category 📖 | CompOp | 8856 mathmath: IsDenseSubsite.mapPreimage_map_of_fac, CategoryTheory.Equivalence.adjointify_η_ε_assoc, CategoryTheory.Sheaf.cartesianMonoidalCategoryLift_val, CategoryTheory.GrothendieckTopology.coneCompEvaluationOfConeCompDiagramFunctorCompEvaluation_pt, CategoryTheory.Triangulated.TStructure.eTruncLT_map_app_eTruncLTι_app, CategoryTheory.Limits.Trident.condition_assoc, SSet.OneTruncation₂.nerveEquiv_apply, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₃, CategoryTheory.shiftFunctorZero_inv_app_obj_of_induced, CategoryTheory.Presheaf.instIsCardinalPresentableFunctorOppositeFreeYonedaOfHasColimitsOfSize, AlgebraicTopology.DoldKan.natTransPInfty_app, CategoryTheory.Triangulated.SpectralObject.Hom.comm, HomotopyCategory.spectralObjectMappingCone_δ'_app, CategoryTheory.GrothendieckTopology.isoSheafify_hom, CategoryTheory.Abelian.SpectralObject.δ_eq_zero_of_isIso₂, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_map_app_hom₃, CategoryTheory.Limits.instPreservesMonomorphismsObjFunctorTypeSigmaConst, Action.resCongr_inv, CategoryTheory.MorphismProperty.LeftFraction.map_compatibility, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_eq, CategoryTheory.SingleFunctors.shiftIso_add, whiskeringRightObjIdIso_hom_app_app, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₁, TopCat.binaryCofan_isColimit_iff, LeftExtension.coconeAtFunctor_map_hom, functorHomEquiv_apply_app, CategoryTheory.SimplicialObject.id_left_app, CategoryTheory.sum.inrCompInverseAssociator_hom_app, FullyFaithful.homNatIsoMaxRight_inv_app, CategoryTheory.MorphismProperty.exists_isPushout_of_isFiltered, CategoryTheory.GrothendieckTopology.W_sheafToPresheaf_map_iff_isIso, CategoryTheory.prodComonad_ε_app, CategoryTheory.LeftExactFunctor.ofExact_map, CategoryTheory.Abelian.SpectralObject.H_map_twoδ₂Toδ₁_toCycles_assoc, SSet.stdSimplex.objMk_bijective, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_skyscraperPresheafHomEquiv_symm, SSet.Subcomplex.lift_ι, CommShift.isoAdd_hom_app, PresheafOfModules.instIsRightAdjointPushforwardCompFunctorOppositeRingCatWhiskerLeftOp, CategoryTheory.Adjunction.compUliftCoyonedaIso_hom_app_app_down, CategoryTheory.Monoidal.tensorHom_app, CategoryTheory.Tor'_obj_obj, CategoryTheory.sheafBotEquivalence_functor, CategoryTheory.MorphismProperty.Comma.mapRightComp_hom_app_left, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerLeftIso_inv_app, CategoryTheory.whiskeringLeft_comp_evaluation, SSet.Truncated.HomotopyCategory.BinaryProduct.iso_inv_toFunctor, CategoryTheory.Enriched.Functor.associator_inv_apply, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_map, CategoryTheory.Adjunction.Triple.isIso_unit_iff_isIso_counit, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_hom_app_zero, CategoryTheory.uliftCoyonedaEquiv_apply, CategoryTheory.Limits.DiagramOfCones.id, CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_app, CategoryTheory.TwoSquare.equivNatTrans_symm_apply, CategoryTheory.Sum.natTransOfWhiskerLeftInlInr_app, SheafOfModules.pushforward_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitNatIso_inv_app, CategoryTheory.instSmallOppositeObjFunctorTypeYoneda, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverse_obj, CategoryTheory.LaxBraidedFunctor.isoMk_inv, CategoryTheory.Abelian.SpectralObject.exact₁', rightKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.sndFunctor_map, PushoutObjObj.inr_ι, isoSum_inv_app_inl, CategoryTheory.Limits.IndizationClosedUnderFilteredColimitsAux.exists_nonempty_limit_obj_of_isColimit, AddCommGrpCat.coyoneda_obj_obj_coe, CategoryTheory.Equivalence.leftOp_unitIso_hom_app, CategoryTheory.linearCoyoneda_obj_additive, CategoryTheory.Monad.ForgetCreatesColimits.commuting, CategoryTheory.WithTerminal.coneEquiv_unitIso_hom_app_hom_left, mapTriangleIdIso_inv_app_hom₃, CategoryTheory.SimplicialObject.whiskering_obj_map_app, CategoryTheory.Monad.monadMonEquiv_unitIso_inv_app_toNatTrans_app, IsDenseSubsite.instIsIsoSheafAppCounitSheafAdjunctionCocontinuous, CategoryTheory.Limits.limitConeOfUnique_cone_π, CategoryTheory.ComposableArrows.opEquivalence_counitIso_inv_app_app, CategoryTheory.Adjunction.ofNatIsoRight_unit, CategoryTheory.PreGaloisCategory.instT2SpaceAutFunctorFintypeCat, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_apply, OplaxMonoidal.ofBifunctor.firstMap₂_app_app_app, coreComp_hom_app_iso_inv, natTransEquiv_apply_app, mapComposableArrowsObjMk₂Iso_inv_app, CategoryTheory.uliftCoyonedaIsoCoyoneda_hom_app_app, SheafOfModules.instAdditivePresheafOfModulesObjFunctorOppositeRingCatIsSheafForget, CategoryTheory.Discrete.sumEquiv_counitIso_inv_app, CategoryTheory.WithTerminal.mkCommaObject_right, CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc, CategoryTheory.coyonedaEquiv_symm_app_apply, isZero, CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_right, HomologicalComplex.singleMapHomologicalComplex_hom_app_ne, CategoryTheory.ComposableArrows.isoMk₁_hom_app, CategoryTheory.StructuredArrow.map_map_right, CategoryTheory.NatTrans.hcomp_id_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon_map, CategoryTheory.Pi.eqToEquivalenceFunctorIso_hom, CategoryTheory.PreGaloisCategory.mulAction_def, CategoryTheory.shiftFunctorAdd'_assoc_inv_app, isLeftKanExtension_iff_isIso, CategoryTheory.preservesFiniteLimits_of_evaluation, leibnizPullback_obj_map, CategoryTheory.Abelian.Preradical.shortComplex_X₁, CategoryTheory.Sheaf.ΓHomEquiv_naturality_left_symm, CategoryTheory.Triangulated.TStructure.truncGEδLT_comp_truncLTι, CategoryTheory.isIso_sheafificationAdjunction_counit, isIso_of_isRightDerivedFunctor_of_inverts, CategoryTheory.Adjunction.toEquivalence_counitIso_hom_app, CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair_hom_app, typeToPartialFunIsoPartialFunToPointed_inv_app_toFun, AlgebraicTopology.DoldKan.Compatibility.equivalence₀_unitIso_hom_app, CategoryTheory.ObjectProperty.ColimitOfShape.toCostructuredArrow_obj, CategoryTheory.Sheaf.isLocallySurjective_sheafToPresheaf_map_iff, CategoryTheory.Idempotents.app_idem_assoc, homObjEquiv_apply_app, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_three_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_left, CategoryTheory.WithInitial.equivComma_functor_obj_right_obj, sheafPushforwardContinuousIso_inv, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app', CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_associator_hom_eq_associator_hom, CategoryTheory.NatIso.mapHomologicalComplex_inv_app_f, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_X₃, CategoryTheory.SingleFunctors.Hom.comm, CategoryTheory.preservesFiniteLimits_iff_lan_preservesFiniteLimits, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app, CategoryTheory.whiskeringRightPreservesLimits, CategoryTheory.GrothendieckTopology.toPlus_plusLift_assoc, CategoryTheory.Adjunction.whiskerLeftLCounitIsoOfIsIsoUnit_hom_app, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.shift_shiftFunctorCompIsoId_hom_app, CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux_fac, CategoryTheory.ComposableArrows.sc'MapIso_inv, liftOfIsRightKanExtension_fac, CategoryTheory.GrothendieckTopology.preservesColimitsOfShape_yoneda_of_ofArrows_inj_mem, CategoryTheory.endofunctorMonoidalCategory_tensorUnit_obj, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp_inv_app_f, CategoryTheory.ULiftYoneda.instFullFunctorOppositeTypeUliftYoneda, CategoryTheory.yoneda_preservesLimit, CategoryTheory.Triangulated.TStructure.truncGEπ_comp_truncGEδLT_assoc, CategoryTheory.Limits.pointwiseBinaryBicone_inr_app, CategoryTheory.evaluationLeftAdjoint_map_app, CategoryTheory.Limits.CategoricalPullback.catCommSq_iso_hom_app, CategoryTheory.Join.inlCompFromSum_hom_app, LightProfinite.Extend.functorOp_obj, CategoryTheory.Limits.colimitHomIsoLimitYoneda_hom_comp_π, AlgebraicGeometry.Scheme.Modules.pushforwardId_inv_app_app, AddCommMonCat.coyoneda_obj_obj_coe, CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj_map_f, CategoryTheory.conjugateEquiv_iso, CategoryTheory.DinatTrans.dinaturality_assoc, rightKanExtensionUniqueOfIso_hom, CategoryTheory.Abelian.SpectralObject.δToCycles_iCycles, CategoryTheory.Limits.diagramIsoPair_hom_app, CategoryTheory.obj_ε_app_assoc, Action.instIsEquivalenceFunctorSingleObjInverse, CategoryTheory.Presieve.shrinkFunctorHomEquiv_apply_coe, SSet.stdSimplex.mem_nonDegenerate_iff_strictMono, SSet.stdSimplex.coe_triangle_down_toOrderHom, CategoryTheory.equivOfTensorIsoUnit_unitIso, CategoryTheory.Presheaf.isSheaf_of_isTerminal, mapHomologicalComplexIdIso_hom_app_f, CategoryTheory.Limits.isIndObject_limit_of_discrete, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_associator, CategoryTheory.Join.mapPairId_hom_app, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafAdjunction_homEquiv_symm_apply, CategoryTheory.Limits.Bicone.toCocone_ι_app_mk, HomologicalComplex.mapBifunctor.ι_D₂, leftOpRightOpEquiv_functor_obj_map, TopCat.Sheaf.interUnionPullbackCone_snd, CategoryTheory.linearCoyoneda_map_app, CategoryTheory.MorphismProperty.instIsStableUnderTransfiniteCompositionOfShapeFunctorMonomorphismsOfHasPullbacksOfHasIterationOfShape, CategoryTheory.Adjunction.whiskerLeftLCounitIsoOfIsIsoUnit_inv_app, CategoryTheory.linearCoyoneda_obj_obj_carrier, SSet.RelativeMorphism.botEquiv_symm_apply_map, HomotopicalAlgebra.FibrantObject.instIsIsoFunctorWhiskerRightHoCatιCompResolutionNatTransOfIsLocalizationWeakEquivalences, HomologicalComplex.mapBifunctor₁₂.ι_D₃_assoc, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_apply, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionHomLeft, rightDerivedNatTrans_id, CategoryTheory.ObjectProperty.instCommShiftHomFunctorLiftCompιIso, CategoryTheory.Limits.WalkingMultispan.functorExt_hom_app, CategoryTheory.CosimplicialObject.whiskering_obj_obj_obj, SSet.Truncated.tensor_map_apply_snd, SSet.Subcomplex.prod_top_le_unionProd, CategoryTheory.Core.forgetFunctorToCore_map_app, CategoryTheory.Comma.mapLeftEq_inv_app_right, CategoryTheory.Abelian.SpectralObject.leftHomologyDataShortComplex_H, shiftIso_add_inv_app, CategoryTheory.Limits.colimitIsoFlipCompColim_inv_app, Monoidal.μNatIso_inv_app, CategoryTheory.Comma.mapLeftIso_inverse_map_right, SSet.oneTruncation₂_obj, AlgebraicGeometry.Scheme.Modules.instFaithfulPresheafOfModulesToPresheafOfModules, CategoryTheory.Equivalence.mapGrp_counitIso, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceInverseπ_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_hom_app_eq, CategoryTheory.shiftFunctorComm_zero_hom_app, CategoryTheory.MorphismProperty.Comma.mapRightIso_counitIso_inv_app_left, SSet.OneTruncation₂.ofNerve₂.natIso_hom_app_map, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionAssocIso_hom, CategoryTheory.Grothendieck.ιCompMap_hom_app_fiber, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app, CategoryTheory.shrinkYoneda_map, CategoryTheory.isSeparator_iff_faithful_preadditiveCoyoneda, flip₂₃Functor_obj_obj_obj_obj, CategoryTheory.NatTrans.rightDerived_comp_assoc, CategoryTheory.Limits.pointwiseBinaryBicone_fst_app, leftExtensionEquivalenceOfIso₁_functor_map_left, CategoryTheory.Equivalence.comp_asNatTrans, isoWhiskerRight_twice_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_naturality_assoc, CategoryTheory.GrothendieckTopology.Point.skyscraperSheafFunctor_obj_obj, HomologicalComplex.singleMapHomologicalComplex_hom_app_self, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_hom_app, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_two, Monoidal.rightUnitor_inv_app, CategoryTheory.GradedObject.ι_mapBifunctorMapMap, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_hom_app_app_down, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, AlgebraicGeometry.StructureSheaf.globalSectionsIso_inv, CategoryTheory.Limits.coneOpEquiv_unitIso, LeftExtension.precomp₂_obj_hom_app, PresheafOfModules.pullback_id_comp, CategoryTheory.Limits.Types.binaryCofan_isColimit_iff, CategoryTheory.Abelian.SpectralObject.homologyDataIdId_left_π, SSet.PtSimplex.RelStruct.δ_map_of_lt, SSet.Subcomplex.toRange_ι, CategoryTheory.Abelian.SpectralObject.EIsoH_hom_opcyclesIsoH_inv_assoc, CategoryTheory.Limits.Cotrident.ofCocone_ι, HomologicalComplex.mapBifunctor₁₂.d_eq, CategoryTheory.NatTrans.unop_whiskerLeft, SSet.Homotopy.congr_homologyMap_singularChainComplexFunctor, CategoryTheory.Limits.colimit.isoColimitCocone_ι_inv, CommShift.isoAdd_inv_app, CategoryTheory.MonadIso.toNatIso_hom, CategoryTheory.Idempotents.toKaroubi_comp_karoubiFunctorCategoryEmbedding, CategoryTheory.Join.pseudofunctorRight_mapComp_inv_toNatTrans_app, CategoryTheory.Limits.multicospanIndexEnd_fst, IsDenseSubsite.mapPreimage_id, opUnopIso_hom_app, CategoryTheory.WithTerminal.equivComma_functor_obj_left_obj, ModuleCat.restrictScalarsCongr_symm, CategoryTheory.Limits.diagramIsoCospan_inv_app, CategoryTheory.MonoidalOpposite.tensorLeftMopIso_hom_app_unmop, CategoryTheory.Triangulated.TStructure.triangleω₁δ_obj_mor₁, CategoryTheory.NatTrans.rightDerivedToHomotopyCategory_id, instIsIsoAppCounitRanAdjunctionOfHasPointwiseRightKanExtension, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_map_app_hom₂, CategoryTheory.equivEssImageOfReflective_unitIso, CategoryTheory.Limits.Trident.app_zero, LightCondensed.ihomPoints_apply, Condensed.instPreservesFiniteProductsOppositeStoneanObjFunctorIsSheafCoherentTopology, CategoryTheory.Limits.IsColimit.fac, CategoryTheory.shrinkYonedaEquiv_comp, sheafAdjunctionCocontinuous_homEquiv_apply_hom, whiskeringRight₂_obj_obj_map_app, CategoryTheory.eval_app, CategoryTheory.GrothendieckTopology.toSheafify_naturality_assoc, CategoryTheory.OverPresheafAux.costructuredArrowPresheafToOver_map, CategoryTheory.Subfunctor.Subpresheaf.range_eq_ofSection', CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberDesc, CategoryTheory.ExactFunctor.forget_map, SSet.Subcomplex.prodIso_hom, CategoryTheory.LocalizerMorphism.natTransCommShift_hom, CategoryTheory.Abelian.SpectralObject.liftOpcycles_fromOpcycles_assoc, Monoidal.commTensorLeft_hom_app, CategoryTheory.ObjectProperty.preservesLimitsOfShape_eq_iSup, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_hom, CategoryTheory.Limits.map_id_right_eq_curry_swap_map, AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_inv_app, IsDenseSubsite.instIsEquivalenceSheafSheafPushforwardContinuous, CategoryTheory.Monad.ofMon_η, CategoryTheory.HasShift.Induced.add_inv_app_obj, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_ι_presheafHom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_inv_app_hom, AlgebraicGeometry.opensCone_pt, CategoryTheory.Limits.Cone.postcomposeComp_hom_app_hom, CategoryTheory.Adjunction.Localization.