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.ComposableArrows.fourδ₄Toδ₃_app_zero, CategoryTheory.Limits.colimCompFlipIsoWhiskerColim_inv_app_app, CategoryTheory.Limits.parallelPair.eqOfHomEq_inv_app, CategoryTheory.Limits.FormalCoproduct.cosimplicialObjectFunctor_map_app, CategoryTheory.sum.inlCompAssociator_inv_app, CategoryTheory.Functor.unopId_hom_app, HomologicalComplex₂.flipEquivalenceCounitIso_hom_app_f_f, CategoryTheory.Functor.commShift₂_comm_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_inv_app_snd_app, CategoryTheory.Limits.CompleteLattice.finiteLimitCone_cone_π_app, CategoryTheory.FinitaryExtensive.isPullback_initial_to, CategoryTheory.WithInitial.liftToInitialUnique_inv_app, CategoryTheory.prod.functorProdToProdFunctorAssociator_inv_app, CategoryTheory.instIsReflexivePairMapAppCounitObj, CategoryTheory.WithInitial.mapComp_inv_app, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_hom_c_app, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv_assoc, CategoryTheory.Limits.Types.Limit.lift_π_apply', AddCommGrpCat.binaryProductLimitCone_cone_π_app_right, CategoryTheory.Iso.inv_hom_id_app_assoc, CategoryTheory.Functor.limitIsoOfIsRightKanExtension_inv_π, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_hom_app_snd_app, CategoryTheory.PreservesFiniteLimitsOfFlat.fac, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app_assoc, CategoryTheory.Limits.walkingCospanOpEquiv_unitIso_hom_app, CategoryTheory.Functor.FullyFaithful.hasShift.map_zero_inv_app, 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.Comonad.ForgetCreatesColimits'.liftedCocone_ι_app_f, AlgebraicGeometry.Scheme.Cover.functorOfLocallyDirectedHomBase_app, CategoryTheory.CostructuredArrow.mapIso_inverse_map_right, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₂, CategoryTheory.uliftYonedaIsoYoneda_inv_app_app_down, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_hom_app, CategoryTheory.Localization.lift₂_iso_hom_app_app₁, CategoryTheory.Adjunction.instIsIsoMapAppCounitOfFaithfulOfFull, CategoryTheory.Functor.Monoidal.transport_ε_assoc, HomologicalComplex.mapBifunctor₁₂.d₂_eq, ModuleCat.restrictScalarsCongr_inv_app, commBialgCatEquivComonCommAlgCat_counitIso_hom_app, CategoryTheory.Functor.Monoidal.transport_δ_assoc, AlgebraicGeometry.PresheafedSpace.map_comp_c_app, CategoryTheory.Limits.opSpan_inv_app, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_neg, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_counitIso_hom_app_right_app, CategoryTheory.SingleFunctors.shiftIso_add'_inv_app, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right_assoc, CategoryTheory.IsPullback.of_isLimit_cone, CategoryTheory.Limits.coyonedaCompLimIsoCones_hom_app_app, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoColimitUncurryWhiskeringLeft₂_hom, CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_right, CategoryTheory.Limits.colimitCoconeOfUnique_isColimit_desc, CategoryTheory.toOverUnitPullback_hom_app_left, CategoryTheory.Limits.mapPairIso_hom_app, CategoryTheory.Functor.sheafPushforwardContinuousId'_hom_app_val_app, CategoryTheory.Monad.left_unit_assoc, Condensed.isoFinYoneda_inv_app, CategoryTheory.Limits.pullbackObjIso_inv_comp_snd, CategoryTheory.ExponentiableMorphism.coev_ev, CategoryTheory.Limits.limit.lift_π, CategoryTheory.Limits.IsColimit.fac_assoc, AlgebraicGeometry.SheafedSpace.isColimit_exists_rep, AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_inv_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso_inv_app_app, CategoryTheory.Subfunctor.equalizer_obj, CategoryTheory.compEvaluation_inv_app, TopCat.Presheaf.stalkFunctor_map_germ_apply', CategoryTheory.Comonad.adj_unit, CategoryTheory.Adjunction.map_ε_comp_counit_app_unit, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_app, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₂, CategoryTheory.SingleFunctors.hom_inv_id_hom_app, AlgebraicTopology.DoldKan.P_f_naturality, CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_right, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_val_app, SSet.Truncated.HomotopyCategory.descOfTruncation_obj_mk, CategoryTheory.Limits.wideEqualizer.trident_π_app_zero, CategoryTheory.Limits.cospanExt_inv_app_right, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_invApp, CategoryTheory.TransfiniteCompositionOfShape.ici_incl, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₃, SimplicialObject.Split.cofan_inj_naturality_symm, CategoryTheory.MonoidalOpposite.tensorLeftIso_inv_app_unmop, CategoryTheory.Limits.LimitPresentation.w_assoc, CommGrpCat.coyoneda_map_app, CategoryTheory.Sum.swapCompInr_inv_app, CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_three, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_hom, CategoryTheory.Limits.colimitYonedaHomIsoLimitRightOp_π_apply, CategoryTheory.WithInitial.opEquiv_unitIso_hom_app, CategoryTheory.obj_η_app, CategoryTheory.Limits.FormalCoproduct.evalCompInclIsoId_hom_app_app, CategoryTheory.Comma.unopFunctorCompFst_hom_app, TopologicalSpace.OpenNhds.inclusionMapIso_inv_app, CategoryTheory.Sheaf.isConstant_iff_isIso_counit_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_map, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_map_snd_app, CategoryTheory.Over.coprod_map_app, ModuleCat.monoidalClosed_pre_app, CategoryTheory.Adjunction.homEquiv_leftAdjointUniq_hom_app, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_apply, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_hom_app_hom_hom, CategoryTheory.Bicategory.associatorNatIsoMiddle_inv_app, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_hom_assoc, CategoryTheory.ShiftMkCore.zero_add_inv_app, SSet.associator_inv_app_apply, 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, CategoryTheory.Quotient.natTransLift_app, CategoryTheory.Functor.ranAdjunction_unit_app, CategoryTheory.Limits.Types.FilteredColimit.isColimit_eq_iff', CategoryTheory.pullbackShiftFunctorAdd'_inv_app, CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_app_π, CategoryTheory.Limits.end_.condition_assoc, Profinite.exists_locallyConstant_fin_two, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.Functor.shiftIso_hom_naturality, CategoryTheory.WithInitial.ofCommaMorphism_app, CategoryTheory.Sheaf.ΓRes_naturality, CategoryTheory.Monad.Algebra.unit, CategoryTheory.Functor.coreComp_inv_app_iso_hom, CategoryTheory.ShortComplex.mapNatTrans_τ₃, 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, SheafOfModules.pushforwardNatIso_hom, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app_assoc, CategoryTheory.prodOpEquiv_counitIso_inv_app, CategoryTheory.TwistShiftData.shiftFunctor_map, CategoryTheory.Comonad.beckCoalgebraFork_π_app, CategoryTheory.MonoidalOpposite.tensorIso_inv_app_unmop, CategoryTheory.MonoidalOpposite.mopMopEquivalence_counitIso_hom_app, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_app_assoc, CategoryTheory.TwistShiftData.shiftFunctorZero_inv_app, CategoryTheory.ShortComplex.pOpcyclesNatTrans_app, CategoryTheory.bifunctorComp₂₃Obj_map_app, CategoryTheory.Equivalence.core_unitIso_inv_app_iso_inv, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp_hom_app_f, CategoryTheory.Functor.lanAdjunction_counit_app, CategoryTheory.MonoidalCategory.rightUnitorNatIso_hom_app, CategoryTheory.Adjunction.unit_comp_map_eq_iff, CategoryTheory.Functor.pointwiseLeftKanExtension_desc_app, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_obj_map_app, CategoryTheory.Functor.isIso_lanAdjunction_counit_app_iff, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.secondMap₃_app_app_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_val_app, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk_assoc, groupCohomology.isoShortComplexH2_inv, CategoryTheory.Adjunction.isIso_counit_app_iff_mem_essImage, CategoryTheory.shiftFunctorCompIsoId_zero_zero_inv_app, CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_inv_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_inv_app'_assoc, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_inv, CategoryTheory.WithTerminal.equivComma_unitIso_hom_app_app, CategoryTheory.prod.prodFunctorToFunctorProdAssociator_hom_app_app, CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse_assoc, CategoryTheory.DinatTrans.dinaturality, TopCat.piFan_π_app, CategoryTheory.Functor.coreComp_inv_app_iso_inv, CategoryTheory.Adjunction.shift_unit_app_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionHom, HomologicalComplex.homologyFunctorIso_inv_app, CategoryTheory.SmallObject.instIsIsoRightAppArrowιIteration, CategoryTheory.oppositeShiftFunctorAdd_hom_app, TopCat.coconeOfCoconeForget_ι_app, CategoryTheory.ComposableArrows.homMk₀_app, CochainComplex.liftCycles_shift_homologyπ_assoc, CategoryTheory.Equivalence.counitInv_naturality_assoc, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_inv_app, CategoryTheory.Comma.colimitAuxiliaryCocone_ι_app, CategoryTheory.Limits.Fan.mk_π_app, ContinuousCohomology.const_app_hom, CategoryTheory.FunctorToTypes.prod.snd_app, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂, CategoryTheory.curryingIso_hom_toFunctor_map_app, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_fst, CategoryTheory.Functor.leftOpRightOpIso_inv_app, CategoryTheory.Functor.mapTriangleIdIso_hom_app_hom₁, HomotopicalAlgebra.CofibrantObject.HoCat.adjCounit'_app, CategoryTheory.Sheaf.sheafifyCocone_ι_app_val, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatTrans_app, CategoryTheory.MorphismProperty.Over.mapId_hom_app_left, SSet.RelativeMorphism.map_coe, CategoryTheory.Under.postAdjunctionLeft_unit_app, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app', CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_hom_app_hom_app, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_app, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.Functor.mapTriangleIdIso_hom_app_hom₂, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop, CategoryTheory.SingleFunctors.postcompIsoOfIso_inv_hom_app, CategoryTheory.WithTerminal.opEquiv_unitIso_inv_app, CategoryTheory.Functor.ShiftSequence.induced_shiftMap_assoc, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.relativeGluingData_natTrans_app, CategoryTheory.LocalizerMorphism.isIso_iff_of_hasLeftResolutions, CategoryTheory.Functor.pushforwardContinuousSheafificationCompatibility_hom_app_val, CategoryTheory.OverPresheafAux.unitForward_naturality₁, CategoryTheory.Limits.diagramIsoParallelPair_inv_app, CategoryTheory.MonoidalCategory.DayConvolution.whiskerRight_comp_unit_app, CategoryTheory.Adjunction.commShiftIso_hom_app_counit_app_shift, CategoryTheory.ComposableArrows.fourδ₄Toδ₃_app_three, CategoryTheory.MorphismProperty.Over.pullbackComp_left_fst_fst, Profinite.Extend.functor_map, CategoryTheory.LaxFunctor.mapComp_assoc_right_app_assoc, SheafOfModules.pushforwardPushforwardEquivalence_counit_app_val_app, CategoryTheory.Limits.coneOfAdj_π, CategoryTheory.Discrete.natIsoFunctor_inv_app, removeOp_app, CategoryTheory.Bicategory.associatorNatIsoRight_inv_app, CategoryTheory.Limits.colimitCoyonedaHomIsoLimitLeftOp_π_apply, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.convolutionUnitApp_eq, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app, CategoryTheory.Limits.cospanExt_hom_app_right, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂'_obj_map_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_map, CategoryTheory.PreGaloisCategory.endMulEquivAutGalois_pi, Condensed.locallyConstantIsoFinYoneda_hom_app, CategoryTheory.Pi.comapComp_hom_app, AlgebraicTopology.DoldKan.hσ'_naturality, TopCat.Presheaf.ext_iff, app_sub, naturality_assoc, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_left_right, CategoryTheory.GlueData.diagramIso_hom_app_right, ModuleCat.homEquiv_extendScalarsId, CategoryTheory.Limits.Concrete.isColimit_rep_eq_of_exists, CategoryTheory.MonoidalCategory.prodCompExternalProduct_hom_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_hom_app_snd_app, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_isoPointwiseLeftKanExtension_hom, app_neg, CategoryTheory.toOverUnitPullback_inv_app_left, CategoryTheory.NatIso.cancel_natIso_hom_left, CategoryTheory.Comma.mapRightIso_inverse_map_left, CategoryTheory.Functor.sheafPushforwardContinuousComp'_hom_app_val_app, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app_assoc, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.firstMap_app_app_app, CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv, CategoryTheory.Limits.Cofork.app_one_eq_π, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_inv_app_val_app, CategoryTheory.Equivalence.counit_app_functor, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_apply, CategoryTheory.Limits.spanIsoMk_inv_app, AlgebraicGeometry.Scheme.exists_isOpenCover_and_isAffine, CategoryTheory.GrothendieckTopology.Plus.toPlus_apply, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