Iso

📁 Source: Mathlib/CategoryTheory/Iso.lean

Statistics

Metric	Count
Definitions mapIso, hom, homFromEquiv, homToEquiv, instInhabited, instTransIso, inv, refl, trans, «term_≪≫_», asIso, inv, «term_≅_»	13
Theorems mapIso_hom, mapIso_inv, mapIso_refl, mapIso_symm, mapIso_trans, map_hom_inv, map_hom_inv_assoc, map_inv, map_inv_hom, map_inv_hom_assoc, map_isIso, inv_hom, inv_inv, comp_inv_eq, comp_isIso, comp_isIso', epi_of_iso, eq_comp_inv, eq_inv_comp, eq_inv_of_hom_inv_id, eq_inv_of_inv_hom_id, hom_inv_id, hom_inv_id_assoc, id, inv_comp, inv_comp_assoc, inv_comp_eq, inv_eq_inv, inv_eq_of_hom_inv_id, inv_eq_of_inv_hom_id, inv_hom_id, inv_hom_id_assoc, inv_id, inv_inv, inv_isIso, mono_of_iso, of_isIso_comp_left, of_isIso_comp_right, of_isIso_fac_left, of_isIso_fac_right, out, cancel_iso_hom_left, cancel_iso_hom_right, cancel_iso_hom_right_assoc, cancel_iso_inv_left, cancel_iso_inv_right, cancel_iso_inv_right_assoc, comp_hom_eq_id, comp_inv_eq, comp_inv_eq_id, eq_comp_inv, eq_inv_comp, ext, ext_iff, ext_inv, homFromEquiv_apply, homFromEquiv_symm_apply, homToEquiv_apply, homToEquiv_symm_apply, hom_comp_eq_id, hom_eq_inv, hom_inv_id, hom_inv_id_assoc, inv_comp_eq, inv_comp_eq_id, inv_eq_hom, inv_eq_inv, inv_ext, inv_ext', inv_hom_id, inv_hom_id_assoc, isIso_hom, isIso_inv, map_hom_inv_id, map_hom_inv_id_assoc, map_inv_hom_id, map_inv_hom_id_assoc, nonempty_iso_refl, nonempty_iso_symm, refl_hom, refl_inv, refl_symm, refl_trans, self_symm_id, self_symm_id_assoc, symm_bijective, symm_eq_iff, symm_hom, symm_inv, symm_mk, symm_self_id, symm_self_id_assoc, symm_symm_eq, trans_assoc, trans_def, trans_hom, trans_inv, trans_mk, trans_refl, trans_symm, asIso_hom, asIso_inv, comp_hom_eq_id, comp_inv_eq_id, eq_of_inv_eq_inv, hom_comp_eq_id, inv_comp_eq_id, isIso_comp_left_iff, isIso_comp_right_iff, isIso_of_comp_hom_eq_id, isIso_of_hom_comp_eq_id	111
Total	124

CategoryTheory

Definitions

Name	Category	Theorems
asIso 📖	CompOp	17 math math: equivEssImageOfReflective_unitIso, instIsMonHomHomAsIso, OverClass.instHomIsOverInvAsIso, Over.preservesTerminalIso_pullback, asIso_inv, OverClass.instHomIsOverHomAsIso, Functor.CoreMonoidal.ofOplaxMonoidal_εIso, rightDistributor_assoc, leftDistributor_rightDistributor_assoc, asIso_hom, Limits.prodComparisonNatIso_inv, equivEssImageOfReflective_counitIso, ShortComplex.HomologyData.ofIsIsoLeftRightHomologyComparison'_iso, leftDistributor_assoc, Subfunctor.equivalenceMonoOver_counitIso, Functor.CoreMonoidal.ofOplaxMonoidal_μIso, Limits.coprodComparisonNatIso_inv
inv 📖	CompOp	269 math math: Limits.imageSubobjectCompIso_hom_arrow, MonoidalCategory.hom_inv_whiskerRight', IsIso.inv_eq_of_hom_inv_id, ShortComplex.HomologyData.ofIso_right_p, MonoidalCategory.MonoidalRightAction.actionHomRight_hom_inv', DerivedCategory.right_fac, Limits.map_ι_comp_inv_sigmaComparison_assoc, Limits.MonoFactorisation.ofArrowIso_e, MonoidalCategory.whiskerLeft_hom_inv'_assoc, AlgebraicTopology.NormalizedMooreComplex.obj_d, Limits.pullback_inv_snd_fst_of_left_isIso, MonoidalCategory.whiskerLeft_inv_hom'_assoc, StructuredArrow.commaMapEquivalenceInverse_map, Limits.pullbackConeOfLeftIso_π_app_left, Limits.cokernelCompIsIso_hom, Functor.Initial.limitIso_hom, PreZeroHypercover.inv_hom_h₀_comp_f_assoc, Limits.IsImage.ofArrowIso_lift, NatIso.naturality_1', AlgebraicGeometry.Scheme.inv_app, comp_hom_eq_id, Functor.closedIhom_obj_map, ShortComplex.LeftHomologyData.ofEpiOfIsIsoOfMono'_i, StructuredArrow.commaMapEquivalenceCounitIso_hom_app_left_right, MonoidalCategory.inv_hom_id_tensor'_assoc, Functor.Monoidal.inv_μ, StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_right, MonoidalCategory.hom_inv_id_tensor'_assoc, Limits.CatCospanTransform.inv_left, Groupoid.vertexGroup.inv_eq_inv, Limits.coneOfDiagramTerminal_π_app, NatIso.inv_map_inv_app, Adjunction.Triple.rightToLeft_eq_units, Comma.inv_left, MonoidalCategory.MonoidalRightAction.hom_inv_actionHomLeft'_assoc, CartesianMonoidalCategory.prodComparisonBifunctorNatIso_inv, coev_expComparison, NatIso.naturality_1'_assoc, IsIso.inv_comp, IsIso.inv_comp_eq, PreZeroHypercover.inv_hom_h₀_comp_f, ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom, PreZeroHypercover.inv_inv_h₀_comp_f, Pseudofunctor.mkOfLax'_mapComp_hom, MonoidalCategory.tensor_inv_hom_id', Limits.coprodComparison_inv_natural, Bicategory.inv_whiskerRight, Limits.CategoricalPullback.inv_fst, Functor.map_hom_inv, IsIso.inv_inv, Limits.colimit.ι_inv_pre, Functor.LeftLinear.inv_μₗ, MonoidalCategory.inv_tensor, IsIso.inv_id, Limits.pushoutCoconeOfLeftIso_inl, SingleObj.inv_as_inv, DerivedCategory.right_fac_of_isStrictlyLE_of_isStrictlyGE, IsIso.inv_isIso, IsIso.inv_hom_id, MonoidalCategory.MonoidalRightAction.inv_actionHomLeft, Functor.map_hom_inv_assoc, NatTrans.CommShift.of_isIso, Limits.map_inr_inv_coprodComparison_assoc, MonoidalCategory.MonoidalLeftAction.inv_actionHomLeft, hom_comp_eq_id, OverClass.asOverHom_inv, IsIso.eq_inv_comp, GlueData.t'_iji, ProjectiveResolution.extMk_hom, MonoidalCategory.MonoidalRightAction.hom_inv_actionHomLeft', comp_inv_eq_id, IsIso.inv_comp_assoc, Limits.kernelIsIsoComp_inv, MonoidalCategory.MonoidalRightAction.inv_actionHomRight, Limits.map_inr_inv_coprodComparison, Limits.pullbackConeOfRightIso_π_app_right, Limits.pushout_inr_inv_inl_of_right_isIso_assoc, MonoidalCategory.MonoidalRightAction.inv_actionHom, MonoidalCategory.MonoidalRightAction.actionHomRight_hom_inv'_assoc, asIso_inv, PrelaxFunctor.map₂_inv_hom_isIso, Localization.Construction.lift_map, PrelaxFunctor.map₂_inv_hom_isIso_assoc, Pseudofunctor.mkOfLax'_mapId_hom, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_invApp, Arrow.inv_left, Limits.kernelSubobjectIsoComp_inv_arrow, DerivedCategory.left_fac_of_isStrictlyLE_of_isStrictlyGE, Adjunction.Triple.rightToLeft_eq_counits, Functor.Monoidal.inv_η, MonoidalCategory.MonoidalLeftAction.hom_inv_actionHomLeft'_assoc, Limits.pullbackConeOfLeftIso_fst, Limits.pushoutCoconeOfLeftIso_ι_app_left, CartesianMonoidalCategory.inv_prodComparison_map_fst_assoc, Adjunction.toEquivalence_counitIso_inv_app, Adjunction.toEquivalence_unitIso_inv_app, Functor.map_inv, CartesianMonoidalCategory.inv_prodComparison_map_snd_assoc, Limits.MonoFactorisation.ofCompIso_m, Comma.left_hom_inv_right, PrelaxFunctor.map₂_inv, Limits.inv_prodComparison_map_fst, Limits.MonoFactorisation.ofIsoComp_e, Limits.CatCospanTransform.inv_base, Functor.RightLinear.inv_μᵣ, MonoidalCategory.MonoidalLeftAction.actionHomRight_inv_hom'_assoc, Limits.pullbackConeOfRightIso_snd, MonoidalCategory.whiskerLeft_inv_hom', MonoidalCategory.MonoidalLeftAction.actionHomRight_inv_hom', StructuredArrow.commaMapEquivalenceInverse_obj, MonoidalCategory.inv_hom_id_tensor', MonoidalCategory.tensor_inv_hom_id'_assoc, Comma.inv_right, MonoidalCategory.whiskerLeft_hom_inv', StructuredArrow.commaMapEquivalenceFunctor_obj_left, IsIso.hom_inv_id_assoc, StructuredArrow.commaMapEquivalenceFunctor_map_left, IsIso.eq_inv_of_inv_hom_id, Comma.inv_left_hom_right, Limits.inv_piComparison_comp_map_π, Limits.coconeOfDiagramInitial_ι_app, uncurry_expComparison, MonoidalCategory.hom_inv_whiskerRight'_assoc, CartesianMonoidalCategory.prodComparison_inv_natural_whiskerLeft, GlueData.t'_jii, Limits.CatCospanTransform.inv_whiskerRight, ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono_p, CartesianMonoidalCategory.prodComparisonNatIso_inv, PreZeroHypercover.inv_inv_h₀_comp_f_assoc, Localization.Construction.WhiskeringLeftEquivalence.inverse_obj_map, Limits.CatCospanTransform.inv_right, Functor.Monoidal.inv_ε, MonoidalCategory.MonoidalLeftAction.actionHomRight_hom_inv'_assoc, Limits.CatCospanTransform.inv_whiskerLeft, AlgebraicGeometry.Scheme.inv_appTop, Adjunction.inv_counit_map, StructuredArrow.commaMapEquivalenceFunctor_map_right, MonoidalCategory.MonoidalRightAction.actionHomRight_inv_hom', Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapIdIso_inv, IsIso.eq_comp_inv, MonoidalCategory.MonoidalRightAction.inv_hom_actionHomLeft'_assoc, Functor.map_inv_hom_assoc, MonoidalCategory.MonoidalLeftAction.actionHomRight_hom_inv', CartesianMonoidalCategory.prodComparison_inv_natural_whiskerRight_assoc, Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapIdIso_hom, Adjunction.Triple.leftToRight_eq_counits, Limits.coprodComparison_inv_natural_assoc, Functor.IsCoverDense.presheafIso_inv, expComparison_ev, Functor.Monoidal.inv_δ, IsIso.eq_inv_of_hom_inv_id, unop_inv, CartesianMonoidalCategory.inv_prodComparison_map_snd, Arrow.inv_left_hom_right, inv_eqToHom, CartesianMonoidalCategory.prodComparison_inv_natural, IsIso.Iso.inv_inv, Limits.pullback_inv_snd_fst_of_left_isIso_assoc, StructuredArrow.commaMapEquivalenceCounitIso_hom_app_right_right, AlgebraicGeometry.Scheme.Hom.inv_appTop, MonoidalCategory.MonoidalLeftAction.inv_actionHomRight, MonoidalCategory.inv_whiskerLeft, InjectiveResolution.extMk_hom, IsIso.inv_eq_inv, Subgroupoid.coe_inv_coe', IsHomLift.lift_id_inv_isIso, Center.isoMk_inv_f, NatIso.naturality_2'_assoc, CartesianMonoidalCategory.inv_prodComparison_map_fst, Pretriangulated.productTriangle_mor₃, Limits.imageSubobjectCompIso_hom_arrow_assoc, op_inv, Localization.Construction.liftToPathCategory_map, Limits.IndObjectPresentation.extend_isColimit_desc_app, NatIso.naturality_2', IsIso.comp_inv_eq, DerivedCategory.right_fac_of_isStrictlyLE, MonoidalCategory.MonoidalRightAction.actionHomRight_inv_hom'_assoc, PrelaxFunctor.map₂_hom_inv_isIso, inv_comp_eq_id, imageToKernel_zero_right, Bicategory.Pith.pseudofunctorToPith_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_iso_inv, Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapCompIso_inv, Functor.inv_whiskerLeft, StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_right, MonoidalCategory.MonoidalRightAction.inv_hom_actionHomLeft', Limits.pullback_inv_fst_snd_of_right_isIso, Bicategory.inv_whiskerLeft, IsIso.Iso.inv_hom, MonoidalCategory.hom_inv_id_tensor', AlgebraicGeometry.Spec.map_inv, Limits.CategoricalPullback.inv_snd, MorphismProperty.Comma.inv_hom, Pseudofunctor.mkOfOplax'_mapId_inv, IsIso.hom_inv_id, Limits.pushout_inl_inv_inr_of_right_isIso_assoc, MonoidalCategory.tensor_hom_inv_id'_assoc, MonoidalCategory.MonoidalLeftAction.inv_hom_actionHomLeft'_assoc, NatIso.isIso_inv_app, Groupoid.isoEquivHom_symm_apply_inv, Limits.pullback_inv_fst_snd_of_right_isIso_assoc, IsIso.inv_eq_of_inv_hom_id, OverClass.instHomIsOverInv, StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_left, Adjunction.Triple.leftToRight_app, StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_left, CartesianMonoidalCategory.prodComparison_inv_natural_whiskerRight, NonPreadditiveAbelian.diag_σ_assoc, Functor.LeftLinear.inv_δₗ, MonoidalCategory.inv_whiskerRight, Pseudofunctor.mkOfOplax'_mapComp_inv, Arrow.inv_right, Limits.image.compIso_inv_comp_image_ι_assoc, Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapCompIso_hom, MonoidalCategory.MonoidalLeftAction.inv_actionHom, IsIso.hom_inv_id_apply, Arrow.left_hom_inv_right, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_hom_app, instIsComonHomInv, Limits.prodComparison_inv_natural_assoc, Limits.inv_prodComparison_map_snd_assoc, IsIso.inv_hom_id_assoc, NonPreadditiveAbelian.lift_σ_assoc, Limits.pushout_inl_inv_inr_of_right_isIso, Limits.map_inl_inv_coprodComparison, CartesianMonoidalCategory.prodComparison_inv_natural_whiskerLeft_assoc, Limits.prodComparison_inv_natural, MonoidalCategory.inv_hom_whiskerRight'_assoc, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_invApp, PrelaxFunctor.map₂_hom_inv_isIso_assoc, MonoidalCategory.inv_hom_whiskerRight', Groupoid.inv_eq_inv, IsIso.inv_hom_id_apply, Limits.pushoutCoconeOfRightIso_inr, MonoidalCategory.tensor_hom_inv_id', Limits.pushoutCoconeOfRightIso_ι_app_right, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_invApp, MonoidalCategory.MonoidalLeftAction.hom_inv_actionHomLeft', Over.ε_pullback_left, Functor.RightLinear.inv_δᵣ, Limits.inv_prodComparison_map_snd, Limits.map_inl_inv_coprodComparison_assoc, Limits.pushout_inr_inv_inl_of_right_isIso, DerivedCategory.left_fac_of_isStrictlyGE, AlgebraicGeometry.Scheme.Hom.inv_app, Limits.map_ι_comp_inv_sigmaComparison, Limits.inv_prodComparison_map_fst_assoc, AlgebraicGeometry.Scheme.Modules.inv_app, StructuredArrow.commaMapEquivalenceCounitIso_inv_app_left_right, InjectiveResolution.extEquivCohomologyClass_symm_mk_hom, Limits.colimit.ι_inv_pre_assoc, StructuredArrow.commaMapEquivalenceFunctor_obj_right, Functor.inv_whiskerRight, Core.functorToCore_map_iso_inv, CartesianMonoidalCategory.prodComparison_inv_natural_assoc, Limits.inv_piComparison_comp_map_π_assoc, Adjunction.inv_map_unit, StructuredArrow.commaMapEquivalenceCounitIso_inv_app_right_right, IsHomLift.inv, DerivedCategory.left_fac, Limits.image.compIso_inv_comp_image_ι, GrpObj.inv_inv, NatIso.inv_inv_app, StructuredArrow.commaMapEquivalenceFunctor_obj_hom, Abelian.coimIsoIm_inv_app, MonoidalCategory.MonoidalLeftAction.inv_hom_actionHomLeft', Functor.map_inv_hom, Functor.Final.colimitIso_inv, IsSubterminal.isoDiag_hom
«term_≅_» 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
asIso_hom 📖	mathematical	—	Iso.hom asIso	—	—
asIso_inv 📖	mathematical	—	Iso.inv asIso inv	—	—
comp_hom_eq_id 📖	mathematical	—	CategoryStruct.comp Category.toCategoryStruct CategoryStruct.id inv	—	Iso.comp_inv_eq_id
comp_inv_eq_id 📖	mathematical	—	CategoryStruct.comp Category.toCategoryStruct inv CategoryStruct.id	—	Iso.comp_hom_eq_id
eq_of_inv_eq_inv 📖	—	inv	—	—	cancel_epi IsIso.epi_of_iso IsIso.inv_isIso IsIso.inv_hom_id
hom_comp_eq_id 📖	mathematical	—	CategoryStruct.comp Category.toCategoryStruct CategoryStruct.id inv	—	Iso.hom_comp_eq_id
inv_comp_eq_id 📖	mathematical	—	CategoryStruct.comp Category.toCategoryStruct inv CategoryStruct.id	—	Iso.inv_comp_eq_id
isIso_comp_left_iff 📖	mathematical	—	IsIso CategoryStruct.comp Category.toCategoryStruct	—	IsIso.of_isIso_comp_left IsIso.comp_isIso
isIso_comp_right_iff 📖	mathematical	—	IsIso CategoryStruct.comp Category.toCategoryStruct	—	IsIso.of_isIso_comp_right IsIso.comp_isIso
isIso_of_comp_hom_eq_id 📖	mathematical	CategoryStruct.comp Category.toCategoryStruct CategoryStruct.id	IsIso	—	comp_hom_eq_id IsIso.inv_isIso
isIso_of_hom_comp_eq_id 📖	mathematical	CategoryStruct.comp Category.toCategoryStruct CategoryStruct.id	IsIso	—	hom_comp_eq_id IsIso.inv_isIso

CategoryTheory.Functor

Definitions

Name	Category	Theorems
mapIso 📖	CompOp	73 math math: map_homCongr, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo, leftExtensionEquivalenceOfIso₁_functor_map_left, CategoryTheory.eqToIso_map, CategoryTheory.Monoidal.transportStruct_associator, FullyFaithful.isoEquiv_apply, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isoBot, CategoryTheory.CostructuredArrow.mapIso_unitIso_hom_app_left, CategoryTheory.comonadToFunctor_mapIso_comonad_iso_mk, CategoryTheory.CostructuredArrow.mapIso_functor_map_left, leftExtensionEquivalenceOfIso₁_inverse_map_left, CompHausLike.sigmaComparison_eq_comp_isos, map_isoCongr, CategoryTheory.CostructuredArrow.mapIso_unitIso_inv_app_left, CategoryTheory.eqToIso_map_trans, CategoryTheory.ShortComplex.RightHomologyData.mapOpcyclesIso_eq, mapIso_injective, map_conj, map_conjAut, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_mapIso_mkNatIso_eq_mkIso, mapIso_refl, CategoryTheory.TransfiniteCompositionOfShape.map_isoBot, CategoryTheory.Sum.natIsoOfWhiskerLeftInlInr_eq, CategoryTheory.CostructuredArrow.mapIso_counitIso_hom_app_left, AlgebraicGeometry.PresheafedSpace.sheafIsoOfIso_inv, leftExtensionEquivalenceOfIso₁_inverse_map_right, CategoryTheory.CostructuredArrow.mapIso_functor_map_right, mapIso_trans, leftExtensionEquivalenceOfIso₁_counitIso_inv_app_right_app, AlgebraicGeometry.Scheme.Hom.comp_appIso, CategoryTheory.ShortComplex.LeftHomologyData.mapLeftHomologyIso_eq, AlgebraicGeometry.Scheme.Hom.id_appIso, CategoryTheory.Monoidal.transportStruct_leftUnitor, CategoryTheory.Monoidal.transportStruct_rightUnitor, CategoryTheory.Equivalence.inverseFunctorMapIso_symm_eq_isoInverseOfIsoFunctor, AlgebraicGeometry.Scheme.isoSpec_Spec, CategoryTheory.StructuredArrow.mapIso_unitIso_inv_app_right, CategoryTheory.StructuredArrow.mapIso_functor_map_left, CategoryTheory.Localization.Monoidal.lifting₂CurriedTensorPost_iso, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_isoBot, CategoryTheory.monadToFunctor_mapIso_monad_iso_mk, CategoryTheory.CartesianMonoidalCategory.preservesTerminalIso_comp, CategoryTheory.ShortComplex.RightHomologyData.mapRightHomologyIso_eq, HomologicalComplex₂.totalShift₁Iso_trans_totalShift₂Iso, mapIso_symm, CategoryTheory.ShortComplex.LeftHomologyData.mapCyclesIso_eq, mapIso_inv, CategoryTheory.CartesianMonoidalCategory.prodComparisonIso_comp, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_assoc, CategoryTheory.StructuredArrow.mapIso_unitIso_hom_app_right, CategoryTheory.StructuredArrow.mapIso_inverse_map_right, CategoryTheory.ShortComplex.LeftHomologyData.mapHomologyIso_eq, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isColimit, leftExtensionEquivalenceOfIso₁_unitIso_hom_app_right_app, CochainComplex.mapBifunctorShift₁Iso_trans_mapBifunctorShift₂Iso, CompHausLike.LocallyConstant.sigmaComparison_comp_sigmaIso, CategoryTheory.Localization.Monoidal.lifting₂CurriedTensorPre_iso, CategoryTheory.StructuredArrow.mapIso_functor_map_right, CategoryTheory.ShortComplex.HomologyData.map_iso, Action.Iso.conj_ρ, CategoryTheory.StructuredArrow.mapIso_inverse_map_left, mapIso_hom, preimageIso_mapIso, CategoryTheory.CostructuredArrow.mapIso_inverse_map_right, leftExtensionEquivalenceOfIso₁_counitIso_hom_app_right_app, CategoryTheory.CostructuredArrow.mapIso_inverse_map_left, AlgebraicTopology.DoldKan.N₁Γ₀_app, leftExtensionEquivalenceOfIso₁_functor_map_right, leftExtensionEquivalenceOfIso₁_unitIso_inv_app_right_app, CategoryTheory.CostructuredArrow.mapIso_counitIso_inv_app_left, CategoryTheory.ShortComplex.RightHomologyData.mapHomologyIso'_eq, CategoryTheory.StructuredArrow.mapIso_counitIso_hom_app_right, CategoryTheory.StructuredArrow.mapIso_counitIso_inv_app_right

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
mapIso_hom 📖	mathematical	—	CategoryTheory.Iso.hom obj mapIso map	—	—
mapIso_inv 📖	mathematical	—	CategoryTheory.Iso.inv obj mapIso map	—	—
mapIso_refl 📖	mathematical	—	mapIso CategoryTheory.Iso.refl obj	—	CategoryTheory.Iso.ext map_id
mapIso_symm 📖	mathematical	—	mapIso CategoryTheory.Iso.symm obj	—	—
mapIso_trans 📖	mathematical	—	mapIso CategoryTheory.Iso.trans obj	—	CategoryTheory.Iso.ext map_comp
map_hom_inv 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct obj map CategoryTheory.inv CategoryTheory.CategoryStruct.id	—	map_isIso map_inv CategoryTheory.IsIso.hom_inv_id
map_hom_inv_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct obj map CategoryTheory.inv	—	CategoryTheory.Category.assoc CategoryTheory.Category.id_comp Mathlib.Tactic.Reassoc.eq_whisker' map_hom_inv
map_inv 📖	mathematical	—	map CategoryTheory.inv obj map_isIso	—	CategoryTheory.IsIso.eq_inv_of_hom_inv_id map_isIso map_comp CategoryTheory.IsIso.hom_inv_id map_id
map_inv_hom 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct obj map CategoryTheory.inv CategoryTheory.CategoryStruct.id	—	map_isIso map_inv CategoryTheory.IsIso.inv_hom_id
map_inv_hom_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct obj map CategoryTheory.inv	—	CategoryTheory.Category.assoc CategoryTheory.Category.id_comp Mathlib.Tactic.Reassoc.eq_whisker' map_inv_hom
map_isIso 📖	mathematical	—	CategoryTheory.IsIso obj map	—	CategoryTheory.Iso.isIso_hom

CategoryTheory.IsIso

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
comp_inv_eq 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.inv	—	—
comp_isIso 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct	—	CategoryTheory.Iso.isIso_hom
comp_isIso' 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct	—	comp_isIso
epi_of_iso 📖	mathematical	—	CategoryTheory.Epi	—	inv_hom_id_assoc
eq_comp_inv 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.inv	—	—
eq_inv_comp 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.inv	—	CategoryTheory.Iso.eq_inv_comp
eq_inv_of_hom_inv_id 📖	mathematical	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.CategoryStruct.id	CategoryTheory.inv	—	inv_eq_of_hom_inv_id
eq_inv_of_inv_hom_id 📖	mathematical	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.CategoryStruct.id	CategoryTheory.inv	—	inv_eq_of_inv_hom_id
hom_inv_id 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.inv CategoryTheory.CategoryStruct.id	—	out
hom_inv_id_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.inv	—	CategoryTheory.Category.assoc CategoryTheory.Category.id_comp Mathlib.Tactic.Reassoc.eq_whisker' hom_inv_id
id 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct	—	CategoryTheory.Category.comp_id
inv_comp 📖	mathematical	—	CategoryTheory.inv CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct comp_isIso	—	inv_eq_of_hom_inv_id comp_isIso CategoryTheory.Category.assoc hom_inv_id_assoc hom_inv_id
inv_comp_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.inv comp_isIso	—	comp_isIso CategoryTheory.Category.assoc Mathlib.Tactic.Reassoc.eq_whisker' inv_comp
inv_comp_eq 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.inv	—	CategoryTheory.Iso.inv_comp_eq
inv_eq_inv 📖	mathematical	—	CategoryTheory.inv	—	CategoryTheory.Iso.inv_eq_inv
inv_eq_of_hom_inv_id 📖	mathematical	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.CategoryStruct.id	CategoryTheory.inv	—	—
inv_eq_of_inv_hom_id 📖	mathematical	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.CategoryStruct.id	CategoryTheory.inv	—	—
inv_hom_id 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.inv CategoryTheory.CategoryStruct.id	—	out
inv_hom_id_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.inv	—	CategoryTheory.Category.assoc CategoryTheory.Category.id_comp Mathlib.Tactic.Reassoc.eq_whisker' inv_hom_id
inv_id 📖	mathematical	—	CategoryTheory.inv CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct id	—	inv_eq_of_hom_inv_id id CategoryTheory.Category.comp_id
inv_inv 📖	mathematical	—	CategoryTheory.inv inv_isIso	—	inv_eq_of_hom_inv_id inv_isIso inv_hom_id
inv_isIso 📖	mathematical	—	CategoryTheory.IsIso CategoryTheory.inv	—	CategoryTheory.Iso.isIso_inv
mono_of_iso 📖	mathematical	—	CategoryTheory.Mono	—	—
of_isIso_comp_left 📖	mathematical	—	CategoryTheory.IsIso	—	CategoryTheory.Category.id_comp inv_hom_id CategoryTheory.Category.assoc comp_isIso inv_isIso
of_isIso_comp_right 📖	mathematical	—	CategoryTheory.IsIso	—	CategoryTheory.Category.comp_id hom_inv_id CategoryTheory.Category.assoc' comp_isIso inv_isIso
of_isIso_fac_left 📖	mathematical	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct	CategoryTheory.IsIso	—	of_isIso_comp_left
of_isIso_fac_right 📖	mathematical	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct	CategoryTheory.IsIso	—	of_isIso_comp_right
out 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.CategoryStruct.id	—	—

CategoryTheory.IsIso.Iso

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
inv_hom 📖	mathematical	—	CategoryTheory.inv CategoryTheory.Iso.hom CategoryTheory.Iso.isIso_hom CategoryTheory.Iso.inv	—	CategoryTheory.IsIso.inv_eq_of_inv_hom_id CategoryTheory.Iso.isIso_hom CategoryTheory.Iso.inv_hom_id
inv_inv 📖	mathematical	—	CategoryTheory.inv CategoryTheory.Iso.inv CategoryTheory.Iso.isIso_inv CategoryTheory.Iso.hom	—	CategoryTheory.IsIso.inv_eq_of_hom_inv_id CategoryTheory.Iso.isIso_inv CategoryTheory.Iso.inv_hom_id