ε_app, CategoryTheory.Pseudofunctor.DescentData.pullFunctorCompIso_inv_app_hom, CategoryTheory.Limits.Cone.unop_ι, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitNatIso_hom_app, CategoryTheory.nerve.instFullCatTruncatedOfNatNatNerveFunctor₂, CategoryTheory.FunctorToTypes.coprod.desc_inr, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_isLimit_lift, curryingEquiv_symm_apply_obj_obj, CategoryTheory.Equivalence.sheafCongr_functor, CategoryTheory.GrothendieckTopology.uliftYonedaIsoYoneda_inv_app_hom_app_down, SSet.horn₃₁.desc.multicofork_π_two, CategoryTheory.Adjunction.rightAdjointUniq_trans, CategoryTheory.Limits.colimitLimitToLimitColimit_isIso, mapBifunctorHomologicalComplexObj_map_f_f, mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app_assoc, CategoryTheory.PullbackShift.adjunction_counit, SSet.stdSimplex.δ_zero_eq_const, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_functor, CategoryTheory.Equivalence.unitIso_hom_app_comp_inverse_map_η_functor_assoc, CategoryTheory.Square.mapFunctor_obj, CategoryTheory.MonoOver.congr_unitIso, CompHausLike.LocallyConstant.functor_obj_obj, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_app_hom_assoc, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_left_app, CategoryTheory.MorphismProperty.Comma.mapRightIso_unitIso_inv_app_right, CategoryTheory.iterated_mateEquiv_conjugateEquiv, CategoryTheory.FunctorToTypes.prodMk_fst, CategoryTheory.GradedObject.mapTrifunctorMapFunctorObj_obj_map, CategoryTheory.Presheaf.coherentExtensiveEquivalence_inverse_map_hom, CategoryTheory.Limits.Cone.ofTrident_π, mapCommGrpCompIso_inv_app_hom_hom_hom, CategoryTheory.LeftExactFunctor.forget_map, CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse, CategoryTheory.Sum.functorEquivFunctorCompFstIso_inv_app_app, mapCommMonNatIso_inv_app_hom_hom, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₁, AlgebraicGeometry.StructureSheaf.comap_id, CategoryTheory.functor_skeletal, CategoryTheory.OverPresheafAux.unitAux_hom, CategoryTheory.Limits.fiberwiseColimit_map, CategoryTheory.Quotient.natIsoLift_inv, CategoryTheory.cocones_map_app_app, LeftExtension.precomp₂_map_right, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_unitIso, CategoryTheory.IndParallelPairPresentation.hf, PresheafOfModules.instIsLocallySurjectiveToSheafify, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.F_obj, CategoryTheory.Monoidal.leftUnitor_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_app_snd_app, SSet.Truncated.sk.full, CategoryTheory.Equivalence.sheafCongr.inverse_obj_obj_map, CategoryTheory.whiskeringRightPreservesColimits, mapTriangleIso_inv_app_hom₁, CategoryTheory.Subfunctor.Subpresheaf.range_eq_ofSection, IsEventuallyConstantFrom.cocone_ι_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_whiskerRight, CategoryTheory.Triangulated.TStructure.eTruncGEπ_naturality_assoc, SSet.ι₀_snd_assoc, CategoryTheory.Discrete.sumEquiv_unitIso_inv_app, CategoryTheory.Limits.ReflexiveCofork.app_one_eq_π, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_π_app, CategoryTheory.GradedObject.ι_mapBifunctorMapObjDesc, SSet.Truncated.HomotopyCategory.descOfTruncation_comp, CategoryTheory.NatIso.cancel_natIso_hom_right, CategoryTheory.MonoidalSingleObj.endMonoidalStarFunctorEquivalence_counitIso, condensedSetToTopCat_obj_carrier, CategoryTheory.MonoidalCategory.externalProductBifunctor_obj_obj, CategoryTheory.Limits.FormalCoproduct.cechIsoCechNerve_hom_app, flip₁₃_map_app_app, AlgebraicTopology.DoldKan.N₁_map_f, CategoryTheory.ComposableArrows.isIso_iff₂, instIsRightDerivedFunctorLiftInvFac, CondensedMod.IsSolid.isIso_solidification_map, CategoryTheory.Abelian.SpectralObject.zero₂_assoc, CategoryTheory.Limits.DiagramOfCocones.mkOfHasColimits_coconePoints, CategoryTheory.instFullMonFunctorOppositeMonCatYonedaMon, CategoryTheory.SimplicialThickening.SimplicialCategory.comp_id, IsOpenMap.pullbackIso_hom_app_app, AlgebraicGeometry.StructureSheaf.const_mul_rev, leftDerivedNatTrans_fac_assoc, CategoryTheory.NonemptyParallelPairPresentationAux.hf, AlgebraicGeometry.ΓSpec.isIso_adjunction_counit, CategoryTheory.MonoidalCategory.endofunctorMonoidalCategory.evaluationRightAction_actionHomLeft, CategoryTheory.instLocallySmallFunctor, CategoryTheory.FunctorToTypes.functorHomEquiv_symm_apply_app_app, PresheafOfModules.toPresheaf_preservesFiniteLimits, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_map, CategoryTheory.MonoidalCategory.tensorRightTensor_hom_app, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₃, LightCondensed.instPreservesFiniteProductsOppositeLightProfiniteObjFunctorIsSheafCoherentTopology, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_inv_app_hom_app, CategoryTheory.iterated_mateEquiv_conjugateEquiv_symm, CategoryTheory.MonoidalCategory.tensorLeftTensor_inv_app, CategoryTheory.NatTrans.IsMonoidal.instHomFunctorAssociator, CategoryTheory.GrothendieckTopology.Point.toPresheafFiberOfIsCofiltered_w_assoc, CategoryTheory.Limits.spanCompIso_inv_app_zero, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_app_assoc, Monoidal.natTransIsMonoidal_of_transport, CategoryTheory.WithInitial.opEquiv_unitIso_inv_app, SSet.Subcomplex.mem_unionProd_iff, CategoryTheory.MorphismProperty.isIso_fst'_self, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafFunctor_map_app, CategoryTheory.NatIso.inv_map_hom_app, CategoryTheory.Limits.Cocone.toOver_ι_app, CategoryTheory.Triangulated.TStructure.natTransTruncLTOfLE_trans, CategoryTheory.Equivalence.counitIso_inv_app_comp_functor_map_η_inverse, CategoryTheory.Abelian.SpectralObject.cokernelSequenceCycles_X₁, CategoryTheory.NatTrans.flipApp_app, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_functor, AlgebraicTopology.DoldKan.HigherFacesVanish.inclusionOfMooreComplexMap, mapTriangleIso_inv_app_hom₃, CategoryTheory.ShortComplex.π₁Toπ₂_comp_π₂Toπ₃_assoc, CategoryTheory.Abelian.SpectralObject.cokernelSequenceCyclesEIso_hom_τ₁, CategoryTheory.Limits.cospanUnop_hom_app, CategoryTheory.Under.postComp_inv_app_right, CategoryTheory.orderDualEquivalence_unitIso, CategoryTheory.Triangulated.TStructure.triangleω₁δ_obj_obj₂, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_distinguished, CategoryTheory.Limits.Multicofork.ofπ_ι_app, CategoryTheory.Equivalence.sheafCongr.unitIso_inv_app_hom_app, AddCommMonCat.equivalence_unitIso, SSet.modelCategoryQuillen.I_le_monomorphisms, CategoryTheory.Idempotents.instIsEquivalenceFunctorKaroubiFunctorExtension₂, AlgebraicGeometry.Scheme.restrictFunctorΓ_inv_app, CategoryTheory.Sheaf.instIsLocallySurjectiveAppArrowILocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, CategoryTheory.Triangulated.TStructure.eTruncLTLTIsoLT_inv_hom_id_app, Condensed.hom_ext_iff, CategoryTheory.FunctorToTypes.instHasImagesFunctorType, partialFunEquivPointed_counitIso_inv_app_toFun, CategoryTheory.Arrow.augmentedCechNerve_hom_app, isoSum_inv_app_inr, CategoryTheory.ran_isSheaf_of_isCocontinuous, SSet.instIsDiscreteHomotopyCategoryObjTruncatedOfNatNatTruncationSimplexCategoryStdSimplexMk, CategoryTheory.shrinkYonedaEquiv_symm_map_assoc, SSet.oneTruncation₂_map, CategoryTheory.Limits.cospanIsoMk_inv_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedAction_obj_obj, CategoryTheory.Abelian.SpectralObject.instMonoFromOpcycles, mapCocone_ι_app, CategoryTheory.Limits.Cocone.whiskeringEquivalence_counitIso, CategoryTheory.TwistShiftData.z_zero_zero, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₂, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_apply, SSet.horn.faceSingletonComplIso_inv_ι_assoc, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_incl_app, full_whiskeringRight_obj, commBialgCatEquivComonCommAlgCat_unitIso_inv_app, CategoryTheory.lan_preservesFiniteLimits_of_flat, TopCat.Presheaf.generateEquivalenceOpensLe_unitIso, partialFunEquivPointed_unitIso_hom_app, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_left_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_map_snd_app, AlgebraicGeometry.StructureSheaf.comap_comp, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_app_apply, CategoryTheory.Limits.parallelPairOpIso_inv_app_zero, CategoryTheory.Limits.HasColimit.isoOfEquivalence_inv_π, CategoryTheory.CatCenter.app_sub, shiftIso_add', CategoryTheory.SimplicialObject.whiskering_obj_obj_σ, SheafOfModules.pushforwardNatIso_inv, CategoryTheory.FreeMonoidalCategory.normalizeIsoAux_inv_app, CategoryTheory.Comonad.ComonadicityInternal.unitFork_π_app, CategoryTheory.ProdPreservesConnectedLimits.γ₂_app, CorepresentableBy.uniqueUpToIso_inv, CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_left, CategoryTheory.SingleFunctors.id_hom, CategoryTheory.Idempotents.functorExtension₁CompWhiskeringLeftToKaroubiIso_inv_app_app_f, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_eq_iff', CategoryTheory.Limits.ι_colimitCompWhiskeringLeftIsoCompColimit_hom_assoc, CategoryTheory.GrothendieckTopology.liftToDiagramLimitObjAux_fac_assoc, CategoryTheory.Limits.colimit.cocone_ι, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_naturality_left_symm, CategoryTheory.NatIso.pi_hom, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom, instIsLeftAdjointDiscreteTensorLeftCompIncl, CategoryTheory.Monad.mul_def, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_comp, PresheafOfModules.Sheafify.add_smul, CategoryTheory.sum.inlCompInrCompInverseAssociator_hom_app_down_down, uliftCoyonedaCoreprXIso_hom_app, CategoryTheory.NatTrans.removeLeftOp_id, isLimitConeOfIsRightKanExtension_lift, CategoryTheory.Limits.Pi.cone_π, ModuleCat.extendScalarsId_hom_app_one_tmul, CategoryTheory.SimplicialObject.comp_right, CategoryTheory.Adjunction.mapMon_unit, CategoryTheory.isCoseparator_iff_faithful_preadditiveYoneda, IsCoverDense.Types.sheafIso_inv_hom, CategoryTheory.SimplicialObject.Augmented.point_map, Profinite.Extend.functorOp_map, CategoryTheory.Iso.core_inv_app_iso_hom, CategoryTheory.GrothendieckTopology.W_eq_inverseImage_isomorphisms, CategoryTheory.instAdditiveObjFunctorAdditiveFunctor, AlgebraicTopology.singularChainComplexFunctor_exactAt_of_totallyDisconnectedSpace, CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_left_app, CategoryTheory.Under.forgetMapInitial_inv_app, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.hf, CategoryTheory.Enriched.Functor.whiskerLeft_app_apply, SSet.stdSimplex.faceSingletonIso_zero_hom_comp_ι_eq_δ, CategoryTheory.Abelian.SpectralObject.sc₂_X₃, SSet.stdSimplex.ι₁_whiskerLeft_toSSetObjI_μ, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_hom_app_app, CategoryTheory.instMonoFunctorWhiskerRightOfPreservesMonomorphisms, isCardinalAccessible_of_isLimit, CategoryTheory.Triangulated.TStructure.natTransTruncLEOfLE_ι_assoc, CategoryTheory.Limits.HasLimit.isoOfNatIso_inv_π_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_map_app, CategoryTheory.NatIso.op_rightUnitor, CategoryTheory.NatTrans.CommShiftCore.shift_app_comm, map_shiftFunctorComm_hom_app, CategoryTheory.WithInitial.isColimitEquiv_apply_desc_right, CategoryTheory.Join.mapPairEquiv_unitIso, CategoryTheory.Comma.map_final, AlgebraicGeometry.exists_isAffineOpen_preimage_eq, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_hom_app_snd_app, CategoryTheory.MorphismProperty.instIsStableUnderTransfiniteCompositionOfShapeFunctorFunctorCategoryOfHasIterationOfShape, CategoryTheory.Idempotents.functorExtension₂_map_app_f, CategoryTheory.Limits.coneUnopOfCoconeEquiv_counitIso, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₁, CategoryTheory.Join.mapPairEquiv_counitIso, CategoryTheory.PreGaloisCategory.endEquivSectionsFibers_π, CategoryTheory.Paths.liftNatIso_inv_app, sumIsoExt_hom_app_inl, SSet.Subcomplex.fromPreimage_ι_assoc, isoWhiskerRight_trans, SSet.Subcomplex.toSSetFunctor_map, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app, AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf_map, CategoryTheory.Limits.CoconeMorphism.w, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_ι_inv, SSet.Subcomplex.unionProd.isPushout, SSet.iSup_subcomplexOfSimplex_prod_eq_top, CategoryTheory.Equivalence.rightOp_counitIso_inv_app, HomologicalComplex.mapBifunctor.