.Presheaf.isLocallyInjective_iff_injective_of_separated, CategoryTheory.piEquivalenceFunctorDiscrete_counitIso, CategoryTheory.SingleFunctors.shiftIso_add'_hom_app, CategoryTheory.Functor.whiskeringLeft₃_obj_obj_obj_obj_map_app_app, CategoryTheory.Comma.mapLeftId_inv_app_right, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_inv_app_op_one, CategoryTheory.Equivalence.sheafCongr.counitIso_inv_app_val_app, CategoryTheory.Functor.mapMatComp_inv_app, groupHomology.coinvariantsMk_comp_H0Iso_inv_assoc, CategoryTheory.Sieve.functorPushforward_equivalence_eq_pullback, CategoryTheory.Limits.opHomCompWhiskeringLimYonedaIsoCocones_inv_app_app, PresheafOfModules.freeObjDesc_app, CategoryTheory.StructuredArrow.mapNatIso_functor_map_left, CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp_assoc, AlgebraicGeometry.LocallyRingedSpace.comp_c_app, CategoryTheory.sheafSectionsNatIsoEvaluation_inv_app, CategoryTheory.nerveMap_app_mk₀, CategoryTheory.GradedObject.ι_mapBifunctorLeftUnitor_hom_apply_assoc, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd_assoc, CategoryTheory.FunctorToTypes.prod_ext'_iff, unop_app, CategoryTheory.Functor.mapDerivedCategoryFactorsh_hom_app, CategoryTheory.OplaxFunctor.mapComp_naturality_right_app, CategoryTheory.Adjunction.Localization.η_app, CategoryTheory.StructuredArrow.map₂_obj_hom, CategoryTheory.sum.inlCompInverseAssociator_hom_app_down_down, CategoryTheory.Functor.sheafAdjunctionCocontinuous_unit_app_val, CategoryTheory.Limits.HasBiproductsOfShape.colimIsoLim_inv_app, CategoryTheory.StructuredArrow.mapNatIso_counitIso_inv_app_right, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_hom_app_unop, CategoryTheory.Sieve.toUliftFunctor_app_down_coe, CategoryTheory.NatIso.cancel_natIso_inv_left, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_zero, CategoryTheory.WithInitial.coconeEquiv_unitIso_inv_app_hom_right, CategoryTheory.Tor'_map_app, CategoryTheory.Functor.mapDifferentialObject_map_f, CategoryTheory.ProjectiveResolution.fromLeftDerivedZero_eq, CategoryTheory.oppositeShiftFunctorAdd'_inv_app, CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit, CategoryTheory.Functor.whiskeringRight_map_app_app, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_inv_assoc, CategoryTheory.Functor.lanUnit_app_app_lanAdjunction_counit_app_app_assoc, AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_toGlued, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_map_right, CategoryTheory.GrothendieckTopology.Point.sheafFiberCompIso_inv_app, 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, CategoryTheory.Functor.whiskeringLeft₂_obj_obj_map_app_app, HomologicalComplex.homologyFunctorSingleIso_hom_app, CategoryTheory.right_unitality_app, CategoryTheory.Abelian.FunctorCategory.imageObjIso_inv, CategoryTheory.Adjunction.homEquiv_id, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_inv_app_fst_app, CategoryTheory.Functor.instIsIsoAppRanCounit_1, CategoryTheory.Limits.Cones.postcomposeComp_hom_app_hom, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_hom_app, CategoryTheory.Limits.cospanExt_hom_app_left, TopCat.Presheaf.presheafEquivOfIso_inverse_map_app, CategoryTheory.Equivalence.adjointify_η_ε, TopCat.Presheaf.stalkFunctor_map_germ_assoc, CategoryTheory.Limits.Cocone.extensions_app, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_map_app, CategoryTheory.MonoidalCategory.externalProductFlip_inv_app_app_app_app, CategoryTheory.LaxFunctor.mapComp_assoc_left_app_assoc, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₁, HomologicalComplex.mapBifunctor.d₁_eq, CategoryTheory.Limits.ColimitPresentation.bind_ι_app, CategoryTheory.Under.forgetCone_π_app, CategoryTheory.Equivalence.inverse_counitInv_comp, CategoryTheory.Functor.PullbackObjObj.ofHasPullback_fst, CategoryTheory.WithTerminal.liftToTerminalUnique_hom_app, CategoryTheory.Limits.diagramIsoSpan_hom_app, TopologicalSpace.OpenNhds.inclusionMapIso_hom_app, CategoryTheory.Limits.Types.surjective_π_app_zero_of_surjective_map_aux, CategoryTheory.Functor.Monoidal.whiskerLeft_app_snd_assoc, CategoryTheory.flipCompEvaluation_inv_app, CategoryTheory.Functor.FullyFaithful.hasShift.map_zero_hom_app, CategoryTheory.Functor.Fiber.fiberInclusionCompIsoConst_hom_app, CategoryTheory.Cat.leftUnitor_inv_app, CategoryTheory.