CategoryTheory.Iso

Definitions

Name	Category	Theorems
hom 📖	CompOp	5280 math math: CategoryTheory.Equivalence.adjointify_η_ε_assoc, CategoryTheory.Localization.Monoidal.leftUnitor_hom_app, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₃, inv_hom_id_triangle_hom₃_assoc, CategoryTheory.Limits.Cones.postcomposeId_hom_app_hom, CategoryTheory.GrothendieckTopology.isoSheafify_hom, SemimoduleCat.MonoidalCategory.triangle, CategoryTheory.Over.associator_hom_left_snd_fst_assoc, CategoryTheory.ObjectProperty.isoMk_hom, CategoryTheory.MorphismProperty.LeftFraction.map_compatibility, CategoryTheory.Limits.pushoutIsoOpPullback_inr_hom_assoc, CategoryTheory.GrothendieckTopology.overMapPullbackId_hom_app_val_app, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyπ_comp_leftHomologyIso_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_eq, Sequential.homeoOfIso_apply, CategoryTheory.InjectiveResolution.Hom.hom'_f, CategoryTheory.Pseudofunctor.mapComp'_naturality_1_assoc, CategoryTheory.Functor.whiskeringRightObjIdIso_hom_app_app, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π, AlgebraicGeometry.AffineSpace.map_Spec_map, CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv_assoc, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, HomologicalComplex.pOpcycles_restrictionOpcyclesIso_hom_assoc, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_assoc, CategoryTheory.MonoidalCategory.tensor_left_unitality, CategoryTheory.sum.inrCompInverseAssociator_hom_app, CategoryTheory.Over.prodLeftIsoPullback_hom_snd_assoc, CategoryTheory.PreZeroHypercover.isoMk_hom_h₀, AlgCat.hom_inv_apply, CategoryTheory.Functor.CommShift.isoAdd_hom_app, CategoryTheory.Adjunction.compUliftCoyonedaIso_hom_app_app_down, CategoryTheory.SingleFunctors.postcompPostcompIso_hom_hom_app, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_hom_app_zero, CategoryTheory.MonoidalCategory.associator_naturality_middle_assoc, groupHomology.π_comp_H2Iso_hom_assoc, CategoryTheory.BraidedCategory.braiding_naturality_right, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_hom_left, CategoryTheory.biproduct_ι_comp_leftDistributor_hom_assoc, CategoryTheory.MonObj.instIsMonHomHomAssociator, CategoryTheory.Limits.cokernelBiproductιIso_hom, CategoryTheory.Mat_.additiveObjIsoBiproduct_hom_π, HomologicalComplex.extendSingleIso_inv_f, CategoryTheory.Equivalence.leftOp_unitIso_hom_app, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_hom_app_val_app, CategoryTheory.WithTerminal.coneEquiv_unitIso_hom_app_hom_left, DistLat.hom_inv_apply, CategoryTheory.Pseudofunctor.DescentData.ofObj_hom, HomologicalComplex.restrictionToTruncGE'_f_eq_iso_hom_pOpcycles_iso_inv, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst_assoc, CategoryTheory.MonoidalCategory.DayConvolution.braidingHomCorepresenting_app, AlgebraicGeometry.Scheme.Hom.toPartialMap_hom, CategoryTheory.Functor.coreComp_hom_app_iso_inv, CategoryTheory.Monoidal.InducingFunctorData.rightUnitor_eq, CategoryTheory.Limits.BinaryFan.rightUnitor_hom, AlgebraicGeometry.Scheme.map_PrimeSpectrum_basicOpen_of_affine, CategoryTheory.uliftCoyonedaIsoCoyoneda_hom_app_app, CategoryTheory.LaxFunctor.mapComp'_whiskerRight_comp_mapComp', CategoryTheory.Limits.imageSubobject_arrow_assoc, HomologicalComplex.singleMapHomologicalComplex_hom_app_ne, CategoryTheory.ModObj.one_smul_assoc, CategoryTheory.tensorLeftHomEquiv_symm_coevaluation_comp_whiskerLeft, CategoryTheory.Functor.OplaxMonoidal.δ_comp_tensorHom_η, CategoryTheory.eHom_whisker_cancel, CategoryTheory.Pi.eqToEquivalenceFunctorIso_hom, CategoryTheory.PreGaloisCategory.mulAction_def, CategoryTheory.Pseudofunctor.map₂_associator_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst_assoc, CategoryTheory.Functor.LaxMonoidal.associativity_assoc, ModuleCat.MonoidalCategory.braiding_hom_apply, CategoryTheory.MonoidalCategory.MonoidalRightAction.unit_actionHomRight_assoc, CategoryTheory.Adjunction.toEquivalence_counitIso_hom_app, CategoryTheory.BraidedCategory.yang_baxter', CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair_hom_app, CategoryTheory.Functor.OplaxMonoidal.associativity, AlgebraicTopology.DoldKan.Compatibility.equivalence₀_unitIso_hom_app, CategoryTheory.PreZeroHypercover.inv_hom_h₀, CategoryTheory.Limits.imageSubobjectCompIso_hom_arrow, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_left, CategoryTheory.Functor.sheafPushforwardContinuousIso_inv, CategoryTheory.ShortComplex.HomologyData.canonical_iso_hom, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app', CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_associator_hom_eq_associator_hom, CategoryTheory.SingleFunctors.Hom.comm, CategoryTheory.LaxFunctor.map₂_associator_assoc, 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, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv_assoc, CategoryTheory.shift_shiftFunctorCompIsoId_hom_app, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_appTop, HomologicalComplex.dFrom_comp_xNextIsoSelf, CategoryTheory.Subobject.underlyingIso_hom_comp_eq_mk_assoc, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo, CommSemiRingCat.hom_inv_apply, CategoryTheory.Limits.CategoricalPullback.catCommSq_iso_hom_app, CategoryTheory.Join.inlCompFromSum_hom_app, CategoryTheory.Bicategory.Adj.rightUnitor_hom_τl, CategoryTheory.DifferentialObject.shiftFunctor_obj_d, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_hom_inv_assoc, CategoryTheory.Limits.colimitHomIsoLimitYoneda_hom_comp_π, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_naturality_assoc, TopCat.pullbackIsoProdSubtype_hom_fst, CategoryTheory.Limits.CatCospanTransform.associator_hom_right_app, CategoryTheory.SmallObject.SuccStruct.prop.arrowIso_hom_left, CategoryTheory.GradedObject.isoMk_hom, LightCondensed.lanPresheafIso_hom, CategoryTheory.Functor.rightKanExtensionUniqueOfIso_hom, CategoryTheory.Limits.diagramIsoPair_hom_app, HomologicalComplex.π_homologyIsoSc'_hom, CategoryTheory.Functor.mapHomologicalComplexIdIso_hom_app_f, CategoryTheory.ShortComplex.HomologyData.ofIso_right_p, Mathlib.Tactic.Bicategory.evalWhiskerLeft_nil, CategoryTheory.Limits.limitUnopIsoUnopColimit_hom_comp_ι, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_associator, groupCohomology.toCocycles_comp_isoCocycles₁_hom, CategoryTheory.Limits.PreservesEqualizer.iso_hom, CategoryTheory.Join.mapPairId_hom_app, CategoryTheory.Limits.Types.Small.productIso_hom_comp_eval, HomologicalComplex.homologyπ_extendHomologyIso_hom, CategoryTheory.Limits.prod.rightUnitor_hom, CategoryTheory.ShortComplex.opcyclesIsoRightHomology_hom_inv_id, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_hom_hom, LightCondensed.isoFinYonedaComponents_hom_apply, CategoryTheory.Limits.ConeMorphism.hom_inv_id, CategoryTheory.Limits.biprod.uniqueUpToIso_hom, CategoryTheory.Limits.IsColimit.uniqueUpToIso_hom, CategoryTheory.ObjectProperty.instCommShiftHomFunctorLiftCompιIso, CategoryTheory.mop_hom_leftUnitor, CategoryTheory.Limits.WalkingMultispan.functorExt_hom_app, CategoryTheory.BraidedCategory.braiding_tensor_right_hom, CategoryTheory.Functor.LaxMonoidal.whiskerLeft_μ_comp_μ_assoc, groupCohomology.isoCocycles₁_hom_comp_i_apply, CategoryTheory.Core.forgetFunctorToCore_map_app, CategoryTheory.Comma.mapLeftIso_inverse_map_right, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceInverseπ_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_hom_app_eq, CategoryTheory.shiftFunctorComm_zero_hom_app, CategoryTheory.op_hom_leftUnitor, SSet.OneTruncation₂.ofNerve₂.natIso_hom_app_map, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionAssocIso_hom, CategoryTheory.Grothendieck.ιCompMap_hom_app_fiber, CategoryTheory.MonoidalOpposite.unmop_hom_braiding, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_assoc, HomologicalComplex₂.totalFlipIso_hom_f_D₁, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_map_left, CategoryTheory.ExactPairing.coevaluation_evaluation'', CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_naturality_assoc, CategoryTheory.MonoidalCategory.rightUnitor_monoidal_assoc, HomologicalComplex.singleMapHomologicalComplex_hom_app_self, CategoryTheory.Limits.Types.Small.productIso_hom_comp_eval_apply, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_hom_app, CategoryTheory.Functor.mapConeMapCone_hom_hom, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_hom_app_app_down, CategoryTheory.ShortComplex.homologyOpIso_hom_naturality, CategoryTheory.Abelian.PreservesCoimage.iso_hom_π_assoc, AlgebraicGeometry.Scheme.PartialMap.ext_iff, HomologicalComplex.singleObjHomologySelfIso_hom_singleObjOpcyclesSelfIso_hom_assoc, CategoryTheory.unmop_hom_rightUnitor, TannakaDuality.FiniteGroup.toRightFDRepComp_in_rightRegular, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_inv_app_val_app, Bimod.TensorBimod.π_tensor_id_actRight, CategoryTheory.FreeMonoidalCategory.mk_ρ_hom, CategoryTheory.NatTrans.unop_whiskerLeft, CategoryTheory.Localization.Preadditive.homEquiv_symm_apply, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_hom_inv, CategoryTheory.Functor.CommShift.isoAdd_inv_app, CategoryTheory.MonoidalCategory.tensor_inv_hom_id_assoc, CategoryTheory.MonadIso.toNatIso_hom, HomologicalComplex.singleObjCyclesSelfIso_hom_singleObjOpcyclesSelfIso_hom_assoc, MulEquiv.toCommMonCatIso_hom, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_whiskerRight, CategoryTheory.Functor.opUnopIso_hom_app, Action.inv_hom_hom_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app_assoc, CategoryTheory.MonoidalOpposite.tensorLeftMopIso_hom_app_unmop, HomologicalComplex.XIsoOfEq_hom_comp_XIsoOfEq_hom, CategoryTheory.Pseudofunctor.map₂_associator_app_assoc, CategoryTheory.Functor.OplaxMonoidal.δ_comp_η_tensorHom_assoc, AlgebraicGeometry.Scheme.Pullback.Triplet.tensorCongr_trans_hom, CategoryTheory.NatTrans.naturality_2, CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_snd_assoc, CategoryTheory.SmallObject.SuccStruct.extendToSucc_map_le_succ, CategoryTheory.LocalizerMorphism.natTransCommShift_hom, CategoryTheory.Limits.biprod.braid_natural, CategoryTheory.Functor.Monoidal.commTensorLeft_hom_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_hom, AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_inv_app, CategoryTheory.Limits.coprod.symmetry, CategoryTheory.HasShift.Induced.add_inv_app_obj, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapId_hom_iso, CategoryTheory.Adjunction.Localization.ε_app, CategoryTheory.Pseudofunctor.DescentData.pullFunctorCompIso_inv_app_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitNatIso_hom_app, CategoryTheory.Adjunction.rightAdjointUniq_trans, CategoryTheory.Functor.mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app_assoc, comp_inv_eq, CategoryTheory.Functor.LaxMonoidal.right_unitality, CategoryTheory.Equivalence.unitIso_hom_app_comp_inverse_map_η_functor_assoc, CategoryTheory.Limits.biprod_isoCoprod_hom, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_app_hom_assoc, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_left_app, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.isMonHom_counitIsoAux, CategoryTheory.ExactPairing.evaluation_coevaluation, HomologicalComplex.pOpcycles_opcyclesIsoSc'_hom, CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse, CategoryTheory.ExactPairing.coevaluation_evaluation', CategoryTheory.OverPresheafAux.unitAux_hom, CategoryTheory.Limits.Cones.equivalenceOfReindexing_inverse, CategoryTheory.Limits.fiberwiseColimit_map, groupCohomology.π_comp_H0IsoOfIsTrivial_hom_assoc, FundamentalGroupoidFunctor.piIso_hom, CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom, CategoryTheory.Lax.StrongTrans.vComp_naturality_hom, AugmentedSimplexCategory.inr_comp_associator, CategoryTheory.Monoidal.leftUnitor_hom_app, HomologicalComplex.pOpcycles_singleObjOpcyclesSelfIso_inv, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_app_snd_app, AlgebraicGeometry.Scheme.Hom.toNormalization_inl_normalizationCoprodIso_hom_assoc, CategoryTheory.Limits.pullbackProdSndIsoProd_hom_snd, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_whiskerRight, CategoryTheory.MonoOver.mapIso_functor, CategoryTheory.Bicategory.whiskerLeft_inv_hom, CategoryTheory.StrictlyUnitaryLaxFunctor.mapIdIso_hom, CategoryTheory.Limits.coprod.associator_naturality, CategoryTheory.Aut.ext_iff, CategoryTheory.NatIso.cancel_natIso_hom_right, CategoryTheory.Functor.sheafPushforwardContinuousComp'_inv_app_val_app, CategoryTheory.MonoidalCategory.inv_hom_id_tensor_assoc, CategoryTheory.Limits.pullbackDiagonalMapIso.hom_fst, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_hom_app_app_val, CategoryTheory.MonoidalCategory.tensorRightTensor_hom_app, CategoryTheory.PreservesImage.factorThruImage_comp_hom, CategoryTheory.Limits.CatCospanTransform.comp_whiskerLeft_assoc, CategoryTheory.NatTrans.IsMonoidal.instHomFunctorAssociator, Representation.repOfTprodIso_apply, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_app_assoc, CategoryTheory.Functor.Monoidal.natTransIsMonoidal_of_transport, CategoryTheory.Limits.pushoutIsoOpPullback_inl_hom, CategoryTheory.Bicategory.whiskerRight_comp_assoc, CompactlyGenerated.homeoOfIso_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_apply, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_assoc, CategoryTheory.HalfBraiding.naturality_assoc, CategoryTheory.BraidedCategory.braiding_tensor_right_hom_assoc, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom, HomologicalComplex.singleObjOpcyclesSelfIso_hom, CategoryTheory.op_inv_associator, groupCohomology.toCocycles_comp_isoCocycles₂_hom_apply, CategoryTheory.Limits.ConeMorphism.inv_hom_id_assoc, imageToKernel_unop, CategoryTheory.Limits.pullbackFstFstIso_hom, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_naturality, CategoryTheory.ModObj.mul_smul_assoc, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_specStalkEquiv, groupHomology.chainsMap_f_3_comp_chainsIso₃_apply, CategoryTheory.Limits.ι_comp_colimitOpIsoOpLimit_hom_assoc, CategoryTheory.Over.inv_left_hom_left_assoc, CategoryTheory.Dial.leftUnitor_naturality, AddEquiv.toAddMonCatIso_hom, HomologicalComplex₂.totalShift₂Iso_hom_naturality_assoc, CategoryTheory.coprod_inr_rightDistrib_hom_assoc, CategoryTheory.OplaxFunctor.map₂_associator, CategoryTheory.Bicategory.inv_hom_whiskerRight_whiskerRight_assoc, CategoryTheory.zeroMul_hom, partialFunEquivPointed_unitIso_hom_app, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_left_assoc, CategoryTheory.CartesianMonoidalCategory.associator_hom_fst_assoc, CategoryTheory.Bicategory.Adj.rIso_inv, CategoryTheory.Bicategory.mateEquiv_comp_id_right, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_hom_eq_germ, CategoryTheory.shift_shift', CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_hom, CategoryTheory.Limits.HasColimit.isoOfEquivalence_inv_π, groupCohomology.cocyclesIso₀_hom_comp_f, CategoryTheory.InjectiveResolution.ι'_f_zero, CommAlgCat.braiding_hom_hom, SheafOfModules.pushforwardNatIso_inv, CategoryTheory.Bicategory.inv_hom_whiskerRight_assoc, CategoryTheory.Bicategory.inv_hom_whiskerRight, CategoryTheory.Limits.ι_colimitCompWhiskeringLeftIsoCompColimit_hom_assoc, HomologicalComplex.extend.d_comp_eq_zero_iff, CategoryTheory.NatIso.pi_hom, CategoryTheory.Center.associator_hom_f, CategoryTheory.sum.inlCompInrCompInverseAssociator_hom_app_down_down, CategoryTheory.Functor.uliftCoyonedaCoreprXIso_hom_app, CategoryTheory.Functor.Monoidal.εIso_hom, ModuleCat.extendScalarsId_hom_app_one_tmul, CategoryTheory.Adjunction.mapMon_unit, core_inv_app_iso_hom, CategoryTheory.MonoidalCategory.leftUnitor_naturality, CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_fst_assoc, CategoryTheory.Cat.associator_hom_app, CategoryTheory.Quiv.homEquivOfIso_symm_apply, CategoryTheory.Limits.kernelBiprodSndIso_hom, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_point, CategoryTheory.MonObj.instIsMonHomHomBraiding, SSet.stdSimplex.faceSingletonIso_zero_hom_comp_ι_eq_δ, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_hom_app_app, CategoryTheory.Arrow.hom_inv_id_right_assoc, SemiRingCat.inv_hom_apply, HomologicalComplex.pOpcyclesIso_hom, AlgebraicGeometry.AffineSpace.SpecIso_hom_appTop, CategoryTheory.MonoidalCategory.pentagon_hom_inv_assoc, groupCohomology.π_comp_H0Iso_hom, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_app_assoc, CategoryTheory.NatTrans.CommShiftCore.shift_app_comm, CategoryTheory.Limits.cokernelCompIsIso_hom, CategoryTheory.Functor.map_shiftFunctorComm_hom_app, CategoryTheory.Comma.map_final, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_hom_app_snd_app, CategoryTheory.ShortComplex.mapOpcyclesIso_hom_naturality_assoc, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₁, CategoryTheory.Bicategory.Adjunction.homEquiv₂_symm_apply, groupCohomology.π_comp_H1Iso_hom_assoc, CategoryTheory.Functor.sumIsoExt_hom_app_inl, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_rightHomologyIso_inv, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app, ModuleCat.ι_coprodIsoDirectSum_hom_apply, CategoryTheory.Equivalence.rightOp_counitIso_inv_app, CategoryTheory.WithInitial.liftToInitialUnique_hom_app, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_assoc, TopologicalSpace.OpenNhds.inclusionMapIso_hom, ModuleCat.restrictScalarsComp'App_hom_apply, FintypeCat.uSwitch_map_uSwitch_map, CategoryTheory.Functor.curryObjCompIso_hom_app_app, CategoryTheory.Dial.rightUnitor_hom_f, CategoryTheory.Limits.image.compIso_hom_comp_image_ι, CategoryTheory.GrothendieckTopology.overMapPullback_comp_id, CategoryTheory.GradedObject.Monoidal.associator_naturality, CategoryTheory.Pseudofunctor.map₂_left_unitor_assoc, CategoryTheory.Functor.uncurryObjFlip_hom_app, HomologicalComplex.homologyι_singleObjOpcyclesSelfIso_inv_assoc, CommAlgCat.inv_hom_apply, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_fst, HomologicalComplex.extendHomologyIso_hom_naturality, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id_app, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom, CategoryTheory.OplaxFunctor.map₂_associator_app, CategoryTheory.Oplax.LaxTrans.vComp_naturality_id, CategoryTheory.StrictPseudofunctorCore.map₂_left_unitor, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_morphismRestrict_assoc, BoolRing.Iso.mk_hom_hom', CategoryTheory.Functor.Initial.limitIso_hom, CategoryTheory.curryingIso_hom_toFunctor_obj_map, CategoryTheory.CatCommSq.hInv_iso_inv_app, ModuleCat.cokernel_π_cokernelIsoRangeQuotient_hom_apply, CategoryTheory.GrothendieckTopology.overMapPullbackId_inv_app_val_app, AlgebraicGeometry.Scheme.SpecToEquivOfField_eq_iff, CategoryTheory.Limits.ColimitPresentation.changeDiag_ι, CategoryTheory.Equivalence.leftOp_unitIso_inv_app, CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_cancel_hom_app, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_naturality_assoc, CategoryTheory.Limits.prod.pentagon_assoc, CategoryTheory.PreZeroHypercover.inv_hom_h₀_comp_f_assoc, CategoryTheory.instIsMonHomHomAsIso, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality_assoc, AlgebraicGeometry.PresheafedSpace.isoOfComponents_inv, CategoryTheory.MonObj.mul_assoc, CategoryTheory.Triangulated.TStructure.triangle_iso_exists, CategoryTheory.Limits.BinaryFan.braiding_hom_snd_assoc, CategoryTheory.MonoidalCategory.associator_naturality_assoc, CategoryTheory.PreZeroHypercover.inv_hom_s₀_apply, CategoryTheory.Dial.rightUnitor_naturality, CategoryTheory.MonObj.ofIso_mul, CategoryTheory.EnrichedCat.leftUnitor_hom_out_app, CategoryTheory.Pseudofunctor.mapComp'_hom_comp_whiskerLeft_mapComp'_hom, Homotopy.mkInductiveAux₃, CategoryTheory.Functor.shiftIso_hom_app_comp, CategoryTheory.Bicategory.conjugateEquiv_adjunction_id_symm, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom_assoc, CategoryTheory.CartesianMonoidalCategory.lift_leftUnitor_hom_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_assoc, StalkSkyscraperPresheafAdjunctionAuxs.counit_app, CategoryTheory.Limits.PreservesColimitPair.iso_hom, CategoryTheory.Pretriangulated.shiftFunctorZero_op_inv_app, inv_hom_id_triangle_hom₂, CategoryTheory.ShortComplex.RightHomologyMapData.homologyMap_eq, CategoryTheory.StructuredArrow.mapIso_inverse_obj_hom, Bimod.whiskerLeft_hom, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₂, CategoryTheory.Limits.image.compIso_hom_comp_image_ι_assoc, CategoryTheory.Under.postCongr_inv_app_right, Rep.indCoindNatIso_hom_app, CategoryTheory.Oplax.OplaxTrans.StrongCore.naturality_hom, CategoryTheory.BraidedCategory.braiding_tensor_left_inv, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerRightIso_hom_app, CategoryTheory.Functor.OplaxMonoidal.associativity_assoc, asOver_hom, CategoryTheory.cosimplicialSimplicialEquiv_counitIso_hom_app_app, CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_inv_assoc, CategoryTheory.Over.hom_left_inv_left, CategoryTheory.ProjectiveResolution.iso_hom_naturality_assoc, CategoryTheory.sum.inrCompInrCompInverseAssociator_hom_app_down, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₃, CategoryTheory.Core.isoMk_hom_iso, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.ofIso, CategoryTheory.Limits.opProdIsoCoprod_hom_snd_assoc, CategoryTheory.MonoidalCategory.whiskerRight_tensor_symm, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_leftUnitor, CategoryTheory.Functor.pi'CompEval_hom_app, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_rightUnitor_hom_hom, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.leftMapₗ_app, CategoryTheory.Limits.biproduct.whiskerEquiv_inv, Mathlib.Tactic.Monoidal.evalWhiskerLeft_of_cons, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerRight, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app, TopCat.sigmaIsoSigma_hom_ι, CategoryTheory.InjectiveResolution.iso_hom_naturality, CategoryTheory.Functor.FullyFaithful.homNatIsoMaxRight_hom_app_down, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp_assoc, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_unitIso_hom_app_f, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app, CategoryTheory.Equivalence.core_inverse_map_iso_hom, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app_assoc, CategoryTheory.Grpd.piIsoPi_hom_π, CategoryTheory.CartesianMonoidalCategory.whiskerLeft_toUnit_comp_rightUnitor_hom, HomologicalComplex.extendHomologyIso_hom_naturality_assoc, CategoryTheory.Over.forgetMapTerminal_hom_app, DerivedCategory.instCommShiftHomologicalComplexIntUpHomFunctorQuotientCompQhIso, CategoryTheory.Adjunction.leftAdjointUniq_refl, CategoryTheory.eqToHom_iso_hom_naturality_assoc, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app, CategoryTheory.Limits.π_comp_cokernelIsoOfEq_hom_assoc, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_associator, CategoryTheory.NatTrans.CommShift.leftUnitor, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_map_app_app, CategoryTheory.GrothendieckTopology.ι_plusCompIso_hom_assoc, CategoryTheory.Limits.Cones.ext_hom_hom, CategoryTheory.Functor.mapTriangle_obj, eHomCongr_hom, groupCohomology.H0IsoOfIsTrivial_hom, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_app_assoc, CategoryTheory.BraidedCategory.ofBifunctor.Forward.secondMap₃_app_app_app, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_hom_app, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_one, AlgebraicGeometry.Proj.basicOpenIsoAway_hom, CategoryTheory.CatCommSq.hId_iso_hom_app, TopCat.uliftFunctorCompForgetIso_hom_app, SemimoduleCat.MonoidalCategory.rightUnitor_hom_apply, CoalgCat.MonoidalCategoryAux.associator_hom_toLinearMap, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp_app, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_comp_naturality_hom, inl_coprodIsoPushout_hom, CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtension_map_leftKanExtensionObjIsoColimit_hom, AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_hom_app, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_hom_app, inv_hom_id, CategoryTheory.Limits.PushoutCocone.unop_π_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_inv_app, CategoryTheory.Limits.prod.rightUnitor_hom_naturality, CategoryTheory.MonoidalCategory.DayFunctor.equiv_unitIso_hom_app, CategoryTheory.MonoidalCategory.tensorLeftTensor_hom_app, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app, CategoryTheory.StrictPseudofunctor.id_mapComp_hom, CategoryTheory.Functor.mapGrpIdIso_hom_app_hom_hom, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_hom_app_hom_apply, CategoryTheory.Limits.inr_inl_pushoutRightPushoutInlIso_hom_assoc, CategoryTheory.unop_inv_associator, CategoryTheory.Join.mapWhiskerRight_leftUnitor_hom, CategoryTheory.Limits.Multifork.ext_hom_hom, CategoryTheory.Limits.Multifork.isoOfι_hom_hom, SimplicialObject.opFunctor_obj_σ, CategoryTheory.braiding_tensorUnit_left_assoc, CategoryTheory.mop_hom_rightUnitor, CategoryTheory.Localization.Monoidal.associator_hom_app, CategoryTheory.Localization.Monoidal.pentagon_aux₁, CategoryTheory.Limits.CatCospanTransform.rightUnitor_hom_left_app, CochainComplex.mappingCone.homologySequenceδ_triangleh, CategoryTheory.Under.mapIso_functor, CategoryTheory.NatTrans.instCommShiftPullbackShiftHomFunctorNatIsoComp, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_comp_ι, CategoryTheory.CostructuredArrow.mapIso_functor_obj_hom, CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_self_succ, CategoryTheory.Discrete.natIsoFunctor_hom_app, CategoryTheory.MonoidalCategory.externalProductCompDiagIso_hom_app_app, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id_assoc, groupHomology.cyclesMap_comp_isoCycles₂_hom, HomologicalComplex₂.total.mapIso_hom, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_left_right, isoInverseComp_inv_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_hom_app_fst_app, AugmentedSimplexCategory.inr_comp_inl_comp_associator, CategoryTheory.Functor.EssImageSubcategory.associator_hom_def, CategoryTheory.Limits.pullbackAssoc_hom_snd_fst_assoc, CategoryTheory.Functor.commShift₂_comm, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_obj, map_inv_hom_id_app_assoc, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.secondMap₁_app_app_app, AlgebraicGeometry.Scheme.stalkMap_congr_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id_assoc, groupHomology.comp_d₂₁_eq, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv, CategoryTheory.MonoidalCategory.associatorNatIso_hom_app, CategoryTheory.GrothendieckTopology.whiskerRight_toSheafify_sheafifyCompIso_hom_assoc, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_left, CategoryTheory.Functor.pentagon, CategoryTheory.MonObj.ofIso_one, CategoryTheory.Functor.mapCoconeWhisker_hom_hom, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂_assoc, CategoryTheory.Limits.colimitCoyonedaHomIsoLimit'_π_apply, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_assoc, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inr_assoc, MonObj.mopEquivCompForgetIso_hom_app_unmop, CategoryTheory.Bimon.equivMonComonUnitIsoAppXAux_hom, CategoryTheory.Cat.Hom.isoMk_hom, groupHomology.toCycles_comp_isoCycles₂_hom_assoc, CategoryTheory.Monoidal.associator_hom_app, AlgebraicGeometry.Scheme.hom_inv_apply, CategoryTheory.Limits.prod.rightUnitor_hom_naturality_assoc, CategoryTheory.Bicategory.pentagon_hom_hom_inv_hom_hom_assoc, CategoryTheory.coprod_inl_leftDistrib_hom, CategoryTheory.Oplax.OplaxTrans.categoryStruct_id_naturality, CategoryTheory.MonoidalCategory.rightUnitor_tensor_hom, CategoryTheory.Join.isoMkFunctor_hom_app, CategoryTheory.Equivalence.leftOp_counitIso_inv_app, CategoryTheory.NatTrans.unop_whiskerLeft_assoc, CategoryTheory.Functor.Monoidal.map_associator_assoc, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_inv_τr, Bimod.TensorBimod.whiskerLeft_π_actLeft, CategoryTheory.MorphismProperty.Over.pullbackComp_hom_app_left, AlgCat.inv_hom_apply, CategoryTheory.Localization.SmallHom.equiv_equiv_symm, CategoryTheory.Functor.CommShift.isoZero_hom_app, linearEquivIsoModuleIso_hom, CategoryTheory.Presheaf.instIsLeftKanExtensionFunctorOppositeTypeLanOpHomCompULiftYonedaIsoULiftYonedaCompLan, CategoryTheory.Grp.leftUnitor_hom_hom, CategoryTheory.LocalizerMorphism.commShift_iso_hom_app, CategoryTheory.Cat.Hom.toNatIso_hom, CategoryTheory.Limits.inl_comp_pushoutObjIso_hom, CategoryTheory.Comma.mapRightIso_counitIso_inv_app_left, AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_hom_app, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom, CategoryTheory.ShortComplex.mapCyclesIso_hom_iCycles_assoc, CategoryTheory.Bicategory.whiskerRightIso_hom, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_assoc, CategoryTheory.Limits.Fork.isoForkOfι_hom_hom, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app, CategoryTheory.GradedObject.mapBifunctorObjObjSingle₀Iso_hom, CategoryTheory.Limits.limitOpIsoOpColimit_hom_comp_ι_assoc, AugmentedSimplexCategory.inr_comp_inl_comp_associator_assoc, HomologicalComplex₂.D₂_totalShift₁XIso_hom_assoc, CategoryTheory.Limits.pushoutIsoUnopPullback_inr_hom, CategoryTheory.Limits.Cocones.precomposeEquivalence_functor, CategoryTheory.Comma.mapRightEq_hom_app_right, CategoryTheory.Limits.CatCospanTransform.triangle_assoc, Frm.Iso.mk_hom, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.secondMap₁_app_app_app, CategoryTheory.CartesianMonoidalCategory.braiding_hom_snd_assoc, CategoryTheory.Limits.BinaryFan.braiding_hom_fst_assoc, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_hom, AlgebraicGeometry.Scheme.Hom.preimageIso_hom_ι_assoc, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_hom_iCycles_assoc, CategoryTheory.Limits.PreservesPushout.inr_iso_hom_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftUnitor_actionHom_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app_assoc, CategoryTheory.ChosenPullbacksAlong.unit_pullbackComp_hom_assoc, CategoryTheory.ShortComplex.mapHomologyIso_hom_naturality, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.leftMapᵣ_app, CategoryTheory.Comma.mapRightIso_counitIso_inv_app_right, CategoryTheory.Functor.Monoidal.transport_μ, CategoryTheory.Limits.Types.pullbackIsoPullback_hom_fst, CategoryTheory.OplaxFunctor.mapComp_assoc_left_app_assoc, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂, HomologicalComplex.biprodXIso_hom_fst, HomologicalComplex₂.D₂_totalShift₂XIso_hom_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_hom_app, CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoCofanPt_assoc, CategoryTheory.sheafificationNatIso_hom_app_val, CategoryTheory.ShortComplex.opcyclesIsoRightHomology_inv_hom_id_assoc, CategoryTheory.BraidedCategory.hexagon_reverse_assoc, CategoryTheory.Functor.commShiftIso_comp_hom_app, CategoryTheory.inv_hom_id_apply, CategoryTheory.Grothendieck.transportIso_hom_base, CategoryTheory.Comma.mapLeftEq_hom_app_left, CategoryTheory.Monad.algebraEquivOfIsoMonads_inverse, CategoryTheory.HalfBraiding.naturality, CategoryTheory.Functor.coreId_hom_app_iso_hom, AlgebraicGeometry.ValuativeCriterion.Existence.instIsLocalHomCarrierRingHomHomHomCommRingCat, CategoryTheory.Monad.monadMonEquiv_counitIso_hom_app_hom, CategoryTheory.MonoOver.mapIso_unitIso, HomologicalComplex.extend_op_d_assoc, CategoryTheory.constantCommuteCompose_hom_app_val, CategoryTheory.Limits.image.eq_fac, CategoryTheory.WithTerminal.mapComp_hom_app, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_flip_hom_app, CategoryTheory.Bicategory.Adjunction.homEquiv₁_apply, CategoryTheory.StrictPseudofunctorCore.map₂_associator, CategoryTheory.Limits.desc_op_comp_opCoproductIsoProduct'_hom, CategoryTheory.MonoidalCategory.curriedAssociatorNatIso_hom_app_app_app, hom_eq_inv, inv_hom_id_triangle_hom₁, AlgebraicGeometry.Scheme.Hom.toNormalization_inr_normalizationCoprodIso_hom, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_associator, CategoryTheory.monoidalOfHasFiniteProducts.associator_hom, CategoryTheory.Limits.colimit.homIso_hom, CategoryTheory.Limits.prod.associator_naturality_assoc, CategoryTheory.Limits.WidePullbackShape.functorExt_hom_app, CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_left_inv, groupCohomology.comp_d₁₂_eq, CategoryTheory.Functor.Monoidal.tensorObjComp_hom_app, CategoryTheory.Join.mapWhiskerLeft_whiskerRight, CategoryTheory.eqToIso.hom, CategoryTheory.Center.whiskerLeft_comm, SimplicialObject.opFunctor_obj_map, CategoryTheory.Limits.PreservesCokernel.π_iso_hom_assoc, CategoryTheory.Functor.FullyFaithful.autMulEquivOfFullyFaithful_symm_apply_hom, CategoryTheory.Monad.algebraFunctorOfMonadHomId_hom_app_f, Bimod.actRight_one, CategoryTheory.kernelOpUnop_hom, CategoryTheory.mop_inv_associator, AlgebraicGeometry.Scheme.Cover.gluedCover_t, FintypeCat.equivEquivIso_apply_hom, CategoryTheory.Functor.IsCoverDense.isoOver_hom_app, AlgebraicGeometry.Scheme.SpecΓIdentity_hom_app, CategoryTheory.Functor.currying₃_unitIso_hom_app_app_app_app, CategoryTheory.Functor.FullyFaithful.compUliftCoyonedaCompWhiskeringLeft_hom_app_app_down, CategoryTheory.Limits.inr_inr_pushoutRightPushoutInlIso_hom, CategoryTheory.Limits.limitIsoLimitCurryCompLim_hom_π_π_assoc, Homotopy.extend_hom_eq, CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_fst, CategoryTheory.Limits.prodComparisonNatIso_hom, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_unit_app, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom_assoc, CategoryTheory.FunctorToTypes.binaryProductEquiv_apply, CategoryTheory.Functor.LaxBraided.braided, CategoryTheory.Functor.LaxMonoidal.left_unitality_assoc, SemimoduleCat.MonoidalCategory.associator_naturality, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_leftUnitor, SSet.opFunctorCompOpFunctorIso_hom_app_app, CategoryTheory.Bimon.instIsMonHomComonHomEquivMonComonCounitIsoAppX, CategoryTheory.ProjectiveResolution.cochainComplex_d, CategoryTheory.Limits.initialIsoIsInitial_hom, CategoryTheory.Pseudofunctor.map₂_left_unitor, CategoryTheory.Limits.pushoutIsoUnopPullback_inl_hom_assoc, CategoryTheory.Bicategory.Pith.leftUnitor_inv_iso_hom, CategoryTheory.Limits.colimitCurrySwapCompColimIsoColimitCurryCompColim_ι_ι_hom, CategoryTheory.MonoidalCategory.whiskerRight_tensor, CategoryTheory.FreeGroupoid.mapComp_hom_app, CategoryTheory.Bimon.instIsComonHomHomEquivMonComonCounitIsoAppXAux, CategoryTheory.GradedObject.Monoidal.pentagon, SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_hom_app, CategoryTheory.Comma.mapRightIso_functor_map_left, TopCat.Presheaf.pushforwardToOfIso_app, CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_right, CategoryTheory.Bicategory.associator_naturality_right_assoc, CategoryTheory.Pseudofunctor.CoGrothendieck.map_map_fiber, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_right, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerLeft_naturality_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_hom_inv, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁_assoc, CategoryTheory.Limits.coprod.pentagon, CategoryTheory.Bicategory.hom_inv_whiskerRight_whiskerRight_assoc, HomologicalComplex.Hom.next_eq, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd_assoc, CochainComplex.shiftShortComplexFunctorIso_add'_hom_app, CategoryTheory.Bicategory.triangle_assoc_comp_left, CategoryTheory.Limits.pullbackProdFstIsoProd_hom_fst_assoc, CategoryTheory.Limits.IsColimit.homIso_hom, CategoryTheory.WithInitial.opEquiv_counitIso_hom_app, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_hom_app, CategoryTheory.GrothendieckTopology.OneHypercover.isoMk_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_hom_app_hom, CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso_hom_app, groupCohomology.map_H0Iso_hom_f_apply, CategoryTheory.Quotient.lift.isLift_hom, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_right, CategoryTheory.MonoidalCategory.id_whiskerLeft, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι, CategoryTheory.Bimon.equivMonComonUnitIsoApp_hom_hom_hom, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_hom_app_hom_hom_app, CategoryTheory.Limits.colimitIsoSwapCompColim_hom_app, CategoryTheory.Over.braiding_inv_left, QuadraticModuleCat.ofIso_hom, CategoryTheory.Localization.HasProductsOfShapeAux.adj_counit_app, CategoryTheory.Monad.algebraEquivOfIsoMonads_unitIso, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_hom_app_val_app, CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIso_hom, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_hom_comp_homologyIso_inv, CategoryTheory.Functor.mapTriangleCompIso_hom_app_hom₂, CategoryTheory.Limits.kernelSubobjectIsoComp_hom_arrow, CategoryTheory.Adjunction.compYonedaIso_hom_app_app, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology_inv_homologyι_assoc, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapCompIso_hom, CategoryTheory.Functor.currying_counitIso_hom_app_app, CategoryTheory.leftUnitor_hom_apply, CategoryTheory.leftDistributor_hom, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.associator_hom_unit_unit, CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapComp_hom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.w_app, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_fiber, HomologicalComplex.restrictionCyclesIso_hom_iCycles, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompCoyoneda, CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_snd, CategoryTheory.Functor.prod'CompSnd_hom_app, isoInverseComp_hom_app, AddCommGrpCat.neg_hom_apply, CategoryTheory.Functor.mapActionComp_hom, CategoryTheory.ShortComplex.leftRightHomologyComparison_fac, CategoryTheory.BasedNatIso.id_hom, CategoryTheory.Limits.pushoutIsoUnopPullback_inr_hom_assoc, Profinite.NobelingProof.spanFunctorIsoIndexFunctor_hom_app_hom_hom_apply_coe, CategoryTheory.Limits.piObjIso_hom_comp_π, inv_comp_eq_id, Bimod.left_assoc_assoc, RingCat.inv_hom_apply, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app, ModuleCat.restrictScalarsId'App_hom_naturality, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.IsSifted.factorization_prodComparison_colim, CategoryTheory.NatIso.naturality_1, CategoryTheory.NatIso.inv_map_inv_app, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv, CategoryTheory.Equivalence.core_unitIso_hom_app_iso_inv, CategoryTheory.DifferentialObject.shiftZero_hom_app_f, CategoryTheory.Limits.PreservesProduct.iso_hom, imageToKernel_op, AlgebraicGeometry.Scheme.Pullback.tensorCongr_SpecTensorTo, CategoryTheory.Limits.kernelBiprodFstIso_hom, CategoryTheory.FunctorToTypes.map_inv_map_hom_apply, CategoryTheory.Oplax.StrongTrans.Modification.whiskerLeft_naturality, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_hom_assoc, CategoryTheory.Grp.rightUnitor_hom_hom_hom, CategoryTheory.Bicategory.conjugateEquiv_apply, inv_hom_id_triangle_hom₂_assoc, CategoryTheory.Functor.ShiftSequence.induced.isoZero_hom_app_obj, CategoryTheory.Bicategory.whiskerRight_comp_symm, CategoryTheory.Functor.IsCartesian.domainUniqueUpToIso_inv_isHomLift, CategoryTheory.rightUnitor_inv_braiding, CategoryTheory.ThinSkeleton.fromThinSkeleton_map, CategoryTheory.GradedObject.Monoidal.rightUnitor_naturality_assoc, HomologicalComplex.XIsoOfEq_hom_comp_d_assoc, CategoryTheory.Limits.PreservesTerminal.iso_hom, CategoryTheory.Adjunction.Triple.rightToLeft_eq_units, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv, CategoryTheory.Bicategory.Pith.comp₂_iso_hom_assoc, CategoryTheory.GlueData.t'_iij, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_inv_app_left, CategoryTheory.NatTrans.instCommShiftPullbackShiftHomFunctorNatIsoId, CategoryTheory.StructuredArrow.eta_hom_right, CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_inv, CategoryTheory.GradedObject.Monoidal.symmetry, CategoryTheory.Cat.leftUnitor_hom_app, CategoryTheory.Bicategory.associator_eqToHom_hom_assoc, Preord.inv_hom_apply, ModuleCat.exteriorPower.iso₀_hom_naturality, CategoryTheory.Limits.inr_inl_pushoutLeftPushoutInrIso_hom, CategoryTheory.shift_shift_neg', CategoryTheory.Functor.LaxMonoidal.ofBifunctor.firstMap₃_app_app_app, CategoryTheory.NatTrans.CommShift.shift_comm, CategoryTheory.NatTrans.naturality_2_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocNatIso_hom_app_app_app, HomologicalComplex.truncLE'_d_eq_toCycles, CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_snd, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_inv_app, CategoryTheory.Limits.kernelFactorThruImage_hom_comp_ι_assoc, CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inr_assoc, CategoryTheory.LocalizerMorphism.commShift_iso_inv_app, CategoryTheory.Bicategory.whiskerRight_id, CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv'_assoc, CategoryTheory.Grothendieck.isoMk_inv_fiber, CategoryTheory.MonoOver.mapIso_counitIso, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_hom, CategoryTheory.HasShift.Induced.add_hom_app_obj, CategoryTheory.ComonadIso.toNatIso_hom, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_hom_fac_app, CategoryTheory.biproduct_ι_comp_rightDistributor_hom, CategoryTheory.rightDistributor_hom_comp_biproduct_π_assoc, equivIsoIso_hom, CategoryTheory.Limits.image.isoStrongEpiMono_hom_comp_ι, CategoryTheory.CatCommSq.hComp_iso_hom_app, Semigrp.hom_inv_apply, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompPointIso_hom_app, homFromEquiv_symm_apply, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app, groupHomology.π_comp_H0Iso_hom_assoc, CategoryTheory.symmetricOfHasFiniteProducts_braiding_hom, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans, CategoryTheory.Discrete.compNatIsoDiscrete_hom_app, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_hom_fac_app, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality, CochainComplex.homotopyUnop_hom_eq, CategoryTheory.Over.leftUnitor_hom_left, CategoryTheory.CostructuredArrow.mapIso_unitIso_hom_app_left, CategoryTheory.Limits.Types.binaryProductIso_hom_comp_snd_apply, CategoryTheory.Dial.triangle, HomologicalComplex₂.ι_totalShift₁Iso_hom_f_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.hom_inv_actionHomLeft_assoc, CategoryTheory.Functor.mapProjectiveResolution_π, CategoryTheory.Limits.instIsIsoHomHomCocone, CategoryTheory.Adjunction.localization_unit_app, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd_assoc, CategoryTheory.ObjectProperty.isoHom_inv_id_hom, CategoryTheory.Limits.isoZeroBiprod_hom, CategoryTheory.Limits.isoZeroOfEpiZero_hom, CategoryTheory.IsHomLift.isoOfIsoLift_hom, AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimage, CategoryTheory.Oplax.LaxTrans.naturality_comp_assoc, CategoryTheory.Limits.colimitYonedaHomIsoLimit'_π_apply, CategoryTheory.Prod.symmetry_hom_app, CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_hom_app_app_val, AlgebraicGeometry.Scheme.isoSpec_hom, CategoryTheory.OverClass.instHomIsOverHomOfInv, HomologicalComplex.ι_mapBifunctorAssociatorX_hom, CommGrpCat.hom_inv_apply, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionActionOfMonoidalFunctorToEndofunctorMopIso_hom_app_unmop_app, CategoryTheory.HopfObj.mul_antipode, CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_snd_assoc, CategoryTheory.Functor.IsRepresentedBy.of_natIso, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_right, CategoryTheory.Join.mapWhiskerLeft_whiskerLeft, CategoryTheory.MonoidalCategory.MonoidalRightAction.inv_hom_actionHomLeft, HomologicalComplex.extend.XOpIso_hom_d_op, AlgebraicGeometry.Scheme.Modules.pseudofunctor_right_unitality_assoc, CategoryTheory.Join.inrCompFromSum_hom_app, CategoryTheory.Limits.Types.coequalizerIso_π_comp_hom_apply, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_c_app, CategoryTheory.OppositeShift.adjunction_unit, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_hom_whiskerRight_π_assoc, ModuleCat.restrictScalarsComp'_hom_app, CategoryTheory.Localization.Monoidal.pentagon_aux₂, CategoryTheory.Comma.toPUnitIdEquiv_counitIso_hom_app, CategoryTheory.MonoidalCategory.id_tensor_rightUnitor_inv_assoc, CategoryTheory.ShortComplex.leftRightHomologyComparison'_fac, CategoryTheory.FreeGroupoid.mapId_hom_app, Preord.hom_inv_apply, CategoryTheory.Functor.Monoidal.map_associator, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.biprodAddEquiv_symm_biprodIsoProd_hom_toBiprod_apply, Semigrp.inv_hom_apply, CategoryTheory.Functor.mapMatComp_hom_app, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π_assoc, CategoryTheory.Sigma.mapComp_hom_app, CategoryTheory.Limits.biproductBiproductIso_hom, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_id, AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_hom_π, CategoryTheory.SmallObject.SuccStruct.ofCocone_map_assoc, CategoryTheory.Limits.kernelBiproductπIso_hom, CategoryTheory.MonoidalCategory.whiskerRight_id_symm_assoc, CategoryTheory.Limits.kernelCompMono_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom, AlgebraicGeometry.Proj.basicOpenToSpec_app_top, CategoryTheory.cokernelOpOp_hom, CategoryTheory.Endofunctor.Algebra.functorOfNatTransComp_hom_app_f, CategoryTheory.Limits.biprod.symmetry, CategoryTheory.ShortComplex.op_pOpcycles_opcyclesOpIso_hom, CategoryTheory.PreZeroHypercover.instIsIsoH₀Hom, HomologicalComplex.forgetEval_hom_app, HomologicalComplex.homologyι_singleObjOpcyclesSelfIso_inv, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.Functor.compConstIso_hom_app_app, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_app_assoc, commBialgCatEquivComonCommAlgCat_unitIso_hom_app, CategoryTheory.Functor.coreComp_hom_app_iso_hom, CategoryTheory.CatCommSq.vId_iso_hom_app, CategoryTheory.Precoverage.ZeroHypercover.isoMk_hom, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_apply, Rep.coindFunctorIso_hom_app_hom_hom_apply_hom_hom_apply, CategoryTheory.Monoidal.InducingFunctorData.associator_eq, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_apply, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_fst, CategoryTheory.Codiscrete.natIsoFunctor_hom_app, CategoryTheory.Bicategory.whiskerLeft_hom_inv, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app, Bimod.id_whiskerLeft_bimod, CategoryTheory.Limits.Pi.reindex_hom_π_assoc, ModuleCat.MonoidalCategory.associator_hom_apply, AlgebraicGeometry.Scheme.Opens.isoOfLE_hom_ι_assoc, CategoryTheory.Dial.braiding_naturality_right, toCoalgEquiv_toCoalgHom, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_snd, CategoryTheory.WithTerminal.liftStar_hom, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_apply, groupHomology.d₁₀ArrowIso_hom_left, CategoryTheory.MonoidalCategory.tensor_whiskerLeft_symm_assoc, CategoryTheory.Bicategory.mateEquiv_id_comp_right, CategoryTheory.Adjunction.conjugateEquiv_leftAdjointCompIso_inv, AlgebraicGeometry.LocallyRingedSpace.iso_inv_base_hom_base_apply, CategoryTheory.Bicategory.leftUnitor_comp_inv, CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences, CategoryTheory.Functor.curryObjProdComp_hom_app_app, CategoryTheory.Limits.Pi.reindex_hom_π, CategoryTheory.GradedObject.CofanMapObjFun.inj_iso_hom, CategoryTheory.oppositeShiftFunctorAdd_inv_app, LinOrd.hom_inv_apply, CategoryTheory.Functor.associator_hom_app, CategoryTheory.Functor.shiftIso_zero_hom_app, CategoryTheory.Limits.inr_comp_pushoutObjIso_hom_assoc, groupHomology.cycles₁IsoOfIsTrivial_hom_apply, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoImage_ι, CategoryTheory.BraidedCategory.braiding_tensor_left_hom, CategoryTheory.MonoOver.mkArrowIso_hom_hom_left, CategoryTheory.Functor.rightOpComp_hom_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomLeft_action_assoc, CategoryTheory.braiding_inv_tensorUnit_right_assoc, CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_inv, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_map_app_app, AlgebraicGeometry.SheafedSpace.isoMk_hom, AlgebraicGeometry.SpecMap_ΓSpecIso_hom, CategoryTheory.Limits.kernelSubobject_arrow_assoc, HomologicalComplex.extend.XOpIso_hom_d_op_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality_app, CategoryTheory.image_ι_op_comp_imageUnopOp_hom, CategoryTheory.OverPresheafAux.unitAuxAuxAux_hom, CategoryTheory.EnrichedCat.rightUnitor_hom_out_app, CategoryTheory.Limits.HasColimit.isoOfEquivalence_hom_π, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_whisker_right, CategoryTheory.StrictPseudofunctor.comp_mapComp_hom, CategoryTheory.Limits.biproduct.isoProduct_hom, HomologicalComplex.extendSingleIso_inv_f_assoc, CategoryTheory.Limits.inr_inl_pushoutRightPushoutInlIso_hom, CategoryTheory.Bicategory.leftZigzagIso_hom, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_apply, CategoryTheory.Functor.rightOpLeftOpIso_hom_app, CategoryTheory.Discrete.monoidalFunctorComp_isMonoidal, CategoryTheory.Equalizer.firstObjEqFamily_hom, CategoryTheory.Preadditive.commGrpEquivalence_unitIso_hom_app, HomologicalComplex.XIsoOfEq_inv_comp_XIsoOfEq_inv, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_hom_inv, CategoryTheory.CartesianMonoidalCategory.prodComparisonIso_hom, Bicategory.Opposite.bicategory_associator_hom_unop2, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.bottomMapₗ_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app, AlgebraicGeometry.Scheme.isoOfEq_hom_ι, CategoryTheory.OplaxFunctor.PseudoCore.mapCompIso_hom, CategoryTheory.StrictPseudofunctor.comp_mapId_hom, FinBddDistLat.hom_inv_apply, CategoryTheory.ProjectiveResolution.isoLeftDerivedObj_hom_naturality_assoc, HomotopyCategory.isoOfHomotopyEquiv_hom, Bimod.TensorBimod.actRight_one', CategoryTheory.Functor.mapMonCompIso_hom_app_hom, isoOfQuasiIsoAt_hom, CategoryTheory.MonObj.mul_leftUnitor, eq_comp_inv, CategoryTheory.Adjunction.mapCommMon_unit, HomologicalComplex.extendHomologyIso_hom_homologyι_assoc, SimplicialObject.opFunctor_map_app, CategoryTheory.Join.mapIsoWhiskerLeft_hom, CategoryTheory.LaxFunctor.mapComp_assoc_right_app, CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_hom_assoc, CategoryTheory.Limits.Cocone.toCostructuredArrowCompProj_hom_app, hom_inv_id_app_app_assoc, CategoryTheory.Functor.functorialityCompPostcompose_hom_app_hom, CategoryTheory.Oplax.OplaxTrans.associator_hom_as_app, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_hom_hom₂, HomologicalComplex.mapBifunctorFlipIso_hom_naturality_assoc, CategoryTheory.unmop_hom_associator, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d, hom_inv_id_eval_assoc, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_hom_inv_assoc, HomologicalComplex.restriction_d_eq, CategoryTheory.Pseudofunctor.toOplax_mapComp, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app_assoc, CategoryTheory.FunctorToTypes.binaryCoproductEquiv_apply, AlgebraicGeometry.PresheafedSpace.isoOfComponents_hom, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_right_app, HomologicalComplex.dTo_eq, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₁, CategoryTheory.CartesianMonoidalCategory.lift_braiding_hom, CategoryTheory.Bimon.compatibility_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomLeft_action, CategoryTheory.PreZeroHypercover.inv_hom_h₀_comp_f, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_app, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_ι, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom, CategoryTheory.ModObj.mul_smul'_assoc, CategoryTheory.Bicategory.inv_hom_whiskerRight_whiskerRight, inv_eq_hom, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp, AlgebraicGeometry.Scheme.isoSpec_hom_naturality, CategoryTheory.Bicategory.Prod.sectR_mapComp_inv, CategoryTheory.Pi.associator_hom_apply, HomologicalComplex.natIsoSc'_hom_app_τ₃, CategoryTheory.Bicategory.Prod.fst_mapComp_hom, CategoryTheory.Limits.fiberwiseColimitLimitIso_hom_app, CategoryTheory.Limits.kernelIsoOfEq_hom_comp_ι, CategoryTheory.FreeMonoidalCategory.normalize_naturality, CategoryTheory.Limits.Types.binaryProductIso_hom_comp_fst_apply, CategoryTheory.Cat.freeMapIdIso_hom_app, CategoryTheory.Limits.opCoproductIsoProduct'_comp_self, CategoryTheory.Comma.rightIso_hom, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_hom_inv_assoc, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.ShortComplex.leftHomologyMap_op, CategoryTheory.InjectiveResolution.toRightDerivedZero_eq, CategoryTheory.Bicategory.id_whiskerLeft_symm, CategoryTheory.Pseudofunctor.mapComp'_naturality_1, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitIso_hom_naturality_assoc, CategoryTheory.Functor.opId_hom_app, CategoryTheory.Dial.associator_hom_F, groupHomology.chainsMap_f_3_comp_chainsIso₃, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_hom_app_fst_app, CategoryTheory.Over.mapCongr_hom_app_left, CategoryTheory.Limits.opCoproductIsoProduct'_hom_comp_proj, CategoryTheory.Pseudofunctor.mkOfLax'_mapComp_hom, CategoryTheory.Functor.shift_map_op_assoc, CategoryTheory.Equivalence.funInvIdAssoc_hom_app, CategoryTheory.Over.postCongr_inv_app_left, CategoryTheory.Localization.Monoidal.lifting_isMonoidal, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_η_app, CategoryTheory.coreCategory_inv_iso_inv, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitIso_hom_naturality_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_inv_app, CategoryTheory.Limits.CoconeMorphism.hom_inv_id_assoc, CategoryTheory.Localization.Monoidal.triangle_aux₃, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app', CategoryTheory.Functor.OplaxRightLinear.δᵣ_unitality_hom_assoc, CategoryTheory.Functor.FullyFaithful.preimageIso_hom, CategoryTheory.PreGaloisCategory.connected_component_unique, AlgebraicGeometry.Scheme.hom_base_inv_base, CategoryTheory.Limits.ι_colimitLimitIso_limit_π, CategoryTheory.Functor.mapContActionCongr_hom, CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_hom_app_unmop_unmop, CategoryTheory.WithInitial.inclLift_hom_app, CategoryTheory.Over.mapComp_hom_app_left, CategoryTheory.Functor.Final.ι_colimitIso_hom_assoc, CategoryTheory.Limits.Cocones.precomposeEquivalence_unitIso, groupCohomology.cocycles₁IsoOfIsTrivial_hom_hom_apply_apply, CategoryTheory.Limits.walkingCospanOpEquiv_counitIso_hom_app, TopologicalSpace.Opens.mapId_hom_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_inv_hom, CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_fst_fst_assoc, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_app, CategoryTheory.MonoidalCategory.unitors_equal, ProfiniteAddGrp.hom_neg_apply, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_inv, CategoryTheory.GradedObject.ι_mapBifunctorComp₁₂MapObjIso_hom_assoc, CategoryTheory.Comma.equivProd_unitIso_hom_app_left, TopologicalSpace.Opens.mapComp_hom_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionUnitIso_hom, CategoryTheory.Adjunction.mapCommMon_counit, CategoryTheory.Limits.biprod.mapBiprod_hom_desc, CategoryTheory.coprod_inl_rightDistrib_hom, CategoryTheory.Coyoneda.objOpOp_hom_app, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app, HomologicalComplex.singleObjHomologySelfIso_hom_singleObjOpcyclesSelfIso_hom, CategoryTheory.Limits.productUniqueIso_hom, CategoryTheory.Monad.algebraFunctorOfMonadHomEq_hom_app_f, CategoryTheory.Functor.mapCommGrpCompIso_hom_app_hom_hom_hom, CategoryTheory.Join.pseudofunctorLeft_mapId_hom_toNatTrans_app, BddOrd.Iso.mk_hom, HomotopicalAlgebra.AttachCells.ofArrowIso_g₂, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_app_assoc, CategoryTheory.sheafComposeIso_hom_fac, CategoryTheory.Limits.biproduct.mapIso_hom, CategoryTheory.Limits.fst_opProdIsoCoprod_hom_assoc, CategoryTheory.Idempotents.functorExtension₂CompWhiskeringLeftToKaroubiIso_hom_app_app_f, CategoryTheory.Functor.ι_colimitIsoColimitGrothendieck_hom, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_naturality, CategoryTheory.Pretriangulated.binaryProductTriangleIsoBinaryBiproductTriangle_hom_hom₂, HomotopicalAlgebra.PrepathObject.symm_p, CategoryTheory.GradedObject.mapBifunctorMapMapIso_hom, CategoryTheory.MonoidalCategory.hom_inv_whiskerRight_assoc, CategoryTheory.IsPushout.inr_isoPushout_hom_assoc, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_inv_app, CategoryTheory.Limits.limitConstTerminal_hom, CategoryTheory.Pseudofunctor.map₂_associator_app, CategoryTheory.Cat.rightUnitor_hom_toNatTrans, CategoryTheory.Limits.spanCompIso_hom_app_zero, CategoryTheory.Functor.const.opObjUnop_hom_app, groupCohomology.dArrowIso₀₁_hom_right, SemimoduleCat.MonoidalCategory.braiding_naturality_right, CategoryTheory.Mon.trivial_mon_mul, ModuleCat.uliftFunctorForgetIso_hom_app, CategoryTheory.Functor.prod'CompFst_hom_app, Condensed.isoFinYonedaComponents_hom_apply, CategoryTheory.PullbackShift.adjunction_unit, Bipointed.swapEquiv_counitIso_hom_app_toFun, CategoryTheory.MonoidalCategory.inv_hom_whiskerRight_assoc, CategoryTheory.SmallObject.SuccStruct.extendToSuccObjIso_hom_naturality_assoc, CategoryTheory.GradedObject.singleCompEval_hom_app, CategoryTheory.Lax.OplaxTrans.naturality_comp, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_inv_toNatTrans_app_val_app, CategoryTheory.FreeGroupoid.liftNatIso_hom_app, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_hom_left, CategoryTheory.compEvaluation_hom_app, CategoryTheory.ShortComplex.cyclesOpIso_hom_naturality, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_hom_π_π, CategoryTheory.Arrow.square_from_iso_invert, CategoryTheory.Limits.inl_inl_pushoutLeftPushoutInrIso_hom_assoc, op_hom, groupCohomology.toCocycles_comp_isoCocycles₂_hom, SheafOfModules.pullback_map_ιFree_comp_pullbackObjFreeIso_hom_assoc, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_SpecMap_awayMap_right_assoc, HomologicalComplex.singleObjCyclesSelfIso_hom_naturality, CategoryTheory.Bicategory.whiskerRight_comp_symm_assoc, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_hom_hom₁, CategoryTheory.Pseudofunctor.DescentData.iso_hom, CategoryTheory.Oplax.StrongTrans.Modification.whiskerRight_naturality, CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_right_hom, CategoryTheory.coprod_inr_rightDistrib_hom, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app_assoc, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_hom, CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inl, CategoryTheory.Dial.leftUnitor_hom_f, CategoryTheory.Limits.spanOp_hom_app, CategoryTheory.Limits.limitIsoSwapCompLim_hom_app, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_assoc, CategoryTheory.Limits.pullbackProdSndIsoProd_hom_fst, ModuleCat.imageIsoRange_hom_subtype, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom, CategoryTheory.Bicategory.Adj.rightUnitor_hom_τr, eHomCongr_comp_assoc, AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_snd, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_hom_comp_π_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_inv_app, CategoryTheory.Limits.limitIsoFlipCompLim_hom_app, CategoryTheory.NatTrans.shift_comm_assoc, toIsometryEquiv_toFun, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapId_inv_iso_inv, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality, CategoryTheory.Functor.CoreMonoidal.left_unitality, CategoryTheory.Functor.IsCartesian.of_iso_comp, CategoryTheory.Adjunction.mapCommGrp_unit, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app, CategoryTheory.conjugateEquiv_leftUnitor_hom, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₃_app, ProfiniteAddGrp.neg_hom_apply, CategoryTheory.shiftFunctorAdd_zero_add_hom_app, CategoryTheory.Idempotents.functorExtension₁CompWhiskeringLeftToKaroubiIso_hom_app_app_f, CategoryTheory.Functor.instCommShiftHomotopyCategoryIntUpDerivedCategoryHomMapDerivedCategoryFactorsh, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_naturality, CategoryTheory.Limits.limitCompCoyonedaIsoCone_hom_app, Bicategory.Opposite.bicategory_leftUnitor_hom_unop2, CategoryTheory.Limits.ι_comp_colimitRightOpIsoUnopLimit_hom_assoc, HomologicalComplex₂.flipEquivalenceUnitIso_hom_app_f_f, CategoryTheory.Adjunction.leftAdjointUniq_hom_app_counit_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id_app, CategoryTheory.Bicategory.comp_whiskerLeft_symm, CochainComplex.shiftFunctorZero_inv_app_f, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_assoc, CategoryTheory.SingleFunctors.Hom.comm_assoc, CategoryTheory.CostructuredArrow.mapIso_functor_map_left, CategoryTheory.ι_preservesColimitIso_hom_assoc, comp_hom_eq_id, CategoryTheory.shiftFunctorComm_hom_app_comp_shift_shiftFunctorAdd_hom_app, CategoryTheory.Localization.Monoidal.μ_natural_right, CategoryTheory.Limits.CatCospanTransform.whiskerRight_id, HomologicalComplex.extendMap_f, CategoryTheory.left_unitality_app_assoc, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom, CategoryTheory.ShortComplex.homologyMapIso_hom, CategoryTheory.Functor.mapCommMonNatIso_hom_app_hom_hom, CategoryTheory.Limits.Cone.toStructuredArrowCompToUnderCompForget_hom_app, CategoryTheory.Comma.equivProd_counitIso_hom_app, CategoryTheory.CartesianMonoidalCategory.braiding_hom_fst, CategoryTheory.MonoidalCategory.whisker_assoc_assoc, CommAlgCat.algEquivOfIso_apply, CategoryTheory.Limits.lift_comp_kernelIsoOfEq_hom_assoc, CategoryTheory.Localization.homEquiv_eq, CategoryTheory.Oplax.StrongTrans.naturality_comp, PartOrdEmb.hom_inv_apply, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_id, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_hom_assoc, CategoryTheory.GrothendieckTopology.whiskerRight_toPlus_comp_plusCompIso_hom, CategoryTheory.Limits.HasZeroObject.zeroIsoTerminal_hom, CategoryTheory.OplaxFunctor.map₂_leftUnitor_assoc, CategoryTheory.prodOpEquiv_unitIso_hom_app, CategoryTheory.leftUnitor_inv_braiding_assoc, CategoryTheory.NatTrans.op_whiskerRight_assoc, CategoryTheory.Bicategory.conjugateEquiv_id_comp_right_apply, CategoryTheory.Adjunction.leftAdjointUniq_trans_app_assoc, CategoryTheory.Functor.rightUnitor_hom_app, CategoryTheory.PreGaloisCategory.toAut_surjective_isGalois_finite_family, HomologicalComplex.extend.mapX_some, Mathlib.Tactic.Monoidal.evalHorizontalComp_nil_nil, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp_app, CategoryTheory.Functor.leftOpId_hom_app, CategoryTheory.Grp.leftUnitor_hom_hom_hom, AlgebraicGeometry.Scheme.IdealSheafData.comapIso_hom_snd_assoc, CategoryTheory.WithTerminal.opEquiv_unitIso_hom_app, CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoSelf_hom, Rep.standardComplex.εToSingle₀_comp_eq, CategoryTheory.Functor.Final.colimitIso_hom, CategoryTheory.PreGaloisCategory.toAut_hom_app_apply, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_assoc, CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_inv_hom, CategoryTheory.Limits.equalizerPullbackMapIso_hom_fst_assoc, CategoryTheory.Comma.mapLeftId_hom_app_right, LinOrd.inv_hom_apply, CategoryTheory.braiding_rightUnitor_aux₁, CategoryTheory.ShortComplex.RightHomologyMapData.homologyMap_comm, CategoryTheory.Over.postCongr_hom_app_left, CompHausLike.sigmaComparison_eq_comp_isos, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict, CategoryTheory.Functor.CoreMonoidal.μIso_hom_natural_left, CategoryTheory.Localization.Monoidal.triangle_aux₁_assoc, CategoryTheory.Preadditive.smul_iso_hom, CategoryTheory.Oplax.StrongTrans.naturality_id_assoc, CategoryTheory.Functor.Monoidal.map_associator'_assoc, CategoryTheory.MonoidalCategory.DayConvolution.hexagon_forward, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_inv_app_unop, CategoryTheory.Dial.rightUnitor_hom_F, FundamentalGroupoidFunctor.prodIso_hom, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_comp, CategoryTheory.ShortComplex.mapLeftHomologyIso_hom_naturality, PresheafOfModules.isoMk_hom_app, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_app, CategoryTheory.leftDistributor_hom_comp_biproduct_π, CategoryTheory.Equivalence.changeFunctor_unitIso_hom_app, CategoryTheory.WithTerminal.opEquiv_counitIso_hom_app, CategoryTheory.Oplax.LaxTrans.naturality_id, CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_inv_assoc, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_left_unitor, CategoryTheory.LocalizerMorphism.smallShiftedHomMap_mk, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.associator_naturality, CategoryTheory.Mathlib.Tactic.MonTauto.associator_hom_comp_tensorHom_tensorHom_assoc, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_ihom_ev_app_assoc, AlgebraicGeometry.Scheme.isoSpec_hom_naturality_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_hom_app, CategoryTheory.Limits.braid_natural_assoc, TopCat.prodIsoProd_hom_snd_assoc, CommAlgCat.isoMk_hom, CategoryTheory.Oplax.OplaxTrans.naturality_comp, CategoryTheory.MorphismProperty.Comma.isoFromComma_hom, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app_assoc, CategoryTheory.MonoidalCategory.DayConvolution.associator_inv_unit_unit, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_hom, HomologicalComplex.mapBifunctorAssociatorX_hom_D₂, CategoryTheory.Join.pseudofunctorLeft_mapComp_hom_toNatTrans_app, CategoryTheory.StructuredArrow.mapNatIso_functor_obj_hom, CategoryTheory.CostructuredArrow.mapIso_unitIso_inv_app_left, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_inv_hom_assoc, CategoryTheory.MonadIso.mk_hom_toNatTrans, CategoryTheory.MonoidalCategory.DayConvolution.hexagon_reverse, groupCohomology.H1IsoOfIsTrivial_H1π_apply_apply, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_hom_app, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.iso_hom, Rep.indCoindIso_hom_hom_hom, AlgCat.hom_hom_associator, CategoryTheory.MonoidalCategory.tensorIso_hom, groupCohomology.comp_d₂₃_eq, CategoryTheory.Lax.LaxTrans.naturality_comp, CategoryTheory.PreservesImage.factorThruImage_comp_hom_assoc, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_naturality_assoc, CategoryTheory.Limits.coprodComparisonNatIso_hom, CategoryTheory.Functor.mapTriangleIso_hom_app_hom₁, CategoryTheory.Limits.BinaryFan.braiding_hom_snd, AlgebraicGeometry.Scheme.hom_base_inv_base_assoc, inv_comp_eq, CategoryTheory.NatTrans.CommShift.associator, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom, map_hom_inv_id_assoc, CategoryTheory.Functor.IsEventuallyConstantTo.isoMap_hom, CategoryTheory.Functor.CommShift.ofIso_commShiftIso_hom_app, CategoryTheory.Limits.Sigma.whiskerEquiv_hom, CategoryTheory.Limits.limit.isoLimitCone_hom_π_assoc, CategoryTheory.Quotient.LiftCommShift.iso_hom_app, CategoryTheory.Oplax.StrongTrans.id_naturality_inv, CategoryTheory.Limits.pullback_symmetry_hom_of_epi_eq, CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj_hom_naturality_assoc, CategoryTheory.OplaxFunctor.mapComp_assoc_left_app, Action.hom_inv_hom, CategoryTheory.Functor.Monoidal.coreMonoidalTransport_μIso_hom, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_snd, CategoryTheory.Lax.OplaxTrans.vComp_naturality_comp, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_assoc, ModuleCat.cokernel_π_cokernelIsoRangeQuotient_hom, CategoryTheory.Functor.relativelyRepresentable.symmetryIso_hom, ModuleCat.extendScalars_assoc_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst, FinBddDistLat.inv_hom_apply, CategoryTheory.Preadditive.neg_iso_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_assoc, CategoryTheory.MonoidalCategory.id_tensor_rightUnitor_inv, prodIsoPullback_hom_fst_assoc, CategoryTheory.Over.prodLeftIsoPullback_hom_snd, HomologicalComplex.mkHomFromDouble_f₀, CategoryTheory.Limits.parallelPairOpIso_hom_app_one, CategoryTheory.Pseudofunctor.map₂_right_unitor_assoc, CategoryTheory.Functor.mapTriangleInvRotateIso_hom_app_hom₃, CategoryTheory.monoidalOfHasFiniteProducts.associator_hom_snd_fst, CategoryTheory.Bicategory.Prod.sectL_mapComp_hom, CategoryTheory.Limits.biprod.braiding_map_braiding_assoc, LinOrd.Iso.mk_hom, CategoryTheory.Limits.coprod.leftUnitor_hom, SSet.Subcomplex.eqToIso_hom, CategoryTheory.Limits.PullbackCone.op_ι_app, CategoryTheory.ShortComplex.opcyclesOpIso_hom_naturality_assoc, CategoryTheory.Functor.Monoidal.coreMonoidalTransport_εIso_hom, hom_inv_id_triangle_hom₂, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_hom_app, CategoryTheory.coprodComparison_tensorRight_braiding_hom, ModuleCat.hom_inv_apply, CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_eq, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_comp_mapComp'_inv, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_hom_right, TopCat.Presheaf.pushforwardEq_hom_app, CategoryTheory.MonoidalCategory.whiskerRight_id_symm, CategoryTheory.GradedObject.mapBifunctorRightUnitorCofan_inj, CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality_app, CategoryTheory.Equivalence.symmEquivInverse_obj_counitIso_hom, hom_inv_id_triangle_hom₂_assoc, CategoryTheory.Limits.inr_pushoutZeroZeroIso_hom, CategoryTheory.Quiv.homEquivOfIso_apply, CategoryTheory.Join.mapWhiskerRight_whiskerRight, CategoryTheory.FunctorToTypes.inv_hom_id_app_apply, CategoryTheory.ShiftMkCore.add_zero_hom_app, CategoryTheory.ShortComplex.mapHomologyIso_hom_naturality_assoc, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_inv_hom, CategoryTheory.Idempotents.DoldKan.N₂_map_isoΓ₀_hom_app_f, CategoryTheory.Limits.opCoproductIsoProduct_hom_comp_π, CategoryTheory.Sum.swapCompInl_hom_app, CategoryTheory.Functor.FullyFaithful.autMulEquivOfFullyFaithful_apply_hom, CategoryTheory.Bicategory.unitors_equal, CategoryTheory.StructuredArrow.mapNatIso_functor_map_right, CategoryTheory.GradedObject.Monoidal.symmetry_assoc, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc, ModuleCat.exteriorPower.iso₁_hom_naturality, Bimod.TensorBimod.middle_assoc', CategoryTheory.Bicategory.associator_naturality_right, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counitIso_hom_app_tensor_assoc, CategoryTheory.MonoidalCategory.DayConvolution.pentagon, HomologicalComplex.singleObjHomologySelfIso_hom_singleObjHomologySelfIso_inv_assoc, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_hom_app_f, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc_assoc, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_snd, CategoryTheory.ShortComplex.LeftHomologyMapData.homologyMap_comm, CategoryTheory.Limits.diagramIsoCospan_hom_app, CategoryTheory.Limits.Cocones.extendId_hom_hom, ModuleCat.MonoidalCategory.leftUnitor_hom_apply, AddCommGrpCat.coyonedaForget_hom_app_app_hom, CategoryTheory.GradedObject.mapTrifunctorMapIso_hom, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_unitIso_hom_app_f_f, CategoryTheory.Monad.comparisonForget_hom_app, SemimoduleCat.hom_hom_rightUnitor, CategoryTheory.Limits.biprod.braiding_map_braiding, CategoryTheory.tensorRightHomEquiv_symm_coevaluation_comp_whiskerRight, CategoryTheory.MonoidalOpposite.tensorIso_hom_app_unmop, CategoryTheory.Monad.algebraFunctorOfMonadHomComp_hom_app_f, CategoryTheory.Limits.CatCospanTransform.leftIso_hom, ModuleCat.exteriorPower.iso₀_hom_apply, HomologicalComplex.opcyclesMapIso_hom, CategoryTheory.Cat.rightUnitor_hom_app, groupHomology.cyclesMap_comp_cyclesIso₀_hom_apply, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app_assoc, CategoryTheory.Quiv.inv_map_hom_map_of_iso, CategoryTheory.GrothendieckTopology.isoToPlus_hom, CategoryTheory.Limits.Wedge.ext_hom_hom, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.g'_eq, AlgebraicGeometry.pullbackSpecIso_hom_base, CategoryTheory.shiftComm_hom_comp_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocIso_hom_naturality_assoc, CategoryTheory.SmallObject.SuccStruct.extendToSuccObjIso_hom_naturality, CategoryTheory.Oplax.LaxTrans.id_naturality, CategoryTheory.Functor.OplaxMonoidal.δ_comp_whiskerLeft_δ_assoc, ModuleCat.restrictScalarsId'App_hom_apply, groupCohomology.π_comp_H0IsoOfIsTrivial_hom, CategoryTheory.TwistShiftData.shiftFunctorZero_hom_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomLeft_tensor, CategoryTheory.Limits.inl_inl_pushoutLeftPushoutInrIso_hom, CategoryTheory.Functor.Monoidal.transport_ε, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_id, CategoryTheory.Limits.Cones.whiskeringEquivalence_inverse, AlgebraicGeometry.Scheme.Opens.toSpecΓ_appTop_assoc, CategoryTheory.NatTrans.app_homology, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_app_fst_app, CategoryTheory.Pseudofunctor.mapComp_id_right_hom, CategoryTheory.WithTerminal.inclLift_hom_app, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_point_assoc, CategoryTheory.ShortComplex.homologyMap'_op, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp, CategoryTheory.Oplax.StrongTrans.Modification.naturality_assoc, CategoryTheory.CostructuredArrow.eta_hom_left, CategoryTheory.Quotient.liftCommShift_compatibility, groupCohomology.comp_d₀₁_eq, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality_assoc, CategoryTheory.Limits.kernelBiproductToSubtypeIso_hom, CategoryTheory.MonObj.mul_def, CategoryTheory.ShortComplex.HomologyData.ofIso_left_i, CategoryTheory.Adjunction.mapGrp_unit, CategoryTheory.Limits.imageMonoIsoSource_hom_self, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_hom_fac_assoc, CategoryTheory.MonoidalCategory.hom_inv_whiskerRight, Mathlib.Tactic.Monoidal.evalComp_cons, CategoryTheory.Limits.opHomCompWhiskeringLimYonedaIsoCocones_hom_app_app_app, CategoryTheory.MonoidalCategory.triangle_assoc, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_associator_hom_as_app, CategoryTheory.Functor.coreId_inv_app_iso_hom, HomologicalComplex.homologyπ_singleObjHomologySelfIso_hom_assoc, Action.mkIso_hom_hom, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocIso_hom_naturality, CategoryTheory.Functor.isoShift_hom_naturality, CategoryTheory.Adjunction.map_restrictFullyFaithful_unit_app_assoc, AlgebraicGeometry.Scheme.stalkMap_congr_point_assoc, CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoSelf_hom_assoc, CategoryTheory.Functor.CommShift.isoZero'_inv_app, typeToPartialFunIsoPartialFunToPointed_hom_app_toFun, CategoryTheory.Limits.IsLimit.ofIsoLimit_lift, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_hom_τr, symm_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_shift, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₁, ModuleCat.restrictScalarsId'App_hom_naturality_assoc, CategoryTheory.Limits.opParallelPairIso_hom_app_zero, CategoryTheory.Localization.Monoidal.associator_naturality₃, CategoryTheory.Over.associator_hom_left_fst, HomologicalComplex.singleMapHomologicalComplex_inv_app_self, CategoryTheory.MonObj.one_mul_assoc, MulEquiv.toSingleObjEquiv_unitIso_hom, CategoryTheory.Functor.coreprW_hom_app, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.bottomMapᵣ_app, CategoryTheory.Limits.ColimitPresentation.map_ι, CategoryTheory.Limits.inr_zeroCoprodIso_hom, CategoryTheory.BraidedCategory.braiding_tensor_left_inv_assoc, HomologicalComplex.restrictionMap_f'_assoc, groupHomology.toCycles_comp_isoCycles₁_hom_apply, CategoryTheory.Adjunction.leftAdjointUniq_hom_counit, CategoryTheory.Functor.CoreMonoidal.associativity_assoc, CategoryTheory.NatTrans.CommShift.rightUnitor, CategoryTheory.Biprod.unipotentUpper_hom, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_1, CategoryTheory.MonoidalCategory.associator_naturality_middle, CategoryTheory.Limits.lift_comp_kernelIsoOfEq_hom, CategoryTheory.OplaxFunctor.map₂_associator_app_assoc, CategoryTheory.Localization.Monoidal.map_hexagon_forward, CategoryTheory.Comon.mkIso'_hom_hom, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp, CommRingCat.HomTopology.precompHomeomorph_apply, HomologicalComplex₂.XXIsoOfEq_hom_ιTotal_assoc, CategoryTheory.PreZeroHypercover.isoMk_hom_s₀, SheafOfModules.pushforwardNatTrans_id, CategoryTheory.LaxFunctor.map₂_associator_app_assoc, HomologicalComplex.extendSingleIso_hom_f_assoc, CategoryTheory.Bicategory.conjugateEquiv_comp_id_right_apply, CategoryTheory.Functor.commShiftOfLocalization_iso_inv_app, CategoryTheory.Limits.diagramIsoParallelPair_hom_app, AugmentedSimplexCategory.inl_comp_inl_comp_associator_assoc, CommBialgCat.bialgEquivOfIso_apply, CategoryTheory.Functor.CoreMonoidal.right_unitality_assoc, CategoryTheory.Equalizer.Presieve.Arrows.compatible_iff, CategoryTheory.Pi.isoApp_hom, CategoryTheory.ShortComplex.RightHomologyMapData.opcyclesMap_comm, CategoryTheory.Lax.LaxTrans.id_naturality, HomologicalComplex.homologyMapIso_hom, Rep.coinvariantsTensorIndIso_hom, groupCohomology.map_H0Iso_hom_f, AlgebraicTopology.DoldKan.Γ₀NondegComplexIso_hom_f, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_comp_assoc, CategoryTheory.Functor.commShiftOfLocalization.iso_inv_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.whiskerLeft_actionHomLeft_assoc, CategoryTheory.flipCompEvaluation_hom_app, CategoryTheory.Center.braiding_hom_f, CategoryTheory.GrpObj.tensorHom_inv_inv_mul_assoc, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_assoc, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom, CategoryTheory.Limits.FormalCoproduct.coproductIsoSelf_hom_f, CategoryTheory.Localization.lift₃NatIso_hom, CategoryTheory.ShortComplex.op_pOpcycles_opcyclesOpIso_hom_assoc, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality_assoc, CategoryTheory.ShortComplex.RightHomologyData.copy_ι, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_associator, CategoryTheory.Limits.kernelIsIsoComp_hom, CategoryTheory.Localization.Monoidal.μ_natural_left_assoc, CategoryTheory.PreGaloisCategory.comp_autMap, CategoryTheory.ShortComplex.leftHomologyIso_hom_naturality, CategoryTheory.simplicialCosimplicialEquiv_unitIso_hom_app, CategoryTheory.Adjunction.leftAdjointUniq_hom_app_counit, CategoryTheory.Limits.pullbackZeroZeroIso_hom_snd, CategoryTheory.Functor.LeftExtension.postcompose₂ObjMkIso_inv_right_app, CategoryTheory.NatTrans.instCommShiftOppositeShiftHomFunctorNatIsoId, CategoryTheory.Over.prodLeftIsoPullback_hom_fst_assoc, AlgebraicTopology.DoldKan.N₁Γ₀_hom_app_f_f, groupCohomology.π_comp_H1Iso_hom, CategoryTheory.Bicategory.instIsIsoHomLeftZigzagHom, CategoryTheory.Limits.colimitYonedaHomIsoLimit_π_apply, CategoryTheory.NatTrans.rightOpWhiskerRight, CategoryTheory.Functor.Monoidal.transport_δ, CategoryTheory.MonoidalCategory.associator_monoidal, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_hom, CategoryTheory.Functor.inlCompSum'_hom_app, CategoryTheory.cokernelUnopOp_hom, CategoryTheory.ExponentiableMorphism.pushforwardId_hom_counit_assoc, CategoryTheory.GradedObject.ι_mapBifunctorRightUnitor_hom_apply, CategoryTheory.Functor.OplaxLeftLinear.δₗ_unitality_hom_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_app, CategoryTheory.Join.mapPairComp_hom_app_right, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_hom, AlgebraicGeometry.Scheme.stalkClosedPointTo_fromSpecStalk, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst, CategoryTheory.PreservesImage.iso_hom, CategoryTheory.ProjectiveResolution.isoLeftDerivedObj_hom_naturality, CategoryTheory.Bicategory.associator_eqToHom_inv, CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan_inj, CategoryTheory.Localization.Preadditive.homEquiv_apply, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app, CategoryTheory.SmallObject.SuccStruct.extendToSuccRestrictionLEIso_hom_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_associator_assoc, CategoryTheory.Limits.inr_pushoutAssoc_hom_assoc, CategoryTheory.Functor.CoreMonoidal.μIso_hom_natural_left_assoc, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_app_assoc, AlgebraicGeometry.tilde.isoTop_hom, CategoryTheory.WithInitial.liftStar_lift_map, HomologicalComplex.homologyIsoSc'_hom_ι_assoc, AlgebraicGeometry.Scheme.stalkMap_hom_inv_assoc, CategoryTheory.Functor.leftOpRightOpIso_hom_app, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_inv_fac_assoc, CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_snd, CategoryTheory.MonoidalClosed.id_eq, CategoryTheory.MonoidalCategory.MonoidalLeftAction.tensor_actionHomRight, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom, groupHomology.cyclesIso₀_comp_H0π_apply, SSet.stdSimplex.faceSingletonIso_zero_hom_comp_ι_eq_δ_assoc, CategoryTheory.Limits.mulIsInitial_hom, CategoryTheory.shiftFunctorComm_hom_app_comp_shift_shiftFunctorAdd_hom_app_assoc, HomotopicalAlgebra.Precylinder.symm_i_assoc, AddEquiv.toAddGrpIso_hom, CategoryTheory.Mat_.embeddingLiftIso_hom_app, CategoryTheory.CartesianMonoidalCategory.lift_rightUnitor_hom_assoc, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj_assoc, CategoryTheory.ProjectiveResolution.extMk_hom, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom, AlgebraicGeometry.Scheme.Opens.toSpecΓ_appTop, CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_fst_assoc, CochainComplex.HomComplex.Cochain.fromSingleMk_v, AlgebraicGeometry.Scheme.Hom.isoOpensRange_hom_ι_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_whiskerLeft, CategoryTheory.Functor.shiftIso_add_hom_app, GrpWithZero.Iso.mk_hom, CategoryTheory.Functor.mapMonNatIso_hom_app_hom, CategoryTheory.shiftFunctorAdd_inv_app_obj_of_induced, CategoryTheory.Functor.mapTriangleIso_hom_app_hom₂, CategoryTheory.Oplax.OplaxTrans.categoryStruct_comp_naturality, CategoryTheory.Join.mapWhiskerLeft_whiskerRight_assoc, CategoryTheory.Limits.opParallelPairIso_hom_app_one, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_rightHomologyIso_inv_assoc, op2_hom_unop2, CategoryTheory.typeEquiv_unitIso_hom_app, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_hom_assoc, CategoryTheory.Limits.CatCospanTransform.associator_hom_left_app, CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_fst, CategoryTheory.unmop_inv_associator, CategoryTheory.Limits.coproductUniqueIso_hom, hom_inv_id, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_unit_app_left, CategoryTheory.Limits.yonedaCompLimIsoCocones_hom_app_app, CategoryTheory.Over.inv_left_hom_left, CategoryTheory.Over.starPullbackIsoStar_hom_app_left, AlgebraicTopology.DoldKan.Γ₂N₂ToKaroubiIso_hom_app, CategoryTheory.StructuredArrow.mapNatIso_unitIso_hom_app_right, CategoryTheory.Limits.Multicofork.ext_hom_hom, CategoryTheory.Pi.evalCompEqToEquivalenceFunctor_hom, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_naturality, CategoryTheory.Abelian.Ext.mapExactFunctor_hom, HomologicalComplex₂.totalFlipIsoX_hom_D₂_assoc, CategoryTheory.ShortComplex.RightHomologyMapData.rightHomologyMap_eq, CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id, CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_hom_apply, CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp_hom_hom₁, CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_hom_apply, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_app, CategoryTheory.Adjunction.conjugateEquiv_leftAdjointIdIso_hom, TopCat.homeoOfIso_apply, CategoryTheory.simplicialCosimplicialEquiv_counitIso_hom_app_app, HomologicalComplex.isoHomologyι_hom, CategoryTheory.Comon.tensorObj_counit, CategoryTheory.PrelaxFunctor.map₂_hom_inv, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_hom_hom₃, CategoryTheory.MonoidalCategory.id_tensor_associator_naturality, CategoryTheory.Limits.ι_colimitCompWhiskeringLeftIsoCompColimit_hom, CategoryTheory.Functor.mapTriangleCompIso_hom_app_hom₃, Rep.coindResAdjunction_unit_app, HomologicalComplex.XIsoOfEq_hom_comp_d, CategoryTheory.Limits.ι_comp_sigmaObjIso_hom, CategoryTheory.Limits.Pi.whiskerEquiv_inv, AlgebraicGeometry.Scheme.Hom.isoOpensRange_hom_ι, CategoryTheory.Localization.Monoidal.map_hexagon_reverse, CategoryTheory.Limits.biprod.associator_hom, CategoryTheory.GradedObject.mapBifunctorObjSingle₀ObjIso_hom, AugmentedSimplexCategory.inr_comp_associator_assoc, CategoryTheory.Triangulated.Octahedron.map_m₃, HomotopicalAlgebra.PathObject.symm_p_assoc, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_hom_eq_germ, CategoryTheory.Pseudofunctor.StrongTrans.Modification.naturality, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_μ, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_hom_app_app, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp_app, CategoryTheory.SmallObject.SuccStruct.ofCoconeObjIso_hom_naturality, CategoryTheory.WithInitial.coconeEquiv_unitIso_hom_app_hom_right, AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_fst_assoc, HomologicalComplex.opcyclesOpIso_hom_naturality_assoc, CategoryTheory.Localization.lift₂_iso_hom_app_app₂, CategoryTheory.ProjectiveResolution.Hom.hom'_f_assoc, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_hom_app, CategoryTheory.ShortComplex.HomologyData.comm_assoc, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i, CategoryTheory.MorphismProperty.Over.mapCongr_hom_app_left, CategoryTheory.Functor.shiftIso_add'_hom_app, ModuleCat.inv_hom_apply, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app, CategoryTheory.Functor.Monoidal.transport_μ_assoc, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app, ProfiniteGrp.inv_hom_apply, CategoryTheory.BraidedCategory.ofBifunctor.Forward.secondMap₂_app_app_app, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_obj_obj_map, CategoryTheory.associator_hom_apply_1, AlgebraicGeometry.ΓSpecIso_obj_hom, CategoryTheory.ShortComplex.leftHomologyIso_hom_naturality_assoc, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom_assoc, CategoryTheory.Functor.LaxMonoidal.left_unitality, CategoryTheory.Bicategory.pentagon_inv_inv_hom_hom_inv, CategoryTheory.Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor, CategoryTheory.Limits.PreservesLimitPair.iso_hom, CategoryTheory.TwoSquare.GuitartExact.vComp'_iff_of_equivalences, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₁, CategoryTheory.Comon.monoidal_leftUnitor_hom_hom, CategoryTheory.tensorLeftHomEquiv_tensor, CategoryTheory.Preadditive.commGrpEquivalenceAux_hom_app_hom_hom_hom, AlgebraicGeometry.Scheme.homeoOfIso_apply, CategoryTheory.ModObj.one_smul'_assoc, CategoryTheory.Functor.CommShift.ofComp_compatibility, CategoryTheory.Functor.OplaxMonoidal.δ_comp_δ_whiskerRight_assoc, HomologicalComplex.cyclesIsoSc'_hom_iCycles_assoc, AlgebraicGeometry.Spec.germ_stalkMapIso_hom_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_assoc, CategoryTheory.Discrete.functorComp_hom_app, CategoryTheory.BraidedCategory.braiding_naturality, TopCat.sigmaIsoSigma_hom_ι_assoc, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom, CategoryTheory.right_unitality_app_assoc, CategoryTheory.Functor.mapCoconeMapCocone_hom_hom, CategoryTheory.FreeBicategory.mk_left_unitor_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app_assoc, CategoryTheory.Equivalence.rightOp_unitIso_hom_app, CategoryTheory.Over.conePostIso_hom_app_hom, SSet.OneTruncation₂.ofNerve₂.natIso_hom_app_obj, CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_cancel_hom_app, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom, inr_coprodIsoPushout_hom_assoc, CategoryTheory.Limits.reflexivePair.compRightIso_hom_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.rightUnitor_actionHom, CategoryTheory.η_app_obj, TopCat.Sheaf.objSupIsoProdEqLocus_hom_fst, CategoryTheory.Functor.IsStronglyCartesian.of_iso, CategoryTheory.ExactPairing.evaluation_coevaluation', CategoryTheory.MonoidalCategory.DayFunctor.equiv_counitIso_hom_app, CategoryTheory.Limits.colimitLimitToLimitColimitCone_hom, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_awayι, CategoryTheory.NatIso.mapHomologicalComplex_hom_app_f, CategoryTheory.Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor_assoc, CategoryTheory.Localization.isoOfHom_hom, CategoryTheory.ShortComplex.asIsoHomologyπ_hom, CategoryTheory.Functor.essImage.liftFunctorCompIso_hom_app, CategoryTheory.shiftFunctorAdd'_zero_add_inv_app, ModuleCat.restrictScalarsComp'App_hom_naturality_assoc, CategoryTheory.BraidedCategory.hexagon_reverse_inv, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyπ_comp_leftHomologyIso_hom_assoc, CategoryTheory.cokernel.π_unop, CategoryTheory.Functor.curry₃ObjProdComp_hom_app_app_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_whiskerRight_assoc, HomotopicalAlgebra.PathObject.symm_p, CategoryTheory.Functor.rightDerivedNatIso_hom, CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIsoWhisker_hom_right, CategoryTheory.Functor.whiskeringLeftObjIdIso_hom_app_app, CategoryTheory.Limits.prod.leftUnitor_hom_naturality_assoc, CategoryTheory.BraidedCategory.curriedBraidingNatIso_hom_app_app, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.secondMap_app_app_app, CategoryTheory.MonObj.instIsMonHomHomLeftUnitor, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology_inv_homologyι, CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_hom_app, CategoryTheory.Functor.IsCartesian.of_comp_iso, CategoryTheory.Limits.ι_colimitFiberwiseColimitIso_hom_assoc, CategoryTheory.SimplicialObject.isoCoskOfIsCoskeletal_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_hom_app_hom_hom_app, CategoryTheory.Bicategory.Pith.rightUnitor_hom_iso, CategoryTheory.Subobject.mapIsoToOrderIso_apply, CategoryTheory.Functor.Monoidal.map_rightUnitor_assoc, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_id_assoc, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom, HomologicalComplex.restriction.sc'Iso_hom_τ₂, CategoryTheory.Functor.map_shift_unop, CategoryTheory.ShortComplex.LeftHomologyData.copy_i, CategoryTheory.PreGaloisCategory.toAut_surjective_isGalois, CategoryTheory.GradedObject.ι_mapBifunctorComp₂₃MapObjIso_hom, CategoryTheory.Dial.rightUnitorImpl_hom_F, CategoryTheory.Functor.IsCoverDense.presheafIso_hom_app, CategoryTheory.Limits.IsTerminal.uniqueUpToIso_hom, CategoryTheory.Center.leftUnitor_hom_f, CategoryTheory.Limits.Cones.equivalenceOfReindexing_counitIso, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_counitIso, AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_ι_assoc, CategoryTheory.HopfObj.antipode_comul, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_base, HomologicalComplex.singleObjCyclesSelfIso_hom_singleObjOpcyclesSelfIso_hom, CategoryTheory.OplaxFunctor.mapComp_assoc_left, Mathlib.Tactic.Bicategory.evalComp_cons, CategoryTheory.Adjunction.leftAdjointUniq_trans_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_app, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_app, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp_assoc, TopologicalSpace.Opens.mapMapIso_functor, RingEquiv.toRingCatIso_hom, inv_hom_id_app_app, CategoryTheory.Discrete.productEquiv_counitIso_hom_app, groupHomology.π_comp_H2Iso_hom, CategoryTheory.Limits.limit.isoLimitCone_hom_π, CategoryTheory.InjectiveResolution.isoRightDerivedObj_hom_naturality, CategoryTheory.Functor.LeftExtension.postcompose₂_map_right_app, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.mk₀_f_comp_biprodAddEquiv_symm_biprodIsoProd_hom, HomologicalComplex.opcyclesOpIso_hom_toCycles_op, CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatIso_hom, CategoryTheory.Limits.MultispanIndex.SymmStruct.iso_hom_fst, CategoryTheory.Biprod.unipotentLower_hom, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map, CategoryTheory.ComposableArrows.Exact.opcyclesIsoCycles_hom_fac_assoc, CategoryTheory.Lax.LaxTrans.naturality_comp_assoc, HeytAlg.hom_inv_apply, HomologicalComplex.extendCyclesIso_hom_naturality_assoc, CategoryTheory.Join.mapIsoWhiskerRight_hom_app, CategoryTheory.Limits.FormalCoproduct.inj_comp_cofanPtIsoSelf_hom_assoc, CategoryTheory.unop_inv_leftUnitor, CategoryTheory.Equivalence.CommShift.instCommShiftHomFunctorCounitIso, CategoryTheory.Limits.Types.coequalizerIso_π_comp_hom, CategoryTheory.Bicategory.pentagon_assoc, CategoryTheory.ULift.equivalence_counitIso_hom_app, CategoryTheory.Localization.Monoidal.triangle_aux₁, CategoryTheory.Functor.op_commShiftIso_hom_app_assoc, CategoryTheory.braiding_hom_apply, SemimoduleCat.hom_inv_apply, CategoryTheory.pullbackShiftFunctorZero'_hom_app, CategoryTheory.Functor.OplaxMonoidal.oplax_associativity, groupHomology.pOpcycles_comp_opcyclesIso_hom_apply, CategoryTheory.Limits.Types.binaryCoproductIso_inr_comp_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_inv_app, CategoryTheory.MonoidalCategory.rightUnitor_tensor_hom_assoc, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app_assoc, SheafOfModules.pushforwardCongr_hom_app_val_app, CategoryTheory.e_assoc', CategoryTheory.SmallObject.SuccStruct.ofCoconeObjIso_hom_naturality_assoc, TopCat.isoOfHomeo_hom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_leftUnitor, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoOfRangeEq_hom, CategoryTheory.ShortComplex.cyclesIsoKernel_hom, ModuleCat.restrictScalarsCongr_hom_app, CategoryTheory.Monoidal.rightUnitor_hom, CategoryTheory.pullbackShiftFunctorZero_hom_app, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerLeft_assoc, CategoryTheory.Limits.opSpan_hom_app, groupHomology.isoShortComplexH1_hom, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃'_obj_map_app, compInverseIso_inv_app, CategoryTheory.Adjunction.restrictFullyFaithful_homEquiv_apply, CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_hom, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_SpecMap_awayMap_right, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac, CategoryTheory.curryingIso_hom_toFunctor_obj_obj, CategoryTheory.CatCenter.smul_iso_hom_eq'_assoc, CategoryTheory.GrothendieckTopology.overMapPullback_assoc_assoc, CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id_app, CategoryTheory.MonoidalCategory.triangle_assoc_comp_right_inv, AddCommMonCat.neg_hom_apply, HomologicalComplex.mapBifunctorAssociatorX_hom_D₃_assoc, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app_assoc, ContAction.resCongr_hom, CategoryTheory.Comma.equivProd_unitIso_hom_app_right, CategoryTheory.SmallObject.iterationObjRightIso_hom, TopCat.Presheaf.presheafEquivOfIso_unitIso_hom_app_app, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom, CategoryTheory.TwoSquare.GuitartExact.whiskerVertical_iff, TopCat.Presheaf.stalkCongr_hom, CategoryTheory.IsPushout.inr_isoIsPushout_hom_assoc, ModuleCat.MonoidalCategory.rightUnitor_hom_apply, CategoryTheory.NatTrans.op_whiskerRight, CategoryTheory.ComposableArrows.Exact.opcyclesIsoCycles_hom_fac, CategoryTheory.Discrete.sumEquiv_unitIso_hom_app, CategoryTheory.Functor.mapTriangle_map_hom₁, CategoryTheory.MonoidalCategory.tensor_associativity_assoc, CategoryTheory.BraidedCategory.ofBifunctor.Forward.secondMap₁_app_app_app, CategoryTheory.Oplax.LaxTrans.naturality_comp, groupCohomology.isoCocycles₂_hom_comp_i, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_hom_τl, CategoryTheory.Enriched.Functor.associator_hom_apply, CategoryTheory.SmallObject.SuccStruct.prop.arrowIso_hom_right, SheafOfModules.pullbackObjFreeIso_hom_naturality_assoc, CategoryTheory.PreservesImage.hom_comp_map_image_ι, CategoryTheory.NatTrans.CommShiftCore.shift_app, CategoryTheory.Limits.pullbackDiagonalMapIso.hom_snd_assoc, groupCohomology.π_comp_H0Iso_hom_apply, CategoryTheory.CatCommSq.vInv_iso_hom_app, CategoryTheory.Functor.ShiftSequence.induced_shiftIso_hom_app_obj, AlgCat.hom_hom_rightUnitor, Rep.resIndAdjunction_homEquiv_symm_apply, CategoryTheory.NatTrans.shift_comm, CategoryTheory.Functor.ranCompIsoOfPreserves_hom_app, CategoryTheory.lift_comp_preservesLimitIso_hom_assoc, CategoryTheory.Abelian.PreservesImage.iso_hom_ι, CategoryTheory.ShortComplex.mapHomologyIso'_hom_naturality, CategoryTheory.Functor.instCommShiftCochainComplexIntDerivedCategoryHomMapDerivedCategoryFactors, CategoryTheory.Oplax.StrongTrans.isoMk_hom_as_app, CategoryTheory.LocalizerMorphism.homMap_apply, CategoryTheory.Functor.functorialityCompPrecompose_hom_app_hom, CategoryTheory.NatTrans.unop_whiskerRight, groupHomology.comp_d₁₀_eq, CategoryTheory.ShortComplex.LeftHomologyData.copy_π, CategoryTheory.Limits.Cone.equiv_hom_fst, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id_app, CategoryTheory.BraidedCategory.yang_baxter, AlgebraicGeometry.germ_stalkClosedPointIso_hom_assoc, CategoryTheory.MorphismProperty.Over.pullbackComp_inv_app_left, CategoryTheory.Comma.mapRightIso_functor_obj_hom, CategoryTheory.shift_equiv_triangle, CategoryTheory.Limits.imageSubobjectIso_comp_image_map, TwoP.swapEquiv_unitIso_hom_app_hom_toFun, retract_i, CategoryTheory.Functor.flipping_counitIso_hom_app_app_app, CategoryTheory.BraidedCategory.braiding_naturality_left, CategoryTheory.ShortComplex.opcyclesOpIso_hom_toCycles_op_assoc, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_hom_assoc, CategoryTheory.Pseudofunctor.mapComp'_hom_naturality_assoc, CategoryTheory.Pseudofunctor.mapComp'_naturality_2_assoc, CategoryTheory.Pseudofunctor.Grothendieck.categoryStruct_id_fiber, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_inv_app_app, CategoryTheory.Limits.PreservesPullback.iso_hom_fst, CategoryTheory.Limits.Cones.whiskeringEquivalence_unitIso, CategoryTheory.Limits.colimitCoyonedaHomIsoLimitUnop_π_apply, CategoryTheory.shiftFunctorZero_hom_app_obj_of_induced, CategoryTheory.Dial.hexagon_reverse, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_hom_app, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_assoc, smoothSheafCommRing.forgetStalk_hom_comp_evalHom_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_right, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_naturality_app, CategoryTheory.ProjectiveResolution.π'_f_zero_assoc, CategoryTheory.ProjectiveResolution.iso_hom_naturality, HomologicalComplex.truncLE'Map_f_eq_cyclesMap, CategoryTheory.PreGaloisCategory.exists_lift_of_mono_of_isConnected, CategoryTheory.Limits.Types.binaryCoproductIso_inl_comp_hom_apply, CategoryTheory.Join.mkFunctorLeft_hom_app, CategoryTheory.Functor.OplaxLeftLinear.δₗ_associativity, CategoryTheory.Adjunction.comp_counit, CategoryTheory.Limits.limitRightOpIsoOpColimit_hom_comp_ι, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans, CategoryTheory.ShortComplex.opcyclesOpIso_hom_naturality, CategoryTheory.CatCommSq.iso_hom_naturality, CategoryTheory.Bicategory.pentagon_inv_inv_hom_inv_inv, CategoryTheory.Equivalence.changeFunctor_counitIso_hom_app, AddMonCat.neg_hom_apply, CategoryTheory.Localization.Monoidal.map_hexagon_reverse_assoc, groupCohomology.dArrowIso₀₁_hom_left, CategoryTheory.Pseudofunctor.mkOfLax'_mapId_hom, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerLeftIso_hom_app, HomologicalComplex₂.D₁_totalShift₂XIso_hom_assoc, CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc, map_inv_hom_id_app, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app_assoc, CategoryTheory.Functor.OplaxRightLinear.δᵣ_associativity, hom_inv_id_app, CategoryTheory.MonoidalCategory.whiskerLeftIso_hom, RingEquiv.toCommRingCatIso_hom, app_hom, CategoryTheory.Limits.HasLimit.isoOfEquivalence_hom_π, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_app, ringCatIsoToRingEquiv_toRingHom, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π, CategoryTheory.NatIso.naturality_1_assoc, CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_hom, CategoryTheory.Limits.Types.equalizerIso_hom_comp_subtype_apply, CategoryTheory.Adjunction.mapMon_counit, CategoryTheory.Localization.Monoidal.μ_natural_left, CategoryTheory.PreGaloisCategory.evaluation_aut_bijective_of_isGalois, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom'_assoc, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app_assoc, CategoryTheory.ShortComplex.LeftHomologyMapData.homologyMap_eq, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_apply, CategoryTheory.Lax.LaxTrans.naturality_id_assoc, map_hom_inv_id, CategoryTheory.ChosenPullbacksAlong.iso_pullback_obj, CategoryTheory.MonoidalCategory.leftUnitor_monoidal, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp_assoc, CategoryTheory.Functor.ι_colimitIsoColimitGrothendieck_hom_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app_assoc, CategoryTheory.ShortComplex.leftHomologyMapIso'_hom, SSet.Truncated.Edge.map_associator_hom, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom, CategoryTheory.OverClass.instHomIsOverHomAsIso, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_inv_iso_inv, groupHomology.toCycles_comp_isoCycles₁_hom_assoc, MulEquiv.toSingleObjEquiv_counitIso_hom, CategoryTheory.Oplax.OplaxTrans.rightUnitor_hom_as_app, AlgebraicGeometry.Scheme.stalkMap_congr_hom_assoc, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom, CategoryTheory.Limits.pullbackAssoc_hom_snd_snd, CategoryTheory.OplaxFunctor.map₂_associator_assoc, groupHomology.π_comp_H0Iso_hom_apply, CategoryTheory.Limits.prodZeroIso_hom, CategoryTheory.Functor.mapGrpNatIso_hom_app_hom_hom, CategoryTheory.Under.postEquiv_counitIso, CategoryTheory.Pseudofunctor.map₂_whisker_left, CategoryTheory.Adjunction.toEquivalence_unitIso_hom_app, CategoryTheory.Bimon.instIsComonHomMonHomEquivMonComonUnitIsoAppX, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionActionOfMonoidalFunctorToEndofunctorIso_hom_app_app, CategoryTheory.ShortComplex.mapNatIso_hom, CategoryTheory.TransfiniteCompositionOfShape.map_isColimit, CategoryTheory.Join.mapWhiskerLeft_associator_hom, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_ι_assoc, CategoryTheory.Groupoid.isoEquivHom_apply, CategoryTheory.Cat.isoOfEquiv_hom, CategoryTheory.regularTopology.mapToEqualizer_eq_comp, CategoryTheory.Limits.IsLimit.uniqueUpToIso_hom, CategoryTheory.GrothendieckTopology.uliftYonedaCompSheafToPresheaf_hom_app_app, CategoryTheory.Groupoid.isoEquivHom_symm_apply_hom, CategoryTheory.Functor.mapTriangleRotateIso_hom_app_hom₂, CategoryTheory.LaxFunctor.mapComp'_whiskerRight_comp_mapComp'_assoc, CategoryTheory.Under.postComp_hom_app_right, CategoryTheory.MonoidalCategory.inv_hom_id_tensor, CategoryTheory.shiftFunctorAdd'_add_zero_inv_app, CategoryTheory.FunctorToTypes.binaryProductIso_hom_comp_snd, CategoryTheory.Pseudofunctor.StrongTrans.isoMk_hom_as_app, CategoryTheory.Adjunction.Triple.rightToLeft_eq_counits, HomologicalComplex.singleObjHomologySelfIso_inv_homologyι_assoc, AlgebraicGeometry.Scheme.Modules.pseudofunctor_right_unitality, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_assoc, CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id_app_assoc, TopologicalSpace.Opens.mapMapIso_unitIso, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τl, CategoryTheory.kernelUnopOp_hom, CategoryTheory.Limits.Sigma.ι_isoColimit_hom_assoc, ModuleCat.hom_hom_leftUnitor, AddEquiv.toAddCommGrpIso_hom, CategoryTheory.Lax.StrongTrans.toLax_naturality, CategoryTheory.Functor.mapComposableArrowsObjMk₂Iso_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.LocalizerMorphism.commShift_iso_hom_app_assoc, CategoryTheory.NatTrans.op_whiskerLeft_assoc, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_right, CategoryTheory.ProjectiveResolution.Hom.hom'_f, symm_inv, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_right, AlgebraicGeometry.StructureSheaf.globalSectionsIso_hom, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInlIso_hom_app_app, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id, CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence_hom, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_inv_app_left, CategoryTheory.ShortComplex.homologyOpIso_hom_naturality_assoc, CategoryTheory.Pseudofunctor.toOplax_mapId, CommBialgCat.inv_hom_apply, GrpCat.hom_inv_apply, CategoryTheory.ComposableArrows.sc'MapIso_hom, CategoryTheory.Functor.mapCommMonIdIso_hom_app_hom_hom, CategoryTheory.Limits.CokernelCofork.mapIsoOfIsColimit_hom, TopologicalSpace.Opens.overEquivalence_unitIso_hom_app_left, AlgebraicGeometry.Scheme.Spec.residue_residueFieldIso_hom_assoc, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_left, inv_hom_id_app_app_app, CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_fst_assoc, CommRingCat.hom_inv_apply, ModuleCat.hom_hom_rightUnitor, CategoryTheory.Limits.opProductIsoCoproduct'_comp_self, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_inv, SSet.stdSimplex.faceSingletonIso_one_hom_comp_ι_eq_δ, CategoryTheory.Equivalence.invFunIdAssoc_hom_app, CategoryTheory.PrelaxFunctor.map₂_hom_inv_assoc, Mathlib.Tactic.Bicategory.evalWhiskerLeft_of_cons, CategoryTheory.tensorRightHomEquiv_symm_coevaluation_comp_whiskerLeft, HomologicalComplex.Hom.isoOfComponents_hom_f, CategoryTheory.Limits.HasZeroObject.zeroIsoIsTerminal_hom, CategoryTheory.ShortComplex.homologyMap_mapNatTrans, CompactlyGenerated.isoOfHomeo_hom, CategoryTheory.Arrow.inv_hom_id_right, CategoryTheory.Limits.FormalCoproduct.isoOfComponents_hom_φ, CategoryTheory.Limits.Cones.postcomposeEquivalence_unitIso, CategoryTheory.BraidedCategory.hexagon_reverse, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_rightUnitor, groupHomology.π_comp_H0IsoOfIsTrivial_hom_apply, CategoryTheory.Equivalence.unitIso_hom_app_comp_inverse_map_η_functor, CategoryTheory.CostructuredArrow.mapIso_counitIso_hom_app_left, CategoryTheory.MonoidalCategory.associator_naturality_left, CategoryTheory.Functor.fullyFaithfulCancelRight_hom_app, CochainComplex.HomComplex.Cochain.rightUnshift_v, CategoryTheory.Mon.associator_hom_hom, compInverseIso_hom_app, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_hom_app_app, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_hom_assoc, CategoryTheory.Localization.Monoidal.rightUnitor_naturality, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_hom_app_snd_app, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerLeft_naturality, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac, CategoryTheory.HopfObj.antipode_comul₂, CategoryTheory.Limits.Cones.postcomposeEquivalence_counitIso, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_hom_app_fst_app, SimplicialObject.Splitting.ofIso_isColimit', CochainComplex.shiftShortComplexFunctor'_hom_app_τ₂, CategoryTheory.Functor.LaxLeftLinear.μₗ_unitality_assoc, CategoryTheory.Limits.walkingSpanOpEquiv_counitIso_hom_app, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_inv_hom, CategoryTheory.Equalizer.Presieve.compatible_iff, CategoryTheory.Bicategory.Pith.whiskerRight_iso_hom, AlgebraicGeometry.Scheme.Hom.appIso_hom', CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv, CategoryTheory.Over.associator_hom_left_snd_fst, CategoryTheory.Limits.Types.binaryCoproductIso_inr_comp_hom_apply, CategoryTheory.cokernel.π_op, CategoryTheory.Functor.constCompWhiskeringLeftIso_hom_app_app, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv, Sequential.isoOfHomeo_hom, CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_hom, CochainComplex.shiftFunctorAdd'_inv_app_f', CategoryTheory.Limits.FormalCoproduct.inj_comp_cofanPtIsoSelf_hom, CategoryTheory.Bicategory.hom_inv_whiskerRight_whiskerRight, CategoryTheory.Bicategory.Pith.rightUnitor_inv_iso_inv, CategoryTheory.Bicategory.LeftExtension.whiskerIdCancel_right, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_app, CategoryTheory.BraidedCategory.braiding_tensor_left_hom_assoc, CategoryTheory.Limits.Cocones.extendComp_hom_hom, HomologicalComplex.truncGE'_d_eq, CategoryTheory.Dial.braiding_hom_f, CategoryTheory.Limits.prod.triangle, CategoryTheory.Limits.Cofan.ext_hom_hom, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_fst, toEquiv_fun, CategoryTheory.Functor.ShiftSequence.induced.shiftIso_hom_app_obj, HeytAlg.inv_hom_apply, CategoryTheory.Functor.coreCompInclusionIso_hom_app, CategoryTheory.lift_comp_preservesLimitIso_hom, AlgebraicTopology.DoldKan.N₂Γ₂ToKaroubiIso_hom_app, CategoryTheory.Equivalence.changeInverse_counitIso_inv_app, CategoryTheory.Functor.Monoidal.coreMonoidalTransport_μIso_inv, CategoryTheory.SingleFunctors.postcompIsoOfIso_hom_hom_app, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_0, Rep.finsuppTensorRight_hom_hom, CategoryTheory.Functor.commShiftIso_hom_naturality_assoc, QuadraticModuleCat.forget₂_map_associator_hom, CategoryTheory.Bicategory.Pith.associator_hom_iso, ModuleCat.exteriorPower.iso₀_hom_naturality_assoc, inv_hom_id_app_app_assoc, CategoryTheory.ShortComplex.opcyclesIsoRightHomology_inv_hom_id, CategoryTheory.monoidalOfHasFiniteProducts.associator_hom_snd_snd, MulEquiv.toMagmaCatIso_hom, CategoryTheory.shiftFunctorAdd'_zero_add_hom_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app, CategoryTheory.Limits.opCospan_hom_app, CategoryTheory.Functor.mapTriangleCommShiftIso_hom_app_hom₃, AlgebraicGeometry.PresheafedSpace.restrictTopIso_hom, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict, CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_hom_comp_i_assoc, AlgebraicGeometry.PresheafedSpace.sheafIsoOfIso_inv, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_assoc, Bimod.middle_assoc_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π, CategoryTheory.Functor.isLeftDerivedFunctor_of_inverts, CategoryTheory.Functor.unopOpIso_hom_app, CategoryTheory.Functor.ShiftSequence.induced_shiftIso_hom_app_obj_assoc, CategoryTheory.Localization.SmallShiftedHom.equiv_shift', CategoryTheory.ShortComplex.rightHomologyIso_hom_comp_homologyι, CategoryTheory.ShortComplex.mapRightHomologyIso_hom_naturality, groupCohomology.π_comp_H0Iso_hom_assoc, CategoryTheory.Limits.coprod.mapIso_hom, CategoryTheory.Subobject.isoOfEq_hom, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.functorToInterchangeIso_hom_app_app, SSet.stdSimplex.isoNerve_hom_app_apply, CategoryTheory.Cat.opFunctorInvolutive_hom_app_toFunctor_map, CategoryTheory.GradedObject.Monoidal.hexagon_reverse, CategoryTheory.Lax.LaxTrans.naturality_id, CategoryTheory.Mat_.isoBiproductEmbedding_hom, CategoryTheory.LaxBraidedFunctor.isoMk_hom, CategoryTheory.functorProdFunctorEquivUnitIso_hom_app, CategoryTheory.Functor.ι_colimitIsoOfIsLeftKanExtension_hom, CategoryTheory.SmallObject.ιFunctorObj_eq, CategoryTheory.Limits.IsImage.isoExt_hom_m, CategoryTheory.Lax.StrongTrans.naturality_comp_assoc, CategoryTheory.Bicategory.associator_naturality_left_assoc, CategoryTheory.Functor.sumIsoExt_hom_app_inr, ModuleCat.imageIsoRange_hom_subtype_assoc, linearEquivIsoModuleIsoₛ_hom, CategoryTheory.StrictPseudofunctorCore.map₂_right_unitor, CategoryTheory.Cat.opFunctorInvolutive_hom_app_toFunctor_obj, CategoryTheory.ShortComplex.RightHomologyMapData.rightHomologyMap_comm, CategoryTheory.Bicategory.triangle_assoc_comp_right_inv_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_app_assoc, CategoryTheory.Limits.limit.conePointUniqueUpToIso_hom_comp_assoc, CategoryTheory.WithTerminal.lift_map_liftStar, CategoryTheory.Bicategory.hom_inv_whiskerRight, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_symm_app, SSet.stdSimplex.faceSingletonComplIso_hom_ι, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app, CategoryTheory.Bicategory.prod_rightUnitor_hom_fst, CategoryTheory.Mathlib.Tactic.MonTauto.associator_hom_comp_tensorHom_tensorHom, CategoryTheory.Adjunction.leftAdjointCompIso_inv_app, CategoryTheory.Bicategory.Adjunction.left_triangle, CochainComplex.mappingCone.map_inr, CategoryTheory.CatCommSq.vComp_iso_hom_app, CategoryTheory.Under.mapCongr_hom_app, CategoryTheory.LocalizerMorphism.commShift_iso_inv_app_assoc, CategoryTheory.GlueData.t'_comp_eq_pullbackSymmetry_assoc, CategoryTheory.PreZeroHypercover.pullbackIso_hom_h₀, CategoryTheory.LocalizerMorphism.equiv_smallHomMap', HomologicalComplex.mapBifunctorFlipIso_hom_naturality, AlgebraicGeometry.Scheme.Pullback.tensorCongr_SpecTensorTo_assoc, AlgebraicGeometry.Scheme.isoSpec_Spec_hom, CategoryTheory.PreZeroHypercover.inv_hom_h₀_assoc, CategoryTheory.SingleFunctors.inv_hom_id_hom_assoc, CategoryTheory.isMonHom_ofIso, HomologicalComplex₂.D₁_totalShift₁XIso_hom_assoc, CategoryTheory.preservesColimitNatIso_hom_app, CategoryTheory.Limits.Cowedge.ext_hom_hom, CategoryTheory.oppositeShiftFunctorZero_inv_app, CategoryTheory.ExactPairing.evaluation_coevaluation'', Homotopy.extend.homAux_eq, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom_assoc, CategoryTheory.MonoidalCategory.triangle_assoc_comp_right, CategoryTheory.CostructuredArrow.mapIso_functor_map_right, CategoryTheory.Equivalence.mkIso_hom, CategoryTheory.Functor.isoSum_hom_app_inl, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_SpecMap_awayMap_left, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_hom_app, CategoryTheory.Bicategory.Prod.fst_mapId_hom, CategoryTheory.Bicategory.triangle_assoc_comp_right_inv, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂, CategoryTheory.Bicategory.associator_naturality_middle, AlgebraicGeometry.Scheme.Hom.inl_normalizationCoprodIso_hom_fromNormalization_assoc, HomologicalComplex.homologyOp_hom_naturality_assoc, pointedToBipointedCompBipointedToPointedSnd_hom_app_toFun, CategoryTheory.Functor.mapMonIdIso_hom_app_hom, CategoryTheory.Limits.kernelIsoOfEq_hom_comp_ι_assoc, CategoryTheory.Limits.zeroProdIso_hom, CategoryTheory.Limits.Types.equalizerIso_hom_comp_subtype, CategoryTheory.MonoidalCategory.triangle_assoc_comp_right_inv_assoc, CategoryTheory.NatIso.prod_hom, CategoryTheory.SymmetricCategory.braiding_swap_eq_inv_braiding, CategoryTheory.Limits.cokernelBiprodInrIso_hom, CategoryTheory.Center.Hom.comm, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocIso_hom_naturality, CategoryTheory.Functor.map_shiftFunctorComm_assoc, CategoryTheory.IsPushout.inl_isoIsPushout_hom_assoc, CategoryTheory.Pseudofunctor.mkOfOplax'_mapId_hom, Bimod.one_actLeft_assoc, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_right_assoc, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_hom_app_coe, CategoryTheory.Functor.ShiftSequence.induced_isoShiftZero_hom_app_obj_assoc, CategoryTheory.Oplax.LaxTrans.vComp_naturality_comp, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompYoneda, CategoryTheory.MonObj.mul_one, CategoryTheory.Functor.OplaxMonoidal.right_unitality_hom, CategoryTheory.Pseudofunctor.mkOfOplax'_mapComp_hom, CategoryTheory.Adjunction.adjToComonadIso_hom_toNatTrans_app, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp_assoc, CategoryTheory.Monoidal.associator_hom, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp, CommMonCat.inv_hom_apply, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.e_hom_app, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_hom_eq_germ_apply, CategoryTheory.EnrichedCat.associator_hom_out_app, CoalgCat.MonoidalCategoryAux.leftUnitor_hom_toLinearMap, CategoryTheory.Limits.colimitHomIsoLimitYoneda_hom_comp_π_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_app_assoc, SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁_hom_app_f_f, CategoryTheory.Functor.map_shiftFunctorCompIsoId_hom_app_assoc, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_hom_τl, CommBialgCat.hom_inv_apply, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₁, CategoryTheory.Over.iteratedSliceEquivOverMapIso_hom_app_left_left, CategoryTheory.Comma.toIdPUnitEquiv_unitIso_hom_app_right, CategoryTheory.Bicategory.leftUnitorNatIso_hom_app, CategoryTheory.Functor.Braided.braided, CategoryTheory.Limits.CatCospanTransform.rightUnitor_hom_base_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, SSet.Truncated.HomotopyCategory.BinaryProduct.iso_hom_toFunctor, unop_hom_inv_id_app, CompHausLike.LocallyConstant.locallyConstantIsoContinuousMap_hom, HomologicalComplex.homologyπ_restrictionHomologyIso_hom, AddSemigrp.neg_hom_apply, inv_hom_id_assoc, CategoryTheory.Center.isoMk_hom, CategoryTheory.Functor.commShiftIso_hom_naturality, TannakaDuality.FiniteGroup.equivApp_hom, CategoryTheory.Oplax.StrongTrans.naturality_naturality_assoc, CategoryTheory.Functor.CommShift.comp_commShiftIso_hom_app, CategoryTheory.Limits.biprod.associator_natural_assoc, CategoryTheory.BraidedCategory.yang_baxter_assoc, CategoryTheory.MonoidalCategory.leftUnitor_naturality_assoc, HomologicalComplex.XIsoOfEq_hom_comp_XIsoOfEq_inv_assoc, HomologicalComplex.ι_mapBifunctorAssociatorX_hom_assoc, CategoryTheory.Limits.pushoutIsoUnopPullback_inl_hom, CategoryTheory.Bicategory.Prod.sectL_mapId_hom, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_hom_hom, CategoryTheory.MonoidalCategory.associator_monoidal_assoc, CategoryTheory.ComposableArrows.opEquivalence_unitIso_hom_app, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.firstMap₂_app_app_app, CategoryTheory.Quiv.hom_map_inv_map_of_iso, HomologicalComplex.ιOrZero_mapBifunctorAssociatorX_hom, CategoryTheory.eHom_whisker_cancel_assoc, SemiNormedGrp.inv_hom_apply, CategoryTheory.MonoidalCategory.id_whiskerLeft_assoc, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_id_naturality_hom, CategoryTheory.Limits.CatCospanTransform.rightIso_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.unit_actionHomRight_assoc, CategoryTheory.Bicategory.InducedBicategory.bicategory_rightUnitor_hom_hom, toAlgEquiv_apply, CategoryTheory.Functor.mapComposableArrowsObjMk₁Iso_hom_app, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_left_app, AddEquiv.toAddSemigrpIso_hom, CategoryTheory.Bicategory.LeftExtension.IsKan.uniqueUpToIso_hom_right, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.leftUnitor_naturality, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_hom_app_app_hom_hom, CategoryTheory.Limits.CategoricalPullback.Hom.w_assoc, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_hom_eq_germ_apply, AlgebraicTopology.DoldKan.N₂Γ₂_compatible_with_N₁Γ₀, CategoryTheory.CartesianMonoidalCategory.lift_lift_associator_hom, AlgebraicGeometry.Scheme.ΓSpecIso_naturality, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv, CategoryTheory.Center.Hom.comm_assoc, CategoryTheory.Grp.associator_hom_hom_hom, AddSemigrp.hom_neg_apply, CategoryTheory.Limits.piObjIso_hom_comp_π_assoc, AlgebraicGeometry.Scheme.restrictFunctorΓ_hom_app, CategoryTheory.Bicategory.Pith.whiskerLeft_iso_hom, CategoryTheory.ShortComplex.opcyclesIsoCokernel_hom, AlgebraicGeometry.Scheme.stalkMap_congr_hom, CategoryTheory.ShortComplex.LeftHomologyMapData.leftHomologyMap_comm, SemiNormedGrp₁.iso_isometry, CategoryTheory.Limits.CatCospanTransform.triangle_inv, CategoryTheory.Limits.pullbackAssoc_hom_snd_fst, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_hom_app_app, CategoryTheory.MonoidalCategory.id_whiskerLeft_symm_assoc, CategoryTheory.Pseudofunctor.map₂_whisker_left_assoc, CategoryTheory.IsPullback.isoIsPullback_hom_fst_assoc, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τr, HomologicalComplex.opcyclesOpIso_hom_naturality, CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_hom_assoc, CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_left, CategoryTheory.isoCartesianComon_hom_hom, CategoryTheory.Limits.Cones.postcomposeEquivalence_functor, CategoryTheory.Bicategory.leftUnitor_whiskerRight, CategoryTheory.Limits.Cones.extendIso_inv_hom, HasFibers.Fib.mkIsoSelfIsHomLift, CategoryTheory.Localization.liftNatTrans_app, CategoryTheory.ULift.equivalence_unitIso_hom, CategoryTheory.ShortComplex.Splitting.ofIso_s, CategoryTheory.PreZeroHypercover.pullbackIso_hom_s₀, cancel_iso_hom_right_assoc, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.counitIso_hom_app_app_hom, AlgebraicGeometry.Scheme.Opens.isoOfLE_hom_ι, CategoryTheory.Join.pseudofunctorRight_mapId_hom_toNatTrans_app, CategoryTheory.Under.forgetMapInitial_hom_app, Condensed.lanPresheafNatIso_hom_app, Rep.coindResAdjunction_homEquiv_apply, CategoryTheory.Functor.triangle, CategoryTheory.Functor.instIsLeftDerivedFunctorLiftHomFac, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftUnitor_actionHom, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp_assoc, HomologicalComplex.π_homologyIsoSc'_hom_assoc, CategoryTheory.PreGaloisCategory.exists_autMap, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_hom_π, CategoryTheory.Limits.colimCompFlipIsoWhiskerColim_hom_app_app, CategoryTheory.Pi.left_unitor_hom_apply, CategoryTheory.Discrete.sumEquiv_counitIso_hom_app, CategoryTheory.Comma.mapRightIso_functor_map_right, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.Pretriangulated.shiftFunctorZero_op_hom_app, AlgebraicGeometry.Scheme.Modules.pushforwardComp_hom_app_app, CategoryTheory.Oplax.StrongTrans.naturality_id, groupHomology.isoCycles₂_hom_comp_i_apply, CategoryTheory.MonoidalCategory.associator_conjugation_assoc, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_assoc, CategoryTheory.Bicategory.associator_eqToHom_inv_assoc, CategoryTheory.MonoidalCategory.pentagon_hom_inv, AlgebraicGeometry.Scheme.iso_inv_base_hom_base, AlgebraicGeometry.Scheme.Hom.inl_normalizationCoprodIso_hom_fromNormalization, AlgebraicGeometry.germ_stalkClosedPointIso_hom, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_iso_hom_app, CategoryTheory.Bicategory.prod_leftUnitor_hom_snd, groupCohomology.π_comp_H0IsoOfIsTrivial_hom_apply, Units.toAut_hom, QuadraticModuleCat.toIsometry_hom_leftUnitor, CategoryTheory.DifferentialObject.shiftFunctorAdd_hom_app_f, CategoryTheory.ChosenPullbacksAlong.pullbackId_hom_counit, CategoryTheory.ι_colimitCompWhiskeringRightIsoColimitComp_hom, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_hom_app_hom_left, CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_assoc, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_hom_f_f, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_hom_app_app, CategoryTheory.Limits.piPiIso_hom, groupCohomology.toCocycles_comp_isoCocycles₁_hom_assoc, HomologicalComplex.biprodXIso_hom_fst_assoc, QuadraticModuleCat.toIsometry_hom_rightUnitor, CategoryTheory.HalfBraiding.monoidal_assoc, CategoryTheory.Grp.mkIso'_hom_hom_hom, Rep.resIndAdjunction_counit_app, ContAction.resComp_hom, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_assoc, HomologicalComplex.isoHomologyπ_hom, CategoryTheory.Center.whiskerRight_comm, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_hom_hom, CochainComplex.shiftFunctorZero'_hom_app_f, CategoryTheory.Limits.fiberwiseColimitLimitIso_inv_app, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatIso_hom, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_inverse, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_assoc, SimplicialObject.Splitting.ofIso_ι, CategoryTheory.Bicategory.whiskerLeft_inv_hom_whiskerRight_assoc, CategoryTheory.Functor.PushoutObjObj.ι_iso_of_iso_right_hom, CategoryTheory.Cat.freeMapCompIso_hom_app, CategoryTheory.Equivalence.sheafCongr.unitIso_hom_app_val_app, CategoryTheory.Comon.monoidal_associator_hom_hom, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.isoAux_hom_app, CategoryTheory.Limits.inr_pushoutAssoc_hom, CategoryTheory.op_inv_leftUnitor, CategoryTheory.tensorRightHomEquiv_tensor, CategoryTheory.biproduct_ι_comp_leftDistributor_hom, groupHomology.π_comp_H0IsoOfIsTrivial_hom, CategoryTheory.ShortComplex.LeftHomologyMapData.leftHomologyMap_eq, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_rightUnitor_hom_as_app, map_hom_inv_id_app, CategoryTheory.Functor.op_commShiftIso_inv_app_assoc, HomologicalComplex.mapBifunctorAssociatorX_hom_D₂_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.action_actionHomRight_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_id, CategoryTheory.Dial.associatorImpl_hom_F, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_hom_app_snd_app, CategoryTheory.Functor.mapGrpCompIso_hom_app_hom_hom, CategoryTheory.Functor.map_shiftFunctorCompIsoId_hom_app, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom_assoc, CategoryTheory.Limits.cokernelBiproductFromSubtypeIso_hom, SimplicialObject.opFunctor_obj_δ, CategoryTheory.Limits.biprod.braiding'_hom, Action.leftRegularTensorIso_hom_hom, HomologicalComplex.restrictionHomologyIso_hom_homologyι, CategoryTheory.Functor.FullyFaithful.homNatIso'_hom_app_down, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom, CategoryTheory.Bicategory.pentagon, CategoryTheory.Limits.Fan.ext_hom_hom, CategoryTheory.MonoidalCategory.pentagon_inv_hom, CategoryTheory.Comonad.comparisonForget_hom_app, SheafOfModules.conjugateEquiv_pullbackComp_inv, CategoryTheory.NatTrans.CommShiftCore.shift_app_assoc, CategoryTheory.MonoidalCategory.tensor_hom_inv_id_assoc, AlgebraicTopology.DoldKan.whiskerLeft_toKaroubi_N₂Γ₂_hom, CategoryTheory.Limits.sigmaSigmaIso_hom, CategoryTheory.braiding_rightUnitor_assoc, CategoryTheory.WithTerminal.liftFromOverComp_hom_app, CommAlgCat.hom_inv_apply, CategoryTheory.Functor.LaxMonoidal.tensorHom_ε_comp_μ_assoc, AlgCat.hom_hom_leftUnitor, CategoryTheory.shiftFunctorCompIsoId_add'_hom_app, CategoryTheory.Bicategory.rightUnitor_naturality_assoc, CategoryTheory.MonoidalCategory.DayConvolution.triangle, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_comp, CategoryTheory.ProjectiveResolution.leftDerived_app_eq, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_apply, CategoryTheory.coreCategory_inv_iso_hom, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_iso_hom_app, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_assoc, groupHomology.cyclesMap_comp_isoCycles₂_hom_assoc, AlgebraicGeometry.Scheme.toSpecΓ_appTop, CategoryTheory.Limits.colimitFlipIsoCompColim_hom_app, CategoryTheory.monoidalOfHasFiniteCoproducts.associator_hom, HomologicalComplex₂.ιTotal_totalFlipIso_f_hom_assoc, CategoryTheory.Functor.IsCoverDense.Types.sheafIso_hom_val, CategoryTheory.Limits.pullbackLeftPullbackSndIso_hom_snd_assoc, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.leftUnitor_hom_unit_app, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom, FintypeCat.equivEquivIso_symm_apply_apply, CategoryTheory.MonoidalCategory.MonoidalLeftAction.associator_actionHom_assoc, CategoryTheory.MorphismProperty.Over.mapComp_hom_app_left, CategoryTheory.toOverIteratedSliceForwardIsoPullback_hom_app_left, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.unitIso_hom_app_hom_app, CategoryTheory.Functor.CommShift₂.comm, CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_hom, MonObj.mopEquiv_counitIso_hom_app_hom_unmop, CategoryTheory.pullbackShiftFunctorAdd'_hom_app, CategoryTheory.Dial.leftUnitor_hom_F, SemimoduleCat.MonoidalCategory.braiding_hom_apply, CategoryTheory.Under.mapComp_hom, CategoryTheory.Functor.limitIsoOfIsRightKanExtension_hom_π_assoc, CategoryTheory.FreeMonoidalCategory.mk_l_hom, CategoryTheory.BraidedCategory.braiding_naturality_assoc, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_ι_assoc, CategoryTheory.OplaxFunctor.map₂_rightUnitor_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_rightUnitor_assoc, ModuleCat.exteriorPower.iso₁_hom_apply, CategoryTheory.CartesianMonoidalCategory.associator_hom_fst, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_counitIso_inv_app_right_app, CategoryTheory.Functor.Monoidal.μIso_hom, CategoryTheory.Lax.LaxTrans.vComp_naturality_id, CategoryTheory.ShortComplex.opcyclesIsoX₂_inv_hom_id_assoc, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_hom_c_app, CategoryTheory.Monoidal.InducingFunctorData.tensorHom_eq, CategoryTheory.eComp_op_eq_assoc, CategoryTheory.MonObj.Mon_tensor_mul_one, CategoryTheory.Limits.Cones.whiskeringEquivalence_counitIso, CategoryTheory.Lax.OplaxTrans.id_naturality, CategoryTheory.Pretriangulated.shortComplexOfDistTriangleIsoOfIso_hom_τ₃, CategoryTheory.Functor.LaxMonoidal.ε_tensorHom_comp_μ_assoc, HomologicalComplex.extend_op_d, CategoryTheory.Limits.CatCospanTransform.whiskerRight_comp, CategoryTheory.Limits.CatCospanTransform.leftUnitor_hom_left_app, CategoryTheory.Functor.whiskerLeft_twice, CategoryTheory.GrothendieckTopology.uliftYonedaIsoYoneda_hom_app_val_app, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence, CategoryTheory.braiding_leftUnitor_aux₂, CategoryTheory.braiding_tensorUnit_left, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_right, HomologicalComplex.extend.rightHomologyData_p, CategoryTheory.Equivalence.congrLeft_unitIso_inv_app, CategoryTheory.Functor.LeftExtension.postcompose₂ObjMkIso_hom_right_app, CategoryTheory.CechNerveTerminalFrom.wideCospan.limitIsoPi_hom_comp_pi_assoc, CategoryTheory.MonoidalOpposite.unmopEquiv_counitIso_hom_app, CategoryTheory.coprod_inl_leftDistrib_hom_assoc, CategoryTheory.mateEquiv_symm_apply, map_inv_hom_id, CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois_apply, CategoryTheory.FreeMonoidalCategory.mk_α_hom, CategoryTheory.MonObj.Mon_tensor_one_mul, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_assoc, CategoryTheory.ShortComplex.leftRightHomologyComparison_eq, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_assoc, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app, AlgebraicTopology.DoldKan.toKaroubiCompN₂IsoN₁_hom_app, CategoryTheory.Functor.mapTriangleInvRotateIso_inv_app_hom₁, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_hom_app_app_snd, smoothSheafCommRing.forgetStalk_hom_comp_evalHom, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIso_hom_app_hom, CategoryTheory.Oplax.OplaxTrans.naturality_id_assoc, CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map_assoc, CategoryTheory.Limits.IsImage.e_isoExt_hom, CategoryTheory.Join.InclLeftCompRightOpOpEquivFunctor_hom_app, isoFunctorOfIsoInverse_inv_app, CategoryTheory.Functor.leftOpRightOpEquiv_unitIso_hom_app, CategoryTheory.CostructuredArrow.mapNatIso_inverse_obj_hom, CategoryTheory.Dial.hexagon_forward, CategoryTheory.MonoidalCategory.DayConvolution.symmetry, CategoryTheory.Adjunction.leftAdjointUniq_trans_app, CategoryTheory.flippingIso_hom_toFunctor_obj_obj_map, CategoryTheory.rightUnitor_inv_braiding_assoc, groupHomology.map_id_comp_H0Iso_hom_assoc, HomologicalComplex.biprodXIso_hom_snd, CategoryTheory.OplaxFunctor.map₂_leftUnitor, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id_assoc, HomologicalComplex.stupidTruncMap_stupidTruncXIso_hom_assoc, PartOrdEmb.inv_hom_apply, CategoryTheory.Limits.Cones.extendIso_hom_hom, CategoryTheory.SmallObject.SuccStruct.restrictionLTOfCoconeIso_hom_app, HomologicalComplex.XIsoOfEq_inv_comp_XIsoOfEq_hom_assoc, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_hom_app_val_app, CategoryTheory.Functor.mapBiproduct_hom, CategoryTheory.ShortComplex.LeftHomologyData.homologyπ_comp_homologyIso_hom_assoc, CategoryTheory.Localization.Monoidal.associator_naturality₂, CategoryTheory.BraidedCategory.hexagon_forward, CategoryTheory.Join.mapWhiskerRight_associator_hom, CategoryTheory.Functor.CoreMonoidal.associativity, CategoryTheory.Limits.IsImage.isoExt_hom, CategoryTheory.Bicategory.pentagon_hom_hom_inv_inv_hom_assoc, CategoryTheory.toOverPullbackIsoToOver_hom_app_left, TopCat.prodIsoProd_hom_snd, ModuleCat.restrictScalarsComp'App_hom_naturality, CochainComplex.homotopyOp_hom_eq, CategoryTheory.shiftFunctorAdd'_add_zero_hom_app, CategoryTheory.ComonadIso.mk_hom_toNatTrans, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, CategoryTheory.Comma.toIdPUnitEquiv_counitIso_hom_app, CategoryTheory.ShortComplex.RightHomologyData.pOpcycles_comp_opcyclesIso_hom, CategoryTheory.shiftComm', CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_right, HomologicalComplex.natIsoSc'_hom_app_τ₂, CategoryTheory.LocalizerMorphism.homMap_apply_assoc, homCongr_apply, CategoryTheory.toSheafify_plusPlusIsoSheafify_hom, CategoryTheory.Limits.opCospan_inv_app, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc, Bicategory.Opposite.op2_rightUnitor_hom, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_hom, CategoryTheory.Equivalence.congrLeft_unitIso_hom_app, CategoryTheory.Over.associator_hom_left_snd_snd_assoc, CategoryTheory.Comma.mapRightComp_hom_app_left, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_left, CategoryTheory.Limits.limitRightOpIsoOpColimit_hom_comp_ι_assoc, CategoryTheory.ExponentiableMorphism.pushforwardComp_hom_counit_assoc, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_app, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_comp, AlgebraicGeometry.Scheme.Pullback.Triplet.tensorCongr_trans_hom_assoc, BddDistLat.inv_hom_apply, CategoryTheory.sum.inlCompAssociator_hom_app, CategoryTheory.Bicategory.Pith.id₂_iso_hom, CategoryTheory.ShortComplex.opcyclesMapIso_hom, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₂, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_inv_app_val_app, CategoryTheory.Limits.biprod.map_lift_mapBiprod, CategoryTheory.Functor.mapTriangleRotateIso_hom_app_hom₃, CategoryTheory.braiding_tensorUnit_right_assoc, CategoryTheory.NatTrans.CommShiftCore.shift_app_comm_assoc, CategoryTheory.Bicategory.associator_hom_congr, AlgebraicGeometry.Scheme.Hom.inr_normalizationCoprodIso_hom_fromNormalization_assoc, groupHomology.π_comp_H1Iso_hom_apply, CategoryTheory.LocalizerMorphism.smallHomMap'_mk, AlgebraicGeometry.Scheme.Hom.residueFieldMap_congr, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.triangle, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂'_map_app_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_whiskerLeft, CommGrpCat.inv_hom_apply, CategoryTheory.Limits.prod.symmetry_assoc, CategoryTheory.MonoidalCategory.whiskerRight_tensor_symm_assoc, CategoryTheory.Limits.inr_comp_pushoutSymmetry_hom_assoc, TopCat.pullbackIsoProdSubtype_hom_snd, CategoryTheory.Mathlib.Tactic.MonTauto.eq_mul_one, CategoryTheory.Bimon.instIsMonHomHomEquivMonComonUnitIsoAppXAux, CategoryTheory.Adjunction.rightAdjointUniq_trans_app_assoc, CategoryTheory.Bicategory.pentagon_inv_inv_hom_inv_inv_assoc, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_counitIso_hom, CategoryTheory.Functor.ranObjObjIsoLimit_hom_π_assoc, CategoryTheory.Functor.sheafPushforwardContinuousComp_hom_app_val_app, HomologicalComplex.cyclesOpIso_hom_naturality_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom_assoc, CochainComplex.shiftFunctorAdd_inv_app_f, CategoryTheory.Adjunction.compPreadditiveYonedaIso_hom_app_app_apply, CategoryTheory.Limits.ι_colimitLimitIso_limit_π_assoc, groupCohomology.map_id_comp_H0Iso_hom_apply, CategoryTheory.Triangulated.Octahedron.map_m₁, CategoryTheory.Functor.LaxMonoidal.tensorUnit_whiskerLeft_comp_leftUnitor_hom, CategoryTheory.Limits.colimIsoFlipCompWhiskerColim_hom_app_app, CategoryTheory.Bicategory.Comonad.comul_assoc, CategoryTheory.GradedObject.mapBifunctorRightUnitor_naturality, CategoryTheory.Limits.preserves_cokernel_iso_comp_cokernel_map, CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_hom_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom, CategoryTheory.Functor.OplaxRightLinear.δᵣ_unitality_hom, CategoryTheory.whiskeringRightCompEvaluation_hom_app, CategoryTheory.shiftFunctorAdd_assoc_hom_app_assoc, HomologicalComplex₂.ι_totalShift₂Iso_hom_f_assoc, AlgebraicGeometry.Scheme.residueFieldCongr_fromSpecResidueField, ChainComplex.augmentTruncate_hom_f_succ, CategoryTheory.Limits.PreservesPushout.inl_iso_hom_assoc, CategoryTheory.Bicategory.comp_whiskerLeft, CategoryTheory.Limits.Cone.equiv_hom_snd, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₁, CategoryTheory.NatTrans.CommShiftCore.shift_comm, HomologicalComplex.XIsoOfEq_hom_naturality_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd, CategoryTheory.coprod_inr_leftDistrib_hom, BddDistLat.Iso.mk_hom, CategoryTheory.Equivalence.symmEquivInverse_obj_counitIso_inv, CategoryTheory.Limits.idZeroEquivIsoZero_apply_hom, HomologicalComplex.biprodXIso_hom_snd_assoc, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₁, groupHomology.toCycles_comp_isoCycles₂_hom, CategoryTheory.conjugateEquiv_rightUnitor_hom, CategoryTheory.LocalizerMorphism.equiv_smallShiftedHomMap, CategoryTheory.Lax.StrongTrans.naturality_id, groupCohomology.map_id_comp_H0Iso_hom, CategoryTheory.Functor.commShiftOfLocalization.iso_inv_app_assoc, CategoryTheory.Limits.PullbackCone.unop_ι_app, CategoryTheory.Limits.biprod.mapIso_hom, CategoryTheory.Limits.Types.pullbackIsoPullback_hom_snd, CategoryTheory.Limits.isInitialMul_hom, CategoryTheory.Limits.pullbackDiagonalMapIso.hom_snd, CategoryTheory.Bicategory.prod_associator_hom_fst, groupHomology.cyclesMap_comp_isoCycles₂_hom_apply, CategoryTheory.SymmetricCategory.symmetry_assoc, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc_apply, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_hom_right_app, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_leftUnitor_hom_as_app, CategoryTheory.Bimon.equivMonComonCounitIsoAppX_hom_hom, CategoryTheory.SingleFunctors.hom_inv_id_hom, CategoryTheory.Functor.IsCocartesian.of_iso_comp, AlgebraicGeometry.Scheme.Hom.preimageIso_hom_ι, CategoryTheory.cosimplicialSimplicialEquiv_unitIso_hom_app, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_hom_naturality_assoc, CategoryTheory.Join.inclRightCompOpEquivInverse_hom_app_op, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv, CategoryTheory.Limits.Types.productIso_hom_comp_eval_apply, AugmentedSimplexCategory.inl_comp_inl_comp_associator, CategoryTheory.Limits.biproduct.isoCoproduct_hom, hom_inv_id_apply, CategoryTheory.MonoidalCategory.leftUnitor_whiskerRight_assoc, AlgebraicGeometry.Scheme.isoOfEq_hom_ι_assoc, CategoryTheory.Limits.pullbackObjIso_hom_comp_fst, CategoryTheory.ProjectiveResolution.π'_f_zero, CategoryTheory.Linear.homCongr_apply, CategoryTheory.Limits.cospanOp_hom_app, Equiv.toIso_hom, Homotopy.ofExtend_hom, CategoryTheory.shiftFunctorZero_hom_app_shift, HomologicalComplex₂.totalFlipIso_hom_f_D₂, ModuleCat.homEquiv_extendScalarsComp, CategoryTheory.ShortComplex.leftRightHomologyComparison'_eq_leftHomologpMap'_comp_iso_hom_comp_rightHomologyMap', CategoryTheory.Pseudofunctor.mapComp_id_left_inv, CategoryTheory.Limits.biprod.conePointUniqueUpToIso_hom, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_hom_naturality, CategoryTheory.ShortComplex.comp_homologyMap_comp_assoc, CategoryTheory.Limits.CatCospanTransform.pentagon_assoc, CategoryTheory.Limits.Cones.eta_hom_hom, CategoryTheory.biproduct_ι_comp_rightDistributor_hom_assoc, CategoryTheory.ShortComplex.rightHomologyMapIso_hom, CategoryTheory.op_hom_braiding, CategoryTheory.MonoidalCategory.MonoidalRightAction.inv_hom_actionHomLeft_assoc, CategoryTheory.Adjunction.CommShift.compatibilityCounit_left, CategoryTheory.Functor.flipping_unitIso_hom_app_app_app, CategoryTheory.Equivalence.inverseFunctorObj'_hom_app, CategoryTheory.PreZeroHypercover.hom_inv_h₀_assoc, Homotopy.mkCoinductiveAux₂_add_one, CategoryTheory.Limits.pullbackSymmetry_hom_of_mono_eq, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τr, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_comp_homologyIso_inv_assoc, CategoryTheory.Functor.op_commShiftIso_inv_app, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_whisker_left, PartOrd.inv_hom_apply, CategoryTheory.ShortComplex.LeftHomologyMapData.cyclesMap_comm, MulEquiv.toMonCatIso_hom, CategoryTheory.Core.functorToCore_map_iso_hom, CategoryTheory.Functor.LaxRightLinear.μᵣ_associativity_assoc, CategoryTheory.Functor.Monoidal.map_associator', CategoryTheory.obj_η_app_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃'_map_app_app, CategoryTheory.Functor.map_braiding_assoc, CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom_assoc, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_ihom_ev_app, AlgebraicGeometry.PresheafedSpace.map_id_c_app, AddCommMonCat.hom_neg_apply, CategoryTheory.Limits.colimitPointwiseProductToProductColimit_app, CategoryTheory.Idempotents.DoldKan.η_inv_app_f, CategoryTheory.Functor.mapTriangleIdIso_hom_app_hom₃, CategoryTheory.MonoidalCategory.MonoidalLeftAction.hom_inv_actionHomLeft_assoc, CategoryTheory.LaxFunctor.map₂_associator, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, LinearEquiv.toModuleIsoₛ_hom, CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id_app_assoc, CategoryTheory.OplaxFunctor.mapComp_id_right_assoc, isIso_hom, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_SpecMap_awayMap_left_assoc, CategoryTheory.Oplax.StrongTrans.naturality_comp_assoc, CategoryTheory.Functor.OplaxMonoidal.δ_comp_whiskerLeft_δ, CategoryTheory.Functor.LeftExtension.coconeAtWhiskerRightIso_hom_hom, CategoryTheory.OverPresheafAux.counitAux_hom, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_hom_app_left, CategoryTheory.Dial.associator_naturality, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapComp_hom, CategoryTheory.MonObj.instIsMonHomHomRightUnitor, HomologicalComplex.single_map_f_self_assoc, CategoryTheory.NatTrans.CommShiftCore.shift_comm_assoc, unop2_hom, toLinearEquiv_apply, CategoryTheory.OplaxFunctor.mapComp_assoc_right, CategoryTheory.GrpObj.isPullback, Frm.inv_hom_apply, Rep.diagonalSuccIsoTensorTrivial_hom_hom_single, CategoryTheory.Bicategory.mateEquiv_eq_iff, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_app, CategoryTheory.ModObj.one_smul', CategoryTheory.coreCategory_id_iso_hom, CategoryTheory.Limits.prod.associator_hom, CategoryTheory.Functor.sheafPushforwardCocontinuousCompSheafToPresheafIso_hom, CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv, CategoryTheory.Limits.BinaryFan.braiding_hom_fst, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_μIso_hom, CategoryTheory.Idempotents.KaroubiUniversal₁.counitIso_hom_app_app_f, CategoryTheory.Functor.CommShift.id_commShiftIso_hom_app, CategoryTheory.isoSheafify_hom, AlgebraicGeometry.AffineSpace.map_SpecMap, CategoryTheory.OplaxFunctor.mapComp_assoc_left_assoc, HomologicalComplex.extend.homologyData'_right_p, HomologicalComplex.extendCyclesIso_hom_iCycles, CategoryTheory.Adjunction.commShiftIso_hom_app_counit_app_shift_assoc, CategoryTheory.SingleFunctors.hom_inv_id_hom_app_assoc, CategoryTheory.Functor.mapBiprod_hom, CategoryTheory.Grothendieck.isoMk_hom_base, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_app_assoc, SheafOfModules.pushforwardComp_hom_app_val_app, CategoryTheory.Limits.kernelSubobject_arrow, CategoryTheory.Pseudofunctor.mapComp'_hom_naturality, CategoryTheory.GlueData.t'_inv, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app, CategoryTheory.GradedObject.CofanMapObjFun.inj_iso_hom_assoc, map_hom_inv_id_eval_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_assoc, TopCat.Presheaf.Pushforward.id_hom_app, CochainComplex.ConnectData.restrictionLEIso_hom_f, CategoryTheory.Adjunction.rightAdjointUniq_hom_counit_assoc, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_id_assoc, CategoryTheory.MonoidalCategory.selRightfAction_actionAssocIso_hom, CategoryTheory.Bicategory.whiskerRight_comp, CategoryTheory.Limits.PreservesPushout.inr_iso_hom, CategoryTheory.Functor.flipIsoCurrySwapUncurry_hom_app_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso_hom_app_app, groupHomology.chainsMap_f_1_comp_chainsIso₁_assoc, CategoryTheory.SingleFunctors.postcomp_shiftIso_inv_app, CategoryTheory.Limits.Multicofork.isoOfπ_hom_hom, Bicategory.Opposite.op2_leftUnitor_hom, CategoryTheory.yonedaGrpObjIsoOfRepresentableBy_hom, CategoryTheory.GradedObject.Monoidal.braiding_naturality_left, CategoryTheory.IsPullback.isoPullback_hom_fst, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc, CategoryTheory.Functor.OplaxMonoidal.δ_comp_η_tensorHom, CategoryTheory.CartesianMonoidalCategory.whiskerLeft_toUnit_comp_rightUnitor_hom_assoc, groupHomology.isoCycles₁_hom_comp_i_apply, HomologicalComplex.truncGE'_d_eq_fromOpcycles, CategoryTheory.MonObj.one_leftUnitor, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_app_hom, CategoryTheory.toOverIsoToOverUnit_hom_app_left, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃'_associator_hom, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_inv_hom, prodIsoPullback_hom_snd, CategoryTheory.Equivalence.changeInverse_counitIso_hom_app, CategoryTheory.WithTerminal.starIsoTerminal_hom, SemimoduleCat.MonoidalCategory.hexagon_forward, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₃, CategoryTheory.Limits.HasLimit.isoOfNatIso_hom_π_assoc, HomologicalComplex.XIsoOfEq_hom_comp_XIsoOfEq_hom_assoc, CategoryTheory.Limits.Cones.extendId_hom_hom, HomologicalComplex.restrictionHomologyIso_hom_homologyι_assoc, CategoryTheory.Functor.mapTriangleRotateIso_hom_app_hom₁, HomologicalComplex₂.D₁_totalShift₁XIso_hom, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv, CategoryTheory.Localization.Monoidal.associator_naturality₁_assoc, CategoryTheory.BraidedCategory.tensorLeftIsoTensorRight_hom_app, groupCohomology.cocyclesIso₀_hom_comp_f_assoc, CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_assoc, HomologicalComplex₂.D₂_totalShift₁XIso_hom, CategoryTheory.Comma.mapLeftEq_hom_app_right, ModuleCat.FreeMonoidal.μIso_hom_freeMk_tmul_freeMk, CategoryTheory.Endofunctor.Algebra.functorOfNatTransId_hom_app_f, CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_hom_desc_assoc, CategoryTheory.StructuredArrow.mapIso_unitIso_inv_app_right, CategoryTheory.Oplax.OplaxTrans.isoMk_hom_as_app, CategoryTheory.ShortComplex.homologyMapIso'_hom, CategoryTheory.Cat.leftUnitor_hom_toNatTrans, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_hom_assoc, Action.instIsIsoHomHom, AlgebraicGeometry.Scheme.iso_hom_base_inv_base, CategoryTheory.Bicategory.whiskerLeft_inv_hom_whiskerRight, AlgebraicGeometry.Scheme.stalkMap_congr_point, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π_assoc, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app_assoc, CategoryTheory.Functor.mapTriangleIso_hom_app_hom₃, CategoryTheory.MonoidalOpposite.tensorLeftUnmopIso_hom_app, CategoryTheory.ShortComplex.opcyclesMapIso'_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.tensor_actionHomRight_assoc, CategoryTheory.Bicategory.whisker_assoc_assoc, CategoryTheory.Limits.PreservesPullback.iso_hom_snd_assoc, CategoryTheory.Limits.spanCompIso_hom_app_right, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_hom_π_π_assoc, CategoryTheory.Grothendieck.transportIso_inv_base, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality_assoc, CategoryTheory.Functor.const.opObjOp_hom_app, groupHomology.cyclesMap_comp_cyclesIso₀_hom, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_counitIso, HomologicalComplex₂.totalFlipIso_hom_f_D₁_assoc, AlgebraicGeometry.Scheme.stalkMap_hom_inv, CategoryTheory.MonObj.one_braiding, CategoryTheory.CartesianMonoidalCategory.whiskerRight_toUnit_comp_leftUnitor_hom, CategoryTheory.GradedObject.single_map_singleObjApplyIsoOfEq_hom, CategoryTheory.MonoidalCategory.externalProductFlip_hom_app_app_app_app, Frm.hom_inv_apply, map_inv_hom_id_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_hom_app_fst_app, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app_assoc, CategoryTheory.CartesianMonoidalCategory.lift_braiding_hom_assoc, CategoryTheory.Bicategory.associator_eqToHom_hom, CategoryTheory.ObjectProperty.isoHom_inv_id_hom_assoc, CategoryTheory.Bicategory.whisker_assoc_symm, CategoryTheory.Limits.ι_comp_colimitRightOpIsoUnopLimit_hom, CategoryTheory.Limits.terminalIsoIsTerminal_hom, CategoryTheory.Comma.opFunctorCompSnd_hom_app, CategoryTheory.Localization.Monoidal.associator_naturality_assoc, CategoryTheory.Lax.StrongTrans.naturality_naturality_assoc, CategoryTheory.MonObj.Mon_tensor_mul_assoc, CategoryTheory.NatTrans.IsMonoidal.instHomFunctorRightUnitor, CategoryTheory.Localization.SmallShiftedHom.equiv_shift, CategoryTheory.op_hom_associator, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom_apply, CategoryTheory.Functor.OplaxMonoidal.left_unitality_hom, CategoryTheory.Functor.LaxLeftLinear.μₗ_associativity, CategoryTheory.Functor.shiftIso_hom_naturality_assoc, Homotopy.mkCoinductiveAux₂_zero, CategoryTheory.Bicategory.Prod.sectL_mapComp_inv, HomotopicalAlgebra.Cylinder.symm_i, CategoryTheory.ShiftMkCore.add_zero_inv_app, imageSubobjectIso_imageToKernel', CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_comp, RingEquiv.toCommSemiRingCatIso_hom, CategoryTheory.HasShift.Induced.zero_hom_app_obj, CategoryTheory.Limits.imageSubobject_arrow, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_assoc, ProfiniteGrp.hom_inv_apply, CategoryTheory.Limits.Types.productIso_hom_comp_eval, CategoryTheory.Bicategory.id_whiskerLeft_assoc, CategoryTheory.Functor.sheafPushforwardContinuousId_hom_app_val_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.rightUnitor_actionHom_assoc, AlgebraicGeometry.PresheafedSpace.sheafIsoOfIso_hom, CategoryTheory.Equalizer.Presieve.Arrows.compatible_iff_of_small, AlgEquiv.toUnder_hom_right_apply, HomologicalComplex.homologyπ_singleObjHomologySelfIso_hom, hom_inv_id_triangle_hom₁, CategoryTheory.Adjunction.shift_unit_app, CategoryTheory.Limits.inl_inl_pushoutAssoc_hom, ModuleCat.kernelIsoKer_hom_ker_subtype, CategoryTheory.InjectiveResolution.iso_hom_naturality_assoc, CategoryTheory.Quotient.natIsoLift_hom, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app_assoc, CategoryTheory.ChosenPullbacksAlong.pullbackId_hom_counit_assoc, HomologicalComplex.cyclesOpIso_hom_naturality, groupHomology.chainsMap_f_3_comp_chainsIso₃_assoc, CategoryTheory.Adjunction.unit_app_commShiftIso_hom_app_assoc, AlgebraicGeometry.Scheme.stalkMap_hom_inv_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc_apply, CategoryTheory.Abelian.PreservesImage.iso_hom_ι_assoc, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_hom_assoc, CategoryTheory.Functor.OplaxLeftLinear.δₗ_unitality_hom, CategoryTheory.op_hom_rightUnitor, CategoryTheory.Limits.cokernelIsoOfEq_hom_comp_desc, HomotopicalAlgebra.PrepathObject.symm_p_assoc, CategoryTheory.Monad.algebraEquivOfIsoMonads_counitIso, CategoryTheory.Limits.pullbackDiagonalMapIdIso_hom_fst_assoc, CategoryTheory.Sigma.inclCompMap_hom_app, CategoryTheory.Functor.RepresentableBy.uniqueUpToIso_hom, unop2_op_hom, CategoryTheory.Functor.sheafPushforwardContinuousId'_inv_app_val_app, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_hom_fac, CategoryTheory.OplaxFunctor.map₂_rightUnitor, prodIsoPullback_hom_snd_assoc, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso_hom_app_f, CategoryTheory.associator_hom_apply, CategoryTheory.NatIso.hom_app_isIso, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app_assoc, Rep.ofMulActionSubsingletonIsoTrivial_hom_hom, CategoryTheory.InjectiveResolution.isoRightDerivedObj_hom_naturality_assoc, 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.tensorHom_eComp_op_eq_assoc, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_assoc, CategoryTheory.Functor.uliftYonedaReprXIso_hom_app, CategoryTheory.ComposableArrows.scMapIso_hom, CategoryTheory.Limits.Sigma.ι_isoColimit_hom, CategoryTheory.Limits.opProdIsoCoprod_hom_fst, CategoryTheory.NatTrans.naturality_1_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_leftUnitor_assoc, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_hom_fac, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app, CategoryTheory.equivYoneda_hom_app, CategoryTheory.CartesianMonoidalCategory.preservesTerminalIso_hom, CategoryTheory.Center.rightUnitor_hom_f, CategoryTheory.Limits.Pi.whiskerEquiv_hom, CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp_hom_hom₃, ModuleCat.ι_coprodIsoDirectSum_hom, TopCat.Presheaf.presheafEquivOfIso_unitIso_inv_app_app, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_comp_ι_assoc, CategoryTheory.Limits.inr_inr_pushoutRightPushoutInlIso_hom_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁'_obj_map_app, CategoryTheory.Comma.mapLeftId_hom_app_left, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_left_assoc, SemiNormedGrp.explicitCokernelIso_hom_π, homToEquiv_apply, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd, CategoryTheory.Limits.Cone.toStructuredArrowCompProj_hom_app, CategoryTheory.ShortComplex.opcyclesIsoX₂_inv_hom_id, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop_assoc, Preord.Iso.mk_hom, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv, CategoryTheory.Limits.pushoutIsoOpPullback_inr_hom, BoolAlg.hom_inv_apply, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_naturality_assoc, CategoryTheory.Pseudofunctor.map₂_left_unitor_app, HomologicalComplex.mapBifunctorAssociatorX_hom_D₁, CategoryTheory.Functor.LaxMonoidal.tensorUnit_whiskerLeft_comp_leftUnitor_hom_assoc, CategoryTheory.Functor.IsCartesian.domainUniqueUpToIso_hom, CategoryTheory.MonoidalCategory.Functor.curriedTensorPreIsoPost_hom_app_app, CategoryTheory.Adjunction.rightAdjointUniq_hom_counit, core_hom_app_iso_inv, CategoryTheory.ShortComplex.LeftHomologyData.homologyIso_hom_comp_leftHomologyIso_inv_assoc, groupHomology.chainsMap_f_0_comp_chainsIso₀_assoc, hom_inv_id_triangle_hom₃, CategoryTheory.Functor.commShiftOfLocalization.iso_hom_app, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_right, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp, Bimod.one_actLeft, CategoryTheory.Bicategory.Prod.snd_mapId_hom, CategoryTheory.NatTrans.app_shift_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality, CategoryTheory.Bicategory.hom_inv_whiskerRight_assoc, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_app_assoc, CategoryTheory.Bicategory.triangle, CategoryTheory.HopfObj.mul_antipode₁, CategoryTheory.GradedObject.comapEq_hom_app, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_unitIso, CategoryTheory.Functor.mapConePostcomposeEquivalenceFunctor_hom_hom, CategoryTheory.Pseudofunctor.StrongTrans.leftUnitor_hom_as_app, CategoryTheory.MonoidalCategory.associator_naturality, CategoryTheory.sum.inrCompAssociator_hom_app_down_down, CategoryTheory.Limits.limit.conePointUniqueUpToIso_hom_comp, CategoryTheory.Limits.pullbackObjIso_hom_comp_fst_assoc, CategoryTheory.Arrow.inv_hom_id_left_assoc, CategoryTheory.Functor.toSheafify_pullbackSheafificationCompatibility, CategoryTheory.Subobject.isoOfMkEqMk_hom, TopCat.piIsoPi_hom_apply, SimplexCategory.revCompRevIso_hom_app, CategoryTheory.MonoidalCategory.whisker_assoc_symm_assoc, hom_inv_id_app_assoc, CategoryTheory.MonoidalOpposite.tensorRightIso_hom_app_unmop, SimplicialObject.opFunctorCompOpFunctorIso_hom_app_app, CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_snd, Bimod.TensorBimod.left_assoc', CategoryTheory.Limits.limit_map_limitObjIsoLimitCompEvaluation_hom_assoc, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapId_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.whiskerLeft_actionHomLeft, HomologicalComplex.singleObjOpcyclesSelfIso_hom_naturality_assoc, AlgebraicGeometry.ΓSpecIso_hom_stalkClosedPointIso_inv, MonObj.mopEquiv_unitIso_hom_app_hom, CategoryTheory.Pseudofunctor.ObjectProperty.mapId_hom_app, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom_assoc, TopCat.Presheaf.stalkPushforward.id, germ_skyscraperPresheafStalkOfSpecializes_hom_assoc, CategoryTheory.NatTrans.rightOpWhiskerRight_assoc, CategoryTheory.CartesianMonoidalCategory.braiding_hom_fst_assoc, isoInverseOfIsoFunctor_inv_app, CategoryTheory.SmallObject.SuccStruct.ofCocone_map_to_top, CategoryTheory.Limits.CatCospanTransform.id_whiskerLeft_assoc, CategoryTheory.DifferentialObject.shiftFunctor_map_f, CategoryTheory.Functor.commShiftIso_id_hom_app, CategoryTheory.Functor.shiftIso_hom_app_comp_assoc, CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_hom_π_π, CategoryTheory.Functor.Fiber.inducedFunctorCompIsoSelf_hom_app, AlgebraicGeometry.IsOpenImmersion.isoOfRangeEq_hom_fac, CategoryTheory.Equivalence.core_counitIso_hom_app_iso_hom, CategoryTheory.ChosenPullbacksAlong.pullbackComp_hom_counit, CategoryTheory.Limits.CatCospanTransform.pentagon, TopCat.Presheaf.whiskerIsoMapGenerateCocone_hom_hom, CategoryTheory.Discrete.natIso_hom_app, CategoryTheory.Limits.PreservesKernel.iso_hom, CategoryTheory.GrothendieckTopology.Cover.multicospanComp_hom_app, CategoryTheory.Functor.mapCommGrpIdIso_hom_app_hom_hom_hom, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_inv_app_val_app, CategoryTheory.FreeBicategory.normalize_naturality, CategoryTheory.Bicategory.Adj.rIso_hom, TopCat.Presheaf.presheafEquivOfIso_functor_obj_obj, HomologicalComplex.d_comp_XIsoOfEq_hom_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransEq_hom_app_f, CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_inv, CategoryTheory.PreZeroHypercover.hom_inv_s₀_apply, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocIso_hom_naturality_assoc, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_hom, CategoryTheory.obj_μ_inv_app, AlgebraicGeometry.IsClosedImmersion.Spec_iff, AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_snd_assoc, Action.ρAut_apply_hom, HomologicalComplex.pOpcycles_extendOpcyclesIso_hom_assoc, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_apply, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app, groupHomology.cyclesMap_comp_isoCycles₁_hom_apply, CategoryTheory.Functor.IsRepresentedBy.uliftYonedaIso_hom, CategoryTheory.Bicategory.conjugateIsoEquiv_apply_hom, groupHomology.toCycles_comp_isoCycles₂_hom_apply, CategoryTheory.monoidalOfHasFiniteCoproducts.rightUnitor_hom, CategoryTheory.Limits.biproduct.whiskerEquiv_hom, CategoryTheory.Bicategory.conjugateIsoEquiv_symm_apply_hom, CategoryTheory.kernelUnopUnop_hom, CategoryTheory.Pseudofunctor.mapComp'_inv_comp_mapComp'_hom, Rep.coinvariantsTensorIndNatIso_hom_app, CategoryTheory.Functor.CommShift.ofIso_commShiftIso_inv_app, CategoryTheory.Comma.opFunctorCompFst_hom_app, CategoryTheory.Bicategory.Pith.hom₂_ext_iff, MagmaCat.hom_inv_apply, CategoryTheory.Lax.StrongTrans.naturality_id_assoc, CategoryTheory.InjectiveResolution.ι'_f_zero_assoc, CategoryTheory.Limits.pullbackAssoc_hom_snd_snd_assoc, CategoryTheory.Comma.toPUnitIdEquiv_unitIso_hom_app_left, HomologicalComplex₂.totalFlipIsoX_hom_D₁, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₃, CategoryTheory.CatCommSq.vInv_iso_inv_app, CategoryTheory.Functor.leftDerivedNatIso_hom, AlgebraicGeometry.Scheme.Pullback.openCoverOfBase'_f, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_naturality₂, CategoryTheory.MonoidalCategory.tensor_η, Bimod.whisker_assoc_bimod, CategoryTheory.Limits.ι_colimitOfIsReflexivePairIsoCoequalizer_hom, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse_assoc, CommGrpCat.coyonedaForget_hom_app_app_hom, CategoryTheory.oppositeShiftFunctorZero_hom_app, CategoryTheory.Comma.mapRightIso_unitIso_hom_app_left, HomologicalComplex.truncLE'_d_eq, ChainComplex.mk'_d, CategoryTheory.MonoidalCategory.selRightfAction_actionAssocIso_inv, CategoryTheory.Limits.equalizerPullbackMapIso_hom_snd_assoc, CategoryTheory.Limits.fiberwiseColimCompEvaluationIso_hom_app, CategoryTheory.Functor.LaxRightLinear.μᵣ_unitality, CategoryTheory.Limits.Fork.op_ι_app, CategoryTheory.Functor.LaxMonoidal.μ_whiskerRight_comp_μ_assoc, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counitIso_hom_app_assoc, CategoryTheory.Limits.prod.leftUnitor_hom, CategoryTheory.ShortComplex.mapCyclesIso_hom_naturality_assoc, CategoryTheory.ι_preservesColimitIso_hom, CategoryTheory.ShortComplex.rightHomologyMap_op, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id_assoc, CategoryTheory.Limits.pullbackLeftPullbackSndIso_hom_snd, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.iso_hom_naturality_assoc, CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_hom_assoc, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_incl, CategoryTheory.associativity_app_assoc, CategoryTheory.Bicategory.Adj.rightUnitor_inv_τr, CategoryTheory.Oplax.OplaxTrans.naturality_id, CategoryTheory.Limits.equalizerSubobject_arrow, CategoryTheory.CatCenter.smul_iso_hom_eq_assoc, ChainComplex.truncateAugment_hom_f, CategoryTheory.endofunctorMonoidalCategory_leftUnitor_hom_app, CategoryTheory.Limits.pullbackZeroZeroIso_hom_fst, CategoryTheory.Limits.Types.binaryProductIso_hom_comp_fst, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₁, CategoryTheory.Bicategory.rightUnitor_comp, CategoryTheory.Bicategory.whiskerRight_id_symm, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_naturality, cancel_iso_hom_left, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_assoc, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_hom_inv, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_assoc, HomologicalComplex.mkHomFromDouble_f₁, CategoryTheory.OplaxFunctor.mapComp_id_right, ModuleCat.hom_hom_associator, CategoryTheory.braiding_rightUnitor_aux₂, CategoryTheory.SymmetricCategory.symmetry, CategoryTheory.shiftZero', CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_hom, CategoryTheory.Limits.Cocones.eta_hom_hom, CategoryTheory.LocalizerMorphism.guitartExact_of_isRightDerivabilityStructure, CategoryTheory.Bicategory.triangle_assoc_comp_right, CategoryTheory.Localization.lift₂NatIso_hom, CategoryTheory.Monoidal.InducingFunctorData.whiskerRight_eq, CategoryTheory.Limits.Pi.map_eq_prod_map, CategoryTheory.Limits.ι_comp_sigmaObjIso_hom_assoc, CategoryTheory.Bicategory.comp_whiskerLeft_assoc, CategoryTheory.Limits.diagramIsoParallelFamily_hom_app, CategoryTheory.Functor.coreId_hom_app_iso_inv, CategoryTheory.Bicategory.InducedBicategory.forget_mapComp_hom, CategoryTheory.Bimon.mul_counit, CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_hom, CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ, CategoryTheory.MonoidalCategory.tensor_whiskerLeft_assoc, CategoryTheory.MonoidalCategory.rightUnitor_naturality_assoc, CategoryTheory.Pseudofunctor.mapComp_id_right_inv, groupCohomology.