ι_D₂_assoc, CategoryTheory.Sheaf.toImage_ι_assoc, CategoryTheory.WithInitial.liftToInitialUnique_hom_app, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans_assoc, CategoryTheory.RightExactFunctor.whiskeringRight_obj_obj_obj, PullbackObjObj.mapArrowRight_right, TopologicalSpace.OpenNhds.inclusionMapIso_hom, CategoryTheory.shiftFunctorAdd'_zero_add, curryObjCompIso_hom_app_app, unopOpIso_inv_app, CategoryTheory.GrothendieckTopology.overMapPullback_comp_id, SSet.Truncated.Path.mk₂_arrow, AlgebraicGeometry.StructureSheaf.const_self, uncurryObjFlip_hom_app, PushoutObjObj.mapArrowRight_id, CategoryTheory.NatTrans.epi_iff_epi_app, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_fst, LightCondensed.ihomPoints_symm_comp, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_map_mkHom_id_homMk, sheafPullbackConstruction.instPreservesFiniteLimitsSheafSheafPullback, PullbackObjObj.mapArrowLeft_id, CategoryTheory.Subobject.inf_le_left, CategoryTheory.Limits.BinaryBicone.toCone_π_app_right, CategoryTheory.yoneda_map_app, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIso_inv_app_hom, CategoryTheory.MorphismProperty.overEquivOfIsInitial_counitIso, AlgebraicTopology.DoldKan.N₂Γ₂ToKaroubiIso_inv_app, CondensedSet.topCatAdjunctionUnit_hom_app_apply, CategoryTheory.Abelian.SpectralObject.cokernelSequenceOpcycles_X₂, CategoryTheory.WithInitial.coconeEquiv_functor_obj_pt, CategoryTheory.MonoidalClosed.ofEquiv_uncurry_def, CategoryTheory.Sum.functorEquiv_functor_map, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_inv_app, CategoryTheory.shiftFunctorComm_eq_refl, CategoryTheory.preservesFiniteColimits_of_evaluation, CategoryTheory.OverPresheafAux.restrictedYoneda_map, CategoryTheory.curryingIso_hom_toFunctor_obj_map, SSet.stdSimplex.obj₀Equiv_symm_apply, CategoryTheory.instReflectsIsomorphismsMonadFunctorMonadToFunctor, CategoryTheory.CatCommSq.hInv_iso_inv_app, CategoryTheory.whiskering_linearCoyoneda, isDense_iff_nonempty_isPointwiseLeftKanExtension, CategoryTheory.Limits.ColimitPresentation.changeDiag_ι, CategoryTheory.Equivalence.leftOp_unitIso_inv_app, CategoryTheory.PreGaloisCategory.autEmbedding_injective, CategoryTheory.Limits.Cone.equiv_inv_pt, CategoryTheory.MorphismProperty.exists_hom_of_isFinitelyPresentable, PresheafOfModules.pullback_comp_id, CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_cancel_hom_app, AlgebraicGeometry.Proj.pow_apply, CategoryTheory.yonedaGrp_obj, Elements.shrinkYoneda_map_app_coconeπOpCompShrinkYonedaObj_ι_app_assoc, SSet.OneTruncation₂.nerveHomEquiv_id, Monoidal.RepresentableBy.tensorObj_homEquiv, descOfIsLeftKanExtension_fac_assoc, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_naturality_left_assoc, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_inl, sectionsFunctor_obj, CategoryTheory.Subfunctor.Subpresheaf.equalizer.fork_ι, mapTriangleRotateIso_inv_app_hom₂, CategoryTheory.Limits.CatCospanTransform.leftIso_inv, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_obj_iso_inv, CategoryTheory.Limits.PushoutCocone.mk_ι_app_zero, AlgebraicTopology.DoldKan.identity_N₂, whiskeringLeft₃ObjObjObj_obj_map_app_app, CategoryTheory.conjugateEquiv_symm_id, CategoryTheory.PreGaloisCategory.instContinuousMulAutFunctorFintypeCat, shiftIso_hom_app_comp, CategoryTheory.Limits.FormalCoproduct.cosimplicialObjectFunctor_obj_obj, CategoryTheory.Abelian.SpectralObject.toCycles_πE_d, postcompose₂_obj_obj_obj_map, Monoidal.commTensorRight_inv_app, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.sndFunctor_obj, AlgebraicGeometry.Spec_presheaf, CategoryTheory.nerve.functorOfNerveMap_map, SSet.opFunctorCompOpFunctorIso_inv_app_app, CategoryTheory.Pretriangulated.shiftFunctorZero_op_inv_app, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_ι_app, CategoryTheory.Idempotents.instIsEquivalenceFunctorKaroubiObjWhiskeringLeftToKaroubi, CategoryTheory.yonedaAddMonObjIsoOfRepresentableBy_hom_app_hom_apply, CategoryTheory.Adjunction.instIsIsoFunctorCounitOfIsEquivalence_1, CategoryTheory.Sheaf.isPullback_χ_truth, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₂, sheafPushforwardContinuous_map_hom_app, LightCondSet.continuous_coinducingCoprod, CategoryTheory.Under.postCongr_inv_app_right, Rep.indCoindNatIso_hom_app, instIsIsoAppRanCounit, CategoryTheory.Sieve.W_shrinkFunctor_ι_of_mem, isColimitCoconeOfIsLeftKanExtension_desc, CategoryTheory.Join.inclRightCompOpEquivInverse_inv_app_op, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_inv_app_hom, CategoryTheory.Localization.liftNatTrans_add, CategoryTheory.Limits.IsLimit.map_π, HomologicalComplex.mapBifunctor.ι_D₁_assoc, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerRightIso_hom_app, CategoryTheory.Presheaf.coconeOfRepresentable_pt, CategoryTheory.Limits.Cocone.whisker_ι, CategoryTheory.Limits.end_.map_π, CategoryTheory.SimplicialObject.Truncated.whiskering_obj_obj_obj, CategoryTheory.cosimplicialSimplicialEquiv_counitIso_hom_app_app, CategoryTheory.MonoidalCategory.externalProductBifunctor_map_app, CategoryTheory.sum.inrCompInrCompInverseAssociator_hom_app_down, CategoryTheory.preservesFiniteColimits_liftToFinset, CategoryTheory.Limits.Cocone.equivalenceOfReindexing_inverse, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₃, CategoryTheory.Abelian.Preradical.shortComplex_g, LightCondSet.epi_iff_locallySurjective_on_lightProfinite, CategoryTheory.GrothendieckTopology.sheafifyMap_sheafifyLift_assoc, CategoryTheory.Sheaf.classifier_χ, SSet.modelCategoryQuillen.mono_of_cofibration, mapTriangleCompIso_inv_app_hom₂, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_leftUnitor, RightExtension.postcompose₂_obj_left_map, CategoryTheory.Triangulated.TStructure.instIsIsoMapObjEIntFunctorETruncLTAppETruncLTι, pi'CompEval_hom_app, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_obj_obj_obj, CategoryTheory.Iso.app_inv, SSet.horn₃₁.exists_desc, CategoryTheory.Limits.mono_of_isLimit_parallelFamily, CategoryTheory.Abelian.SpectralObject.δToCycles_πE, SSet.Subcomplex.range_eq_ofSimplex, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap_apply, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerRight, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app, CategoryTheory.shrinkYonedaMonObjObjEquiv_symm_comp, CategoryTheory.GrothendieckTopology.Point.id_hom, FullyFaithful.homNatIsoMaxRight_hom_app_down, leftOpRightOpEquiv_counitIso_inv_app_app, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp_assoc, CategoryTheory.Adjunction.compCoyonedaIso_inv_app_app, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_unitIso_hom_app_f, CategoryTheory.Subfunctor.Subpresheaf.equalizer.condition, CategoryTheory.IsPullback.of_isLimit_binaryFan_of_isTerminal, CategoryTheory.Grothendieck.map_comp_eq, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app_assoc, CategoryTheory.CosimplicialObject.Augmented.leftOp_right, CategoryTheory.Monad.algebraFunctorOfMonadHomId_inv_app_f, CategoryTheory.IsSifted.colim_preservesBinaryProducts_of_isSifted, CategoryTheory.bifunctorComp₁₂FunctorMap_app_app_app_app, CategoryTheory.Over.forgetMapTerminal_hom_app, DerivedCategory.instCommShiftHomologicalComplexIntUpHomFunctorQuotientCompQhIso, CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_inv_app_app, CategoryTheory.Limits.IsIndObject.isFiltered, CategoryTheory.Adjunction.leftAdjointUniq_refl, CategoryTheory.Limits.Cone.postcomposeEquivalence_functor, SSet.PtSimplex.MulStruct.δ_map_of_gt, CategoryTheory.NatIso.ofComponents'_hom_app, fullyFaithfulCancelRight_inv_app, CategoryTheory.ParametrizedAdjunction.whiskerLeft_map_counit, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_map_snd, CategoryTheory.GrothendieckTopology.preservesLimitsOfShape_plusFunctor, CategoryTheory.OverPresheafAux.restrictedYoneda_obj, CategoryTheory.NatTrans.CommShift.leftUnitor, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_map_app_app, CategoryTheory.GrothendieckTopology.ι_plusCompIso_hom_assoc, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_inv_app_hom_coe, mapTriangle_obj, CategoryTheory.Abelian.Ext.preadditiveYoneda_homologySequenceδ_singleTriangle_apply, LightCondensed.isoFinYoneda_inv_app, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_app_assoc, CategoryTheory.BraidedCategory.ofBifunctor.Forward.secondMap₃_app_app_app, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_hom_app, CategoryTheory.Equivalence.sheafCongr.functor_obj_obj_map, CategoryTheory.Abelian.SpectralObject.shortComplex_X₂, CategoryTheory.Comonad.ForgetCreatesLimits'.liftedCone_π_app_f, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_one, CondensedMod.isDiscrete_tfae, RightExtension.postcompose₂_obj_right, CategoryTheory.CatCommSq.hId_iso_hom_app, SSet.instHasDimensionLETensorUnitOfNatNat, CategoryTheory.linearYoneda_obj_map, CategoryTheory.Limits.coend.map_id, smoothSheafCommRing.ι_evalHom_apply, LeftExtension.postcomp₁_map_right_app, TopCat.uliftFunctorCompForgetIso_hom_app, CategoryTheory.NatIso.unop_rightUnitor, SheafOfModules.evaluationPreservesLimit, CategoryTheory.NatTrans.unop_comp_assoc, mapComposableArrowsObjMk₁Iso_inv_app, IsEventuallyConstantFrom.isIso_ι_of_isColimit', PresheafOfModules.homEquivOfIsLocallyBijective_symm_apply, CategoryTheory.Limits.PullbackCone.π_app_right, CategoryTheory.piEquivalenceFunctorDiscrete_inverse_obj, AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_hom_app, CategoryTheory.Abelian.SpectralObject.d_ιE_fromOpcycles, Action.functorCategoryEquivalence_inverse, CategoryTheory.instFullSheafSheafComposeOfFaithful, CategoryTheory.SingleFunctors.shiftIso_add', CategoryTheory.MorphismProperty.Comma.mapLeftEq_inv_app_right, SimplexCategory.toTopHomeo_symm_naturality, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃'_map_app_app, CategoryTheory.Abelian.SpectralObject.toCycles_πE_d_assoc, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_hom_app, commShiftOp_iso_eq, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left, CategoryTheory.simplicialCosimplicialEquiv_counitIso_inv_app_app, CategoryTheory.Limits.PushoutCocone.unop_π_app, CategoryTheory.EnrichedFunctor.forgetComp_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_inv_app, CategoryTheory.comp_evaluation, CategoryTheory.GrothendieckTopology.plusMap_id, CategoryTheory.MonoidalCategory.DayFunctor.equiv_unitIso_hom_app, CategoryTheory.MonoidalCategory.tensorLeftTensor_hom_app, CategoryTheory.Subfunctor.range_le_equalizer_iff, RingHom.EssFiniteType.exists_eq_comp_ι_app_of_isColimit, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app, CategoryTheory.Limits.diagramIsoParallelFamily_inv_app, CategoryTheory.Presheaf.functorToRepresentables_map, SSet.tensorHom_app_apply, mapGrpIdIso_hom_app_hom_hom, CategoryTheory.whiskeringLeft_preservesLimitsOfShape, CategoryTheory.Limits.functorCategoryHasLimitsOfSize, SheafOfModules.forgetToSheafModuleCat_map_hom, CategoryTheory.Linear.smulOfRingMorphism_smul_eq', CategoryTheory.NatIso.pi'_inv, CategoryTheory.simplicialCosimplicialEquiv_inverse_map, HomologicalComplex.mapBifunctor₂₃.ι_D₃, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_hom_app_hom_apply, AlgebraicGeometry.Proj.mul_apply, AlgebraicGeometry.StructureSheaf.comap_id', CategoryTheory.SimplicialObject.Augmented.toArrow_map_right, CategoryTheory.Limits.IndObjectPresentation.extend_ι_app_app, CategoryTheory.Join.mapWhiskerRight_leftUnitor_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv, SimplicialObject.opFunctor_obj_σ, CategoryTheory.AddMon.EquivLaxMonoidalFunctorPUnit.addUnitIso_inv_app_hom_app, CategoryTheory.Limits.Fork.unop_ι_app_zero, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_inv_app, CategoryTheory.Limits.isClosedUnderLimitsOfShape_isIndObject_walkingParallelPair, inlCompSum'_inv_app, CategoryTheory.Limits.Cocone.ofCotrident_ι, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.unitIso_inv_app_f_f, CochainComplex.mappingCone.homologySequenceδ_triangleh, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_pos_assoc, CategoryTheory.Limits.opCompYonedaSectionsEquiv_symm_apply_coe, CategoryTheory.Cat.Hom₂.eqToHom_toNatTrans, CategoryTheory.Yoneda.naturality, CategoryTheory.prodFunctorToFunctorProd_map, curry_obj_obj_obj, CategoryTheory.ObjectProperty.topEquivalence_counitIso, CategoryTheory.NatTrans.instCommShiftPullbackShiftHomFunctorNatIsoComp, closedIhom_obj_map, CategoryTheory.SingleFunctors.Hom.comp_hom, CategoryTheory.Discrete.natIsoFunctor_hom_app, CategoryTheory.MonoidalCategory.externalProductCompDiagIso_hom_app_app, CondensedSet.hom_naturality_apply, CategoryTheory.Limits.yonedaCompLimIsoCocones_inv_app, CategoryTheory.coyonedaEvaluation_map_down, SSet.Truncated.sk_coreflective, CategoryTheory.Limits.mapPairIso_inv_app, CategoryTheory.Limits.LimitPresentation.w, CategoryTheory.nerveFunctor.faithful, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_isModule, HomologicalComplex.mapBifunctor₂₃.d₂_eq, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_left_right, shiftIso_zero_inv_app, CategoryTheory.Iso.isoInverseComp_inv_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_hom_app_fst_app, CategoryTheory.PreGaloisCategory.toAutMulEquiv_isHomeomorph, SSet.hoFunctor.preservesTerminal', Monoidal.coreMonoidalTransport_εIso_inv, Action.FunctorCategoryEquivalence.counitIso_inv_app_app, Profinite.Extend.cone_π_app, CompHausLike.LocallyConstant.adjunction_counit, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.g_app, commShift₂_comm, CategoryTheory.typeEquiv_functor_map_hom_app, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_obj, CategoryTheory.Preadditive.DoldKan.equivalence_unitIso, SSet.prodStdSimplex.instHasDimensionLETensorObjObjSimplexCategoryStdSimplexMkHAddNat, SSet.Subcomplex.toImage_ι, CategoryTheory.δ_naturalityₗ_assoc, CategoryTheory.Comma.mapLeftIso_functor_map_left, OplaxMonoidal.ofBifunctor.bottomMapₗ_app, CategoryTheory.sheafificationNatIso_hom_app_hom, SSet.Truncated.Edge.map_fst, CategoryTheory.Iso.map_inv_hom_id_app_assoc, CategoryTheory.instFaithfulGrpFunctorOppositeGrpCatYonedaGrp, LaxMonoidal.ofBifunctor.secondMap₁_app_app_app, IsCoverDense.restrictHomEquivHom_naturality_left_symm_assoc, CategoryTheory.Square.mapFunctor_map, CategoryTheory.SimplicialObject.augment_left, Fiber.fiberInclusionCompIsoConst_inv_app, whiskeringRight_obj_id, CategoryTheory.Limits.Cocone.unop_π, AlgebraicTopology.DoldKan.instIsIsoFunctorSimplicialObjectKaroubiNatTrans, CategoryTheory.MonoidalCategory.associatorNatIso_hom_app, Action.functorCategoryEquivalence_unitIso, CompHausLike.LocallyConstantModule.functor_obj_obj_map_hom_apply_apply, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_map_app_fst, SheafOfModules.inl_freeSumIso_hom, CategoryTheory.GrothendieckTopology.whiskerRight_toSheafify_sheafifyCompIso_hom_assoc, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_left, IsLocalization.instDiscreteObjWhiskeringRightFunctorCategoryOfFiniteOfContainsIdentities, pentagon, SSet.stdSimplex.objMk₁_bijective, CategoryTheory.Presheaf.isSeparating, CategoryTheory.Limits.reflexivePair.mkNatIso_hom_app, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_carrier, CategoryTheory.Abelian.SpectralObject.mono_H_map_twoδ₁Toδ₀, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_inv_app_coe, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂_assoc, CategoryTheory.Presheaf.isLeftAdjoint_of_preservesColimits, CategoryTheory.Limits.colimitCoyonedaHomIsoLimit'_π_apply, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_inverse, CategoryTheory.NatIso.cancel_natIso_inv_right_assoc, CategoryTheory.evaluationRightAdjoint_obj_map, pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, Action.leftUnitor_inv_hom, CategoryTheory.