η_ε_app, CategoryTheory.Functor.leftKanExtensionIsoFiberwiseColimit_inv_app, CategoryTheory.GradedObject.mapTrifunctorMapNatTrans_app_app_app, CategoryTheory.shiftFunctorAdd_assoc_inv_app, CategoryTheory.LaxFunctor.map₂_leftUnitor_app, CategoryTheory.Adjunction.left_triangle_components, CategoryTheory.Subfunctor.lift_app_coe, AlgebraicGeometry.PresheafedSpace.colimitCocone_ι_app_c, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₂_assoc, CategoryTheory.Equivalence.core_counitIso_inv_app_iso_inv, CategoryTheory.ComposableArrows.fourδ₃Toδ₂_app_zero, CategoryTheory.Join.InclRightCompRightOpOpEquivFunctor_hom_app, CategoryTheory.Equivalence.unit_app_tensor_comp_inverse_map_δ_functor, CategoryTheory.Join.mapPairRight_inv_app, CategoryTheory.Functor.RightExtension.postcompose₂ObjMkIso_hom_left_app, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂_assoc, CategoryTheory.Limits.IsLimit.isIso_π_app_of_isInitial, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₁, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_inv_app_f, CategoryTheory.Functor.equiv_counitIso, CategoryTheory.WithTerminal.equivComma_unitIso_inv_app_app, CategoryTheory.Iso.map_hom_inv_id_eval_app, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_hom_app, CategoryTheory.Pseudofunctor.Grothendieck.categoryStruct_comp_fiber, CommShiftCore.app_shift_assoc, PresheafOfModules.map_comp_assoc, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app, CategoryTheory.Comma.mapLeftComp_hom_app_right, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_μ_assoc, CategoryTheory.Functor.whiskeringRight₂_obj_map_app_app, CategoryTheory.shiftFunctorAdd'_assoc_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.iso_hom_naturality, retractArrowApp_i, CategoryTheory.Pi.comapId_inv_app, CategoryTheory.Functor.unopComp_hom_app, CategoryTheory.Functor.leibnizPushout_map_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberCompIso_hom_app, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₁, CategoryTheory.μ_naturalityₗ_assoc, AlgebraicTopology.DoldKan.Compatibility.υ_inv_app, CategoryTheory.Functor.compFlipUncurryIso_hom_app, CategoryTheory.Comma.mapRight_map_right, CategoryTheory.Discrete.natIso_inv_app, CategoryTheory.Functor.IsCoverDense.Types.pushforwardFamily_apply, CategoryTheory.SingleFunctors.postcomp_shiftIso_hom_app, CategoryTheory.Limits.CoconeMorphism.map_w, 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, CategoryTheory.ComposableArrows.homMk₁_app, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_unitIso_inv_app_right_app, CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.map_app_f, CategoryTheory.Functor.whiskeringRightObjCompIso_inv_app_app, CategoryTheory.Equivalence.unit_inverse_comp_assoc, CategoryTheory.Join.mkFunctorRight_hom_app, CategoryTheory.Comma.mapFst_inv_app, CategoryTheory.Limits.Cones.postcomposeId_inv_app_hom, HomologicalComplex.natIsoSc'_inv_app_τ₁, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.comp_fst_app, CategoryTheory.LocalizerMorphism.isIso_α_iff_of_isRightDerivabilityStructure, CategoryTheory.SimplicialObject.equivalenceLeftToRight_left_app, CategoryTheory.WithTerminal.coneEquiv_counitIso_hom_app_hom, CategoryTheory.WithInitial.mapId_hom_app, CategoryTheory.presheafHom_map_app_op_mk_id, CategoryTheory.InjectiveResolution.rightDerived_app_eq, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_app_app_germToPullbackStalk, SSet.degenerate_iff_of_isIso, CategoryTheory.Abelian.coimIsoIm_hom_app, CategoryTheory.Cat.whiskerLeft_app, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_comp, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_inv_app, CategoryTheory.Pseudofunctor.ObjectProperty.map₂_app_hom, TopCat.isTopologicalBasis_cofiltered_limit, SSet.ι₀_app_fst, CategoryTheory.Functor.CommShift.isoAdd'_inv_app, CategoryTheory.Adjunction.derivedε_fac_app, CategoryTheory.ComposableArrows.isIso_iff₁, CategoryTheory.Localization.associator_hom_app_app_app, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.topMapₗ_app, CategoryTheory.Functor.CommShift.OfComp.map_iso_hom_app, CategoryTheory.Functor.CommShift.OfComp.map_iso_inv_app_assoc, CategoryTheory.Functor.CommShift.isoZero'_hom_app, CategoryTheory.Bicategory.leftUnitorNatIso_inv_app, CategoryTheory.Equivalence.congrRight_counitIso_inv_app, CategoryTheory.Equivalence.counit_naturality, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.unitIso_inv_app_hom_app, CategoryTheory.Limits.colimit.