π_comp_H2Iso_hom_assoc, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inl, CategoryTheory.Bicategory.whiskerLeft_inv_hom_assoc, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_app_assoc, CategoryTheory.Join.mapWhiskerRight_whiskerLeft, CategoryTheory.Bicategory.associatorNatIsoMiddle_hom_app, CommBialgCat.ofSelfIso_hom, CategoryTheory.Localization.Monoidal.associator_naturality₂_assoc, CategoryTheory.tensorHom_eComp_op_eq, CategoryTheory.preservesLimitIso_hom_π_assoc, CategoryTheory.Limits.Types.binaryProductIso_hom_comp_snd, pointedToBipointedCompBipointedToPointedFst_hom_app_toFun, CategoryTheory.ShortComplex.RightHomologyData.opcyclesIso_hom_comp_descQ, groupCohomology.toCocycles_comp_isoCocycles₂_hom_assoc, prodIsoPullback_hom_fst, HomologicalComplex.single_map_f_self, AlgebraicGeometry.Proj.fromOfGlobalSections_morphismRestrict, CategoryTheory.Functor.leftOpRightOpEquiv_counitIso_hom_app_app, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_assoc, HomologicalComplex.homologyπ_extendHomologyIso_hom_assoc, CategoryTheory.Pseudofunctor.map₂_whisker_right_app_assoc, CategoryTheory.Functor.isLeftKanExtension_iff_postcomp₁, CategoryTheory.shiftFunctorAdd_add_zero_inv_app, CategoryTheory.Adjunction.leftAdjointUniq_hom_counit_assoc, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInrIso_hom_app_app, CategoryTheory.ShortComplex.rightHomologyFunctorOpNatIso_hom_app, CategoryTheory.Pseudofunctor.StrongTrans.Modification.naturality_assoc, CategoryTheory.Bicategory.rightUnitor_naturality, CategoryTheory.MonoidalCategory.inv_hom_whiskerRight, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_hom_left, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_hom_app_hom, Mathlib.Tactic.Monoidal.evalComp_nil_nil, CategoryTheory.GrpObj.mul_inv_rev_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_δ_unmop_app, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_obj_obj_map, CategoryTheory.Functor.currying_unitIso_hom_app_app_app, CategoryTheory.Limits.PreservesCoequalizer.iso_hom, SemiRingCat.hom_inv_apply, CategoryTheory.Limits.PullbackCone.eta_hom_hom, CategoryTheory.Join.pseudofunctorRight_mapComp_hom_toNatTrans_app, unop_hom_inv_id_app_assoc, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapIdIso_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_assoc, CategoryTheory.Adjunction.Triple.leftToRight_eq_counits, CategoryTheory.MonoidalCategory.triangle, AlgebraicGeometry.Scheme.Modules.pushforwardId_hom_app_app, CategoryTheory.InjectiveResolution.isoRightDerivedToHomotopyCategoryObj_hom_naturality_assoc, CategoryTheory.Functor.leftDerived_map_eq, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_ι, CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id_app, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app, CategoryTheory.GradedObject.Monoidal.braiding_naturality_right, AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_fst_assoc, CategoryTheory.WithInitial.inclLiftToInitial_hom_app, CategoryTheory.Lax.StrongTrans.naturality_comp, CategoryTheory.LocalizerMorphism.isRightDerivabilityStructure_iff, CategoryTheory.Bicategory.whiskerLeftIso_hom, CategoryTheory.braiding_rightUnitor, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst, CategoryTheory.Lax.OplaxTrans.naturality_id_assoc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_hom_hom, Mathlib.Tactic.Bicategory.structuralIso_inv, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_rightUnitor_hom_eq_rightUnitor_hom, CategoryTheory.Pseudofunctor.map₂_whisker_right, CategoryTheory.Join.mapWhiskerRight_whiskerLeft_assoc, CategoryTheory.Bicategory.whiskerRight_id_assoc, CategoryTheory.GrothendieckTopology.overMapPullback_comp_id_assoc, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_π, AlgebraicGeometry.Scheme.IdealSheafData.comapIso_hom_snd, CategoryTheory.Limits.CategoricalPullback.Hom.w, CategoryTheory.Grp.rightUnitor_hom_hom, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_apply, CategoryTheory.IsCommComonObj.comul_comm_assoc, SemilatSupCat.Iso.mk_hom_toFun, CategoryTheory.InjectiveResolution.Hom.hom'_f_assoc, Mathlib.Tactic.Monoidal.eval_of, CategoryTheory.Functor.FullyFaithful.hasShift.map_add_hom_app, CategoryTheory.Functor.isoWhiskerRight_hom, CategoryTheory.Bicategory.whisker_assoc_symm_assoc, GrpCat.inv_hom_apply, CategoryTheory.Under.hom_right_inv_right, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left, inv_hom_id_eval_assoc, CategoryTheory.ShortComplex.HomologyMapData.comm, CategoryTheory.Join.mapPairComp_hom_app_left, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom.w_assoc, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_hom_left, Bimod.comp_whiskerLeft_bimod, CategoryTheory.conjugateEquiv_associator_hom, CategoryTheory.Functor.mapTriangle_map_hom₃, CategoryTheory.Localization.Monoidal.pentagon_aux₃, CategoryTheory.Bicategory.conjugateEquiv_apply', Bimod.left_assoc, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₃, CategoryTheory.sum.inrCompInlCompAssociator_hom_app_down_down, CategoryTheory.Limits.spanCompIso_hom_app_left, OrderHom.equivalenceFunctor_counitIso_hom_app_app, CategoryTheory.Limits.FormalCoproduct.evalOpCompInlIsoId_hom_app_app, CategoryTheory.ShortComplex.HomologyMapData.comm_assoc, CategoryTheory.Arrow.iso_w, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_right, CategoryTheory.endofunctorMonoidalCategory_associator_hom_app, CategoryTheory.Functor.IsCoverDense.presheafIso_inv, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom, CategoryTheory.Under.mapId_hom, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_hom_assoc, CategoryTheory.Over.postComp_hom_app_left, CategoryTheory.OplaxFunctor.mapComp_assoc_right_assoc, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_hom_τr, groupHomology.isoShortComplexH2_hom, CompleteLat.Iso.mk_hom, CategoryTheory.MonoidalCategory.triangle_assoc_comp_right_assoc, CategoryTheory.Equivalence.rightOp_counitIso_hom_app, HomologicalComplex.toCycles_cyclesIsoSc'_hom_assoc, CategoryTheory.MonoidalOpposite.mopFunctor_μ, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom'', CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_app_assoc, op2_unop_hom_unop2, trans_hom, ChainComplex.augmentTruncate_hom_f_zero, CategoryTheory.Limits.biproductUniqueIso_hom, CategoryTheory.Limits.coprod.braiding_hom, CategoryTheory.FreeBicategory.mk_associator_hom, CategoryTheory.Limits.CoconeMorphism.hom_inv_id, CategoryTheory.Limits.limIsoFlipCompWhiskerLim_hom_app_app, CategoryTheory.Limits.MultispanIndex.multispanMapIso_hom_app, CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtensionObjIsoColimit_hom, HomologicalComplex.truncGE'Map_f_eq_opcyclesMap, CategoryTheory.Quiv.inv_obj_hom_obj_of_iso, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality_assoc, ModuleCat.kernelIsoKer_hom_ker_subtype_apply, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerRight_assoc, CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIso_hom, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_hom_app_unmop, CategoryTheory.StructuredArrow.mapNatIso_counitIso_hom_app_right, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_id_naturality_inv, ModuleCat.exteriorPower.iso₁_hom_naturality_assoc, CategoryTheory.Limits.biprod.associator_natural, CategoryTheory.Presheaf.isLeftKanExtension_of_preservesColimits, CategoryTheory.typeEquiv_counitIso_hom_app_val_app, CategoryTheory.Under.postEquiv_inverse, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_inv_inv, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitIso_hom_naturality, CategoryTheory.Comma.mapRightId_hom_app_right, CategoryTheory.Limits.prod.braiding_hom, HomologicalComplex.restrictionToTruncGE'.f_eq_iso_hom_pOpcycles_iso_inv, SSet.Truncated.HomotopyCategory.BinaryProduct.associativity'Iso_hom_app, CategoryTheory.Grothendieck.transportIso_inv_fiber, CategoryTheory.GradedObject.single_map_singleObjApplyIso_hom, CategoryTheory.MonoidalCategory.whiskerRightIso_hom, CategoryTheory.left_unitality_app, CategoryTheory.braiding_inv_tensorUnit_left_assoc, CategoryTheory.Functor.FullyFaithful.compYonedaCompWhiskeringLeftMaxRight_hom_app_app_down, CategoryTheory.Limits.PullbackCone.ofCone_π, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app_assoc, CategoryTheory.ExactPairing.evaluation_coevaluation_assoc, groupHomology.chainsMap_f_1_comp_chainsIso₁, ModuleCat.restrictScalarsId'_hom_app, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₃, CategoryTheory.MonoidalCategory.MonoidalRightAction.unit_actionHomRight, CategoryTheory.Functor.LeftExtension.postcompose₂_map_left, comp_inv_eq_id, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_app_assoc, CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc_assoc, CategoryTheory.Limits.biproduct.uniqueUpToIso_hom, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_counit_app_left, CategoryTheory.Join.inclLeftCompOpEquivInverse_hom_app_op, CategoryTheory.Functor.OplaxLeftLinear.δₗ_associativity_assoc, CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_left, AddGrpCat.neg_hom_apply, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_naturality, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_assoc, CategoryTheory.GradedNatTrans.naturality_assoc, CategoryTheory.Adjunction.compCoyonedaIso_hom_app_app, CategoryTheory.ComposableArrows.Exact.cokerIsoKer_hom_fac_assoc, CategoryTheory.Functor.mapConeWhisker_hom_hom, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_hom_fac_assoc, groupHomology.π_comp_H1Iso_hom_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_inv_app_app, CategoryTheory.Limits.Cocone.toCostructuredArrowCompToOverCompForget_hom_app, OrderHom.equivalenceFunctor_unitIso_hom_app, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_leftUnitor_hom_hom, CategoryTheory.IsIso.Iso.inv_inv, hom_inv_id_eval, CategoryTheory.Limits.equalizerPullbackMapIso_hom_snd, groupHomology.chainsMap_f_2_comp_chainsIso₂, CategoryTheory.NatTrans.leftOpWhiskerRight, CategoryTheory.Lax.StrongTrans.naturality_naturality, CategoryTheory.ShortComplex.rightHomologyIso_hom_naturality_assoc, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_left, CategoryTheory.WithInitial.equivComma_unitIso_hom_app_app, CategoryTheory.Localization.lift₃NatTrans_app_app_app, CategoryTheory.ShiftedHom.opEquiv'_zero_add_symm, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_right_right, CategoryTheory.GrpObj.tensorHom_inv_inv_mul, groupHomology.pOpcycles_comp_opcyclesIso_hom, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_hom_assoc, CategoryTheory.Subobject.isoOfMkEq_hom, CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inl_assoc, Bimod.whiskerRight_id_bimod, CategoryTheory.Comma.mapRightId_hom_app_left, SSet.rightUnitor_hom_app_apply, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_assoc, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, CategoryTheory.ProjectiveResolution.leftDerivedToHomotopyCategory_app_eq, CompHausLike.homeoOfIso_apply, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_leftUnitor_hom_eq_leftUnitor_hom, CategoryTheory.Under.postCongr_hom_app_right, CategoryTheory.Over.mapId_hom_app_left, CategoryTheory.Limits.colimit.pre_id, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_hom_app_unop_assoc, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_hom_π_π_assoc, eHomCongr_comp, AddGrpCat.hom_neg_apply, AlgebraicGeometry.Scheme.Hom.toNormalization_inr_normalizationCoprodIso_hom_assoc, SheafOfModules.Presentation.of_isIso_relations, CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_right, CategoryTheory.braiding_leftUnitor_assoc, CategoryTheory.Monoidal.rightUnitor_hom_app, CategoryTheory.sectionsFunctorNatIsoCoyoneda_hom_app_app, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_hom_app_app_down, CategoryTheory.Pseudofunctor.StrongTrans.associator_hom_as_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom.w, AlgebraicGeometry.pullbackSpecIso_hom_fst, CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_hom_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomLeft_tensor_assoc, CategoryTheory.Pseudofunctor.map₂_right_unitor, CategoryTheory.Functor.shift_map_op, CategoryTheory.GradedObject.mapIso_hom, CategoryTheory.Lax.LaxTrans.StrongCore.naturality_hom, SemimoduleCat.hom_hom_associator, CategoryTheory.MonoidalCategory.whiskerRight_id, Homotopy.mkCoinductiveAux₃, CategoryTheory.Bicategory.Pith.associator_inv_iso_inv, CategoryTheory.Limits.biprod.isoProd_hom, CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_fst_snd, CategoryTheory.associator_hom_apply_2_2, Action.FunctorCategoryEquivalence.unitIso_hom_app_hom, CategoryTheory.sheafificationIso_hom_val, CategoryTheory.ShortComplex.rightHomologyMapIso'_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.unit_actionHomRight, CategoryTheory.Localization.Monoidal.leftUnitor_naturality, CategoryTheory.EnrichedFunctor.forgetId_hom_app, CategoryTheory.Limits.ι_comp_colimitOpIsoOpLimit_hom, CategoryTheory.InjectiveResolution.extMk_hom, groupCohomology.isoShortComplexH1_hom, AlgebraicGeometry.Scheme.IdealSheafData.comapIso_hom_fst_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app, BddLat.Iso.mk_hom, CategoryTheory.Pretriangulated.shiftFunctor_op_map, CategoryTheory.DifferentialObject.isoApp_hom, CategoryTheory.InjectiveResolution.cochainComplex_d_assoc, SemimoduleCat.MonoidalCategory.leftUnitor_naturality, CategoryTheory.Bicategory.whiskerLeft_hom_inv_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_whiskerRight, CategoryTheory.Localization.Monoidal.triangle, CategoryTheory.Limits.Sigma.ι_reindex_hom, CategoryTheory.Limits.cospanCompIso_hom_app_left, Action.hom_inv_hom_assoc, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_unitIso, CategoryTheory.Adjunction.rightAdjointUniq_trans_app, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_comp_naturality_inv, CategoryTheory.Bicategory.LeftLift.whiskerOfIdCompIsoSelf_hom_right, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceFunctorProj_hom_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_hom_inv_assoc, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₁, CategoryTheory.Limits.equalizerPullbackMapIso_hom_fst, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_assoc, CategoryTheory.MonObj.mul_associator, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_app_assoc, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_assoc, CategoryTheory.Limits.opProdIsoCoprod_hom_fst_assoc, Mathlib.Tactic.Bicategory.evalWhiskerRight_nil, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app_assoc, CategoryTheory.Functor.isLeftKanExtensionAlongEquivalence, CategoryTheory.op_inv_rightUnitor, ModuleCat.piIsoPi_hom_ker_subtype_apply, CategoryTheory.GrpObj.mul_inv, CategoryTheory.shiftComm_hom_comp, CategoryTheory.Endofunctor.Algebra.functorOfNatTransEq_hom_app_f, CategoryTheory.Join.mapWhiskerLeft_associator_hom_assoc, CategoryTheory.Equivalence.unit_app_tensor_comp_inverse_map_δ_functor_assoc, CategoryTheory.NatTrans.shift_app_assoc, Action.inv_hom_hom, CategoryTheory.Limits.cokernelIsoOfEq_hom_comp_desc_assoc, AlgebraicTopology.DoldKan.Compatibility.υ_hom_app, CategoryTheory.cokernelUnopUnop_hom, CategoryTheory.GradedObject.ι_mapBifunctorLeftUnitor_hom_apply, CategoryTheory.IsCommMonObj.mul_comm, CommRingCat.inv_hom_apply, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_inv_app_eq, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp_app, Action.associator_hom_hom, CategoryTheory.Mon.leftUnitor_hom_hom, CategoryTheory.Functor.constComp_hom_app, CategoryTheory.Localization.Monoidal.associator_naturality, CategoryTheory.IsPushout.inl_isoPushout_hom, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom_assoc, CategoryTheory.SmallObject.SuccStruct.extendToSucc_map, CategoryTheory.Adjunction.rightAdjointUniq_hom_app_counit, CategoryTheory.Limits.imageSubobjectCompIso_hom_arrow_assoc, TopCat.pullbackIsoProdSubtype_hom_apply, CategoryTheory.Limits.limit.homIso_hom, hom_inv_id_app_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_hom_app_app, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom, CategoryTheory.Functor.LaxMonoidal.right_unitality_assoc, CategoryTheory.Equivalence.functor_unitIso_comp, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.pentagon, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_apply, CategoryTheory.Comma.mapFst_hom_app, CategoryTheory.Limits.Cocone.ofPushoutCocone_ι, CategoryTheory.MonObj.one_associator, CategoryTheory.eHom_whisker_cancel_inv_assoc, CategoryTheory.uliftYonedaIsoYoneda_hom_app_app, CategoryTheory.MonoidalClosed.curry'_whiskerRight_comp_assoc, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_hom, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app, CategoryTheory.NatTrans.CommShiftCore.app_shift, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_iso_hom, CategoryTheory.Pseudofunctor.StrongTrans.rightUnitor_hom_as_app, CategoryTheory.Functor.FullyFaithful.compUliftYonedaCompWhiskeringLeft_hom_app_app_down, CategoryTheory.Pseudofunctor.map₂_whisker_left_app_assoc, CategoryTheory.Join.mapWhiskerLeft_rightUnitor_hom, CategoryTheory.Functor.LaxRightLinear.μᵣ_associativity, CategoryTheory.Functor.whiskeringRightObjCompIso_hom_app_app, CategoryTheory.Functor.Monoidal.map_leftUnitor, CategoryTheory.Dial.leftUnitorImpl_hom_F, SSet.Truncated.HomotopyCategory.mkNatIso_hom_app_mk, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app, map_hom_inv_id_eval_app_assoc, HomologicalComplex.extendCyclesIso_hom_naturality, CategoryTheory.PreGaloisCategory.comp_autMap_apply, CategoryTheory.Limits.ι_colimitFiberwiseColimitIso_hom, inhomogeneousCochains.d_eq, AlgebraicGeometry.basicOpen_eq_of_affine', CategoryTheory.Limits.biproduct.whiskerEquiv_inv_eq_lift, CategoryTheory.GradedObject.mapBifunctorRightUnitor_naturality_assoc, CategoryTheory.GradedObject.Monoidal.hexagon_forward, CategoryTheory.ShortComplex.homologyIsoImageICyclesCompPOpcycles_ι, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_inv_assoc, AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom_appTop, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₂, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_hom_hom, CategoryTheory.Lax.StrongTrans.vComp_naturality_inv, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIso_hom_app_hom, Mathlib.Tactic.Bicategory.eval_of, CategoryTheory.LaxFunctor.mapComp_assoc_right_assoc, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_awayι_assoc, RingEquiv.toSemiRingCatIso_hom, inv_hom_id_triangle_hom₁_assoc, CategoryTheory.Limits.ConeMorphism.hom_inv_id_assoc, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_hom, CategoryTheory.Pseudofunctor.mapComp'_naturality_2, ModuleCat.piIsoPi_hom_ker_subtype, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_IsMon_Hom, HomologicalComplex.singleObjHomologySelfIso_hom_naturality, CategoryTheory.Functor.mapActionCongr_hom, CategoryTheory.ShortComplex.leftHomologyFunctorOpNatIso_hom_app, CategoryTheory.FreeMonoidalCategory.normalizeIsoAux_hom_app, CategoryTheory.Oplax.StrongTrans.vcomp_naturality_hom, CategoryTheory.Limits.coequalizer.isoTargetOfSelf_hom, CategoryTheory.Limits.pullbackObjIso_hom_comp_snd_assoc, CategoryTheory.Comma.leftIso_hom, CategoryTheory.Functor.PreservesLeftKanExtension.preserves, CategoryTheory.Limits.colimitIsoFlipCompColim_hom_app, CategoryTheory.toSkeletonFunctor_map_hom, CategoryTheory.Abelian.imageIsoImage_hom_comp_image_ι, CategoryTheory.PreZeroHypercover.hom_inv_h₀, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_obj_iso_hom, CategoryTheory.ModObj.one_smul, LightCondensed.lanPresheafNatIso_hom_app, CategoryTheory.Limits.FormalCoproduct.isoOfComponents_hom_f, CategoryTheory.Lax.StrongTrans.id_naturality_inv, CategoryTheory.Limits.pushoutIsoOpPullback_inl_hom_assoc, ModuleCat.extendScalars_id_comp_assoc, smoothSheafCommRing.ι_forgetStalk_hom_apply, CategoryTheory.LocalizerMorphism.equiv_smallHomMap, CategoryTheory.NatTrans.IsMonoidal.instHomFunctorLeftUnitor, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.guitartExact', TopCat.Sheaf.objSupIsoProdEqLocus_hom_snd, CategoryTheory.Adjunction.CommShift.compatibilityUnit_right, CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_inv_hom_assoc, CategoryTheory.Functor.CommShift.isoAdd'_hom_app, CategoryTheory.flippingIso_hom_toFunctor_obj_map_app, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_app, CategoryTheory.WithTerminal.mapId_hom_app, CategoryTheory.braiding_inv_tensorUnit_right, cancel_iso_hom_right, LinearEquiv.toFGModuleCatIso_hom, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_inv_app_app, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app, CategoryTheory.Join.mapWhiskerRight_rightUnitor_hom, CategoryTheory.Limits.prod.pentagon, CategoryTheory.Functor.CorepresentableBy.uniqueUpToIso_hom, CategoryTheory.Limits.fiberwiseColimCompColimIso_hom_app, CategoryTheory.Functor.mapTriangleCompIso_hom_app_hom₁, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_hom_app_f, CategoryTheory.imageUnopOp_hom_comp_image_ι, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_associator, CategoryTheory.Limits.limitUnopIsoUnopColimit_hom_comp_ι_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app_assoc, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_comp, CategoryTheory.MonoidalOpposite.unmopFunctor_μ, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_app, CategoryTheory.Limits.desc_op_comp_opCoproductIsoProduct_hom, CategoryTheory.Localization.lift₂NatTrans_app_app, ModuleCat.extendScalars_assoc', HomologicalComplex.singleObjHomologySelfIso_hom_naturality_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_id, CategoryTheory.Sum.natIsoOfWhiskerLeftInlInr_hom, CategoryTheory.Equivalence.core_counitIso_hom_app_iso_inv, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_hom_app_val_app, CategoryTheory.Functor.constCompEvaluationObj_hom_app, CategoryTheory.Limits.WalkingMulticospan.functorExt_hom_app, CategoryTheory.Functor.leftKanExtensionIsoFiberwiseColimit_hom_app, CategoryTheory.Limits.biprod.symmetry_assoc, CategoryTheory.MonoidalCategory.tensor_inv_hom_id, smoothSheafCommRing.ι_forgetStalk_hom_assoc, CategoryTheory.Pseudofunctor.map₂_associator, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_assoc, AlgebraicGeometry.Scheme.topIso_hom, CategoryTheory.shiftFunctorAdd_add_zero_hom_app, CategoryTheory.Bicategory.conjugateEquiv_associator_hom, CategoryTheory.StructuredArrow.mapIso_unitIso_hom_app_right, CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ', CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_fst, CategoryTheory.MonoidalCategory.tensor_associativity, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_hom, groupHomology.pOpcycles_comp_opcyclesIso_hom_assoc, CategoryTheory.MonObj.mul_braiding, CategoryTheory.IsPushout.inl_isoPushout_hom_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_assoc, Bimod.triangle_bimod, CategoryTheory.Functor.IsCoverDense.Types.presheafIso_hom_app, AlgebraicGeometry.Scheme.inv_hom_apply, CategoryTheory.Limits.ι_comp_colimitUnopIsoOpLimit_hom_assoc, CategoryTheory.EnrichedFunctor.forgetComp_hom_app, CategoryTheory.Functor.CoreMonoidal.μIso_hom_natural_right, groupCohomology.toCocycles_comp_isoCocycles₁_hom_apply, CategoryTheory.Dial.pentagon, groupHomology.map_id_comp_H0Iso_hom_apply, inr_coprodIsoPushout_hom, CategoryTheory.NatTrans.leftOpWhiskerRight_assoc, ModuleCat.extendScalars_id_comp, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_inv_inv_assoc, CategoryTheory.Functor.leftOpComp_hom_app, CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit_assoc, CategoryTheory.Limits.cospanCompIso_hom_app_one, CategoryTheory.ShortComplex.opcyclesIsoX₂_hom_inv_id_assoc, HomologicalComplex.pOpcycles_opcyclesIsoSc'_hom_assoc, CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero, CategoryTheory.Limits.inr_inl_pushoutAssoc_hom, 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.Limits.CatCospanTransform.associator_hom_base_app, CategoryTheory.Functor.CommShift.isoZero_inv_app, AddMonCat.hom_neg_apply, CochainComplex.HomComplex.Cochain.leftShift_v, CategoryTheory.WithTerminal.inclLiftToTerminal_hom_app, CategoryTheory.Functor.sheafPushforwardContinuousCompSheafToPresheafIso_hom_app_app, CategoryTheory.StrictPseudofunctor.id_mapId_hom, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_counitIso_hom_app_f, CategoryTheory.ExactPairing.coevaluation_evaluation, CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_hom_comp_i, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_app, AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit_map, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app_assoc, groupHomology.cyclesIso₀_comp_H0π_assoc, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.secondMap₃_app_app_app, SemimoduleCat.inv_hom_apply, AlgebraicTopology.DoldKan.Compatibility.τ₁_hom_app, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_inv_fac, CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_hom_assoc, CategoryTheory.Pseudofunctor.DescentData.pullFunctorObjHom_eq_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_assoc, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_hom_f_f, CategoryTheory.Functor.LaxLeftLinear.μₗ_unitality, SheafOfModules.map_ιFree_mapFree_hom, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_right, CategoryTheory.GradedObject.mapBifunctorRightUnitorCofan_inj_assoc, CategoryTheory.Limits.kernelZeroIsoSource_hom, groupCohomology.isoCocycles₁_hom_comp_i, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_hom_app_app_hom, TopCat.Presheaf.presheafEquivOfIso_counitIso_inv_app_app, map_hom_inv_id_app_assoc, HomotopyCategory.homologyFunctor_shiftMap_assoc, HomologicalComplex.double_d, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_hom_app_left, CategoryTheory.rightDistributor_hom_comp_biproduct_π, CategoryTheory.ι_colimitCompWhiskeringRightIsoColimitComp_hom_assoc, HomologicalComplex₂.totalShift₂Iso_hom_naturality, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_app_assoc, CategoryTheory.Linear.homCongr_symm_apply, CategoryTheory.OplaxFunctor.mapComp'_comp_whiskerLeft_mapComp', hom_inv_id_assoc, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.unitIso_hom_app_f_f, CategoryTheory.Functor.isRightKanExtensionId, CategoryTheory.Bicategory.Pith.comp₂_iso_hom, CategoryTheory.Abelian.coimageIsoImage'_hom, CategoryTheory.Bicategory.leftUnitor_naturality_assoc, CategoryTheory.Limits.isoBiprodZero_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.whiskerRight_actionHomLeft, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_functor, CategoryTheory.Lax.StrongTrans.id_naturality_hom, MagmaCat.inv_hom_apply, CategoryTheory.Functor.CoreMonoidal.right_unitality, CategoryTheory.Idempotents.KaroubiKaroubi.unitIso_hom_app_f, CategoryTheory.TwistShiftData.shiftFunctorAdd'_inv_app, CategoryTheory.Limits.pushout.congrHom_hom, CategoryTheory.Bicategory.whisker_assoc, PartOrd.Iso.mk_hom, TopCat.prodIsoProd_hom_apply, CategoryTheory.Limits.equalizerSubobject_arrow_assoc, CategoryTheory.Lax.OplaxTrans.naturality_id, unop_hom, AlgebraicGeometry.Scheme.residue_residueFieldCongr, CochainComplex.HomComplex.Cochain.shift_v, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom, CategoryTheory.MonoidalCategory.tensor_right_unitality, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₃, CochainComplex.shiftFunctorZero_hom_app_f, CategoryTheory.Arrow.hom_inv_id_left, AlgebraicGeometry.Scheme.Hom.appIso_hom, CategoryTheory.Limits.opProdIsoCoprod_hom_snd, CategoryTheory.Sigma.mapId_hom_app, HomologicalComplex.pOpcycles_singleObjOpcyclesSelfIso_inv_assoc, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀, CategoryTheory.Equivalence.core_unitIso_hom_app_iso_hom, FintypeCat.inv_hom_id_apply, CategoryTheory.Functor.rightDerived_map_eq, CategoryTheory.OplaxFunctor.PseudoCore.mapIdIso_hom, CategoryTheory.Subobject.ofLE_mk_le_mk_of_comm, SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_hom_app, CategoryTheory.Idempotents.DoldKan.isoN₁_hom_app_f, CategoryTheory.eHom_whisker_cancel_inv, map_inv_hom_id_eval, AlgebraicTopology.DoldKan.N₁Γ₀_hom_app, AlexDisc.Iso.mk_hom, CategoryTheory.GrpObj.mul_inv_rev, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_εIso_inv, CategoryTheory.coprod_inr_leftDistrib_hom_assoc, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_apply, CategoryTheory.Limits.biprod.braiding_hom, CategoryTheory.GrpObj.mulRight_hom, CategoryTheory.NatIso.naturality_2, CategoryTheory.Functor.opComp_hom_app, CategoryTheory.cokernelOpUnop_hom, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_fst, CategoryTheory.StructuredArrow.mapNatIso_unitIso_inv_app_right, CategoryTheory.ShortComplex.mapCyclesIso_hom_iCycles, CategoryTheory.Functor.ranObjObjIsoLimit_hom_π, AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom, CategoryTheory.Equivalence.rightOp_unitIso_inv_app, CategoryTheory.Functor.mapTriangleCommShiftIso_hom_app_hom₁, CategoryTheory.Bicategory.Prod.sectR_mapComp_hom, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.secondMap₁_app_app_app, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_associator_hom_hom, CategoryTheory.PreservesImage.hom_comp_map_image_ι_assoc, CategoryTheory.Adjunction.leftAdjointCompIso_hom, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_extMk, CategoryTheory.Dial.symmetry, CategoryTheory.CommMon.trivial_mon_mul, CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso_hom_app, CategoryTheory.NatIso.op_hom, CategoryTheory.Functor.isoShift_hom_naturality_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitNatIso_hom_app, AlgebraicGeometry.LocallyRingedSpace.iso_inv_base_hom_base, CategoryTheory.GrothendieckTopology.whiskerRight_toPlus_comp_plusCompIso_hom_assoc, BoolAlg.Iso.mk_hom, CategoryTheory.SingleFunctors.inv_hom_id_hom_app_assoc, Lat.hom_inv_apply, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃, AlgebraicGeometry.Scheme.stalkMap_inv_hom_apply, HomologicalComplex.restrictionMap_f', CategoryTheory.Limits.pullbackSymmetry_hom_comp_snd_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_hom_comp_π, CategoryTheory.Bicategory.associatorNatIsoRight_hom_app, CategoryTheory.Sum.swapCompInr_hom_app, CategoryTheory.ShortComplex.cyclesMapIso'_hom, CategoryTheory.Bicategory.instIsIsoHomRightZigzagHom, CategoryTheory.ComonObj.comul_assoc, TopCat.prodIsoProd_hom_fst, CategoryTheory.Limits.limit.pre_eq, CategoryTheory.ShortComplex.rightHomologyIso_hom_comp_homologyι_assoc, AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_ι, SemiNormedGrp₁.hom_inv_apply, CategoryTheory.Limits.pullbackSymmetry_hom_comp_snd, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_assoc, CategoryTheory.PreGaloisCategory.evaluation_aut_surjective_of_isGalois, HomologicalComplex₂.ιTotal_totalFlipIso_f_hom, CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence_hom, CategoryTheory.ExponentiableMorphism.pushforwardComp_hom_counit, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackId_hom, CategoryTheory.Limits.whiskeringLimYonedaIsoCones_hom_app_app_app, isoCompInverse_hom_app, CategoryTheory.NatTrans.CommShift.of_iso_symm, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app_assoc, CategoryTheory.braiding_leftUnitor, isoInverseOfIsoFunctor_hom_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app_assoc, CategoryTheory.Limits.ColimitPresentation.ofIso_ι, CategoryTheory.Bimon.equivMonComonCounitIsoApp_hom_hom_hom, CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app, CategoryTheory.Limits.prod.symmetry, CategoryTheory.MonoidalCategory.DayConvolution.associator_naturality, CategoryTheory.ComposableArrows.Exact.cokerIsoKer_hom_fac, HomologicalComplex.singleObjCyclesSelfIso_hom_assoc, CategoryTheory.Limits.coprod.rightUnitor_hom, CategoryTheory.Limits.pushout.mapLift_comp, Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply, CategoryTheory.CatCenter.smul_iso_hom_eq', CochainComplex.shiftFunctorAdd'_hom_app_f', CategoryTheory.Limits.Cocones.extendIso_hom_hom, CategoryTheory.BraidedCategory.braiding_naturality_left_assoc, CategoryTheory.IsPullback.isoPullback_hom_snd_assoc, SemilatInfCat.Iso.mk_hom_toFun, CategoryTheory.Monoidal.InducingFunctorData.whiskerLeft_eq, CategoryTheory.Arrow.inv_hom_id_left, map_inv_hom_id_eval_app, CommBialgCat.isoMk_hom, CategoryTheory.Abelian.PreservesCoimage.hom_coimageImageComparison, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_apply, HomologicalComplex.d_comp_XIsoOfEq_hom, PartOrdEmb.Iso.mk_hom, CategoryTheory.Bicategory.mateEquiv_leftUnitor_hom_rightUnitor_inv, CategoryTheory.Adjunction.rightAdjointUniq_trans_assoc, CategoryTheory.Bicategory.LeftExtension.whisker_unit, CategoryTheory.Adjunction.CoreUnitCounit.left_triangle, map_hom_inv_id_eval, CategoryTheory.Limits.ι_reflexiveCoequalizerIsoCoequalizer_hom, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_symm_apply, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_hom_app_hom_hom_hom, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackComp_inv, CategoryTheory.Functor.map_shift_unop_assoc, CategoryTheory.Functor.sheafPushforwardContinuousIso_hom, CategoryTheory.ShiftMkCore.zero_add_hom_app, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₁, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_assoc, CategoryTheory.Over.rightUnitor_hom_left, Bimod.actRight_one_assoc, CochainComplex.augmentTruncate_hom_f_succ, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₁_app, CategoryTheory.Limits.cokernelBiprodInlIso_hom, CategoryTheory.Limits.pullbackProdSndIsoProd_hom_snd_assoc, CategoryTheory.Comma.mapRightComp_hom_app_right, conjAut_hom, homCongr_symm_apply, CochainComplex.shiftEval_hom_app, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app, CategoryTheory.ShortComplex.mapLeftHomologyIso_hom_naturality_assoc, CategoryTheory.Functor.mapConePostcompose_hom_hom, HasFibers.Fib.isoMk_hom, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_hom_iCycles, Rep.finsuppTensorLeft_hom_hom, core_inv_app_iso_inv, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_assoc, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_naturality_assoc, Bimod.middle_assoc, HomologicalComplex.singleCompEvalIsoSelf_hom_app, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_hom_comp_map_π_assoc, CategoryTheory.IsIso.Iso.inv_hom, CategoryTheory.Bicategory.Adj.Bicategory.associator_hom_τr, CategoryTheory.Join.mapIsoWhiskerRight_hom, SSet.nonDegenerateEquivOfIso_apply_coe, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_app_assoc, CategoryTheory.Functor.LaxMonoidal.associativity, CategoryTheory.MonoidalCategory.tensor_left_unitality_assoc, CategoryTheory.MonoidalCategory.whisker_assoc_symm, CategoryTheory.Subobject.underlyingIso_top_hom, CategoryTheory.monoidalOfHasFiniteCoproducts.leftUnitor_hom, CategoryTheory.Functor.isRightKanExtension_iff_precomp, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_assoc, AlgebraicGeometry.Scheme.Pullback.Triplet.Spec_ofPointTensor_SpecTensorTo, CategoryTheory.Bicategory.associatorNatIsoLeft_hom_app, HomologicalComplex.XIsoOfEq_inv_comp_XIsoOfEq_hom, CategoryTheory.Discrete.addMonoidalFunctorComp_isMonoidal, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π_assoc, CategoryTheory.Limits.colimit.isoColimitCocone_ι_hom_assoc, CategoryTheory.ShortComplex.asIsoHomologyι_hom, CategoryTheory.Adjunction.rightAdjointUniq_hom_app_counit_assoc, CategoryTheory.Functor.RightExtension.coneAtWhiskerRightIso_hom_hom, CategoryTheory.Monoidal.InducingFunctorData.leftUnitor_eq, CategoryTheory.Bicategory.LeftLift.whiskerIdCancel_right, SSet.stdSimplex.faceSingletonComplIso_hom_ι_assoc, CategoryTheory.TwistShiftData.shiftFunctorAdd'_hom_app, Action.FunctorCategoryEquivalence.counitIso_hom_app_app, CochainComplex.ConnectData.homologyMap_map_of_eq_succ, CategoryTheory.MonoidalCategory.MonoidalRightAction.hom_inv_actionHomLeft, CategoryTheory.MonoidalOpposite.mop_hom_braiding, CategoryTheory.PrelaxFunctor.map₂_inv_hom_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_hom_app_app, groupHomology.π_comp_H0Iso_hom, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict, BddOrd.hom_inv_apply, CategoryTheory.Oplax.StrongTrans.Modification.naturality, CategoryTheory.Limits.inl_comp_pushoutObjIso_hom_assoc, CategoryTheory.tensorLeftHomEquiv_symm_coevaluation_comp_whiskerRight, CategoryTheory.StructuredArrow.mapIso_inverse_map_right, CategoryTheory.BraidedCategory.hexagon_reverse_inv_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app_assoc, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoColimitUncurryWhiskeringLeft₂_hom_assoc, CategoryTheory.Functor.shiftIso_hom_app_comp_shiftMap, CategoryTheory.ShortComplex.leftHomologyMapIso_hom, CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois_symm_fiber, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_hom, CommRingCat.coyonedaUnique_hom_app_hom_apply, Condensed.isoFinYoneda_hom_app, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_hom_app, groupCohomology.π_comp_H2Iso_hom_apply, CategoryTheory.ShortComplex.homologyMap_op, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_naturality₂, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right, CategoryTheory.LocalizerMorphism.guitartExact_of_isRightDerivabilityStructure', CategoryTheory.Limits.CatCospanTransform.triangle_inv_assoc, CategoryTheory.PreGaloisCategory.autEmbedding_range, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom_assoc, AlgebraicGeometry.Scheme.Modules.pseudofunctor_left_unitality, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_hom_app_app, CategoryTheory.conjugateIsoEquiv_apply_hom, HomologicalComplex.cyclesIsoSc'_hom_iCycles, CategoryTheory.Limits.IsInitial.uniqueUpToIso_hom, CategoryTheory.Limits.pullbackLeftPullbackSndIso_hom_fst_assoc, CategoryTheory.Bicategory.Adj.associator_hom_τr, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom, CategoryTheory.HopfObj.antipode_comul₁, AlgebraicGeometry.Scheme.Modules.pseudofunctor_associativity_assoc, CategoryTheory.Limits.equalizer.isoSourceOfSelf_hom, CategoryTheory.Limits.MonoFactorisation.ofIsoI_e, CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf_hom_right, CategoryTheory.Comon.monoidal_rightUnitor_hom_hom, AlgebraicGeometry.ProjectiveSpectrum.Proj.stalkMap_toSpec, CategoryTheory.Functor.mapMatId_hom_app, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_app, AlgebraicGeometry.pullbackSpecIso_hom_base_assoc, CategoryTheory.Limits.CatCospanTransform.id_whiskerLeft, CategoryTheory.Dial.braiding_hom_F, CategoryTheory.Limits.initialMul_hom, TopCat.hom_inv_id_apply, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_hom_app_f, CategoryTheory.Limits.Sigma.whiskerEquiv_inv, CategoryTheory.GrpObj.ofIso_inv, AlgebraicGeometry.Scheme.IdealSheafData.comapIso_hom_fst, CategoryTheory.Functor.FullyFaithful.hasShift.map_add_inv_app, CategoryTheory.Sieve.pullback_ofArrows_of_iso, CategoryTheory.Bicategory.prod_leftUnitor_hom_fst, CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj_hom_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_left, CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_fst_snd_assoc, CategoryTheory.Limits.KernelFork.mapIsoOfIsLimit_hom, CategoryTheory.Limits.pullbackLeftPullbackSndIso_hom_fst, CategoryTheory.Adjunction.whiskerLeftRUnitIsoOfIsIsoCounit_hom_app, CategoryTheory.ShortComplex.LeftHomologyData.homologyIso_hom_comp_leftHomologyIso_inv, CategoryTheory.Functor.OplaxMonoidal.δ_comp_tensorHom_η_assoc, groupHomology.H0π_comp_H0Iso_hom, CategoryTheory.ExponentiableMorphism.unit_pushforwardId_hom, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_δ_app, CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app_assoc, groupHomology.isoCycles₁_hom_comp_i_assoc, CommMonCat.coyonedaForget_hom_app_app_hom, CategoryTheory.MonoidalCategory.DayConvolution.associator_inv_unit_unit_assoc, AlgebraicGeometry.Scheme.iso_inv_base_hom_base_apply, CategoryTheory.Localization.Monoidal.triangle_aux₂, CategoryTheory.Limits.coprod.triangle, TopologicalSpace.Opens.mapIso_hom_app, CategoryTheory.Functor.isoSum_hom_app_inr, CategoryTheory.Limits.inl_inl_pushoutAssoc_hom_assoc, CategoryTheory.GlueData.ι_gluedIso_hom, CategoryTheory.Limits.CoconeMorphism.inv_hom_id, SSet.associator_hom_app_apply, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τl, MulEquiv.toCommGrpIso_hom, CategoryTheory.Limits.BinaryFan.leftUnitor_hom, ModuleCat.extendScalarsComp_hom_app_one_tmul, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv_apply, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π, CategoryTheory.WithInitial.liftFromUnderComp_hom_app, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_inv_assoc, CategoryTheory.Oplax.OplaxTrans.naturality_comp_assoc, groupHomology.map_id_comp_H0Iso_hom, CategoryTheory.Bicategory.Adjunction.comp_left_triangle_aux, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom_assoc, CategoryTheory.Functor.CommShift.OfComp.map_iso_hom_app_assoc, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_hom_assoc, CategoryTheory.Bicategory.whiskerLeft_hom_inv_whiskerRight, CategoryTheory.CartesianMonoidalCategory.lift_leftUnitor_hom, CochainComplex.ι_mapBifunctorShift₁Iso_hom_f_assoc, groupCohomology.isoShortComplexH2_hom, TopCat.Presheaf.Pushforward.comp_hom_app, CategoryTheory.Functor.LaxMonoidal.whiskerRight_tensorUnit_comp_rightUnitor_hom, SSet.Truncated.HomotopyCategory.BinaryProduct.associativity, CategoryTheory.Functor.mapCoconeOp_hom_hom, CategoryTheory.preservesLimitIso_hom_π, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inr, CategoryTheory.Limits.inl_pushoutRightPushoutInlIso_hom, CategoryTheory.Bicategory.LeftLift.IsKan.uniqueUpToIso_hom_right, CochainComplex.mappingCone.mapHomologicalComplexXIso'_hom, AlgebraicGeometry.Scheme.stalkMap_inv_hom, CategoryTheory.NatTrans.op_whiskerLeft, CategoryTheory.Localization.Monoidal.β_hom_app, CategoryTheory.GrpObj.mul_inv_assoc, CategoryTheory.Limits.HasZeroObject.zeroIsoIsInitial_hom, CategoryTheory.WithInitial.coconeEquiv_counitIso_hom_app_hom, CategoryTheory.ShortComplex.rightHomologyFunctorOpNatIso_inv_app, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_hom_whiskerLeft_π_assoc, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_hom_app_hom_coe, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc, groupCohomology.π_comp_H1Iso_hom_apply, Condensed.lanPresheafExt_hom, HomologicalComplex.pOpcycles_extendOpcyclesIso_hom, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id_app, CategoryTheory.Limits.colimitCoyonedaHomIsoLimit_π_apply, CategoryTheory.Limits.CatCospanTransform.baseIso_hom, CategoryTheory.Adjunction.unit_app_commShiftIso_hom_app, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counitIso_hom_app_tensor, CategoryTheory.Under.inv_right_hom_right, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom, CategoryTheory.Limits.Cones.equivalenceOfReindexing_unitIso, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₃, CategoryTheory.IsCommMonObj.mul_comm_assoc, CategoryTheory.Limits.inl_pushoutRightPushoutInlIso_hom_assoc, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isColimit, HomologicalComplex.mapBifunctorAssociatorX_hom_D₃, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_hom_π_assoc, CategoryTheory.LaxMonoidalFunctor.isoMk_hom, CategoryTheory.Functor.rightOpId_hom_app, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_base_apply, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app_assoc, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_hom_app_hom, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_left, CategoryTheory.Over.braiding_hom_left, HomotopyCategory.homologyShiftIso_hom_app, CategoryTheory.Limits.limCompFlipIsoWhiskerLim_hom_app_app, CategoryTheory.Limits.limitIsoLimitCurryCompLim_hom_π_π, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_assoc, CategoryTheory.Limits.Cocones.ext_hom_hom, CategoryTheory.NatIso.removeOp_hom, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app, CochainComplex.shiftFunctorAdd_hom_app_f, HomologicalComplex.restrictionCyclesIso_hom_iCycles_assoc, CategoryTheory.Lax.LaxTrans.vComp_naturality_comp, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_obj_hom, HomologicalComplex.ι_mapBifunctorFlipIso_hom, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_left, CategoryTheory.Bicategory.id_whiskerLeft, groupHomology.π_comp_H0IsoOfIsTrivial_hom_assoc, CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_hom_app, CategoryTheory.GrothendieckTopology.whiskerRight_toSheafify_sheafifyCompIso_hom, CategoryTheory.Functor.CoreMonoidal.toLaxMonoidal_ε, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_counit_app, AlgebraicGeometry.Proj.basicOpenIsoSpec_hom, CochainComplex.truncateAugment_hom_f, smoothSheafCommRing.ι_forgetStalk_hom, CategoryTheory.GrothendieckTopology.overMapPullbackComp_hom_app_val_app, HomologicalComplex.mkHomFromDouble_f₀_assoc, CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_snd_assoc, CategoryTheory.ComonObj.comul_assoc_assoc, CategoryTheory.Limits.limitCompYonedaIsoCocone_hom_app, CategoryTheory.Functor.lanCompIsoOfPreserves_hom_app, CategoryTheory.Limits.fst_opProdIsoCoprod_hom, AlgebraicGeometry.pullbackSpecIso_hom_fst'_assoc, CategoryTheory.Bicategory.Pith.associator_inv_iso_hom, CategoryTheory.Bicategory.whiskerLeft_hom_inv_whiskerRight_assoc, CategoryTheory.Equalizer.Sieve.compatible_iff, CategoryTheory.Pseudofunctor.mapComp_id_left_hom, CategoryTheory.Functor.Monoidal.μNatIso_hom_app, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict_assoc, CategoryTheory.Functor.IsRepresentedBy.iff_of_isoObj, CategoryTheory.OverPresheafAux.unitAuxAux_hom_app, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_unitIso_hom_app_right_app, CategoryTheory.Idempotents.KaroubiKaroubi.counitIso_hom_app_f_f, TopCat.Presheaf.presheafEquivOfIso_counitIso_hom_app_app, CategoryTheory.Abelian.FunctorCategory.imageObjIso_hom, CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.map_eq_pullHom_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitIso_hom_naturality, CategoryTheory.Subobject.underlyingIso_hom_comp_eq_mk, CategoryTheory.Oplax.LaxTrans.naturality_id_assoc, CategoryTheory.endofunctorMonoidalCategory_rightUnitor_hom_app, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd, algEquivIsoAlgebraIso_hom, CategoryTheory.Limits.pullbackAssoc_hom_fst, CategoryTheory.Pseudofunctor.map₂_whisker_left_app, AlgebraicGeometry.Scheme.instIsOverMapHomCommRingCatResidueFieldCongr, CategoryTheory.Functor.mapContActionComp_hom, CategoryTheory.Limits.PreservesPullback.iso_hom_fst_assoc, Bimod.TensorBimod.one_act_left', CategoryTheory.Limits.colimitYonedaHomIsoLimitOp_π_apply, HomologicalComplex₂.totalShift₁Iso_hom_naturality_assoc, ModuleCat.extendScalars_comp_id_assoc, CategoryTheory.MonoidalCategory.tensorRightTensor_inv_app, CategoryTheory.Functor.CommShift.ofIso_compatibility, CategoryTheory.CartesianMonoidalCategory.lift_lift_associator_hom_assoc, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_apply, CategoryTheory.braiding_tensorUnit_right, CategoryTheory.ModObj.smul_def, CategoryTheory.Functor.OplaxRightLinear.δᵣ_associativity_assoc, CategoryTheory.NatIso.naturality_2_assoc, CategoryTheory.Limits.inl_comp_pushoutSymmetry_hom_assoc, groupHomology.π_comp_H2Iso_hom_apply, CategoryTheory.shiftFunctorComm_hom_app_of_add_eq_zero, CategoryTheory.Limits.PushoutCocone.isoMk_hom_hom, CategoryTheory.Limits.CatCospanTransform.whiskerRight_comp_assoc, CategoryTheory.IsCommComonObj.comul_comm, CategoryTheory.Bicategory.Prod.snd_mapComp_hom, isoFunctorOfIsoInverse_hom_app, CategoryTheory.Under.hom_right_inv_right_assoc, CategoryTheory.InjectiveResolution.isoRightDerivedToHomotopyCategoryObj_hom_naturality, CategoryTheory.prodOpEquiv_counitIso_hom_app, CategoryTheory.Bicategory.leftUnitor_hom_congr, CategoryTheory.ShortComplex.cyclesIsoLeftHomology_hom, CategoryTheory.Comma.mapSnd_hom_app, CategoryTheory.Join.mapWhiskerLeft_whiskerLeft_assoc, CategoryTheory.Oplax.StrongTrans.Modification.whiskerLeft_naturality_assoc, AddCommGrpCat.kernelIsoKer_hom_comp_subtype, CategoryTheory.Limits.Types.coproductIso_ι_comp_hom_apply, CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero_assoc, CategoryTheory.Center.whiskerRight_comm_assoc, AlgebraicGeometry.Scheme.Hom.stalkMap_congr, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_snd, CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapId_hom, HomologicalComplex.homologyFunctorIso_hom_app, TopCat.prodIsoProd_hom_fst_assoc, CategoryTheory.GrothendieckTopology.overMapPullback_id_comp_assoc, CategoryTheory.coreCategory_comp_iso_hom, Rep.diagonalOneIsoLeftRegular_hom_hom, CategoryTheory.ShortComplex.mapRightHomologyIso_hom_naturality_assoc, CategoryTheory.Bicategory.Adj.leftUnitor_inv_τr, CategoryTheory.Localization.Monoidal.μ_natural_right_assoc, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_hom_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionUnitIso_hom, CategoryTheory.Limits.cospanCompIso_hom_app_right, CategoryTheory.Limits.pullbackDiagonalMapIdIso_hom_snd_assoc, CategoryTheory.Functor.IsCocartesian.of_comp_iso, CategoryTheory.Functor.mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app, CategoryTheory.Functor.LaxRightLinear.μᵣ_unitality_assoc, CategoryTheory.Functor.LaxMonoidal.ε_tensorHom_comp_μ, CategoryTheory.Limits.pullbackSymmetry_hom_comp_fst_assoc, CategoryTheory.Dial.associator_hom_f, HomologicalComplex.extendCyclesIso_hom_iCycles_assoc, CategoryTheory.Limits.isoZeroOfMonoZero_hom, CategoryTheory.ShiftedHom.opEquiv'_apply, CategoryTheory.Functor.core_map_iso_hom, CategoryTheory.Functor.LaxMonoidal.whiskerLeft_μ_comp_μ, CategoryTheory.OplaxFunctor.map₂_leftUnitor_app_assoc, CommSemiRingCat.inv_hom_apply, CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_fst_fst, CategoryTheory.Limits.braid_natural, CategoryTheory.CatCommSq.iso_hom_naturality_assoc, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_left, CategoryTheory.Equivalence.leftOp_counitIso_hom_app, CategoryTheory.braiding_leftUnitor_aux₁, CategoryTheory.Arrow.square_to_iso_invert, CategoryTheory.constantSheafAdj_counit_w, CategoryTheory.Limits.colimit_map_colimitObjIsoColimitCompEvaluation_hom, ComplexShape.Embedding.homRestrict_f, CategoryTheory.Limits.pullbackDiagonalMapIso.hom_fst_assoc, HomologicalComplex.singleObjCyclesSelfIso_hom_naturality_assoc, CategoryTheory.oppositeShiftFunctorAdd'_hom_app, CategoryTheory.sum.inlCompInlCompAssociator_hom_app_down, CategoryTheory.MonoidalClosed.whiskerLeft_curry'_comp_assoc, CategoryTheory.unop_hom_rightUnitor, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec, CategoryTheory.SingleFunctors.hom_inv_id_hom_assoc, CategoryTheory.HalfBraiding.monoidal, CategoryTheory.Functor.mapCoconePrecompose_hom_hom, CategoryTheory.Limits.CatCospanTransform.whiskerRight_id_assoc, CategoryTheory.Over.hom_left_inv_left_assoc, CategoryTheory.Join.mapWhiskerRight_whiskerRight_assoc, CategoryTheory.Bicategory.Comonad.comul_assoc_assoc, CompHausLike.LocallyConstant.sigmaComparison_comp_sigmaIso, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂'_obj_obj_map, HomologicalComplex.mkHomFromSingle_f, HomologicalComplex.extend.d_eq, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₂, HomologicalComplex.cyclesOpNatIso_hom_app, AlgebraicGeometry.Scheme.residue_residueFieldCongr_assoc, CategoryTheory.Limits.PreservesPushout.inl_iso_hom, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIdIso_hom_app_hom, CategoryTheory.PreGaloisCategory.exists_lift_of_mono, CochainComplex.shiftFunctorAdd'_hom_app_f, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_right_app, Action.diagonalSuccIsoTensorDiagonal_hom_hom, CategoryTheory.Pretriangulated.exists_iso_binaryBiproduct_of_distTriang, CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_assoc, CategoryTheory.Limits.PreservesCokernel.π_iso_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_assoc, CategoryTheory.Bicategory.Pith.leftUnitor_hom_iso, 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.CartesianMonoidalCategory.lift_snd_comp_fst_comp_assoc, CategoryTheory.Join.mapWhiskerLeft_leftUnitor_hom, AlgebraicGeometry.Scheme.IsLocallyDirected.exists_of_pullback_V_V, groupHomology.cyclesMap_comp_isoCycles₁_hom_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_obj_iso_hom, AlgebraicGeometry.Scheme.Modules.pseudofunctor_left_unitality_assoc, CategoryTheory.ChosenPullbacksAlong.iso_pullback_map, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_morphismRestrict, CategoryTheory.Limits.Cone.mapConeToUnder_hom_hom, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_naturality_assoc, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom', CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_assoc, CategoryTheory.Bicategory.associator_naturality_left, DistLat.Iso.mk_hom, CategoryTheory.HopfObj.mul_antipode₂, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompCoyoneda, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_inv_hom_assoc, Action.rightUnitor_hom_hom, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_app, HomologicalComplex.truncLE'Map_f_eq, groupHomology.toCycles_comp_isoCycles₁_hom, CategoryTheory.WithInitial.starIsoInitial_hom, CategoryTheory.SingleFunctors.inv_hom_id_hom_app, CategoryTheory.Equivalence.core_counitIso_inv_app_iso_hom, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_hom_eq_germ_assoc, unop_inv_hom_id_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_hom_toNatTrans_app_val_app, CategoryTheory.Bicategory.Pith.rightUnitor_inv_iso_hom, HomologicalComplex₂.ι_totalShift₂Iso_hom_f, AlgebraicTopology.DoldKan.N₁Γ₀_inv_app, BoolAlg.inv_hom_apply, SheafOfModules.pullbackObjFreeIso_hom_naturality, eHomCongr_inv, CategoryTheory.MonoidalCategory.rightUnitor_monoidal, hom_inv_id_triangle_hom₃_assoc, CategoryTheory.MonoidalOpposite.tensorLeftIso_hom_app_unmop, Action.diagonalSuccIsoTensorTrivial_hom_hom_apply, HomologicalComplex.dFrom_comp_xNextIso_assoc, CategoryTheory.Limits.colimit_map_colimitObjIsoColimitCompEvaluation_hom_assoc, CategoryTheory.leftDistrib_hom, inverseCompIso_hom_app, HomologicalComplex.toCycles_cyclesIsoSc'_hom, commRingCatIsoToRingEquiv_toRingHom, CategoryTheory.MonObj.mul_assoc_assoc, CategoryTheory.Equivalence.congrLeft_counitIso_hom_app, CategoryTheory.Functor.mapConeOp_hom_hom, CategoryTheory.leftUnitor_inv_braiding, CategoryTheory.Adjunction.leftAdjointUniq_inv_app, CategoryTheory.MonoidalCategory.tensor_whiskerLeft, CategoryTheory.Sigma.descUniq_hom_app, CategoryTheory.ShortComplex.opcyclesIsoRightHomology_hom_inv_id_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_hom_assoc, Bimod.whiskerRight_hom, CategoryTheory.MonoidalCategory.leftUnitor_monoidal_assoc, CategoryTheory.unop_hom_braiding, Lat.inv_hom_apply, CategoryTheory.Core.hom_ext_iff, SemimoduleCat.MonoidalCategory.braiding_naturality, CategoryTheory.GrothendieckTopology.ι_plusCompIso_hom, groupHomology.chainsMap_f_2_comp_chainsIso₂_assoc, CategoryTheory.Oplax.StrongTrans.id_naturality_hom, CategoryTheory.Bicategory.leftUnitor_naturality, CategoryTheory.obj_μ_zero_app, AlgebraicTopology.DoldKan.Compatibility.τ₀_hom_app, CategoryTheory.Limits.inl_comp_pushoutSymmetry_hom, CategoryTheory.Limits.coprod.associator_hom, CategoryTheory.ExponentiableMorphism.unit_pushforwardId_hom_assoc, CategoryTheory.IsPushout.inr_isoIsPushout_hom, BialgEquiv.toBialgIso_hom, Bimod.pentagon_bimod, CategoryTheory.IsPullback.isoIsPullback_hom_fst, CategoryTheory.MonoidalCategory.MonoidalRightAction.whiskerRight_actionHomLeft, HeytAlg.Iso.mk_hom, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst_assoc, HomologicalComplex.extend_d_eq, CategoryTheory.Comma.mapRightEq_hom_app_left, CategoryTheory.Limits.Pi.isoLimit_hom_π, CategoryTheory.Functor.IsStronglyCocartesian.of_iso, CategoryTheory.Functor.commShiftOfLocalization_iso_hom_app, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₂, semiRingCatIsoToRingEquiv_toRingHom, CommAlgCat.associator_hom_hom, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_right, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_hom_assoc, CategoryTheory.Limits.ι_colimitConstInitial_hom, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_assoc, CategoryTheory.LaxFunctor.mapComp_assoc_left, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τl, CategoryTheory.Adjunction.map_restrictFullyFaithful_unit_app, partialFunEquivPointed_counitIso_hom_app_toFun, CategoryTheory.Core.forgetFunctorToCore_obj_map, CategoryTheory.Limits.prod.mapIso_hom, groupCohomology.cocyclesIso₀_hom_comp_f_apply, TwoP.swapEquiv_counitIso_hom_app_hom_toFun, CategoryTheory.MonoidalCategory.rightUnitor_naturality, SheafOfModules.conjugateEquiv_pullbackId_hom, CategoryTheory.Dial.braiding_naturality_left, CategoryTheory.Dial.associatorImpl_hom_f, CategoryTheory.Functor.Monoidal.associator_hom_app, MulEquiv.toGrpIso_hom, CategoryTheory.PreGaloisCategory.endEquivAutGalois_π, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapId_inv_iso_hom, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.firstMap_app_app_app, CategoryTheory.Mon.rightUnitor_hom_hom, CategoryTheory.OplaxFunctor.map₂_rightUnitor_app, CategoryTheory.ShortComplex.mapHomologyIso'_hom_naturality_assoc, CochainComplex.shiftFunctorComm_hom_app_f, CategoryTheory.Grp.braiding_hom_hom, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_right_unitor, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_assoc, ComplexShape.Embedding.homRestrict.f_eq, CategoryTheory.Functor.LaxMonoidal.tensorHom_ε_comp_μ, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_app, Lat.Iso.mk_hom, CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv_assoc, groupHomology.isoCycles₂_hom_comp_i, HomologicalComplex.restrictionToTruncGE'.f_eq_iso_hom_iso_inv, PartOrd.hom_inv_apply, AlgebraicGeometry.Scheme.stalkMap_inv_hom_assoc, CategoryTheory.LaxFunctor.mapComp_assoc_right, CategoryTheory.Functor.leftKanExtensionUniqueOfIso_hom, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d_1_0, CategoryTheory.Limits.limitFlipIsoCompLim_hom_app, CategoryTheory.shiftFunctorAdd_assoc_hom_app, groupHomology.π_comp_H1Iso_hom, CategoryTheory.asIso_hom, CategoryTheory.Bicategory.mateEquiv_apply, CategoryTheory.Bicategory.Adj.associator_hom_τl, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_hom_π_π, CategoryTheory.GradedObject.Monoidal.rightUnitor_naturality, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_rightUnitor, CategoryTheory.Limits.pullback.mapDesc_comp, CategoryTheory.Bicategory.InducedBicategory.bicategory_associator_hom_hom, CategoryTheory.Abelian.DoldKan.comparisonN_hom_app_f, CategoryTheory.Oplax.StrongTrans.naturality_naturality, CategoryTheory.MonoidalOpposite.tensorRightMopIso_hom_app_unmop, CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv', CategoryTheory.Functor.mapTriangleRotateIso_inv_app_hom₃, CategoryTheory.Functor.LaxMonoidal.whiskerRight_tensorUnit_comp_rightUnitor_hom_assoc, HomologicalComplex₂.XXIsoOfEq_hom_ιTotal, SSet.Truncated.HomotopyCategory.BinaryProduct.associativityIso_hom_app, SheafOfModules.pullback_map_ιFree_comp_pullbackObjFreeIso_hom, CategoryTheory.Bicategory.pentagon_hom_hom_inv_inv_hom, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerLeft, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_inv_app_app, CategoryTheory.MonObj.mul_one_assoc, CategoryTheory.PrelaxFunctor.map₂Iso_hom, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapIdIso_hom, CategoryTheory.ShortComplex.Splitting.ofIso_r, SSet.stdSimplex.faceSingletonIso_one_hom_comp_ι_eq_δ_assoc, AlgebraicGeometry.Scheme.ΓSpecIso_naturality_assoc, CategoryTheory.Oplax.OplaxTrans.leftUnitor_hom_as_app, CategoryTheory.GradedObject.Monoidal.leftUnitor_naturality, HomologicalComplex₂.totalShift₁Iso_hom_naturality, CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_hom_assoc, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom, CategoryTheory.Pretriangulated.exists_iso_of_arrow_iso, CategoryTheory.Limits.opCoproductIsoProduct_hom_comp_π_assoc, CategoryTheory.SmallObject.SuccStruct.ofCocone_map, CategoryTheory.Limits.proj_comp_opProductIsoCoproduct'_hom, CategoryTheory.ShiftMkCore.assoc_hom_app, CategoryTheory.rightDistributor_hom, CategoryTheory.Functor.Monoidal.map_leftUnitor_assoc, isLocalHom_of_iso, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop, CategoryTheory.equivYoneda'_hom_val, CategoryTheory.leftAdjointMate_comp, ModuleCat.extendScalars_comp_id, CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.map_eq_pullHom, CategoryTheory.NatTrans.commShift_iso_hom_of_localization, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app, ChainComplex.mk_d, CategoryTheory.functorProdFunctorEquivUnitIso_inv_app, CategoryTheory.Adjunction.adjToMonadIso_hom_toNatTrans_app, CategoryTheory.Limits.pullbackProdFstIsoProd_hom_snd_assoc, toBialgEquiv_toBialgHom, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_hom_app_val_app, CategoryTheory.Equivalence.core_functor_map_iso_hom, CategoryTheory.Functor.commShiftOfLocalization.iso_hom_app_assoc, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_hom, AlgebraicGeometry.ΓSpec_adjunction_homEquiv_eq, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_assoc, Bicategory.Opposite.bicategory_associator_inv_unop2, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_assoc, CategoryTheory.flippingIso_hom_toFunctor_obj_obj_obj, Mathlib.Tactic.Monoidal.evalWhiskerLeft_nil, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₂, CategoryTheory.Limits.PushoutCocone.eta_hom_hom, CategoryTheory.NatTrans.app_shift, CategoryTheory.Lax.OplaxTrans.naturality_comp_assoc, CategoryTheory.ShortComplex.LeftHomologyData.homologyπ_comp_homologyIso_hom, CategoryTheory.Functor.ι_colimitIsoOfIsLeftKanExtension_hom_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id, AlgebraicGeometry.Scheme.Hom.isoImage_hom_ι, CategoryTheory.Bicategory.pentagon_inv_inv_hom_hom_inv_assoc, CategoryTheory.Join.mapPairLeft_hom_app, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransId_hom_app_f, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_hom_comp_ι_assoc, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp, CategoryTheory.EnrichedFunctor.isoMk_hom_out, CategoryTheory.mop_hom_associator, CategoryTheory.OplaxFunctor.mapComp_id_left_assoc, FintypeCat.hom_inv_id_apply, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality, CategoryTheory.Limits.kernelSubobject_arrow_apply, ModuleCat.FreeMonoidal.εIso_hom_one, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapCompIso_hom, DerivedCategory.singleFunctorsPostcompQIso_hom_hom, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₂, AlgebraicGeometry.Scheme.iso_hom_base_inv_base_apply, CategoryTheory.ChosenPullbacksAlong.unit_pullbackComp_hom, LightCondensed.isoFinYoneda_hom_app, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app_assoc, groupHomology.d₁₀ArrowIso_hom_right, CategoryTheory.Pseudofunctor.DescentData.pullFunctorCompIso_hom_app_hom, CategoryTheory.associativity_app, CategoryTheory.Bicategory.Prod.swap_mapComp_hom, SemimoduleCat.MonoidalCategory.hexagon_reverse, SemiNormedGrp.explicitCokernelIso_hom_desc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformPrecomposeObjSquare_iso_hom_comp, CategoryTheory.Limits.parallelPair.eqOfHomEq_hom_app, CategoryTheory.Mathlib.Tactic.MonTauto.associator_hom_comp_tensorHom_tensorHom_comp_assoc, CategoryTheory.rightDistrib_hom, CategoryTheory.Pseudofunctor.DescentData.isoMk_hom_hom, CategoryTheory.CommGrp.trivial_grp_mul, AlgebraicGeometry.Scheme.residueFieldCongr_trans_hom, inv_hom_id_app_app_app_assoc, CategoryTheory.Functor.mapCochainComplexShiftIso_hom_app_f, CategoryTheory.Functor.LaxMonoidal.μ_whiskerRight_comp_μ, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_assoc, Rep.leftRegularTensorTrivialIsoFree_hom_hom_single_tmul_single, CategoryTheory.monoidalOfHasFiniteProducts.rightUnitor_hom, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_inv_app_unop_assoc, CategoryTheory.Functor.OplaxMonoidal.δ_comp_δ_whiskerRight, inv_hom_id_app, HomologicalComplex₂.totalFlipIsoX_hom_D₂, CategoryTheory.SingleFunctors.shiftIso_add_hom_app, CategoryTheory.flippingIso_hom_toFunctor_map_app_app, AlgebraicGeometry.Scheme.Hom.toNormalization_inl_normalizationCoprodIso_hom, CategoryTheory.Grp.associator_hom_hom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_inv_app, CategoryTheory.shiftFunctorCompIsoId_zero_zero_hom_app, AlgebraicGeometry.Scheme.Hom.inv_image, CategoryTheory.Equivalence.inverseFunctorObjIso_hom, CategoryTheory.Arrow.hom_inv_id_right, CategoryTheory.obj_μ_inv_app_assoc, CategoryTheory.MonObj.one_rightUnitor, CategoryTheory.Functor.toEssImageCompι_hom_app, CategoryTheory.e_assoc'_assoc, CategoryTheory.Pseudofunctor.DescentData.pullFunctorObjHom_eq, AlgebraicGeometry.Scheme.residueFieldCongr_fromSpecResidueField_assoc, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_assoc, CategoryTheory.FunctorToTypes.hom_inv_id_app_apply, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁, CategoryTheory.TwoSquare.vComp'_app, SemimoduleCat.hom_hom_leftUnitor, CategoryTheory.Limits.walkingSpanOpEquiv_unitIso_hom_app, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app_assoc, TopCat.Presheaf.presheafEquivOfIso_functor_map_app, groupHomology.cyclesIso₀_comp_H0π, CategoryTheory.ShortComplex.RightHomologyData.pOpcycles_comp_opcyclesIso_hom_assoc, CategoryTheory.Functor.leftUnitor_hom_app, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_comp_assoc, CategoryTheory.Grothendieck.ιCompMap_hom_app_base, CategoryTheory.coprod_inl_rightDistrib_hom_assoc, core_hom_app_iso_hom, CategoryTheory.Bicategory.rightUnitor_comp_assoc, groupCohomology.isoCocycles₂_hom_comp_i_apply, CategoryTheory.Limits.CatCospanTransform.leftUnitor_hom_base_app, CategoryTheory.Arrow.inv_hom_id_right_assoc, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_hom_app, CategoryTheory.TransfiniteCompositionOfShape.map_incl, SheafOfModules.map_ιFree_mapFree_hom_assoc, Mathlib.Tactic.Bicategory.evalComp_nil_cons, CategoryTheory.Equivalence.symmEquivInverse_obj_unitIso_inv, CategoryTheory.Adjunction.comp_unit, CategoryTheory.ExponentiableMorphism.unit_pushforwardComp_hom, CategoryTheory.Bicategory.Adj.leftUnitor_hom_τr, CategoryTheory.Limits.inr_inl_pushoutLeftPushoutInrIso_hom_assoc, CategoryTheory.Limits.pointwiseProductCompEvaluation_hom_app, CategoryTheory.Pseudofunctor.mapId'_hom_naturality, CategoryTheory.conjugateIsoEquiv_symm_apply_hom, CategoryTheory.toSheafify_plusPlusIsoSheafify_hom_assoc, Mathlib.Tactic.Bicategory.evalWhiskerRightAux_of, CategoryTheory.coprodComparison_tensorLeft_braiding_hom, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_hom, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_app, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_app, CategoryTheory.associator_hom_apply_2_1, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_inv_hom_assoc, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc_apply, unop_inv_hom_id_app_assoc, CategoryTheory.ShortComplex.opcyclesOpIso_hom_toCycles_op, inl_coprodIsoPushout_hom_assoc, CategoryTheory.Limits.Cones.equivalenceOfReindexing_functor, CategoryTheory.ShortComplex.RightHomologyMapData.opcyclesMap_eq, CategoryTheory.ShortComplex.rightHomologyIso_hom_naturality, CategoryTheory.Functor.mapTriangleCommShiftIso_hom_app_hom₂, CategoryTheory.Limits.kernelFactorThruImage_hom_comp_ι, CategoryTheory.Adjunction.leftAdjointCompIso_hom_app, groupHomology.inhomogeneousChains.d_eq, CategoryTheory.NatTrans.shift_app_comm_assoc, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse, CategoryTheory.Functor.whiskerRight_twice, CategoryTheory.NatIso.pi'_hom, CategoryTheory.LocalizerMorphism.instCommShiftLocalizationHomFunctorIsoFunctorQLocalizedFunctor, AlgebraicGeometry.Scheme.IdealSheafData.ker_glueDataObjι_appTop, FinBoolAlg.Iso.mk_hom, AlgebraicGeometry.Spec.germ_stalkMapIso_hom, TopologicalSpace.Opens.mapMapIso_counitIso, CategoryTheory.Bicategory.Adjunction.comp_right_triangle_aux, CategoryTheory.MonoidalCategory.MonoidalLeftAction.associator_actionHom, CategoryTheory.NatTrans.shift_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app, CochainComplex.ConnectData.homologyMap_map_of_eq_neg_succ, CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoCofanPt, CategoryTheory.Functor.ShiftSequence.induced_shiftMap, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_app_assoc, AddCommMonCat.coyonedaForget_hom_app_app_hom, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.π_comp_isoHomology_hom, CategoryTheory.Limits.inr_comp_pushoutObjIso_hom, CategoryTheory.Bicategory.Adj.lIso_hom, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.counitIso_hom, CategoryTheory.IsPullback.isoPullback_hom_snd, CategoryTheory.MonoidalCategory.id_tensor_associator_naturality_assoc, BialgEquiv.toHopfAlgIso_hom, CategoryTheory.IsPullback.isoIsPullback_hom_snd_assoc, CategoryTheory.Oplax.StrongTrans.toOplax_naturality, CategoryTheory.Pseudofunctor.mapId'_hom_naturality_assoc, CategoryTheory.ShortComplex.leftHomologyFunctorOpNatIso_inv_app, CategoryTheory.CopyDiscardCategory.discard_tensor, CategoryTheory.Limits.Pi.isoLimit_hom_π_assoc, CategoryTheory.shiftFunctorAdd_hom_app_obj_of_induced, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_succ_succ, CategoryTheory.Comma.mapLeftIso_inverse_map_left, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₂, HomotopicalAlgebra.Precylinder.symm_i, CategoryTheory.Functor.map_shiftFunctorComm, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.unitIso_hom, CategoryTheory.Functor.op_commShiftIso_hom_app, CategoryTheory.Limits.biproduct.mapBiproduct_hom_desc, groupHomology.isoCycles₁_hom_comp_i, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_app_fst_app, CategoryTheory.leftDistributor_hom_comp_biproduct_π_assoc, CategoryTheory.Limits.pullbackProdFstIsoProd_hom_fst, CategoryTheory.Bicategory.Adjunction.homEquiv₁_symm_apply, CategoryTheory.Oplax.StrongTrans.Modification.whiskerRight_naturality_assoc, HomotopyCategory.homologyFunctor_shiftMap, CategoryTheory.Functor.bifunctorComp₁₂Iso_hom_app_app_app, CategoryTheory.Limits.PullbackCone.isoMk_hom_hom, CategoryTheory.MonoidalCategory.whiskerRight_id_assoc, CategoryTheory.Limits.CatCospanTransform.leftUnitor_hom_right_app, CategoryTheory.CatCommSq.hInv_iso_hom_app, CategoryTheory.Comma.mapLeftComp_hom_app_left, CategoryTheory.ComposableArrows.mkOfObjOfMapSucc_exists, CategoryTheory.ComposableArrows.isoMk₀_hom_app, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_comp_homologyIso_inv, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, CategoryTheory.Functor.CoreMonoidal.μIso_hom_natural_right_assoc, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app, CategoryTheory.Functor.bifunctorComp₂₃Iso_hom_app_app_app, CategoryTheory.Limits.inr_pushoutLeftPushoutInrIso_hom_assoc, CategoryTheory.ShortComplex.mapOpcyclesIso_hom_naturality, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_assoc, CategoryTheory.CartesianMonoidalCategory.lift_snd_comp_fst_comp, CategoryTheory.NatIso.cancel_natIso_hom_right_assoc, CategoryTheory.Functor.IsRepresentedBy.of_isoObj, CategoryTheory.Localization.SmallHom.equiv_shift, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₃, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp, AddCommGrpCat.hom_neg_apply, groupHomology.H0π_comp_H0Iso_hom_assoc, CochainComplex.shiftShortComplexFunctorIso_zero_add_hom_app, CategoryTheory.Limits.ι_comp_colimitLeftOpIsoUnopLimit_hom_assoc, HomologicalComplex.XIsoOfEq_hom_comp_XIsoOfEq_inv, CategoryTheory.Pseudofunctor.toOplax_mapId', 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.Limits.HasLimit.isoOfNatIso_hom_π, CategoryTheory.MonoidalClosed.curry'_whiskerRight_comp, AlgebraicGeometry.pullbackSpecIso_hom_fst', CategoryTheory.Localization.liftNatIso_hom, CategoryTheory.Limits.HasBiproductsOfShape.colimIsoLim_hom_app, CategoryTheory.Functor.IsCoverDense.Types.appIso_hom, CategoryTheory.Functor.LaxLeftLinear.μₗ_associativity_assoc, CategoryTheory.Limits.pullbackDiagonalMapIdIso_hom_snd, AlgebraicGeometry.IsOpenImmersion.isoOfRangeEq_hom_fac_assoc, toHopfAlgEquiv_toBialgHom, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inl_assoc, CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_hom_desc, CategoryTheory.Bicategory.Adj.Bicategory.associator_hom_τl, CategoryTheory.Over.mapIso_functor, CategoryTheory.GrpObj.ofIso_mul, CategoryTheory.MonoidalClosed.ofEquiv_curry_def, TopCat.Presheaf.toPushforwardOfIso_app, CategoryTheory.Functor.Monoidal.leftUnitor_hom_app, CategoryTheory.Limits.snd_opProdIsoCoprod_hom_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_obj_map_app, AlgebraicGeometry.IsAffineOpen.ΓSpecIso_hom_fromSpec_app, CategoryTheory.hom_inv_id_apply, AlgebraicGeometry.SpecToEquivOfLocalRing_eq_iff, CategoryTheory.Equivalence.changeInverse_unitIso_hom_app, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso_hom_app_f, CategoryTheory.Adjunction.rightAdjointUniq_refl, CategoryTheory.Adjunction.homEquiv_symm_rightAdjointUniq_hom_app, CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv, CategoryTheory.Pseudofunctor.map₂_whisker_right_app, CategoryTheory.kernelOpOp_hom, HomologicalComplex.truncGE'Map_f_eq, CategoryTheory.Functor.CoreMonoidal.toLaxMonoidal_μ, CategoryTheory.Bicategory.conjugateEquiv_symm_apply', RingCat.hom_inv_apply, TannakaDuality.FiniteGroup.map_mul_toRightFDRepComp, CategoryTheory.unitOfTensorIsoUnit_hom_app, CategoryTheory.StructuredArrow.mapIso_inverse_map_left, CategoryTheory.preservesLimitNatIso_hom_app, CategoryTheory.Functor.isoWhiskerLeft_hom, CategoryTheory.Limits.imageMonoIsoSource_hom_self_assoc, Bipointed.swapEquiv_unitIso_hom_app_toFun, CategoryTheory.Functor.FullyFaithful.homNatIso_hom_app_down, CategoryTheory.Functor.Final.ι_colimitIso_hom, eq_inv_comp, SemimoduleCat.MonoidalCategory.rightUnitor_naturality, CategoryTheory.Monad.monadMonEquiv_unitIso_hom_app_toNatTrans_app, CategoryTheory.Limits.mulInitial_hom, CategoryTheory.Quiv.hom_obj_inv_obj_of_iso, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d_1_0_assoc, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompYoneda, CategoryTheory.Bimon.mul_counit_assoc, HomologicalComplex₂.D₁_totalShift₂XIso_hom, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_hom_app, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom_assoc, CategoryTheory.ShortComplex.cyclesIsoX₂_hom, CategoryTheory.Bicategory.InducedBicategory.isoMk_hom_hom, CategoryTheory.MonoidalCategory.externalProductSwap_hom_app_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_naturality, CategoryTheory.Limits.PreservesPullback.iso_hom_snd, CompHausLike.isoOfHomeo_hom_hom_hom_apply, CategoryTheory.Limits.opCoproductIsoProduct'_hom_comp_proj_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocNatIso_hom_app_app_app, CategoryTheory.shiftFunctorAdd'_assoc_hom_app_assoc, CategoryTheory.Equivalence.congrRight_unitIso_hom_app, CategoryTheory.NatTrans.shift_app_comm, CategoryTheory.Join.mapPairRight_hom_app, CategoryTheory.Functor.limitIsoOfIsRightKanExtension_hom_π, CategoryTheory.Bicategory.whiskerLeft_rightUnitor, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_hom_app_hom, CategoryTheory.SemiCartesianMonoidalCategory.fst_def, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_hom_app_one, CategoryTheory.sheafComposeIso_hom_fac_assoc, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, CategoryTheory.Functor.preimageIso_hom, CategoryTheory.Limits.Cocone.mapCoconeToOver_hom_hom, CategoryTheory.Limits.Sigma.ι_reindex_hom_assoc, MulEquiv.toSemigrpIso_hom, groupHomology.cyclesMap_comp_cyclesIso₀_hom_assoc, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_assoc, CategoryTheory.ShortComplex.LeftHomologyMapData.cyclesMap_eq, CategoryTheory.InducedCategory.isoMk_hom, CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id_assoc, CategoryTheory.Functor.ShiftSequence.induced_isoShiftZero_hom_app_obj, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app_assoc, CategoryTheory.monoidalOfHasFiniteProducts.leftUnitor_hom, CategoryTheory.IsPullback.isoIsPullback_hom_snd, AlgebraicGeometry.Scheme.Hom.toImage_app, HomologicalComplex₂.D₂_totalShift₂XIso_hom, Rep.linearizationTrivialIso_hom_hom, CategoryTheory.Functor.isoCopyObj_hom_app, CategoryTheory.SingleFunctors.shiftIso_zero_hom_app, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_fst, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_hom_app_app, CategoryTheory.Pretriangulated.shortComplexOfDistTriangleIsoOfIso_hom_τ₁, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app_assoc, AddEquiv.toAddMagmaCatIso_hom, CategoryTheory.Pseudofunctor.map₂_left_unitor_app_assoc, CategoryTheory.Limits.preserves_cokernel_iso_comp_cokernel_map_assoc, CategoryTheory.Under.inv_right_hom_right_assoc, CategoryTheory.Adjunction.leftAdjointIdIso_inv_app, CategoryTheory.ShortComplex.LeftHomologyData.liftCycles_comp_cyclesIso_hom_assoc, CategoryTheory.Adjunction.leftAdjointUniq_trans, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_assoc, AlgebraicGeometry.IsAffineOpen.isoSpec_hom, CategoryTheory.Functor.mapIso_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_η_unmop_app, CategoryTheory.Pseudofunctor.map₂_right_unitor_app_assoc, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_inv, CategoryTheory.Pretriangulated.shortComplexOfDistTriangleIsoOfIso_hom_τ₂, CategoryTheory.Pseudofunctor.map₂_right_unitor_app, CategoryTheory.Equivalence.core_unitIso_inv_app_iso_hom, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_naturality_app, CategoryTheory.unop_hom_associator, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.flipFunctorToInterchange_hom_app_app, CategoryTheory.NatTrans.unop_whiskerRight_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_hom_app_app_fst, CategoryTheory.IsPushout.inr_isoPushout_hom, hom_inv_id_app_app_app_assoc, CategoryTheory.ModObj.mul_smul, CategoryTheory.MonoidalOpposite.tensorRightUnmopIso_hom_app, CategoryTheory.MonoidalCategory.leftUnitor_whiskerRight, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_iso_hom_app, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict_assoc, TopCat.sigmaIsoSigma_hom_ι_apply, CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan_inj_assoc, CategoryTheory.GrothendieckTopology.Point.sheafFiberCompIso_hom_app, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_apply, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_obj_map_app, HomologicalComplex.restrictionToTruncGE'_f_eq_iso_hom_iso_inv, CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj_hom_naturality, CategoryTheory.Functor.IsRepresentedBy.iff_natIso, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom''_assoc, CategoryTheory.Limits.biproduct.map_lift_mapBiprod, CategoryTheory.Bimon.equivMonComonCounitIsoAppXAux_hom, CategoryTheory.MonoidalCategory.MonoidalRightAction.action_actionHomRight, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_inv_app_val_app, CategoryTheory.CommGrp.mkIso'_hom_hom_hom_hom, SSet.Subcomplex.topIso_hom, CategoryTheory.Limits.pullback.congrHom_hom, CategoryTheory.Limits.ι_reflexiveCoequalizerIsoCoequalizer_hom_assoc, CategoryTheory.Limits.IsLimit.homIso_hom, CategoryTheory.Limits.CoconeMorphism.inv_hom_id_assoc, CategoryTheory.Limits.cokernelZeroIsoTarget_hom, HomologicalComplex.iCyclesIso_hom, CategoryTheory.RelCat.rel_iso_iff, CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtensionObjIsoColimit_hom_assoc, AlgebraicGeometry.Scheme.Hom.isoImage_hom_ι_assoc, CategoryTheory.GradedObject.Monoidal.triangle, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.firstMap₃_app_app_app, CategoryTheory.liftedLimitMapsToOriginal_hom_π, HomologicalComplex.stupidTruncMap_stupidTruncXIso_hom, CategoryTheory.Bicategory.Pith.inclusion_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.WithInitial.liftStar_hom, CategoryTheory.Functor.LaxBraided.braided_assoc, CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.rightUnitor_naturality, CategoryTheory.Mathlib.Tactic.MonTauto.associator_hom_comp_tensorHom_tensorHom_comp, hom_comp_eq_id, CategoryTheory.Functor.Monoidal.rightUnitor_hom_app, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc, CategoryTheory.Under.postEquiv_unitIso, CategoryTheory.Functor.Monoidal.commTensorRight_hom_app, CategoryTheory.NatTrans.naturality_1, CategoryTheory.Equivalence.sheafCongr.unitIso_inv_app_val_app, AlgebraicGeometry.Scheme.inv_base_hom_base_assoc, CategoryTheory.Sum.functorEquivFunctorCompSndIso_hom_app_app, AlgebraicGeometry.Scheme.Opens.topIso_hom, CategoryTheory.Join.mapIsoWhiskerLeft_hom_app, CategoryTheory.PrelaxFunctor.map₂_inv_hom, AlgebraicTopology.DoldKan.N₁Γ₀_inv_app_f_f, CategoryTheory.Limits.