η_naturality_assoc, leftExtensionEquivalenceOfIso₁_functor_obj_left, CategoryTheory.endofunctorMonoidalCategory_tensorObj_obj, CategoryTheory.Limits.Cone.functorialityEquivalence_inverse, CategoryTheory.GrothendieckTopology.instFaithfulSheafTypeUliftYoneda, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_π_app_left, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_inv_app_hom_apply, cones_map_app, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₃, CategoryTheory.Limits.Cone.postcomposeComp_inv_app_hom, MonObj.mopEquivCompForgetIso_hom_app_unmop, CategoryTheory.Abelian.SpectralObject.δ_toCycles, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_inv_app_app_hom_hom, instIsIsoAppUnitLanAdjunctionOfHasPointwiseLeftKanExtension, CategoryTheory.ComonadIso.toNatIso_inv, CategoryTheory.μ_δ_app_assoc, CategoryTheory.Cat.Hom.isoMk_hom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_inv_app_snd_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_left, IsRightKanExtension.nonempty_isUniversal, CategoryTheory.Monoidal.associator_hom_app, SSet.horn.yonedaEquiv_ι, CategoryTheory.Localization.Construction.natTransExtension_hcomp, CategoryTheory.Join.isoMkFunctor_hom_app, CategoryTheory.GradedObject.Monoidal.instHasMapProdObjFunctorMapBifunctorCurriedTensorSingle₀TensorUnit, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy₂_homEquiv, CategoryTheory.Equivalence.leftOp_counitIso_inv_app, CategoryTheory.TransfiniteCompositionOfShape.fac_assoc, CategoryTheory.η_ε_app_assoc, CategoryTheory.NatTrans.unop_whiskerLeft_assoc, AlgebraicGeometry.StructureSheaf.const_add, CategoryTheory.conjugateEquiv_symm_comp_assoc, CategoryTheory.Limits.coyonedaCompLimIsoCones_inv_app, CategoryTheory.Subfunctor.ofSection_eq_range, CategoryTheory.Limits.Cofork.ofCocone_ι, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_X₁, CategoryTheory.MorphismProperty.Over.pullbackComp_hom_app_left, CategoryTheory.Localization.SmallHom.equiv_equiv_symm, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_sub_apply, CommShift.isoZero_hom_app, CategoryTheory.shrinkYonedaGrp_obj, LeftExtension.IsPointwiseLeftKanExtensionAt.isIso_hom_app, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_inv_app_op_zero, CategoryTheory.Presheaf.instIsLeftKanExtensionFunctorOppositeTypeLanOpHomCompULiftYonedaIsoULiftYonedaCompLan, AlgebraicTopology.AlternatingFaceMapComplex.ε_app_f_succ, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_fst_map, 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, whiskeringLeft_obj_id, CategoryTheory.Limits.multispanIndexCoend_right, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom, CategoryTheory.Abelian.LeftResolution.karoubi.π_app_toKaroubi_obj, CondensedMod.LocallyConstant.instFullModuleCatSheafCompHausCoherentTopologyConstantSheaf, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.natTrans_app_uliftYoneda_obj, CategoryTheory.Abelian.SpectralObject.δ_δ_assoc, CategoryTheory.Limits.MonoCoprod.binaryCofan_inl, CategoryTheory.Abelian.SpectralObject.opcyclesIso_hom_δFromOpcycles, CategoryTheory.Bicategory.associatorNatIsoLeft_inv_app, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_inverse_obj, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one, CategoryTheory.SimplicialObject.Truncated.whiskering_map_app_app, Condensed.discrete_map, PresheafOfModules.toSheafify_app_apply', SSet.Finite.instIsFinitelyPresentableObjSimplexCategoryStdSimplex, rightDerivedNatIso_inv, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_assoc, CategoryTheory.Limits.limitConstTerminal_inv_π_assoc, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_right, CategoryTheory.GradedObject.mapBifunctorObjObjSingle₀Iso_hom, IsCoverDense.Types.sheafIso_hom_hom, CategoryTheory.GradedObject.mapTrifunctorMapObj_ext_iff, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₂, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_inv_assoc, RightExtension.coneAt_pt, CategoryTheory.Comma.mapRightEq_hom_app_right, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_inv_app_snd_app, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.secondMap₁_app_app_app, CategoryTheory.yonedaEquiv_apply, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_right, CategoryTheory.GrothendieckTopology.overMapPullbackId_inv_app_hom_app, CategoryTheory.coprodMonad_μ_app, currying_inverse_obj_obj_obj, CategoryTheory.ChosenPullbacksAlong.unit_pullbackComp_hom_assoc, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ₀_assoc, CategoryTheory.Limits.IndObjectPresentation.instFinalICostructuredArrowFunctorOppositeTypeYonedaToCostructuredArrow, SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_inv_app, opInv_obj, PullbackObjObj.π_fst, LeftExtension.postcomp₁_obj_left, CategoryTheory.Comma.mapRightIso_counitIso_inv_app_right, CategoryTheory.Enriched.FunctorCategory.isLimitConeFunctorEnrichedHom.fac, Monoidal.transport_μ, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_inv_app_app, instIsLeftKanExtensionSimplexCategoryTopCatSSetToTopInvFunctorToTopSimplex, CategoryTheory.Abelian.SpectralObject.homologyDataIdId_left_i, CategoryTheory.GrothendieckTopology.Point.instPreservesFiniteLimitsSheafSheafFiberOfLocallySmallOfHasFiniteLimitsOfAB5OfSize, CategoryTheory.IsFiltered.iff_nonempty_limit, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_unitIso, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_hom_app, CategoryTheory.sum.inlCompInrCompInverseAssociator_inv_app_down_down, CategoryTheory.SimplicialObject.Truncated.cosk.full, SSet.horn₃₂.desc.multicofork_π_one, TopologicalSpace.OpenNhds.inclusionMapIso_inv, SSet.yonedaEquiv_symm_zero, commShiftIso_comp_hom_app, CategoryTheory.instAdditiveObjFunctorAdditiveFunctor_1, CategoryTheory.AddMon.EquivLaxMonoidalFunctorPUnit.counitIso_inv_app_hom, Elements.coconeπOpCompShrinkYonedaObj_pt, AlgebraicGeometry.structureSheafInType.mul_apply, CategoryTheory.Comma.mapLeftEq_hom_app_left, coreId_hom_app_iso_hom, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₂_app, SSet.Subcomplex.topIso_inv_app_coe, CategoryTheory.Abelian.SpectralObject.cyclesIsoH_hom_EIsoH_inv, SSet.prodStdSimplex.orderHomOfSimplex_coe, CategoryTheory.Monad.monadMonEquiv_counitIso_hom_app_hom, CategoryTheory.Triangulated.TStructure.eTruncLTGELTSelfToLTGE_app, CategoryTheory.HasLiftingProperty.transfiniteComposition.hasLift, CategoryTheory.Limits.Cone.fromCostructuredArrow_map_hom, CategoryTheory.MonoOver.mapIso_unitIso, SSet.horn₃₂.ι₁_desc, CategoryTheory.exactFunctor_le_additiveFunctor, CategoryTheory.Limits.Cone.toCostructuredArrow_obj, Monoidal.tensorObj_map, CategoryTheory.constantCommuteCompose_hom_app_val, CategoryTheory.CatCenter.smul_iso_inv_eq', CategoryTheory.Abelian.SpectralObject.homologyDataIdId_left_H, CategoryTheory.Triangulated.TStructure.isIso_eTruncGE_obj_map_truncGEπ_app, CategoryTheory.WithTerminal.mapComp_hom_app, AlgebraicGeometry.StructureSheaf.exists_const, CategoryTheory.Limits.coconeOfCoconeCurry_pt, commShiftIso_map₂CochainComplex_flip_hom_app, CategoryTheory.Triangulated.TStructure.eTruncLTLTToLT_app, CategoryTheory.Equivalence.congrFullSubcategory_counitIso, mapTriangleCommShiftIso_inv_app_hom₁, CategoryTheory.MonoidalCategory.curriedAssociatorNatIso_hom_app_app_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_inv_toNatTrans_app_hom_app, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_inv_colimit_map_assoc, CondensedSet.instIsIsoFunctorCompactlyGeneratedCounitCompactlyGeneratedAdjunction, pointwiseLeftKanExtensionCompIsoOfPreserves_fac_app_assoc, CategoryTheory.Limits.colimit.homIso_hom, CategoryTheory.MonadHom.comp_toNatTrans, CategoryTheory.Limits.WidePullbackShape.functorExt_hom_app, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_inv_app_hom₂, TopCat.Sheaf.pushforward_map, reflective', PullbackObjObj.π_iso_of_iso_left_inv, flipping_functor_map_app_app, leftDerivedNatIso_inv, Monoidal.tensorObjComp_hom_app, CategoryTheory.Join.mapWhiskerLeft_whiskerRight, CategoryTheory.Sheaf.isLocallySurjective_comp, CategoryTheory.Endofunctor.Algebra.functorOfNatTransId_inv_app_f, CategoryTheory.GrothendieckTopology.preservesLimitsOfShape_diagramFunctor, flip₂₃_obj_obj_map, AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex_inv, CategoryTheory.MonoidalCategory.instFaithfulFunctorTensoringRight, SimplicialObject.opFunctor_obj_map, SimplicialObject.Split.forget_obj, CategoryTheory.GradedObject.mapTrifunctor_map_app_app, CategoryTheory.Triangulated.TStructure.truncLEIsoTruncLT_hom_ι_assoc, CategoryTheory.Arrow.mapAugmentedCechNerve_left, CategoryTheory.Join.mkNatIso_inv, CategoryTheory.Abelian.SpectralObject.isZero_H_obj_mk₁_i₀_le', CategoryTheory.Monad.algebraFunctorOfMonadHomId_hom_app_f, IsEventuallyConstantTo.cone_π_app, SSet.prodStdSimplex.nonDegenerateEquiv₁_snd, commGroupAddCommGroupEquivalence_counitIso, IsCoverDense.isoOver_hom_app, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.F_map, AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.structurePresheafInCommRing_obj_carrier, AlgebraicGeometry.Scheme.SpecΓIdentity_hom_app, currying₃_unitIso_hom_app_app_app_app, CategoryTheory.Comma.coneOfPreserves_π_app_right, SSet.Subcomplex.homOfLE_refl, FullyFaithful.compUliftCoyonedaCompWhiskeringLeft_hom_app_app_down, CategoryTheory.Limits.limitIsoLimitCurryCompLim_hom_π_π_assoc, CategoryTheory.Adjunction.instIsIsoFunctorUnitOfIsEquivalence, CategoryTheory.Adjunction.ofNatIsoLeft_unit, CategoryTheory.Limits.prodComparisonNatIso_hom, CategoryTheory.Preadditive.DoldKan.equivalence_functor, CategoryTheory.Idempotents.karoubiUniversal_functor_eq, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_π_app, CategoryTheory.Coyoneda.objOpOp_inv_app, CategoryTheory.GradedObject.comapEquiv_counitIso, CategoryTheory.toOverPullbackIsoToOver_inv_app_left, SheafOfModules.inr_freeSumIso_hom, opComp_inv_app, CategoryTheory.Idempotents.functorExtension_map_app, smoothSheaf.ι_evalHom_apply, partialFunEquivPointed_unitIso_inv_app, curry_obj_uncurry_obj, CategoryTheory.WithInitial.ofCommaObject_obj, CategoryTheory.Limits.CatCospanTransform.inv_left, CategoryTheory.FunctorToTypes.binaryProductEquiv_apply, LeftExtension.precomp_map_right, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₃, CategoryTheory.WithTerminal.equivComma_inverse_obj_obj, CategoryTheory.Sheaf.adjunction_unit_app_hom, Condensed.instPreservesFiniteProductsOppositeProfiniteObjFunctorIsSheafCoherentTopology, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_π_app_walkingParallelPair_one, CategoryTheory.MorphismProperty.Comma.mapRightIso_counitIso_hom_app_right, CategoryTheory.Triangulated.TStructure.triangleω₁δ_map_hom₁, CategoryTheory.ObjectProperty.IsConservativeFamilyOfPoints.isMonoidal_W, SSet.opFunctorCompOpFunctorIso_hom_app_app, CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_app_app, CategoryTheory.Limits.coprodComparisonNatTrans_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.fstFunctor_obj, CategoryTheory.FinitaryExtensive.mono_ι, CategoryTheory.instIsClosedUnderLimitsOfShapeFunctorOppositeTypeIsIndObjectDiscreteOfHasLimitsOfShape, LeftExtension.precomp₂_obj_left, CategoryTheory.Limits.CatCospanTransform.category_id_left, CategoryTheory.HasExactLimitsOfShape.preservesFiniteColimits, CategoryTheory.Limits.colimitCurrySwapCompColimIsoColimitCurryCompColim_ι_ι_hom, CategoryTheory.FreeGroupoid.mapComp_hom_app, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap, CategoryTheory.Equivalence.sheafCongrPrecoherent_functor_obj_obj_obj, CategoryTheory.Equivalence.instPreservesFiniteLimitsFunctorOppositeSheafTransportAndSheafify, CategoryTheory.Equivalence.sheafCongrPreregular_functor_obj_obj_obj, CategoryTheory.Presieve.shrinkFunctorHomEquiv_symm_apply_app, CategoryTheory.FinitaryExtensive.isPullback_initial_to_binaryCofan, CategoryTheory.SimplicialObject.Augmented.w₀, CategoryTheory.BraidedCategory.curriedBraidingNatIso_inv_app_app, RightExtension.coneAt_π_app, Action.whiskerRight_hom, SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_hom_app, ModuleCat.restrictScalarsComp'_inv_app, CategoryTheory.Comma.mapRightIso_functor_map_left, CategoryTheory.μ_naturality₂_assoc, CategoryTheory.TwoSquare.guitartExact_id', AlgebraicTopology.AlternatingCofaceMapComplex.d_eq_unop_d, CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_right, CategoryTheory.WithTerminal.equivComma_counitIso_hom_app_right, prod'CompSnd_inv_app, CategoryTheory.Idempotents.KaroubiKaroubi.counitIso_inv_app_f_f, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁_assoc, CategoryTheory.Presheaf.freeYonedaHomEquiv_comp, CategoryTheory.NatTrans.epi_of_epi_app, PresheafOfModules.free_map_app, CategoryTheory.MonoidalCategory.externalProductBifunctorCurried_obj_obj_obj_map, CategoryTheory.ShortComplex.functorEquivalence_counitIso, CategoryTheory.Limits.lim_map, CategoryTheory.Pi.equivalenceOfEquiv_unitIso, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd_assoc, CochainComplex.shiftShortComplexFunctorIso_add'_hom_app, CategoryTheory.SimplicialObject.instIsRightKanExtensionOppositeTruncatedSimplexCategoryObjCoskAppTruncatedCounitCoskAdjTruncation, CategoryTheory.Limits.IsColimit.homIso_hom, CategoryTheory.Presheaf.comp_χ_eq, CategoryTheory.WithInitial.opEquiv_counitIso_hom_app, CategoryTheory.Adjunction.id_counit, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_hom_app, CategoryTheory.NatIso.ofComponents_inv_app, CategoryTheory.prodComonad_δ_app, SSet.hasDimensionLT_prod, CategoryTheory.WithInitial.isColimitEquiv_symm_apply_desc, CategoryTheory.uliftCoyonedaIsoCoyoneda_inv_app_app_down, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_hom_app_hom, CategoryTheory.Quotient.comp_natTransLift_assoc, CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso_hom_app, CategoryTheory.shiftFunctorCompIsoId_naturality_1, CategoryTheory.Pseudofunctor.toDescentDataAsCoalgebraCompCoalgebraEquivalenceFunctorIso_inv_app_f, SheafOfModules.instIsRightAdjointPushforwardCompSheafRingCatMapSheafPushforwardContinuous, HomologicalComplex.mapBifunctor₂₃.d₃_eq, CategoryTheory.Quotient.lift.isLift_hom, SimplexCategory.toTopHomeo_naturality_apply, CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_right, HomologicalComplex.natIsoSc'_inv_app_τ₂, CategoryTheory.Limits.Cocone.underPost_ι_app, DerivedCategory.singleFunctorsPostcompQIso_inv_hom, CategoryTheory.Limits.multicospanIndexEnd_snd, CategoryTheory.functorProdFunctorEquiv_inverse, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι, CategoryTheory.AddMon.EquivLaxMonoidalFunctorPUnit.addUnitIso_hom_app_hom_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_hom_app_hom_hom_app, CategoryTheory.Limits.colimitIsoSwapCompColim_hom_app, CategoryTheory.Localization.HasProductsOfShapeAux.adj_counit_app, CategoryTheory.Monad.algebraEquivOfIsoMonads_unitIso, CategoryTheory.Limits.coneOfDiagramTerminal_π_app, CategoryTheory.Abelian.SpectralObject.