ι_desc_app, CategoryTheory.MonoidalCategory.leftUnitorNatIso_hom_app, CategoryTheory.forgetAdjToOver_counit_app, CategoryTheory.sum.inrCompInverseAssociator_inv_app, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_mon_one, CategoryTheory.sheafComposeNatTrans_fac, CategoryTheory.Limits.IsLimit.fac, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_app_comp_π_assoc, CategoryTheory.Pi.comapEvalIsoEval_inv_app, CategoryTheory.CostructuredArrow.mapIso_counitIso_inv_app_left, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₁, CategoryTheory.GrothendieckTopology.yonedaEquiv_apply, CategoryTheory.SimplicialObject.Truncated.whiskering_obj_map_app, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst_assoc, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_map_app_hom_hom, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_obj_π_app, CategoryTheory.OplaxFunctor.map₂_rightUnitor_app_assoc, CategoryTheory.IsPushout.of_isColimit_cocone, CategoryTheory.Adjunction.map_μ_comp_counit_app_tensor_assoc, HomologicalComplex.ι_mapBifunctorMap, CategoryTheory.Comma.mapLeftIso_functor_map_right, CategoryTheory.SimplicialObject.augmentedCechNerve_obj_hom_app, CategoryTheory.MonoidalCategory.DayFunctor.ι_comp_isoPointwiseLeftKanExtension_inv, CategoryTheory.Functor.currying_functor_map_app, CategoryTheory.map_coyonedaEquiv, CategoryTheory.shiftFunctorAdd_zero_add_inv_app, CategoryTheory.Adjunction.homEquiv_symm_apply, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_inv_app_hom₁, CategoryTheory.Iso.hom_inv_id_app_app_app, CategoryTheory.shiftFunctorComm_hom_app_of_add_eq_zero_assoc, CategoryTheory.Cat.freeMapIdIso_inv_app, CategoryTheory.Limits.combineCones_π_app_app, AddCommGrpCat.coyonedaType_map_app, CategoryTheory.Adjunction.counit_isSplitMono_of_R_full, CategoryTheory.Functor.bifunctorComp₂₃Iso_inv_app_app_app, CategoryTheory.ihom.ev_coev, ModuleCat.ihom_ev_app, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_inv_app_hom₃, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_hom_app_hom, CategoryTheory.Yoneda.obj_map_id, CategoryTheory.MonoidalClosed.whiskerLeft_curry_ihom_ev_app_assoc, HomologicalComplex.ιOrZero_mapBifunctorAssociatorX_hom_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.w_app_assoc, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_inv_app, CategoryTheory.Limits.spanExt_inv_app_right, CategoryTheory.Discrete.natTrans_app, CategoryTheory.Monoidal.whiskerLeft_app, CochainComplex.liftCycles_shift_homologyπ, CategoryTheory.Adjunction.inv_map_unit, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app_val_app, CategoryTheory.map_yonedaEquiv', HomologicalComplex.natIsoSc'_hom_app_τ₁, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionHom, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_right_right, CategoryTheory.prod.functorProdToProdFunctorAssociator_hom_app, CategoryTheory.StructuredArrow.mapIso_counitIso_hom_app_right, CategoryTheory.Limits.Cowedge.condition, CommMonCat.coyonedaType_map_app, CategoryTheory.Functor.costructuredArrowMapCocone_ι_app, SSet.range_eq_iSup_of_isColimit, CategoryTheory.Over.iteratedSliceForwardIsoPost_hom_app, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.isPullback_natTrans_ι_toBase, CategoryTheory.Cokleisli.Adjunction.toCokleisli_map, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.secondMap_app_app_app, CategoryTheory.Join.inlCompFromSum_inv_app, CategoryTheory.Limits.parallelPairHom_app_zero, CategoryTheory.evaluation_map_app, CategoryTheory.Functor.mapTriangle_map_hom₂, CategoryTheory.Pi.comapEvalIsoEval_hom_app, CategoryTheory.Equivalence.congrRight_counitIso_hom_app, CategoryTheory.Adjunction.functorialityCounit'_app_hom, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceFunctorProj_inv_app, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop_assoc, CategoryTheory.Functor.homEquivOfIsLeftKanExtension_apply_app, CategoryTheory.BasedNatTrans.app_isHomLift, CategoryTheory.Iso.map_inv_hom_id_eval_app_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_right_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality, CategoryTheory.WithInitial.mapComp_hom_app, CategoryTheory.Idempotents.DoldKan.