ι_comp_colimitLeftOpIsoUnopLimit_hom, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_hom_app_fst_app, CategoryTheory.Mon.braiding_hom_hom, CategoryTheory.ExactPairing.coevaluation_evaluation_assoc, TopologicalSpace.Opens.overEquivalence_counitIso_hom_app, CategoryTheory.Functor.reprW_hom_app, CategoryTheory.FreeGroupoid.mapCompLift_hom_app, CategoryTheory.ComposableArrows.opEquivalence_counitIso_hom_app_app, Pointed.Iso.mk_hom_toFun, CategoryTheory.Over.prodLeftIsoPullback_hom_fst, inv_hom_id_triangle_hom₃, CategoryTheory.GrothendieckTopology.overMapPullback_assoc, CategoryTheory.unmop_hom_leftUnitor, CategoryTheory.Bicategory.Prod.sectR_mapId_hom, CategoryTheory.ShortComplex.comp_homologyMap_comp, CategoryTheory.Over.associator_hom_left_fst_assoc, Rep.diagonalSuccIsoFree_hom_hom_single, CategoryTheory.ExponentiableMorphism.pushforwardId_hom_counit, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_hom_eq_germ_assoc, CoalgCat.MonoidalCategoryAux.rightUnitor_hom_toLinearMap, Homotopy.extend.hom_eq, CategoryTheory.Sum.functorEquivFunctorCompFstIso_hom_app_app, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.tensorHom_eq, CategoryTheory.GradedObject.ι_mapBifunctorComp₁₂MapObjIso_hom, CategoryTheory.MonoidalCategory.whisker_assoc, CategoryTheory.Functor.Monoidal.map_rightUnitor, CategoryTheory.MonoidalCategory.associator_naturality_left_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.inv_hom_actionHomLeft_assoc, CategoryTheory.ModObj.mul_smul', CategoryTheory.yonedaYonedaColimit_app_inv, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_symm_apply, CategoryTheory.Limits.snd_opProdIsoCoprod_hom, CategoryTheory.Bicategory.Prod.swap_mapId_hom, SSet.leftUnitor_hom_app_apply, ext_iff, SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁_hom_f_f, CategoryTheory.Limits.PreservesPullback.iso_hom, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionAssocIso_hom, DistLat.inv_hom_apply, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_hom_comp_ι, CategoryTheory.ShortComplex.HomologyData.comm, AlgebraicGeometry.pullbackSpecIso_hom_snd, CategoryTheory.Functor.CoreMonoidal.left_unitality_assoc, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop_assoc, CategoryTheory.NatIso.unop_hom, CategoryTheory.Hom.mulEquivCongrRight_apply, CategoryTheory.Functor.shiftIso_hom_app_comp_shiftMap_of_add_eq_zero, CategoryTheory.Limits.HasLimit.isoOfEquivalence_inv_π, CategoryTheory.Comma.unopFunctorCompSnd_hom_app, CategoryTheory.Functor.CommShift.OfComp.map_iso_inv_app, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_hom_comp_homologyIso_inv_assoc, CategoryTheory.CatCenter.smul_iso_hom_eq, CategoryTheory.rightAdjointMate_comp, CategoryTheory.LaxFunctor.map₂_associator_app, CategoryTheory.FreeBicategory.mk_right_unitor_hom, CategoryTheory.NatTrans.instCommShiftOppositeShiftHomFunctorNatIsoComp, LightCondensed.lanPresheafExt_hom, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app, AlgebraicGeometry.Scheme.residueFieldCongr_trans_hom_assoc, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁, CategoryTheory.Functor.ranCompLimIso_hom_app, CategoryTheory.Functor.mapTriangleInvRotateIso_hom_app_hom₂, CategoryTheory.Limits.prod.leftUnitor_hom_naturality, CategoryTheory.GradedObject.ι_mapBifunctorRightUnitor_hom_apply_assoc, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₂_app, CategoryTheory.Functor.rightDerivedZeroIsoSelf_hom_inv_id_assoc, Action.resComp_hom_app_hom, CategoryTheory.GrpObj.ofIso_one, CategoryTheory.Limits.π_comp_cokernelIsoOfEq_hom, CategoryTheory.Localization.SmallShiftedHom.equiv_apply, AlgebraicGeometry.Scheme.residueFieldCongr_inv, PartialFun.Iso.mk_hom, CategoryTheory.CommMon.mkIso'_hom_hom_hom, CategoryTheory.sheafSectionsNatIsoEvaluation_hom_app, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_app_assoc, CategoryTheory.Limits.CatCospanTransform.triangle, CategoryTheory.Limits.factorThruKernelSubobject_comp_kernelSubobjectIso, HomologicalComplex.homologyOp_hom_naturality, CategoryTheory.Limits.kernel.congr_hom, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberCompIso_hom_app_assoc, CategoryTheory.Core.inclusion_map, CategoryTheory.Limits.pullbackSymmetry_hom_comp_fst, HomotopicalAlgebra.Cylinder.symm_i_assoc, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_assoc, AlgebraicGeometry.Scheme.coe_homeoOfIso, Mathlib.Tactic.Monoidal.evalComp_nil_cons, AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_fst, groupCohomology.map_H0Iso_hom_f_assoc, CategoryTheory.GrothendieckTopology.overMapPullback_id_comp, CategoryTheory.Bicategory.comp_whiskerLeft_symm_assoc, AlgebraicGeometry.Scheme.Hom.normalizationObjIso_hom_val, CategoryTheory.Functor.unopId_hom_app, CategoryTheory.Pi.isoMk_hom, Mathlib.Tactic.Monoidal.evalWhiskerRight_nil, CategoryTheory.Functor.essImage.liftFunctor_map, HomologicalComplex₂.flipEquivalenceCounitIso_hom_app_f_f, CategoryTheory.Functor.commShift₂_comm_assoc, CategoryTheory.NatIso.hcomp_hom, HomologicalComplex.homologyIsoSc'_hom_ι, CategoryTheory.Limits.inr_inl_pushoutAssoc_hom_assoc, AddMagmaCat.neg_hom_apply, FinPartOrd.Iso.mk_hom, CategoryTheory.Functor.whiskerRight_left, inv_hom_id_app_assoc, CategoryTheory.Limits.biproduct.whiskerEquiv_hom_eq_lift, CategoryTheory.IsPushout.inl_isoIsPushout_hom, CategoryTheory.MonObj.one_mul, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_hom_app_snd_app, CategoryTheory.CostructuredArrow.unop_left_comp_underlyingIso_hom_unop, CategoryTheory.Limits.walkingCospanOpEquiv_unitIso_hom_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app_assoc, CategoryTheory.Adjunction.leftAdjointIdIso_hom_app, CategoryTheory.ObjectProperty.isoInv_hom_id_hom_assoc, CategoryTheory.InjectiveResolution.rightDerivedToHomotopyCategory_app_eq, smoothSheafCommRing.forgetStalk_hom_comp_evalHom_apply, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₂, HomologicalComplex.dFrom_comp_xNextIso, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_hom_app, CategoryTheory.Localization.lift₂_iso_hom_app_app₁, CategoryTheory.Functor.Monoidal.transport_ε_assoc, commBialgCatEquivComonCommAlgCat_counitIso_hom_app, CategoryTheory.Functor.Monoidal.transport_δ_assoc, AlgebraicGeometry.PresheafedSpace.map_comp_c_app, map_inv_hom_id_eval_assoc, CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inr, HomologicalComplex.opcyclesOpIso_hom_toCycles_op_assoc, CategoryTheory.Limits.opSpan_inv_app, CategoryTheory.Limits.inr_pushoutLeftPushoutInrIso_hom, HomologicalComplex.singleObjCyclesSelfIso_hom, CategoryTheory.unop_inv_rightUnitor, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_counitIso_hom_app_right_app, CategoryTheory.CartesianMonoidalCategory.lift_snd_fst, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right_assoc, CategoryTheory.Limits.coyonedaCompLimIsoCones_hom_app_app, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoColimitUncurryWhiskeringLeft₂_hom, CategoryTheory.toOverUnitPullback_hom_app_left, CategoryTheory.Limits.mapPairIso_hom_app, CategoryTheory.Functor.sheafPushforwardContinuousId'_hom_app_val_app, HomologicalComplex.restriction_d_eq_assoc, CategoryTheory.Bicategory.leftUnitor_comp, CategoryTheory.MonObj.mul_rightUnitor, ModuleCat.imageIsoRange_hom_subtype_apply, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isoBot_hom, CategoryTheory.Lax.OplaxTrans.vComp_naturality_id, CategoryTheory.Functor.IsCoverDense.sheafIso_hom_val, CategoryTheory.Limits.Cones.extendComp_hom_hom, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_app, CategoryTheory.SingleFunctors.hom_inv_id_hom_app, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id, CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_left_hom, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_val_app, Mathlib.Tactic.Monoidal.evalHorizontalCompAux_of, SemimoduleCat.MonoidalCategory.leftUnitor_hom_apply, CategoryTheory.Cat.associator_hom_toNatTrans, prod_hom, CategoryTheory.Limits.FormalCoproduct.coproductIsoSelf_hom_φ, refl_hom, Mathlib.Tactic.Bicategory.evalComp_nil_nil, CategoryTheory.Cat.Hom.instIsIsoFunctorαCategoryToNatTransHomHom, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₃, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_hom, CategoryTheory.Limits.colimitYonedaHomIsoLimitRightOp_π_apply, CategoryTheory.WithInitial.opEquiv_unitIso_hom_app, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv_apply, CategoryTheory.MonoidalCategory.MonoidalLeftAction.hom_inv_actionHomLeft, CategoryTheory.obj_η_app, CategoryTheory.LaxFunctor.mapComp_assoc_left_assoc, CategoryTheory.ChosenPullbacksAlong.pullbackComp_hom_counit_assoc, CategoryTheory.Limits.FormalCoproduct.evalCompInclIsoId_hom_app_app, CategoryTheory.unop_hom_leftUnitor, CategoryTheory.Comma.unopFunctorCompFst_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_rightUnitor, HomologicalComplex.XIsoOfEq_hom_naturality, CategoryTheory.Bimon.trivial_X_mon_mul, CategoryTheory.CartesianMonoidalCategory.lift_rightUnitor_hom, CategoryTheory.Adjunction.homEquiv_leftAdjointUniq_hom_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_hom_app_hom_hom, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.π_comp_isoHomology_hom_assoc, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_hom_assoc, CategoryTheory.ShiftMkCore.zero_add_inv_app, CategoryTheory.MonoidalCategory.pentagon_inv_hom_assoc, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_unitIso_hom_app_f_f, CategoryTheory.Limits.colimit.isoColimitCocone_ι_hom, CategoryTheory.Limits.biproduct.reindex_hom, FinBddDistLat.Iso.mk_hom, CategoryTheory.MonObj.mul_one_hom, CategoryTheory.GlueData.t'_comp_eq_pullbackSymmetry, CategoryTheory.pullbackShiftFunctorAdd'_inv_app, hom_inv_id_triangle_hom₁_assoc, CategoryTheory.ShortComplex.leftRightHomologyComparison_fac_assoc, CategoryTheory.Pseudofunctor.map₂_whisker_right_assoc, CategoryTheory.Grp.trivial_grp_mul, CategoryTheory.Functor.shiftIso_hom_naturality, CategoryTheory.Pi.braiding_hom_apply, CategoryTheory.Functor.coreComp_inv_app_iso_hom, LinearEquiv.toModuleIso_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_eq, CategoryTheory.Bimon.compatibility, CategoryTheory.Grothendieck.isoMk_hom_fiber, SheafOfModules.pushforwardNatIso_hom, CategoryTheory.GradedObject.Monoidal.leftUnitor_naturality_assoc, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app_assoc, HomologicalComplex.ι_mapBifunctorFlipIso_hom_assoc, CategoryTheory.TwistShiftData.shiftFunctor_map, inv_hom_id_apply, CategoryTheory.MonoidalOpposite.mopMopEquivalence_counitIso_hom_app, HomologicalComplex.extendSingleIso_hom_f, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_app_assoc, AlgebraicGeometry.Scheme.isoSpec_image_zeroLocus, HomologicalComplex.restriction.sc'Iso_hom_τ₃, CategoryTheory.Equivalence.core_unitIso_inv_app_iso_inv, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp_hom_app_f, CategoryTheory.Bicategory.InducedBicategory.forget_mapId_hom, HomologicalComplex.XIsoOfEq_inv_comp_XIsoOfEq_inv_assoc, CategoryTheory.GradedObject.single_map_singleObjApplyIso_hom_assoc, CategoryTheory.eComp_op_eq, CategoryTheory.MonoidalCategory.rightUnitorNatIso_hom_app, HomotopicalAlgebra.AttachCells.ofArrowIso_g₁, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_assoc, CategoryTheory.braiding_inv_tensorUnit_left, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_inv_iso_hom, CategoryTheory.Functor.PushoutObjObj.ι_iso_of_iso_left_hom, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π_assoc, CategoryTheory.coreFunctor_obj_map_iso_hom, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_obj_map_app, CategoryTheory.ShortComplex.Splitting.isoBinaryBiproduct_hom, CategoryTheory.BraidedCategory.braiding_tensor_right_inv_assoc, BddOrd.inv_hom_apply, CategoryTheory.prod.etaIso_hom, CategoryTheory.Bicategory.prod_rightUnitor_hom_snd, CategoryTheory.MonoidalCategory.pentagon_assoc, CategoryTheory.Bicategory.pentagon_hom_hom_inv_hom_hom, CategoryTheory.Bicategory.conjugateEquiv_symm_apply, CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_snd_assoc, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_val_app, CategoryTheory.Bicategory.prod_associator_hom_snd, AlgebraicGeometry.LocallyRingedSpace.iso_hom_base_inv_base, CategoryTheory.Bicategory.Adjunction.right_triangle, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerRight_naturality, CategoryTheory.WithTerminal.equivComma_unitIso_hom_app_app, groupCohomology.map_id_comp_H0Iso_hom_assoc, CategoryTheory.prod.prodFunctorToFunctorProdAssociator_hom_app_app, CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse_assoc, CategoryTheory.GlueData.ι_gluedIso_hom_assoc, CochainComplex.mappingConeHomOfDegreewiseSplitIso_hom_f, CategoryTheory.Limits.pullbackAssoc_hom_fst_assoc, CategoryTheory.Adjunction.shift_unit_app_assoc, groupCohomology.isoCocycles₂_hom_comp_i_assoc, CochainComplex.augmentTruncate_hom_f_zero, CategoryTheory.oppositeShiftFunctorAdd_hom_app, CochainComplex.liftCycles_shift_homologyπ_assoc, CategoryTheory.Limits.pullbackDiagonalMapIdIso_hom_fst, CategoryTheory.monoidalOfHasFiniteProducts.associator_hom_fst, CategoryTheory.Localization.Monoidal.associator_naturality₃_assoc, CategoryTheory.Functor.isRightKanExtension_iff_postcomp₁, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom, CategoryTheory.curryingIso_hom_toFunctor_map_app, CategoryTheory.Functor.mapZeroObject_hom, CategoryTheory.Functor.mapTriangleIdIso_hom_app_hom₁, Rep.coindIso_hom_hom_hom, CategoryTheory.IsPullback.isoPullback_hom_fst_assoc, CategoryTheory.Localization.Monoidal.rightUnitor_hom_app, CategoryTheory.SingleFunctors.inv_hom_id_hom, CategoryTheory.MorphismProperty.Over.mapId_hom_app_left, CategoryTheory.CartesianMonoidalCategory.braiding_hom_snd, CategoryTheory.Bicategory.Equivalence.right_triangle_hom, CategoryTheory.Limits.pullbackProdFstIsoProd_hom_snd, Rep.leftRegularTensorTrivialIsoFree_hom_hom, AlgebraicGeometry.Scheme.localRingHom_comp_stalkIso, 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.Pseudofunctor.mapComp_assoc_right_inv, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop, CategoryTheory.ProjectiveResolution.cochainComplex_d_assoc, CategoryTheory.Functor.ShiftSequence.induced_shiftMap_assoc, CategoryTheory.MonoidalCategory.associator_conjugation, CategoryTheory.Functor.pushforwardContinuousSheafificationCompatibility_hom_app_val, CategoryTheory.MonoidalCategory.associator_inv_conjugation_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_inv, CategoryTheory.Adjunction.commShiftIso_hom_app_counit_app_shift, CategoryTheory.MorphismProperty.Over.pullbackComp_left_fst_fst, CategoryTheory.LaxFunctor.mapComp_assoc_right_app_assoc, CategoryTheory.GlueData.mapGlueData_t', CategoryTheory.OverPresheafAux.counitAuxAux_hom, conj_apply, Mathlib.Tactic.Monoidal.evalWhiskerRightAux_of, groupHomology.H0π_comp_H0Iso_hom_apply, CategoryTheory.Limits.colimitCoyonedaHomIsoLimitLeftOp_π_apply, CategoryTheory.MonoidalCategory.whiskerRight_tensor_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app, CategoryTheory.Over.associator_hom_left_snd_snd, CategoryTheory.Grp.braiding_hom_hom_hom, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom_assoc, CategoryTheory.MonoidalCategory.hom_inv_id_tensor_assoc, CategoryTheory.PreGaloisCategory.endMulEquivAutGalois_pi, Condensed.locallyConstantIsoFinYoneda_hom_app, CategoryTheory.Pi.comapComp_hom_app, CategoryTheory.Bicategory.leftUnitor_comp_inv_assoc, CategoryTheory.Functor.map_braiding, CategoryTheory.Mon.tensorUnit_mul, CategoryTheory.Bicategory.leftUnitor_whiskerRight_assoc, CategoryTheory.GlueData.diagramIso_hom_app_right, FDRep.dualTensorIsoLinHom_hom_hom, ModuleCat.homEquiv_extendScalarsId, CategoryTheory.MonoidalCategory.prodCompExternalProduct_hom_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_hom_app_snd_app, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_isoPointwiseLeftKanExtension_hom, CategoryTheory.NatIso.cancel_natIso_hom_left, CategoryTheory.Functor.sheafPushforwardContinuousComp'_hom_app_val_app, CategoryTheory.eqToHom_iso_hom_naturality, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.firstMap_app_app_app, SemiNormedGrp.hom_inv_apply, Bimod.whiskerRight_comp_bimod, TopCat.inv_hom_id_apply, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_inv_app_val_app, CategoryTheory.Equivalence.CommShift.instCommShiftHomFunctorUnitIso, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_assoc, CategoryTheory.SingleFunctors.shiftIso_add'_hom_app, CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_hom, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence, CategoryTheory.ShortComplex.HomologyData.leftRightHomologyComparison'_eq, HomologicalComplex.dFrom_comp_xNextIsoSelf_assoc, CategoryTheory.Bicategory.rightUnitor_hom_congr, CategoryTheory.Equivalence.sheafCongr.counitIso_inv_app_val_app, CategoryTheory.Arrow.hom_inv_id_left_assoc, HomologicalComplex.singleObjHomologySelfIso_inv_homologyι, HomologicalComplex.mapBifunctorAssociatorX_hom_D₁_assoc, CategoryTheory.StructuredArrow.mapNatIso_functor_map_left, CategoryTheory.Limits.Types.binaryCoproductIso_inl_comp_hom, toLinearMap_toLinearEquiv, CategoryTheory.GradedObject.ι_mapBifunctorLeftUnitor_hom_apply_assoc, CategoryTheory.GradedObject.Monoidal.tensorIso_hom, TopCat.Presheaf.presheafEquivOfIso_functor_obj_map, AlgebraicGeometry.Scheme.isoOfEq_hom, CategoryTheory.Functor.mapDerivedCategoryFactorsh_hom_app, CategoryTheory.sum.inlCompInverseAssociator_hom_app_down_down, CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv_hom_id, CategoryTheory.Limits.HasBiproductsOfShape.colimIsoLim_inv_app, CategoryTheory.StructuredArrow.mapNatIso_counitIso_inv_app_right, CategoryTheory.ShortComplex.opcyclesIsoX₂_hom_inv_id, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_hom_app_unop, SemiNormedGrp₁.inv_hom_apply, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_zero, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_assoc, CategoryTheory.CechNerveTerminalFrom.wideCospan.limitIsoPi_hom_comp_pi, CategoryTheory.OplaxFunctor.mapComp'_comp_whiskerLeft_mapComp'_assoc, groupHomology.chainsMap_f_1_comp_chainsIso₁_apply, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃'_associator_hom_assoc, CategoryTheory.Localization.Monoidal.associator_naturality₁, AlgebraicGeometry.Scheme.Spec.residue_residueFieldIso_hom, CategoryTheory.ProjectiveResolution.fromLeftDerivedZero_eq, CategoryTheory.oppositeShiftFunctorAdd'_inv_app, CategoryTheory.Equivalence.symmEquivInverse_obj_unitIso_hom, CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit, CategoryTheory.Limits.CatCospanTransform.comp_whiskerLeft, HomologicalComplex.Hom.isoApp_hom, CategoryTheory.LocalizerMorphism.smallShiftedHomMap_mk₀, CategoryTheory.Presieve.isSheafFor_ofArrows_comp_iff, Bicategory.Opposite.op2_associator_hom, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.counitIso_hom, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_hom, CategoryTheory.BraidedCategory.braiding_naturality_right_assoc, groupCohomology.isoCocycles₁_hom_comp_i_assoc, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_appTop, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_functor_map_right, CategoryTheory.Subobject.isoOfEqMk_hom, Action.resCongr_hom, CategoryTheory.Limits.biproduct.conePointUniqueUpToIso_hom, CategoryTheory.Abelian.DoldKan.comparisonN_inv_app_f, HomologicalComplex.homologyFunctorSingleIso_hom_app, CategoryTheory.Dial.leftUnitorImpl_hom_f, CategoryTheory.MonoidalCategory.id_whiskerLeft_symm, CategoryTheory.right_unitality_app, CategoryTheory.Limits.Cones.postcomposeComp_hom_app_hom, AlgebraicGeometry.Scheme.localRingHom_comp_stalkIso_apply, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_inv_τr, CategoryTheory.Equivalence.adjointify_η_ε, CategoryTheory.Dial.rightUnitorImpl_hom_f, CategoryTheory.MonoidalCategory.tensor_right_unitality_assoc, CategoryTheory.FunctorToTypes.map_hom_map_inv_apply, HomologicalComplex.singleObjOpcyclesSelfIso_hom_assoc, BddDistLat.hom_inv_apply, CategoryTheory.MonoidalCategory.pentagon, CategoryTheory.Pretriangulated.binaryProductTriangleIsoBinaryBiproductTriangle_hom_hom₃, CategoryTheory.Bicategory.rightZigzagIso_hom, SemimoduleCat.MonoidalCategory.pentagon, CategoryTheory.Functor.OplaxMonoidal.left_unitality_hom_assoc, CategoryTheory.WithTerminal.liftToTerminalUnique_hom_app, CategoryTheory.Limits.diagramIsoSpan_hom_app, TopologicalSpace.OpenNhds.inclusionMapIso_hom_app, CategoryTheory.Functor.FullyFaithful.hasShift.map_zero_hom_app, CategoryTheory.Functor.Fiber.fiberInclusionCompIsoConst_hom_app, CategoryTheory.Functor.leftKanExtensionIsoFiberwiseColimit_inv_app, CategoryTheory.ShortComplex.leftRightHomologyComparison'_fac_assoc, CategoryTheory.Monoidal.leftUnitor_hom, HomologicalComplex.singleObjHomologySelfIso_hom_singleObjHomologySelfIso_inv, CategoryTheory.CartesianMonoidalCategory.rightUnitor_hom, AlgebraicGeometry.pullbackSpecIso_hom_fst_assoc, CategoryTheory.Limits.inl_pushoutZeroZeroIso_hom, CategoryTheory.Equivalence.core_counitIso_inv_app_iso_inv, CategoryTheory.PreGaloisCategory.evaluation_aut_injective_of_isConnected, CategoryTheory.Join.InclRightCompRightOpOpEquivFunctor_hom_app, CategoryTheory.Equivalence.unit_app_tensor_comp_inverse_map_δ_functor, CategoryTheory.Functor.RightExtension.postcompose₂ObjMkIso_hom_left_app, HomologicalComplex₂.totalFlipIsoX_hom_D₁_assoc, CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp_hom_hom₂, CategoryTheory.Limits.cokernelEpiComp_hom, CategoryTheory.Bicategory.InducedBicategory.bicategory_leftUnitor_hom_hom, CategoryTheory.Limits.Bicones.ext_hom_hom, map_hom_inv_id_eval_app, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_hom_app, CategoryTheory.Pseudofunctor.Grothendieck.categoryStruct_comp_fiber, AlgebraicGeometry.Scheme.Pullback.Triplet.tensorCongr_inv, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoImage_ι_assoc, AlgebraicGeometry.Scheme.Modules.pseudofunctor_associativity, CategoryTheory.MonoidalCategory.tensor_whiskerLeft_symm, CategoryTheory.NatTrans.CommShiftCore.app_shift_assoc, CategoryTheory.Limits.biprod.braid_natural_assoc, CategoryTheory.ShortComplex.homologyIsoImageICyclesCompPOpcycles_ι_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.inv_hom_actionHomLeft, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app, Bicategory.Opposite.bicategory_rightUnitor_hom_unop2, CategoryTheory.Comma.mapLeftComp_hom_app_right, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_μ_assoc, CategoryTheory.Limits.HasZeroObject.zeroIsoInitial_hom, HomologicalComplex.singleObjOpcyclesSelfIso_hom_naturality, CategoryTheory.Pretriangulated.binaryProductTriangleIsoBinaryBiproductTriangle_hom_hom₁, CategoryTheory.Limits.ι_colimitOfIsReflexivePairIsoCoequalizer_hom_assoc, CategoryTheory.Limits.colimit.pre_eq, CategoryTheory.shiftFunctorAdd'_assoc_hom_app, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.iso_hom_naturality, CategoryTheory.MonoidalCategory.tensor_hom_inv_id, CategoryTheory.Functor.rightKanExtensionUnique_hom, CategoryTheory.Functor.unopComp_hom_app, CategoryTheory.Functor.OplaxMonoidal.right_unitality_hom_assoc, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberCompIso_hom_app, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₁, CategoryTheory.Limits.Types.coproductIso_ι_comp_hom, CategoryTheory.Functor.compFlipUncurryIso_hom_app, CategoryTheory.Grothendieck.transportIso_hom_fiber, MonCat.inv_hom_apply, CategoryTheory.SingleFunctors.postcomp_shiftIso_hom_app, CategoryTheory.Pseudofunctor.CoGrothendieck.compIso_hom_app, HomologicalComplex.extendHomologyIso_hom_homologyι, CategoryTheory.whiskeringLeftCompEvaluation_hom_app, HomologicalComplex.mkHomFromDouble_f₁_assoc, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_unitIso_inv_app_right_app, CoalgEquiv.toCoalgIso_hom, CategoryTheory.Limits.Cocones.extendIso_inv_hom, CategoryTheory.Join.mkFunctorRight_hom_app, Rep.FiniteCyclicGroup.resolution.π_f, CategoryTheory.Mon.mkIso'_hom_hom, CategoryTheory.FunctorToTypes.binaryProductIso_hom_comp_fst, SemimoduleCat.MonoidalCategory.braiding_naturality_left, CategoryTheory.Limits.inr_comp_pushoutSymmetry_hom, HomologicalComplex.restriction.sc'Iso_hom_τ₁, CategoryTheory.WithTerminal.coneEquiv_counitIso_hom_app_hom, CategoryTheory.Pseudofunctor.mapComp'_hom_comp_mapComp'_hom_whiskerRight, CategoryTheory.WithInitial.mapId_hom_app, CategoryTheory.MonoidalCategory.tensoringRight_η, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τr, CategoryTheory.rightUnitor_hom_apply, Condensed.lanPresheafIso_hom, CategoryTheory.InjectiveResolution.rightDerived_app_eq, CategoryTheory.Abelian.coimIsoIm_hom_app, CategoryTheory.Limits.diagonal_pullback_fst, CategoryTheory.ShortComplex.LeftHomologyData.liftCycles_comp_cyclesIso_hom, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_left, NonemptyFinLinOrd.Iso.mk_hom, CategoryTheory.ObjectProperty.isoInv_hom_id_hom, CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_hom, CategoryTheory.Limits.cokernelImageι_hom, CategoryTheory.Functor.CommShift.isoAdd'_inv_app, AddEquiv.toAddCommMonCatIso_hom, CategoryTheory.Localization.associator_hom_app_app_app, CategoryTheory.Bicategory.triangle_assoc, CategoryTheory.Limits.inr_coprodZeroIso_hom, CategoryTheory.Functor.CommShift.OfComp.map_iso_hom_app, CategoryTheory.Functor.CommShift.OfComp.map_iso_inv_app_assoc, CategoryTheory.Functor.CommShift.isoZero'_hom_app, Action.β_hom_hom, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst_assoc, AlgebraicGeometry.LocallyRingedSpace.iso_hom_base_inv_base_apply, CategoryTheory.Localization.Monoidal.map_hexagon_forward_assoc, CategoryTheory.TwoSquare.GuitartExact.whiskerVertical, CategoryTheory.MonoidalCategory.leftUnitorNatIso_hom_app, CategoryTheory.Limits.Cocones.precomposeEquivalence_counitIso, CategoryTheory.Sigma.natIso_hom, CategoryTheory.SemiCartesianMonoidalCategory.snd_def, CategoryTheory.MonObj.one_mul_hom, CategoryTheory.Limits.limitOpIsoOpColimit_hom_comp_ι, CategoryTheory.Mat_.additiveObjIsoBiproduct_hom_π_assoc, CategoryTheory.MonoidalCategory.associator_inv_conjugation, CategoryTheory.CostructuredArrow.mapIso_counitIso_inv_app_left, CategoryTheory.Center.whiskerLeft_comm_assoc, CategoryTheory.BraidedCategory.hexagon_forward_assoc, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₁, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst_assoc, germ_skyscraperPresheafStalkOfSpecializes_hom, CategoryTheory.Limits.cokernel.congr_hom, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_obj_obj_map, CategoryTheory.OplaxFunctor.map₂_rightUnitor_app_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_inv_fac_assoc, CategoryTheory.Oplax.StrongTrans.vcomp_naturality_inv, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict_assoc, CategoryTheory.MonoidalCategory.hom_inv_id_tensor, CategoryTheory.GradedObject.ι_mapBifunctorComp₂₃MapObjIso_hom_assoc, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv, CategoryTheory.Limits.prod.associator_naturality, CategoryTheory.shiftFunctorAdd_zero_add_inv_app, hom_inv_id_app_app_app, Action.leftUnitor_hom_hom, CategoryTheory.shiftFunctorComm_hom_app_of_add_eq_zero_assoc, AlgebraicGeometry.SheafedSpace.restrictTopIso_hom, CategoryTheory.Pi.right_unitor_hom_apply, AlgebraicGeometry.Scheme.stalkMap_congr, CategoryTheory.Bicategory.associator_naturality_middle_assoc, CategoryTheory.Limits.instIsIsoHomHomCone, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_hom_app_hom, HomologicalComplex.ιOrZero_mapBifunctorAssociatorX_hom_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.eq_one_mul, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.w_app_assoc, CategoryTheory.MonoidalCategory.associator_naturality_right_assoc, CochainComplex.liftCycles_shift_homologyπ, HomologicalComplex.natIsoSc'_hom_app_τ₁, CategoryTheory.prod.functorProdToProdFunctorAssociator_hom_app, CategoryTheory.StructuredArrow.mapIso_counitIso_hom_app_right, CategoryTheory.Pseudofunctor.toOplax_mapComp', CategoryTheory.Adjunction.mapCommGrp_counit, CategoryTheory.Over.iteratedSliceForwardIsoPost_hom_app, CategoryTheory.Functor.LaxMonoidal.ofBifunctor.secondMap_app_app_app, CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_inv_assoc, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom, CategoryTheory.Functor.mapTriangle_map_hom₂, CategoryTheory.LaxFunctor.map₂_leftUnitor_hom, CategoryTheory.Pi.comapEvalIsoEval_hom_app, groupHomology.isoCycles₂_hom_comp_i_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_hom, CategoryTheory.Equivalence.congrRight_counitIso_hom_app, CategoryTheory.Bicategory.Adj.leftUnitor_hom_τl, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop_assoc, map_inv_hom_id_eval_app_assoc, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_hom_whiskerLeft_π, groupHomology.comp_d₃₂_eq, groupCohomology.π_comp_H2Iso_hom, CategoryTheory.ExponentiableMorphism.unit_pushforwardComp_hom_assoc, CategoryTheory.WithInitial.mapComp_hom_app, CategoryTheory.Idempotents.DoldKan.η_hom_app_f, groupHomology.chainsMap_f_0_comp_chainsIso₀, CategoryTheory.Limits.π_comp_opProductIsoCoproduct_hom, AlgebraicGeometry.Scheme.inv_base_hom_base, CategoryTheory.Functor.lanCompColimIso_hom_app, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_hom_iso, CommMonCat.hom_inv_apply, CategoryTheory.Bicategory.Equivalence.left_triangle_hom, HomologicalComplex.cyclesMapIso_hom, CategoryTheory.Sigma.inclDesc_hom_app, CategoryTheory.Limits.ι_colimitConstInitial_hom_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_hom_app_app, CategoryTheory.OplaxFunctor.mapComp_id_left, commSemiRingCatIsoToRingEquiv_toRingHom, CategoryTheory.GradedNatTrans.naturality, CategoryTheory.Arrow.iso_w', CategoryTheory.StructuredArrow.mapIso_counitIso_inv_app_right, CategoryTheory.ShiftMkCore.assoc_hom_app_assoc, CategoryTheory.Equivalence.changeFunctor_counitIso_inv_app, AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_app, AlgebraicGeometry.Scheme.Hom.inr_normalizationCoprodIso_hom_fromNormalization, HomologicalComplex.homologyπ_restrictionHomologyIso_hom_assoc, CategoryTheory.BraidedCategory.braiding_tensor_right_inv, CategoryTheory.Comma.mapRightIso_unitIso_hom_app_right, CategoryTheory.GlueData.diagramIso_hom_app_left, ModuleCat.extendScalars_assoc, CategoryTheory.Equivalence.congrRight_unitIso_inv_app, CategoryTheory.NatIso.inv_inv_app, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_right, CategoryTheory.shift_neg_shift', CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIsoWhisker_hom_right, CategoryTheory.Bicategory.triangle_assoc_comp_right_assoc, SheafOfModules.pushforwardNatTrans_comp, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_hom_whiskerRight_π, CategoryTheory.Adjunction.mapGrp_counit, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_counitIso_hom, MonCat.hom_inv_apply, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_obj_obj_map, CategoryTheory.Limits.ConeMorphism.inv_hom_id, commGroupIsoToMulEquiv_apply, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app_assoc, inv_eq_inv, HomologicalComplex₂.totalFlipIso_hom_f_D₂_assoc, inv_hom_id_eval, HomologicalComplex.pOpcycles_restrictionOpcyclesIso_hom, CategoryTheory.Limits.limit_map_limitObjIsoLimitCompEvaluation_hom, CategoryTheory.ShortComplex.cyclesMapIso_hom, HomologicalComplex₂.ι_totalShift₁Iso_hom_f, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app_assoc, CategoryTheory.ShiftedHom.opEquiv'_add_symm, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_hom_app, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_inv_fac, CategoryTheory.Bicategory.rightUnitorNatIso_hom_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app, CategoryTheory.Pi.comapId_hom_app, QuadraticModuleCat.hom_hom_associator, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_inv_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd_assoc, CategoryTheory.Functor.leftKanExtensionUnique_hom, AddMagmaCat.hom_neg_apply, CategoryTheory.Limits.pullbackObjIso_hom_comp_snd, CategoryTheory.MonoidalCategory.associator_naturality_right, CategoryTheory.Abelian.PreservesCoimage.iso_hom_π, CategoryTheory.Quiv.equivOfIso_apply, CategoryTheory.BraidedCategory.ofBifunctor.Forward.firstMap₃_app_app_app, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply, CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_hom_hom_assoc, CategoryTheory.Limits.PreservesPushout.iso_hom, CategoryTheory.Bicategory.leftUnitor_comp_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_hom_app, CategoryTheory.Functor.mapCommMonCompIso_hom_app_hom_hom, CategoryTheory.associator_hom, CategoryTheory.Limits.ι_comp_colimitUnopIsoOpLimit_hom, AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_fst, CategoryTheory.functorProdFunctorEquivCounitIso_hom_app_app, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_right_assoc, SemimoduleCat.MonoidalCategory.associator_hom_apply, CochainComplex.ι_mapBifunctorShift₁Iso_hom_f, CategoryTheory.Adjunction.rightAdjointUniq_inv_app, CategoryTheory.NatIso.ofComponents_hom_app, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_app_assoc, CochainComplex.ShiftSequence.shiftIso_hom_app, CategoryTheory.MonoidalCategory.tensoringRight_μ, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_app, addCommGroupIsoToAddEquiv_apply, groupHomology.chainsMap_f_2_comp_chainsIso₂_apply, CategoryTheory.Limits.pullbackProdSndIsoProd_hom_fst_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_shift, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_assoc, CategoryTheory.Limits.CatCospanTransform.rightUnitor_hom_right_app, CategoryTheory.mateEquiv_apply, CategoryTheory.CartesianMonoidalCategory.leftUnitor_hom, groupHomology.cyclesMap_comp_isoCycles₁_hom, CategoryTheory.ShortComplex.mapCyclesIso_hom_naturality, CategoryTheory.ShortComplex.cyclesOpIso_hom_naturality_assoc, CategoryTheory.CartesianMonoidalCategory.whiskerRight_toUnit_comp_leftUnitor_hom_assoc, HomologicalComplex.Hom.prev_eq, CategoryTheory.InjectiveResolution.cochainComplex_d, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanMapIso_hom, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app_assoc, HomotopyCategory.instCommShiftHomologicalComplexIntUpHomFunctorMapHomotopyCategoryFactors, CochainComplex.mappingCone.map_δ, AlgEquiv.toAlgebraIso_hom, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_εIso_hom, CategoryTheory.Functor.isRightKanExtensionAlongEquivalence, CochainComplex.ConnectData.restrictionGEIso_hom_f, CategoryTheory.Limits.parallelPairOpIso_hom_app_zero, CategoryTheory.IsSubterminal.isoDiag_hom, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerRight_naturality_assoc, Homotopy.mkInductiveAux₂_add_one, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_hom, AlgebraicGeometry.pullbackSpecIso_hom_snd_assoc
homFromEquiv 📖	CompOp	3 math math: homFromEquiv_symm_apply, CategoryTheory.Functor.CorepresentableBy.ofIsoObj_homEquiv, homFromEquiv_apply
homToEquiv 📖	CompOp	3 math math: homToEquiv_apply, homToEquiv_symm_apply, CategoryTheory.Functor.RepresentableBy.ofIsoObj_homEquiv
instInhabited 📖	CompOp	—
instTransIso 📖	CompOp	1 math math: trans_def
inv 📖	CompOp	4806 math math: CategoryTheory.Grp.mkIso_inv_hom, CategoryTheory.Localization.Monoidal.leftUnitor_hom_app, inv_hom_id_triangle_hom₃_assoc, CategoryTheory.shiftFunctorZero_inv_app_obj_of_induced, CategoryTheory.Limits.IsImage.e_isoExt_inv, CategoryTheory.Adjunction.adjToComonadIso_inv_toNatTrans_app, Action.resCongr_inv, CategoryTheory.MorphismProperty.LeftFraction.map_compatibility, CategoryTheory.GrothendieckTopology.overMapPullbackId_hom_app_val_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_eq, CategoryTheory.InjectiveResolution.Hom.hom'_f, CategoryTheory.Pseudofunctor.mapComp'_naturality_1_assoc, AlgebraicGeometry.AffineSpace.map_Spec_map, CategoryTheory.Join.pseudofunctorLeft_mapId_inv_toNatTrans_app, CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv_assoc, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₁, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_assoc, Representation.repOfTprodIso_inv_apply, CategoryTheory.MonoidalCategory.tensor_left_unitality, CategoryTheory.Functor.FullyFaithful.homNatIsoMaxRight_inv_app, CategoryTheory.Quiv.equivOfIso_symm_apply, AlgCat.hom_inv_apply, CategoryTheory.Functor.CommShift.isoAdd_hom_app, smoothSheafCommRing.ι_forgetStalk_inv, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerLeftIso_inv_app, SSet.Truncated.HomotopyCategory.BinaryProduct.iso_inv_toFunctor, CommBialgCat.ofSelfIso_inv, CategoryTheory.Enriched.Functor.associator_inv_apply, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_map, CategoryTheory.Dial.braiding_inv_f, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitNatIso_inv_app, CategoryTheory.LaxBraidedFunctor.isoMk_inv, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_inv_fac_app, AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality_assoc, CategoryTheory.Functor.isoSum_inv_app_inl, HomologicalComplex.extendSingleIso_inv_f, CategoryTheory.Equivalence.leftOp_unitIso_hom_app, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_hom_app_val_app, CategoryTheory.Functor.mapTriangleIdIso_inv_app_hom₃, DistLat.hom_inv_apply, CategoryTheory.Monad.monadMonEquiv_unitIso_inv_app_toNatTrans_app, prod_inv, CategoryTheory.ComposableArrows.opEquivalence_counitIso_inv_app_app, CategoryTheory.Pseudofunctor.DescentData.ofObj_hom, HomologicalComplex.restrictionToTruncGE'_f_eq_iso_hom_pOpcycles_iso_inv, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_apply, CategoryTheory.Functor.coreComp_hom_app_iso_inv, CategoryTheory.Functor.mapComposableArrowsObjMk₂Iso_inv_app, CategoryTheory.Discrete.sumEquiv_counitIso_inv_app, CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc, CategoryTheory.Functor.OplaxMonoidal.δ_comp_tensorHom_η, CategoryTheory.eHom_whisker_cancel, CategoryTheory.Pseudofunctor.map₂_associator_assoc, CategoryTheory.shiftFunctorAdd'_assoc_inv_app, AlgebraicGeometry.Scheme.isoOfEq_inv, CategoryTheory.MonoidalCategory.MonoidalRightAction.unit_actionHomRight_assoc, CategoryTheory.kernelUnopOp_inv, typeToPartialFunIsoPartialFunToPointed_inv_app_toFun, CategoryTheory.PreZeroHypercover.inv_hom_h₀, CategoryTheory.CommComon.trivial_comon_comul, CategoryTheory.StructuredArrow.isoMk_inv_right, ModuleCat.biproductIsoPi_inv_comp_π, CategoryTheory.Functor.sheafPushforwardContinuousIso_inv, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app', CategoryTheory.NatIso.mapHomologicalComplex_inv_app_f, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.Equivalence.sheafCongr.counitIso_hom_app_val_app, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv_assoc, CategoryTheory.ComposableArrows.sc'MapIso_inv, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_appTop, CategoryTheory.Limits.biproduct.mapBiproduct_inv_map_desc, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp_inv_app_f, CategoryTheory.LaxFunctor.whiskerLeft_mapComp'_comp_mapComp'_assoc, CommSemiRingCat.hom_inv_apply, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_hom_inv_assoc, CategoryTheory.Functor.IsStronglyCartesian.domainUniqueUpToIso_hom_isHomLift, AlgebraicGeometry.Scheme.Modules.pushforwardId_inv_app_app, CategoryTheory.IsPullback.isoIsPullback_inv_snd_assoc, RingEquiv.toRingCatIso_inv, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_fst_assoc, CategoryTheory.obj_ε_app_assoc, HomologicalComplex.rightUnitor'_inv, CategoryTheory.Bicategory.Comonad.comul_assoc_flip, TopCat.isoOfHomeo_inv, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_associator, CategoryTheory.Adjunction.whiskerLeftLCounitIsoOfIsIsoUnit_inv_app, CategoryTheory.Limits.ConeMorphism.hom_inv_id, CategoryTheory.BraidedCategory.braiding_tensor_right_hom, CategoryTheory.Functor.LaxMonoidal.whiskerLeft_μ_comp_μ_assoc, CategoryTheory.ShortComplex.cyclesOpIso_inv_op_iCycles_assoc, Action.leftRegularTensorIso_inv_hom, CategoryTheory.EnrichedOrdinaryCategory.homEquiv_comp, CategoryTheory.Comma.mapLeftEq_inv_app_right, CategoryTheory.Limits.PreservesPushout.inr_iso_inv_assoc, CategoryTheory.Functor.ι_colimitIsoOfIsLeftKanExtension_inv_assoc, CategoryTheory.Functor.shiftIso_add_inv_app, CategoryTheory.Limits.colimitIsoFlipCompColim_inv_app, CategoryTheory.Functor.Monoidal.μNatIso_inv_app, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_snd, eHomCongr_inv_comp_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_hom_app_eq, CategoryTheory.shiftFunctorComm_zero_hom_app, CategoryTheory.op_hom_leftUnitor, CategoryTheory.IsPullback.isoIsPullback_inv_snd, AddCommGrpCat.biproductIsoPi_inv_comp_π_apply, CategoryTheory.ShortComplex.pOpcycles_π_isoOpcyclesOfIsColimit_inv_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_assoc, HomologicalComplex.singleMapHomologicalComplex_hom_app_self, CategoryTheory.Subobject.underlyingIso_arrow_assoc, CategoryTheory.Functor.Monoidal.rightUnitor_inv_app, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_hom_app_app_down, groupHomology.map₁_quotientGroupMk'_epi, AlgebraicGeometry.StructureSheaf.globalSectionsIso_inv, CategoryTheory.MonoidalOpposite.unmopFunctor_δ, HomologicalComplex.truncGE.rightHomologyMapData_φQ, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_inv_app_val_app, CategoryTheory.NatTrans.unop_whiskerLeft, CategoryTheory.Localization.Preadditive.homEquiv_symm_apply, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_hom_inv, CategoryTheory.SmallObject.SuccStruct.prop.arrowIso_inv_left, CategoryTheory.e_comp_id, CategoryTheory.Limits.colimit.isoColimitCocone_ι_inv, CategoryTheory.Functor.CommShift.isoAdd_inv_app, AlgebraicGeometry.Scheme.Hom.app_invApp'_assoc, CategoryTheory.MonoidalCategory.tensor_inv_hom_id_assoc, CategoryTheory.Join.pseudofunctorRight_mapComp_inv_toNatTrans_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_whiskerRight, CategoryTheory.Limits.diagramIsoCospan_inv_app, Action.inv_hom_hom_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app_assoc, Bicategory.Opposite.op2_associator_inv, CategoryTheory.Limits.cokernelImageι_inv, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_snd_snd_assoc, CategoryTheory.Pseudofunctor.map₂_associator_app_assoc, CategoryTheory.Functor.OplaxMonoidal.δ_comp_η_tensorHom_assoc, CategoryTheory.Enriched.FunctorCategory.enriched_id_comp, CategoryTheory.NatTrans.naturality_2, CategoryTheory.SmallObject.SuccStruct.extendToSucc_map_le_succ, ModuleCat.restrictScalarsId'App_inv_naturality_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_inv_app, CategoryTheory.HasShift.Induced.add_inv_app_obj, AlgCat.hom_inv_associator, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_inv_app_hom, CategoryTheory.Pseudofunctor.DescentData.pullFunctorCompIso_inv_app_hom, CategoryTheory.Limits.isoZeroBiprod_inv, CategoryTheory.biproduct_ι_comp_rightDistributor_inv, CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_inv_comp_iCycles_assoc, AlgebraicGeometry.Proj.basicOpenIsoSpec_inv_ι_assoc, CategoryTheory.Oplax.OplaxTrans.Modification.whiskerRight_naturality, SSet.horn₃₁.desc.multicofork_π_two, groupHomology.coinvariantsMk_comp_H0Iso_inv_apply, CategoryTheory.Functor.mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app_assoc, comp_inv_eq, CategoryTheory.PullbackShift.adjunction_counit, CategoryTheory.Bicategory.leftUnitor_inv_naturality_assoc, CategoryTheory.ExactPairing.evaluation_coevaluation, CategoryTheory.Functor.mapCommGrpCompIso_inv_app_hom_hom_hom, CategoryTheory.Sum.functorEquivFunctorCompFstIso_inv_app_app, CategoryTheory.IsPullback.isoPullback_inv_fst, CategoryTheory.Functor.mapCommMonNatIso_inv_app_hom_hom, CategoryTheory.ExactPairing.coevaluation_evaluation', CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₁, CategoryTheory.Limits.Cones.equivalenceOfReindexing_inverse, CategoryTheory.Quotient.natIsoLift_inv, CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom, CategoryTheory.Lax.StrongTrans.vComp_naturality_hom, HomologicalComplex.pOpcycles_singleObjOpcyclesSelfIso_inv, CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp_inv_hom₁, CategoryTheory.Limits.initialMul_inv, CategoryTheory.Functor.mapTriangleIso_inv_app_hom₁, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_whiskerRight, CategoryTheory.Bicategory.whiskerLeft_inv_hom, CategoryTheory.Over.associator_inv_left_snd, CategoryTheory.Discrete.sumEquiv_unitIso_inv_app, CategoryTheory.Functor.sheafPushforwardContinuousComp'_inv_app_val_app, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_leftUnitor, CategoryTheory.MonoidalCategory.inv_hom_id_tensor_assoc, Rep.diagonalSuccIsoFree_inv_hom_single, CategoryTheory.Bicategory.Adj.associator_inv_τr, CategoryTheory.InjectiveResolution.isoRightDerivedToHomotopyCategoryObj_inv_naturality_assoc, CategoryTheory.Bicategory.Prod.sectL_mapId_inv, CategoryTheory.Functor.instIsRightDerivedFunctorLiftInvFac, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app, CategoryTheory.Mon.leftUnitor_inv_hom, CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_hom_inv_id, CategoryTheory.SimplicialThickening.SimplicialCategory.comp_id, CategoryTheory.CartesianMonoidalCategory.associator_inv_fst_fst, CategoryTheory.whiskerLeft_coprod_inr_leftDistrib_inv, HomologicalComplex.homologyπ_restrictionHomologyIso_inv_assoc, TopCat.Presheaf.Pushforward.id_inv_app, CategoryTheory.MonoidalCategory.tensorRightTensor_hom_app, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₃, CategoryTheory.MonoidalCategory.tensorLeftTensor_inv_app, CategoryTheory.Limits.CatCospanTransform.comp_whiskerLeft_assoc, 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.Center.braiding_inv_f, CategoryTheory.Equivalence.counitIso_inv_app_comp_functor_map_η_inverse, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_fst_snd_assoc, CategoryTheory.Bicategory.whiskerRight_comp_assoc, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_functor, CategoryTheory.Functor.mapTriangleIso_inv_app_hom₃, CategoryTheory.Under.postComp_inv_app_right, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight_assoc, Rep.coindResAdjunction_counit_app, CategoryTheory.BraidedCategory.braiding_tensor_right_hom_assoc, HomologicalComplex.opcyclesIsoSc'_inv_fromOpcycles, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom, inv_ext', HomologicalComplex.singleObjOpcyclesSelfIso_hom, AlgebraicGeometry.Scheme.restrictFunctorΓ_inv_app, CategoryTheory.op_inv_associator, CategoryTheory.Limits.ConeMorphism.inv_hom_id_assoc, HomologicalComplex.singleObjCyclesSelfIso_inv_iCycles, CategoryTheory.Bicategory.InducedBicategory.bicategory_associator_inv_hom, partialFunEquivPointed_counitIso_inv_app_toFun, CategoryTheory.Functor.isoSum_inv_app_inr, imageToKernel_unop, CategoryTheory.Functor.IsEventuallyConstantTo.coneπApp_eq, CategoryTheory.Limits.map_π_preserves_coequalizer_inv_colimMap, CategoryTheory.Functor.OplaxMonoidal.left_unitality, AlgebraicGeometry.Scheme.Hom.inr_toNormalization_normalizationCoprodIso_inv, CategoryTheory.Limits.cospanIsoMk_inv_app, CategoryTheory.Over.inv_left_hom_left_assoc, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₂, CategoryTheory.IsPullback.isoPullback_inv_snd_assoc, SSet.horn.faceSingletonComplIso_inv_ι_assoc, CategoryTheory.Limits.pullbackSymmetry_inv_comp_snd_assoc, CategoryTheory.Bicategory.inv_hom_whiskerRight_whiskerRight_assoc, commBialgCatEquivComonCommAlgCat_unitIso_inv_app, CategoryTheory.Bicategory.Adj.rIso_inv, CategoryTheory.Bicategory.mateEquiv_comp_id_right, CategoryTheory.Limits.parallelPairOpIso_inv_app_zero, CategoryTheory.shift_shift', CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_hom, CategoryTheory.Limits.HasColimit.isoOfEquivalence_inv_π, CategoryTheory.InjectiveResolution.ι'_f_zero, SheafOfModules.pushforwardNatIso_inv, CategoryTheory.FreeMonoidalCategory.normalizeIsoAux_inv_app, prodIsoPullback_inv_fst, CategoryTheory.Limits.Types.coequalizerIso_quot_comp_inv, HomologicalComplex.opcyclesMapIso_inv, CategoryTheory.Bicategory.inv_hom_whiskerRight_assoc, CategoryTheory.Functor.CorepresentableBy.uniqueUpToIso_inv, CategoryTheory.Idempotents.functorExtension₁CompWhiskeringLeftToKaroubiIso_inv_app_app_f, CategoryTheory.Bicategory.inv_hom_whiskerRight, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_comp, CochainComplex.augmentTruncate_inv_f_zero, CategoryTheory.LaxFunctor.map₂_leftUnitor_assoc, CategoryTheory.Functor.OplaxRightLinear.δᵣ_unitality_inv, groupCohomology.eq_d₀₁_comp_inv, CategoryTheory.Adjunction.mapMon_unit, core_inv_app_iso_hom, CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_left_app, CategoryTheory.Quiv.homEquivOfIso_symm_apply, CategoryTheory.Under.forgetMapInitial_inv_app, CategoryTheory.Bicategory.pentagon_inv, CategoryTheory.Limits.equalizerSubobject_arrow'_assoc, CategoryTheory.MonoidalCategory.associator_inv_naturality_right_assoc, CategoryTheory.ShortComplex.cyclesIsoX₂_hom_inv_id, groupHomology.cyclesIso₀_inv_comp_iCycles_apply, CategoryTheory.Arrow.hom_inv_id_right_assoc, SemiRingCat.inv_hom_apply, AlgebraicGeometry.AffineSpace.SpecIso_hom_appTop, CategoryTheory.Limits.HasLimit.isoOfNatIso_inv_π_assoc, CategoryTheory.IsHomLift.inv_lift, CategoryTheory.MonoidalCategory.pentagon_hom_inv_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocIso_inv_naturality, CategoryTheory.Over.mapIso_inverse, CategoryTheory.Functor.map_shiftFunctorComm_hom_app, CategoryTheory.Comma.map_final, groupHomology.H0IsoOfIsTrivial_inv_eq_π, CategoryTheory.WithTerminal.liftStar_inv, CategoryTheory.Paths.liftNatIso_inv_app, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_rightHomologyIso_inv, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_ι_inv, CategoryTheory.Limits.coprod.associator_inv, CategoryTheory.Equivalence.rightOp_counitIso_inv_app, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_assoc, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_inv_eq_germ_assoc, FintypeCat.uSwitch_map_uSwitch_map, CategoryTheory.Functor.unopOpIso_inv_app, CategoryTheory.GrothendieckTopology.overMapPullback_comp_id, CategoryTheory.Over.rightUnitor_inv_left_fst_assoc, HomologicalComplex.homologyι_singleObjOpcyclesSelfIso_inv_assoc, CommAlgCat.inv_hom_apply, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_fst, CategoryTheory.ShortComplex.RightHomologyData.p_comp_opcyclesIso_inv, CategoryTheory.Oplax.LaxTrans.vComp_naturality_id, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIso_inv_app_hom, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_fst, groupCohomology.eq_d₁₂_comp_inv, CategoryTheory.Limits.PreservesPushout.inr_iso_inv, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_id_fiber, AlgebraicTopology.DoldKan.N₂Γ₂ToKaroubiIso_inv_app, CategoryTheory.MonoidalClosed.ofEquiv_uncurry_def, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_inv_app, AlgebraicTopology.DoldKan.Γ₀NondegComplexIso_inv_f, AlgebraicGeometry.Scheme.Opens.topIso_inv, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition', CategoryTheory.CatCommSq.hInv_iso_inv_app, CategoryTheory.Functor.isDense_iff_nonempty_isPointwiseLeftKanExtension, CategoryTheory.GrothendieckTopology.overMapPullbackId_inv_app_val_app, CategoryTheory.FreeBicategory.mk_left_unitor_inv, CategoryTheory.Equivalence.leftOp_unitIso_inv_app, CategoryTheory.Limits.Cone.equiv_inv_pt, Sequential.homeoOfIso_symm_apply, CategoryTheory.Localization.isoOfHom_inv_hom_id, commGroupIsoToMulEquiv_symm_apply, CategoryTheory.InducedCategory.isoMk_inv, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality_assoc, AlgebraicGeometry.PresheafedSpace.isoOfComponents_inv, CategoryTheory.Functor.mapTriangleRotateIso_inv_app_hom₂, CategoryTheory.Limits.CatCospanTransform.leftIso_inv, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_obj_iso_inv, CategoryTheory.PreZeroHypercover.inv_hom_s₀_apply, AlgebraicTopology.DoldKan.identity_N₂, groupHomology.eq_d₃₂_comp_inv, CategoryTheory.MonObj.ofIso_mul, Homotopy.mkInductiveAux₃, CategoryTheory.Functor.shiftIso_hom_app_comp, CategoryTheory.Limits.FormalCoproduct.coproductIsoSelf_inv_f, CategoryTheory.monoidalOfHasFiniteProducts.associator_inv_fst_snd, CategoryTheory.Functor.Monoidal.commTensorRight_inv_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_assoc, SSet.opFunctorCompOpFunctorIso_inv_app_app, CategoryTheory.Pretriangulated.shiftFunctorZero_op_inv_app, inv_hom_id_triangle_hom₂, CategoryTheory.ShortComplex.RightHomologyMapData.homologyMap_eq, CategoryTheory.Functor.EssImageSubcategory.associator_inv_def, imageToKernel'_kernelSubobjectIso, CategoryTheory.Under.postCongr_inv_app_right, CategoryTheory.Join.inclRightCompOpEquivInverse_inv_app_op, CategoryTheory.CommGrp.mkIso_inv_hom, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_inv_app_hom, CategoryTheory.BraidedCategory.braiding_tensor_left_inv, Action.diagonalSuccIsoTensorDiagonal_inv_hom, HomologicalComplex.leftUnitor'_inv_comm, CategoryTheory.IsHomLift.inv_lift_inv, CategoryTheory.MonoidalCategory.triangle_assoc_comp_left_inv, CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_inv_assoc, CategoryTheory.Over.hom_left_inv_left, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id, CategoryTheory.MonoidalCategory.whiskerRightIso_inv, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left, CategoryTheory.MonoidalCategory.whiskerRight_tensor_symm, CategoryTheory.Functor.mapTriangleCompIso_inv_app_hom₂, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp_assoc, app_inv, CategoryTheory.Limits.biproduct.whiskerEquiv_inv, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_fst_fst, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_inv_left, CategoryTheory.Functor.leftOpRightOpEquiv_counitIso_inv_app_app, CategoryTheory.Adjunction.compCoyonedaIso_inv_app_app, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app, CategoryTheory.Limits.FormalCoproduct.isoOfComponents_inv_φ, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app_assoc, CategoryTheory.Monad.algebraFunctorOfMonadHomId_inv_app_f, CategoryTheory.GrothendieckTopology.OneHypercover.isoMk_inv, CategoryTheory.Dial.rightUnitorImpl_inv_f, CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_inv_app_app, Bimod.TensorBimod.right_assoc', CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app, CategoryTheory.Functor.fullyFaithfulCancelRight_inv_app, AlgebraicGeometry.diagonal_SpecMap, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapCompIso_inv, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_map_app_app, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_inv_app_hom_coe, CategoryTheory.GradedObject.singleObjApplyIso_inv_single_map, LightCondensed.isoFinYoneda_inv_app, eHomCongr_hom, CategoryTheory.Mathlib.Tactic.MonTauto.leftUnitor_inv_one_tensor_mul, AlgebraicGeometry.ι_right_coprodIsoSigma_inv, CategoryTheory.Functor.mapCoconePrecomposeEquivalenceFunctor_inv_hom, CategoryTheory.Functor.mapComposableArrowsObjMk₁Iso_inv_app, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_comp_naturality_hom, CategoryTheory.InjectiveResolution.isoRightDerivedToHomotopyCategoryObj_inv_naturality, AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_hom_app, CategoryTheory.Limits.Cocones.ext_inv_hom, CategoryTheory.Functor.mapCoconePrecompose_inv_hom, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict, CategoryTheory.simplicialCosimplicialEquiv_counitIso_inv_app_app, inv_hom_id, CategoryTheory.Limits.PushoutCocone.unop_π_app, CategoryTheory.EnrichedFunctor.forgetComp_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_inv_app, CategoryTheory.Limits.kernelSubobject_arrow'_apply, CategoryTheory.LaxBraidedFunctor.isoOfComponents_inv_hom_hom_app, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_leftUnitor_inv_hom, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app, CategoryTheory.Limits.diagramIsoParallelFamily_inv_app, CategoryTheory.NatIso.pi'_inv, CategoryTheory.unop_inv_associator, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv, CategoryTheory.ShortComplex.cyclesIsoX₂_hom_inv_id_assoc, SimplicialObject.opFunctor_obj_σ, CategoryTheory.braiding_tensorUnit_left_assoc, CategoryTheory.Limits.BinaryBicones.ext_inv_hom, CategoryTheory.Localization.Monoidal.associator_hom_app, CategoryTheory.Localization.Monoidal.pentagon_aux₁, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_snd_assoc, CategoryTheory.MonoidalCategory.leftUnitor_inv_comp_tensorHom_assoc, CochainComplex.isoHomologyπ₀_inv_naturality_assoc, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_inv_app, CategoryTheory.Functor.inlCompSum'_inv_app, CategoryTheory.Bicategory.InducedBicategory.bicategory_leftUnitor_inv_hom, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.unitIso_inv_app_f_f, CochainComplex.mappingCone.homologySequenceδ_triangleh, CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_self_succ, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_inv_naturality_assoc, CategoryTheory.Limits.yonedaCompLimIsoCocones_inv_app, CategoryTheory.e_id_comp, CategoryTheory.MonoidalCategory.associator_inv_naturality_right, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_app_assoc, CategoryTheory.Limits.mapPairIso_inv_app, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id_assoc, CategoryTheory.Limits.pullbackProdSndIsoProd_inv_fst_snd, HomologicalComplex.restriction.sc'Iso_inv_τ₃, CategoryTheory.CartesianMonoidalCategory.associator_inv_snd, CategoryTheory.Functor.shiftIso_zero_inv_app, isoInverseComp_inv_app, CategoryTheory.ShortComplex.cyclesIsoLeftHomology_hom_inv_id_assoc, CategoryTheory.Functor.Monoidal.coreMonoidalTransport_εIso_inv, Action.FunctorCategoryEquivalence.counitIso_inv_app_app, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp, CategoryTheory.Functor.OplaxLeftLinear.δₗ_associativity_inv, CategoryTheory.Functor.commShift₂_comm, CategoryTheory.Pseudofunctor.StrongTrans.leftUnitor_inv_as_app, AlgebraicGeometry.Scheme.ideal_ker_le_ker_ΓSpecIso_inv_comp, CategoryTheory.Comma.mapLeftIso_functor_map_left, map_inv_hom_id_app_assoc, AlgCat.hom_inv_rightUnitor, CategoryTheory.MonoidalCategory.leftUnitor_inv_whiskerRight, HomologicalComplex.opcyclesOpIso_inv_naturality_assoc, CategoryTheory.Functor.Fiber.fiberInclusionCompIsoConst_inv_app, HomologicalComplex.opcyclesIsoSc'_inv_fromOpcycles_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv, HomologicalComplex.inl_biprodXIso_inv_assoc, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_left, PresheafOfModules.limitPresheafOfModules_map, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_inv_app_coe, CategoryTheory.sheafificationNatIso_inv_app_val, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_inverse, CategoryTheory.NatIso.cancel_natIso_inv_right_assoc, Action.leftUnitor_inv_hom, AlgebraicGeometry.Scheme.isoSpec_inv_toSpecΓ, CategoryTheory.Limits.HasZeroObject.zeroIsoIsInitial_inv, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_inv_app_hom_apply, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₃, CategoryTheory.Functor.Monoidal.map_associator_inv_assoc, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_inv_app_app_hom_hom, CategoryTheory.ComonadIso.toNatIso_inv, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_inv_app_snd_app, AlgebraicGeometry.Scheme.hom_inv_apply, CategoryTheory.Bicategory.pentagon_hom_hom_inv_hom_hom_assoc, CategoryTheory.Oplax.OplaxTrans.categoryStruct_id_naturality, CategoryTheory.Pseudofunctor.mapId'_inv_naturality_assoc, CategoryTheory.Equivalence.leftOp_counitIso_inv_app, CategoryTheory.TransfiniteCompositionOfShape.fac_assoc, CategoryTheory.NatTrans.unop_whiskerLeft_assoc, CategoryTheory.Limits.coyonedaCompLimIsoCones_inv_app, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_inv_τr, Bimod.TensorBimod.whiskerLeft_π_actLeft, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_snd_assoc, CategoryTheory.Limits.inl_inr_pushoutAssoc_inv_assoc, CategoryTheory.MorphismProperty.Over.pullbackComp_hom_app_left, AlgCat.inv_hom_apply, CategoryTheory.Localization.SmallHom.equiv_equiv_symm, CategoryTheory.Functor.CommShift.isoZero_hom_app, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_inv_app_op_zero, CategoryTheory.LocalizerMorphism.commShift_iso_hom_app, CategoryTheory.Comma.mapRightIso_counitIso_inv_app_left, AlgebraicGeometry.Scheme.ι_toIso_inv, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.natTrans_app_uliftYoneda_obj, CategoryTheory.Bicategory.associatorNatIsoLeft_inv_app, CategoryTheory.MonoOver.isoMk_inv, CategoryTheory.Functor.rightDerivedNatIso_inv, CategoryTheory.Limits.limitConstTerminal_inv_π_assoc, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_right, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app, CategoryTheory.ShortComplex.isoMk_inv, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₂, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_inv_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_inv_app_snd_app, CategoryTheory.Equalizer.firstObjEqFamily_inv, CategoryTheory.Limits.Bicones.ext_inv_hom, CategoryTheory.Limits.coprod.braiding_inv, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_hom, RingEquiv.toCommSemiRingCatIso_inv, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app_assoc, CategoryTheory.Limits.Sigma.ι_isoColimit_inv, CategoryTheory.ShortComplex.LeftHomologyData.π_comp_homologyIso_inv, SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_inv_app, CategoryTheory.Limits.PreservesKernel.iso_inv_ι, CategoryTheory.Comma.mapRightIso_counitIso_inv_app_right, CategoryTheory.Bicategory.rightUnitor_inv_naturality, ChainComplex.isoHomologyι₀_inv_naturality_assoc, CategoryTheory.Functor.Monoidal.transport_μ, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_inv_app_app, instIsLeftKanExtensionSimplexCategoryTopCatSSetToTopInvFunctorToTopSimplex, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_hom_app, CategoryTheory.sum.inlCompInrCompInverseAssociator_inv_app_down_down, CategoryTheory.Comon.monoidal_rightUnitor_inv_hom, CategoryTheory.Limits.biproductBiproductIso_inv, SSet.horn₃₂.desc.multicofork_π_one, CategoryTheory.BraidedCategory.hexagon_reverse_assoc, TopologicalSpace.OpenNhds.inclusionMapIso_inv, CategoryTheory.inv_hom_id_apply, AlgebraicGeometry.Scheme.isoOfEq_inv_ι, CategoryTheory.Grothendieck.transportIso_hom_base, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₂_app, SSet.Subcomplex.topIso_inv_app_coe, QuadraticModuleCat.forget₂_map_associator_inv, CategoryTheory.MonoOver.mapIso_unitIso, HomologicalComplex.extend_op_d_assoc, CategoryTheory.Limits.CatCospanTransform.rightUnitor_inv_base_app, CategoryTheory.constantCommuteCompose_hom_app_val, CategoryTheory.CatCenter.smul_iso_inv_eq', CategoryTheory.cokernelUnopUnop_inv, CategoryTheory.Bicategory.Adjunction.homEquiv₁_apply, CategoryTheory.Functor.mapTriangleCommShiftIso_inv_app_hom₁, CategoryTheory.ShortComplex.homologyMapIso_inv, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict_assoc, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_inv_colimit_map_assoc, hom_eq_inv, CategoryTheory.Limits.pullbackDiagonalMapIso.inv_fst_assoc, inv_hom_id_triangle_hom₁, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right, HomologicalComplex.isoHomologyι_inv_hom_id, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_fac_app_assoc, CategoryTheory.Functor.mapConePostcompose_inv_hom, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_inv_app_hom₂, CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_left_inv, CategoryTheory.GlueData.ι_gluedIso_inv, CategoryTheory.BraidedCategory.braiding_inv_naturality_assoc, CategoryTheory.tensorRightHomEquiv_whiskerLeft_comp_evaluation, CategoryTheory.whiskerRight_coprod_inr_rightDistrib_inv_assoc, CategoryTheory.Functor.leftDerivedNatIso_inv, CategoryTheory.Join.mapWhiskerLeft_whiskerRight, CategoryTheory.Pseudofunctor.DescentData.isoMk_inv_hom, CategoryTheory.Endofunctor.Algebra.functorOfNatTransId_inv_app_f, CategoryTheory.Localization.Monoidal.μ_inv_natural_right, CategoryTheory.Bicategory.Pith.whiskerRight_iso_inv, op_inv, SimplicialObject.opFunctor_obj_map, CategoryTheory.Join.mkNatIso_inv, CategoryTheory.mop_inv_associator, AlgebraicGeometry.Scheme.Opens.stalkIso_inv, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_inv_comp_homologyι, CategoryTheory.Functor.LaxRightLinear.μᵣ_unitality_inv_assoc, Homotopy.extend_hom_eq, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_unit_app, groupHomology.π_comp_H1Iso_inv, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_π_app, CategoryTheory.Coyoneda.objOpOp_inv_app, CategoryTheory.toOverPullbackIsoToOver_inv_app_left, HomologicalComplex.isoHomologyι_hom_inv_id, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_inv, CategoryTheory.Functor.opComp_inv_app, partialFunEquivPointed_unitIso_inv_app, CategoryTheory.CartesianMonoidalCategory.associator_inv_fst_snd, CategoryTheory.Bicategory.rightUnitor_inv_congr, CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_fst_snd_assoc, CategoryTheory.ProjectiveResolution.cochainComplex_d, HomologicalComplex.singleObjCyclesSelfIso_inv_homologyπ, CategoryTheory.Bicategory.unitors_inv_equal, CategoryTheory.Bicategory.Pith.leftUnitor_inv_iso_hom, CategoryTheory.ShortComplex.opcyclesMapIso'_inv, CategoryTheory.Limits.PreservesCokernel.iso_inv, CategoryTheory.MonoidalCategory.whiskerRight_tensor, CategoryTheory.BraidedCategory.curriedBraidingNatIso_inv_app_app, ModuleCat.restrictScalarsComp'_inv_app, CategoryTheory.Bicategory.associator_inv_naturality_middle, AlgebraicGeometry.Scheme.Pullback.Triplet.isPullback_SpecMap_tensor, TopCat.Presheaf.pushforwardToOfIso_app, CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_right, CategoryTheory.Limits.biproduct.mapIso_inv, groupHomology.isoCycles₁_inv_comp_iCycles_apply, CategoryTheory.Limits.prod.rightUnitor_inv, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_hom_inv, BoolRing.Iso.mk_inv_hom', CategoryTheory.Functor.prod'CompSnd_inv_app, CategoryTheory.Idempotents.KaroubiKaroubi.counitIso_inv_app_f_f, CategoryTheory.Bicategory.hom_inv_whiskerRight_whiskerRight_assoc, HomologicalComplex.Hom.next_eq, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_hom_app, CategoryTheory.NatIso.ofComponents_inv_app, CategoryTheory.Limits.pullbackAssoc_inv_fst_snd, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom, CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_inv_hom_id_assoc, CategoryTheory.uliftCoyonedaIsoCoyoneda_inv_app_app_down, groupCohomology.dArrowIso₀₁_inv_right, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.leftMapᵣ_app, CategoryTheory.Bicategory.associator_inv_naturality_right, HomologicalComplex.natIsoSc'_inv_app_τ₂, DerivedCategory.singleFunctorsPostcompQIso_inv_hom, CategoryTheory.MonoidalCategory.id_whiskerLeft, groupCohomology.H0IsoOfIsTrivial_inv_apply, CategoryTheory.Over.braiding_inv_left, AlgebraicGeometry.Scheme.isoSpec_inv_preimage_zeroLocus, CochainComplex.HomComplex.Cochain.toSingleMk_v, groupCohomology.eq_d₂₃_comp_inv_assoc, CategoryTheory.Monad.algebraEquivOfIsoMonads_unitIso, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_hom_app_val_app, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_hom_comp_homologyIso_inv, groupCohomology.eq_d₂₃_comp_inv_apply, CategoryTheory.Functor.mapContActionCongr_inv, CategoryTheory.MorphismProperty.Over.mapCongr_inv_app_left, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app_assoc, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.associator_hom_unit_unit, groupCohomology.eq_d₁₂_comp_inv_apply, CategoryTheory.Limits.CatCospanTransform.baseIso_inv, CategoryTheory.FreeBicategory.mk_right_unitor_inv, CategoryTheory.Mon.rightUnitor_inv_hom, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompCoyoneda, CategoryTheory.Functor.Monoidal.map_rightUnitor_inv, CategoryTheory.CommMon.mkIso'_inv_hom_hom, SemimoduleCat.hom_inv_rightUnitor, isoInverseComp_hom_app, CategoryTheory.Over.prodLeftIsoPullback_inv_snd, AddCommGrpCat.neg_hom_apply, CategoryTheory.whiskerLeft_coprod_inl_leftDistrib_inv, CategoryTheory.ShortComplex.leftRightHomologyComparison_fac, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionActionOfMonoidalFunctorToEndofunctorIso_inv_app_app, CategoryTheory.Limits.PreservesPullback.iso_inv_fst_assoc, CategoryTheory.IsPushout.inl_isoIsPushout_inv, CategoryTheory.Limits.Cones.extendId_inv_hom, CategoryTheory.Limits.kernel.congr_inv, inv_comp_eq_id, RingCat.inv_hom_apply, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app, CategoryTheory.whiskerRight_coprod_inl_rightDistrib_inv, CategoryTheory.Over.iteratedSliceForwardIsoPost_inv_app, CategoryTheory.NatIso.naturality_1, CategoryTheory.NatIso.inv_map_inv_app, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv, CategoryTheory.Grothendieck.isoMk_inv_base, CategoryTheory.Comma.mapRightIso_inverse_map_right, LinearEquiv.toModuleIso_inv, CategoryTheory.Equivalence.core_unitIso_hom_app_iso_inv, CategoryTheory.Functor.ranCompLimIso_inv_app, imageToKernel_op, CategoryTheory.FunctorToTypes.map_inv_map_hom_apply, CategoryTheory.ShortComplex.RightHomologyData.copy_p, CategoryTheory.GradedObject.mapIso_inv, CategoryTheory.Limits.Cocones.whiskeringEquivalence_unitIso, CategoryTheory.Bicategory.conjugateEquiv_apply, inv_hom_id_triangle_hom₂_assoc, CategoryTheory.Limits.Multifork.isoOfι_inv_hom, CategoryTheory.Functor.ShiftSequence.induced.isoZero_hom_app_obj, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoColimitUncurryWhiskeringLeft₂_inv_assoc, CategoryTheory.Limits.colimitCurrySwapCompColimIsoColimitCurryCompColim_ι_ι_inv, CategoryTheory.Bicategory.whiskerRight_comp_symm, CategoryTheory.Functor.LaxRightLinear.μᵣ_associativity_inv_assoc, CategoryTheory.rightUnitor_inv_braiding, CategoryTheory.ThinSkeleton.fromThinSkeleton_map, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_inv_τl, CategoryTheory.Adjunction.Triple.rightToLeft_eq_units, HomologicalComplex.pOpcycles_opcyclesIsoSc'_inv_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv, CategoryTheory.Limits.inl_pushoutAssoc_inv_assoc, Bimod.right_assoc, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_inv_app_left, CategoryTheory.HasShift.Induced.zero_inv_app_obj, CategoryTheory.Limits.Cocones.eta_inv_hom, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_single, CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_inv, CategoryTheory.Bicategory.associator_eqToHom_hom_assoc, Preord.inv_hom_apply, CategoryTheory.shift_shift_neg', CategoryTheory.Limits.parallelPairIsoMk_inv_app, CategoryTheory.NatTrans.naturality_2_assoc, HomologicalComplex.truncLE'_d_eq_toCycles, CategoryTheory.Localization.Construction.wInv_eq_isoOfHom_inv, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_inv_app, SemilatSupCat.Iso.mk_inv_toFun, CategoryTheory.Sum.functorEquiv_unitIso_inv_app_app_inl, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimIso_aux_assoc, CategoryTheory.LocalizerMorphism.commShift_iso_inv_app, CategoryTheory.Bicategory.whiskerRight_id, CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv'_assoc, CategoryTheory.Grothendieck.isoMk_inv_fiber, CategoryTheory.MonoOver.mapIso_counitIso, CategoryTheory.HasShift.Induced.add_hom_app_obj, CategoryTheory.Pi.braiding_inv_apply, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₁_app, CategoryTheory.pullbackShiftFunctorZero_inv_app, Semigrp.hom_inv_apply, CategoryTheory.Functor.mapTriangleRotateIso_inv_app_hom₁, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f_assoc, CategoryTheory.Limits.biproduct.isoCoproduct_inv, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans, CategoryTheory.StructuredArrow.eta_inv_right, HomologicalComplex.xPrevIsoSelf_comp_dTo, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_naturality, CategoryTheory.CostructuredArrow.mapIso_unitIso_hom_app_left, CategoryTheory.CatCommSq.iso_inv_naturality, HomologicalComplex₂.ι_totalShift₁Iso_hom_f_assoc, CategoryTheory.Limits.prod.mapIso_inv, CategoryTheory.flippingIso_inv_toFunctor_obj_obj_obj, CategoryTheory.MonoidalCategory.MonoidalRightAction.hom_inv_actionHomLeft_assoc, CategoryTheory.Limits.IsLimit.uniqueUpToIso_inv, CategoryTheory.Limits.Cocones.whiskeringEquivalence_inverse, CategoryTheory.Limits.biprod.isoProd_inv, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₂, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π, CategoryTheory.Limits.inr_opProdIsoCoprod_inv_assoc, CategoryTheory.ObjectProperty.isoHom_inv_id_hom, AlgebraicGeometry.Scheme.Pullback.carrierEquiv_eq_iff, CategoryTheory.Oplax.LaxTrans.naturality_comp_assoc, CategoryTheory.Functor.Monoidal.map_leftUnitor_inv, CategoryTheory.EnrichedCat.associator_inv_out_app, CategoryTheory.Limits.PushoutCocone.isoMk_inv_hom, CategoryTheory.Limits.π_comp_colimitLeftOpIsoUnopLimit_inv, CategoryTheory.WithInitial.liftFromUnderComp_inv_app, HomologicalComplex.opcyclesOpIso_inv_naturality, HeytAlg.Iso.mk_inv, CategoryTheory.preservesColimitNatIso_inv_app, AlgebraicGeometry.Scheme.ι_toIso_inv_assoc, CommGrpCat.hom_inv_apply, CategoryTheory.coreCategory_id_iso_inv, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_right, CategoryTheory.Join.mapWhiskerLeft_whiskerLeft, CategoryTheory.Limits.Cone.toStructuredArrowCompProj_inv_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.inv_hom_actionHomLeft, CategoryTheory.Limits.parallelPairOpIso_inv_app_one, AlgebraicGeometry.Scheme.Modules.pseudofunctor_right_unitality_assoc, CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatIso_inv, CategoryTheory.Functor.PreservesRightKanExtension.preserves, CategoryTheory.Localization.Monoidal.pentagon_aux₂, AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_pullbackHom, CategoryTheory.MonoidalCategory.rightUnitor_inv_comp_tensorHom_assoc, CategoryTheory.MonoidalCategory.id_tensor_rightUnitor_inv_assoc, CategoryTheory.MonoidalCategory.prodCompExternalProduct_inv_app, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.functorToInterchangeIso_inv_app_app, CategoryTheory.ShortComplex.leftRightHomologyComparison'_fac, Preord.hom_inv_apply, Semigrp.inv_hom_apply, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_id, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_inv_app_app_fst, CategoryTheory.SmallObject.SuccStruct.ofCocone_map_assoc, CategoryTheory.MonoidalCategory.whiskerRight_id_symm_assoc, AlgebraicGeometry.Proj.basicOpenToSpec_app_top, CategoryTheory.Comma.mapSnd_inv_app, Condensed.lanPresheafExt_inv, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp, HomologicalComplex.homologyι_singleObjOpcyclesSelfIso_inv, CategoryTheory.GradedObject.Monoidal.rightUnitor_inv_apply, HomologicalComplex₂.ιTotal_totalFlipIso_f_inv_assoc, CategoryTheory.Preadditive.commGrpEquivalence_unitIso_inv_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_inv_app_snd_app, CategoryTheory.CopyDiscardCategory.copy_unit, CategoryTheory.GradedObject.Monoidal.leftUnitor_inv_apply, CategoryTheory.WithTerminal.opEquiv_counitIso_inv_app, CategoryTheory.Functor.IsEventuallyConstantTo.isoMap_inv_hom_id, CategoryTheory.tensorRightHomEquiv_whiskerRight_comp_evaluation, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_fst, CategoryTheory.toOverIsoToOverUnit_inv_app_left, CategoryTheory.Cat.Hom.isoMk_inv, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_inv_app_hom_left, CategoryTheory.Functor.flipping_counitIso_inv_app_app_app, CategoryTheory.Bicategory.whiskerLeft_hom_inv, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app, CategoryTheory.Under.mapCongr_inv_app, CategoryTheory.Limits.Types.binaryProductIso_inv_comp_fst, Bimod.id_whiskerLeft_bimod, CategoryTheory.Equivalence.congrLeft_counitIso_inv_app, CategoryTheory.Pseudofunctor.mapComp'_inv_naturality, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_snd, prodIsoPullback_inv_fst_assoc, CategoryTheory.GradedObject.isoMk_inv, CategoryTheory.MonoidalCategory.tensor_whiskerLeft_symm_assoc, CategoryTheory.Bicategory.mateEquiv_id_comp_right, CategoryTheory.Adjunction.conjugateEquiv_leftAdjointCompIso_inv, CategoryTheory.Functor.Initial.limitIso_inv, AlgebraicGeometry.LocallyRingedSpace.iso_inv_base_hom_base_apply, CategoryTheory.Bicategory.leftUnitor_comp_inv, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_inv_π_assoc, HomologicalComplex.XIsoOfEq_inv_naturality_assoc, CategoryTheory.Limits.kernel_map_comp_preserves_kernel_iso_inv_assoc, AlgebraicGeometry.Scheme.Modules.pushforwardComp_inv_app_app, CategoryTheory.oppositeShiftFunctorAdd_inv_app, LinOrd.hom_inv_apply, unop2_inv, CategoryTheory.LaxMonoidalFunctor.isoOfComponents_inv_hom_app, CategoryTheory.Limits.pushoutIsoUnopPullback_inv_snd, CategoryTheory.BraidedCategory.braiding_tensor_left_hom, CategoryTheory.obj_zero_map_μ_app_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomLeft_action_assoc, CategoryTheory.braiding_inv_tensorUnit_right_assoc, CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_inv, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_map_app_app, CategoryTheory.Limits.equalizerPullbackMapIso_inv_ι_snd, CategoryTheory.Functor.isoShift_inv_naturality_assoc, CochainComplex.mappingCone.inl_v_triangle_mor₃_f, CategoryTheory.Limits.HasColimit.isoOfEquivalence_hom_π, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_app, CategoryTheory.Mat_.ι_additiveObjIsoBiproduct_inv_assoc, CategoryTheory.Functor.ι_colimitIsoColimitGrothendieck_inv_assoc, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_whisker_right, CategoryTheory.Biprod.unipotentLower_inv, HomologicalComplex₂.ι_totalShift₁Iso_inv_f, HomologicalComplex.extendSingleIso_inv_f_assoc, PartialFun.Iso.mk_inv, CategoryTheory.Functor.mapContActionComp_inv, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_obj_obj, CategoryTheory.Limits.pullbackAssoc_inv_fst_snd_assoc, HomologicalComplex.natIsoSc'_inv_app_τ₃, HomologicalComplex.XIsoOfEq_inv_comp_XIsoOfEq_inv, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_hom_inv, CategoryTheory.OverClass.instHomIsOverInvAsIso, Bicategory.Opposite.bicategory_associator_hom_unop2, CategoryTheory.Limits.inl_opProdIsoCoprod_inv_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app, CompHausLike.LocallyConstant.locallyConstantIsoContinuousMap_inv_apply, SSet.nonDegenerateEquivOfIso_symm_apply_coe, CategoryTheory.Functor.OplaxRightLinear.δᵣ_associativity_inv, CategoryTheory.CatCenter.smul_iso_inv_eq'_assoc, FinBddDistLat.hom_inv_apply, CategoryTheory.Over.rightUnitor_inv_left_fst, AlgebraicGeometry.Scheme.ker_ideal_of_isPullback_of_isOpenImmersion, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_fiber, CategoryTheory.Functor.LeftExtension.coconeAtWhiskerRightIso_inv_hom, eq_comp_inv, CategoryTheory.Adjunction.mapCommMon_unit, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality_assoc, SimplicialObject.opFunctor_map_app, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_snd_fst, groupCohomology.cocyclesIso₀_inv_comp_iCocycles, CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj_inv_naturality_assoc, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_appTop_coord, HomologicalComplex.XIsoOfEq_inv_naturality, CategoryTheory.Limits.pullbackObjIso_inv_comp_fst_assoc, hom_inv_id_app_app_assoc, CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp_inv_hom₃, CategoryTheory.Limits.HasZeroObject.zeroIsoTerminal_inv, CategoryTheory.unmop_hom_associator, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id, Rep.indCoindIso_inv_hom_hom, hom_inv_id_eval_assoc, CategoryTheory.ShortComplex.cyclesIsoX₂_inv_hom_id_assoc, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_hom_inv_assoc, HomologicalComplex.restriction_d_eq, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality', CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app_assoc, AlgebraicGeometry.PresheafedSpace.isoOfComponents_hom, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_μ_unmop_app, CategoryTheory.Bimon.compatibility_assoc, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ_ΓToStalk, CategoryTheory.Functor.FullyFaithful.homNatIso_inv_app_down, CategoryTheory.Limits.equalizerPullbackMapIso_inv_ι_fst, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomLeft_action, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionUnitIso_inv, CategoryTheory.IsPushout.inr_isoPushout_inv_assoc, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_inv, CategoryTheory.Over.mapCongr_inv_app_left, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom, CategoryTheory.Bicategory.inv_hom_whiskerRight_whiskerRight, inv_eq_hom, Rep.diagonalSuccIsoFree_inv_hom_single_single, CategoryTheory.Limits.Types.binaryCoproductIso_inl_comp_inv, CategoryTheory.Limits.pushoutIsoUnopPullback_inv_fst, CategoryTheory.sheafificationIso_inv_val, CategoryTheory.ComonObj.comul_counit, groupCohomology.H1IsoOfIsTrivial_inv_apply, CategoryTheory.Bicategory.Prod.sectR_mapComp_inv, CategoryTheory.Limits.fiberwiseColimitLimitIso_hom_app, CategoryTheory.Limits.inr_pushoutLeftPushoutInrIso_inv, groupHomology.