δToCycles_cyclesIso_inv_assoc, mapTriangleCompIso_hom_app_hom₂, AlgebraicGeometry.Scheme.LocalRepresentability.isRepresentable, CategoryTheory.Subfunctor.Subpresheaf.preimage_id, RightExtension.postcomp₁_obj_left_map, SSet.instIsStableUnderFilteredColimitsMonomorphisms, CategoryTheory.Adjunction.compYonedaIso_hom_app_app, CategoryTheory.Pi.equivalenceOfEquiv_counitIso, PresheafOfModules.freeYonedaEquiv_symm_app, SSet.Subcomplex.toRange_ι_assoc, CommRingCat.coyoneda_map_app, currying_counitIso_hom_app_app, CategoryTheory.zero_map, CategoryTheory.Sheaf.isLocallySurjective_iff_epi, mapContActionCongr_inv, CategoryTheory.MorphismProperty.Over.mapCongr_inv_app_left, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.associator_hom_unit_unit, CategoryTheory.Limits.Cotrident.π_eq_app_one, CategoryTheory.Abelian.SpectralObject.cyclesMap_id, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.w_app, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_fiber, CategoryTheory.Limits.CatCospanTransform.baseIso_inv, RightExtension.postcomp₁_map_right, CategoryTheory.Abelian.SpectralObject.cyclesIso_hom_i, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompCoyoneda, CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_comp, CategoryTheory.Limits.colimit.ι_map, prod'CompSnd_hom_app, SSet.RelativeMorphism.Homotopy.h₀_assoc, CategoryTheory.Limits.cospanIsoMk_hom_app, CategoryTheory.FunctorToTypes.binaryProductCone_pt_obj, CategoryTheory.MonoidalCategory.endofunctorMonoidalCategory.evaluationRightAction_actionUnitIso, CategoryTheory.Limits.coconeUnopOfConeEquiv_unitIso, AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf', CategoryTheory.Iso.isoInverseComp_hom_app, CategoryTheory.Over.opEquivOpUnder_unitIso, mapActionComp_hom, SSet.Subcomplex.unionProd.image_β_inv, CategoryTheory.AdditiveFunctor.ofExact_obj_fst, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionActionOfMonoidalFunctorToEndofunctorIso_inv_app_app, CategoryTheory.Limits.constCone_pt, Profinite.NobelingProof.spanFunctorIsoIndexFunctor_hom_app_hom_hom_apply_coe, CategoryTheory.Limits.piObjIso_hom_comp_π, Action.FunctorCategoryEquivalence.functor_obj_obj, LeibnizAdjunction.adj_unit_app_left, TopCat.Sheaf.interUnionPullbackCone_fst, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_map_app, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map, CategoryTheory.GrothendieckTopology.Point.toPresheafFiberMap_presheafFiberMapObjIso_hom_assoc, CategoryTheory.Over.iteratedSliceForwardIsoPost_inv_app, pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, whiskeringLeft₃Obj_map, CategoryTheory.IsSifted.factorization_prodComparison_colim, CategoryTheory.SimplicialObject.Augmented.toArrow_map_left, CategoryTheory.uliftYonedaEquiv_symm_comp, AlgebraicTopology.alternatingFaceMapComplex_obj_d, CategoryTheory.NatIso.naturality_1, CategoryTheory.NatIso.inv_map_inv_app, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_map_app, CategoryTheory.Limits.Cone.whisker_π, instIsLeftAdjointSSetTopCatToTop, CategoryTheory.Comma.mapRightIso_inverse_map_right, CategoryTheory.Equivalence.core_unitIso_hom_app_iso_inv, CategoryTheory.DifferentialObject.shiftZero_hom_app_f, ranCompLimIso_inv_app, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app, CategoryTheory.PreGaloisCategory.instTotallyDisconnectedSpaceAutFunctorFintypeCat, sheafPushforwardContinuousNatTrans_app_hom, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_hom_assoc, ShiftSequence.induced.isoZero_hom_app_obj, CategoryTheory.Sum.functorEquiv_unit_app_app_inr, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoColimitUncurryWhiskeringLeft₂_inv_assoc, CategoryTheory.Limits.colimitCurrySwapCompColimIsoColimitCurryCompColim_ι_ι_inv, CategoryTheory.Limits.Cocone.toCostructuredArrow_map, CategoryTheory.Triangulated.TStructure.eTruncGEπ_bot, CategoryTheory.Limits.hasColimitCompEvaluation, Fiber.fiberInclusion_comp_eq_const, CategoryTheory.WithTerminal.equivComma_functor_obj_left_map, whiskeringLeft₃_map_app_app_app_app_app_app, SimplexCategory.revEquivalence_unitIso, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε, CategoryTheory.MonoidalCategory.DayFunctor.id_natTrans, SSet.prodStdSimplex.objEquiv_apply_fst, SSet.stdSimplex.map_id, SSet.Subcomplex.lift_ι_assoc, SheafOfModules.evaluationPreservesLimitsOfShape, CategoryTheory.NatTrans.vcomp_app', CategoryTheory.Abelian.SpectralObject.pOpcycles_δFromOpcycles, LightCondensed.discrete_map, CategoryTheory.Adjunction.Triple.rightToLeft_eq_units, SSet.Homotopy.h₁_assoc, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_inv_app_left, CategoryTheory.HasShift.Induced.zero_inv_app_obj, AlgebraicGeometry.Scheme.LocalRepresentability.instIsLocallySurjectiveHomYonedaGluedToSheafOfIsLocallySurjectiveZariskiTopologyDescFunctorOppositeType, CategoryTheory.Limits.Types.pUnitCocone_ι_app, CategoryTheory.NatTrans.instCommShiftPullbackShiftHomFunctorNatIsoId, curry₃_obj_obj_map_app, CategoryTheory.WithTerminal.mkCommaMorphism_left_app, CategoryTheory.shift_shift_neg', SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_quotMk, CategoryTheory.Limits.parallelPairIsoMk_inv_app, CategoryTheory.Limits.IsColimit.mono_ι_app_of_isFiltered, LaxMonoidal.ofBifunctor.firstMap₃_app_app_app, CategoryTheory.NatTrans.CommShift.shift_comm, CategoryTheory.Sheaf.cartesianMonoidalCategoryLift_hom, CategoryTheory.evaluationAdjunctionLeft_unit_app_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocNatIso_hom_app_app_app, CategoryTheory.Limits.colimMap_eq, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_inv_app, CategoryTheory.Sum.functorEquiv_unitIso_inv_app_app_inl, CategoryTheory.SimplicialObject.Augmented.toArrow_obj_left, CategoryTheory.LocalizerMorphism.commShift_iso_inv_app, CategoryTheory.GradedObject.ιMapBifunctor₁₂BifunctorMapObj_eq_assoc, CategoryTheory.Sheaf.isPullback_square_op_map_yoneda_presheafToSheaf_yoneda_iff, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality_assoc, CategoryTheory.NatIso.op_trans, CategoryTheory.MonoOver.mapIso_counitIso, CategoryTheory.HasShift.Induced.add_hom_app_obj, CategoryTheory.ComonadIso.toNatIso_hom, rightKanExtensionCompIsoOfPreserves_hom_fac_app, CategoryTheory.TwoSquare.equivalenceJ_unitIso, CategoryTheory.Limits.coend.condition, CategoryTheory.IsSifted.instIsIsoObjFunctorTypeColimTensorObjProdComparison, CategoryTheory.Pi.sum_obj_obj, CategoryTheory.Limits.FormalCoproduct.cechIsoAugmentedCechNerve_hom_left, CategoryTheory.sheafToPresheaf_μ, CategoryTheory.Triangulated.TStructure.ω₁δ_naturality_assoc, CategoryTheory.NatTrans.mapHomologicalComplex_id, DerivedCategory.homologyFunctorFactorsh_hom_app_quotient_obj_assoc, CategoryTheory.SimplicialObject.Truncated.cosk.faithful, CategoryTheory.GradedObject.mapTrifunctorObj_obj_obj, CategoryTheory.Presheaf.isIso_of_isLeftKanExtension, HomologicalComplex.asFunctor_obj_X, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₁_app, CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLift_assoc, whiskeringLeft_obj_comp, CategoryTheory.CatCommSq.hComp_iso_hom_app, CategoryTheory.pullbackShiftFunctorZero_inv_app, DerivedCategory.homologyFunctorFactors_hom_naturality, mapTriangleRotateIso_inv_app_hom₁, CategoryTheory.Under.liftCone_pt, CategoryTheory.GrothendieckTopology.isIso_toSheafify, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompPointIso_hom_app, CategoryTheory.NatTrans.rightOp_comp, CategoryTheory.Cat.Hom.inv_hom_id_toNatTrans, CategoryTheory.Discrete.compNatIsoDiscrete_hom_app, CategoryTheory.uliftCoyonedaEquiv_uliftCoyoneda_map, leftKanExtensionCompIsoOfPreserves_hom_fac_app, RepresentableBy.coyoneda_homEquiv, CategoryTheory.Square.flipEquivalence_unitIso, CategoryTheory.CostructuredArrow.mapIso_unitIso_hom_app_left, CategoryTheory.TwoSquare.equivNatTrans_apply, CategoryTheory.CatCommSq.iso_inv_naturality, PullbackObjObj.mapArrowLeft_comp, CategoryTheory.coyonedaEquiv_comp, CategoryTheory.uliftYonedaEquiv_symm_apply_app, CategoryTheory.flippingIso_inv_toFunctor_obj_obj_obj, mapProjectiveResolution_π, CategoryTheory.Adjunction.localization_unit_app, CategoryTheory.WithTerminal.equivComma_functor_obj_right, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₂, CategoryTheory.NatTrans.app_naturality, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_left, CategoryTheory.Adjunction.colim_preservesColimits, HomologicalComplex.complexOfFunctorsToFunctorToComplex_obj, SimplicialObject.Split.forget_map, OneHypercoverDenseData.essSurj.presheafMap_π_assoc, CategoryTheory.Limits.PushoutCocone.isoMk_inv_hom, CategoryTheory.Limits.colimitYonedaHomIsoLimit'_π_apply, CategoryTheory.Prod.symmetry_hom_app, AlgebraicGeometry.Proj.one_apply, Condensed.epi_iff_surjective_on_stonean, CategoryTheory.WithInitial.liftFromUnderComp_inv_app, CategoryTheory.NatTrans.Equifibered.comp, CategoryTheory.preservesColimitNatIso_inv_app, CategoryTheory.conjugateEquiv_symm_apply_app, CategoryTheory.Abelian.SpectralObject.homologyDataIdId_iso_inv, SSet.modelCategoryQuillen.fibrations_eq, CategoryTheory.Presheaf.isLocallyInjective_presheafToSheaf_map_iff, HomologicalComplex.ι_mapBifunctorAssociatorX_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionActionOfMonoidalFunctorToEndofunctorMopIso_hom_app_unmop_app, sheafPushforwardContinuousId'_hom_app_hom_app, HomologicalComplex.mapBifunctor₁₂.ι_D₁_assoc, CategoryTheory.MorphismProperty.Comma.mapLeftEq_inv_app_left, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality, AlgebraicGeometry.StructureSheaf.to_basicOpen_epi, CategoryTheory.bifunctorComp₂₃_obj, IsRepresentedBy.of_natIso, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_right, CategoryTheory.Join.mapWhiskerLeft_whiskerLeft, CategoryTheory.yonedaAddMon_obj, CategoryTheory.Limits.Cone.toStructuredArrowCompProj_inv_app, HomologicalComplex.instHasMapProdObjGradedObjectFunctorMapBifunctorXπ, CategoryTheory.Triangulated.TStructure.π_truncGTIsoTruncGE_hom_ι_app_assoc, SSet.Subcomplex.unionProd.symmIso_inv, CategoryTheory.Limits.parallelPairOpIso_inv_app_one, instFullOppositeTypeRestrictedULiftYonedaOfIsDense, CategoryTheory.ε_η_app_assoc, CategoryTheory.instEpiSheafTypeToImage, CategoryTheory.Limits.PullbackCone.mk_π_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_right_unitality_assoc, CategoryTheory.Join.inrCompFromSum_hom_app, CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatIso_inv, PreservesRightKanExtension.preserves, flipping_inverse_obj_obj_map, CommMonCat.coyonedaType_obj_map, CategoryTheory.OppositeShift.adjunction_unit, CategoryTheory.ε_naturality_assoc, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_hom_whiskerRight_π_assoc, ModuleCat.restrictScalarsComp'_hom_app, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_tensorDec, LightProfinite.Extend.cocone_ι_app, CategoryTheory.Comma.toPUnitIdEquiv_counitIso_hom_app, sheafAdjunctionCocontinuous_counit_app_val, CategoryTheory.MonoidalCategory.prodCompExternalProduct_inv_app, CategoryTheory.Equivalence.mkHom_id_inverse, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.functorToInterchangeIso_inv_app_app, LeftExtension.precomp_obj_hom_app, CategoryTheory.FreeGroupoid.mapId_hom_app, CategoryTheory.Limits.Cocone.equivalenceOfReindexing_functor, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.biprodAddEquiv_symm_biprodIsoProd_hom_toBiprod_apply, CategoryTheory.Limits.IsColimit.ι_map, CategoryTheory.WithTerminal.ofCommaObject_obj, mapMatComp_hom_app, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π_assoc, CategoryTheory.Limits.Types.binaryCoproductCocone_ι_app, CategoryTheory.Sigma.mapComp_hom_app, CategoryTheory.conjugateEquiv_apply_app, CategoryTheory.BinaryCofan.isVanKampen_iff, LeibnizAdjunction.adj_counit_app_left, CategoryTheory.CatCenter.mul_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_inv_app_app_fst, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_incl, isoWhiskerLeft_trans_isoWhiskerRight, CategoryTheory.Idempotents.app_p_comp, CategoryTheory.MorphismProperty.Comma.mapRightIso_counitIso_inv_app_right, CategoryTheory.Triangulated.TStructure.eTruncGEIsoGEGE_hom_inv_id_app_assoc, CategoryTheory.toSheafify_sheafifyLift_assoc, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom, CategoryTheory.Limits.compYonedaSectionsEquiv_apply_app, isRightDerivedFunctor_iff_of_inverts, CategoryTheory.Endofunctor.Algebra.functorOfNatTransComp_hom_app_f, CategoryTheory.Comma.mapSnd_inv_app, CategoryTheory.GradedObject.mapBifunctor_obj_obj, CategoryTheory.MorphismProperty.functorCategory_isomorphisms, SSet.modelCategoryQuillen.cofibrations_eq, Condensed.lanPresheafExt_inv, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp, HomologicalComplex.forgetEval_hom_app, rightKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, compConstIso_hom_app_app, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_app_assoc, CategoryTheory.NatIso.op_isoWhiskerLeft, CategoryTheory.Preadditive.commGrpEquivalence_unitIso_inv_app, commBialgCatEquivComonCommAlgCat_unitIso_hom_app, coreComp_hom_app_iso_hom, CategoryTheory.CatCommSq.vId_iso_hom_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_inv_app_snd_app, CategoryTheory.evaluationRightAdjoint_map_app, imageSieve_eq_imageSieve, CategoryTheory.WithTerminal.opEquiv_counitIso_inv_app, CategoryTheory.frobeniusMorphism_mate, CategoryTheory.Idempotents.karoubiUniversal₁_functor, CategoryTheory.GrothendieckTopology.instFullSheafTypeYoneda, CategoryTheory.Localization.liftNatTrans_zero, CategoryTheory.Monad.monadToMon_obj, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_fst, CategoryTheory.toOverIsoToOverUnit_inv_app_left, CategoryTheory.MonoidalCategory.DayFunctor.equiv_inverse_obj_functor, CategoryTheory.Cat.Hom.isoMk_inv, CategoryTheory.GrothendieckTopology.preserveFiniteLimits_plusFunctor, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_inv_app_hom_left, CategoryTheory.Codiscrete.natIsoFunctor_hom_app, SimplicialObject.Split.comp_F, flipping_counitIso_inv_app_app_app, CategoryTheory.Abelian.SpectralObject.