η_hom_app_f, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_right, CategoryTheory.Over.lift_map, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_left, CategoryTheory.Functor.lanCompColimIso_hom_app, AlgebraicGeometry.SheafedSpace.Γ_map_op, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_right, CategoryTheory.Pretriangulated.preadditiveCoyoneda_homologySequenceδ_apply, Profinite.exists_hom, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm_assoc, AlgebraicTopology.DoldKan.natTransQ_app, CategoryTheory.μ_app, CategoryTheory.Adjunction.Triple.leftToRight_app_map_adj₁_unit_app, CategoryTheory.Sigma.inclDesc_hom_app, CategoryTheory.Over.postAdjunctionLeft_counit_app_left, CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_inv_apply, CategoryTheory.Arrow.augmentedCechConerve_hom_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_hom_app_app, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_symm_apply, CategoryTheory.LaxFunctor.map₂_leftUnitor_app_assoc, CategoryTheory.Comma.mapRightComp_inv_app_left, CategoryTheory.Cat.eqToHom_app, CategoryTheory.StructuredArrow.mapIso_counitIso_inv_app_right, CategoryTheory.ShiftMkCore.assoc_hom_app_assoc, CategoryTheory.Equivalence.changeFunctor_counitIso_inv_app, CategoryTheory.GradedObject.ι_mapTrifunctorMapMap, CategoryTheory.Reflective.instIsIsoAppUnitReflectorAdjunctionA, CategoryTheory.Limits.parallelPair.ext_inv_app, AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_app, CategoryTheory.SingleFunctors.shiftIso_zero_inv_app, StalkSkyscraperPresheafAdjunctionAuxs.toSkyscraperPresheaf_app, CategoryTheory.Functor.whiskeringLeft₃ObjObjObj_map_app_app_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply_assoc, CategoryTheory.BasedNatTrans.isHomLift, CategoryTheory.Adjunction.Triple.rightToLeft_app_adj₂_unit_app_assoc, CategoryTheory.Comma.mapRightIso_unitIso_hom_app_right, CategoryTheory.Over.mapComp_inv_app_left, CategoryTheory.GlueData.diagramIso_hom_app_left, CategoryTheory.Enriched.FunctorCategory.functorEnrichedId_app, TwoP.swapEquiv_unitIso_inv_app_hom_toFun, CategoryTheory.Equivalence.congrRight_unitIso_inv_app, CategoryTheory.NatIso.inv_inv_app, CategoryTheory.Adjunction.shift_counit_app_assoc, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_right, CategoryTheory.shift_neg_shift', CategoryTheory.Monoidal.Reflective.instIsIsoMapTensorHomAppUnit, CategoryTheory.Limits.spanExt_inv_app_left, CategoryTheory.ihom.coev_ev_assoc, SheafOfModules.pushforwardNatTrans_comp, CategoryTheory.Join.edgeTransform_app, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_counit, CommShift₂.commShift_app, CategoryTheory.Equivalence.functor_unit_comp_assoc, CategoryTheory.Limits.mapPair_left, CategoryTheory.Limits.Fork.equalizer_ext, CategoryTheory.yonedaGrp_naturality, CategoryTheory.Pi.comapComp_inv_app, CategoryTheory.Sheaf.instEpiAppArrowILocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, CategoryTheory.Adjunction.unit_naturality_assoc, CategoryTheory.Functor.currying_inverse_map_app_app, CategoryTheory.Functor.PullbackObjObj.isPullback, 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.Equivalence.symmEquivInverse_map_app, AlgebraicGeometry.SheafedSpace.comp_c_app', CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app_assoc, CategoryTheory.ShiftedHom.opEquiv'_add_symm, CategoryTheory.Sigma.inclDesc_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_hom_app, CategoryTheory.Functor.functorHomEquiv_symm_apply_app_app, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.mem_incl_app, CategoryTheory.Bicategory.rightUnitorNatIso_hom_app, CategoryTheory.Functor.PushoutObjObj.ofHasPushout_ι, CategoryTheory.Adjunction.Triple.mono_leftToRight_app_iff, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app, CategoryTheory.Pi.comapId_hom_app, SSet.stdSimplex.isoNerve_inv_app_apply, HomologicalComplex.forgetEval_inv_app, CategoryTheory.colimitYonedaHomEquiv_π_apply, CategoryTheory.Adjunction.comp_unit_app, CategoryTheory.Abelian.coimIsoIm_inv_app, AlgebraicGeometry.PresheafedSpace.ofRestrict_c_app, CategoryTheory.Functor.whiskeringLeft_map_app_app, CategoryTheory.Adjunction.whiskerLeft_counit_app_app, CategoryTheory.TwoSquare.ext_iff, CategoryTheory.Limits.Types.isLimitEquivSections_symm