π_comp_H2Iso_inv_assoc, HomologicalComplex.homologyπ_extendHomologyIso_inv, HomologicalComplex.homologyπ_restrictionHomologyIso_inv, CategoryTheory.Limits.opCoproductIsoProduct'_comp_self, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.mkIso_inv_fst, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_hom_inv_assoc, AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv_assoc, CategoryTheory.Functor.congr_inv_of_congr_hom, AlgebraicGeometry.Scheme.Pullback.residueFieldCongr_inv_residueFieldMap_ofPoint, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.ShortComplex.leftHomologyMap_op, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃_associator_inv, CategoryTheory.InjectiveResolution.toRightDerivedZero_eq, CategoryTheory.Bicategory.id_whiskerLeft_symm, CategoryTheory.CartesianMonoidalCategory.braiding_inv_fst_assoc, HomologicalComplex.iCyclesIso_inv_hom_id, CategoryTheory.Pseudofunctor.mapComp'_naturality_1, ModuleCat.biprodIsoProd_inv_comp_snd_apply, CategoryTheory.PreZeroHypercover.inv_inv_h₀_comp_f, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoColimitUncurryWhiskeringLeft₂_inv, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd, CategoryTheory.Functor.shift_map_op_assoc, CategoryTheory.Over.postCongr_inv_app_left, CategoryTheory.Functor.opUnopIso_inv_app, CategoryTheory.coreCategory_inv_iso_inv, CategoryTheory.GrothendieckTopology.sheafifyCompIso_inv_eq_sheafifyLift, groupHomology.eq_d₂₁_comp_inv, CategoryTheory.Functor.FullyFaithful.preimageIso_inv, CategoryTheory.Functor.ι_leftKanExtensionObjIsoColimit_inv_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_inv_app, CategoryTheory.Limits.CoconeMorphism.hom_inv_id_assoc, HomologicalComplex.pOpcycles_opcyclesIsoSc'_inv, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_obj_left, CategoryTheory.Localization.Monoidal.triangle_aux₃, CategoryTheory.ShortComplex.homologyOpIso_inv_naturality, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_inv_app, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app', CategoryTheory.Limits.ι_comp_sigmaObjIso_inv, AlgebraicGeometry.Scheme.hom_base_inv_base, CategoryTheory.ShortComplex.mapOpcyclesIso_inv_naturality, HomologicalComplex.cyclesOpIso_inv_naturality_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocIso_inv_naturality_assoc, CategoryTheory.Limits.Cocones.precomposeEquivalence_unitIso, CategoryTheory.Limits.coprod.mapIso_inv, CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_fst, CategoryTheory.Limits.map_π_preserves_coequalizer_inv_colimMap_desc, CategoryTheory.MonoidalCategory.triangle_assoc_comp_left_inv_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_inv_hom, CategoryTheory.Limits.LimitPresentation.changeDiag_π, CategoryTheory.MonoidalCategory.rightUnitor_tensor_inv_assoc, CategoryTheory.Functor.mapTriangleInvRotateIso_inv_app_hom₃, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_app, ProfiniteAddGrp.hom_neg_apply, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_inv, CategoryTheory.FunctorToTypes.binaryCoproductEquiv_symm_apply, SSet.Subcomplex.topIso_inv_ι, CategoryTheory.Adjunction.mapCommMon_counit, CategoryTheory.Bicategory.Adj.rightUnitor_inv_τl, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app, CategoryTheory.Functor.unopId_inv_app, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_inv, CategoryTheory.LaxFunctor.PseudoCore.mapCompIso_inv, OrderHom.equivalenceFunctor_counitIso_inv_app_app, CategoryTheory.ProjectiveResolution.isoLeftDerivedObj_inv_naturality_assoc, Action.FunctorCategoryEquivalence.unitIso_inv_app_hom, CategoryTheory.Dial.associatorImpl_inv_F, CategoryTheory.Limits.π_comp_colimitUnopIsoOpLimit_inv, CategoryTheory.IsSubterminal.isoDiag_inv, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_app_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.associator_inv_comp_tensorHom_tensorHom_assoc, CategoryTheory.Functor.mapActionComp_inv, CategoryTheory.obj_μ_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality, SheafOfModules.ιFree_mapFree_inv_assoc, CategoryTheory.MonoidalCategory.hom_inv_whiskerRight_assoc, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right_assoc, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_inv_app, CategoryTheory.Pseudofunctor.map₂_associator_app, CategoryTheory.Limits.Types.equalizerIso_inv_comp_ι, CategoryTheory.Functor.coreId_inv_app_iso_inv, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_fst_assoc, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_inv_app_hom_hom_app, CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id, CategoryTheory.MonoidalCategory.inv_hom_whiskerRight_assoc, CategoryTheory.LaxMonoidalFunctor.isoMk_inv, CategoryTheory.MonoidalOpposite.tensorLeftUnmopIso_inv_app, CategoryTheory.Lax.OplaxTrans.naturality_comp, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_inv_toNatTrans_app_val_app, isoOfQuasiIsoAt_hom_inv_id, CategoryTheory.Arrow.square_from_iso_invert, HomologicalComplex.extendCyclesIso_inv_iCycles_assoc, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv, CategoryTheory.flippingIso_inv_toFunctor_obj_map_app, CategoryTheory.Bicategory.leftUnitor_inv_whiskerRight_assoc, CategoryTheory.Bicategory.whiskerRight_comp_symm_assoc, CategoryTheory.Bimon.trivial_comon_comul_hom, CategoryTheory.Oplax.StrongTrans.Modification.whiskerRight_naturality, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_app_assoc, HomologicalComplex.singleObjCyclesSelfIso_inv_naturality_assoc, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_iso_inv_app, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict_assoc, CategoryTheory.Over.prodLeftIsoPullback_inv_fst, CategoryTheory.ι_preservesColimitIso_inv_assoc, CategoryTheory.IsPushout.inr_isoPushout_inv, CategoryTheory.FreeGroupoid.mapCompLift_inv_app, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.homologyπ_isoHomology_inv_assoc, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_inv_right, CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapId_inv, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_coproductIsoSelf_inv_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom, CategoryTheory.Bicategory.Adj.rightUnitor_hom_τr, eHomCongr_comp_assoc, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_coproductIsoSelf_inv, CategoryTheory.Functor.LaxLeftLinear.μₗ_associativity_inv_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_inv_app, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapId_inv_iso_inv, CategoryTheory.Adjunction.mapCommGrp_unit, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app, CategoryTheory.Functor.curry₃ObjProdComp_inv_app_app_app, CategoryTheory.coreFunctor_obj_map_iso_inv, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_inv_colimit_map, CategoryTheory.conjugateEquiv_leftUnitor_hom, CategoryTheory.Limits.IsImage.ofIsoI_lift, CategoryTheory.WithTerminal.coneEquiv_counitIso_inv_app_hom, CategoryTheory.Functor.Final.ι_colimitIso_inv, CategoryTheory.shiftFunctorCompIsoId_add'_inv_app, ProfiniteAddGrp.neg_hom_apply, CategoryTheory.shiftFunctorAdd_zero_add_hom_app, Rep.coinvariantsTensorIndIso_inv, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_associator_inv_hom, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_naturality, CategoryTheory.OrthogonalReflection.iteration_map_succ, CategoryTheory.Pseudofunctor.mapComp'_inv_naturality_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionAssocIso_inv, CategoryTheory.Grp.associator_inv_hom_hom, CategoryTheory.Bicategory.comp_whiskerLeft_symm, CochainComplex.shiftFunctorZero_inv_app_f, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_assoc, CategoryTheory.Limits.Types.coproductIso_mk_comp_inv, CategoryTheory.MonoidalCategory.rightUnitor_inv_naturality, CategoryTheory.StrictlyUnitaryPseudofunctor.id_mapComp_inv, CategoryTheory.Bicategory.Pith.id₂_iso_inv, CategoryTheory.associator_inv_apply, comp_hom_eq_id, CategoryTheory.Limits.CatCospanTransform.whiskerRight_id, AlgebraicGeometry.IsAffineOpen.isoSpec_inv, TopCat.sigmaIsoSigma_inv_apply, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_left, CategoryTheory.Limits.Pi.reindex_inv_π_assoc, SSet.horn.faceSingletonComplIso_inv_ι, HomologicalComplex.extendMap_f, CompHausLike.homeoOfIso_symm_apply, HomologicalComplex₂.ι_totalShift₂Iso_inv_f_assoc, CategoryTheory.CartesianMonoidalCategory.lift_lift_associator_inv_assoc, CategoryTheory.Limits.Cocones.equivalenceOfReindexing_functor_obj, CategoryTheory.Sigma.mapComp_inv_app, CategoryTheory.Over.prodLeftIsoPullback_inv_snd_assoc, SemimoduleCat.MonoidalCategory.rightUnitor_inv_apply, CategoryTheory.Over.rightUnitor_inv_left_snd, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_map_left, CategoryTheory.Functor.mapCoconeOp_inv_hom, CategoryTheory.MonoidalCategory.whisker_assoc_assoc, CategoryTheory.Limits.spanCompIso_inv_app_left, CategoryTheory.Localization.homEquiv_eq, CategoryTheory.Oplax.StrongTrans.naturality_comp, PartOrdEmb.hom_inv_apply, AlgebraicGeometry.Proj.pullbackAwayιIso_inv_snd_assoc, CategoryTheory.leftUnitor_inv_braiding_assoc, CategoryTheory.NatTrans.op_whiskerRight_assoc, CategoryTheory.Bicategory.conjugateEquiv_id_comp_right_apply, CategoryTheory.CartesianMonoidalCategory.lift_lift_associator_inv, CategoryTheory.Oplax.OplaxTrans.associator_inv_as_app, HomologicalComplex.pOpcycles_restrictionOpcyclesIso_inv, DistLat.Iso.mk_inv, CategoryTheory.Comma.mapRightId_inv_app_left, CategoryTheory.EnrichedCategory.comp_id, HomologicalComplex.extend.mapX_some, CategoryTheory.Functor.FullyFaithful.compUliftYonedaCompWhiskeringLeft_inv_app_app_down, CategoryTheory.Bicategory.Adjunction.homEquiv₂_apply, CategoryTheory.Pseudofunctor.mkOfLax'_mapId_inv, CategoryTheory.Functor.isoShift_inv_naturality, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_assoc, HomologicalComplex.inr_biprodXIso_inv, CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_inv_hom, LinOrd.inv_hom_apply, CategoryTheory.CommSq.vert_inv, CategoryTheory.braiding_rightUnitor_aux₁, AlgebraicGeometry.Scheme.ΓSpecIso_inv, AlgebraicGeometry.Scheme.Hom.app_appIso_inv_assoc, HomologicalComplex.restriction.sc'Iso_inv_τ₁, CategoryTheory.rightDistributor_inv_comp_biproduct_π, CategoryTheory.Localization.Monoidal.triangle_aux₁_assoc, CategoryTheory.Pretriangulated.Triangle.isoMk_inv, CategoryTheory.Oplax.StrongTrans.naturality_id_assoc, 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.MonoidalCategory.associator_inv_naturality_left_assoc, CategoryTheory.GradedObject.singleCompEval_inv_app, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_app, CategoryTheory.Oplax.LaxTrans.naturality_id, TopCat.pullbackIsoProdSubtype_inv_fst_assoc, CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_inv_assoc, CategoryTheory.ComposableArrows.opEquivalence_unitIso_inv_app, CategoryTheory.Pseudofunctor.toLax_mapComp, CategoryTheory.LocalizerMorphism.smallShiftedHomMap_mk, CategoryTheory.Dial.rightUnitorImpl_inv_F, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.counitIso_inv, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_inv_app, AlgebraicGeometry.pullbackSpecIso_inv_snd, AlgebraicGeometry.Scheme.isoSpec_inv_image_zeroLocus, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₃, CategoryTheory.Oplax.OplaxTrans.naturality_comp, CategoryTheory.Limits.PreservesKernel.iso_inv_ι_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.leftUnitor_inv_one_tensor_mul_assoc, HomologicalComplex.Hom.isoOfComponents_inv_f, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app_assoc, CategoryTheory.MonoidalCategory.DayConvolution.associator_inv_unit_unit, CategoryTheory.ShortComplex.rightHomologyMapIso_inv, CategoryTheory.Limits.Types.Small.productIso_inv_comp_π, ModuleCat.restrictScalarsId'App_inv_naturality, CategoryTheory.CostructuredArrow.mapIso_unitIso_inv_app_left, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_inv_hom_assoc, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_inv_naturality, CategoryTheory.MonoidalCategory.DayConvolution.hexagon_reverse, ModuleCat.imageIsoRange_inv_image_ι_apply, HomologicalComplex.cyclesOpNatIso_inv_app, toAlgEquiv_symm_apply, CategoryTheory.MonoidalCategory.DayFunctor.equiv_counitIso_inv_app, CategoryTheory.Lax.LaxTrans.naturality_comp, ChainComplex.truncateAugment_inv_f, CategoryTheory.Mon.tensorObj_one, AddCommGrpCat.coyonedaForget_inv_app_app, CategoryTheory.Subobject.factorThru_mk_self, CategoryTheory.Adjunction.unit_app_shift_commShiftIso_inv_app, CategoryTheory.Center.rightUnitor_inv_f, AlgebraicGeometry.Proj.pullbackAwayιIso_inv_fst, CategoryTheory.Comma.mapRightComp_inv_app_right, CategoryTheory.Pseudofunctor.DescentData.iso_inv, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_naturality_assoc, CategoryTheory.SmallObject.SuccStruct.restrictionLTOfCoconeIso_inv_app, AlgebraicGeometry.Scheme.hom_base_inv_base_assoc, inv_comp_eq, ModuleCat.restrictScalarsId'_inv_app, CategoryTheory.GlueData.ι_gluedIso_inv_assoc, CategoryTheory.kernelUnopUnop_inv, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π, CategoryTheory.ComposableArrows.isoMk₅_inv, map_hom_inv_id_assoc, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_right, CategoryTheory.Functor.compFlipUncurryIso_inv_app, CategoryTheory.Functor.CommShift.ofIso_commShiftIso_hom_app, CategoryTheory.Limits.Sigma.whiskerEquiv_hom, CategoryTheory.Quotient.LiftCommShift.iso_hom_app, CategoryTheory.Oplax.StrongTrans.id_naturality_inv, CategoryTheory.preservesColimitIso_inv_comp_desc, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen_topIso_inv, CommAlgCat.algEquivOfIso_symm_apply, Action.hom_inv_hom, CategoryTheory.Functor.Monoidal.coreMonoidalTransport_μIso_hom, AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_snd, CategoryTheory.Adjunction.compUliftCoyonedaIso_inv_app_app_down, CategoryTheory.Lax.OplaxTrans.vComp_naturality_comp, CategoryTheory.MonoidalCategory.id_tensor_associator_inv_naturality, FintypeCat.equivEquivIso_symm_apply_symm_apply, ModuleCat.extendScalars_assoc_assoc, CategoryTheory.Limits.biprod.lift_mapBiprod, FinBddDistLat.inv_hom_apply, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_assoc, CategoryTheory.MonoidalCategory.id_tensor_rightUnitor_inv, CategoryTheory.e_comp_id_assoc, CategoryTheory.EnrichedCategory.id_comp, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_leftUnitor_inv_as_app, CategoryTheory.Limits.walkingCospanOpEquiv_counitIso_inv_app, CategoryTheory.Bicategory.Prod.sectL_mapComp_hom, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc_assoc, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_assoc, TopologicalSpace.Opens.inclusion'_top_functor, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso_inv_app_f, CategoryTheory.Bicategory.associator_inv_naturality_left, CategoryTheory.WithInitial.mapId_inv_app, CategoryTheory.Functor.ι_colimitIsoOfIsLeftKanExtension_inv, CategoryTheory.MorphismProperty.Over.isoMk_inv_left, AddEquiv.toAddMagmaCatIso_inv, CategoryTheory.Limits.PreservesPullback.iso_inv_snd, CategoryTheory.Limits.Cofan.ext_inv_hom, hom_inv_id_triangle_hom₂, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_hom_app, CategoryTheory.Functor.constComp_inv_app, CategoryTheory.Functor.FullyFaithful.autMulEquivOfFullyFaithful_apply_inv, ModuleCat.hom_inv_apply, CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_eq, CategoryTheory.Limits.π_reflexiveCoequalizerIsoCoequalizer_inv_assoc, Bipointed.swapEquiv_unitIso_inv_app_toFun, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_comp_mapComp'_inv, TopCat.Presheaf.presheafEquivOfIso_inverse_obj_map, CategoryTheory.Bimon.equivMonComonCounitIsoAppXAux_inv, CategoryTheory.MonoidalCategory.whiskerRight_id_symm, id_tensor_π_preserves_coequalizer_inv_colimMap_desc, smoothSheafCommRing.forgetStalk_inv_comp_eval_assoc, CategoryTheory.Equivalence.symmEquivInverse_obj_counitIso_hom, hom_inv_id_triangle_hom₂_assoc, AlgebraicGeometry.Scheme.fromSpecStalk_appTop, CategoryTheory.Bicategory.leftUnitor_inv_naturality, CategoryTheory.Join.mapWhiskerRight_whiskerRight, CategoryTheory.FunctorToTypes.inv_hom_id_app_apply, CategoryTheory.ShiftMkCore.add_zero_hom_app, CategoryTheory.GradedObject.singleObjApplyIsoOfEq_inv_single_map, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_inv_hom, CategoryTheory.Limits.PreservesPullback.iso_inv_fst, AlgebraicGeometry.pullbackRestrictIsoRestrict_inv_fst, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_map_left, CategoryTheory.Limits.CatCospanTransform.rightIso_inv, CategoryTheory.Functor.OplaxMonoidal.oplax_right_unitality, CategoryTheory.Cat.associator_inv_app, CategoryTheory.Limits.inr_pushoutLeftPushoutInrIso_inv_assoc, CategoryTheory.Bicategory.whiskerRightIso_inv, CategoryTheory.Limits.MultispanIndex.multispanMapIso_inv_app, HomologicalComplex.singleObjHomologySelfIso_hom_singleObjHomologySelfIso_inv_assoc, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_snd, HomologicalComplex.cyclesIsoSc'_inv_iCycles_assoc, CategoryTheory.Limits.prod.leftUnitor_inv_naturality_assoc, AlgebraicGeometry.Scheme.Pullback.Triplet.Spec_map_tensor_isPullback, addCommGroupIsoToAddEquiv_symm_apply, AlgebraicGeometry.IsOpenImmersion.isoOfRangeEq_inv_fac_assoc, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_snd_snd, CategoryTheory.kernelOpUnop_inv, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_right_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π_assoc, CategoryTheory.Quiv.inv_map_hom_map_of_iso, CategoryTheory.Oplax.LaxTrans.id_naturality, CategoryTheory.SmallObject.SuccStruct.prop.arrowIso_inv_right, CategoryTheory.Functor.OplaxMonoidal.δ_comp_whiskerLeft_δ_assoc, CategoryTheory.Limits.coequalizer.isoTargetOfSelf_inv, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomLeft_tensor, SheafOfModules.pushforwardComp_inv_app_val_app, CategoryTheory.Enriched.FunctorCategory.enriched_id_comp_assoc, CategoryTheory.CartesianMonoidalCategory.lift_braiding_inv, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_id, CategoryTheory.Limits.kernelBiprodFstIso_inv, AddEquiv.toAddMonCatIso_inv, CategoryTheory.endofunctorMonoidalCategory_associator_inv_app, AlgebraicGeometry.Scheme.Opens.toSpecΓ_appTop_assoc, CategoryTheory.NatTrans.app_homology, CategoryTheory.Pseudofunctor.mapComp_id_right_hom, CategoryTheory.Functor.currying_counitIso_inv_app_app, CategoryTheory.ShortComplex.homologyMap'_op, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_inv_app_hom, CategoryTheory.Adjunction.mapGrp_unit, CategoryTheory.Monad.Algebra.isoMk_inv_f, CategoryTheory.MonoidalCategory.hom_inv_whiskerRight, CategoryTheory.Over.associator_inv_left_fst_fst_assoc, CategoryTheory.Functor.coreId_inv_app_iso_hom, CategoryTheory.Under.mapId_inv, CategoryTheory.ShortComplex.leftHomologyMapIso_inv, CategoryTheory.Limits.pullbackSymmetry_inv_comp_fst_assoc, CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_inv, CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_inv_desc_assoc, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_base, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_inv_left, smoothSheafCommRing.forgetStalk_inv_comp_eval, CategoryTheory.Functor.CommShift.isoZero'_inv_app, CategoryTheory.Grothendieck.ιCompMap_inv_app_fiber, CategoryTheory.Bicategory.Adj.Bicategory.rightUnitor_hom_τr, CategoryTheory.StrictPseudofunctor.comp_mapId_inv, symm_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_shift, CategoryTheory.op_inv_braiding, retract_r, HomologicalComplex.singleMapHomologicalComplex_inv_app_self, CategoryTheory.PreGaloisCategory.autIsoFibers_inv_app, CategoryTheory.Preadditive.smul_iso_inv, groupHomology.coinvariantsMk_comp_H0Iso_inv, CategoryTheory.Pseudofunctor.ObjectProperty.mapId_inv_app, CategoryTheory.Limits.PreservesLimitPair.iso_inv_fst_assoc, AddCommGrpCat.biprodIsoProd_inv_comp_snd_apply, CategoryTheory.Grp.rightUnitor_inv_hom_hom, CategoryTheory.Limits.Cocone.toCostructuredArrowCompToOverCompForget_inv_app, CategoryTheory.Limits.PreservesPushout.inl_iso_inv, CategoryTheory.Limits.CatCospanTransform.rightUnitor_inv_right_app, CategoryTheory.Bicategory.Comonad.comul_assoc_flip_assoc, AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTrans, CategoryTheory.BraidedCategory.braiding_tensor_left_inv_assoc, HomologicalComplex.restrictionMap_f'_assoc, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_1, CategoryTheory.CatCommSq.hId_iso_inv_app, AlgebraicGeometry.IsAffineOpen.algebraMap_Spec_obj, CategoryTheory.Limits.limCompFlipIsoWhiskerLim_inv_app_app, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp, CategoryTheory.MonoidalClosed.assoc, CategoryTheory.Limits.prod_rightUnitor_inv_naturality_assoc, HomologicalComplex.extendSingleIso_hom_f_assoc, CategoryTheory.Bicategory.conjugateEquiv_comp_id_right_apply, CategoryTheory.Functor.commShiftOfLocalization_iso_inv_app, CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id_app, CategoryTheory.MorphismProperty.Under.isoMk_inv_right, CategoryTheory.Adjunction.map_restrictFullyFaithful_counit_app, CategoryTheory.e_assoc_assoc, CategoryTheory.Functor.IsStronglyCartesian.domainIsoOfBaseIso_inv, CommMonCat.coyonedaForget_inv_app_app, CategoryTheory.WithInitial.coconeEquiv_counitIso_inv_app_hom, CategoryTheory.Lax.LaxTrans.id_naturality, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₃, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_comp_assoc, CategoryTheory.Functor.commShiftOfLocalization.iso_inv_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.whiskerLeft_actionHomLeft_assoc, CategoryTheory.ShortComplex.cyclesMapIso'_inv, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_assoc, CategoryTheory.Limits.pullbackZeroZeroIso_inv_fst, CategoryTheory.ShortComplex.opcyclesIsoCokernel_inv, CategoryTheory.Bicategory.leftUnitor_inv_whiskerRight, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd, CategoryTheory.Pi.left_unitor_inv_apply, CategoryTheory.Localization.isoOfHom_op_inv, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_inv_assoc, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality_assoc, CochainComplex.isoHomologyπ₀_inv_naturality, CategoryTheory.ShortComplex.RightHomologyData.copy_ι, CategoryTheory.GradedObject.Monoidal.pentagon_inv, CategoryTheory.Limits.IsImage.isoExt_inv_m, CategoryTheory.ShortComplex.RightHomologyData.p_comp_opcyclesIso_inv_assoc, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_associator, CategoryTheory.MonoidalCategory.leftUnitor_inv_whiskerRight_assoc, Action.resId_inv_app_hom, CategoryTheory.IsPullback.isoPullback_inv_snd, CategoryTheory.Functor.LeftExtension.postcompose₂ObjMkIso_inv_right_app, CategoryTheory.Functor.CommShift.comp_commShiftIso_inv_app, isoOfQuasiIsoAt_inv_hom_id, CategoryTheory.Limits.pullbackIsoOpPushout_inv_fst_assoc, smoothSheafCommRing.forgetStalk_inv_comp_eval_apply, AlgebraicTopology.DoldKan.N₁Γ₀_hom_app_f_f, CategoryTheory.Functor.sheafPushforwardContinuousCompSheafToPresheafIso_inv_app_app, CategoryTheory.MorphismProperty.Over.mapId_inv_app_left, groupCohomology.dArrowIso₀₁_inv_left, CategoryTheory.NatTrans.rightOpWhiskerRight, CategoryTheory.Limits.BinaryFan.braiding_inv_snd, CategoryTheory.equivYoneda'_inv_val, CategoryTheory.Functor.Monoidal.transport_δ, CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_inv_π_π, Rep.coinvariantsTensorIndNatIso_inv_app, CategoryTheory.Under.isoMk_inv_right, CategoryTheory.Limits.walkingCospanOpEquiv_unitIso_inv_app, CategoryTheory.Functor.sumIsoExt_inv_app_inr, CategoryTheory.ShortComplex.mapRightHomologyIso_inv_naturality, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_assoc, CategoryTheory.Bicategory.associator_eqToHom_inv, CategoryTheory.leftUnitor_inv_apply, AddEquiv.toAddCommMonCatIso_inv, CategoryTheory.Localization.Preadditive.homEquiv_apply, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_app, CategoryTheory.Functor.CoreMonoidal.toOplaxMonoidal_δ, AlgebraicGeometry.ΓSpec.adjunction_counit_app, TopCat.prodIsoProd_inv_snd_assoc, AlgebraicGeometry.Scheme.coe_homeoOfIso_symm, CategoryTheory.OverPresheafAux.unitAuxAuxAux_inv, CategoryTheory.MonoidalCategory.tensoringRight_δ, CategoryTheory.Limits.cokernelBiprodInlIso_inv, CategoryTheory.unmop_inv_leftUnitor, CategoryTheory.Limits.inl_pushoutRightPushoutInlIso_inv, CategoryTheory.Limits.FormalCoproduct.isoOfComponents_inv_f, Lat.Iso.mk_inv, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.secondMap₂_app_app_app, CategoryTheory.preservesLimitIso_inv_π_assoc, AlgebraicGeometry.Scheme.stalkMap_hom_inv_assoc, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_inv_fac_assoc, CategoryTheory.Functor.ranCompIsoOfPreserves_inv_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.tensor_actionHomRight, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom, CategoryTheory.Comma.mapLeftComp_inv_app_left, CategoryTheory.MonoidalClosed.assoc_assoc, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv_assoc, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj_assoc, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc_apply, TopCat.prodIsoProd_inv_fst_assoc, CategoryTheory.ProjectiveResolution.extMk_hom, AlgebraicGeometry.Proj.basicOpenIsoSpec_inv_ι, CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIso_inv, groupHomology.eq_d₃₂_comp_inv_apply, CategoryTheory.coreCategory_comp_iso_inv, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom, AlgebraicGeometry.Scheme.Opens.toSpecΓ_appTop, CategoryTheory.CategoryOfElements.isoMk_inv, CategoryTheory.Limits.pullbackProdFstIsoProd_inv_fst, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_whiskerLeft, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_inv_hom₃, CategoryTheory.shiftFunctorAdd_inv_app_obj_of_induced, CategoryTheory.Oplax.OplaxTrans.categoryStruct_comp_naturality, CategoryTheory.Join.mapWhiskerLeft_whiskerRight_assoc, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_rightHomologyIso_inv_assoc, CategoryTheory.Over.leftUnitor_inv_left_fst, HomologicalComplex.restrictionHomologyIso_inv_homologyι_assoc, Bicategory.Opposite.bicategory_leftUnitor_inv_unop2, CategoryTheory.Limits.cospanCompIso_inv_app_left, CategoryTheory.Functor.mapTriangleCompIso_inv_app_hom₃, CategoryTheory.Functor.rightOpId_inv_app, CategoryTheory.unmop_inv_associator, CategoryTheory.Bicategory.Prod.sectR_mapId_inv, CategoryTheory.WithInitial.inclLiftToInitial_inv_app, CategoryTheory.GradedObject.Monoidal.ιTensorObj₃_associator_inv_assoc, SSet.horn₃₁.desc.multicofork_π_two_assoc, hom_inv_id, ModuleCat.hom_inv_associator, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_unit_app_left, CategoryTheory.Over.inv_left_hom_left, CategoryTheory.Limits.PushoutCocone.ofCocone_ι, CategoryTheory.Over.postEquiv_inverse, CategoryTheory.StructuredArrow.mapNatIso_unitIso_hom_app_right, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec_assoc, CategoryTheory.Abelian.Ext.mapExactFunctor_hom, ModuleCat.lof_coprodIsoDirectSum_inv, CategoryTheory.ShortComplex.RightHomologyMapData.rightHomologyMap_eq, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_app, CategoryTheory.Adjunction.conjugateEquiv_leftAdjointIdIso_hom, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_presheafMap, CategoryTheory.PrelaxFunctor.map₂_hom_inv, CategoryTheory.Limits.Pi.whiskerEquiv_inv, CategoryTheory.Localization.Monoidal.map_hexagon_reverse, CategoryTheory.OplaxFunctor.mapComp_assoc_right_app, CategoryTheory.Join.isoMkFunctor_inv_app, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_μ, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransId_inv_app_f, CategoryTheory.Enriched.FunctorCategory.enriched_comp_id_assoc, CategoryTheory.Limits.biproduct.reindex_inv, AlgebraicGeometry.Scheme.Hom.preimageIso_inv_ι, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec, CategoryTheory.MonoidalCategory.associator_inv_naturality, CategoryTheory.Over.forgetMapTerminal_inv_app, CategoryTheory.ProjectiveResolution.Hom.hom'_f_assoc, RingEquiv.toCommRingCatIso_inv, CategoryTheory.Limits.opCoproductIsoProduct'_inv_comp_inj, SSet.horn₃₁.desc.multicofork_π_zero_assoc, ModuleCat.inv_hom_apply, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app, CategoryTheory.Join.mapIsoWhiskerRight_inv, CategoryTheory.Functor.Monoidal.transport_μ_assoc, ProfiniteGrp.inv_hom_apply, CategoryTheory.sectionsFunctorNatIsoCoyoneda_inv_app_coe, CategoryTheory.Limits.Pi.isoLimit_inv_π, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_obj_obj_map, CategoryTheory.ShortComplex.LeftHomologyData.π_comp_leftHomologyIso_inv_assoc, CategoryTheory.Limits.idZeroEquivIsoZero_apply_inv, ChainComplex.augmentTruncate_inv_f_succ, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_inv_app_app, AlgebraicGeometry.ΓSpecIso_obj_hom, CategoryTheory.Limits.CokernelCofork.mapIsoOfIsColimit_inv, Action.instIsIsoHomInv, CategoryTheory.MonoidalCategory.rightUnitor_inv_naturality_assoc, CategoryTheory.ULift.equivalence_unitIso_inv, CategoryTheory.Localization.SmallHom.equiv_mkInv, CategoryTheory.Pretriangulated.binaryProductTriangleIsoBinaryBiproductTriangle_inv_hom₂, CategoryTheory.Limits.Types.coequalizerIso_quot_comp_inv_apply, CategoryTheory.Bicategory.pentagon_inv_inv_hom_hom_inv, SSet.leftUnitor_inv_app_apply, Bimod.right_assoc_assoc, AlgebraicGeometry.Proj.pullbackAwayιIso_inv_snd, AlgebraicGeometry.Proj.pullbackAwayιIso_inv_fst_assoc, CategoryTheory.tensorLeftHomEquiv_tensor, CategoryTheory.NatIso.prod_inv, AlgebraicGeometry.pullbackSpecIso_inv_fst'_assoc, CategoryTheory.Functor.OplaxMonoidal.δ_comp_δ_whiskerRight_assoc, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan_inv_app_app_apply_eq_id, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_assoc, CategoryTheory.Localization.liftNatIso_inv, CategoryTheory.eqToHom_iso_inv_naturality, CategoryTheory.Limits.spanOp_inv_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app_assoc, CategoryTheory.GrothendieckTopology.toSheafify_comp_sheafifyCompIso_inv_assoc, CategoryTheory.Over.isoMk_inv_left, CategoryTheory.Limits.PushoutCocone.eta_inv_hom, CategoryTheory.Equivalence.rightOp_unitIso_hom_app, CategoryTheory.EnrichedCat.rightUnitor_inv_out_app, CategoryTheory.Join.pseudofunctorLeft_mapComp_inv_toNatTrans_app, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv_assoc, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv, CategoryTheory.Functor.shiftIso_inv_naturality, CategoryTheory.ExactPairing.evaluation_coevaluation', CochainComplex.HomComplex.Cochain.leftUnshift_v, CategoryTheory.Limits.kernelIsIsoComp_inv, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInrIso_inv_app_app, CategoryTheory.Limits.colimitLimitToLimitColimitCone_hom, AlgebraicGeometry.Scheme.IsLocallyDirected.homOfLE_tAux, CategoryTheory.Functor.isDenseAt_eq_isPointwiseLeftKanExtensionAt, CategoryTheory.shiftFunctorAdd'_zero_add_inv_app, CategoryTheory.MorphismProperty.Comma.isoMk_inv_left, CategoryTheory.BraidedCategory.hexagon_reverse_inv, CategoryTheory.Bicategory.Pseudofunctor.ofLaxFunctorToLocallyGroupoid_mapIdIso_inv, CategoryTheory.Limits.productUniqueIso_inv, CategoryTheory.Arrow.isoMk_inv_left, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_whiskerRight_assoc, CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_snd_apply, CategoryTheory.Functor.mapMonNatIso_inv_app_hom, CategoryTheory.Adjunction.shift_counit_app, CategoryTheory.Limits.Cone.ofPullbackCone_π, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_id_assoc, CategoryTheory.Functor.map_shift_unop, isoOfQuasiIsoAt_inv_hom_id_assoc, CategoryTheory.Limits.Cones.equivalenceOfReindexing_counitIso, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_counitIso, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₂, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv, CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_inv_app, CategoryTheory.Bicategory.Comonad.counit_comul_assoc, CategoryTheory.OplaxFunctor.mapComp_assoc_left, CategoryTheory.curryingIso_inv_toFunctor_obj_map_app, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd_assoc, Bicategory.Opposite.op2_rightUnitor_inv, Frm.Iso.mk_inv, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp_assoc, HomologicalComplex.leftUnitor'_inv_comm_assoc, CategoryTheory.Adjunction.map_restrictFullyFaithful_counit_app_assoc, inv_hom_id_app_app, CategoryTheory.Functor.LaxRightLinear.μᵣ_associativity_inv, CategoryTheory.Limits.LimitPresentation.ofIso_π, CategoryTheory.GradedObject.singleObjApplyIso_inv_single_map_assoc, CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_snd, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.image_preimage_is_empty, CategoryTheory.Lax.LaxTrans.naturality_comp_assoc, HeytAlg.hom_inv_apply, CategoryTheory.unop_inv_leftUnitor, CategoryTheory.Functor.OplaxLeftLinear.δₗ_unitality_inv, CategoryTheory.Limits.prod.leftUnitor_inv, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_iso_inv_app, CategoryTheory.Functor.Monoidal.map_leftUnitor_inv_assoc, CategoryTheory.Localization.Monoidal.triangle_aux₁, CategoryTheory.Functor.op_commShiftIso_hom_app_assoc, CategoryTheory.Functor.FullyFaithful.compYonedaCompWhiskeringLeftMaxRight_inv_app_app, SemimoduleCat.hom_inv_apply, SSet.rightUnitor_inv_app_apply, Sequential.isoOfHomeo_inv, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_inv_app, CategoryTheory.Mon.mkIso_inv_hom, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app_assoc, NonemptyFinLinOrd.Iso.mk_inv, CategoryTheory.Over.leftUnitor_inv_left_snd, AlgebraicGeometry.AffineTargetMorphismProperty.arrow_mk_iso_iff, SSet.Truncated.HomotopyCategory.BinaryProduct.left_unitality, CategoryTheory.CartesianMonoidalCategory.associator_inv_snd_assoc, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst_assoc, CategoryTheory.Limits.initialIsoIsInitial_inv, CategoryTheory.Bicategory.prod_rightUnitor_inv_fst, AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_inv_snd_assoc, HomologicalComplex.pOpcyclesIso_inv_hom_id, FintypeCat.equivEquivIso_apply_inv, TopologicalSpace.Opens.mapIso_inv_app, CategoryTheory.Limits.opSpan_hom_app, ModuleCat.kernelIsoKer_inv_kernel_ι_apply, CategoryTheory.Limits.π_comp_colimitLeftOpIsoUnopLimit_inv_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃'_obj_map_app, CategoryTheory.obj_zero_map_μ_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionActionOfMonoidalFunctorToEndofunctorMopIso_inv_app_unmop_app, compInverseIso_inv_app, CategoryTheory.ComposableArrows.isoMkSucc_inv, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_snd', groupHomology.cyclesIso₀_inv_comp_cyclesMap_apply, CategoryTheory.Limits.piObjIso_inv_comp_π, CategoryTheory.GrothendieckTopology.overMapPullback_assoc_assoc, CategoryTheory.MonoidalCategory.triangle_assoc_comp_right_inv, AddCommMonCat.neg_hom_apply, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_app_assoc, CategoryTheory.GradedObject.mapBifunctorMapMapIso_inv, CategoryTheory.ShortComplex.homologyπ_comp_leftHomologyIso_inv, CategoryTheory.Dial.leftUnitor_inv_f, CategoryTheory.DifferentialObject.shiftZero_inv_app_f, CategoryTheory.CommSq.horiz_inv, TopCat.Presheaf.presheafEquivOfIso_unitIso_hom_app_app, CategoryTheory.Bicategory.Adj.iso₂Mk_inv_τl, CategoryTheory.TwoSquare.GuitartExact.whiskerVertical_iff, CategoryTheory.Bimon.one_comul, CategoryTheory.NatTrans.op_whiskerRight, LightCondensed.isoFinYonedaComponents_inv_comp, CategoryTheory.ShortComplex.leftHomologyIso_inv_naturality_assoc, CategoryTheory.Oplax.LaxTrans.naturality_comp, HomologicalComplex.cyclesIsoSc'_inv_iCycles, CategoryTheory.Limits.ι_colimitFiberwiseColimitIso_inv_assoc, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_inv_π_π, CategoryTheory.Monad.algebraFunctorOfMonadHomEq_inv_app_f, CategoryTheory.NatTrans.CommShiftCore.shift_app, CategoryTheory.Limits.PreservesPushout.inl_iso_inv_assoc, CategoryTheory.Limits.cokernelBiprodInrIso_inv, CategoryTheory.SingleFunctors.isoMk_inv_hom, CategoryTheory.CartesianMonoidalCategory.rightUnitor_inv_fst, CategoryTheory.CatCommSq.vInv_iso_hom_app, CategoryTheory.Functor.ShiftSequence.induced_shiftIso_hom_app_obj, CategoryTheory.ShortComplex.opcyclesMapIso_inv, CategoryTheory.MonoidalOpposite.mop_inv_braiding, CategoryTheory.ShortComplex.fromOpcycles_op_cyclesOpIso_inv_assoc, CategoryTheory.Functor.Monoidal.map_associator_inv, CategoryTheory.rightDistributor_inv, CategoryTheory.Limits.limitUnopIsoUnopColimit_inv_comp_π_assoc, TopCat.piIsoPi_inv_π_apply, CategoryTheory.preservesLimitIso_inv_π, AlgebraicGeometry.Scheme.IdealSheafData.ideal_comap_of_isOpenImmersion, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_fst, CategoryTheory.Enriched.FunctorCategory.homEquiv_comp, CategoryTheory.whiskeringRightCompEvaluation_inv_app, CategoryTheory.Functor.associator_inv_app, CategoryTheory.Limits.whiskeringLimYonedaIsoCones_inv_app_app, CategoryTheory.MonoidalCategory.tensorIso_inv, groupCohomology.isoCocycles₁_inv_comp_iCocycles_apply, CategoryTheory.LocalizerMorphism.homMap_apply, CategoryTheory.CostructuredArrow.mapNatIso_functor_obj_hom, CategoryTheory.typeEquiv_unitIso_inv_app, CategoryTheory.Functor.functorialityCompPrecompose_hom_app_hom, CategoryTheory.NatTrans.unop_whiskerRight, AlgebraicGeometry.AffineSpace.SpecIso_inv_appTop_coord, CategoryTheory.Over.mapId_inv_app_left, CategoryTheory.ShortComplex.LeftHomologyData.copy_π, Action.diagonalSuccIsoTensorTrivial_inv_hom_apply, CategoryTheory.Bicategory.conjugateIsoEquiv_apply_inv, CategoryTheory.BraidedCategory.yang_baxter, CategoryTheory.Sigma.natIso_inv, CategoryTheory.GrothendieckTopology.Cover.multicospanComp_inv_app, CategoryTheory.MorphismProperty.Over.pullbackComp_inv_app_left, CategoryTheory.WithInitial.starIsoInitial_inv, CategoryTheory.shift_equiv_triangle, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_inv_app, CategoryTheory.asIso_inv, CategoryTheory.Comma.toIdPUnitEquiv_unitIso_inv_app_right, CategoryTheory.Pseudofunctor.mapComp'_naturality_2_assoc, CategoryTheory.associator_inv, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_inv_app_app, SemimoduleCat.hom_inv_leftUnitor, SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_inv_app, CategoryTheory.Dial.hexagon_reverse, CategoryTheory.Pseudofunctor.mapComp_id_left_inv_assoc, CategoryTheory.Comma.toPUnitIdEquiv_unitIso_inv_app_left, CategoryTheory.factorThruImage_comp_imageUnopOp_inv, CategoryTheory.ProjectiveResolution.π'_f_zero_assoc, CategoryTheory.TransfiniteCompositionOfShape.fac, HomologicalComplex.truncLE'Map_f_eq_cyclesMap, CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_fst_snd, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst, CategoryTheory.GrothendieckTopology.uliftYonedaCompSheafToPresheaf_inv_app_app, CategoryTheory.Adjunction.comp_counit, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans, CategoryTheory.Limits.opProdIsoCoprod_inv_inl, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_inv_app_unmop, CategoryTheory.Bicategory.pentagon_inv_inv_hom_inv_inv, CategoryTheory.Equivalence.changeFunctor_counitIso_hom_app, CategoryTheory.Over.leftUnitor_inv_left_snd_assoc, AddMonCat.neg_hom_apply, CategoryTheory.Localization.Monoidal.map_hexagon_reverse_assoc, CategoryTheory.Comon.mkIso_inv_hom, CategoryTheory.FreeMonoidalCategory.mk_l_inv, CategoryTheory.GlueData.diagramIso_inv_app_left, CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_inv_eq_germ_apply, map_inv_hom_id_app, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app_assoc, hom_inv_id_app, CategoryTheory.MonoidalCategory.associator_inv_naturality_middle_assoc, CategoryTheory.Limits.HasLimit.isoOfEquivalence_hom_π, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_app, CategoryTheory.Bimon.equivMonComonUnitIsoAppX_inv_hom, CategoryTheory.Limits.limitConstTerminal_inv_π, CategoryTheory.ComonObj.counit_comul_assoc, CategoryTheory.Limits.KernelFork.mapIsoOfIsLimit_inv, CategoryTheory.NatIso.naturality_1_assoc, CategoryTheory.CartesianMonoidalCategory.rightUnitor_inv_snd_assoc, HomologicalComplex.xPrevIso_comp_dTo, CategoryTheory.Limits.pullbackProdSndIsoProd_inv_fst_snd_assoc, CategoryTheory.Adjunction.mapMon_counit, CategoryTheory.ComonObj.counit_comul_hom, CategoryTheory.preservesLimitNatIso_inv_app, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom'_assoc, TopCat.Presheaf.whiskerIsoMapGenerateCocone_inv_hom, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app_assoc, CategoryTheory.Pretriangulated.preadditiveYoneda_homologySequenceδ_apply, CategoryTheory.ShortComplex.LeftHomologyMapData.homologyMap_eq, CategoryTheory.Limits.image.isoStrongEpiMono_inv_comp_mono, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_apply, CategoryTheory.Lax.LaxTrans.naturality_id_assoc, map_hom_inv_id, CategoryTheory.PreservesImage.inv_comp_image_ι_map, SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁_inv_f_f, CategoryTheory.Limits.pullbackProdFstIsoProd_inv_snd_snd, CategoryTheory.ChosenPullbacksAlong.iso_pullback_obj, CategoryTheory.Limits.BinaryFan.rightUnitor_inv, AlgebraicGeometry.Scheme.Hom.appIso_inv_app, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_inv, CategoryTheory.Cat.isoOfEquiv_inv, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app_assoc, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id, CategoryTheory.OplaxFunctor.mapComp'_comp_mapComp'_whiskerRight, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_inv_iso_inv, CategoryTheory.Limits.kernelSubobjectIsoComp_inv_arrow, CommRingCat.HomTopology.precompHomeomorph_symm_apply, CategoryTheory.Limits.pushoutIsoOpPullback_inv_fst, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_ι_inv_assoc, CategoryTheory.Dial.braiding_inv_F, CategoryTheory.GradedObject.mapBifunctorObjSingle₀ObjIso_inv, CategoryTheory.Pseudofunctor.map₂_whisker_left, CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_inv, groupCohomology.eq_d₀₁_comp_inv_apply, CategoryTheory.Join.mapWhiskerLeft_associator_hom, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_inv_app_app, CochainComplex.ConnectData.restrictionLEIso_inv_f, CategoryTheory.Abelian.imageIsoImage_inv, HomologicalComplex.ι_mapBifunctorFlipIso_inv_assoc, CategoryTheory.MonoidalCategory.inv_hom_id_tensor, CategoryTheory.shiftFunctorAdd'_add_zero_inv_app, CategoryTheory.Functor.mapCommMonCompIso_inv_app_hom_hom, CategoryTheory.Functor.Monoidal.μ_of_cartesianMonoidalCategory, CategoryTheory.Adjunction.Triple.rightToLeft_eq_counits, HomologicalComplex.singleObjHomologySelfIso_inv_homologyι_assoc, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_assoc, AlgebraicGeometry.Scheme.Modules.pseudofunctor_right_unitality, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app, TopologicalSpace.Opens.mapMapIso_unitIso, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τl, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.LocalizerMorphism.commShift_iso_hom_app_assoc, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₃, CategoryTheory.NatTrans.op_whiskerLeft_assoc, CategoryTheory.Monoidal.rightUnitor_inv_app, CategoryTheory.BraidedCategory.hexagon_forward_inv_assoc, CategoryTheory.Functor.RightExtension.coneAtWhiskerRightIso_inv_hom, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_inv_hom₁, CategoryTheory.Functor.Monoidal.map_associator_inv', AlgebraicGeometry.IsAffineOpen.isoSpec_inv_toSpecΓ, CategoryTheory.ProjectiveResolution.Hom.hom'_f, symm_inv, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_right, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_id, CategoryTheory.typeEquiv_counitIso_inv_app_val_app, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_inv_app_left, CategoryTheory.OverPresheafAux.counitAuxAux_inv, CommBialgCat.inv_hom_apply, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, GrpCat.hom_inv_apply, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_left, inv_hom_id_app_app_app, CategoryTheory.Grp.leftUnitor_inv_hom_hom, AlgebraicGeometry.IsAffineOpen.toSpecΓ_isoSpec_inv, CategoryTheory.WithTerminal.liftToTerminalUnique_inv_app, AlgebraicGeometry.Scheme.Hom.appIso_inv_naturality, AlgebraicGeometry.Scheme.IsLocallyDirected.fst_inv_eq_snd_inv, CommRingCat.hom_inv_apply, AlgebraicTopology.DoldKan.N₂Γ₂_inv_app_f_f, CategoryTheory.Bicategory.prod_associator_inv_fst, CategoryTheory.Limits.opProductIsoCoproduct'_comp_self, CategoryTheory.WithTerminal.mapComp_inv_app, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_inv, CategoryTheory.PrelaxFunctor.map₂_hom_inv_assoc, CategoryTheory.Functor.LaxMonoidal.right_unitality_inv, CategoryTheory.Limits.π_comp_colimitOpIsoOpLimit_inv_assoc, CategoryTheory.ShortComplex.homologyMap_mapNatTrans, π_tensor_id_preserves_coequalizer_inv_desc, CategoryTheory.ShortComplex.rightHomologyMapIso'_inv, CategoryTheory.Arrow.inv_hom_id_right, CategoryTheory.Arrow.isoMk_inv_right, CategoryTheory.SmallObject.SuccStruct.iterationFunctor_map_succ_assoc, MulEquiv.toMonCatIso_inv, ModuleCat.biprodIsoProd_inv_comp_snd, CategoryTheory.Limits.Cones.postcomposeEquivalence_unitIso, CategoryTheory.BraidedCategory.hexagon_reverse, CategoryTheory.CostructuredArrow.mapIso_counitIso_hom_app_left, LightCondensed.isoLocallyConstantOfIsColimit_inv, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerRightIso_inv_app, HomologicalComplex.singleObjCyclesSelfIso_inv_homologyπ_assoc, ModuleCat.piIsoPi_inv_kernel_ι_apply, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_germ_apply, CategoryTheory.ShortComplex.rightHomologyIso_inv_naturality_assoc, CategoryTheory.GrothendieckTopology.toPlus_comp_plusCompIso_inv, CategoryTheory.Limits.biprod.braiding_inv, CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_snd_assoc, CategoryTheory.Enriched.FunctorCategory.functorEnriched_id_comp, compInverseIso_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_inv_app_fst_app, AlgebraicGeometry.ΓSpec.left_triangle, CategoryTheory.Functor.mapCommGrpNatIso_inv_app_hom_hom_hom, CategoryTheory.Adjunction.toEquivalence_counitIso_inv_app, CategoryTheory.Limits.colimitIsoSwapCompColim_inv_app, CategoryTheory.HopfObj.antipode_comul₂, CategoryTheory.Limits.Cones.postcomposeEquivalence_counitIso, SimplexCategory.revCompRevIso_inv_app, CompactlyGenerated.isoOfHomeo_inv, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app, CategoryTheory.Limits.Types.Small.productIso_inv_comp_π_apply, CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj_inv_app, AlgebraicGeometry.ι_left_coprodIsoSigma_inv, CategoryTheory.Adjunction.toEquivalence_unitIso_inv_app, CategoryTheory.Functor.postcomposeWhiskerLeftMapCone_inv_hom, TopCat.uliftFunctorCompForgetIso_inv_app, CategoryTheory.ComposableArrows.scMapIso_inv, CategoryTheory.Functor.mapZeroObject_inv, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv, CategoryTheory.monoidalOfHasFiniteCoproducts.rightUnitor_inv, CategoryTheory.Limits.PreservesLimitPair.iso_inv_snd, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₃, CategoryTheory.Dial.associator_inv_f, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv, CategoryTheory.Limits.imageMonoIsoSource_inv_ι, ModuleCat.lof_coprodIsoDirectSum_inv_apply, CategoryTheory.Over.postComp_inv_app_left, CochainComplex.shiftFunctorAdd'_inv_app_f', CategoryTheory.Bicategory.hom_inv_whiskerRight_whiskerRight, CategoryTheory.monoidalOfHasFiniteProducts.associator_inv_snd, CategoryTheory.Bicategory.Pith.rightUnitor_inv_iso_inv, CategoryTheory.Bicategory.prod_rightUnitor_inv_snd, CategoryTheory.Limits.π_comp_cokernelIsoOfEq_inv_assoc, groupHomology.d₁₀ArrowIso_inv_right, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_cofanPtIsoSelf_inv_assoc, CategoryTheory.BraidedCategory.braiding_tensor_left_hom_assoc, CategoryTheory.Pretriangulated.isoTriangleOfIso₁₂_inv_hom₂, HomologicalComplex.truncGE'_d_eq, CategoryTheory.Mathlib.Tactic.MonTauto.rightUnitor_inv_tensor_one_mul_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_right, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_fst, CategoryTheory.Functor.ShiftSequence.induced.shiftIso_hom_app_obj, AlgebraicGeometry.Scheme.isoSpec_inv_naturality_assoc, CategoryTheory.Equivalence.inverseFunctorObjIso_inv, HeytAlg.inv_hom_apply, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self, CategoryTheory.GradedObject.mapBifunctorRightUnitor_inv_naturality_assoc, CategoryTheory.Equivalence.changeInverse_counitIso_inv_app, CategoryTheory.Functor.Monoidal.coreMonoidalTransport_μIso_inv, ModuleCat.range_mkQ_cokernelIsoRangeQuotient_inv, TannakaDuality.FiniteGroup.equivApp_inv, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_0, CategoryTheory.Comma.mapRightEq_inv_app_left, inv_hom_id_app_app_assoc, CategoryTheory.flippingIso_inv_toFunctor_map_app_app, CategoryTheory.shiftFunctorAdd'_zero_add_hom_app, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_inv_f_f, CategoryTheory.MonadIso.toNatIso_inv, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app, CategoryTheory.Functor.lanCompColimIso_inv_app, CategoryTheory.Limits.opCospan_hom_app, AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_inv_fst, PresheafOfModules.isoMk_inv_app, CategoryTheory.ComposableArrows.map'_inv_eq_inv_map', AlgebraicGeometry.PresheafedSpace.sheafIsoOfIso_inv, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_assoc, CategoryTheory.SingleFunctors.shiftIso_add_inv_app, CategoryTheory.whiskerLeft_coprod_inl_leftDistrib_inv_assoc, CategoryTheory.Functor.ShiftSequence.induced_shiftIso_hom_app_obj_assoc, CategoryTheory.Localization.SmallShiftedHom.equiv_shift', CategoryTheory.CostructuredArrow.eta_inv_left, CategoryTheory.BraidedCategory.braiding_inv_naturality_right_assoc, CategoryTheory.Dial.rightUnitor_inv_f, CategoryTheory.MonObj.tensorObj.one_def, cancel_iso_inv_left, CategoryTheory.GradedObject.Monoidal.hexagon_reverse, CategoryTheory.Lax.LaxTrans.naturality_id, CategoryTheory.ForgetEnrichment.homOf_comp, CategoryTheory.Limits.PreservesPullback.iso_inv_snd_assoc, CategoryTheory.Grp.rightUnitor_inv_hom, AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_pullbackHom_assoc, CategoryTheory.Functor.mapBiproduct_inv, CategoryTheory.functorProdFunctorEquivUnitIso_hom_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_inv_app_hom, CategoryTheory.Functor.commShiftIso_comp_inv_app, TwoP.swapEquiv_counitIso_inv_app_hom_toFun, CategoryTheory.Lax.StrongTrans.naturality_comp_assoc, AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_inv_fst_assoc, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_map_right, HomologicalComplex.inl_biprodXIso_inv, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocNatIso_inv_app_app_app, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_rightUnitor_inv_as_app, CategoryTheory.Bicategory.prod_leftUnitor_inv_fst, CategoryTheory.Limits.spanCompIso_inv_app_right, CategoryTheory.GlueData.diagramIso_inv_app_right, CategoryTheory.Bicategory.triangle_assoc_comp_right_inv_assoc, AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv, HomologicalComplex.fromOpcycles_op_cyclesOpIso_inv_assoc, CategoryTheory.EnrichedFunctor.forgetId_inv_app, CategoryTheory.Monad.algebraEquivOfIsoMonads_functor, CategoryTheory.Bicategory.hom_inv_whiskerRight, CategoryTheory.WithTerminal.inclLiftToTerminal_inv_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app, CategoryTheory.Limits.HasLimit.isoOfNatIso_inv_π, CategoryTheory.Adjunction.leftAdjointCompIso_inv_app, CategoryTheory.Bicategory.Adjunction.left_triangle, MulEquiv.toCommGrpIso_inv, CategoryTheory.Functor.mapCochainComplexShiftIso_inv_app_f, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_fst, CategoryTheory.LocalizerMorphism.commShift_iso_inv_app_assoc, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_ε, CategoryTheory.cokernelOpUnop_inv, CategoryTheory.LocalizerMorphism.equiv_smallHomMap', CategoryTheory.Functor.map_shiftFunctorCompIsoId_inv_app_assoc, Rep.resIndAdjunction_homEquiv_apply, AlgEquiv.toUnder_inv_right_apply, CochainComplex.shiftFunctorAdd'_inv_app_f, CategoryTheory.Limits.map_π_preserves_coequalizer_inv_colimMap_assoc, CategoryTheory.PreZeroHypercover.inv_hom_h₀_assoc, CategoryTheory.SingleFunctors.inv_hom_id_hom_assoc, CategoryTheory.Sigma.descUniq_inv_app, AlgebraicGeometry.Scheme.IdealSheafData.comapIso_inv_subschemeι_assoc, CategoryTheory.Limits.coprodZeroIso_inv, CategoryTheory.oppositeShiftFunctorZero_inv_app, CategoryTheory.MonoidalCategory.externalProductCompDiagIso_inv_app_app, CategoryTheory.Functor.prod'CompFst_inv_app, Homotopy.extend.homAux_eq, CategoryTheory.MonoidalCategory.triangle_assoc_comp_right, CategoryTheory.Functor.mapTriangleCommShiftIso_inv_app_hom₃, CategoryTheory.Comonad.comparisonForget_inv_app, CategoryTheory.Equivalence.changeInverse_unitIso_inv_app, CochainComplex.truncateAugment_inv_f, AlgebraicGeometry.Scheme.Hom.app_invApp', CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_hom_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompPointIso_inv_app, CategoryTheory.Over.rightUnitor_inv_left_snd_assoc, CategoryTheory.LaxFunctor.whiskerLeft_mapComp'_comp_mapComp', CategoryTheory.Functor.rightOpLeftOpIso_inv_app, CategoryTheory.Bicategory.triangle_assoc_comp_right_inv, AlgebraicGeometry.Scheme.image_basicOpen, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso_inv_app_f, CategoryTheory.MonoidalCategory.triangle_assoc_comp_right_inv_assoc, CategoryTheory.SymmetricCategory.braiding_swap_eq_inv_braiding, CategoryTheory.Join.mapPairComp_inv_app_right, CategoryTheory.Limits.Types.pullbackIsoPullback_inv_snd, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_inv_naturality_assoc, CategoryTheory.ShortComplex.cyclesOpIso_inv_naturality, CategoryTheory.Functor.map_shiftFunctorComm_assoc, CategoryTheory.GradedObject.CofanMapObjFun.ιMapObj_iso_inv, CategoryTheory.kernel.ι_unop, CategoryTheory.Functor.ShiftSequence.induced_isoShiftZero_hom_app_obj_assoc, CategoryTheory.Oplax.LaxTrans.vComp_naturality_comp, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompYoneda, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp_assoc, CategoryTheory.Functor.Monoidal.map_associator_inv'_assoc, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp, CommMonCat.inv_hom_apply, CochainComplex.mappingCone.inl_v_triangle_mor₃_f_assoc, AlgebraicGeometry.pullbackSpecIso_inv_fst, AlgCat.hom_inv_leftUnitor, CategoryTheory.Mathlib.Tactic.MonTauto.associator_inv_comp_tensorHom_tensorHom_comp, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_inv_left_app, CategoryTheory.Bicategory.prod_leftUnitor_inv_snd, CategoryTheory.Over.iteratedSliceEquivOverMapIso_inv_app_left_left, CategoryTheory.Limits.Cone.mapConeToUnder_inv_hom, CategoryTheory.Limits.inr_comp_pushoutSymmetry_inv_assoc, CategoryTheory.ShiftMkCore.assoc_inv_app_assoc, CommBialgCat.hom_inv_apply, CategoryTheory.Comma.mapLeftComp_inv_app_right, CategoryTheory.Comma.equivProd_counitIso_inv_app, CategoryTheory.endofunctorMonoidalCategory_rightUnitor_inv_app, SemimoduleCat.hom_inv_associator, CategoryTheory.Limits.spanExt_inv_app_zero, unop2_op_inv, CategoryTheory.associator_inv_apply_1_2, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_map_app_app, unop_hom_inv_id_app, MulEquiv.toSingleObjEquiv_unitIso_inv, AddSemigrp.neg_hom_apply, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_inv_τl, Condensed.isoLocallyConstantOfIsColimit_inv, inv_hom_id_assoc, CategoryTheory.Limits.Cones.extendComp_inv_hom, CategoryTheory.Limits.biproduct.conePointUniqueUpToIso_inv, CategoryTheory.Join.mapPairLeft_inv_app, CategoryTheory.cosimplicialSimplicialEquiv_counitIso_inv_app_app, CategoryTheory.Codiscrete.natIsoFunctor_inv_app, ModuleCat.uliftFunctorForgetIso_inv_app, TopCat.pullbackIsoProdSubtype_inv_snd_apply, CategoryTheory.BraidedCategory.yang_baxter_assoc, CategoryTheory.Limits.biprod.associator_inv_natural_assoc, HomologicalComplex.XIsoOfEq_hom_comp_XIsoOfEq_inv_assoc, CategoryTheory.Subobject.isoOfEqMk_inv, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_hom_hom, CategoryTheory.Quiv.hom_map_inv_map_of_iso, HomologicalComplex.singleObjOpcyclesSelfIso_inv_naturality, CategoryTheory.eHom_whisker_cancel_assoc, SemiNormedGrp.inv_hom_apply, CategoryTheory.MonoidalCategory.id_whiskerLeft_assoc, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right_assoc, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_id_naturality_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.unit_actionHomRight_assoc, CategoryTheory.Limits.biprod.braiding'_inv, CategoryTheory.Limits.mulInitial_inv, CategoryTheory.MonoidalClosed.curry'_comp, HomologicalComplex.cyclesOpIso_inv_naturality, CoalgEquiv.toCoalgIso_inv, CategoryTheory.Functor.isoCopyObj_inv_app, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv, AddSemigrp.hom_neg_apply, CategoryTheory.Limits.limit.conePointUniqueUpToIso_inv_comp_assoc, CategoryTheory.Limits.CatCospanTransform.triangle_inv, CategoryTheory.Functor.uncurryObjFlip_inv_app, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_inv_app_hom, CategoryTheory.Bicategory.mateEquiv_symm_apply, CategoryTheory.MonoidalCategory.id_whiskerLeft_symm_assoc, CategoryTheory.Pseudofunctor.map₂_whisker_left_assoc, CategoryTheory.CatCommSq.iso_inv_naturality_assoc, CategoryTheory.Limits.CatCospanTransform.leftUnitor_inv_right_app, groupHomology.H1AddEquivOfIsTrivial_single, CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_left, CategoryTheory.Limits.pullbackProdFstIsoProd_inv_snd_fst, CategoryTheory.Limits.Cones.extendIso_inv_hom, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id, CategoryTheory.ComposableArrows.isoMk₂_inv, CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_inv_assoc, CategoryTheory.Localization.liftNatTrans_app, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_inv_app_app, smoothSheafCommRing.ι_forgetStalk_inv_apply, CategoryTheory.ShortComplex.Splitting.ofIso_s, CategoryTheory.Mat_.embeddingLiftIso_inv_app, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_counitIso_inv_app_f, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_map_fiber, CategoryTheory.Pseudofunctor.StrongTrans.whiskerRight_naturality_comp_assoc, CategoryTheory.sum.inrCompInrCompInverseAssociator_inv_app_down, ModuleCat.FreeMonoidal.εIso_inv_freeMk, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_fst_assoc, CategoryTheory.Functor.mapHomologicalComplexIdIso_inv_app_f, CategoryTheory.Limits.Types.binaryCoproductIso_inr_comp_inv_apply, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_fst, CategoryTheory.Pretriangulated.shiftFunctorZero_op_hom_app, CategoryTheory.Subobject.isoOfMkEq_inv, CategoryTheory.Oplax.StrongTrans.naturality_id, CategoryTheory.CommMon.mkIso_inv_hom_hom, CategoryTheory.Abelian.factorThruImage_comp_coimageIsoImage'_inv, CategoryTheory.MonoidalCategory.associator_conjugation_assoc, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_assoc, CategoryTheory.Bicategory.associator_eqToHom_inv_assoc, CategoryTheory.Subobject.underlyingIso_arrow, CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_fst, CategoryTheory.MonoidalCategory.pentagon_hom_inv, CategoryTheory.prodOpEquiv_unitIso_inv_app, AlgebraicGeometry.Scheme.iso_inv_base_hom_base, CategoryTheory.GradedObject.mapBifunctorRightUnitor_inv_apply, CategoryTheory.GradedObject.ι_mapBifunctorComp₁₂MapObjIso_inv, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply, CategoryTheory.Over.postEquiv_counitIso, CategoryTheory.Limits.Fan.ext_inv_hom, AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv, CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_inv_hom_id, CategoryTheory.Grp.braiding_inv_hom, CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor, CategoryTheory.Limits.cokernelBiproductιIso_inv, CategoryTheory.Functor.ranObjObjIsoLimit_inv_π_assoc, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_assoc, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_hom_app_app, CategoryTheory.OplaxFunctor.mapComp_assoc_right_app_assoc, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π_assoc, CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_inv_hom, SheafOfModules.pushforwardCongr_inv_app_val_app, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_inv, CategoryTheory.HalfBraiding.monoidal_assoc, groupCohomology.isoCocycles₂_inv_comp_iCocycles_apply, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_inv_π_assoc, CategoryTheory.Limits.fiberwiseColimitLimitIso_inv_app, CategoryTheory.Functor.IsCoverDense.Types.appIso_inv, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv_desc_assoc, CategoryTheory.e_id_comp_assoc, CategoryTheory.MonoidalOpposite.tensorRightUnmopIso_inv_app, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_assoc, HomologicalComplex₂.flipEquivalenceUnitIso_inv_app_f_f, CategoryTheory.Limits.coprod.leftUnitor_inv, TopCat.pullbackIsoProdSubtype_inv_fst, CategoryTheory.Limits.pullbackIsoOpPushout_inv_fst, CategoryTheory.Bicategory.whiskerLeft_inv_hom_whiskerRight_assoc, CategoryTheory.Limits.cospanCompIso_inv_app_right, CategoryTheory.Equivalence.sheafCongr.unitIso_hom_app_val_app, CategoryTheory.Pseudofunctor.StrongTrans.isoMk_inv_as_app, groupCohomology.isoCocycles₁_inv_comp_iCocycles, CategoryTheory.op_inv_leftUnitor, CategoryTheory.Functor.Monoidal.tensorObjComp_inv_app, CategoryTheory.tensorRightHomEquiv_tensor, CategoryTheory.Hom.mulEquivCongrRight_symm_apply, CategoryTheory.ShortComplex.LeftHomologyMapData.leftHomologyMap_eq, map_hom_inv_id_app, CategoryTheory.Functor.op_commShiftIso_inv_app_assoc, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.topMapᵣ_app, CategoryTheory.Limits.kernelBiproductπIso_inv, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₂, CategoryTheory.MonoidalCategory.MonoidalRightAction.action_actionHomRight_assoc, CategoryTheory.ShortComplex.mapRightHomologyIso_inv_naturality_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_id, CategoryTheory.WithTerminal.starIsoTerminal_inv, CategoryTheory.prod.prodFunctorToFunctorProdAssociator_inv_app_app, CategoryTheory.Endofunctor.Algebra.isoMk_inv_f, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocNatIso_inv_app_app_app, SimplicialObject.opFunctor_obj_δ, CategoryTheory.Bicategory.InducedBicategory.bicategory_rightUnitor_inv_hom, CategoryTheory.Functor.mapTriangleInvRotateIso_inv_app_hom₂, groupHomology.eq_d₂₁_comp_inv_assoc, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv, ModuleCat.imageIsoRange_inv_image_ι, CategoryTheory.Functor.leftOpId_inv_app, Rep.ofMulActionSubsingletonIsoTrivial_inv_hom, CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence_inv, CategoryTheory.MonoidalCategory.pentagon_inv_hom, TopologicalSpace.Opens.mapMapIso_inverse, CategoryTheory.Limits.pullbackIsoOpPushout_inv_snd, SheafOfModules.conjugateEquiv_pullbackComp_inv, CategoryTheory.NatTrans.CommShiftCore.shift_app_assoc, CategoryTheory.MonoidalCategory.tensor_hom_inv_id_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_inv_app_snd_app, CategoryTheory.EnrichedCat.leftUnitor_inv_out_app, TopCat.Presheaf.Pushforward.comp_inv_app, AlgebraicGeometry.Scheme.toIso_inv_ι_assoc, AlgebraicGeometry.SheafedSpace.restrictTopIso_inv, CommAlgCat.hom_inv_apply, CategoryTheory.Functor.LaxMonoidal.tensorHom_ε_comp_μ_assoc, CategoryTheory.ForgetEnrichment.homTo_comp, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_comp, CategoryTheory.ProjectiveResolution.leftDerived_app_eq, CategoryTheory.coreCategory_inv_iso_hom, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_assoc, CategoryTheory.Equivalence.invFunIdAssoc_inv_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_inv_app_snd_app, HomologicalComplex.homologyπ_extendHomologyIso_inv_assoc, HomologicalComplex₂.ι_totalShift₁Iso_inv_f_assoc, CategoryTheory.Limits.colimit.isoColimitCocone_ι_inv_assoc, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.leftUnitor_hom_unit_app, AlgebraicGeometry.Scheme.Hom.appIso_inv_naturality_assoc, CategoryTheory.Limits.PullbackCone.eta_inv_hom, CategoryTheory.GrothendieckTopology.sheafToPresheaf_map_sheafComposeNatTrans_eq_sheafifyCompIso_inv, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_inv_app_zero, CategoryTheory.Limits.inl_comp_pushoutSymmetry_inv, CategoryTheory.Functor.CommShift₂.comm, CategoryTheory.pullbackShiftFunctorAdd'_hom_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom, groupHomology.cyclesIso₀_inv_comp_iCycles, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv_assoc, CategoryTheory.ComonObj.comul_assoc_flip, HomologicalComplex₂.XXIsoOfEq_inv_ιTotal_assoc, TopologicalSpace.Opens.mapId_inv_app, CategoryTheory.Localization.Monoidal.μ_inv_natural_left_assoc, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_inv_app, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_counitIso_inv_app_right_app, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_snd_fst_assoc, AlgebraicGeometry.Scheme.IdealSheafData.comapIso_inv_subschemeι, CategoryTheory.Lax.LaxTrans.vComp_naturality_id, CategoryTheory.Functor.isoWhiskerLeft_inv, SemimoduleCat.MonoidalCategory.braiding_inv_apply, CategoryTheory.shiftFunctorZero_inv_app_shift, CategoryTheory.Bimon.equivMonComonUnitIsoAppXAux_inv, CategoryTheory.CechNerveTerminalFrom.wideCospan.limitIsoPi_inv_comp_pi, CategoryTheory.Monoidal.InducingFunctorData.tensorHom_eq, CategoryTheory.Limits.Cones.eta_inv_hom, CategoryTheory.Limits.WalkingMultispan.functorExt_inv_app, ChainComplex.isoHomologyι₀_inv_naturality, CategoryTheory.MonObj.Mon_tensor_mul_one, CategoryTheory.Adjunction.commShiftIso_inv_app_counit_app_assoc, CategoryTheory.Limits.CatCospanTransform.associator_inv_left_app, CategoryTheory.Functor.CommShift.id_commShiftIso_inv_app, CategoryTheory.Lax.OplaxTrans.id_naturality, CategoryTheory.Limits.inl_pushoutLeftPushoutInrIso_inv, CategoryTheory.CommGrp.mkIso_inv_hom_hom_hom, CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIsoWhisker_inv_right, CategoryTheory.Functor.LaxMonoidal.ε_tensorHom_comp_μ_assoc, CategoryTheory.Localization.lift₂NatIso_inv, CategoryTheory.Precoverage.ZeroHypercover.isoMk_inv, CategoryTheory.StructuredArrow.mapNatIso_inverse_obj_hom, CategoryTheory.Over.associator_inv_left_fst_snd, HomologicalComplex₂.total.mapIso_inv, CategoryTheory.CommGrp.mkIso'_inv_hom_hom_hom, CategoryTheory.Functor.commShiftIso_inv_naturality_assoc, HomologicalComplex.extend_op_d, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₃, CategoryTheory.Endofunctor.Algebra.functorOfNatTransEq_inv_app_f, CategoryTheory.Limits.CatCospanTransform.whiskerRight_comp, CategoryTheory.Functor.whiskerLeft_twice, MulEquiv.toSingleObjEquiv_counitIso_inv, Rep.diagonalOneIsoLeftRegular_inv_hom, CategoryTheory.braiding_tensorUnit_left, CategoryTheory.Limits.PushoutCocone.op_π_app, ModuleCat.hom_inv_rightUnitor, CategoryTheory.Equivalence.congrLeft_unitIso_inv_app, AlgebraicGeometry.Scheme.Hom.appIso_inv_appLE_assoc, CategoryTheory.shiftFunctorAdd'_assoc_inv_app_assoc, CategoryTheory.mateEquiv_symm_apply, CategoryTheory.Functor.sheafPushforwardContinuousComp_inv_app_val_app, map_inv_hom_id, CategoryTheory.MonObj.Mon_tensor_one_mul, CategoryTheory.Limits.Cone.equiv_inv_π, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_assoc, CategoryTheory.ShortComplex.leftRightHomologyComparison_eq, CategoryTheory.CartesianMonoidalCategory.associator_inv_fst_snd_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_assoc, CategoryTheory.Bicategory.LeftLift.whisker_unit, CategoryTheory.Limits.CategoricalPullback.Hom.w', CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app, CategoryTheory.Functor.mapTriangleInvRotateIso_inv_app_hom₁, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_assoc, CategoryTheory.Oplax.OplaxTrans.naturality_id_assoc, CategoryTheory.Limits.pullbackProdFstIsoProd_inv_snd_snd_assoc, CategoryTheory.Limits.π_comp_colimitOpIsoOpLimit_inv, CategoryTheory.WithTerminal.inclLift_inv_app, isoFunctorOfIsoInverse_inv_app, CategoryTheory.Cat.opFunctorInvolutive_inv_app_toFunctor_map, CategoryTheory.rightUnitor_inv_braiding_assoc, HomologicalComplex.mkHomToSingle_f, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id_assoc, PartOrdEmb.inv_hom_apply, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIso_inv_app_hom, HomologicalComplex.XIsoOfEq_inv_comp_XIsoOfEq_hom_assoc, CategoryTheory.Limits.Types.binaryCoproductIso_inr_comp_inv, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_hom_app_val_app, CategoryTheory.Join.mapWhiskerRight_associator_hom, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, CategoryTheory.Bicategory.pentagon_hom_hom_inv_inv_hom_assoc, CategoryTheory.Limits.reflexivePair.mkNatIso_inv_app, CategoryTheory.Abelian.PreservesImage.iso_inv_ι_assoc, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π_assoc, CategoryTheory.shiftFunctorAdd'_add_zero_hom_app, CategoryTheory.Limits.walkingSpanOpEquiv_unitIso_inv_app, CategoryTheory.ComposableArrows.isoMk_inv, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_μIso_inv, CategoryTheory.Limits.pullbackProdSndIsoProd_inv_fst_fst, CategoryTheory.Limits.PreservesInitial.iso_hom, CategoryTheory.LocalizerMorphism.homMap_apply_assoc, homCongr_apply, CategoryTheory.Limits.Fork.ext_inv, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.Bicategory.Adj.leftUnitor_inv_τl, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_obj_iso_inv, CategoryTheory.Functor.LaxMonoidal.associativity_inv, CategoryTheory.Limits.opCospan_inv_app, CategoryTheory.Limits.instIsIsoHomInvCone, CategoryTheory.Equivalence.congrLeft_unitIso_hom_app, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv, SSet.Truncated.HomotopyCategory.mkNatIso_inv_app_mk, isIso_inv, CategoryTheory.preservesColimitIso_inv_comp_desc_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_inv_app_snd_app, CategoryTheory.Monoidal.leftUnitor_inv_app, CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_comp, BddDistLat.inv_hom_apply, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_inv_app_val_app, CategoryTheory.Functor.mapTriangleRotateIso_hom_app_hom₃, CategoryTheory.braiding_tensorUnit_right_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_ε_app, Condensed.isoFinYonedaComponents_inv_comp, CategoryTheory.whiskerRight_ι_colimitCompWhiskeringRightIsoColimitComp_inv_assoc, CategoryTheory.LocalizerMorphism.smallHomMap'_mk, Rep.coindIso_inv_hom_hom, CategoryTheory.Functor.sheafPushforwardCocontinuousCompSheafToPresheafIso_inv, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂'_map_app_app, HomologicalComplex.π_homologyIsoSc'_inv_assoc, AlgebraicGeometry.Spec_zeroLocus_eq_zeroLocus, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_whiskerLeft, CommGrpCat.inv_hom_apply, CategoryTheory.MonoidalCategory.whiskerRight_tensor_symm_assoc, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoOfRangeEq_inv, CategoryTheory.Limits.biproduct.isoProduct_inv, CategoryTheory.Limits.pointwiseProductCompEvaluation_inv_app, CategoryTheory.ShortComplex.RightHomologyData.homologyIso_inv_comp_homologyι_assoc, CategoryTheory.Bicategory.pentagon_inv_inv_hom_inv_inv_assoc, CochainComplex.shiftFunctorAdd_inv_app_f, TopologicalSpace.Opens.overEquivalence_counitIso_inv_app, CategoryTheory.sum.inrCompInlCompAssociator_inv_app_down_down, CategoryTheory.Center.leftUnitor_inv_f, CategoryTheory.CartesianMonoidalCategory.braiding_inv_snd, CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_hom_hom, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom, CategoryTheory.Limits.cospanExt_inv_app_one, HomologicalComplex₂.ι_totalShift₂Iso_hom_f_assoc, CategoryTheory.Limits.BinaryFan.braiding_inv_fst_assoc, CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_right_inv, CategoryTheory.Bicategory.comp_whiskerLeft, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₂, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst, CategoryTheory.Mon.associator_inv_hom, CategoryTheory.Equivalence.symmEquivInverse_obj_counitIso_inv, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_inv_π, CategoryTheory.conjugateEquiv_rightUnitor_hom, CategoryTheory.LocalizerMorphism.equiv_smallShiftedHomMap, CategoryTheory.FreeGroupoid.mapComp_inv_app, CategoryTheory.Lax.StrongTrans.naturality_id, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₁, CategoryTheory.Adjunction.unit_app_shift_commShiftIso_inv_app_assoc, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_inv_app, CategoryTheory.Functor.commShiftOfLocalization.iso_inv_app_assoc, CategoryTheory.OrthogonalReflection.iteration_map_succ_assoc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_inv_app_hom, CategoryTheory.Functor.isDenseAt_iff, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality_assoc, CategoryTheory.Localization.Monoidal.μ_inv_natural_right_assoc, CategoryTheory.Bicategory.LeftExtension.ofCompId_hom, CategoryTheory.SingleFunctors.hom_inv_id_hom, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_inv_app, CategoryTheory.Functor.IsCoverDense.Types.presheafIso_inv_app, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv, hom_inv_id_apply, CategoryTheory.ProjectiveResolution.π'_f_zero, CategoryTheory.Linear.homCongr_apply, CategoryTheory.Pseudofunctor.toLax_mapId', AlgebraicGeometry.Scheme.isoSpec_inv_naturality, CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_snd_snd_assoc, Homotopy.ofExtend_hom, HomologicalComplex.leftUnitor'_inv, ModuleCat.homEquiv_extendScalarsComp, CategoryTheory.Equivalence.changeFunctor_unitIso_inv_app, CategoryTheory.IsPushout.inr_isoIsPushout_inv, CategoryTheory.Pseudofunctor.mapComp_id_left_inv, TopCat.Sheaf.objSupIsoProdEqLocus_inv_snd, CategoryTheory.monoidalOfHasFiniteCoproducts.leftUnitor_inv, CategoryTheory.Limits.Pi.reindex_inv_π, CategoryTheory.unitOfTensorIsoUnit_inv_app, CategoryTheory.Limits.imageSubobjectCompIso_inv_arrow_assoc, TopologicalSpace.Opens.overEquivalence_unitIso_inv_app_left, QuadraticModuleCat.toIsometry_inv_rightUnitor, CategoryTheory.ShortComplex.comp_homologyMap_comp_assoc, groupCohomology.cocycles₁IsoOfIsTrivial_inv_hom_apply_coe, CategoryTheory.Functor.LaxMonoidal.associativity_inv_assoc, TopCat.pullbackIsoProdSubtype_inv_snd, CategoryTheory.sum.inlCompInlCompAssociator_inv_app_down, AlgebraicGeometry.Scheme.isoOfEq_inv_ι_assoc, smoothSheafCommRing.ι_forgetStalk_inv_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.inv_hom_actionHomLeft_assoc, CategoryTheory.Adjunction.CommShift.compatibilityCounit_left, AlgebraicGeometry.Scheme.Hom.preimageIso_inv_ι_assoc, CategoryTheory.PreZeroHypercover.hom_inv_h₀_assoc, Homotopy.mkCoinductiveAux₂_add_one, HomologicalComplex.xPrevIso_comp_dTo_assoc, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τr, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_comp_homologyIso_inv_assoc, CategoryTheory.Join.pseudofunctorRight_mapId_inv_toNatTrans_app, CategoryTheory.Functor.op_commShiftIso_inv_app, CategoryTheory.Comma.unopFunctorCompSnd_inv_app, CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_whisker_left, PartOrd.inv_hom_apply, PresheafOfModules.map_comp, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃'_map_app_app, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right, CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_inv_desc, CategoryTheory.LocalizerMorphism.guitartExact_of_isLeftDerivabilityStructure', CategoryTheory.ShiftedHom.opEquiv'_symm_apply, CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom_assoc, CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_fst_assoc, AlgebraicGeometry.PresheafedSpace.map_id_c_app, AddCommMonCat.hom_neg_apply, CategoryTheory.Limits.colimitPointwiseProductToProductColimit_app, CategoryTheory.Idempotents.DoldKan.η_inv_app_f, CategoryTheory.Limits.inr_pushoutRightPushoutInlIso_inv, AddCommGrpCat.kernelIsoKer_inv_comp_ι, CategoryTheory.MonoidalCategory.MonoidalLeftAction.hom_inv_actionHomLeft_assoc, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, AlgebraicGeometry.SheafedSpace.GlueData.ι_isoPresheafedSpace_inv, CategoryTheory.Bicategory.associator_inv_naturality_left_assoc, HomologicalComplex.extend.rightHomologyData_g', CategoryTheory.OplaxFunctor.mapComp_id_right_assoc, CategoryTheory.Bicategory.whiskerLeftIso_inv, CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_mapId, CategoryTheory.SmallObject.SuccStruct.iterationFunctor_map_succ, ModuleCat.restrictScalarsComp'App_inv_naturality, CategoryTheory.Oplax.StrongTrans.naturality_comp_assoc, TopCat.prodIsoProd_inv_fst, CategoryTheory.Functor.OplaxMonoidal.δ_comp_whiskerLeft_δ, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_hom_app_left, CategoryTheory.SmallObject.SuccStruct.extendToSuccRestrictionLEIso_inv_app, HomologicalComplex.single_map_f_self_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocIso_inv_naturality_assoc, CategoryTheory.Endofunctor.Coalgebra.isoMk_inv_f, groupHomology.eq_d₁₀_comp_inv, CategoryTheory.MonoidalCategory.tensoringRight_ε, CategoryTheory.OplaxFunctor.mapComp_assoc_right, CategoryTheory.Limits.biproductUniqueIso_inv, Frm.inv_hom_apply, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_inv_app_f, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_obj_hom_app, CategoryTheory.Comma.isoMk_inv_left, algEquivIsoAlgebraIso_inv, CategoryTheory.Adjunction.adjToMonadIso_inv_toNatTrans_app, CategoryTheory.Limits.limit.isoLimitCone_inv_π_assoc, CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_inv_apply, CategoryTheory.CatCenter.smul_iso_inv_eq_assoc, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_inv_naturality_assoc, groupHomology.isoShortComplexH1_inv, AlgebraicGeometry.AffineSpace.map_SpecMap, CategoryTheory.OplaxFunctor.mapComp_assoc_left_assoc, CategoryTheory.Limits.CatCospanTransform.associator_inv_base_app, CategoryTheory.Center.associator_inv_f, CategoryTheory.SingleFunctors.hom_inv_id_hom_app_assoc, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_ε_assoc, CategoryTheory.Bicategory.InducedBicategory.forget_mapId_inv, CategoryTheory.Functor.Monoidal.transport_η_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_app_assoc, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_inv_app, AlgebraicTopology.DoldKan.toKaroubiCompN₂IsoN₁_inv_app, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_unitIso_inv_app_f, groupHomology.eq_d₁₀_comp_inv_assoc, CategoryTheory.Bicategory.pentagon_inv_assoc, CategoryTheory.Idempotents.KaroubiUniversal₁.counitIso_inv_app_app_f, CategoryTheory.GradedObject.mapBifunctorObjObjSingle₀Iso_inv, map_hom_inv_id_eval_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitIso_inv_naturality_assoc, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_id_assoc, CategoryTheory.MonoidalCategory.selRightfAction_actionAssocIso_hom, CategoryTheory.Bicategory.whiskerRight_comp, CategoryTheory.Limits.pullbackProdSndIsoProd_inv_fst_fst_assoc, CompactlyGenerated.homeoOfIso_symm_apply, CategoryTheory.Bicategory.rightUnitorNatIso_inv_app, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd, CategoryTheory.Mon.mkIso'_inv_hom, CategoryTheory.Pseudofunctor.StrongTrans.associator_inv_as_app, LinearEquiv.toModuleIsoₛ_inv, CategoryTheory.SingleFunctors.postcomp_shiftIso_inv_app, CategoryTheory.shiftFunctorAdd_assoc_inv_app_assoc, CategoryTheory.Limits.PreservesLimitPair.iso_inv_snd_assoc, CategoryTheory.Limits.pullbackDiagonalMapIso.inv_snd_fst, ModuleCat.restrictScalarsComp'App_inv_naturality_assoc, CategoryTheory.Bicategory.Comonad.comul_counit_assoc, HomologicalComplex.extend.homologyData'_left_i, CategoryTheory.Functor.OplaxMonoidal.