δ_δ, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app, CategoryTheory.Abelian.SpectralObject.cyclesMap_i, CategoryTheory.Under.mapCongr_inv_app, SSet.opEquivalence_inverse, CategoryTheory.PreGaloisCategory.instEssSurjContActionFintypeCatHomObjFiniteAutFunctorFunctorToContActionOfFiberFunctor, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.presheafHom_naturality, CategoryTheory.Equivalence.congrLeft_counitIso_inv_app, OneHypercoverDenseData.essSurj.presheafObjObjIso.inv_π, CategoryTheory.Abelian.SpectralObject.cyclesIso_hom_i_assoc, IsDenseSubsite.mapPreimage_map, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_snd, CategoryTheory.Limits.preservesColimit_of_evaluation, CategoryTheory.Localization.Lifting.compLeft_iso, CategoryTheory.Over.conePost_obj_π_app, instFaithfulProdCurry, initial_const_initial, SSet.stdSimplex.objMk₁_surjective, CategoryTheory.Presheaf.classifier_Ω, CategoryTheory.Limits.multicospanIndexEnd_right, CategoryTheory.Limits.Cocone.w_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁'_map_app_app, CategoryTheory.Triangulated.TStructure.instAdditiveObjEIntFunctorETruncLT, CategoryTheory.Adjunction.conjugateEquiv_leftAdjointCompIso_inv, isoWhiskerLeft_twice, AlgebraicGeometry.Scheme.Modules.instIsIsoFunctorCounitRestrictAdjunction, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_inv_π_assoc, CategoryTheory.TwoSquare.GuitartExact.vComp_iff_of_equivalences, curryObjProdComp_hom_app_app, CategoryTheory.RightExactFunctor.whiskeringLeft_map_app, AlgebraicGeometry.Scheme.Modules.pushforwardComp_inv_app_app, CategoryTheory.Sheaf.mem_essImage_of_isConstant, CategoryTheory.GrothendieckTopology.preservesLimitsOfShape_sheafification, CategoryTheory.oppositeShiftFunctorAdd_inv_app, CategoryTheory.Idempotents.app_p_comm, associator_hom_app, shiftIso_zero_hom_app, CategoryTheory.Presheaf.truth_app, CategoryTheory.Presheaf.restrictedULiftYoneda_obj_map, CategoryTheory.Limits.inr_comp_pushoutObjIso_hom_assoc, ModuleCat.HasLimit.productLimitCone_cone_π, CategoryTheory.MonoidalClosedFunctor.comparison_iso, CommRingCat.coyoneda_obj_obj_carrier, rightOpComp_hom_app, rightAdjointObjIsDefined_iff, CategoryTheory.obj_zero_map_μ_app_assoc, comp_flip_uncurry_eq, SSet.instFiniteTensorUnit, CategoryTheory.FunctorCategory.prod_preservesColimits, SSet.Edge.ofTruncated_edge, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_map_app_app, CategoryTheory.NatTrans.instIsClosedUnderLimitsOfShapeOverFunctorEquifiberedHomDiscretePUnitOfHasCoproductsOfShapeHom, CategoryTheory.comonadToFunctor_mapIso_comonad_iso_mk, isoShift_inv_naturality_assoc, ModuleCat.HasColimit.colimitCocone_ι_app, CategoryTheory.Triangulated.TStructure.triangleω₁δ_map_hom₂, CategoryTheory.ExactFunctor.forget_obj, CategoryTheory.LeftExactFunctor.forget_obj, CategoryTheory.GrothendieckTopology.overMapPullbackComp_hom_app_hom_app, CategoryTheory.Presheaf.comp_isLocallySurjective_iff, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_comp_mapHomotopyCategory_fst, instIsCorepresentableObjOppositeTypeUliftCoyoneda, CategoryTheory.hasLimitsEssentiallySmallSite, CategoryTheory.Limits.HasColimit.isoOfEquivalence_hom_π, CategoryTheory.Triangulated.TStructure.eTruncLTLTIsoLT_inv_hom_id_app_eTruncLT_obj, CategoryTheory.Equivalence.inverseFunctor_obj, HomologicalComplex.mapBifunctorMapHomotopy.comm₁, SSet.horn₂₂.sq, CategoryTheory.Presheaf.preservesColimitsOfSize_of_isLeftKanExtension, mapContActionComp_inv, AlgebraicTopology.DoldKan.instIsIsoFunctorKaroubiSimplicialObjectNatTrans, CategoryTheory.GrothendieckTopology.overMapPullbackId_hom_app_hom_app, IsCoverDense.Types.appHom_valid_glue, CategoryTheory.Subfunctor.equalizer.lift_ι', CategoryTheory.Limits.Cofork.unop_π_app_one, AddCommGrpCat.Colimits.colimitCocone_ι_app, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_obj_obj, PresheafOfModules.toPresheaf_map_toSheafify, mapGrpFunctor_obj, rightOpLeftOpIso_hom_app, CategoryTheory.Discrete.monoidalFunctorComp_isMonoidal, CategoryTheory.Abelian.SpectralObject.HasSpectralSequence.isZero_H_obj_mk₁_i₀_le, rightDerived_fac_assoc, TopCat.sigmaCofan_ι_app, uncurry_obj_curry_obj, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_fst_map, HomologicalComplex.natIsoSc'_inv_app_τ₃, CategoryTheory.Subfunctor.Subpresheaf.ofSection_eq_range', AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap, CategoryTheory.Preadditive.commGrpEquivalence_unitIso_hom_app, CategoryTheory.Equivalence.sheafCongr.functor_obj_obj_obj, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd, CategoryTheory.Comonad.ForgetCreatesColimits'.newCocone_ι_app, LaxMonoidal.ofBifunctor.bottomMapₗ_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app, CategoryTheory.Abelian.Preradical.isRadical_iff_isZero, SSet.nonDegenerateEquivOfIso_symm_apply_coe, CategoryTheory.Limits.spanUnop_inv_app, CategoryTheory.CatCenter.smul_iso_inv_eq'_assoc, CommRingCat.coyoneda_obj_map, CategoryTheory.yonedaFunctor_reflectsLimits, postcompose₃_obj_obj_obj_map_app, CategoryTheory.Limits.piConst_map_app, mapMonCompIso_hom_app_hom, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃'_obj_map_app, CategoryTheory.isIso_toSheafify, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_symm_apply_right, CategoryTheory.Adjunction.sheafPushforwardContinuous_unit_app_hom_app, CategoryTheory.Limits.Cocone.fromCostructuredArrow_ι_app, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_fiber, AlgebraicTopology.DoldKan.N₁_obj_p, LeftExtension.coconeAtWhiskerRightIso_inv_hom, CategoryTheory.Triangulated.TStructure.π_truncGTIsoTruncGE_inv_ι_app, CategoryTheory.Limits.Cone.fromStructuredArrow_π_app, CategoryTheory.Equivalence.symm_unitIso, CategoryTheory.Cat.exp_obj, SSet.Subcomplex.image_id, CategoryTheory.WithTerminal.commaFromOver_map_left, CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_right, TopCat.Sheaf.id_app, CategoryTheory.Adjunction.mapCommMon_unit, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedAction_map_app, CategoryTheory.WithInitial.equivComma_functor_obj_right_map, SimplicialObject.opFunctor_map_app, RightExtension.precomp_map_left, CategoryTheory.Limits.FormalCoproduct.cochainComplexFunctor_map_f, CategoryTheory.μ_naturalityᵣ_assoc, CategoryTheory.Preadditive.DoldKan.equivalence_counitIso, CategoryTheory.Join.mapIsoWhiskerLeft_hom, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_hom_app_hom_app, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.isPushout, CategoryTheory.Limits.Cocone.toCostructuredArrowCompProj_hom_app, LeftExtension.IsPointwiseLeftKanExtension.isLeftKanExtension, CategoryTheory.Limits.pullbackObjIso_inv_comp_fst_assoc, CategoryTheory.Iso.hom_inv_id_app_app_assoc, functorialityCompPostcompose_hom_app_hom, Profinite.exists_locallyConstant_finite_aux, CategoryTheory.preservesFiniteLimits_liftToFinset, DerivedCategory.shiftMap_homologyFunctor_map_Q_assoc, CategoryTheory.Equivalence.mapHomologicalComplex_unitIso, CategoryTheory.Limits.Cone.fromCostructuredArrow_obj_π, CategoryTheory.NatTrans.epi_iff_epi_app', CategoryTheory.shrinkYonedaMon_map, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app_assoc, CategoryTheory.Triangulated.TStructure.spectralObject_ω₁, CategoryTheory.FunctorToTypes.binaryCoproductEquiv_apply, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_mul_app, CategoryTheory.Limits.instHasFiniteLimitsFunctor, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_right_app, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.const_s', CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.left_triangle_components, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_μ_unmop_app, mapBifunctorHomologicalComplexObj_obj_X_d, FullyFaithful.homNatIso_inv_app_down, CategoryTheory.Abelian.SpectralObject.toCycles_descCycles, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionUnitIso_inv, isIso_whiskerRight, pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_app, ranCounit_app_whiskerLeft_ranAdjunction_unit_app_assoc, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_inv, CategoryTheory.Over.mapCongr_inv_app_left, CategoryTheory.Abelian.SpectralObject.fromOpcycles_H_map_twoδ₁Toδ₀, CategoryTheory.IsCofiltered.iff_nonempty_limit, CategoryTheory.FunctorToTypes.instHasStrongEpiMonoFactorisationsFunctorType, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp, AlgebraicGeometry.StructureSheaf.comap_const, CategoryTheory.Limits.Types.FilteredColimit.colimit_eq_iff_aux, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.fstFunctor_map, CochainComplex.homologyFunctorFactors_hom_app_homologyδOfTriangle_assoc, HomologicalComplex.natIsoSc'_hom_app_τ₃, SSet.stdSimplex.ext_iff, CategoryTheory.Limits.fiberwiseColimitLimitIso_hom_app, CategoryTheory.RightExactFunctor.whiskeringRight_map_app, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃'_obj_obj_obj, CategoryTheory.Cat.freeMapIdIso_hom_app, Condensed.id_hom, curryingFlipEquiv_symm_apply_map_app, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality', CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.mkIso_inv_fst, PresheafOfModules.Sheafify.map_smul_eq, CategoryTheory.Localization.comp_liftNatTrans, CommShift₂.commShift_flip_map, Final.extendCocone_obj_ι_app, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_hom_app_hom₃, CategoryTheory.Idempotents.instIsEquivalenceFunctorKaroubiFunctorExtension, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.uliftCoyonedaEquiv_symm_apply_app, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.sheafCondition_of_sheaf, CategoryTheory.Limits.instIsRightAdjointFunctorLim, CategoryTheory.NatIso.isIso_of_isIso_app, CategoryTheory.Sheaf.instHasColimitsOfShape, opId_hom_app, CategoryTheory.Core.forgetFunctorToCore_obj_obj, CategoryTheory.GrothendieckTopology.Point.presheafFiberOfIsCofilteredCocone_ι_app, CategoryTheory.Under.lift_obj, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoColimitUncurryWhiskeringLeft₂_inv, AlgebraicGeometry.Proj.sub_apply, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_hom_app_fst_app, CategoryTheory.HasExactColimitsOfShape.preservesFiniteLimits, sheafPullbackConstruction.instIsRightAdjointSheafSheafPushforwardContinuousOfHasWeakSheafify, CategoryTheory.Over.mapCongr_hom_app_left, CategoryTheory.Coyoneda.ULiftCoyoneda.instFullOppositeFunctorTypeUliftCoyoneda, CategoryTheory.ProdPreservesConnectedLimits.forgetCone_π, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_obj_obj_obj₁, shift_map_op_assoc, PresheafOfModules.instFaithfulFunctorOppositeAbToPresheaf, CategoryTheory.Limits.coker.condition_assoc, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isColimit_desc, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_jointly_surjective, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_π_app, CategoryTheory.FunctorToTypes.prodMk_snd, CategoryTheory.Equivalence.funInvIdAssoc_hom_app, CategoryTheory.Limits.ConeMorphism.w, CategoryTheory.Over.postCongr_inv_app_left, CategoryTheory.LocalizerMorphism.LeftResolution.opEquivalence_unitIso, CategoryTheory.GrothendieckTopology.Point.tensorHom_comp_toPresheafFiber_μ_assoc, IsDenseSubsite.mapPreimage_comp_assoc, CategoryTheory.SimplicialObject.Truncated.trunc_obj_obj, CategoryTheory.Adjunction.leftAdjointCompNatTrans₀₁₃_eq_conjugateEquiv_symm, CategoryTheory.Localization.Monoidal.lifting_isMonoidal, opUnopIso_inv_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_η_app, CategoryTheory.monadToFunctor_obj, CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι_assoc, CategoryTheory.GrothendieckTopology.sheafifyCompIso_inv_eq_sheafifyLift, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_hom, IsCoverDense.Types.pushforwardFamily_def, CategoryTheory.Limits.LimitPresentation.self_π, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_inv_app, SSet.opFunctor_map, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_inverse_map_hom, CategoryTheory.GrothendieckTopology.sheafifyMap_id, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_inv_app, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app', AddCommMonCat.coyonedaType_obj_map, CategoryTheory.Limits.ι_comp_sigmaObjIso_inv, CategoryTheory.eqToHom_app, CategoryTheory.Limits.