_apply, CategoryTheory.Limits.pullbackObjIso_hom_comp_snd, CategoryTheory.uliftCoyonedaEquiv_comp, CategoryTheory.Cat.freeMapCompIso_inv_app, CategoryTheory.Functor.IsCoverDense.Types.naturality_assoc, CategoryTheory.BraidedCategory.ofBifunctor.Forward.firstMap₃_app_app_app, CategoryTheory.BraidedCategory.tensorLeftIsoTensorRight_inv_app, CategoryTheory.Limits.colimitFlipIsoCompColim_inv_app, CategoryTheory.yonedaEquiv_symm_app_apply, CategoryTheory.Adjunction.adjunctionOfEquivLeft_unit_app, CategoryTheory.Adjunction.leftAdjointCompNatTrans_app, CategoryTheory.TwoSquare.vId_app, ModuleCat.ExtendRestrictScalarsAdj.unit_app, SSet.Truncated.StrictSegal.spineToSimplex_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_hom_app, CategoryTheory.Functor.mapCommMonCompIso_hom_app_hom_hom, CategoryTheory.evaluationAdjunctionLeft_counit_app, CategoryTheory.ComposableArrows.homMk₃_app_zero, CategoryTheory.WithTerminal.coneEquiv_functor_map_hom, CategoryTheory.Join.mapIsoWhiskerRight_inv_app, CategoryTheory.Pseudofunctor.mapId'_inv_naturality, CategoryTheory.Functor.mapBifunctorHomologicalComplex_obj_obj_d_f, CategoryTheory.Monad.algebraFunctorOfMonadHom_map_f, CategoryTheory.functorProdFunctorEquivCounitIso_hom_app_app, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_right_assoc, CochainComplex.ι_mapBifunctorShift₁Iso_hom_f, CategoryTheory.Adjunction.rightAdjointUniq_inv_app, CategoryTheory.NatIso.ofComponents_hom_app, CategoryTheory.Monad.right_unit_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_app_assoc, CochainComplex.ShiftSequence.shiftIso_hom_app, CategoryTheory.MorphismProperty.FunctorsInverting.hom_ext_iff, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInlIso_inv_app_app, CategoryTheory.MonoidalCategory.tensoringRight_μ, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_shift, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_assoc, CategoryTheory.Limits.CatCospanTransform.rightUnitor_hom_right_app, CategoryTheory.Functor.structuredArrowMapCone_π_app, CategoryTheory.Functor.whiskeringLeftObjCompIso_inv_app_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_inv_app_fst_app, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_app, sum_app_inr, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_map_app_app_app, AlgebraicGeometry.tilde.toOpen_map_app, CategoryTheory.Limits.compYonedaSectionsEquiv_symm_apply_coe, CategoryTheory.yonedaEquiv_comp, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app_assoc, CategoryTheory.Adjunction.Quadruple.epi_leftTriple_rightToLeft_app_iff_mono_rightTriple_leftToRight_app, CategoryTheory.Comma.coneOfPreserves_π_app_left, CochainComplex.mappingCone.map_δ, CategoryTheory.unitCompPartialBijective_symm_apply, CategoryTheory.ihom.coev_ev, CategoryTheory.bifunctorComp₁₂Obj_map_app, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_εIso_hom, CategoryTheory.Functor.currying_inverse_obj_map_app, CategoryTheory.Limits.parallelPairOpIso_hom_app_zero, CategoryTheory.Functor.IsCoverDense.Types.naturality, CategoryTheory.LiftRightAdjoint.instIsCoreflexivePairMapAppUnitOtherMap, AlgebraicGeometry.LocallyRingedSpace.stalkMap_germ, CategoryTheory.Functor.mapComposableArrows_map_app
id 📖	CompOp	6 math math: CategoryTheory.BasedNatTrans.id_toNatTrans, id_app', CategoryTheory.Adjunction.CoreUnitCounit.right_triangle, CategoryTheory.Functor.whiskerRight_id, CategoryTheory.Functor.whiskerLeft_id, CategoryTheory.Adjunction.CoreUnitCounit.left_triangle
instInhabited 📖	CompOp	—
vcomp 📖	CompOp	3 math math: vcomp_app, CategoryTheory.BasedNatTrans.comp_toNatTrans, vcomp_eq_comp

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
ext 📖	—	app	—	—	—
ext_iff 📖	mathematical	—	app	—	ext
id_app' 📖	mathematical	—	app id CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj	—	—
naturality 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Functor.map app	—	—
naturality' 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj app CategoryTheory.Functor.map	—	naturality
naturality_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Functor.map app	—	CategoryTheory.Category.assoc Mathlib.Tactic.Reassoc.eq_whisker' naturality
vcomp_app 📖	mathematical	—	app vcomp CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj	—	—

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