δ_comp_η_tensorHom, CategoryTheory.Limits.pullbackProdFstIsoProd_inv_fst_assoc, CategoryTheory.FreeGroupoid.mapId_inv_app, HomologicalComplex.truncGE'_d_eq_fromOpcycles, CategoryTheory.ShortComplex.cyclesIsoLeftHomology_hom_inv_id, CategoryTheory.Limits.limitFlipIsoCompLim_inv_app, CategoryTheory.MonObj.one_leftUnitor, CategoryTheory.Adjunction.compYonedaIso_inv_app_app, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f, CategoryTheory.Under.mapIso_inverse, CategoryTheory.yonedaGrpObjIsoOfRepresentableBy_inv, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_inv_hom, CategoryTheory.Pi.isoApp_inv, CategoryTheory.Equivalence.changeInverse_counitIso_hom_app, CategoryTheory.Pseudofunctor.toLax_mapId, CategoryTheory.Functor.leftUnitor_inv_app, SheafOfModules.Presentation.map_relations_I, CategoryTheory.Functor.coreCompInclusionIso_inv_app, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIsoAux_inv, CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_assoc, CategoryTheory.FreeGroupoid.liftNatIso_inv_app, CategoryTheory.ShortComplex.asIsoHomologyπ_inv_comp_homologyπ, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_apply, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv, CategoryTheory.StructuredArrow.mapIso_unitIso_inv_app_right, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_hom_assoc, CategoryTheory.ShortComplex.homologyι_comp_asIsoHomologyι_inv, AlgebraicGeometry.Scheme.iso_hom_base_inv_base, CategoryTheory.Bicategory.whiskerLeft_inv_hom_whiskerRight, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom_app_assoc, CategoryTheory.MonoidalCategory.DayConvolution.braidingInvCorepresenting_app, ModuleCat.imageIsoRange_inv_image_ι_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitIso_inv_naturality, CategoryTheory.CartesianMonoidalCategory.associator_inv_fst_fst_assoc, id_tensor_π_preserves_coequalizer_inv_desc, ModuleCat.MonoidalCategory.rightUnitor_inv_apply, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.flipFunctorToInterchange_inv_app_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.tensor_actionHomRight_assoc, CategoryTheory.Bicategory.whisker_assoc_assoc, HomologicalComplex.d_comp_XIsoOfEq_inv_assoc, CategoryTheory.Abelian.PreservesCoimage.iso_inv_π, AlgebraicGeometry.AffineSpace.SpecIso_inv_over_assoc, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatIso_inv, CategoryTheory.Limits.limitOpIsoOpColimit_inv_comp_π_assoc, CategoryTheory.Grothendieck.transportIso_inv_base, CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_inv_assoc, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₁, CategoryTheory.PreZeroHypercover.instIsIsoH₀Inv, CategoryTheory.Functor.PushoutObjObj.ι_iso_of_iso_left_inv, CategoryTheory.PreZeroHypercover.inv_inv_h₀_comp_f_assoc, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₂, MonObj.mopEquivCompForgetIso_inv_app_unmop, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_counitIso, AlgebraicGeometry.Scheme.stalkMap_hom_inv, CategoryTheory.Functor.sumIsoExt_inv_app_inl, PresheafOfModules.colimitPresheafOfModules_map, CategoryTheory.ShortComplex.opcyclesOpIso_inv_naturality, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_assoc, Frm.hom_inv_apply, CategoryTheory.MonoidalCategory.pentagon_inv_assoc, HomologicalComplex.XIsoOfEq_inv_comp_d, map_inv_hom_id_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app_assoc, CategoryTheory.Bicategory.associator_eqToHom_hom, CategoryTheory.ObjectProperty.isoHom_inv_id_hom_assoc, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_fst, CategoryTheory.Bicategory.whisker_assoc_symm, HomologicalComplex.XIsoOfEq_inv_comp_d_assoc, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π, CategoryTheory.Localization.SmallShiftedHom.equiv_shift, CategoryTheory.op_hom_associator, CategoryTheory.Bicategory.Prod.sectL_mapComp_inv, CategoryTheory.WithInitial.opEquiv_counitIso_inv_app, CategoryTheory.Functor.IsCartesian.domainUniqueUpToIso_inv, CategoryTheory.ShiftMkCore.add_zero_inv_app, AlgEquiv.toAlgebraIso_inv, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_obj, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.leftMapₗ_app, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_comp, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_snd_coe, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id_assoc, Bipointed.swapEquiv_counitIso_inv_app_toFun, CategoryTheory.Functor.IsEventuallyConstantFrom.coconeιApp_eq, AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv_assoc, CategoryTheory.IsPushout.inl_isoPushout_inv, HomologicalComplex₂.XXIsoOfEq_inv_ιTotal, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.mkIso_inv_snd, ProfiniteGrp.hom_inv_apply, refl_inv, CategoryTheory.StructuredArrow.mapIso_functor_map_left, CategoryTheory.Bicategory.id_whiskerLeft_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.e_inv_app, CategoryTheory.ShortComplex.LeftHomologyData.π_comp_homologyIso_inv_assoc, CategoryTheory.Functor.flipping_unitIso_inv_app_app_app, HomologicalComplex.iCyclesIso_hom_inv_id, CategoryTheory.liftedLimitMapsToOriginal_inv_map_π, CategoryTheory.Bimon.equivMonComonUnitIsoApp_inv_hom_hom, SheafOfModules.ιFree_mapFree_inv, CategoryTheory.Adjunction.CoreUnitCounit.right_triangle, hom_inv_id_triangle_hom₁, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_inv_app_one, CategoryTheory.Join.inclLeftCompOpEquivInverse_inv_app_op, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app_assoc, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self_apply, CategoryTheory.Bicategory.InducedBicategory.forget_mapComp_inv, AlgebraicGeometry.Scheme.stalkMap_hom_inv_apply, groupHomology.H1ToTensorOfIsTrivial_H1π_single, CategoryTheory.op_hom_rightUnitor, CategoryTheory.Monad.algebraEquivOfIsoMonads_counitIso, CategoryTheory.FreeMonoidalCategory.mk_ρ_inv, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanMapIso_inv, CategoryTheory.Functor.sheafPushforwardContinuousId'_inv_app_val_app, CategoryTheory.IsHomLift.isoOfIsoLift_hom_inv_id, CategoryTheory.Over.associator_inv_left_fst_fst, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_app_assoc, AlgebraicGeometry.Scheme.Hom.normalizationCoprodIso_inv_coprodDesc_fromNormalization, CategoryTheory.Limits.Cones.postcomposeComp_inv_app_hom, CategoryTheory.Functor.IsEventuallyConstantTo.isoMap_hom_inv_id, CategoryTheory.Preadditive.commGrpEquivalenceAux_inv_app_hom_hom_hom, groupCohomology.cocyclesMk₁_eq, AlgebraicGeometry.pullbackSpecIso_inv_snd_assoc, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop, unop_inv, CategoryTheory.SimplicialThickening.SimplicialCategory.assoc, CategoryTheory.Functor.mapConePostcomposeEquivalenceFunctor_inv_hom, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_assoc, SSet.Subcomplex.topIso_inv_ι_assoc, CategoryTheory.Limits.map_π_preserves_coequalizer_inv_assoc, CategoryTheory.NatTrans.naturality_1_assoc, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_hom_fac, CategoryTheory.IsCommMonObj.mul_comm'_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app, pointedToBipointedCompBipointedToPointedSnd_inv_app_toFun, CategoryTheory.Presieve.isSheafFor_over_map_op_comp_iff, equivIsoIso_inv, ModuleCat.MonoidalCategory.leftUnitor_inv_apply, CategoryTheory.Limits.Pi.whiskerEquiv_hom, TopCat.Presheaf.presheafEquivOfIso_unitIso_inv_app_app, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁'_obj_map_app, CategoryTheory.Cat.associator_inv_toNatTrans, CategoryTheory.MonoidalOpposite.mopMopEquivalence_counitIso_inv_app, CategoryTheory.Equivalence.core_functor_map_iso_inv, CategoryTheory.Pretriangulated.shortComplexOfDistTriangleIsoOfIso_inv_τ₁, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop_assoc, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv, CategoryTheory.Cat.leftUnitor_inv_toNatTrans, CategoryTheory.Limits.PreservesEqualizer.iso_inv_ι, CategoryTheory.Functor.Monoidal.commTensorLeft_inv_app, Rep.linearizationTrivialIso_inv_hom, BoolAlg.hom_inv_apply, TopCat.pullbackIsoProdSubtype_inv_fst_apply, CategoryTheory.Join.mapPairId_inv_app, CategoryTheory.Functor.const.opObjOp_inv_app, CategoryTheory.Bicategory.associator_inv_naturality_right_assoc, core_hom_app_iso_inv, CategoryTheory.ShortComplex.LeftHomologyData.homologyIso_hom_comp_leftHomologyIso_inv_assoc, CategoryTheory.Limits.cokernelEpiComp_inv, hom_inv_id_triangle_hom₃, CategoryTheory.Comma.mapLeftId_inv_app_left, CategoryTheory.InjectiveResolution.isoRightDerivedObj_inv_naturality, CategoryTheory.Functor.commShiftOfLocalization.iso_hom_app, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_right, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_comp, CategoryTheory.Functor.mapMonIdIso_inv_app_hom, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π, isoCompInverse_inv_app, CategoryTheory.NatTrans.app_shift_assoc, CategoryTheory.Bicategory.hom_inv_whiskerRight_assoc, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_app_assoc, CategoryTheory.HopfObj.mul_antipode₁, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_unitIso, CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_inv, CategoryTheory.cosimplicialSimplicialEquiv_unitIso_inv_app, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_limit_map, CategoryTheory.Arrow.inv_hom_id_left_assoc, CategoryTheory.Limits.prod.associator_inv, CategoryTheory.Limits.isoZeroOfMonoZero_inv, CategoryTheory.ε_app_obj, HomologicalComplex.singleObjCyclesSelfIso_inv_iCycles_assoc, SemimoduleCat.MonoidalCategory.associator_inv_apply, CommAlgCat.braiding_inv_hom, CategoryTheory.MonoidalCategory.whisker_assoc_symm_assoc, hom_inv_id_app_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.whiskerLeft_actionHomLeft, AlgebraicGeometry.ΓSpecIso_hom_stalkClosedPointIso_inv, CategoryTheory.Grp.braiding_inv_hom_hom, CategoryTheory.NatTrans.rightOpWhiskerRight_assoc, pointedToBipointedCompBipointedToPointedFst_inv_app_toFun, isoInverseOfIsoFunctor_inv_app, CategoryTheory.SmallObject.SuccStruct.ofCocone_map_to_top, CategoryTheory.Limits.CatCospanTransform.id_whiskerLeft_assoc, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_apply, CategoryTheory.Grothendieck.ιCompMap_inv_app_base, CategoryTheory.Over.conePostIso_inv_app_hom, CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair_inv_app, CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id_app, CategoryTheory.Functor.shiftIso_hom_app_comp_assoc, CategoryTheory.Limits.Fork.equivOfIsos_inverse_obj_ι, CategoryTheory.Functor.curryObjCompIso_inv_app_app, CategoryTheory.Limits.Cofork.ext_inv, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapIdIso_inv, CategoryTheory.Limits.inl_inr_pushoutAssoc_inv, CategoryTheory.ShortComplex.homologyπ_comp_leftHomologyIso_inv_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd_assoc, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_inv_app_val_app, CategoryTheory.LaxBraidedFunctor.isoOfComponents_inv_hom_app, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd, CategoryTheory.Bicategory.Adj.rIso_hom, HomotopicalAlgebra.CofibrantObject.HoCat.adjCounitIso_inv_app, AlexDisc.Iso.mk_inv, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom, CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_inv, CategoryTheory.PreZeroHypercover.hom_inv_s₀_apply, SSet.Subcomplex.eqToIso_inv, CategoryTheory.Limits.pullbackDiagonalMapIso.inv_fst, CommAlgCat.associator_inv_hom, CategoryTheory.Limits.Cocones.extendComp_inv_hom, CategoryTheory.Limits.sigmaSigmaIso_inv, MulEquiv.toSemigrpIso_inv, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app, CategoryTheory.Functor.OplaxMonoidal.associativity_inv, CategoryTheory.GrothendieckTopology.isoToPlus_inv, CategoryTheory.Equivalence.core_inverse_map_iso_inv, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv, CategoryTheory.Limits.biproduct.whiskerEquiv_hom, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_inv_fac, CategoryTheory.Functor.leftOpComp_inv_app, CategoryTheory.Pseudofunctor.mapComp'_inv_comp_mapComp'_hom, op2_unop_inv_unop2, CategoryTheory.Functor.CommShift.ofIso_commShiftIso_inv_app, CategoryTheory.Limits.IsTerminal.uniqueUpToIso_inv, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_π_assoc, MagmaCat.hom_inv_apply, CategoryTheory.Lax.StrongTrans.naturality_id_assoc, CategoryTheory.InjectiveResolution.ι'_f_zero_assoc, CategoryTheory.ShortComplex.homologyOpIso_inv_naturality_assoc, CategoryTheory.CatCommSq.vInv_iso_inv_app, CategoryTheory.CartesianMonoidalCategory.braiding_inv_fst, AlgebraicGeometry.Scheme.Pullback.openCoverOfBase'_f, CochainComplex.shiftFunctorZero'_inv_app_f, Bimod.whisker_assoc_bimod, CategoryTheory.Functor.FullyFaithful.autMulEquivOfFullyFaithful_symm_apply_inv, FinBoolAlg.Iso.mk_inv, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse_assoc, CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_cofanPtIsoSelf_inv, AlgebraicGeometry.pullbackSpecIso_inv_fst_assoc, SemilatInfCat.Iso.mk_inv_toFun, CategoryTheory.Functor.constCompEvaluationObj_inv_app, CategoryTheory.oppositeShiftFunctorZero_hom_app, CategoryTheory.Comma.mapRightIso_unitIso_hom_app_left, HomologicalComplex.inr_biprodXIso_inv_assoc, HomologicalComplex.truncLE'_d_eq, CategoryTheory.MonoidalCategory.selRightfAction_actionAssocIso_inv, CategoryTheory.Limits.limitCompYonedaIsoCocone_inv, HomologicalComplex.singleMapHomologicalComplex_inv_app_ne, CategoryTheory.WithInitial.equivComma_unitIso_inv_app_app, CategoryTheory.MonoidalOpposite.tensorRightIso_inv_app_unmop, AlgebraicGeometry.IsOpenImmersion.app_eq_appIso_inv_app_of_comp_eq, HomologicalComplex.pOpcycles_extendOpcyclesIso_inv, CategoryTheory.Functor.LaxMonoidal.μ_whiskerRight_comp_μ_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.associator_inv_comp_tensorHom_tensorHom_comp_assoc, AlgebraicGeometry.IsOpenImmersion.ΓIso_inv, CategoryTheory.functorProdFunctorEquivCounitIso_inv_app_app, CategoryTheory.ShortComplex.rightHomologyMap_op, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id_assoc, groupHomology.eq_d₃₂_comp_inv_assoc, CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_hom_assoc, LinOrd.Iso.mk_inv, CategoryTheory.Limits.Types.binaryProductIso_inv_comp_snd, CategoryTheory.Bicategory.Adj.rightUnitor_inv_τr, CategoryTheory.Oplax.OplaxTrans.naturality_id, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv_desc, CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_cancel_inv_app, CategoryTheory.Functor.mapTriangleOpCompTriangleOpEquivalenceFunctorApp_inv_hom₂, CategoryTheory.Bicategory.whiskerRight_id_symm, CategoryTheory.Functor.lanCompIsoOfPreserves_inv_app, CategoryTheory.Cat.Hom.instIsIsoFunctorαCategoryToNatTransInvHom, BddOrd.Iso.mk_inv, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_hom_inv, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_inv_comp_π, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_assoc, CategoryTheory.OplaxFunctor.mapComp_id_right, CategoryTheory.Comma.opFunctorCompFst_inv_app, CategoryTheory.shiftZero', AlgebraicGeometry.Scheme.Opens.isoOfLE_inv_ι, CategoryTheory.Functor.mapActionCongr_inv, CategoryTheory.Bicategory.triangle_assoc_comp_right, CategoryTheory.WithInitial.inclLift_inv_app, CategoryTheory.Monoidal.InducingFunctorData.whiskerRight_eq, CategoryTheory.Limits.Pi.map_eq_prod_map, CategoryTheory.Mat_.ι_additiveObjIsoBiproduct_inv, CategoryTheory.Bicategory.comp_whiskerLeft_assoc, CategoryTheory.Functor.coreId_hom_app_iso_inv, CategoryTheory.MonoidalCategory.tensor_whiskerLeft_assoc, CategoryTheory.Functor.mapTriangleCompIso_inv_app_hom₁, CategoryTheory.Pseudofunctor.mapComp_id_right_inv, AlgebraicGeometry.PresheafedSpace.toRestrictTop_c, CategoryTheory.ModObj.assoc_flip, CategoryTheory.Bicategory.whiskerLeft_inv_hom_assoc, CategoryTheory.Functor.pi'CompEval_inv_app, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd_assoc, CategoryTheory.CartesianMonoidalCategory.rightUnitor_inv_snd, CategoryTheory.Join.mapWhiskerRight_whiskerLeft, CategoryTheory.Functor.isLeftKanExtensionId, SSet.horn₃₂.desc.multicofork_π_zero_assoc, HomologicalComplex.single_map_f_self, AlgebraicGeometry.Scheme.Hom.fromNormalization_app_assoc, CategoryTheory.Dial.isoMk_inv_F, AlgebraicGeometry.Scheme.isoSpec_inv_toSpecΓ_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_assoc, CategoryTheory.CatCommSq.hComp_iso_inv_app, CategoryTheory.Pseudofunctor.map₂_whisker_right_app_assoc, ContinuousMap.piComparison_fac, CategoryTheory.ShortComplex.LeftHomologyData.lift_K_comp_cyclesIso_inv_assoc, Rep.finsuppTensorRight_inv_hom, CategoryTheory.Functor.isLeftKanExtension_iff_postcomp₁, CategoryTheory.Functor.Monoidal.ε_of_cartesianMonoidalCategory, AlgebraicGeometry.Scheme.Hom.isoImage_inv_ι, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp, CategoryTheory.DifferentialObject.shiftFunctorAdd_inv_app_f, CategoryTheory.shiftFunctorAdd_add_zero_inv_app, CategoryTheory.Dial.associator_inv_F, CategoryTheory.Limits.HasZeroObject.zeroIsoInitial_inv, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃_assoc, AlgebraicGeometry.Scheme.GlueData.ι_isoCarrier_inv, CategoryTheory.ShortComplex.rightHomologyFunctorOpNatIso_hom_app, CategoryTheory.Over.prodLeftIsoPullback_inv_fst_assoc, CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_inv_right, CategoryTheory.Bicategory.LeftExtension.IsKan.uniqueUpToIso_inv_right, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_μ_app, CategoryTheory.Limits.kernel_map_comp_preserves_kernel_iso_inv, CategoryTheory.Functor.currying_unitIso_inv_app_app_app, CategoryTheory.MonoidalCategory.inv_hom_whiskerRight, CategoryTheory.coreFunctor_map_app_iso_inv, CategoryTheory.Limits.cokernelIsoOfEq_inv_comp_desc, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι, AlgebraicGeometry.Scheme.Hom.isoImage_inv_ι_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_obj_obj_map, SemiRingCat.hom_inv_apply, CategoryTheory.Bicategory.Pith.whiskerLeft_iso_inv, CategoryTheory.Discrete.productEquiv_counitIso_inv_app, CategoryTheory.Equivalence.counitIso_inv_app_comp_functor_map_η_inverse_assoc, Rep.indCoindNatIso_inv_app, CategoryTheory.MonoidalCategory.whiskerLeftIso_inv, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isoBot_inv, CategoryTheory.MonoidalCategory.curriedAssociatorNatIso_inv_app_app_app, unop_hom_inv_id_app_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_assoc, CategoryTheory.Functor.mapCoconeWhisker_inv_hom, CategoryTheory.Adjunction.Triple.leftToRight_eq_counits, CategoryTheory.Functor.leftDerived_map_eq, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_assoc, CategoryTheory.Pretriangulated.binaryProductTriangleIsoBinaryBiproductTriangle_inv_hom₃, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app, CategoryTheory.LaxFunctor.map₂_rightUnitor_assoc, CategoryTheory.Lax.StrongTrans.naturality_comp, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_inv_assoc, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.fromBiprod_biprodIsoProd_inv_apply, CategoryTheory.ShiftedHom.opEquiv_symm_apply_comp, CategoryTheory.Localization.isoOfHom_hom_inv_id, CategoryTheory.Lax.OplaxTrans.naturality_id_assoc, Mathlib.Tactic.Bicategory.structuralIso_inv, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app, AlgebraicTopology.DoldKan.Γ₂N₂ToKaroubiIso_inv_app, AlgebraicGeometry.Scheme.toOpen_eq, CategoryTheory.GrothendieckTopology.toSheafify_comp_sheafifyCompIso_inv, CategoryTheory.Limits.pullbackProdFstIsoProd_inv_snd_fst_assoc, CategoryTheory.Pseudofunctor.map₂_whisker_right, CategoryTheory.Sigma.inclCompMap_inv_app, CategoryTheory.Join.mapWhiskerRight_whiskerLeft_assoc, CategoryTheory.MonoidalClosed.comp_id_assoc, CategoryTheory.MonoidalCategory.unitors_inv_equal, CategoryTheory.Bicategory.whiskerRight_id_assoc, CategoryTheory.GrothendieckTopology.overMapPullback_comp_id_assoc, CategoryTheory.Functor.rightOpComp_inv_app, CategoryTheory.Limits.cospanCompIso_inv_app_one, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_apply, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₁, CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_inv_apply, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_inv_app_hom_hom_hom, CategoryTheory.InjectiveResolution.Hom.hom'_f_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_inv_app_fst_app, CategoryTheory.Functor.FullyFaithful.hasShift.map_add_hom_app, CategoryTheory.Bicategory.whisker_assoc_symm_assoc, HomologicalComplex.xPrevIsoSelf_comp_dTo_assoc, GrpCat.inv_hom_apply, CategoryTheory.Under.hom_right_inv_right, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_inv_app_app, CategoryTheory.Functor.Monoidal.μIso_inv, inv_hom_id_eval_assoc, CategoryTheory.Functor.opId_inv_app, groupHomology.isoCycles₂_inv_comp_iCycles_apply, Bimod.comp_whiskerLeft_bimod, CategoryTheory.Functor.OplaxRightLinear.δᵣ_associativity_inv_assoc, CategoryTheory.ComonObj.comul_counit_hom_assoc, CategoryTheory.MorphismProperty.Comma.isoFromComma_inv, CategoryTheory.Localization.Monoidal.pentagon_aux₃, CategoryTheory.Bicategory.conjugateEquiv_apply', CategoryTheory.CostructuredArrow.isoMk_inv_left, ModuleCat.range_mkQ_cokernelIsoRangeQuotient_inv_apply, CategoryTheory.Arrow.iso_w, groupHomology.isoCycles₂_inv_comp_iCycles_assoc, CategoryTheory.Enriched.FunctorCategory.enriched_assoc_assoc, CategoryTheory.Functor.leftKanExtensionUniqueOfIso_inv, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_right, CategoryTheory.Functor.IsCoverDense.presheafIso_inv, cancel_iso_inv_right, CategoryTheory.MorphismProperty.Comma.isoMk_inv_right, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_inv_app_app_snd, CategoryTheory.Functor.const.opObjUnop_inv_app, CategoryTheory.OplaxFunctor.mapComp_assoc_right_assoc, CategoryTheory.Abelian.PreservesImage.iso_inv_ι, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_hom_τr, Rep.coindResAdjunction_homEquiv_symm_apply, CategoryTheory.MonoidalCategory.triangle_assoc_comp_right_assoc, HomologicalComplex.singleCompEvalIsoSelf_inv_app, CategoryTheory.Functor.IsCoverDense.Types.sheafIso_inv_val, CategoryTheory.Equivalence.rightOp_counitIso_hom_app, CategoryTheory.curryingIso_inv_toFunctor_obj_obj_obj, CategoryTheory.Limits.isInitialMul_inv, CategoryTheory.Functor.OplaxMonoidal.oplax_left_unitality, CategoryTheory.Pseudofunctor.StrongTrans.rightUnitor_inv_as_app, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_app_assoc, CategoryTheory.Limits.CoconeMorphism.hom_inv_id, AddCommGrpCat.biprodIsoProd_inv_comp_desc, HomologicalComplex.truncGE'Map_f_eq_opcyclesMap, CategoryTheory.SmallObject.πFunctorObj_eq, CategoryTheory.Quiv.inv_obj_hom_obj_of_iso, CategoryTheory.LaxFunctor.map₂_leftUnitor, CategoryTheory.StructuredArrow.mapNatIso_counitIso_hom_app_right, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_id_naturality_inv, CategoryTheory.Mathlib.Tactic.MonTauto.rightUnitor_inv_tensor_one_mul, CategoryTheory.SingleFunctors.postcompPostcompIso_inv_hom_app, CategoryTheory.Sum.functorEquivFunctorCompSndIso_inv_app_app, CategoryTheory.Biprod.unipotentUpper_inv, CategoryTheory.Discrete.compNatIsoDiscrete_inv_app, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_inv_inv, CategoryTheory.Limits.colimIsoFlipCompWhiskerColim_inv_app_app, CategoryTheory.ShortComplex.mapCyclesIso_inv_naturality_assoc, CategoryTheory.LaxFunctor.mapComp_assoc_left_app, CategoryTheory.Limits.kernelFactorThruImage_inv_comp_ι, AlgebraicGeometry.ΓSpecIso_inv_ΓSpec_adjunction_homEquiv, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_flip_inv_app, CategoryTheory.Mathlib.Tactic.MonTauto.associator_inv_comp_tensorHom_tensorHom, CategoryTheory.Bicategory.conjugateEquiv_adjunction_id, HomologicalComplex.restrictionToTruncGE'.f_eq_iso_hom_pOpcycles_iso_inv, CategoryTheory.Grothendieck.transportIso_inv_fiber, CategoryTheory.Sum.functorEquiv_unitIso_inv_app_app_inr, CategoryTheory.braiding_inv_tensorUnit_left_assoc, CategoryTheory.Cat.rightUnitor_inv_app, CategoryTheory.BraidedCategory.braiding_inv_naturality_left_assoc, groupHomology.cyclesMk₂_eq, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app_assoc, CategoryTheory.ExactPairing.evaluation_coevaluation_assoc, CategoryTheory.Functor.Final.ι_colimitIso_inv_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.unit_actionHomRight, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.isConnected, AddEquiv.toAddGrpIso_inv, HasFibers.Fib.isoMk_inv, CategoryTheory.Limits.inl_comp_pushoutObjIso_inv, CategoryTheory.Limits.pullbackObjIso_inv_comp_fst, CategoryTheory.Bicategory.Prod.snd_mapId_inv, comp_inv_eq_id, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_app_assoc, CategoryTheory.Limits.Trident.ext_inv, CategoryTheory.Limits.LimitPresentation.map_π, CategoryTheory.Limits.pullbackAssoc_inv_snd_assoc, CategoryTheory.shift_shiftFunctorCompIsoId_inv_app, CategoryTheory.ChosenPullbacksAlong.isoInv_mapPullbackAdj_counit_app_left, CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_left, AddGrpCat.neg_hom_apply, Pointed.Iso.mk_inv_toFun, CategoryTheory.Comon.monoidal_tensorUnit_comon_comul, CategoryTheory.MonoOver.mkArrowIso_inv_hom_left, CategoryTheory.Functor.currying₃_unitIso_inv_app_app_app_app, CategoryTheory.Limits.prodZeroIso_iso_inv_snd, AddCommGrpCat.biprodIsoProd_inv_comp_snd, groupHomology.isoCycles₁_inv_comp_iCycles_assoc, CategoryTheory.ShortComplex.pOpcycles_π_isoOpcyclesOfIsColimit_inv, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_hom_fac_assoc, CategoryTheory.Functor.whiskeringLeftObjIdIso_inv_app_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_inv_app_app, CategoryTheory.Cat.opFunctorInvolutive_inv_app_toFunctor_obj, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac, CategoryTheory.Functor.Monoidal.transport_η, CategoryTheory.IsIso.Iso.inv_inv, hom_inv_id_eval, CategoryTheory.MonoidalCategory.associatorNatIso_inv_app, AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv, CategoryTheory.NatTrans.leftOpWhiskerRight, CategoryTheory.Limits.limitCompCoyonedaIsoCone_inv, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_left, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_inv_ι_assoc, Action.resComp_inv_app_hom, CategoryTheory.biproduct_ι_comp_rightDistributor_inv_assoc, CategoryTheory.Cat.rightUnitor_inv_toNatTrans, CategoryTheory.Localization.lift₃NatTrans_app_app_app, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_hom_assoc, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv_assoc, CategoryTheory.ShortComplex.asIsoHomologyπ_inv_comp_homologyπ_assoc, Bimod.whiskerRight_id_bimod, CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_fst_assoc, CategoryTheory.ShiftedHom.opEquiv'_symm_op_opShiftFunctorEquivalence_counitIso_inv_app_op_shift, CategoryTheory.Pseudofunctor.mapComp'_comp_id_inv_assoc, CategoryTheory.ProjectiveResolution.leftDerivedToHomotopyCategory_app_eq, 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, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv, groupHomology.cyclesIso₀_inv_comp_cyclesMap_assoc, eHomCongr_comp, CategoryTheory.Functor.IsCoverDense.sheafIso_inv_val, groupHomology.π_comp_H2Iso_inv, CategoryTheory.Limits.imageSubobject_arrow'_assoc, CategoryTheory.Bicategory.LeftLift.ofIdComp_hom, AddGrpCat.hom_neg_apply, CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id_assoc, CategoryTheory.Functor.essImage.liftFunctorCompIso_inv_app, CategoryTheory.Bicategory.rightZigzagIso_inv, CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_right, groupCohomology.eq_d₂₃_comp_inv, CategoryTheory.Limits.CatCospanTransform.mkIso_inv_base, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'_inv, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_hom_app_app_down, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomLeft_tensor_assoc, CategoryTheory.Functor.shift_map_op, CategoryTheory.Limits.limitIsoSwapCompLim_inv_app, CategoryTheory.Functor.mapTriangleCommShiftIso_inv_app_hom₂, CategoryTheory.Functor.LaxLeftLinear.μₗ_associativity_inv, CategoryTheory.MonoidalCategory.whiskerRight_id, Homotopy.mkCoinductiveAux₃, CategoryTheory.Bicategory.Pith.associator_inv_iso_inv, CategoryTheory.Bicategory.rightUnitor_comp_inv, AlgebraicGeometry.Spec_zeroLocus, CategoryTheory.Sum.swapCompInl_inv_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.unit_actionHomRight, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_inv_app_fst_app, CategoryTheory.Functor.LaxLeftLinear.μₗ_unitality_inv, CategoryTheory.Limits.biprod.conePointUniqueUpToIso_inv, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp_assoc, CategoryTheory.InjectiveResolution.extMk_hom, CategoryTheory.Limits.inr_comp_pushoutObjIso_inv, AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality, CategoryTheory.Localization.isoOfHom_hom_inv_id_assoc, CategoryTheory.Subobject.isoOfEq_inv, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app, CategoryTheory.Limits.Types.pullbackIsoPullback_inv_fst, CategoryTheory.Pretriangulated.shiftFunctor_op_map, CategoryTheory.Idempotents.functorExtension₂CompWhiskeringLeftToKaroubiIso_inv_app_app_f, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_inv_comp_π, CategoryTheory.Limits.IsInitial.uniqueUpToIso_inv, CategoryTheory.InjectiveResolution.cochainComplex_d_assoc, CategoryTheory.Limits.BinaryFan.braiding_inv_fst, CategoryTheory.Limits.Wedge.ext_inv_hom, CategoryTheory.Bicategory.whiskerLeft_hom_inv_assoc, CategoryTheory.CatCenter.smul_iso_inv_eq, CategoryTheory.Limits.Multicofork.ext_inv_hom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_whiskerRight, CategoryTheory.Limits.Types.pullbackIsoPullback_inv_fst_apply, CategoryTheory.Limits.coproductUniqueIso_inv, Action.hom_inv_hom_assoc, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_unitIso, CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_comp_naturality_inv, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_hom_inv_assoc, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₁, HomologicalComplex.homologyFunctorSingleIso_inv_app, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_assoc, AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_inv_snd, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_app_assoc, CategoryTheory.Subobject.mapIsoToOrderIso_symm_apply, CategoryTheory.Functor.RightExtension.postcompose₂ObjMkIso_inv_left_app, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_assoc, SimplicialObject.opFunctorCompOpFunctorIso_inv_app_app, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π_assoc, CategoryTheory.op_inv_rightUnitor, CategoryTheory.Limits.inr_comp_pushoutSymmetry_inv, CommBialgCat.bialgEquivOfIso_symm_apply, CategoryTheory.Join.mapWhiskerLeft_associator_hom_assoc, ComplexShape.Embedding.liftExtend_f, CategoryTheory.NatTrans.shift_app_assoc, Action.inv_hom_hom, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict_assoc, CategoryTheory.NatIso.cancel_natIso_inv_right, CategoryTheory.Limits.CatCospanTransform.leftUnitor_inv_left_app, CategoryTheory.Center.isoMk_inv_f, groupCohomology.isoCocycles₂_inv_comp_iCocycles, CategoryTheory.sheafComposeIso_inv_fac_assoc, CommRingCat.inv_hom_apply, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_inv_app_eq, Rep.finsuppTensorLeft_inv_hom, CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_inv_app_unmop_unmop, CategoryTheory.Functor.inrCompSum'_inv_app, CategoryTheory.Functor.mapIso_inv, HomologicalComplex.isoHomologyπ_hom_inv_id, CategoryTheory.ShortComplex.cyclesIsoLeftHomology_inv_hom_id, AlgebraicGeometry.Scheme.SpecΓIdentity_inv_app, CategoryTheory.Limits.Cones.ext_inv_hom, CategoryTheory.SmallObject.SuccStruct.extendToSucc_map, CategoryTheory.simplicialCosimplicialEquiv_unitIso_inv_app, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_inv_comp_π_assoc, CategoryTheory.Limits.inr_pushoutZeroZeroIso_inv, CategoryTheory.Functor.RightExtension.postcompose₂_map_left_app, CategoryTheory.ComposableArrows.isoMk₀_inv_app, CategoryTheory.GradedObject.CofanMapObjFun.ιMapObj_iso_inv_assoc, CategoryTheory.zeroMul_inv, CategoryTheory.isoSheafify_inv, CategoryTheory.Limits.colimitConstInitial_inv, CategoryTheory.sum.inrCompAssociator_inv_app_down_down, hom_inv_id_app_app, CategoryTheory.Limits.pullbackDiagonalMapIso.inv_snd_fst_assoc, CategoryTheory.Bimon.equivMonComonCounitIsoAppX_inv_hom, groupCohomology.δ₀_apply, CategoryTheory.ComonObj.counit_comul_hom_assoc, CategoryTheory.Limits.inl_pushoutLeftPushoutInrIso_inv_assoc, CategoryTheory.GrothendieckTopology.overMapPullbackComp_inv_app_val_app, CategoryTheory.Pseudofunctor.Grothendieck.map_map_fiber, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₃_app, CategoryTheory.Limits.equalizerPullbackMapIso_inv_ι_snd_assoc, SSet.horn₃₁.desc.multicofork_π_three_assoc, asOver_inv, CategoryTheory.MonObj.one_associator, CategoryTheory.eHom_whisker_cancel_inv_assoc, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app, CategoryTheory.NatTrans.CommShiftCore.app_shift, CategoryTheory.Pseudofunctor.map₂_whisker_left_app_assoc, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst, CategoryTheory.Limits.cokernel.congr_inv, CategoryTheory.Limits.inr_pushoutRightPushoutInlIso_inv_assoc, CategoryTheory.equivYoneda_inv_app, AddCommGrpCat.biprodIsoProd_inv_comp_desc_apply, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_obj, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app, CategoryTheory.presheafToSheafCompComposeAndSheafifyIso_inv_app, map_hom_inv_id_eval_app_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_right, HomologicalComplex.extend.leftHomologyData_i, CategoryTheory.StrictPseudofunctor.comp_mapComp_inv, inhomogeneousCochains.d_eq, CategoryTheory.Limits.pullbackSymmetry_inv_comp_fst, CategoryTheory.Limits.pullback.diagonal_comp, HomologicalComplex.extend.comp_d_eq_zero_iff, CategoryTheory.unop_inv_braiding, HomologicalComplex.restrictionCyclesIso_inv_iCycles_assoc, CategoryTheory.Limits.biproduct.whiskerEquiv_inv_eq_lift, CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_snd_fst_assoc, MulEquiv.toMagmaCatIso_inv, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_inv_assoc, CategoryTheory.Adjunction.localization_counit_app, CategoryTheory.Functor.mapGrpIdIso_inv_app_hom_hom, CategoryTheory.Comma.unopFunctorCompFst_inv_app, CategoryTheory.Lax.StrongTrans.vComp_naturality_inv, CategoryTheory.Limits.inl_comp_pushoutObjIso_inv_assoc, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_fst_assoc, CategoryTheory.Over.prodComparisonIso_pullback_Spec_inv_left_fst_fst', CategoryTheory.LaxFunctor.mapComp_assoc_right_assoc, inv_hom_id_triangle_hom₁_assoc, CategoryTheory.Limits.ConeMorphism.hom_inv_id_assoc, CategoryTheory.Pseudofunctor.mapComp'_naturality_2, CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id_app_assoc, CategoryTheory.Limits.opProdIsoCoprod_inv_inr, CategoryTheory.ShortComplex.leftHomologyFunctorOpNatIso_hom_app, CategoryTheory.Limits.coprod.rightUnitor_inv, CategoryTheory.Oplax.StrongTrans.vcomp_naturality_hom, SSet.horn₃₁.desc.multicofork_π_zero, CategoryTheory.Pi.evalCompEqToEquivalenceFunctor_inv, CategoryTheory.Functor.PushoutObjObj.ι_iso_of_iso_right_inv, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_inv_app_app, CategoryTheory.toSkeletonFunctor_map_hom, CategoryTheory.Monad.algebraFunctorOfMonadHomComp_inv_app_f, CategoryTheory.Limits.BinaryFan.braiding_inv_snd_assoc, CategoryTheory.PreZeroHypercover.hom_inv_h₀, CategoryTheory.ComonObj.comul_counit_assoc, groupCohomology.cocyclesMk₂_eq, CategoryTheory.Functor.FullyFaithful.compUliftCoyonedaCompWhiskeringLeft_inv_app_app_down, Rep.leftRegularTensorTrivialIsoFree_inv_hom, CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_fst_apply, CategoryTheory.MonoidalCategory.leftUnitor_inv_naturality, CategoryTheory.Core.isoMk_inv_iso, CategoryTheory.Limits.PreservesLimitPair.iso_inv_fst, ComplexShape.Embedding.liftExtend.f_eq, CategoryTheory.Limits.CatCospanTransform.associator_inv_right_app, CategoryTheory.Lax.StrongTrans.id_naturality_inv, CategoryTheory.Limits.ι_comp_sigmaObjIso_inv_assoc, AddCommGrpCat.biprodIsoProd_inv_comp_fst_apply, CategoryTheory.Comma.equivProd_unitIso_inv_app_right, CategoryTheory.LocalizerMorphism.equiv_smallHomMap, CategoryTheory.Limits.CatCospanTransform.mkIso_inv_right, CategoryTheory.instIsComonHomInvOfHom, CategoryTheory.Adjunction.CommShift.compatibilityUnit_right, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_inv_app_fst_app, CategoryTheory.Pi.isoMk_inv, CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_inv_hom_assoc, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_inv_eq_ofRestrict, CategoryTheory.Functor.Monoidal.associator_inv_app, CategoryTheory.Functor.CommShift.isoAdd'_hom_app, CategoryTheory.Pseudofunctor.mapComp_id_right_inv_app, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app_assoc, CategoryTheory.braiding_inv_tensorUnit_right, AlgebraicGeometry.Scheme.isoSpec_Spec_inv, CategoryTheory.mop_inv_leftUnitor, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_inv_app_app, CategoryTheory.Pseudofunctor.mapComp_id_left_hom_app, CategoryTheory.Limits.equalizerSubobject_arrow', CategoryTheory.Limits.Cowedge.ext_inv_hom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_iso_inv_app, CategoryTheory.ShortComplex.leftHomologyMapIso'_inv, TopCat.Sheaf.objSupIsoProdEqLocus_inv_eq_iff, CategoryTheory.Pi.eqToEquivalenceFunctorIso_inv, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_associator, CategoryTheory.Bicategory.Adj.Bicategory.associator_inv_τl, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app_assoc, HomologicalComplex.homologyIsoSc'_inv_ι, CochainComplex.ConnectData.restrictionGEIso_inv_f, CategoryTheory.Localization.lift₂NatTrans_app_app, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles, HomologicalComplex.restrictionHomologyIso_inv_homologyι, CategoryTheory.MonoidalOpposite.tensorRightMopIso_inv_app_unmop, ModuleCat.extendScalars_assoc', CategoryTheory.Limits.Types.coproductIso_mk_comp_inv_apply, CategoryTheory.IsPullback.isoIsPullback_inv_fst_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_id, ModuleCat.piIsoPi_inv_kernel_ι, HomologicalComplex.singleObjHomologySelfIso_inv_naturality_assoc, CategoryTheory.Equivalence.core_counitIso_hom_app_iso_inv, HomologicalComplex.pOpcyclesIso_hom_inv_id_assoc, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_hom_app_val_app, CategoryTheory.Functor.leftKanExtensionIsoFiberwiseColimit_hom_app, CategoryTheory.MonoidalCategory.tensor_inv_hom_id, CategoryTheory.Monad.comparisonForget_inv_app, CategoryTheory.NatIso.removeOp_inv, CategoryTheory.Pseudofunctor.map₂_associator, FinPartOrd.Iso.mk_inv, CategoryTheory.shiftFunctorAdd_add_zero_hom_app, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, CategoryTheory.Limits.MonoFactorisation.ofIsoI_m, CategoryTheory.StructuredArrow.mapIso_unitIso_hom_app_right, Action.mkIso_inv_hom, CategoryTheory.Limits.Sigma.ι_reindex_inv, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_fst, CategoryTheory.Grp.leftUnitor_inv_hom, HomologicalComplex₂.ι_totalShift₂Iso_inv_f, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_assoc, AlgebraicGeometry.Scheme.inv_hom_apply, CategoryTheory.Limits.π_comp_colimitRightOpIsoUnopLimit_inv, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_fac_app, CategoryTheory.Functor.constCompWhiskeringLeftIso_inv_app_app, CategoryTheory.Functor.RightExtension.postcompose₂_map_right, AlgebraicGeometry.basicOpenIsoSpecAway_inv_homOfLE_assoc, CategoryTheory.NatTrans.leftOpWhiskerRight_assoc, CategoryTheory.Oplax.OplaxTrans.Modification.whiskerRight_naturality_assoc, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_inv_inv_assoc, CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit_assoc, CategoryTheory.Over.leftUnitor_inv_left_fst_assoc, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv, CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero, CategoryTheory.Functor.RepresentableBy.uniqueUpToIso_inv, CategoryTheory.whiskerRight_coprod_inl_rightDistrib_inv_assoc, CategoryTheory.Functor.CommShift.isoZero_inv_app, AddMonCat.hom_neg_apply, CategoryTheory.mop_inv_rightUnitor, groupHomology.cyclesMk₁_eq, CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitIso_inv_naturality_assoc, Bicategory.Opposite.op2_leftUnitor_inv, CommRingCat.coyonedaUnique_inv_app_hom_apply, CategoryTheory.ExactPairing.coevaluation_evaluation, CategoryTheory.Functor.commShiftIso_inv_naturality, CategoryTheory.Limits.kernelSubobject_arrow'_assoc, CategoryTheory.Limits.limitIsoLimitCurryCompLim_inv_π, AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit_map, CategoryTheory.unmop_inv_rightUnitor, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_app_assoc, CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_inv, SemimoduleCat.inv_hom_apply, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_iso_inv, CategoryTheory.Bicategory.Pseudofunctor.ofOplaxFunctorToLocallyGroupoid_mapCompIso_inv, CategoryTheory.NatIso.pi_inv, CategoryTheory.Bicategory.Adj.associator_inv_τl, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj, CategoryTheory.Comma.mapLeftIso_functor_obj_hom, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_inv_fac, CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_hom_assoc, CategoryTheory.Pseudofunctor.DescentData.pullFunctorObjHom_eq_assoc, prodIsoPullback_inv_snd, CategoryTheory.Oplax.OplaxTrans.rightUnitor_inv_as_app, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_assoc, toEquiv_symm_fun, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.unitIso_inv, CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_cancel_inv_app, CategoryTheory.LaxFunctor.map₂_rightUnitor_app_assoc, CategoryTheory.rightDistributor_inv_comp_biproduct_π_assoc, CategoryTheory.Enriched.FunctorCategory.enriched_assoc, TopCat.Presheaf.presheafEquivOfIso_counitIso_inv_app_app, map_hom_inv_id_app_assoc, HomotopyCategory.homologyFunctor_shiftMap_assoc, AddCommGrpCat.biproductIsoPi_inv_comp_π, CochainComplex.augmentTruncate_inv_f_succ, CategoryTheory.Subobject.underlyingIso_inv_top_arrow_assoc, HomologicalComplex.double_d, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_hom_app_left, CategoryTheory.Linear.homCongr_symm_apply, hom_inv_id_assoc, CategoryTheory.Limits.inl_comp_pushoutSymmetry_inv_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.whiskerRight_actionHomLeft, FundamentalGroupoidFunctor.piIso_inv, CategoryTheory.Lax.StrongTrans.id_naturality_hom, AlgebraicGeometry.ΓSpec.right_triangle, CategoryTheory.Enriched.FunctorCategory.functorEnriched_id_comp_assoc, MagmaCat.inv_hom_apply, ModuleCat.FreeMonoidal.μIso_inv_freeMk, CategoryTheory.Limits.π_colimitOfIsReflexivePairIsoCoequalizer_inv, CategoryTheory.TwistShiftData.shiftFunctorAdd'_inv_app, CategoryTheory.Bicategory.whisker_assoc, CategoryTheory.Lax.OplaxTrans.naturality_id, CategoryTheory.Functor.mapBiprod_inv, CochainComplex.HomComplex.Cochain.shift_v, CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom, CategoryTheory.Limits.Types.binaryProductIso_inv_comp_fst_apply, CategoryTheory.MonoidalCategory.tensor_right_unitality, CategoryTheory.Join.mapPairComp_inv_app_left, CategoryTheory.Arrow.hom_inv_id_left, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_inv_comp_rightHomologyι_assoc, inv_ext, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_inv_app_hom_coe', ContAction.resCongr_inv, CategoryTheory.Functor.limitIsoOfIsRightKanExtension_inv_π_assoc, CategoryTheory.DifferentialObject.isoApp_inv, HomologicalComplex.pOpcycles_singleObjOpcyclesSelfIso_inv_assoc, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology_hom_comp_ι_assoc, CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_inv_assoc, CategoryTheory.Functor.unopComp_inv_app, CategoryTheory.CatCommSq.vComp_iso_inv_app, FintypeCat.inv_hom_id_apply, CategoryTheory.Functor.rightDerived_map_eq, CategoryTheory.DifferentialObject.mkIso_inv_f, CategoryTheory.Subobject.ofLE_mk_le_mk_of_comm, CategoryTheory.IsPushout.inl_isoPushout_inv_assoc, CategoryTheory.Limits.ι_colimitFiberwiseColimitIso_inv, CategoryTheory.Limits.PreservesCoproduct.inv_hom, CategoryTheory.eHom_whisker_cancel_inv, map_inv_hom_id_eval, AlgebraicTopology.DoldKan.N₁Γ₀_hom_app, CategoryTheory.Comma.leftIso_inv, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_εIso_inv, CategoryTheory.Functor.preimageIso_inv, CategoryTheory.Functor.mapMonCompIso_inv_app_hom, CategoryTheory.NatIso.naturality_2, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_left, CategoryTheory.Limits.CategoricalPullback.catCommSq_iso_inv_app, CategoryTheory.StructuredArrow.mapIso_functor_obj_hom, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_fst, CategoryTheory.GradedObject.Monoidal.pentagon_inv_assoc, CategoryTheory.Limits.Cocone.mapCoconeToOver_inv_hom, CategoryTheory.StructuredArrow.mapNatIso_unitIso_inv_app_right, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc, CategoryTheory.BasedNatIso.id_inv, CategoryTheory.Bicategory.InducedBicategory.isoMk_inv_hom, CategoryTheory.GradedObject.Monoidal.tensorIso_inv, CategoryTheory.Dial.isoMk_hom_F, CategoryTheory.Equivalence.rightOp_unitIso_inv_app, CategoryTheory.Functor.LaxLeftLinear.μₗ_unitality_inv_assoc, CategoryTheory.ComposableArrows.isoMk₃_inv, CategoryTheory.Functor.OplaxLeftLinear.δₗ_unitality_inv_assoc, CategoryTheory.Bicategory.Prod.sectR_mapComp_hom, CategoryTheory.Mat_.isoBiproductEmbedding_inv, CategoryTheory.MonoidalCategory.leftUnitor_inv_comp_tensorHom, CategoryTheory.curryingIso_inv_toFunctor_map_app_app, CategoryTheory.Adjunction.leftAdjointCompIso_hom, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv_assoc, CategoryTheory.Functor.rightKanExtensionUniqueOfIso_inv, CategoryTheory.Functor.FullyFaithful.homNatIso'_inv_app_down, CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj_inv_naturality, AlgebraicGeometry.LocallyRingedSpace.iso_inv_base_hom_base, CategoryTheory.Limits.CategoricalPullback.Hom.w'_assoc, TopCat.pullbackIsoProdSubtype_inv_snd_assoc, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_fst_fst_assoc, CategoryTheory.SingleFunctors.inv_hom_id_hom_app_assoc, Lat.hom_inv_apply, SSet.horn₃₂.desc.multicofork_π_three, AlgebraicGeometry.Scheme.stalkMap_inv_hom_apply, CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_snd, HomologicalComplex.restrictionMap_f', CategoryTheory.kernel.ι_op, CategoryTheory.Join.InclLeftCompRightOpOpEquivFunctor_inv_app, CategoryTheory.ULift.equivalence_counitIso_inv_app, AlgebraicGeometry.basicOpenIsoSpecAway_inv_homOfLE, CategoryTheory.ShortComplex.HomologyData.canonical_iso_inv, CategoryTheory.Bicategory.Adj.lIso_inv, CategoryTheory.Over.postEquiv_unitIso, AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_map, FundamentalGroupoidFunctor.prodIso_inv, CategoryTheory.Limits.limit.pre_eq, SemiNormedGrp₁.hom_inv_apply, CategoryTheory.Grp.mkIso_inv_hom_hom, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_left, CategoryTheory.Endofunctor.Algebra.functorOfNatTransComp_inv_app_f, CategoryTheory.Bicategory.associator_inv_congr, Units.toAut_inv, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackId_hom, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app_assoc, isoInverseOfIsoFunctor_hom_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app_assoc, CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app, toIsometryEquiv_invFun, CategoryTheory.Bimon.one_comul_assoc, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv_assoc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_inv_hom, CategoryTheory.NatIso.inv_app_isIso, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.counitIso_inv, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_map, CategoryTheory.Limits.isoZeroOfEpiZero_inv, HomologicalComplex.cyclesMapIso_inv, CategoryTheory.Limits.π_reflexiveCoequalizerIsoCoequalizer_inv, AddCommGrpCat.biprodIsoProd_inv_comp_fst, CategoryTheory.Subobject.underlyingIso_inv_top_arrow, CategoryTheory.Limits.WidePullbackShape.functorExt_inv_app, CategoryTheory.GrothendieckTopology.isoSheafify_inv, FinBddDistLat.Iso.mk_inv, CategoryTheory.Over.associator_inv_left_fst_snd_assoc, CategoryTheory.Comon.monoidal_leftUnitor_inv_hom, CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id, CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_hom_inv_id_assoc, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_apply, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_inv, op2_inv_unop2, CategoryTheory.Monoidal.InducingFunctorData.whiskerLeft_eq, CategoryTheory.Arrow.inv_hom_id_left, map_inv_hom_id_eval_app, CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_inv_right_app, CategoryTheory.Comma.mapRightId_inv_app_right, CategoryTheory.Bicategory.mateEquiv_leftUnitor_hom_rightUnitor_inv, CategoryTheory.PreZeroHypercover.pullbackIso_inv_h₀, SemimoduleCat.MonoidalCategory.leftUnitor_inv_apply, CategoryTheory.ShortComplex.mapCyclesIso_inv_naturality, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_π_app_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor_app, map_hom_inv_id_eval, CategoryTheory.Functor.mapConeOp_inv_hom, TopologicalSpace.Opens.mapComp_inv_app, MulEquiv.toGrpIso_inv, HomologicalComplex.singleObjCyclesSelfIso_inv_naturality, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_hom_apply, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_inv, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackComp_inv, CategoryTheory.Functor.map_shift_unop_assoc, CategoryTheory.Functor.sheafPushforwardContinuousIso_hom, CategoryTheory.Limits.Types.productIso_inv_comp_π_apply, CategoryTheory.Limits.Types.productIso_inv_comp_π, CategoryTheory.ShiftMkCore.zero_add_hom_app, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_comp, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_assoc, CategoryTheory.Comma.opFunctorCompSnd_inv_app, homCongr_symm_apply, CategoryTheory.ObjectProperty.isoMk_inv, CategoryTheory.Functor.mapCommGrpIdIso_inv_app_hom_hom_hom, CategoryTheory.whiskerRight_coprod_inr_rightDistrib_inv, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app, CategoryTheory.Limits.kernelIsoOfEq_inv_comp_ι, CategoryTheory.Functor.whiskeringRightObjIdIso_inv_app_app, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_counitIso_inv, CategoryTheory.IsHomLift.lift_id_inv, core_inv_app_iso_inv, CategoryTheory.Pretriangulated.isoTriangleOfIso₁₂_inv_hom₁, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_assoc, CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence_inv, CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃, CategoryTheory.IsIso.Iso.inv_hom, CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_inv, CategoryTheory.Limits.zeroProdIso_inv_snd, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_app_assoc, CategoryTheory.instIsMonHomInvOfHom, CategoryTheory.MonoidalCategory.tensor_left_unitality_assoc, CategoryTheory.MonoidalCategory.whisker_assoc_symm, CategoryTheory.Monoidal.associator_inv_app, CategoryTheory.LocalizerMorphism.guitartExact_of_isLeftDerivabilityStructure, groupHomology.H1CoresCoinfOfTrivial_g, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_assoc, HomologicalComplex.XIsoOfEq_inv_comp_XIsoOfEq_hom, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_inv_assoc, HomologicalComplex.singleObjOpcyclesSelfIso_inv_naturality_assoc, CategoryTheory.Comma.mapRightIso_inverse_obj_hom, CategoryTheory.TwistShiftData.shiftFunctorAdd'_hom_app, CochainComplex.ConnectData.homologyMap_map_of_eq_succ, CategoryTheory.Limits.piPiIso_inv, CategoryTheory.MonoidalCategory.MonoidalRightAction.hom_inv_actionHomLeft, CategoryTheory.Abelian.PreservesImage.factorThruImage_iso_inv_assoc, CategoryTheory.MonoidalCategory.externalProductSwap_inv_app_app, CategoryTheory.NatIso.op_inv, CategoryTheory.PrelaxFunctor.map₂_inv_hom_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_hom_app_app, CategoryTheory.Oplax.StrongTrans.isoMk_inv_as_app, CategoryTheory.Bicategory.Prod.fst_mapComp_inv, BddOrd.hom_inv_apply, PresheafOfModules.map_id, CategoryTheory.ComonadIso.mk_inv_toNatTrans, CommGrpCat.coyonedaForget_inv_app_app, CategoryTheory.Limits.IsColimit.uniqueUpToIso_inv, CategoryTheory.eHomEquiv_comp, CategoryTheory.BraidedCategory.hexagon_reverse_inv_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom, CategoryTheory.Limits.fiberwiseColimCompColimIso_inv_app, CategoryTheory.MonoidalCategory.pentagon_inv, CategoryTheory.Limits.kernelIsoOfEq_inv_comp_ι_assoc, CategoryTheory.sum.inlCompInverseAssociator_inv_app_down_down, CategoryTheory.Functor.shiftIso_hom_app_comp_shiftMap, CategoryTheory.GrothendieckTopology.uliftYonedaIsoYoneda_inv_app_val_app_down, MulEquiv.toCommMonCatIso_inv, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.Grp.associator_inv_hom, CategoryTheory.ShortComplex.homologyMap_op, CategoryTheory.Functor.shiftIso_add'_inv_app, CategoryTheory.Limits.opProdIsoCoprod_inv_inr_assoc, CategoryTheory.Limits.WalkingMulticospan.functorExt_inv_app, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, CategoryTheory.Limits.CatCospanTransform.triangle_inv_assoc, CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_fst, HomologicalComplex.π_homologyIsoSc'_inv, HomologicalComplex.singleObjHomologySelfIso_inv_naturality, AlgebraicGeometry.Scheme.Modules.pseudofunctor_left_unitality, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_hom_app_app, TopCat.prodIsoProd_inv_snd, CategoryTheory.Mon.braiding_inv_hom, AlgebraicGeometry.Scheme.Hom.isoOpensRange_inv_comp_assoc, CategoryTheory.Functor.mapTriangleIso_inv_app_hom₂, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom, CategoryTheory.HopfObj.antipode_comul₁, AlgebraicGeometry.Scheme.Modules.pseudofunctor_associativity_assoc, CategoryTheory.WithTerminal.coneEquiv_unitIso_inv_app_hom_left, CategoryTheory.instIsMod_HomInvOfHom, groupHomology.cyclesIso₀_inv_comp_cyclesMap, Profinite.NobelingProof.spanFunctorIsoIndexFunctor_inv_app, CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_π, AlgebraicGeometry.ProjectiveSpectrum.Proj.stalkMap_toSpec, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_app, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_toSpecΓ_assoc, CategoryTheory.Limits.CatCospanTransform.id_whiskerLeft, TopCat.hom_inv_id_apply, CategoryTheory.Join.InclRightCompRightOpOpEquivFunctor_inv_app, CategoryTheory.Limits.Sigma.whiskerEquiv_inv, CategoryTheory.GrpObj.ofIso_inv, AlgebraicGeometry.Scheme.Hom.normalizationCoprodIso_inv_coprodDesc_fromNormalization_assoc, TopCat.piIsoPi_inv_π, CategoryTheory.Limits.limit.isoLimitCone_inv_π, CategoryTheory.Functor.FullyFaithful.hasShift.map_add_inv_app, CategoryTheory.Sieve.pullback_ofArrows_of_iso, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_inv_hom₂, AlgebraicGeometry.pullbackRestrictIsoRestrict_inv_fst_assoc, CategoryTheory.Limits.pullbackZeroZeroIso_inv_snd, CategoryTheory.Functor.IsCoverDense.isoOver_inv_app, CategoryTheory.Limits.inl_pushoutAssoc_inv, CategoryTheory.ShortComplex.LeftHomologyData.homologyIso_hom_comp_leftHomologyIso_inv, CategoryTheory.Functor.OplaxMonoidal.δ_comp_tensorHom_η_assoc, cancel_iso_inv_right_assoc, CommAlgCat.isoMk_inv, CategoryTheory.Limits.cospanExt_inv_app_left, AlgebraicGeometry.Scheme.GlueData.ι_isoLocallyRingedSpace_inv, CategoryTheory.Pseudofunctor.whiskerLeft_mapComp'_inv_comp_mapComp'₀₁₃_inv_app_assoc, CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app_assoc, CategoryTheory.MonoidalCategory.DayConvolution.associator_inv_unit_unit_assoc, AlgebraicGeometry.Scheme.iso_inv_base_hom_base_apply, CategoryTheory.Limits.limitOpIsoOpColimit_inv_comp_π, TopCat.Sheaf.objSupIsoProdEqLocus_inv_fst, CategoryTheory.Dial.leftUnitor_inv_F, CategoryTheory.conjugateIsoEquiv_apply_inv, TopCat.homeoOfIso_symm_apply, CategoryTheory.Limits.CoconeMorphism.inv_hom_id, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τl, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv_apply, CategoryTheory.Limits.fiberwiseColimCompEvaluationIso_inv_app, CategoryTheory.Limits.cokernelIsoOfEq_inv_comp_desc_assoc, CategoryTheory.Bicategory.whiskerLeft_rightUnitor_inv_assoc, CategoryTheory.Oplax.OplaxTrans.naturality_comp_assoc, CategoryTheory.Limits.kernelZeroIsoSource_inv, CategoryTheory.Bicategory.Adjunction.comp_left_triangle_aux, CategoryTheory.Functor.CommShift.OfComp.map_iso_hom_app_assoc, CategoryTheory.Bicategory.whiskerLeft_hom_inv_whiskerRight, CategoryTheory.GrpObj.mulRight_inv, CategoryTheory.symmetricOfHasFiniteProducts_braiding_inv, CochainComplex.ι_mapBifunctorShift₁Iso_hom_f_assoc, CategoryTheory.Monad.monadMonEquiv_counitIso_inv_app_hom, CategoryTheory.Limits.FormalCoproduct.evalCompInclIsoId_inv_app_app, homToEquiv_symm_apply, MonObj.mopEquiv_counitIso_inv_app_hom_unmop, CategoryTheory.ShortComplex.rightHomologyIso_inv_naturality, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_inv_app_hom_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocIso_inv_naturality, CategoryTheory.Limits.inr_inr_pushoutAssoc_inv_assoc, CategoryTheory.Limits.limitIsoLimitCurryCompLim_inv_π_assoc, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_germ, homFromEquiv_apply, CategoryTheory.MonoidalOpposite.unmop_inv_braiding, CategoryTheory.Dial.associatorImpl_inv_f, CategoryTheory.Presieve.piComparison_fac, linearEquivIsoModuleIso_inv, AlgebraicGeometry.Scheme.stalkMap_inv_hom, inl_coprodIsoPushout_inv, CategoryTheory.NatTrans.op_whiskerLeft, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app, AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_map_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_inv_app_app, CategoryTheory.Limits.pullbackObjIso_inv_comp_snd_assoc, CategoryTheory.ShortComplex.rightHomologyFunctorOpNatIso_inv_app, LightCondensed.lanPresheafExt_inv, CategoryTheory.Pseudofunctor.mkOfOplax'_mapId_inv, AlgebraicGeometry.Scheme.fromSpecStalk_app, AlgebraicGeometry.SpecMap_residueFieldIsoBase_inv, CategoryTheory.Limits.kernelBiprodSndIso_inv, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_inv_f_f, CategoryTheory.Under.inv_right_hom_right, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom, CategoryTheory.Limits.Cones.equivalenceOfReindexing_unitIso, CategoryTheory.Limits.isoBiprodZero_inv, CategoryTheory.Functor.functorialityCompPrecompose_inv_app_hom, CategoryTheory.ShortComplex.mapOpcyclesIso_inv_naturality_assoc, CategoryTheory.Limits.inl_pushoutZeroZeroIso_inv, CategoryTheory.CechNerveTerminalFrom.wideCospan.limitIsoPi_inv_comp_pi_assoc, CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac, CategoryTheory.flippingIso_inv_toFunctor_obj_obj_map, CategoryTheory.Functor.commShiftIso_id_inv_app, CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso_inv_app, AlgebraicGeometry.SpecMap_residueFieldIsoBase_inv_assoc, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp_assoc, CategoryTheory.Functor.mapGrpNatIso_inv_app_hom_hom, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_inv_app_hom_hom_app, CategoryTheory.Limits.pullbackDiagonalMapIso.inv_snd_snd_assoc, CategoryTheory.CostructuredArrow.mapNatIso_functor_map_left, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app_assoc, HomologicalComplex.extendCyclesIso_inv_iCycles, CategoryTheory.Limits.IsColimit.ofIsoColimit_desc, CategoryTheory.Pseudofunctor.mapComp'_comp_id_hom, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_left, HomotopyCategory.homologyShiftIso_hom_app, ChainComplex.augmentTruncate_inv_f_zero, CategoryTheory.Lax.LaxTrans.vComp_naturality_comp, CategoryTheory.ShortComplex.homologyπ_comp_asIsoHomologyπ_inv_assoc, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_apply, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd, HomologicalComplex.restriction.sc'Iso_inv_τ₂, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_obj_hom, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv_assoc, CategoryTheory.obj_μ_app_assoc, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIdIso_inv_app_hom, CategoryTheory.Bicategory.id_whiskerLeft, CategoryTheory.ChosenPullbacksAlong.iso_mapPullbackAdj_counit_app, CategoryTheory.Limits.inr_opProdIsoCoprod_inv, CategoryTheory.Pretriangulated.Triangle.functorIsoMk_inv, CategoryTheory.Quotient.lift.isLift_inv, CategoryTheory.Limits.IsImage.isoExt_inv, CategoryTheory.Sigma.mapId_inv_app, CategoryTheory.conjugateIsoEquiv_symm_apply_inv, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_germ, CategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso_inv, ModuleCat.biprodIsoProd_inv_comp_fst, inverseCompIso_inv_app, CategoryTheory.Comon.mkIso'_inv_hom, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_obj_map, CategoryTheory.Bicategory.Pith.associator_inv_iso_hom, CategoryTheory.Bicategory.whiskerLeft_hom_inv_whiskerRight_assoc, CategoryTheory.Pseudofunctor.mapComp_id_left_hom, CategoryTheory.Bicategory.prod_associator_inv_snd, CategoryTheory.pullbackShiftFunctorZero'_inv_app, CategoryTheory.ShortComplex.leftHomologyIso_inv_naturality, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_unitIso_hom_app_right_app, CategoryTheory.Pretriangulated.isoTriangleOfIso₁₃_inv_hom₁, TopCat.Presheaf.presheafEquivOfIso_counitIso_hom_app_app, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv, CategoryTheory.Join.mkFunctorRight_inv_app, CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.map_eq_pullHom_assoc, CategoryTheory.Oplax.LaxTrans.naturality_id_assoc, Rep.resIndAdjunction_unit_app, SSet.Truncated.HomotopyCategory.BinaryProduct.right_unitality, HomologicalComplex.isoHomologyπ_inv_hom_id_assoc, CategoryTheory.Under.mapComp_inv, HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_apply, CategoryTheory.Pseudofunctor.map₂_whisker_left_app, CategoryTheory.Limits.mulIsInitial_inv, CategoryTheory.MonoidalCategory.rightUnitor_inv_comp_tensorHom, CategoryTheory.Functor.isRightDerivedFunctor_of_inverts, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.homologyπ_isoHomology_inv, CategoryTheory.MorphismProperty.Over.mapComp_inv_app_left, CategoryTheory.StrictlyUnitaryLaxFunctorCore.map₂_rightUnitor, CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_obj_right_as, CategoryTheory.Limits.imageSubobjectCompIso_inv_arrow, CategoryTheory.MonoidalCategory.tensorRightTensor_inv_app, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_inv_π, CategoryTheory.braiding_tensorUnit_right, CompHausLike.isoOfHomeo_inv_hom_hom_apply, CategoryTheory.BraidedCategory.braiding_inv_naturality_left, CategoryTheory.NatIso.naturality_2_assoc, CategoryTheory.shiftFunctorComm_hom_app_of_add_eq_zero, AlgebraicGeometry.IsAffineOpen.fromSpec_top, CategoryTheory.Limits.PushoutCocone.isoMk_hom_hom, CategoryTheory.InjectiveResolution.iso_inv_naturality_assoc, CategoryTheory.MonoidalClosed.compTranspose_eq, CategoryTheory.Limits.CatCospanTransform.whiskerRight_comp_assoc, isoFunctorOfIsoInverse_hom_app, CategoryTheory.Groupoid.isoEquivHom_symm_apply_inv, CategoryTheory.Under.hom_right_inv_right_assoc, CategoryTheory.ShiftedHom.opEquiv_symm_apply, CategoryTheory.Over.starPullbackIsoStar_inv_app_left, instIsMonoidalInvFunctor, CategoryTheory.Join.mapWhiskerLeft_whiskerLeft_assoc, CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero_assoc, CategoryTheory.ComonObj.comul_counit_hom, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_snd, CategoryTheory.ShortComplex.opcyclesIsoX₂_inv, CategoryTheory.Limits.Cocones.precomposeEquivalence_inverse, HomologicalComplex₂.flipEquivalenceCounitIso_inv_app_f_f, CategoryTheory.Functor.mapTriangleIdIso_inv_app_hom₁, CategoryTheory.Limits.imageMonoIsoSource_inv_ι_assoc, CategoryTheory.Functor.mapGrpCompIso_inv_app_hom_hom, AlgebraicGeometry.Scheme.map_basicOpen_map, CategoryTheory.Limits.cospanOp_inv_app, CategoryTheory.GrothendieckTopology.overMapPullback_id_comp_assoc, CategoryTheory.kernelOpOp_inv, CategoryTheory.Bicategory.Adj.leftUnitor_inv_τr, Preord.Iso.mk_inv, CategoryTheory.leftDistributor_inv, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_hom_app, AlgebraicGeometry.pullbackSpecIso_inv_fst', CategoryTheory.Functor.mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app, CategoryTheory.Bicategory.rightUnitor_inv_naturality_assoc, CategoryTheory.Functor.LaxMonoidal.ε_tensorHom_comp_μ, CategoryTheory.Limits.opProdIsoCoprod_inv_inl_assoc, CategoryTheory.Pseudofunctor.CoGrothendieck.compIso_inv_app, CategoryTheory.Oplax.OplaxTrans.isoMk_inv_as_app, ModuleCat.biproductIsoPi_inv_comp_π_apply, CategoryTheory.Limits.CatCospanTransform.leftUnitor_inv_base_app, CategoryTheory.MonoidalCategory.rightUnitor_tensor_inv, CategoryTheory.Functor.LaxMonoidal.whiskerLeft_μ_comp_μ, Action.β_inv_hom, CommSemiRingCat.inv_hom_apply, CategoryTheory.Functor.core_map_iso_inv, CategoryTheory.Adjunction.leftAdjointCompNatTrans₀₂₃_eq_conjugateEquiv_symm, CategoryTheory.Prod.symmetry_inv_app, CategoryTheory.Limits.biprod.uniqueUpToIso_inv, CategoryTheory.Equivalence.leftOp_counitIso_hom_app, CategoryTheory.braiding_leftUnitor_aux₁, CategoryTheory.Arrow.square_to_iso_invert, CategoryTheory.oppositeShiftFunctorAdd'_hom_app, CategoryTheory.ComposableArrows.isoMk₁_inv_app, CategoryTheory.Pretriangulated.binaryProductTriangleIsoBinaryBiproductTriangle_inv_hom₁, CategoryTheory.Comma.toPUnitIdEquiv_counitIso_inv_app, CategoryTheory.unop_hom_rightUnitor, CategoryTheory.SingleFunctors.hom_inv_id_hom_assoc, groupHomology.isoCycles₁_inv_comp_iCycles, PartOrd.Iso.mk_inv, CategoryTheory.Limits.Cocones.extendId_inv_hom, CategoryTheory.MonoidalCategory.leftUnitorNatIso_inv_app, CategoryTheory.HalfBraiding.monoidal, CategoryTheory.toOverIteratedSliceForwardIsoPullback_inv_app_left, CategoryTheory.Limits.CatCospanTransform.whiskerRight_id_assoc, CategoryTheory.Over.hom_left_inv_left_assoc, CategoryTheory.Join.mapWhiskerRight_whiskerRight_assoc, CategoryTheory.tensorLeftHomEquiv_whiskerLeft_comp_evaluation, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂'_obj_obj_map, CategoryTheory.Limits.pushoutIsoOpPullback_inv_snd, CategoryTheory.MonoidalCategory.Functor.curriedTensorPreIsoPost_inv_app_app, HomologicalComplex.extend.d_eq, AlgebraicGeometry.IsAffineOpen.isLocalization_stalk', CochainComplex.shiftShortComplexFunctor'_inv_app_τ₃, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceInverseπ_inv_app, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_assoc, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_assoc, CategoryTheory.ShortComplex.cyclesIsoX₂_inv_hom_id, CategoryTheory.Quotient.LiftCommShift.iso_inv_app, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app, CategoryTheory.Limits.limit.conePointUniqueUpToIso_inv_comp, HomologicalComplex.iCyclesIso_inv_hom_id_assoc, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_unitIso_inv_app_f_f, AlgebraicGeometry.Scheme.Modules.pseudofunctor_left_unitality_assoc, CategoryTheory.ChosenPullbacksAlong.iso_pullback_map, CategoryTheory.Functor.relativelyRepresentable.symmetryIso_inv, CategoryTheory.ShortComplex.mapHomologyIso_inv_naturality, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom', CategoryTheory.Pseudofunctor.whiskerLeft_mapId_inv_assoc, CategoryTheory.Functor.LaxMonoidal.right_unitality_inv_assoc, CategoryTheory.Limits.image_map_comp_imageSubobjectIso_inv, groupHomology.isoShortComplexH2_inv, CategoryTheory.Functor.IsCartesian.domainUniqueUpToIso_hom_isHomLift, CategoryTheory.Limits.opProductIsoCoproduct'_inv_comp_lift, CategoryTheory.HopfObj.mul_antipode₂, CategoryTheory.MonadIso.mk_inv_toNatTrans, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompCoyoneda, CategoryTheory.Bicategory.whiskerLeft_whiskerLeft_inv_hom_assoc, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_app, HomologicalComplex.truncLE'Map_f_eq, CategoryTheory.Limits.pullbackIsoOpPushout_inv_snd_assoc, CategoryTheory.SingleFunctors.inv_hom_id_hom_app, CategoryTheory.Limits.FormalCoproduct.coproductIsoSelf_inv_φ, CategoryTheory.Limits.BinaryFan.leftUnitor_inv, ModuleCat.hom_inv_leftUnitor, CategoryTheory.Equivalence.core_counitIso_inv_app_iso_hom, CategoryTheory.Limits.piObjIso_inv_comp_π_assoc, unop_inv_hom_id_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_hom_toNatTrans_app_val_app, CategoryTheory.Functor.isLeftKanExtension_iff_precomp, CategoryTheory.Bicategory.Pith.rightUnitor_inv_iso_hom, TopCat.Presheaf.presheafEquivOfIso_inverse_obj_obj, HomologicalComplex₂.ι_totalShift₂Iso_hom_f, AlgebraicTopology.DoldKan.N₁Γ₀_inv_app, CategoryTheory.Bicategory.Pith.comp₂_iso_inv_assoc, CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_snd_snd, AlgebraicGeometry.Scheme.Hom.inl_toNormalization_normalizationCoprodIso_inv_assoc, BoolAlg.inv_hom_apply, CategoryTheory.Functor.ranObjObjIsoLimit_inv_π, CategoryTheory.Sum.natIsoOfWhiskerLeftInlInr_inv, eHomCongr_inv, AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_inv_ι_app, hom_inv_id_triangle_hom₃_assoc, CategoryTheory.leftUnitor_inv_braiding, CategoryTheory.Functor.OplaxMonoidal.left_unitality_assoc, CategoryTheory.Adjunction.leftAdjointUniq_inv_app, CategoryTheory.MonoidalCategory.tensor_whiskerLeft, CategoryTheory.Limits.Cocone.toCostructuredArrowCompProj_inv_app, HomologicalComplex.fromOpcycles_op_cyclesOpIso_inv, CategoryTheory.leftDistributor_inv_comp_biproduct_π_assoc, Lat.inv_hom_apply, CategoryTheory.Functor.IsEventuallyConstantTo.isoMap_hom_inv_id_assoc, CategoryTheory.IsPushout.inl_isoIsPushout_inv_assoc, CategoryTheory.WithTerminal.mapId_inv_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionUnitIso_inv, CategoryTheory.Oplax.StrongTrans.id_naturality_hom, CategoryTheory.obj_μ_zero_app, CategoryTheory.Functor.mapTriangleIdIso_inv_app_hom₂, CategoryTheory.Dial.leftUnitorImpl_inv_f, CategoryTheory.IsCommMonObj.mul_comm', CategoryTheory.Limits.map_π_preserves_coequalizer_inv_desc, CategoryTheory.ShortComplex.opcyclesIsoRightHomology_inv, CategoryTheory.MonoidalCategory.MonoidalRightAction.whiskerRight_actionHomLeft, CategoryTheory.Comonad.Coalgebra.isoMk_inv_f, CategoryTheory.Bicategory.Adj.Bicategory.associator_inv_τr, CategoryTheory.Monoidal.associator_inv, HomologicalComplex.extend_d_eq, AlgebraicGeometry.diagonal_Spec_map, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_ι_inv, CategoryTheory.Monoidal.rightUnitor_inv, CategoryTheory.Functor.commShiftOfLocalization_iso_hom_app, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_left, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict, CategoryTheory.Join.inrCompFromSum_inv_app, CategoryTheory.eqToHom_iso_inv_naturality_assoc, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv, CategoryTheory.Functor.OplaxRightLinear.δᵣ_unitality_inv_assoc, CategoryTheory.WithTerminal.liftFromOverComp_inv_app, CategoryTheory.Comma.mapRightEq_inv_app_right, CategoryTheory.StructuredArrow.mapIso_functor_map_right, CategoryTheory.BraidedCategory.hexagon_forward_inv, CategoryTheory.Limits.π_comp_colimitRightOpIsoUnopLimit_inv_assoc, CategoryTheory.LaxFunctor.mapComp_assoc_left, CategoryTheory.Limits.reflexivePair.compRightIso_inv_app, CategoryTheory.Bicategory.Comonad.counit_comul, CategoryTheory.IsPushout.inr_isoIsPushout_inv_assoc, CategoryTheory.Functor.curryObjProdComp_inv_app_app, SheafOfModules.conjugateEquiv_pullbackId_hom, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapId_inv_iso_hom, AlgebraicGeometry.stalkClosedPointIso_inv, CategoryTheory.EnrichedFunctor.isoMk_inv_out, CategoryTheory.Limits.Types.binaryProductIso_inv_comp_snd_apply, CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_assoc, CategoryTheory.Functor.LaxMonoidal.tensorHom_ε_comp_μ, CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv_assoc, CategoryTheory.Localization.SmallShiftedHom.equiv_mk₀Inv, CategoryTheory.Idempotents.KaroubiKaroubi.unitIso_inv_app_f, HomologicalComplex.restrictionToTruncGE'.f_eq_iso_hom_iso_inv, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv, CategoryTheory.Join.mkFunctorLeft_inv_app, CategoryTheory.ComonObj.counit_comul, PartOrd.hom_inv_apply, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₃, AlgebraicGeometry.Scheme.stalkMap_inv_hom_assoc, CategoryTheory.ComposableArrows.isoMk₄_inv, CategoryTheory.LaxFunctor.mapComp_assoc_right, CategoryTheory.MonoidalOpposite.unmopEquiv_counitIso_inv_app, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d_1_0, CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIsoWhisker_inv_right, CategoryTheory.Limits.limIsoFlipCompWhiskerLim_inv_app_app, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_assoc_apply, CategoryTheory.Abelian.DoldKan.comparisonN_hom_app_f, CategoryTheory.eHomEquiv_comp_assoc, groupHomology.isoCycles₂_inv_comp_iCycles, CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv', CategoryTheory.Functor.mapTriangleRotateIso_inv_app_hom₃, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_apply, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_f, HomologicalComplex.extendHomologyIso_inv_homologyι, AlgebraicGeometry.basicOpen_eq_of_affine, groupHomology.mkH1OfIsTrivial_apply, CategoryTheory.Bicategory.pentagon_hom_hom_inv_inv_hom, CategoryTheory.Limits.prod.braiding_inv, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_inv_app_app, CategoryTheory.Functor.toEssImageCompι_inv_app, CategoryTheory.Pseudofunctor.mkOfOplax'_mapComp_inv, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition'_assoc, CategoryTheory.ShortComplex.Splitting.ofIso_r, inr_coprodIsoPushout_inv, CategoryTheory.Limits.limit.id_pre, CategoryTheory.MonObj.mul_assoc_flip_assoc, CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id_app_assoc, groupCohomology.isoCocycles₁_inv_comp_iCocycles_assoc, CategoryTheory.ShortComplex.LeftHomologyData.lift_K_comp_cyclesIso_inv, CategoryTheory.Comon.monoidal_associator_inv_hom, CategoryTheory.Comma.toIdPUnitEquiv_counitIso_inv_app, Action.associator_inv_hom, CategoryTheory.SmallObject.SuccStruct.ofCocone_map, CategoryTheory.MonoidalCategory.DayFunctor.equiv_unitIso_inv_app, HomologicalComplex.Hom.isoApp_inv, CategoryTheory.Enriched.FunctorCategory.functorEnriched_comp_id_assoc, CategoryTheory.PrelaxFunctor.map₂Iso_inv, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop, CategoryTheory.leftAdjointMate_comp, AlgebraicGeometry.PresheafedSpace.toRestrictTop_base, CategoryTheory.Functor.OplaxMonoidal.right_unitality_assoc, CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.map_eq_pullHom, CategoryTheory.Pseudofunctor.mapComp_id_right_hom_app, CategoryTheory.functorProdFunctorEquivUnitIso_inv_app, CategoryTheory.Limits.HasZeroObject.zeroIsoIsTerminal_inv, SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁_inv_app_f_f, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_hom_app_val_app, CategoryTheory.Enriched.FunctorCategory.functorEnriched_assoc_assoc, CategoryTheory.Functor.commShiftOfLocalization.iso_hom_app_assoc, CategoryTheory.Pseudofunctor.whiskerLeft_mapId_hom_assoc, Bicategory.Opposite.bicategory_associator_inv_unop2, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_assoc, CategoryTheory.endofunctorMonoidalCategory_leftUnitor_inv_app, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_inv_app_app, CategoryTheory.NatTrans.app_shift, CategoryTheory.Lax.OplaxTrans.naturality_comp_assoc, CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv_assoc, CategoryTheory.Limits.limitRightOpIsoOpColimit_inv_comp_π_assoc, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_comp_mapComp'₀₁₃_hom_app_assoc, CategoryTheory.Pseudofunctor.StrongTrans.whiskerLeft_naturality_id, CategoryTheory.Equivalence.Equivalence_mk'_counitInv, CategoryTheory.Bicategory.pentagon_inv_inv_hom_hom_inv_assoc, CategoryTheory.Limits.limitIsoFlipCompLim_inv_app, CategoryTheory.Functor.flipIsoCurrySwapUncurry_inv_app_app, CategoryTheory.IsPullback.isoPullback_inv_fst_assoc, AlgebraicGeometry.AffineSpace.SpecIso_inv_over, CategoryTheory.MonoidalCategory.associator_inv_naturality_assoc, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp, CategoryTheory.Limits.image.compIso_inv_comp_image_ι_assoc, CategoryTheory.mop_hom_associator, CategoryTheory.OplaxFunctor.mapComp_id_left_assoc, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.firstMap₃_app_app_app, FintypeCat.hom_inv_id_apply, CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality, CategoryTheory.whiskerRight_ι_colimitCompWhiskeringRightIsoColimitComp_inv, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_inv_comp_rightHomologyι, AlgebraicGeometry.Scheme.iso_hom_base_inv_base_apply, CategoryTheory.Functor.sheafPushforwardContinuousId_inv_app_val_app, TopCat.prodIsoProd_inv_fst_apply, CategoryTheory.Limits.π_colimitOfIsReflexivePairIsoCoequalizer_inv_assoc, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app_assoc, CategoryTheory.Pseudofunctor.DescentData.pullFunctorCompIso_hom_app_hom, CategoryTheory.MonoidalCategory.leftUnitor_inv_naturality_assoc, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₂, CommBialgCat.isoMk_inv, AlgebraicGeometry.Scheme.toIso_inv_ι, SemimoduleCat.MonoidalCategory.hexagon_reverse, CategoryTheory.Enriched.FunctorCategory.homEquiv_comp_assoc, CategoryTheory.Dial.rightUnitor_inv_F, CategoryTheory.Limits.pullbackSymmetry_inv_comp_snd, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformPrecomposeObjSquare_iso_hom_comp, QuadraticModuleCat.toIsometry_inv_leftUnitor, CategoryTheory.Limits.Multifork.ext_inv_hom, inv_hom_id_app_app_app_assoc, CategoryTheory.Functor.LaxMonoidal.μ_whiskerRight_comp_μ, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_inv_app_unop_assoc, CategoryTheory.Functor.OplaxMonoidal.δ_comp_δ_whiskerRight, CategoryTheory.StrictPseudofunctor.id_mapId_inv, inv_hom_id_app, CategoryTheory.OppositeShift.adjunction_counit, CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf_inv_right, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_inv_naturality, CategoryTheory.Functor.bifunctorComp₁₂Iso_inv_app_app_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_inv_app, AlgebraicGeometry.Scheme.Hom.inv_image, CategoryTheory.GradedObject.ι_mapBifunctorComp₂₃MapObjIso_inv, CategoryTheory.Arrow.hom_inv_id_right, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.f'_eq, CategoryTheory.Functor.rightDerivedZeroIsoSelf_inv, CategoryTheory.MonObj.one_rightUnitor, CategoryTheory.Pseudofunctor.DescentData.pullFunctorObjHom_eq, prodIsoPullback_inv_snd_assoc, CochainComplex.shiftEval_inv_app, AlgebraicGeometry.Scheme.Hom.inr_toNormalization_normalizationCoprodIso_inv_assoc, CategoryTheory.StrictlyUnitaryLaxFunctor.mapIdIso_inv, CategoryTheory.Mod_.assoc_flip, CategoryTheory.FreeBicategory.mk_associator_inv, groupHomology.π_comp_H1Iso_inv_apply, CategoryTheory.Pretriangulated.shortComplexOfDistTriangleIsoOfIso_inv_τ₂, CategoryTheory.FunctorToTypes.hom_inv_id_app_apply, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitNatIso_inv_app, CategoryTheory.TwoSquare.vComp'_app, CategoryTheory.Join.mapIsoWhiskerLeft_inv_app, CategoryTheory.Pi.right_unitor_inv_apply, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app_assoc, CategoryTheory.MonoidalCategory.id_tensor_associator_inv_naturality_assoc, CategoryTheory.Equivalence.inverseFunctorObj'_inv_app, CategoryTheory.Bicategory.Adj.iso₂Mk_inv_τr, HomologicalComplex.homologyIsoSc'_inv_ι_assoc, CategoryTheory.Functor.rightUnitor_inv_app, CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_comp_assoc, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_inv, CategoryTheory.GradedObject.comapEq_inv_app, CategoryTheory.CartesianMonoidalCategory.braiding_inv_snd_assoc, CategoryTheory.Functor.mapConeMapCone_inv_hom, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_inv_eq_germ, CategoryTheory.Arrow.inv_hom_id_right_assoc, CategoryTheory.Equivalence.symmEquivInverse_obj_unitIso_inv, CategoryTheory.Limits.Multicofork.isoOfπ_inv_hom, CategoryTheory.Mon.one_def, CategoryTheory.Adjunction.comp_unit, CategoryTheory.Bicategory.Adj.leftUnitor_hom_τr, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₁, CategoryTheory.MonoOver.mapIso_inverse, CategoryTheory.FreeMonoidalCategory.mk_α_inv, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_inv_app, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_app, CategoryTheory.Functor.shiftIso_inv_naturality_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHomRight_inv_hom_assoc, CategoryTheory.biproduct_ι_comp_leftDistributor_inv, unop_inv_hom_id_app_assoc, CategoryTheory.ProjectiveResolution.iso_inv_naturality, CategoryTheory.ShortComplex.RightHomologyMapData.opcyclesMap_eq, CategoryTheory.Bicategory.LeftLift.IsKan.uniqueUpToIso_inv_right, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst_assoc, CategoryTheory.Limits.