ι_colimitLimitIso_limit_π, mapContActionCongr_hom, CategoryTheory.Abelian.SpectralObject.isZero_H_obj_mk₁_i₃_le', CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_hom_app_unmop_unmop, CategoryTheory.WithInitial.inclLift_hom_app, CategoryTheory.OverPresheafAux.counitForward_naturality₁, CategoryTheory.Over.mapComp_hom_app_left, SSet.Subcomplex.toImage_ι_assoc, CategoryTheory.TransfiniteCompositionOfShape.ici_F, CategoryTheory.Limits.piFunctor_obj_obj, triangleIso, Condensed.isSheafStonean, CategoryTheory.CategoryOfElements.structuredArrowEquivalence_counitIso, CategoryTheory.linearYoneda_obj_obj_carrier, CategoryTheory.Limits.walkingCospanOpEquiv_counitIso_hom_app, TopologicalSpace.Opens.mapId_hom_app, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_unitIso_inv_app_hom, CategoryTheory.CosimplicialObject.Truncated.whiskering_obj_obj_obj, Rep.instLinearModuleCatObjFunctorCoinvariantsTensor, PresheafOfModules.instFullSheafOfModulesCompObjFunctorOppositeRingCatIsSheafForgetRestrictScalars, CategoryTheory.Limits.LimitPresentation.changeDiag_π, CategoryTheory.Limits.Cone.postcomposeEquivalence_unitIso, CategoryTheory.Bicategory.postcomposing_obj, mapTriangleInvRotateIso_inv_app_hom₃, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app_assoc, CategoryTheory.Triangulated.TStructure.truncLTι_comp_truncGEπ_assoc, CategoryTheory.Abelian.SpectralObject.comp_hom, CategoryTheory.GradedObject.ι_mapBifunctorComp₁₂MapObjIso_hom_assoc, OneHypercoverDenseData.essSurj, CategoryTheory.Comma.equivProd_unitIso_hom_app_left, CategoryTheory.FunctorToTypes.binaryCoproductEquiv_symm_apply, TopologicalSpace.Opens.mapComp_hom_app, SSet.Subcomplex.topIso_inv_ι, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionUnitIso_hom, CategoryTheory.Adjunction.mapCommMon_counit, SSet.prodStdSimplex.strictMono_orderHomOfSimplex_iff, CategoryTheory.Limits.ι_colimitLimitToLimitColimit_π, CategoryTheory.SimplicialObject.Truncated.rightExtensionInclusion_hom_app, CategoryTheory.GradedObject.mapBifunctorMap_obj_map, CategoryTheory.Coyoneda.objOpOp_hom_app, CategoryTheory.SmallObject.SuccStruct.ofNatTrans_X₀, mapCommGrpFunctor_obj, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst, PushoutObjObj.mapArrowRight_left, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app, HomologicalComplex.mapBifunctor₁₂.hom_ext_iff, unopId_inv_app, CategoryTheory.Presheaf.instIsIsoFunctorOfIsLeftKanExtensionOppositeType, HomologicalComplex.mapBifunctor₂₃.ι_mapBifunctor₂₃Desc, sSetTopAdj_homEquiv_stdSimplex_zero, SSet.horn₃₁.ι₂_desc_assoc, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_inv, CategoryTheory.Monad.algebraFunctorOfMonadHomEq_hom_app_f, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_map, SSet.prod_δ_snd, OrderHom.equivalenceFunctor_counitIso_inv_app_app, CategoryTheory.Cat.ihom_obj, Action.FunctorCategoryEquivalence.unitIso_inv_app_hom, mapCommGrpCompIso_hom_app_hom_hom_hom, CategoryTheory.Limits.BinaryBicone.toCocone_ι_app_right, SSet.Subcomplex.ofSimplexProd_eq_range, smoothSheaf.ι_evalHom_assoc, CategoryTheory.Limits.Types.binaryProductFunctor_obj_map, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_map, CategoryTheory.Localization.Lifting.ofIsos_iso, CategoryTheory.Limits.colimit.toOver_ι_app, whiskeringRight₂_obj_obj_obj_map, CategoryTheory.sheafComposeIso_hom_fac, instIsLeftKanExtensionObjLanAppLanUnit, SSet.Truncated.Edge.CompStruct.tensor_simplex_snd, CategoryTheory.Limits.Types.FilteredColimit.isColimit_eq_iff, CategoryTheory.Limits.Cone.extend_π, CategoryTheory.Abelian.SpectralObject.EToCycles_i_assoc, mapActionComp_inv, CategoryTheory.MorphismProperty.Comma.mapLeftIso_unitIso_inv_app_right, CategoryTheory.obj_μ_app, Action.FunctorCategoryEquivalence.functor_map_app, CategoryTheory.Idempotents.functorExtension₂CompWhiskeringLeftToKaroubiIso_hom_app_app_f, CategoryTheory.Limits.Multicofork.snd_app_right_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality, CategoryTheory.μ_naturalityₗ, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_tensorHom_app, CategoryTheory.Localization.essSurj_mapComposableArrows_of_hasRightCalculusOfFractions, CategoryTheory.Limits.Bicone.toCone_π_app_mk, CategoryTheory.GradedObject.mapTrifunctorMapFunctorObj_map_app, SSet.stdSimplex.face_eq_ofSimplex, CategoryTheory.Limits.coneOfCoconeRightOp_π, CategoryTheory.extensiveTopology.isSheaf_yoneda_obj, CategoryTheory.GrothendieckTopology.sheafifyMap_sheafifyLift, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_inv_app, CategoryTheory.Limits.limitConstTerminal_hom, CompHausLike.LocallyConstant.counitApp_app, leftDerivedNatTrans_comp_assoc, CategoryTheory.Cat.rightUnitor_hom_toNatTrans, CategoryTheory.Bicategory.precomposingCat_map, CategoryTheory.Limits.spanCompIso_hom_app_zero, CategoryTheory.Limits.fiberwiseColim_obj, homObjEquiv_symm_apply_app, const.opObjUnop_hom_app, IsCoverDense.sheafHom_eq, AlgebraicGeometry.StructureSheaf.comap_apply, CommMonCat.coyoneda_obj_map, ModuleCat.uliftFunctorForgetIso_hom_app, prod'CompFst_hom_app, coreId_inv_app_iso_inv, SSet.PtSimplex.RelStruct.δ_castSucc_map, CategoryTheory.eHomFunctor_obj_obj, CategoryTheory.instReflectsIsomorphismsFunctorObjWhiskeringRight, CategoryTheory.Abelian.Preradical.ι_π_assoc, CategoryTheory.PreGaloisCategory.instFullContActionFintypeCatHomObjFiniteAutFunctorFunctorToContAction, CategoryTheory.PullbackShift.adjunction_unit, Bipointed.swapEquiv_counitIso_hom_app_toFun, SSet.prod_σ_fst, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_inv_app_hom_hom_app, leftDerivedZeroIsoSelf_inv_hom_id, SSet.stdSimplex.obj₀Equiv_apply, LeftExtension.postcompose₂_obj_right_map, SSet.horn₃₁.desc.multicofork_pt, CategoryTheory.LaxMonoidalFunctor.isoMk_inv, CategoryTheory.GradedObject.singleCompEval_hom_app, CategoryTheory.MonoidalOpposite.tensorLeftUnmopIso_inv_app, CategoryTheory.Limits.Trident.condition, CategoryTheory.FreeGroupoid.liftNatIso_hom_app, CategoryTheory.compEvaluation_hom_app, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_hom_π_π, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, CategoryTheory.MonoidalCategory.DayFunctor.equiv_inverse_map_natTrans, CategoryTheory.flippingIso_inv_toFunctor_obj_map_app, CategoryTheory.AdditiveFunctor.ofLeftExact_map, OneHypercoverDenseData.essSurj.presheafObj_mapPreimage_condition, CategoryTheory.NatTrans.mapHomotopyCategory_comp, HomologicalComplex.mapBifunctor₁₂.ι_mapBifunctor₁₂Desc, CategoryTheory.RightExactFunctor.ofExact_map_hom, HomologicalComplex.mapBifunctor₁₂.ι_D₂_assoc, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_comp_mapHomotopyCategory_snd, PullbackObjObj.π_iso_of_iso_right_hom, LightCondSet.instIsIsoFunctorSequentialCounitSequentialAdjunction, HomologicalComplex.mapBifunctor₂₃.ιOrZero_eq_zero, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.functor_obj_obj_map, CategoryTheory.Sheaf.instIsIsoAppCounitConstantSheafAdjOfFaithfulOfFullConstantSheafOfIsConstant, SSet.prodStdSimplex.objEquiv_δ_apply, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv, CategoryTheory.WithTerminal.commaFromOver_obj_right, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_iso_inv_app, CategoryTheory.NatTrans.app_nsmul, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_hom, CategoryTheory.Enriched.FunctorCategory.enrichedId_π_assoc, CategoryTheory.δ_naturalityᵣ_assoc, HomologicalComplex.mapBifunctor.hom_ext_iff, AlgebraicGeometry.isSheaf_propQCTopology_iff, CategoryTheory.bifunctorComp₂₃_map_app_app, CategoryTheory.Abelian.Preradical.IsIdempotent.isIso_whiskerLeft_r_ι, AddMonCat.equivalence_counitIso, opUnopEquiv_counitIso, CategoryTheory.shrinkYonedaGrp_map, PushoutObjObj.mapArrowRight_comp_assoc, AddCommMonCat.coyonedaType_map_app, CategoryTheory.EnrichedFunctor.category_id_out, CategoryTheory.LeftExactFunctor.whiskeringRight_map_app, CategoryTheory.NatTrans.op_id, CategoryTheory.instFullMonFunctorOppositeMonCatyonedaAddMon, CategoryTheory.CatCenter.mul_app', SheafOfModules.evaluationPreservesLimitsOfSize, HomologicalComplex.ι_mapBifunctorDesc, CategoryTheory.FreeGroupoid.mapCompLift_inv_app, CategoryTheory.GrothendieckTopology.Point.instPreservesColimitsOfSizeFunctorOppositePresheafFiber, CategoryTheory.MorphismProperty.FunctorsInverting.id_hom, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_inv_right, sheafAdjunctionCocontinuous_unit_app_hom, CategoryTheory.Limits.BinaryBicone.toCone_π_app_left, CategoryTheory.Limits.spanOp_hom_app, CategoryTheory.Limits.limitIsoSwapCompLim_hom_app, CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieve, CategoryTheory.faithful_linearYoneda, AlgebraicTopology.karoubi_alternatingFaceMapComplex_d, CategoryTheory.Abelian.Ext.preadditiveCoyoneda_homologySequenceδ_singleTriangle_apply, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_hom_comp_π_assoc, CategoryTheory.WithTerminal.coneEquiv_functor_obj_π_app_star, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_inv_app, CategoryTheory.Limits.limitIsoFlipCompLim_hom_app, CategoryTheory.Prod.braiding_unitIso, CategoryTheory.NatTrans.shift_comm_assoc, Profinite.Extend.functorOp_obj, CategoryTheory.Abelian.SpectralObject.epi_H_map_twoδ₁Toδ₀', CategoryTheory.GrothendieckTopology.Point.W_isInvertedBy_presheafFiber', CategoryTheory.Subfunctor.preimage_comp, CategoryTheory.Adjunction.mapCommGrp_unit, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app, CategoryTheory.Limits.coneOfDiagramInitial_π_app, curry₃ObjProdComp_inv_app_app_app, CategoryTheory.coreFunctor_obj_map_iso_inv, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_inv_colimit_map, CategoryTheory.conjugateEquiv_leftUnitor_hom, CategoryTheory.Sum.functorEquiv_inverse_map, CategoryTheory.shrinkYonedaEquiv_symm_app_shrinkYonedaObjObjEquiv_symm, CategoryTheory.instPreservesFiniteBiproductsTensorRight, PullbackObjObj.mapArrowRight_comp_assoc, CategoryTheory.Limits.CategoricalPullback.mkNatIso_inv_app_snd, CategoryTheory.WithTerminal.coneEquiv_counitIso_inv_app_hom, IsCoverDense.sheafIso_hom_hom, CategoryTheory.shiftFunctorCompIsoId_add'_inv_app, CategoryTheory.ShortComplex.functorEquivalence_functor, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₃_app, CategoryTheory.shiftFunctorAdd_zero_add_hom_app, CategoryTheory.Abelian.LeftResolution.karoubi_π, CategoryTheory.Idempotents.functorExtension₁CompWhiskeringLeftToKaroubiIso_hom_app_app_f, Rep.coinvariantsTensorIndIso_inv, instCommShiftHomotopyCategoryIntUpDerivedCategoryHomMapDerivedCategoryFactorsh, CategoryTheory.Triangulated.TStructure.ω₁_map, CategoryTheory.Abelian.SpectralObject.toCycles_cyclesMap, CategoryTheory.Limits.Cocone.functorialityEquivalence_counitIso, CategoryTheory.Limits.limitCompCoyonedaIsoCone_hom_app, IsCoverDense.restrictHomEquivHom_naturality_right_symm, CategoryTheory.Adjunction.homEquiv_ofNatIsoRight_apply, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionAssocIso_inv, CategoryTheory.uliftYonedaEquiv_apply, CategoryTheory.Limits.instHasColimitObjFunctorConstInitial, HomologicalComplex₂.flipEquivalenceUnitIso_hom_app_f_f, CategoryTheory.Limits.WidePullbackShape.mkCone_π_app, CategoryTheory.prod.associativity_counitIso, CategoryTheory.isZero_Tor'_succ_of_projective, CategoryTheory.Adjunction.leftAdjointUniq_hom_app_counit_assoc, CategoryTheory.Monad.ForgetCreatesLimits.newCone_π_app, CategoryTheory.Limits.spanExt_hom_app_right, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_map, CategoryTheory.NatTrans.comp_app_assoc, ModuleCat.binaryProductLimitCone_cone_π_app_right, CochainComplex.shiftFunctorZero_inv_app_f, CategoryTheory.Sheaf.terminal_obj, CategoryTheory.WithInitial.mkCommaMorphism_right_app, CategoryTheory.shiftFunctorAdd'_assoc, CategoryTheory.SingleFunctors.Hom.comm_assoc, CategoryTheory.Sheaf.imageι_hom, CategoryTheory.Triangulated.TStructure.eTruncGEπ_naturality, CategoryTheory.Limits.FormalCoproduct.powerBifunctor_map_app, CategoryTheory.CostructuredArrow.mapIso_functor_map_left, CategoryTheory.HasLiftingProperty.transfiniteComposition.hasLiftingProperty_ι_app_bot, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.functor_obj_obj_obj, CategoryTheory.shiftFunctorComm_hom_app_comp_shift_shiftFunctorAdd_hom_app, CategoryTheory.Monad.monToMonad_obj, CategoryTheory.HasSheafify.isLeftExact, CategoryTheory.Abelian.SpectralObject.homologyDataIdId_iso_hom, currying_inverse_obj_obj_map, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObjObj_mon_one, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_fst_obj, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_left, CategoryTheory.Presheaf.isSheaf_yoneda', LightCondensed.comp_hom, SSet.horn.faceSingletonComplIso_inv_ι, CategoryTheory.Abelian.SpectralObject.IsFirstQuadrant.isZero₂, CategoryTheory.NatTrans.CommShift₂.commShift_flipApp, CategoryTheory.piEquivalenceFunctorDiscrete_functor_obj, CategoryTheory.is_coprod_iff_isPushout, CategoryTheory.Limits.Types.FilteredColimit.jointly_surjective_of_isColimit₂, SSet.Subcomplex.toSSetFunctor_obj, CategoryTheory.left_unitality_app_assoc, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_obj_obj, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_hom_app_hom₁, CategoryTheory.Abelian.SpectralObject.comp_hom_assoc, CategoryTheory.GrothendieckTopology.Point.Hom.sheafFiber_comp_assoc, CategoryTheory.μ_naturality₂, CategoryTheory.Sigma.mapComp_inv_app, CategoryTheory.LeftExactFunctor.whiskeringRight_obj_map, PresheafOfModules.toPresheaf_preservesLimit, AlgebraicTopology.alternatingFaceMapComplex_map_f, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ, RightExtension.mk_hom, PresheafOfModules.toPresheaf_obj_coe, flip₁₃_obj_map_app, CategoryTheory.Abelian.SpectralObject.πE_ιE, mapCommMonNatIso_hom_app_hom_hom, CategoryTheory.Localization.instFullFunctorWhiskeringLeftFunctor', CategoryTheory.AdditiveFunctor.ofRightExact_map, leftExtensionEquivalenceOfIso₁_inverse_map_left, CategoryTheory.GradedObject.ι_mapBifunctor₁₂BifunctorDesc, OplaxMonoidal.ofBifunctor.secondMap₂_app_app_app, SSet.stdSimplex.δ_zero_toSSetObjI, CategoryTheory.Over.coprod_obj, CategoryTheory.Limits.Cone.toStructuredArrowCompToUnderCompForget_hom_app, SSet.Truncated.Edge.id_tensor_id, SSet.horn₃₁.