π_comp_colimitUnopIsoOpLimit_inv_assoc, CategoryTheory.Localization.isoOfHom_inv_hom_id_assoc, CategoryTheory.Bicategory.Comonad.comul_counit, CategoryTheory.Adjunction.leftAdjointCompIso_hom_app, groupHomology.inhomogeneousChains.d_eq, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₂, groupHomology.cycles₁IsoOfIsTrivial_inv_apply, groupHomology.eq_d₂₁_comp_inv_apply, CategoryTheory.Functor.whiskerRight_twice, CategoryTheory.Bicategory.leftZigzagIso_inv, TopologicalSpace.Opens.mapMapIso_counitIso, CategoryTheory.Bicategory.Adjunction.comp_right_triangle_aux, Bimod.isoOfIso_inv_hom, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_apply, CategoryTheory.NatTrans.shift_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app, CategoryTheory.Limits.pullbackProdSndIsoProd_inv_snd_assoc, CochainComplex.ConnectData.homologyMap_map_of_eq_neg_succ, CategoryTheory.Limits.inr_comp_pushoutObjIso_inv_assoc, CategoryTheory.Functor.ShiftSequence.induced_shiftMap, CategoryTheory.monoidalOfHasFiniteCoproducts.associator_inv, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_app_assoc, CategoryTheory.Limits.biprod.associator_inv_natural, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_comp_fiber, CategoryTheory.Limits.cokernelCompIsIso_inv, CategoryTheory.Functor.mapCommMonIdIso_inv_app_hom_hom, CategoryTheory.ShortComplex.leftHomologyFunctorOpNatIso_inv_app, CategoryTheory.shiftFunctorAdd_hom_app_obj_of_induced, CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_succ_succ, CategoryTheory.Limits.biprod.mapBiprod_inv_map_desc, CategoryTheory.Functor.map_shiftFunctorComm, CategoryTheory.IsPullback.isoIsPullback_inv_fst, CategoryTheory.Functor.op_commShiftIso_hom_app, groupHomology.cyclesMk₀_eq, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_inv_naturality, AlgebraicGeometry.Spec.fromSpecStalk_eq, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, CategoryTheory.Bicategory.Adjunction.homEquiv₁_symm_apply, CategoryTheory.Oplax.StrongTrans.Modification.whiskerRight_naturality_assoc, HomologicalComplex.isoHomologyι_hom_inv_id_assoc, HomotopyCategory.homologyFunctor_shiftMap, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over, CategoryTheory.Limits.biprod.mapIso_inv, CategoryTheory.Functor.Fiber.inducedFunctorCompIsoSelf_inv_app, CategoryTheory.Limits.terminalIsoIsTerminal_inv, CategoryTheory.MonoidalCategory.whiskerRight_id_assoc, CategoryTheory.CatCommSq.hInv_iso_hom_app, CategoryTheory.ComposableArrows.mkOfObjOfMapSucc_exists, CategoryTheory.ShortComplex.mapHomologyIso_inv_naturality_assoc, CategoryTheory.Bicategory.Prod.swap_mapComp_inv, CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_comp_homologyIso_inv, CategoryTheory.Limits.pullbackProdSndIsoProd_inv_snd, CategoryTheory.Equivalence.mkIso_inv, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app, CategoryTheory.Equivalence.Equivalence_mk'_unitInv, HomologicalComplex.pOpcyclesIso_inv_hom_id_assoc, CategoryTheory.cokernelUnopOp_inv, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen', CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_assoc, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₁, MonObj.mopEquiv_unitIso_inv_app_hom, CategoryTheory.Localization.SmallHom.equiv_shift, CategoryTheory.Limits.prodComparisonNatIso_inv, CategoryTheory.Limits.opProductIsoCoproduct_inv_comp_lift, AddCommGrpCat.hom_neg_apply, CategoryTheory.StrictlyUnitaryPseudofunctor.toStrictlyUnitaryLaxFunctor_mapComp, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv_assoc, HomologicalComplex.XIsoOfEq_hom_comp_XIsoOfEq_inv, CategoryTheory.Limits.diagramIsoSpan_inv_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, HomologicalComplex.truncGE'.homologyι_truncGE'XIsoOpcycles_inv_d, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_inv_app_hom_hom, CategoryTheory.Limits.HasBiproductsOfShape.colimIsoLim_hom_app, CategoryTheory.NatIso.unop_inv, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionAssocIso_inv, CategoryTheory.MonoidalCategory.rightUnitorNatIso_inv_app, CategoryTheory.PreservesImage.iso_inv, CategoryTheory.Limits.instIsIsoHomInvCocone, CategoryTheory.ShortComplex.LeftHomologyData.π_comp_leftHomologyIso_inv, SemiNormedGrp.explicitCokernelIso_inv_π, CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso_inv_app, CategoryTheory.Limits.kernelFactorThruImage_inv_comp_ι_assoc, CategoryTheory.Limits.pullback_map_eq_pullbackFstFstIso_inv, CategoryTheory.Bicategory.Prod.snd_mapComp_inv, CategoryTheory.MonoidalCategory.associator_inv_naturality_left, CategoryTheory.GrpObj.ofIso_mul, CategoryTheory.Limits.pullback.congrHom_inv, TopCat.Presheaf.toPushforwardOfIso_app, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_obj_map_app, CategoryTheory.hom_inv_id_apply, CategoryTheory.Bicategory.Pith.comp₂_iso_inv, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_inv_app_val_app_hom_hom, CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv, CategoryTheory.Pseudofunctor.map₂_whisker_right_app, HomologicalComplex.truncGE'Map_f_eq, CategoryTheory.curryingIso_inv_toFunctor_obj_obj_map, CategoryTheory.Bicategory.conjugateEquiv_symm_apply', CategoryTheory.Abelian.PreservesCoimage.iso_inv_π_assoc, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₃, RingCat.hom_inv_apply, Action.rightUnitor_inv_hom, CategoryTheory.Pi.associator_inv_apply, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_counitIso_inv, CategoryTheory.Limits.whiskerLeft_ι_colimitCompWhiskeringLeftIsoCompColimit_inv, eq_inv_comp, CategoryTheory.Adjunction.commShiftIso_inv_app_counit_app, HomologicalComplex.dFrom_eq, CategoryTheory.Quiv.hom_obj_inv_obj_of_iso, CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id_assoc, CategoryTheory.Abelian.LeftResolution.map_chainComplex_d_1_0_assoc, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompYoneda, AlgebraicTopology.DoldKan.Γ₂N₁_inv, CategoryTheory.Functor.mapMatId_inv_app, CategoryTheory.Limits.Fork.isoForkOfι_inv_hom, CategoryTheory.MonoidalCategory.leftUnitor_tensor_hom_assoc, CategoryTheory.ShortComplex.cyclesOpIso_inv_op_iCycles, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_inv_assoc, CategoryTheory.InjectiveResolution.isoRightDerivedObj_inv_naturality_assoc, CategoryTheory.Equivalence.congrRight_unitIso_hom_app, CategoryTheory.Bicategory.whiskerLeft_rightUnitor, CochainComplex.HomComplex.Cochain.rightShift_v, CategoryTheory.Functor.mapConeWhisker_inv_hom, CategoryTheory.Functor.Monoidal.leftUnitor_inv_app, groupCohomology.cocyclesMk₀_eq, CategoryTheory.ShortComplex.LeftHomologyMapData.cyclesMap_eq, CategoryTheory.Limits.π_comp_cokernelIsoOfEq_inv, CategoryTheory.Functor.ShiftSequence.induced_isoShiftZero_hom_app_obj, CategoryTheory.sheafComposeIso_inv_fac, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_extMk, CategoryTheory.Functor.Monoidal.εIso_inv, CategoryTheory.Limits.walkingSpanOpEquiv_counitIso_inv_app, CategoryTheory.Limits.Sigma.ι_isoColimit_inv_assoc, OrderHom.equivalenceFunctor_unitIso_inv_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app_assoc, eHomCongr_inv_comp, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_fst, HomologicalComplex.d_comp_XIsoOfEq_inv, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app_assoc, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_inv_comp_π_assoc, CategoryTheory.Under.inv_right_hom_right_assoc, CategoryTheory.Adjunction.leftAdjointIdIso_inv_app, CategoryTheory.Functor.map_shiftFunctorCompIsoId_inv_app, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_assoc, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_inv, CategoryTheory.Equivalence.core_unitIso_inv_app_iso_hom, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_obj, CategoryTheory.unop_hom_associator, groupCohomology.isoShortComplexH1_inv, CategoryTheory.NatTrans.unop_whiskerRight_assoc, CategoryTheory.Limits.Cone.toStructuredArrowCompToUnderCompForget_inv_app, AlgebraicTopology.DoldKan.identity_N₂_objectwise, hom_inv_id_app_app_app_assoc, CategoryTheory.Localization.Monoidal.μ_inv_natural_left, CategoryTheory.Limits.pushout.congrHom_inv, CategoryTheory.Limits.biproduct.uniqueUpToIso_inv, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_apply, CategoryTheory.MonoidalCategory.leftUnitor_inv_tensor_id_assoc, CategoryTheory.BraidedCategory.braiding_inv_naturality_right, CategoryTheory.CostructuredArrow.mapNatIso_functor_map_right, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_obj_map_app, HomologicalComplex.restrictionToTruncGE'_f_eq_iso_hom_iso_inv, CategoryTheory.CartesianMonoidalCategory.rightUnitor_inv_fst_assoc, CategoryTheory.ι_preservesColimitIso_inv, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_ε_unmop_app, CategoryTheory.MonoidalOpposite.tensorLeftMopIso_inv_app_unmop, CategoryTheory.MonoidalCategory.MonoidalRightAction.action_actionHomRight, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_inv_app_val_app, CategoryTheory.Limits.diagramIsoPair_inv_app, AlgebraicGeometry.Scheme.image_zeroLocus, CategoryTheory.tensorLeftHomEquiv_whiskerRight_comp_evaluation, groupHomology.cyclesIso₀_inv_comp_iCycles_assoc, CategoryTheory.Limits.CoconeMorphism.inv_hom_id_assoc, CategoryTheory.obj_ε_app, CategoryTheory.braiding_inv_apply, CategoryTheory.EnrichedCategory.assoc, CategoryTheory.ShortComplex.cyclesOpIso_inv_naturality_assoc, ModuleCat.extendScalarsId_inv_app_apply, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_ofRestrict, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_snd_assoc, CategoryTheory.CostructuredArrow.mapIso_inverse_obj_hom, CategoryTheory.Cat.Hom.toNatIso_inv, CategoryTheory.Limits.opParallelPairIso_inv_app_zero, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_inv, hom_comp_eq_id, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_unitIso_inv_app_f_f, CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_snd_fst, CategoryTheory.NatTrans.naturality_1, CategoryTheory.Equivalence.sheafCongr.unitIso_inv_app_val_app, AlgebraicGeometry.Scheme.inv_base_hom_base_assoc, CategoryTheory.PrelaxFunctor.map₂_inv_hom, AlgebraicTopology.DoldKan.N₁Γ₀_inv_app_f_f, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv_assoc, CategoryTheory.MonoidalClosed.comp_id, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τr, CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_snd_snd_assoc, CategoryTheory.Limits.CategoricalPullback.mkIso_inv_snd, CategoryTheory.ExactPairing.coevaluation_evaluation_assoc, ModuleCat.MonoidalCategory.braiding_inv_apply, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_inv_f_hom_apply, inv_hom_id_triangle_hom₃, CategoryTheory.GrothendieckTopology.overMapPullback_assoc, CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_fst_snd, CategoryTheory.Limits.Pi.isoLimit_inv_π_assoc, CategoryTheory.ShortComplex.comp_homologyMap_comp, CategoryTheory.Limits.opParallelPairIso_inv_app_one, Homotopy.extend.hom_eq, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.tensorHom_eq, CategoryTheory.MonoidalCategory.whisker_assoc, HomologicalComplex.isoHomologyπ_hom_inv_id_assoc, CategoryTheory.whiskeringLeftCompEvaluation_inv_app, CategoryTheory.CatCommSq.vId_iso_inv_app, AlgebraicGeometry.Scheme.IsLocallyDirected.homOfLE_tAux_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.inv_hom_actionHomLeft_assoc, CategoryTheory.Comma.equivProd_unitIso_inv_app_left, CategoryTheory.yonedaYonedaColimit_app_inv, CategoryTheory.Limits.inl_opProdIsoCoprod_inv, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_symm_apply, CategoryTheory.imageUnopOp_inv_comp_op_factorThruImage, CategoryTheory.rightUnitor_inv_apply, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_inv_π, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_inv_assoc, CategoryTheory.PreZeroHypercover.isoMk_inv_h₀, CategoryTheory.Limits.prod.leftUnitor_inv_naturality, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransEq_inv_app_f, DistLat.inv_hom_apply, CategoryTheory.NatIso.hcomp_inv, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop_assoc, CategoryTheory.Discrete.functorComp_inv_app, AlgebraicGeometry.IsAffineOpen.fromSpec_app_of_le, CategoryTheory.Limits.HasLimit.isoOfEquivalence_inv_π, CategoryTheory.Functor.CommShift.OfComp.map_iso_inv_app, trans_inv, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_hom_comp_homologyIso_inv_assoc, CategoryTheory.rightAdjointMate_comp, CategoryTheory.Adjunction.whiskerLeftRUnitIsoOfIsIsoCounit_inv_app, CategoryTheory.Pseudofunctor.toLax_mapComp', CategoryTheory.Subobject.isoOfMkEqMk_inv, CategoryTheory.OplaxFunctor.mapComp'_comp_mapComp'_whiskerRight_assoc, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app, CochainComplex.ShiftSequence.shiftIso_inv_app, CategoryTheory.Functor.compConstIso_inv_app_app, AlgebraicGeometry.Scheme.Hom.app_appIso_inv, CategoryTheory.MonoidalOpposite.mopFunctor_δ, CategoryTheory.ProjectiveResolution.isoLeftDerivedObj_inv_naturality, CategoryTheory.Equivalence.funInvIdAssoc_inv_app, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_inv_app_f, AlgebraicGeometry.Scheme.residueFieldCongr_inv, HomologicalComplex.pOpcycles_restrictionOpcyclesIso_inv_assoc, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_inv, CategoryTheory.ShortComplex.RightHomologyData.opcyclesIso_inv_comp_descOpcycles_assoc, CategoryTheory.PreZeroHypercover.isoMk_inv_s₀, CategoryTheory.Limits.cokernelZeroIsoTarget_inv, CategoryTheory.Functor.OplaxMonoidal.right_unitality, CategoryTheory.Functor.leftKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.ShortComplex.fromOpcycles_op_cyclesOpIso_inv, AlgebraicGeometry.PresheafedSpace.restrictTopIso_inv, CategoryTheory.StrictPseudofunctor.id_mapComp_inv, CategoryTheory.Limits.colimCompFlipIsoWhiskerColim_inv_app_app, CategoryTheory.Limits.parallelPair.eqOfHomEq_inv_app, SSet.horn₃₂.desc.multicofork_π_zero, inl_coprodIsoPushout_inv_assoc, CategoryTheory.GrothendieckTopology.overMapPullback_id_comp, CategoryTheory.sum.inlCompAssociator_inv_app, CategoryTheory.Bicategory.comp_whiskerLeft_symm_assoc, CategoryTheory.prod.etaIso_inv, CategoryTheory.Functor.isoWhiskerRight_inv, CategoryTheory.Functor.essImage.liftFunctor_map, CategoryTheory.Functor.commShift₂_comm_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_inv_app_snd_app, AddMagmaCat.neg_hom_apply, CategoryTheory.WithInitial.liftToInitialUnique_inv_app, CategoryTheory.prod.functorProdToProdFunctorAssociator_inv_app, CategoryTheory.WithInitial.mapComp_inv_app, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv_assoc, SSet.horn₃₂.desc.multicofork_π_three_assoc, CategoryTheory.Limits.equalizerPullbackMapIso_inv_ι_fst_assoc, CategoryTheory.Functor.whiskerRight_left, inv_hom_id_app_assoc, CategoryTheory.Functor.limitIsoOfIsRightKanExtension_inv_π, CategoryTheory.Limits.lift_comp_kernelIsoOfEq_inv, ModuleCat.kernelIsoKer_inv_kernel_ι, CategoryTheory.Limits.biproduct.whiskerEquiv_hom_eq_lift, HomologicalComplex.extendHomologyIso_inv_homologyι_assoc, HomologicalComplex.pOpcycles_extendOpcyclesIso_inv_assoc, CategoryTheory.Limits.Types.pullbackIsoPullback_inv_snd_apply, CategoryTheory.Functor.FullyFaithful.hasShift.map_zero_inv_app, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_snd, CategoryTheory.ShortComplex.RightHomologyData.opcyclesIso_inv_comp_descOpcycles, CategoryTheory.ProjectiveResolution.iso_inv_naturality_assoc, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app_assoc, CategoryTheory.Adjunction.leftAdjointIdIso_hom_app, CategoryTheory.Limits.pullbackAssoc_inv_snd, CategoryTheory.ObjectProperty.isoInv_hom_id_hom_assoc, CategoryTheory.InjectiveResolution.rightDerivedToHomotopyCategory_app_eq, CategoryTheory.CostructuredArrow.mapIso_inverse_map_right, SSet.horn₃₂.desc.multicofork_π_one_assoc, CategoryTheory.MonoidalClosed.leftDistrib_inv, CategoryTheory.uliftYonedaIsoYoneda_inv_app_app_down, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIso_inv_fst, CategoryTheory.Subobject.underlyingIso_arrow_apply, CategoryTheory.Limits.kernel.mapIso_inv, ModuleCat.restrictScalarsCongr_inv_app, groupCohomology.eq_d₁₂_comp_inv_assoc, CategoryTheory.Functor.Monoidal.transport_δ_assoc, map_inv_hom_id_eval_assoc, CategoryTheory.BraidedCategory.braiding_inv_naturality, CategoryTheory.Limits.opSpan_inv_app, BialgEquiv.toHopfAlgIso_inv, CategoryTheory.unop_inv_rightUnitor, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_counitIso_hom_app_right_app, CategoryTheory.SingleFunctors.shiftIso_add'_inv_app, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app, CategoryTheory.Functor.IsEventuallyConstantTo.isoMap_inv_hom_id_assoc, CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_snd', HomologicalComplex.iCyclesIso_hom_inv_id_assoc, CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_right, CategoryTheory.Limits.whiskerLeft_ι_colimitCompWhiskeringLeftIsoCompColimit_inv_assoc, CategoryTheory.Functor.sheafPushforwardContinuousId'_hom_app_val_app, HomologicalComplex.restriction_d_eq_assoc, HomologicalComplex.pOpcyclesIso_hom_inv_id, Condensed.isoFinYoneda_inv_app, CategoryTheory.Bicategory.leftUnitor_comp, CategoryTheory.Limits.pullbackObjIso_inv_comp_snd, CategoryTheory.Limits.pullbackAssoc_inv_fst_fst_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_inv_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso_inv_app_app, CategoryTheory.ShortComplex.homologyMapIso'_inv, CategoryTheory.compEvaluation_inv_app, CategoryTheory.Lax.OplaxTrans.vComp_naturality_id, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₂, CategoryTheory.SingleFunctors.hom_inv_id_hom_app, CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_id, CategoryTheory.Functor.PullbackObjObj.π_iso_of_iso_left_hom, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_val_app, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimIso_aux, CategoryTheory.Limits.cospanExt_inv_app_right, CategoryTheory.Grp.mkIso'_inv_hom_hom, CategoryTheory.ComonObj.comul_assoc_flip_assoc, CategoryTheory.MonoidalOpposite.tensorLeftIso_inv_app_unmop, CategoryTheory.Sum.swapCompInr_inv_app, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv_apply, CategoryTheory.MonoidalCategory.MonoidalLeftAction.hom_inv_actionHomLeft, CategoryTheory.LaxFunctor.mapComp_assoc_left_assoc, BddDistLat.Iso.mk_inv, CategoryTheory.Bicategory.LeftLift.whiskerOfIdCompIsoSelf_inv_right, AddEquiv.toAddSemigrpIso_inv, CategoryTheory.unop_hom_leftUnitor, inr_coprodIsoPushout_inv_assoc, TopologicalSpace.OpenNhds.inclusionMapIso_inv_app, Rep.barComplex.d_comp_diagonalSuccIsoFree_inv_eq, groupHomology.d₁₀ArrowIso_inv_left, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_map, CategoryTheory.Limits.cokernelBiproductFromSubtypeIso_inv, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, CategoryTheory.Bicategory.associatorNatIsoMiddle_inv_app, CategoryTheory.Functor.LaxRightLinear.μᵣ_unitality_inv, CategoryTheory.isoCartesianComon_inv_hom, CategoryTheory.Limits.map_π_preserves_coequalizer_inv, CategoryTheory.ShiftMkCore.zero_add_inv_app, CategoryTheory.MonoidalCategory.pentagon_inv_hom_assoc, SSet.associator_inv_app_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π, Action.ρAut_apply_inv, CategoryTheory.CostructuredArrow.mapIso_inverse_map_left, CategoryTheory.Comma.isoMk_inv_right, CategoryTheory.ShortComplex.cyclesIsoKernel_inv, CategoryTheory.pullbackShiftFunctorAdd'_inv_app, hom_inv_id_triangle_hom₁_assoc, CategoryTheory.ShortComplex.leftRightHomologyComparison_fac_assoc, CategoryTheory.Pseudofunctor.map₂_whisker_right_assoc, CategoryTheory.Limits.kernelCompMono_inv, CategoryTheory.LocalizerMorphism.isLeftDerivabilityStructure_iff, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_limit_map_assoc, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.Functor.coreComp_inv_app_iso_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_eq, CategoryTheory.Bimon.compatibility, CategoryTheory.Monoidal.leftUnitor_inv, CategoryTheory.prodOpEquiv_counitIso_inv_app, CategoryTheory.TwistShiftData.shiftFunctor_map, inv_hom_id_apply, CategoryTheory.MonoidalOpposite.tensorIso_inv_app_unmop, HomologicalComplex.extendSingleIso_hom_f, CategoryTheory.OverClass.instHomIsOverInvOfHom, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_app_assoc, CategoryTheory.ShortComplex.homologyπ_comp_asIsoHomologyπ_inv, CategoryTheory.TwistShiftData.shiftFunctorZero_inv_app, CategoryTheory.Equivalence.core_unitIso_inv_app_iso_inv, CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd_assoc, HomologicalComplex.XIsoOfEq_inv_comp_XIsoOfEq_inv_assoc, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst_assoc, CategoryTheory.Functor.Monoidal.map_rightUnitor_inv_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_assoc, CategoryTheory.braiding_inv_tensorUnit_left, CategoryTheory.Bicategory.Pith.pseudofunctorToPith_mapComp_inv_iso_hom, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_obj_map_app, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology_hom_comp_ι, CategoryTheory.BraidedCategory.braiding_tensor_right_inv_assoc, BddOrd.inv_hom_apply, CategoryTheory.Bicategory.pentagon_hom_hom_inv_hom_hom, CategoryTheory.Bicategory.conjugateEquiv_symm_apply, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_val_app, AlgebraicGeometry.LocallyRingedSpace.iso_hom_base_inv_base, groupCohomology.isoShortComplexH2_inv, CategoryTheory.Bicategory.Adjunction.right_triangle, CategoryTheory.shiftFunctorCompIsoId_zero_zero_inv_app, CategoryTheory.Bicategory.triangle_assoc_comp_left_inv, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerRight_naturality, CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_inv_app, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_inv, CategoryTheory.Enriched.FunctorCategory.functorEnriched_assoc, AlgebraicGeometry.IsAffineOpen.toSpecΓ_isoSpec_inv_assoc, CategoryTheory.Adjunction.leftAdjointCompNatTrans_assoc, AlgebraicGeometry.PresheafedSpace.restrict_top_presheaf, CategoryTheory.Functor.LaxMonoidal.left_unitality_inv, CategoryTheory.Functor.coreComp_inv_app_iso_inv, AlgebraicGeometry.IsOpenImmersion.isoOfRangeEq_inv_fac, HomologicalComplex.homologyFunctorIso_inv_app, CategoryTheory.Functor.mapCoconeMapCocone_inv_hom, CategoryTheory.oppositeShiftFunctorAdd_hom_app, groupHomology.eq_d₁₀_comp_inv_apply, CategoryTheory.Limits.inl_pushoutRightPushoutInlIso_inv_assoc, CochainComplex.liftCycles_shift_homologyπ_assoc, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_inv_app, CategoryTheory.Limits.Types.equalizerIso_inv_comp_ι_apply, LinearEquiv.toFGModuleCatIso_inv, CategoryTheory.Functor.isRightKanExtension_iff_postcomp₁, Homotopy.mkInductiveAux₂_zero, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom, CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_fst_assoc, ContAction.resComp_inv, CategoryTheory.Functor.leftOpRightOpIso_inv_app, CategoryTheory.Localization.Monoidal.rightUnitor_hom_app, CategoryTheory.SingleFunctors.inv_hom_id_hom, CategoryTheory.Bicategory.Equivalence.right_triangle_hom, CategoryTheory.Functor.ι_colimitIsoColimitGrothendieck_inv, CategoryTheory.Limits.CategoricalPullback.mkIso_inv_fst, AlgebraicGeometry.Scheme.localRingHom_comp_stalkIso, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv, AlgebraicGeometry.Scheme.Hom.isoOpensRange_inv_comp, CategoryTheory.SingleFunctors.postcompIsoOfIso_inv_hom_app, CategoryTheory.ProjectiveResolution.cochainComplex_d_assoc, CategoryTheory.WithTerminal.opEquiv_unitIso_inv_app, CategoryTheory.Functor.ShiftSequence.induced_shiftMap_assoc, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom, CategoryTheory.MonoidalCategory.associator_conjugation, CategoryTheory.MonoidalCategory.associator_inv_conjugation_assoc, CategoryTheory.Limits.diagramIsoParallelPair_inv_app, CategoryTheory.InjectiveResolution.iso_inv_naturality, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_inv, CategoryTheory.ShortComplex.opcyclesOpIso_inv_naturality_assoc, CategoryTheory.GlueData.mapGlueData_t', CategoryTheory.Discrete.natIsoFunctor_inv_app, HomologicalComplex.rightUnitor'_inv_comm, conj_apply, CategoryTheory.Bicategory.associatorNatIsoRight_inv_app, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.convolutionUnitApp_eq, CategoryTheory.MonoidalCategory.whiskerRight_tensor_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app, CategoryTheory.ShortComplex.homologyι_comp_asIsoHomologyι_inv_assoc, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_inv_π_assoc, CategoryTheory.MonoidalCategory.hom_inv_id_tensor_assoc, CategoryTheory.Over.associator_inv_left_snd_assoc, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π_assoc, AddEquiv.toAddCommGrpIso_inv, CategoryTheory.Localization.homEquiv_isoOfHom_inv, CategoryTheory.Bicategory.leftUnitor_comp_inv_assoc, CategoryTheory.Limits.lift_comp_kernelIsoOfEq_inv_assoc, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_left_right, ModuleCat.homEquiv_extendScalarsId, CategoryTheory.toOverUnitPullback_inv_app_left, CategoryTheory.Comma.mapRightIso_inverse_map_left, CategoryTheory.Functor.sheafPushforwardContinuousComp'_hom_app_val_app, SSet.horn₃₁.desc.multicofork_π_three, CategoryTheory.Limits.pullbackDiagonalMapIso.inv_snd_snd, SemiNormedGrp.hom_inv_apply, Bimod.whiskerRight_comp_bimod, TopCat.inv_hom_id_apply, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_inv_app_val_app, CategoryTheory.MonoidalClosed.id_comp, CategoryTheory.Bicategory.leftUnitor_inv_congr, CategoryTheory.Functor.LaxMonoidal.left_unitality_inv_assoc, CategoryTheory.Dial.isoMk_inv_f, CategoryTheory.Limits.spanIsoMk_inv_app, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.Bicategory.conjugateIsoEquiv_symm_apply_inv, CategoryTheory.Limits.kernelBiproductToSubtypeIso_inv, CategoryTheory.Limits.limitUnopIsoUnopColimit_inv_comp_π, groupCohomology.eq_d₀₁_comp_inv_assoc, CategoryTheory.Join.mapIsoWhiskerLeft_inv, CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc, CategoryTheory.Comma.mapLeftId_inv_app_right, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_inv_app_op_one, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapComp_inv, CategoryTheory.Equivalence.sheafCongr.counitIso_inv_app_val_app, CategoryTheory.Arrow.hom_inv_id_left_assoc, CategoryTheory.Functor.mapMatComp_inv_app, HomologicalComplex.singleObjHomologySelfIso_inv_homologyι, groupHomology.coinvariantsMk_comp_H0Iso_inv_assoc, CategoryTheory.Limits.opHomCompWhiskeringLimYonedaIsoCocones_inv_app_app, CategoryTheory.sheafSectionsNatIsoEvaluation_inv_app, CategoryTheory.IsHomLift.isoOfIsoLift_inv_hom_id, CategoryTheory.Limits.imageSubobject_arrow', CategoryTheory.Limits.biprod.isoCoprod_inv, HomotopyCategory.isoOfHomotopyEquiv_inv, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitIso_inv_naturality, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd_assoc, CategoryTheory.Bicategory.Prod.swap_mapId_inv, CategoryTheory.Functor.mapDerivedCategoryFactorsh_hom_app, CategoryTheory.Adjunction.Localization.η_app, CategoryTheory.SimplicialThickening.SimplicialCategory.id_comp, CategoryTheory.Limits.HasBiproductsOfShape.colimIsoLim_inv_app, CategoryTheory.StructuredArrow.mapNatIso_counitIso_inv_app_right, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_hom_app_unop, CategoryTheory.NatIso.cancel_natIso_inv_left, SemiNormedGrp₁.inv_hom_apply, CategoryTheory.Pseudofunctor.mkOfLax'_mapComp_inv, CategoryTheory.WithInitial.coconeEquiv_unitIso_inv_app_hom_right, CategoryTheory.MonoidalCategory.tensor_ε, CategoryTheory.StrictlyUnitaryPseudofunctor.comp_mapId_inv, CategoryTheory.oppositeShiftFunctorAdd'_inv_app, CompleteLat.Iso.mk_inv, CategoryTheory.Equivalence.symmEquivInverse_obj_unitIso_hom, CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit, CategoryTheory.Limits.CatCospanTransform.comp_whiskerLeft, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_ι, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_inv_assoc, CategoryTheory.LocalizerMorphism.smallShiftedHomMap_mk₀, CategoryTheory.Bimon.equivMonComonCounitIsoApp_inv_hom_hom, CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_hom, imageToKernel_comp_mono, CategoryTheory.Limits.pullbackFstFstIso_inv, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_appTop, linearEquivIsoModuleIsoₛ_inv, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_germ_assoc, CategoryTheory.GrothendieckTopology.Point.sheafFiberCompIso_inv_app, CategoryTheory.Limits.FormalCoproduct.evalOpCompInlIsoId_inv_app_app, CategoryTheory.Abelian.DoldKan.comparisonN_inv_app_f, CategoryTheory.MonoidalCategory.id_whiskerLeft_symm, groupHomology.π_comp_H1Iso_inv_assoc, CategoryTheory.Abelian.FunctorCategory.imageObjIso_inv, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_inv_app_fst_app, CategoryTheory.Enriched.FunctorCategory.functorEnriched_comp_id, AlgebraicGeometry.Scheme.localRingHom_comp_stalkIso_apply, CategoryTheory.Bicategory.Adj.Bicategory.leftUnitor_inv_τr, TopCat.Presheaf.presheafEquivOfIso_inverse_map_app, CategoryTheory.MonoidalCategory.externalProductFlip_inv_app_app_app_app, CategoryTheory.MonoidalCategory.tensor_right_unitality_assoc, CategoryTheory.LaxFunctor.mapComp_assoc_left_app_assoc, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₁, CategoryTheory.FunctorToTypes.map_hom_map_inv_apply, HomologicalComplex.singleObjOpcyclesSelfIso_hom_assoc, BddDistLat.hom_inv_apply, CategoryTheory.flipCompEvaluation_inv_app, CategoryTheory.Limits.cokernel.mapIso_inv, CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality'_assoc, CategoryTheory.Limits.kernelSubobject_arrow', CategoryTheory.Cat.leftUnitor_inv_app, CategoryTheory.associator_inv_apply_2, CategoryTheory.Functor.leftKanExtensionIsoFiberwiseColimit_inv_app, CategoryTheory.ShortComplex.leftRightHomologyComparison'_fac_assoc, CategoryTheory.Limits.map_π_preserves_coequalizer_inv_colimMap_desc_assoc, CategoryTheory.Bicategory.associator_inv_naturality_middle_assoc, CategoryTheory.biproduct_ι_comp_leftDistributor_inv_assoc, CategoryTheory.shiftFunctorAdd_assoc_inv_app, HomologicalComplex.singleObjHomologySelfIso_hom_singleObjHomologySelfIso_inv, CategoryTheory.LaxFunctor.map₂_leftUnitor_app, CategoryTheory.Bicategory.rightUnitor_comp_inv_assoc, CategoryTheory.Equivalence.core_counitIso_inv_app_iso_inv, groupHomology.mapCycles₁_quotientGroupMk'_epi, CategoryTheory.Join.mapPairRight_inv_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τl, CategoryTheory.Functor.RightExtension.postcompose₂ObjMkIso_hom_left_app, CategoryTheory.Pretriangulated.isoTriangleOfIso₁₃_inv_hom₃, CategoryTheory.Limits.opCoproductIsoProduct_inv_comp_ι, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₁, CategoryTheory.Comma.rightIso_inv, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_inv_app_f, CategoryTheory.Functor.leftKanExtensionUnique_inv, AlgebraicGeometry.Scheme.Hom.fromNormalization_app, AlgebraicGeometry.Spec_stalkClosedPointIso, CategoryTheory.WithTerminal.equivComma_unitIso_inv_app_app, CategoryTheory.Limits.Cocones.whiskeringEquivalence_counitIso, map_hom_inv_id_eval_app, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_hom_app, AlgebraicGeometry.Scheme.Pullback.Triplet.tensorCongr_inv, CategoryTheory.Limits.Cones.postcomposeEquivalence_inverse, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_assoc, AlgebraicGeometry.Scheme.Modules.pseudofunctor_associativity, CategoryTheory.Mon.tensor_one, CategoryTheory.MonoidalCategory.tensor_whiskerLeft_symm, CategoryTheory.NatTrans.CommShiftCore.app_shift_assoc, PresheafOfModules.map_comp_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.inv_hom_actionHomLeft, CategoryTheory.Pseudofunctor.whiskerRight_mapId_hom_app, CategoryTheory.Pretriangulated.shortComplexOfDistTriangleIsoOfIso_inv_τ₃, CategoryTheory.Limits.biprod.associator_inv, ModuleCat.restrictScalarsId'App_inv_apply, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_μ_assoc, HomologicalComplex.isoHomologyι_inv_hom_id_assoc, CategoryTheory.Limits.colimit.pre_eq, CategoryTheory.Preadditive.neg_iso_inv, CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv, CategoryTheory.Limits.inr_inr_pushoutAssoc_inv, CategoryTheory.Limits.CatCospanTransform.mkIso_inv_left, CategoryTheory.MonoidalCategory.tensor_hom_inv_id, CategoryTheory.Pi.comapId_inv_app, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_apply, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₁, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_inv_π_π_assoc, AlgebraicTopology.DoldKan.Compatibility.υ_inv_app, CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_three, CategoryTheory.Grothendieck.transportIso_hom_fiber, MonCat.inv_hom_apply, CochainComplex.mappingCone.mapHomologicalComplexXIso'_inv, CategoryTheory.Discrete.natIso_inv_app, CategoryTheory.LocalizerMorphism.IsLeftDerivabilityStructure.guitartExact', CategoryTheory.SingleFunctors.postcomp_shiftIso_hom_app, groupHomology.π_comp_H2Iso_inv_apply, commBialgCatEquivComonCommAlgCat_counitIso_inv_app, CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_unitIso_inv_app_right_app, CategoryTheory.Functor.whiskeringRightObjCompIso_inv_app_app, HomologicalComplex.homologyMapIso_inv, CategoryTheory.Limits.Cocones.extendIso_inv_hom, CategoryTheory.e_assoc, Rep.FiniteCyclicGroup.resolution.π_f, CategoryTheory.Comma.mapFst_inv_app, CategoryTheory.Limits.Cones.postcomposeId_inv_app_hom, HomologicalComplex.natIsoSc'_inv_app_τ₁, CategoryTheory.GrothendieckTopology.plusCompIso_inv_eq_plusLift, CategoryTheory.MonoidalCategory.associator_inv_naturality_middle, CategoryTheory.leftDistributor_inv_comp_biproduct_π, CategoryTheory.GradedObject.mapBifunctorRightUnitor_inv_naturality, QuadraticModuleCat.ofIso_inv, CategoryTheory.Pseudofunctor.mapComp'_hom_comp_mapComp'_hom_whiskerRight, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τr, CategoryTheory.Core.functorToCore_map_iso_inv, CategoryTheory.Functor.OplaxLeftLinear.δₗ_associativity_inv_assoc, CategoryTheory.InjectiveResolution.rightDerived_app_eq, CategoryTheory.Limits.diagonal_pullback_fst, ModuleCat.restrictScalarsComp'App_inv_apply, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_inv_app, CategoryTheory.ShortComplex.mapNatIso_inv, CategoryTheory.PreservesImage.inv_comp_image_ι_map_assoc, CategoryTheory.ShortComplex.mapLeftHomologyIso_inv_naturality, CategoryTheory.cokernelOpOp_inv, CategoryTheory.ObjectProperty.isoInv_hom_id_hom, CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_hom, CategoryTheory.Functor.CommShift.isoAdd'_inv_app, CategoryTheory.Localization.associator_hom_app_app_app, CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.topMapₗ_app, CategoryTheory.Functor.CommShift.OfComp.map_iso_hom_app, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_ι_inv_assoc, CategoryTheory.Functor.CommShift.OfComp.map_iso_inv_app_assoc, CategoryTheory.Functor.CommShift.isoZero'_hom_app, CategoryTheory.Bicategory.leftUnitorNatIso_inv_app, CategoryTheory.Equivalence.congrRight_counitIso_inv_app, AlgebraicGeometry.LocallyRingedSpace.iso_hom_base_inv_base_apply, CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_fst, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.unitIso_inv_app_hom_app, BoolAlg.Iso.mk_inv, CategoryTheory.TwoSquare.GuitartExact.whiskerVertical, SheafOfModules.Presentation.map_π_eq, CategoryTheory.Limits.Cocones.precomposeEquivalence_counitIso, CategoryTheory.MorphismProperty.LeftFraction.map_eq, AlgebraicGeometry.IsOpenImmersion.lift_app, CategoryTheory.sum.inrCompInverseAssociator_inv_app, CategoryTheory.eqToIso.inv, CategoryTheory.Pi.comapEvalIsoEval_inv_app, CategoryTheory.Functor.OplaxMonoidal.associativity_inv_assoc, CategoryTheory.MonoidalCategory.associator_inv_conjugation, CategoryTheory.CostructuredArrow.mapIso_counitIso_inv_app_left, CategoryTheory.Functor.rightKanExtensionCompIsoOfPreserves_inv_fac_assoc, isoOfQuasiIsoAt_hom_inv_id_assoc, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_ι_assoc, CategoryTheory.Dial.leftUnitorImpl_inv_F, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_obj_obj_map, CategoryTheory.Limits.equalizer.isoSourceOfSelf_inv, CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_comp_mapComp'_hom_whiskerRight, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_inv_fac_assoc, CategoryTheory.Localization.isoOfHom_id_inv, CategoryTheory.ShortComplex.cyclesMapIso_inv, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.toBiprod_apply, RingEquiv.toSemiRingCatIso_inv, CategoryTheory.Oplax.StrongTrans.vcomp_naturality_inv, Equiv.toIso_inv, CategoryTheory.Comma.mapLeftIso_functor_map_right, CategoryTheory.MonoidalCategory.hom_inv_id_tensor, CategoryTheory.Limits.zeroCoprodIso_inv, CategoryTheory.MonoidalCategory.DayFunctor.ι_comp_isoPointwiseLeftKanExtension_inv, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv, CategoryTheory.shiftFunctorAdd_zero_add_inv_app, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_inv_app_hom₁, hom_inv_id_app_app_app, BddLat.Iso.mk_inv, CategoryTheory.shiftFunctorComm_hom_app_of_add_eq_zero_assoc, CategoryTheory.Cat.freeMapIdIso_inv_app, PartOrdEmb.Iso.mk_inv, CategoryTheory.Functor.bifunctorComp₂₃Iso_inv_app_app_app, Bicategory.Opposite.bicategory_rightUnitor_inv_unop2, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_inv_app_hom₃, CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_snd, CategoryTheory.Functor.rightKanExtensionUnique_inv, CategoryTheory.NatTrans.CommShift.of_iso_inv, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_inv_app, CategoryTheory.Limits.spanExt_inv_app_right, CategoryTheory.Limits.Types.binaryCoproductIso_inl_comp_inv_apply, CochainComplex.liftCycles_shift_homologyπ, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app_val_app, AlgebraicTopology.DoldKan.Γ₂N₂_inv, CategoryTheory.Limits.prod_rightUnitor_inv_naturality, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_right_right, CategoryTheory.monoidalOfHasFiniteProducts.associator_inv, CategoryTheory.StructuredArrow.mapIso_counitIso_hom_app_right, CategoryTheory.Oplax.OplaxTrans.OplaxFunctor.bicategory_associator_inv_as_app, CategoryTheory.GradedObject.ι_mapBifunctorComp₂₃MapObjIso_inv_assoc, CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_inv_assoc, CategoryTheory.Oplax.OplaxTrans.leftUnitor_inv_as_app, CategoryTheory.Adjunction.mapCommGrp_counit, CategoryTheory.associator_inv_apply_1_1, TopCat.Presheaf.stalkCongr_inv, CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_inv_assoc, CategoryTheory.Join.inlCompFromSum_inv_app, CategoryTheory.Functor.CoreMonoidal.toOplaxMonoidal_η, CategoryTheory.Bicategory.Prod.fst_mapId_inv, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceFunctorProj_inv_app, CategoryTheory.Bicategory.LanLift.CommuteWith.lanLiftCompIso_inv, map_inv_hom_id_eval_app_assoc, CategoryTheory.Comon.trivial_comon_comul, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_right_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality, CategoryTheory.Idempotents.DoldKan.η_hom_app_f, HomologicalComplex.restrictionCyclesIso_inv_iCycles, AlgebraicGeometry.Scheme.inv_base_hom_base, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_left, CategoryTheory.ShortComplex.mapLeftHomologyIso_inv_naturality_assoc, CategoryTheory.GradedObject.ι_mapBifunctorComp₁₂MapObjIso_inv_assoc, CategoryTheory.Pretriangulated.preadditiveCoyoneda_homologySequenceδ_apply, CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_snd_snd, CategoryTheory.ShortComplex.asIsoHomologyι_inv_comp_homologyι_assoc, CommMonCat.hom_inv_apply, CategoryTheory.Limits.image.compIso_inv_comp_image_ι, CategoryTheory.Bicategory.Equivalence.left_triangle_hom, CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_inv_apply, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_symm_apply, CategoryTheory.OplaxFunctor.mapComp_id_left, CategoryTheory.LaxFunctor.map₂_leftUnitor_app_assoc, CategoryTheory.Comma.mapRightComp_inv_app_left, CategoryTheory.Arrow.iso_w', CategoryTheory.Limits.Sigma.ι_reindex_inv_assoc, CategoryTheory.StructuredArrow.mapIso_counitIso_inv_app_right, CategoryTheory.Equivalence.changeFunctor_counitIso_inv_app, CategoryTheory.MonoidalCategory.leftUnitor_inv_tensor_id, CategoryTheory.Limits.parallelPair.ext_inv_app, CategoryTheory.SingleFunctors.shiftIso_zero_inv_app, AlgebraicGeometry.Scheme.Hom.inl_toNormalization_normalizationCoprodIso_inv, HomologicalComplex.ι_mapBifunctorFlipIso_inv, AlgebraicGeometry.Scheme.Hom.appIso_inv_appLE, CategoryTheory.ShortComplex.mapHomologyIso'_inv_naturality_assoc, CategoryTheory.BraidedCategory.braiding_tensor_right_inv, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply_assoc, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_inv, CategoryTheory.Comma.mapRightIso_unitIso_hom_app_right, CategoryTheory.Over.mapComp_inv_app_left, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_inv_assoc, ModuleCat.extendScalars_assoc, TwoP.swapEquiv_unitIso_inv_app_hom_toFun, CategoryTheory.Equivalence.congrRight_unitIso_inv_app, ModuleCat.MonoidalCategory.associator_inv_apply, CategoryTheory.NatIso.inv_inv_app, CategoryTheory.Adjunction.shift_counit_app_assoc, CategoryTheory.LaxFunctor.map₂_rightUnitor, CategoryTheory.shift_neg_shift', TopCat.piIsoPi_inv_π_assoc, CategoryTheory.Bicategory.triangle_assoc_comp_right_assoc, CategoryTheory.Limits.spanExt_inv_app_left, Rep.leftRegularTensorTrivialIsoFree_inv_hom_single_single, groupCohomology.isoCocycles₂_inv_comp_iCocycles_assoc, CategoryTheory.Adjunction.mapGrp_counit, MonCat.hom_inv_apply, CategoryTheory.Limits.map_π_preserves_coequalizer_inv_desc_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_obj_obj_map, CategoryTheory.Limits.ConeMorphism.inv_hom_id, CategoryTheory.Pi.comapComp_inv_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_inv_app_fst_app, CategoryTheory.ShiftMkCore.assoc_inv_app, CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv_app_assoc, BialgEquiv.toBialgIso_inv, inv_eq_inv, CategoryTheory.Limits.limitRightOpIsoOpColimit_inv_comp_π, inv_hom_id_eval, CategoryTheory.Limits.pullbackAssoc_inv_fst_fst, HomologicalComplex₂.ι_totalShift₁Iso_hom_f, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict, CategoryTheory.Sigma.inclDesc_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_hom_app, CategoryTheory.Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_inv_fac, CategoryTheory.ComonObj.instTensorUnit_comul, CategoryTheory.WithInitial.liftStar_inv, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_app, CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst_assoc, TopCat.prodIsoProd_inv_snd_apply, SSet.stdSimplex.isoNerve_inv_app_apply, HomologicalComplex.forgetEval_inv_app, CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_inv_assoc, AlgebraicGeometry.SheafedSpace.isoMk_inv, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_inv_ι, AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ_assoc, CategoryTheory.Abelian.coimIsoIm_inv_app, CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_inv_comp_iCycles, π_tensor_id_preserves_coequalizer_inv_colimMap_desc, AddMagmaCat.hom_neg_apply, GrpWithZero.Iso.mk_inv, CategoryTheory.ShortComplex.abCyclesIso_inv_apply_iCycles, CategoryTheory.Cat.freeMapCompIso_inv_app, CategoryTheory.BraidedCategory.tensorLeftIsoTensorRight_inv_app, CategoryTheory.CartesianMonoidalCategory.fullSubcategory_rightUnitor_inv_hom, CategoryTheory.monoidalOfHasFiniteProducts.associator_inv_fst_fst, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit, AlgebraicGeometry.Scheme.Opens.isoOfLE_inv_ι_assoc, CategoryTheory.Limits.colimitFlipIsoCompColim_inv_app, CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_hom_hom_assoc, CategoryTheory.LaxFunctor.PseudoCore.mapIdIso_inv, CategoryTheory.MonObj.mul_assoc_flip, CategoryTheory.PreZeroHypercover.pullbackIso_inv_s₀, ModuleCat.biprodIsoProd_inv_comp_fst_apply, CategoryTheory.Bicategory.leftUnitor_comp_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_hom_app, CategoryTheory.Functor.Final.colimitIso_inv, CategoryTheory.Enriched.FunctorCategory.enriched_comp_id, CategoryTheory.Join.mapIsoWhiskerRight_inv_app, CategoryTheory.Pseudofunctor.mapId'_inv_naturality, CategoryTheory.ShortComplex.cyclesIsoLeftHomology_inv_hom_id_assoc, AlgebraicGeometry.Scheme.Spec_fromSpecStalk, CochainComplex.ι_mapBifunctorShift₁Iso_hom_f, CategoryTheory.Adjunction.rightAdjointUniq_inv_app, CategoryTheory.Localization.lift₃NatIso_inv, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInlIso_inv_app_app, CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_shift, CategoryTheory.MonoidalClosed.id_comp_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_assoc, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π, CategoryTheory.mateEquiv_apply, CategoryTheory.Functor.whiskeringLeftObjCompIso_inv_app_app, CategoryTheory.ShortComplex.mapHomologyIso'_inv_naturality, CategoryTheory.GradedObject.mapTrifunctorMapIso_inv, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_inv_app_fst_app, CategoryTheory.Limits.coprodComparisonNatIso_inv, CategoryTheory.CartesianMonoidalCategory.lift_braiding_inv_assoc, CategoryTheory.Pseudofunctor.mapComp_assoc_left_inv_app, QuadraticModuleCat.hom_inv_associator, HomologicalComplex.Hom.prev_eq, CategoryTheory.InjectiveResolution.cochainComplex_d, CategoryTheory.ShortComplex.Splitting.isoBinaryBiproduct_inv, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app_assoc, HomologicalComplex₂.ιTotal_totalFlipIso_f_inv, HomologicalComplex.isoHomologyπ_inv_hom_id, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_εIso_hom, CategoryTheory.Bicategory.triangle_assoc_comp_left_inv_assoc, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right, CategoryTheory.whiskerLeft_coprod_inr_leftDistrib_inv_assoc, CategoryTheory.Pseudofunctor.StrongTrans.Modification.whiskerRight_naturality_assoc, CategoryTheory.ShortComplex.asIsoHomologyι_inv_comp_homologyι, Homotopy.mkInductiveAux₂_add_one
refl 📖	CompOp	335 math math: CategoryTheory.ShortComplex.HomologyData.ofIsColimitCokernelCofork_iso, Action.resCongr_inv, CategoryTheory.GlueData.diagramIso_app_right, CategoryTheory.Limits.spanCompIso_app_left, CategoryTheory.Monoidal.InducingFunctorData.rightUnitor_eq, CategoryTheory.Discrete.sumEquiv_counitIso_inv_app, eHomCongr_refl, CategoryTheory.Limits.diagramIsoPair_hom_app, CategoryTheory.eq_counitIso, CategoryTheory.Limits.coconeEquivalenceOpConeOp_unitIso, AlgebraicGeometry.Scheme.ofRestrict_appIso, CategoryTheory.Bicategory.Pith.inclusion_mapComp, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_unitIso, CategoryTheory.FreeBicategory.lift_mapId, CategoryTheory.Discrete.sumEquiv_unitIso_inv_app, CategoryTheory.MonoidalSingleObj.endMonoidalStarFunctorEquivalence_counitIso, toEquiv_id, CategoryTheory.Bicategory.Prod.sectL_mapId_inv, CategoryTheory.WithInitial.opEquiv_unitIso_inv_app, CategoryTheory.orderDualEquivalence_unitIso, AddCommMonCat.equivalence_unitIso, BialgEquiv.toHopfAlgIso_refl, BialgEquiv.toBialgIso_refl, CategoryTheory.CostructuredArrow.prodEquivalence_counitIso, CategoryTheory.Under.equivalenceOfIsInitial_counitIso, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_inv_app, CategoryTheory.shiftFunctorComm_eq_refl, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_counitIso, HomologicalComplex₂.shiftFunctor₂XXIso_refl, CategoryTheory.Bicategory.Adj.forget₁_mapId, CategoryTheory.Monad.algebraFunctorOfMonadHomId_inv_app_f, CategoryTheory.Pi.isoApp_refl, CategoryTheory.Over.equivalenceOfIsTerminal_counitIso, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_hom_app, CategoryTheory.Limits.PushoutCocone.unop_π_app, CategoryTheory.ObjectProperty.topEquivalence_counitIso, CategoryTheory.Comon.Comon_EquivMon_OpOp_counitIso, refl_conj, CategoryTheory.Comma.opEquiv_counitIso, self_symm_id, CategoryTheory.TransportEnrichment.forgetEnrichmentEquiv_counitIso, CategoryTheory.WithTerminal.mapComp_hom_app, CategoryTheory.Monad.algebraFunctorOfMonadHomId_hom_app_f, commGroupAddCommGroupEquivalence_counitIso, CategoryTheory.Functor.Final.coconesEquiv_unitIso, CoalgEquiv.toCoalgIso_refl, CategoryTheory.WithInitial.opEquiv_counitIso_hom_app, CategoryTheory.CosimplicialObject.eqToIso_refl, CategoryTheory.Over.opEquivOpUnder_unitIso, CategoryTheory.Functor.mapActionComp_hom, CategoryTheory.Limits.Cocones.whiskeringEquivalence_unitIso, CategoryTheory.TransfiniteCompositionOfShape.iic_isoBot, CategoryTheory.TwoSquare.equivalenceJ_unitIso, CategoryTheory.Square.flipEquivalence_unitIso, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_c_app, CategoryTheory.WithTerminal.opEquiv_counitIso_inv_app, CategoryTheory.Monoidal.InducingFunctorData.associator_eq, CategoryTheory.Localization.Lifting.compLeft_iso, CategoryTheory.Functor.mapContActionComp_inv, unop_refl, HomologicalComplex.XIsoOfEq_rfl, toBialgEquiv_refl, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_zero, CategoryTheory.Bicategory.Prod.sectR_mapComp_inv, CategoryTheory.equivToOverUnit_unitIso, CategoryTheory.LocalizerMorphism.LeftResolution.opEquivalence_unitIso, ChainComplex.single₀ObjXSelf, CoalgCat.comonEquivalence_counitIso, CategoryTheory.StructuredArrow.preEquivalence_unitIso, CategoryTheory.Limits.Cocones.precomposeEquivalence_unitIso, CategoryTheory.CategoryOfElements.structuredArrowEquivalence_counitIso, CategoryTheory.Monad.algebraFunctorOfMonadHomEq_hom_app_f, CategoryTheory.Over.postAdjunctionLeft_unit_app_left, CategoryTheory.Functor.mapActionComp_inv, CategoryTheory.Functor.Initial.conesEquiv_counitIso, AddMonCat.equivalence_counitIso, CategoryTheory.StructuredArrow.ofCommaSndEquivalence_unitIso, CategoryTheory.Limits.spanOp_hom_app, CategoryTheory.Presheaf.coherentExtensiveEquivalence_counitIso, CategoryTheory.Prod.braiding_unitIso, CategoryTheory.StructuredArrow.ofCommaSndEquivalence_counitIso, CategoryTheory.prod.associativity_counitIso, CategoryTheory.WithTerminal.opEquiv_unitIso_hom_app, CategoryTheory.ObjectProperty.fullSubcategoryCongr_unitIso, CategoryTheory.WithTerminal.opEquiv_counitIso_hom_app, CategoryTheory.prod.associativity_unitIso, CategoryTheory.StructuredArrow.prodEquivalence_unitIso, CategoryTheory.ObjectProperty.topEquivalence_unitIso, CategoryTheory.Bicategory.Prod.sectL_mapComp_hom, CategoryTheory.WithInitial.mapId_inv_app, HopfAlgCat.MonoidalCategory.inducingFunctorData_εIso, CategoryTheory.Limits.PullbackCone.op_ι_app, CategoryTheory.Limits.pullbackConeEquivBinaryFan_counitIso, CategoryTheory.Limits.MultispanIndex.multispanMapIso_inv_app, CategoryTheory.Monad.algebraFunctorOfMonadHomComp_hom_app_f, CategoryTheory.Pseudofunctor.ObjectProperty.ι_naturality, CategoryTheory.ForgetEnrichment.equiv_unitIso, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_counitIso, CategoryTheory.Presheaf.functorEnrichedHomCoyonedaObjEquiv_naturality, coreId, trans_refl, CategoryTheory.MonoidalOpposite.mopEquiv_unitIso, HopfAlgCat.MonoidalCategory.inducingFunctorData_μIso, CategoryTheory.Bicategory.Prod.sectR_mapId_inv, CategoryTheory.Limits.spanCompIso_app_zero, CategoryTheory.TwoSquare.equivalenceJ_counitIso, CategoryTheory.DifferentialObject.isoApp_refl, HomologicalComplex₂.XXIsoOfEq_rfl, CategoryTheory.Pi.optionEquivalence_unitIso, CategoryTheory.Limits.spanOp_inv_app, CategoryTheory.GlueData.diagramIso_app_left, homCongr_refl, CategoryTheory.Functor.mapIso_refl, SheafOfModules.Presentation.quasicoherentData_presentation, CategoryTheory.Limits.Cones.equivalenceOfReindexing_counitIso, CategoryTheory.Pseudofunctor.id_mapId, CategoryTheory.Limits.opSpan_hom_app, CategoryTheory.MonoidalCategory.whiskerRightIso_refl, ContAction.resCongr_hom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_counitIso, CategoryTheory.Discrete.sumEquiv_unitIso_hom_app, CoalgCat.MonoidalCategory.inducingFunctorData_μIso, CategoryTheory.Limits.spanCompIso_app_right, CategoryTheory.Monad.algebraFunctorOfMonadHomEq_inv_app_f, CoalgCat.MonoidalCategory.inducingFunctorData_εIso, CategoryTheory.Limits.cokernelIsoOfEq_refl, CategoryTheory.GrothendieckTopology.Cover.multicospanComp_inv_app, CategoryTheory.Limits.Cones.whiskeringEquivalence_unitIso, CategoryTheory.ShortComplex.HomologyData.ofHasCokernel_iso, CategoryTheory.Equivalence.refl_counitIso, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_counitIso, HomologicalComplex₂.shiftFunctor₁XXIso_refl, CategoryTheory.forgetEnrichmentOppositeEquivalence_unitIso, CategoryTheory.MonoidalSingleObj.endMonoidalStarFunctorEquivalence_unitIso, symm_self_id, CategoryTheory.TransfiniteCompositionOfShape.map_isColimit, CategoryTheory.piEquivalenceFunctorDiscrete_unitIso, CategoryTheory.sheafBotEquivalence_unitIso, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app, AlgebraicGeometry.Scheme.Opens.ι_appIso, CategoryTheory.MonoidalCategory.whiskerLeftIso_refl, CategoryTheory.WithTerminal.mapComp_inv_app, CategoryTheory.GrpObj.mulRight_one, CategoryTheory.Limits.Cones.postcomposeEquivalence_unitIso, toCoalgEquiv_refl, CategoryTheory.Limits.Cones.postcomposeEquivalence_counitIso, CategoryTheory.Equivalence.changeFunctor_refl, CategoryTheory.Functor.Initial.conesEquiv_unitIso, CategoryTheory.Limits.opCospan_hom_app, CategoryTheory.prod.rightUnitorEquivalence_counitIso, CategoryTheory.Bicategory.Prod.sectL_mapId_hom, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorEquivalence_unitIso, CategoryTheory.Discrete.sumEquiv_counitIso_hom_app, refl_trans, CategoryTheory.ShortComplex.opEquiv_counitIso, ContAction.resComp_hom, CategoryTheory.equivToOverUnit_counitIso, CategoryTheory.ObjectProperty.fullSubcategoryCongr_counitIso, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_hom_c_app, CategoryTheory.CostructuredArrow.prodEquivalence_unitIso, CategoryTheory.Limits.Cones.whiskeringEquivalence_counitIso, CategoryTheory.TransfiniteCompositionOfShape.ici_isoBot, CategoryTheory.Limits.PushoutCocone.op_π_app, CategoryTheory.Limits.opCospan_inv_app, commAlgCatEquivUnder_counitIso, CategoryTheory.Under.equivalenceOfIsInitial_unitIso, CategoryTheory.Limits.PullbackCone.unop_ι_app, CoalgCat.comonEquivalence_unitIso, CategoryTheory.Limits.cospanOp_hom_app, toIsometryEquiv_refl, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_counitIso, CategoryTheory.Over.opEquivOpUnder_counitIso, CategoryTheory.Functor.equiv_unitIso, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_inv_app, CategoryTheory.forgetEnrichmentOppositeEquivalence_counitIso, CategoryTheory.Comon.Comon_EquivMon_OpOp_unitIso, SheafOfModules.Presentation.map_relations_I, CategoryTheory.eqToIso_refl, AlgebraicGeometry.Scheme.residueFieldCongr_refl, CategoryTheory.coalgebraEquivOver_counitIso, CategoryTheory.opOpEquivalence_unitIso, CategoryTheory.Bicategory.Prod.sectL_mapComp_inv, CategoryTheory.WithInitial.opEquiv_counitIso_inv_app, refl_inv, FundamentalGroupoid.punitEquivDiscretePUnit_unitIso, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_unitIso, AlgebraicGeometry.Scheme.isoOfEq_rfl, CategoryTheory.rightDualIso_id, CategoryTheory.Equivalence.symmEquiv_counitIso, Mathlib.Tactic.Bicategory.naturality_id, CategoryTheory.algebraEquivUnder_unitIso, CategoryTheory.prod.leftUnitorEquivalence_counitIso, CategoryTheory.GrothendieckTopology.Cover.multicospanComp_hom_app, CategoryTheory.Over.iteratedSliceEquiv_unitIso, CategoryTheory.WithInitial.equivComma_unitIso_inv_app_app, CategoryTheory.prod.rightUnitorEquivalence_unitIso, CategoryTheory.RelCat.opEquivalence_counitIso, CategoryTheory.Functor.isoWhiskerLeft_refl, CategoryTheory.ShrinkHoms.equivalence_counitIso, CategoryTheory.Equivalence.symmEquiv_unitIso, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_unitIso, CategoryTheory.orderDualEquivalence_counitIso, Mathlib.Tactic.Monoidal.eval_of, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_inv_app_app, CategoryTheory.CostructuredArrow.ofCommaFstEquivalence_counitIso, CategoryTheory.Limits.MultispanIndex.multispanMapIso_hom_app, CategoryTheory.Comma.opEquiv_unitIso, CategoryTheory.Presheaf.coherentExtensiveEquivalence_unitIso, Mathlib.Tactic.Monoidal.naturality_id, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation_iso, CategoryTheory.NatIso.op_refl, op_refl, CategoryTheory.SimplicialObject.eqToIso_refl, CategoryTheory.WithInitial.equivComma_unitIso_hom_app_app, BialgCat.MonoidalCategory.inducingFunctorData_μIso, CategoryTheory.algebraEquivUnder_counitIso, CategoryTheory.prod.leftUnitorEquivalence_unitIso, groupAddGroupEquivalence_unitIso, CategoryTheory.Pi.optionEquivalence_counitIso, CategoryTheory.opOpEquivalence_counitIso, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_hom_app_app, refl_symm, Mathlib.Tactic.Bicategory.eval_of, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_inv_app_app, CategoryTheory.Monad.algebraFunctorOfMonadHomComp_inv_app_f, CategoryTheory.WithTerminal.mapId_hom_app, groupAddGroupEquivalence_counitIso, CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorEquivalence_counitIso, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_isoBot, CategoryTheory.Over.equivalenceOfIsTerminal_unitIso, CategoryTheory.Over.iteratedSliceEquiv_counitIso, CategoryTheory.Groupoid.invEquivalence_counitIso, toHopfAlgEquiv_refl, CategoryTheory.Functor.isoWhiskerRight_refl, CategoryTheory.Bicategory.Pith.inclusion_mapId, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_one, CategoryTheory.eq_unitIso, ContAction.resCongr_inv, CategoryTheory.subterminalsEquivMonoOverTerminal_unitIso, CategoryTheory.ShortComplex.HomologyData.ofIsLimitKernelFork_iso, CategoryTheory.Bicategory.Prod.sectR_mapComp_hom, commGroupAddCommGroupEquivalence_unitIso, CategoryTheory.MonoidalCoherence.refl_iso, CategoryTheory.Pseudofunctor.id_mapComp, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_inv, CategoryTheory.ShortComplex.HomologyData.ofZeros_iso, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalence_unitIso, SimplexCategory.iso_eq_iso_refl, CategoryTheory.Functor.Final.coconesEquiv_counitIso, CategoryTheory.Monoidal.InducingFunctorData.leftUnitor_eq, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_zero, CategoryTheory.CartesianMonoidalCategory.prodComparisonIso_id, CategoryTheory.subterminalsEquivMonoOverTerminal_counitIso, CategoryTheory.Square.arrowArrowEquivalence'_unitIso, CategoryTheory.CategoryOfElements.structuredArrowEquivalence_unitIso, CategoryTheory.ForgetEnrichment.equiv_counitIso, CategoryTheory.TransportEnrichment.forgetEnrichmentEquiv_unitIso, CategoryTheory.Limits.Cones.equivalenceOfReindexing_unitIso, CategoryTheory.Functor.mapContActionComp_hom, AddMonCat.equivalence_unitIso, CategoryTheory.Limits.coconeEquivalenceOpConeOp_counitIso, CategoryTheory.Limits.cospanOp_inv_app, AddCommMonCat.equivalence_counitIso, CategoryTheory.Limits.cospanCompIso_app_one, CategoryTheory.CostructuredArrow.ofCommaFstEquivalence_unitIso, CategoryTheory.WithTerminal.mapId_inv_app, CategoryTheory.LocalizerMorphism.LeftResolution.opEquivalence_counitIso, CategoryTheory.coalgebraEquivOver_unitIso, CategoryTheory.Prod.braiding_counitIso, CategoryTheory.Limits.cospanCompIso_app_left, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_unitIso, CategoryTheory.Under.opEquivOpOver_counitIso, CategoryTheory.StructuredArrow.preEquivalence_counitIso, CategoryTheory.NatIso.unop_refl, CategoryTheory.Limits.parallelPair.eqOfHomEq_hom_app, FundamentalGroupoid.punitEquivDiscretePUnit_counitIso, CategoryTheory.Equivalence.refl_unitIso, Mathlib.Tactic.Bicategory.evalWhiskerRightAux_of, QuadraticModuleCat.ofIso_refl, CategoryTheory.FreeBicategory.lift_mapComp, CategoryTheory.Under.postAdjunctionRight_counit_app_right, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_counitIso, CategoryTheory.Square.arrowArrowEquivalence'_counitIso, CategoryTheory.Groupoid.invEquivalence_unitIso, CategoryTheory.CartesianMonoidalCategory.preservesTerminalIso_id, CategoryTheory.ShortComplex.opEquiv_unitIso, CategoryTheory.Limits.kernelIsoOfEq_refl, CategoryTheory.StructuredArrow.prodEquivalence_counitIso, CategoryTheory.sheafBotEquivalence_counitIso, CategoryTheory.Under.opEquivOpOver_unitIso, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit_unitIso, CategoryTheory.Limits.diagramIsoPair_inv_app, CategoryTheory.Square.arrowArrowEquivalence_unitIso, CategoryTheory.Bicategory.Prod.sectR_mapId_hom, CategoryTheory.ShrinkHoms.equivalence_unitIso, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_one, CategoryTheory.Over.mapCongr_rfl, CategoryTheory.leftDualIso_id, CategoryTheory.Limits.parallelPair.eqOfHomEq_inv_app, CategoryTheory.WithInitial.mapComp_inv_app, CategoryTheory.Limits.opSpan_inv_app, Mathlib.Tactic.Monoidal.evalHorizontalCompAux_of, refl_hom, CategoryTheory.WithInitial.opEquiv_unitIso_hom_app, CategoryTheory.WithTerminal.equivComma_unitIso_hom_app_app, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalence_counitIso, BialgCat.MonoidalCategory.inducingFunctorData_εIso, ContAction.resComp_inv, CategoryTheory.WithTerminal.opEquiv_unitIso_inv_app, CategoryTheory.Enriched.FunctorCategory.functorEnrichedHom_map, Mathlib.Tactic.Monoidal.evalWhiskerRightAux_of, CategoryTheory.piEquivalenceFunctorDiscrete_counitIso, CategoryTheory.Bicategory.Adj.forget₁_mapComp, Action.resCongr_hom, CategoryTheory.Abelian.FunctorCategory.imageObjIso_inv, AlgebraicGeometry.Scheme.Pullback.Triplet.tensorCongr_refl, CategoryTheory.ShortComplex.HomologyData.ofHasKernel_iso, TopologicalSpace.Opens.mapIso_refl, CategoryTheory.BicategoricalCoherence.refl_iso, CategoryTheory.Functor.equiv_counitIso, CategoryTheory.WithTerminal.equivComma_unitIso_inv_app_app, CategoryTheory.Limits.Cocones.whiskeringEquivalence_counitIso, CategoryTheory.WithInitial.mapId_hom_app, CategoryTheory.Limits.Cocones.precomposeEquivalence_counitIso, CategoryTheory.RelCat.opEquivalence_unitIso, CochainComplex.single₀ObjXSelf, CategoryTheory.Square.arrowArrowEquivalence_counitIso, CategoryTheory.WithInitial.mapComp_hom_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_hom_app_app, CategoryTheory.Limits.cospanCompIso_app_right, CategoryTheory.MonoidalOpposite.mopEquiv_counitIso, CategoryTheory.comonEquiv_counitIso, CategoryTheory.ShortComplex.Splitting.homologyData_iso, CategoryTheory.Square.flipEquivalence_counitIso
trans 📖	CompOp	259 math math: CategoryTheory.SingleFunctors.shiftIso_add, SheafOfModules.pushforward_assoc, CategoryTheory.Monoidal.InducingFunctorData.rightUnitor_eq, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo, CategoryTheory.Limits.kernelIsoOfEq_trans, CategoryTheory.Equivalence.mapGrp_counitIso, CategoryTheory.Functor.isoWhiskerRight_twice_assoc, PresheafOfModules.pullback_id_comp, conjAut_apply, isoCongr_symm_apply, imageToKernel_unop, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_map_snd_app, CategoryTheory.Functor.shiftIso_add', CategoryTheory.Monoidal.transportStruct_associator, CategoryTheory.NatIso.op_rightUnitor, CategoryTheory.Join.mapPairEquiv_unitIso, CategoryTheory.Join.mapPairEquiv_counitIso, CategoryTheory.Functor.isoWhiskerRight_trans, CategoryTheory.shiftFunctorAdd'_zero_add, PresheafOfModules.pullback_comp_id, toHopfAlgEquiv_trans, CategoryTheory.BicategoricalCoherence.left'_iso, CategoryTheory.NatIso.unop_rightUnitor, CategoryTheory.SingleFunctors.shiftIso_add', CategoryTheory.Aut.Aut_mul_def, CategoryTheory.Center.tensorUnit_β, self_symm_id, CategoryTheory.MonoidalCoherence.assoc'_iso, CategoryTheory.MonoOver.mapIso_unitIso, Mathlib.Tactic.Bicategory.naturality_rightUnitor, CategoryTheory.GradedObject.comapEquiv_counitIso, homCongr_trans, CategoryTheory.Pi.equivalenceOfEquiv_unitIso, CategoryTheory.Monad.algebraEquivOfIsoMonads_unitIso, CategoryTheory.Pi.equivalenceOfEquiv_counitIso, imageToKernel_op, CategoryTheory.NatIso.op_trans, CategoryTheory.MonoOver.mapIso_counitIso, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isoBot, CategoryTheory.ShortComplex.HomologyData.right_homologyIso_eq_left_homologyIso_trans_iso, CategoryTheory.Functor.isoWhiskerLeft_trans_isoWhiskerRight, CategoryTheory.NatIso.op_isoWhiskerLeft, CategoryTheory.Monoidal.InducingFunctorData.associator_eq, CategoryTheory.Functor.isoWhiskerLeft_twice, CategoryTheory.Pseudofunctor.mapComp_id_left, CategoryTheory.MonoidalCoherence.left_iso, CategoryTheory.MonoidalCoherence.tensor_right_iso, CategoryTheory.MonoidalCategory.tensorIso_def, CategoryTheory.Equivalence.mapHomologicalComplex_unitIso, CategoryTheory.BicategoricalCoherence.tensorRight_iso, CategoryTheory.Limits.fiberwiseColimitLimitIso_hom_app, CategoryTheory.Functor.triangleIso, CategoryTheory.Localization.Lifting.ofIsos_iso, CategoryTheory.eqToIso_trans, CategoryTheory.Center.tensor_β, CategoryTheory.Localization.equivalence_counitIso_app, CategoryTheory.Pseudofunctor.mapComp_id_right, CategoryTheory.BicategoricalCoherence.left_iso, CategoryTheory.shiftFunctorAdd'_assoc, CategoryTheory.Pseudofunctor.mapComp'_comp_id, CategoryTheory.Pseudofunctor.isoMapOfCommSq_horiz_id, unop_trans, CategoryTheory.NatIso.unop_trans, CategoryTheory.eqToIso_map_trans, CategoryTheory.ShortComplex.RightHomologyData.mapOpcyclesIso_eq, CategoryTheory.Equivalence.changeFunctor_trans, trans_conjAut, CategoryTheory.MonoidalCoherence.right'_iso, CategoryTheory.Equivalence.mapMon_unitIso, trans_refl, toBialgEquiv_trans, CategoryTheory.Bicategory.Equivalence.right_triangle, CategoryTheory.Bicategory.Equivalence.left_triangle, coreLeftUnitor, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_map_fst_app, Mathlib.Tactic.Bicategory.naturality_associator, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_app_fst_app, AlgEquiv.toUnder_trans, CategoryTheory.Functor.isoWhiskerLeft_right, CategoryTheory.Pi.isoApp_trans, CategoryTheory.NatIso.op_isoWhiskerRight, CategoryTheory.Center.tensorUnit_snd_β, CategoryTheory.Pseudofunctor.whiskerLeftIso_mapId, CategoryTheory.Limits.Cones.equivalenceOfReindexing_counitIso, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_counitIso, CategoryTheory.GradedObject.comapEquiv_unitIso, CategoryTheory.BicategoricalCoherence.right'_iso, PresheafOfModules.pullback_assoc, op_trans, CategoryTheory.Sum.natIsoOfWhiskerLeftInlInr_eq, CategoryTheory.Functor.isoWhiskerRight_left_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_map_snd_app, CategoryTheory.Functor.isoWhiskerRight_twice, AlgebraicGeometry.Scheme.Pullback.Triplet.tensorCongr_trans, CategoryTheory.Functor.pentagonIso, CategoryTheory.Functor.shiftIso_zero, Mathlib.Tactic.Monoidal.structuralIsoOfExpr_comp, CategoryTheory.NatIso.trans_app, CategoryTheory.BraidedCategory.hexagon_forward_iso, coreAssociator, symm_self_id, SheafOfModules.pullback_comp_id, CategoryTheory.BraidedCategory.yang_baxter_iso, CategoryTheory.Bicategory.adjointifyCounit_left_triangle, eHomCongr_trans, CategoryTheory.Functor.shiftIso_add, Mathlib.Tactic.Monoidal.naturality_associator, CategoryTheory.Equivalence.mapCommGrp_unitIso, CategoryTheory.Functor.commShiftPullback_iso_eq, CategoryTheory.BicategoricalCoherence.tensorRight'_iso, CategoryTheory.Limits.Cones.functorialityEquivalence_unitIso, CategoryTheory.Equivalence.mapCommMon_unitIso, CategoryTheory.Functor.pentagonIso_assoc, CategoryTheory.Pseudofunctor.isoMapOfCommSq_vert_id, refl_trans, CategoryTheory.Functor.isoWhiskerLeft_right_assoc, trans_assoc, trans_def, CategoryTheory.Limits.fiberwiseColimitLimitIso_inv_app, AlgebraicGeometry.Scheme.residueFieldCongr_trans, CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence_inv, CategoryTheory.Functor.mapIso_trans, CategoryTheory.shiftFunctorAdd'_add_zero, AlgebraicGeometry.Scheme.Hom.comp_appIso, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_app_snd_app, CategoryTheory.Oplax.StrongTrans.categoryStruct_comp_naturality, CategoryTheory.Equivalence.mapGrp_unitIso, CategoryTheory.coreCategory_comp_iso, CategoryTheory.NatIso.unop_whiskerRight, SheafOfModules.pullback_id_comp, CategoryTheory.BraidedCategory.hexagon_reverse_iso, toCoalgEquiv_trans, Mathlib.Tactic.Bicategory.naturality_leftUnitor, CategoryTheory.ShortComplex.LeftHomologyData.mapLeftHomologyIso_eq, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_map_fst_app, CategoryTheory.Lax.StrongTrans.categoryStruct_id_naturality, CategoryTheory.NatIso.op_associator, CategoryTheory.Monoidal.transportStruct_leftUnitor, CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_iso, CategoryTheory.Monoidal.transportStruct_rightUnitor, CategoryTheory.ShortComplex.HomologyData.left_homologyIso_eq_right_homologyIso_trans_iso_symm, CategoryTheory.Functor.isoWhiskerLeft_trans_isoWhiskerRight_assoc, CategoryTheory.Functor.triangleIso_assoc, CategoryTheory.rightDistributor_assoc, CategoryTheory.shiftFunctorAdd_assoc, Mathlib.Tactic.Monoidal.naturality_rightUnitor, CategoryTheory.Functor.isoWhiskerLeft_trans_assoc, CategoryTheory.NatIso.unop_leftUnitor, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_counitIso, CategoryTheory.NatIso.unop_associator, CategoryTheory.Limits.Cones.functorialityEquivalence_inverse, CategoryTheory.Localization.Monoidal.lifting₂CurriedTensorPost_iso, CategoryTheory.Monad.algebraEquivOfIsoMonads_counitIso, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_isoBot, CategoryTheory.NatIso.op_leftUnitor, CategoryTheory.Equivalence.mapCommMon_counitIso, Mathlib.Tactic.Bicategory.naturality_id, CategoryTheory.MonoidalCategory.whiskerLeftIso_trans, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_map_fst_app, Mathlib.Tactic.Reassoc.Iso.eq_whisker, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_unitIso, QuadraticModuleCat.ofIso_trans, CategoryTheory.Limits.Cocones.functorialityEquivalence_counitIso, CategoryTheory.Equivalence.mapMon_counitIso, CategoryTheory.leftDistributor_rightDistributor_assoc, CategoryTheory.CartesianMonoidalCategory.preservesTerminalIso_comp, CategoryTheory.Equivalence.trans_counitIso, isoCongr_apply, CategoryTheory.MonoidalCategory.tensorIso_def', Mathlib.Tactic.Monoidal.evalComp_nil_nil, CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_iso, CategoryTheory.Equivalence.mapHomologicalComplex_counitIso, CategoryTheory.ShortComplex.RightHomologyData.mapRightHomologyIso_eq, CategoryTheory.Limits.cokernelIsoOfEq_trans, CategoryTheory.SymmetricCategory.rightDistrib_of_leftDistrib, CategoryTheory.Cat.Hom.toNatIso_rightUnitor, CategoryTheory.Limits.Cones.functorialityEquivalence_counitIso, trans_hom, HomologicalComplex₂.totalShift₁Iso_trans_totalShift₂Iso, Mathlib.Tactic.Monoidal.naturality_id, CategoryTheory.DifferentialObject.isoApp_trans, CategoryTheory.GradedObject.comapEq_trans, SheafOfModules.pullback_assoc, toEquiv_comp, SheafOfModules.Presentation.of_isIso_relations, coreRightUnitor, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_unitIso, CategoryTheory.ShortComplex.LeftHomologyData.mapCyclesIso_eq, CategoryTheory.Center.tensorObj_snd_β, CategoryTheory.CartesianMonoidalCategory.prodComparisonIso_comp, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_app_fst_app, CategoryTheory.MonoidalCoherence.left'_iso, CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence_hom, trans_symm, CategoryTheory.Pseudofunctor.mapComp'_id_comp, CategoryTheory.Monoidal.InducingFunctorData.leftUnitor_eq, PresheafOfModules.pushforward_assoc, CategoryTheory.ShortComplex.LeftHomologyData.mapHomologyIso_eq, CategoryTheory.Functor.isoWhiskerRight_left, BialgEquiv.toBialgIso_trans, CategoryTheory.Limits.Cones.equivalenceOfReindexing_unitIso, SheafOfModules.pushforward_comp_id, Mathlib.Tactic.Monoidal.naturality_leftUnitor, trans_conj, CochainComplex.mapBifunctorShift₁Iso_trans_mapBifunctorShift₂Iso, BialgEquiv.toHopfAlgIso_trans, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_map_snd_app, CategoryTheory.shiftFunctorComm_eq, CategoryTheory.BicategoricalCoherence.assoc_iso, CategoryTheory.Equivalence.mapCommGrp_counitIso, CategoryTheory.Functor.ShiftSequence.shiftIso_add, coreComp, CategoryTheory.Limits.Cocones.functorialityEquivalence_inverse, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_app_snd_app, CategoryTheory.MonoidalCoherence.assoc_iso, CategoryTheory.MonoidalCoherence.right_iso, Mathlib.Tactic.Bicategory.evalComp_nil_cons, CategoryTheory.Oplax.StrongTrans.categoryStruct_id_naturality, CategoryTheory.Functor.isoWhiskerLeft_trans, CategoryTheory.Pseudofunctor.DescentData.pullFunctorEquivalence_counitIso, CategoryTheory.Functor.isoWhiskerRight_trans_assoc, CategoryTheory.Lax.StrongTrans.categoryStruct_comp_naturality, CategoryTheory.Pseudofunctor.comp_mapComp, SheafOfModules.pushforward_id_comp, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_map_fst_app, coreWhiskerRight, CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_tensor, CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_iso, self_symm_id_assoc, symm_self_id_assoc, CategoryTheory.Equivalence.trans_unitIso, CategoryTheory.NatIso.unop_whiskerLeft, trans_inv, Mathlib.Tactic.Monoidal.evalComp_nil_cons, CategoryTheory.Pseudofunctor.DescentData.pullFunctorEquivalence_unitIso, CategoryTheory.Functor.ShiftSequence.shiftIso_zero, CategoryTheory.BicategoricalCoherence.assoc'_iso, Mathlib.Tactic.Bicategory.evalComp_nil_nil, CategoryTheory.Pseudofunctor.isoMapOfCommSq_eq, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_map_snd_app, CategoryTheory.leftDistributor_assoc, AlgebraicTopology.DoldKan.N₁Γ₀_app, PresheafOfModules.pushforward_id_comp, CategoryTheory.BicategoricalCoherence.right_iso, CategoryTheory.Pseudofunctor.comp_mapId, CoalgEquiv.toCoalgIso_trans, CategoryTheory.Limits.Cocones.functorialityEquivalence_unitIso, CategoryTheory.MonoidalCategory.whiskerRightIso_trans, coreWhiskerLeft, Mathlib.Tactic.Bicategory.structuralIsoOfExpr_comp, CategoryTheory.Pseudofunctor.whiskerRightIso_mapId, CategoryTheory.ShortComplex.RightHomologyData.mapHomologyIso'_eq, PresheafOfModules.pushforward_comp_id, CategoryTheory.Sum.functorEquiv_counitIso, trans_mk, toIsometryEquiv_trans, CategoryTheory.MonoidalCoherence.tensor_right'_iso, conjAut_trans
«term_≪≫_» 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
cancel_iso_hom_left 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct hom	—	CategoryTheory.IsIso.epi_of_iso isIso_hom
cancel_iso_hom_right 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct hom	—	CategoryTheory.IsIso.mono_of_iso isIso_hom
cancel_iso_hom_right_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct hom	—	CategoryTheory.IsIso.mono_of_iso isIso_hom
cancel_iso_inv_left 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct inv	—	CategoryTheory.cancel_epi CategoryTheory.IsIso.epi_of_iso isIso_inv
cancel_iso_inv_right 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct inv	—	CategoryTheory.cancel_mono CategoryTheory.IsIso.mono_of_iso isIso_inv
cancel_iso_inv_right_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct inv	—	CategoryTheory.IsIso.mono_of_iso isIso_inv
comp_hom_eq_id 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct hom CategoryTheory.CategoryStruct.id inv	—	eq_comp_inv CategoryTheory.Category.id_comp
comp_inv_eq 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct inv hom	—	CategoryTheory.Category.assoc inv_hom_id CategoryTheory.Category.comp_id hom_inv_id
comp_inv_eq_id 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct inv CategoryTheory.CategoryStruct.id hom	—	CategoryTheory.Category.id_comp
eq_comp_inv 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct inv hom	—	comp_inv_eq
eq_inv_comp 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct inv hom	—	inv_comp_eq
ext 📖	—	hom	—	—	—
ext_iff 📖	mathematical	—	hom	—	ext
ext_inv 📖	—	inv	—	—	—
homFromEquiv_apply 📖	mathematical	—	DFunLike.coe Equiv Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct EquivLike.toFunLike Equiv.instEquivLike homFromEquiv CategoryTheory.CategoryStruct.comp inv	—	—
homFromEquiv_symm_apply 📖	mathematical	—	DFunLike.coe Equiv Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct EquivLike.toFunLike Equiv.instEquivLike Equiv.symm homFromEquiv CategoryTheory.CategoryStruct.comp hom	—	—
homToEquiv_apply 📖	mathematical	—	DFunLike.coe Equiv Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct EquivLike.toFunLike Equiv.instEquivLike homToEquiv CategoryTheory.CategoryStruct.comp hom	—	—
homToEquiv_symm_apply 📖	mathematical	—	DFunLike.coe Equiv Quiver.Hom CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct EquivLike.toFunLike Equiv.instEquivLike Equiv.symm homToEquiv CategoryTheory.CategoryStruct.comp inv	—	—
hom_comp_eq_id 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct hom CategoryTheory.CategoryStruct.id inv	—	eq_inv_comp CategoryTheory.Category.comp_id
hom_eq_inv 📖	mathematical	—	hom inv	—	symm_inv inv_eq_inv
hom_inv_id 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct hom inv CategoryTheory.CategoryStruct.id	—	—
hom_inv_id_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct hom inv	—	CategoryTheory.Category.assoc CategoryTheory.Category.id_comp Mathlib.Tactic.Reassoc.eq_whisker' hom_inv_id
inv_comp_eq 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct inv hom	—	hom_inv_id_assoc inv_hom_id_assoc
inv_comp_eq_id 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct inv CategoryTheory.CategoryStruct.id hom	—	CategoryTheory.Category.comp_id
inv_eq_hom 📖	mathematical	—	inv hom	—	symm_hom
inv_eq_inv 📖	mathematical	—	inv hom	—	ext
inv_ext 📖	mathematical	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct hom CategoryTheory.CategoryStruct.id	inv	—	hom_comp_eq_id
inv_ext' 📖	mathematical	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct hom CategoryTheory.CategoryStruct.id	inv	—	hom_comp_eq_id
inv_hom_id 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct inv hom CategoryTheory.CategoryStruct.id	—	—
inv_hom_id_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct inv hom	—	CategoryTheory.Category.assoc CategoryTheory.Category.id_comp Mathlib.Tactic.Reassoc.eq_whisker' inv_hom_id
isIso_hom 📖	mathematical	—	CategoryTheory.IsIso hom	—	hom_inv_id inv_hom_id
isIso_inv 📖	mathematical	—	CategoryTheory.IsIso inv	—	isIso_hom
map_hom_inv_id 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Functor.map hom inv CategoryTheory.CategoryStruct.id	—	—
map_hom_inv_id_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Functor.map hom inv	—	CategoryTheory.Category.assoc CategoryTheory.Category.id_comp Mathlib.Tactic.Reassoc.eq_whisker' map_hom_inv_id
map_inv_hom_id 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Functor.map inv hom CategoryTheory.CategoryStruct.id	—	—
map_inv_hom_id_assoc 📖	mathematical	—	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.obj CategoryTheory.Functor.map inv hom	—	CategoryTheory.Category.assoc CategoryTheory.Category.id_comp Mathlib.Tactic.Reassoc.eq_whisker' map_inv_hom_id
nonempty_iso_refl 📖	mathematical	—	CategoryTheory.Iso	—	—
nonempty_iso_symm 📖	mathematical	—	CategoryTheory.Iso	—	—
refl_hom 📖	mathematical	—	hom refl CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct	—	—
refl_inv 📖	mathematical	—	inv refl CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct	—	—
refl_symm 📖	mathematical	—	symm refl	—	—
refl_trans 📖	mathematical	—	trans refl	—	ext CategoryTheory.Category.id_comp
self_symm_id 📖	mathematical	—	trans symm refl	—	ext hom_inv_id
self_symm_id_assoc 📖	mathematical	—	trans symm	—	trans_assoc self_symm_id refl_trans
symm_bijective 📖	mathematical	—	Function.Bijective CategoryTheory.Iso symm	—	Function.bijective_iff_has_inverse symm_symm_eq
symm_eq_iff 📖	mathematical	—	symm	—	Function.Bijective.injective symm_bijective
symm_hom 📖	mathematical	—	hom symm inv	—	—
symm_inv 📖	mathematical	—	inv symm hom	—	—
symm_mk 📖	mathematical	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.CategoryStruct.id	symm	—	—
symm_self_id 📖	mathematical	—	trans symm refl	—	ext inv_hom_id
symm_self_id_assoc 📖	mathematical	—	trans symm	—	trans_assoc symm_self_id refl_trans
symm_symm_eq 📖	mathematical	—	symm	—	—
trans_assoc 📖	mathematical	—	trans	—	ext CategoryTheory.Category.assoc
trans_def 📖	mathematical	—	CategoryTheory.Iso instTransIso trans	—	—
trans_hom 📖	mathematical	—	hom trans CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct	—	—
trans_inv 📖	mathematical	—	inv trans CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct	—	—
trans_mk 📖	mathematical	CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct CategoryTheory.CategoryStruct.id	trans	—	—
trans_refl 📖	mathematical	—	trans refl	—	ext CategoryTheory.Category.comp_id
trans_symm 📖	mathematical	—	symm trans	—	—

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