ι₃_desc_assoc, CategoryTheory.Comma.equivProd_counitIso_hom_app, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂'_obj_map_app, CategoryTheory.Subfunctor.image_comp, SSet.Subcomplex.instSubsingletonHomToSSetBot, CategoryTheory.Limits.PullbackCone.combine_π_app, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_obj_X₂, CategoryTheory.Limits.spanCompIso_inv_app_left, Action.FunctorCategoryEquivalence.functor_δ, CategoryTheory.MorphismProperty.colimitsOfShape.of_isColimit, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone_isColimit_desc, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_apply_app, CategoryTheory.Localization.homEquiv_eq, CategoryTheory.Triangulated.TStructure.isZero_eTruncGE_obj_obj, CategoryTheory.CategoryOfElements.CreatesLimitsAux.liftedCone_π_app_coe, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_id, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_hom_assoc, CategoryTheory.GrothendieckTopology.whiskerRight_toPlus_comp_plusCompIso_hom, CategoryTheory.prodOpEquiv_unitIso_hom_app, CategoryTheory.NatTrans.op_whiskerRight_assoc, CategoryTheory.Adjunction.leftAdjointUniq_trans_app_assoc, CategoryTheory.preadditiveYoneda_obj, CategoryTheory.bifunctorComp₁₂Obj_obj_obj, LightProfinite.lightToProfinite_map_proj_eq, SSet.instBalanced, rightUnitor_hom_app, CategoryTheory.Comma.mapRightId_inv_app_left, CategoryTheory.PreGaloisCategory.toAut_surjective_isGalois_finite_family, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality', CategoryTheory.GradedObject.ιMapBifunctorBifunctor₂₃MapObj_eq_assoc, CategoryTheory.preservesColimitsOfShape_of_isCardinalPresentable_of_essentiallySmall, CategoryTheory.SingleFunctors.comp_hom_assoc, CategoryTheory.isFinitelyPresentable_iff_preservesFilteredColimitsOfSize, CategoryTheory.linearCoyoneda_obj_obj_isAddCommGroup, FullyFaithful.compUliftYonedaCompWhiskeringLeft_inv_app_app_down, AlgebraicGeometry.StructureSheaf.toPushforwardStalkAlgHom_apply, CategoryTheory.ShortComplex.π₁Toπ₂_comp_π₂Toπ₃, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_obj, CategoryTheory.GrothendieckTopology.preservesSheafification_iff_of_adjunctions, CategoryTheory.Limits.IsColimit.ι_map_assoc, CategoryTheory.AdditiveFunctor.ofExact_map, SSet.Subcomplex.unionProd.image_β_hom, leftOpId_hom_app, CategoryTheory.WithTerminal.opEquiv_unitIso_hom_app, CategoryTheory.Abelian.SpectralObject.fromOpcycles_H_map_twoδ₁Toδ₀_assoc, CategoryTheory.Limits.CatCospanTransform.category_id_right, Rep.standardComplex.εToSingle₀_comp_eq, OplaxMonoidal.ofBifunctor.firstMap₁_app_app_app, CategoryTheory.PreGaloisCategory.toAut_hom_app_apply, isoShift_inv_naturality, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality_apply, leftExtensionEquivalenceOfIso₁_inverse_obj_left, CategoryTheory.Comma.mapLeftId_hom_app_right, CategoryTheory.tensoringRight_linear, AlgebraicGeometry.Scheme.ΓSpecIso_inv, CategoryTheory.MorphismProperty.Comma.mapRightId_inv_app_right, CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_exists, CategoryTheory.Over.postCongr_hom_app_left, PushoutObjObj.ofHasPushout_pt, postcompose₃_obj_obj_map_app_app, CategoryTheory.μ_naturalityᵣ, CategoryTheory.Adjunction.compPreadditiveYonedaIso_inv_app_app_apply, CategoryTheory.Join.mapWhiskerRight_comp, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₃, CategoryTheory.MonoidalCategory.DayConvolution.hexagon_forward, leftOpRightOpEquiv_unitIso_inv_app, map_opShiftFunctorEquivalence_unitIso_inv_app_unop, CategoryTheory.ObjectProperty.fullSubcategoryCongr_unitIso, CategoryTheory.GradedObject.singleCompEval_inv_app, CategoryTheory.Adjunction.Triple.whiskerRight_rightToLeft_assoc, CategoryTheory.Equivalence.changeFunctor_unitIso_hom_app, CategoryTheory.WithTerminal.opEquiv_counitIso_hom_app, CategoryTheory.Limits.Cocone.tensor_ι_app, HasFibers.comp_const, SSet.prodStdSimplex.objEquiv_naturality, IsCoverDense.faithful_sheafPushforwardContinuous, TopCat.toSSetObj₀Equiv_symm_apply, CategoryTheory.Sheaf.tensorProd_isSheaf, CategoryTheory.ComposableArrows.opEquivalence_unitIso_inv_app, CategoryTheory.SimplicialObject.Augmented.const_obj_hom, instFullProdCurry₃, OneHypercoverDenseData.essSurj.presheafMap_restriction_assoc, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.counitIso_inv, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_inv_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiberOfIsCofiltered_naturality, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_hom_app, CategoryTheory.ParametrizedAdjunction.hasLiftingProperty_iff, SheafOfModules.isSheaf, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₃, sectionsFunctor_map_coe, CommGrpCat.coyonedaType_map_app, CategoryTheory.ComposableArrows.isoMkSucc_hom, CategoryTheory.instIsIsoFunctorOppositeSheafSheafComposeNatTrans, OneHypercoverDenseData.essSurj.presheafObjObjIso.inv_π_assoc, CategoryTheory.Limits.Multiequalizer.multifork_π_app_left, CategoryTheory.Cat.HasLimits.limitCone_π_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app_assoc, CategoryTheory.instIsMonoidalFunctorOppositeWOfHasSheafComposeForgetOfHasEnoughPoints, CategoryTheory.MonoidalCategory.DayConvolution.associator_inv_unit_unit, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_hom, HomologicalComplex.mapBifunctorAssociatorX_hom_D₂, CategoryTheory.Join.pseudofunctorLeft_mapComp_hom_toNatTrans_app, CategoryTheory.Sheaf.toImage_ι, CategoryTheory.StructuredArrow.mapNatIso_functor_obj_hom, SSet.modelCategoryQuillen.instHasLiftingPropertyιHornHAddNatOfNatOfFibration, CategoryTheory.CostructuredArrow.mapIso_unitIso_inv_app_left, CategoryTheory.MonadIso.mk_hom_toNatTrans, CategoryTheory.MonoidalCategory.DayConvolution.hexagon_reverse, IsCoverDense.restrictHomEquivHom_naturality_left, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObjObj_mon_mul, CategoryTheory.Idempotents.DoldKan.hε, CategoryTheory.uliftYonedaEquiv_symm_map, CategoryTheory.GrothendieckTopology.W.transport_isMonoidal, CategoryTheory.Limits.ConeMorphism.map_w_assoc, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_hom_app, CategoryTheory.Enriched.FunctorCategory.homEquiv_apply_π, HomologicalComplex.cyclesOpNatIso_inv_app, CategoryTheory.Abelian.SpectralObject.p_opcyclesIso_inv, cones_obj, CategoryTheory.Monoidal.monFunctorCategoryEquivalence_unitIso, CategoryTheory.preadditiveYonedaMap_app, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app', postcompose₃_obj_obj_obj_obj_obj, CategoryTheory.MonoidalCategory.DayFunctor.equiv_counitIso_inv_app, CategoryTheory.WithInitial.mkCommaObject_right_obj, SSet.stdSimplex.spineId_arrow_apply_zero, CategoryTheory.shrinkYoneda_obj, CategoryTheory.sheafBotEquivalence_inverse_map_hom, SSet.prod_δ_fst, CategoryTheory.prod.associativity_unitIso, CategoryTheory.Abelian.SpectralObject.πE_EIsoH_hom_assoc, SSet.comp_app_assoc, AddCommGrpCat.coyonedaForget_inv_app_app, CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcyclesE_X₃, CategoryTheory.instPreservesFiniteColimitsSheafExtensiveTopologyFunctorOppositeSheafToPresheafOfPreadditiveOfHasFiniteColimits, CategoryTheory.bifunctorComp₁₂Functor_obj, CategoryTheory.Adjunction.unit_app_shift_commShiftIso_inv_app, CategoryTheory.Limits.FormalCoproduct.cechIsoAugmentedCechNerve_inv_left, CategoryTheory.Comma.mapRightComp_inv_app_right, HomologicalComplex.quasiIso_iff_evaluation, CategoryTheory.Limits.Cocone.functorialityEquivalence_unitIso, instAdditiveOfNat, CategoryTheory.SingleFunctors.Hom.id_hom, CategoryTheory.Limits.coprodComparisonNatIso_hom, CategoryTheory.SmallObject.SuccStruct.restrictionLTOfCoconeIso_inv_app, mapTriangleIso_hom_app_hom₁, CategoryTheory.Abelian.SpectralObject.d_EIsoH_hom, CategoryTheory.TwistShiftData.assoc, whiskerRight_id', ModuleCat.restrictScalarsId'_inv_app, AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex_homotopyHomInvId, CategoryTheory.NatTrans.CommShift.associator, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π, CategoryTheory.ComposableArrows.isoMk₅_inv, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_right, SimplicialObject.opEquivalence_counitIso, CategoryTheory.MorphismProperty.fst'_self_eq_snd, compFlipUncurryIso_inv_app, CommShift.ofIso_commShiftIso_hom_app, CategoryTheory.Presieve.isSheafFor_iff_bijective_shrinkFunctor_ι_comp, CategoryTheory.NatTrans.leftOp_id, CategoryTheory.Limits.limit.isoLimitCone_hom_π_assoc, LightCondensed.ofSheafLightProfinite_obj, CategoryTheory.Quotient.LiftCommShift.iso_hom_app, CategoryTheory.Enriched.FunctorCategory.diagram_map_app, CategoryTheory.SimplicialObject.Augmented.whiskering_map_app_right, CommShift₂.commShift_map, CategoryTheory.LeftExactFunctor.whiskeringLeft_map_app, Monoidal.coreMonoidalTransport_μIso_hom, CategoryTheory.IsSifted.colim_preservesLimits_pair_of_sSifted, lanUnit_app_app_lanAdjunction_counit_app_app, CategoryTheory.PreGaloisCategory.instFaithfulActionFintypeCatAutFunctorFunctorToAction, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_snd, CategoryTheory.Adjunction.compUliftCoyonedaIso_inv_app_app_down, CategoryTheory.Abelian.SpectralObject.isIso_H_map_twoδ₁Toδ₀, CategoryTheory.presheafHom_obj, CategoryTheory.Limits.IsColimit.homEquiv_apply, ModuleCat.extendScalars_assoc_assoc, CategoryTheory.ObjectProperty.topEquivalence_unitIso, CategoryTheory.Equivalence.counitIso_functor_comp, pointwiseLeftKanExtension_map, CategoryTheory.NatTrans.app_add, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_π_app, AlgebraicTopology.DoldKan.Γ₂_obj_p_app, CategoryTheory.MorphismProperty.Comma.mapLeftIso_counitIso_hom_app_right, lanUnit_app_whiskerLeft_lanAdjunction_counit_app, CategoryTheory.NatIso.unop_trans, whiskerLeft_obj_map_bijective_of_isCoverDense, CategoryTheory.Limits.parallelPairOpIso_hom_app_one, CategoryTheory.Limits.walkingCospanOpEquiv_counitIso_inv_app, mapTriangleInvRotateIso_hom_app_hom₃, CategoryTheory.ObjectProperty.IsConservativeFamilyOfPoints.jointlyReflectMonomorphisms, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc_assoc, IsCoverDense.sheafHom_restrict_eq, CategoryTheory.comonadToFunctor_obj, CategoryTheory.ThinSkeleton.map₂_obj, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso_inv_app_f, CategoryTheory.WithInitial.mapId_inv_app, SSet.Subcomplex.eqToIso_hom, AlgebraicGeometry.isBasis_preimage_isAffineOpen, CategoryTheory.Adjunction.instIsIsoFunctorCounitOfIsEquivalence, CategoryTheory.Limits.PullbackCone.op_ι_app, whiskeringLeft₃ObjObjMap_app, CategoryTheory.Abelian.SpectralObject.isIso_fromOpcycles, SSet.yonedaEquiv_symm_comp, Monoidal.coreMonoidalTransport_εIso_hom, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_hom_app, constComp_inv_app, CategoryTheory.Abelian.SpectralObject.zero₃, Bipointed.swapEquiv_unitIso_inv_app_toFun, CategoryTheory.RightExactFunctor.forget_map, TopCat.Presheaf.presheafEquivOfIso_inverse_obj_map, CategoryTheory.ComonadHom.id_toNatTrans, CategoryTheory.typeEquiv_inverse_obj, CategoryTheory.GradedObject.mapBifunctorRightUnitorCofan_inj, SSet.stdSimplex.range_δ, SSet.PtSimplex.RelStruct.δ_castSucc_map_assoc, CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc, CategoryTheory.Equivalence.symmEquivInverse_obj_counitIso_hom, CategoryTheory.Limits.evaluationPreservesLimits, CategoryTheory.essImage_yonedaMon, CategoryTheory.Join.mapWhiskerRight_whiskerRight, CategoryTheory.Presheaf.isLocallySurjective_comp_iff, CategoryTheory.FunctorToTypes.inv_hom_id_app_apply, CategoryTheory.Limits.preservesLimitsOfShape_of_evaluation, CategoryTheory.Abelian.Preradical.toColon_hom_left_app_colon_ι_app_assoc, CategoryTheory.Adjunction.Quadruple.epi_leftTriple_leftToRight_iff_mono_rightTriple_rightToLeft, CategoryTheory.ShiftMkCore.add_zero_hom_app, CategoryTheory.FinitaryExtensive.mono_inl_of_isColimit, CategoryTheory.Idempotents.DoldKan.N₂_map_isoΓ₀_hom_app_f, CategoryTheory.Limits.pullbackConeEquivBinaryFan_counitIso, CategoryTheory.Sum.swapCompInl_hom_app, SSet.PtSimplex.MulStruct.δ_succ_succ_map_assoc, CategoryTheory.Equivalence.inverseFunctor_map, CategoryTheory.Limits.CatCospanTransform.rightIso_inv, CategoryTheory.Abelian.SpectralObject.rightHomologyDataShortComplex_ι, CategoryTheory.StructuredArrow.mapNatIso_functor_map_right, CategoryTheory.Limits.Cocone.equivalenceOfReindexing_counitIso, CategoryTheory.Presheaf.coherentExtensiveEquivalence_unitIso_hom_app_hom_app, CategoryTheory.Sheaf.epi_of_isLocallySurjective', CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_app_fac, CategoryTheory.PreGaloisCategory.instEssSurjContActionFintypeCatHomObjFiniteAutFunctorFunctorToContAction, CategoryTheory.Bicategory.yoneda₀_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counitIso_hom_app_tensor_assoc, CategoryTheory.MonoidalCategory.DayConvolution.pentagon, CategoryTheory.MorphismProperty.Comma.mapLeftComp_hom_app_left, CategoryTheory.Triangulated.TStructure.instIsIsoFunctorETruncLTGELTSelfToGELT, CategoryTheory.Limits.coneOfConeCurry_pt, CategoryTheory.GrothendieckTopology.W_iff_isIso_map_of_adjunction, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_shortExact, CategoryTheory.Limits.MultispanIndex.multispanMapIso_inv_app, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_hom_app_f, CategoryTheory.Bicategory.precomposing_map_app, DerivedCategory.shiftMap_homologyFunctor_map_Qh_assoc, CategoryTheory.flipFunctor_obj, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc_assoc, Module.Flat.iff_rTensor_preserves_shortComplex_exact, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_snd, CategoryTheory.Triangulated.TStructure.truncLEIsoTruncLT_hom_ι, CategoryTheory.Limits.diagramIsoCospan_hom_app, CategoryTheory.simplicialToCosimplicialAugmented_map_left, CategoryTheory.NatTrans.leftDerivedToHomotopyCategory_comp_assoc, AddCommGrpCat.coyonedaForget_hom_app_app_hom, CategoryTheory.GradedObject.mapTrifunctorMapIso_hom, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_unitIso_hom_app_f_f, HomologicalComplex.mapBifunctorMapHomotopy.zero₁, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom, CategoryTheory.IsFinitelyPresentable.exists_hom_of_isColimit_under, CategoryTheory.Monad.comparisonForget_hom_app, CategoryTheory.GrothendieckTopology.W_isInvertedBy_whiskeringRight_presheafToSheaf, CategoryTheory.Monoidal.tensorUnit_map, CategoryTheory.OverPresheafAux.YonedaCollection.map₂_snd, HomologicalComplex.mapBifunctor₂₃.d₃_eq_zero, CategoryTheory.MonoidalOpposite.tensorIso_hom_app_unmop, isDense_iff_fullyFaithful_restrictedULiftYoneda, CategoryTheory.Sheaf.ΓHomEquiv_naturality_left, CategoryTheory.Sheaf.classifier_truth, CategoryTheory.SimplicialObject.Truncated.rightExtensionInclusion_left, CategoryTheory.NatTrans.mapHomologicalComplex_comp, CategoryTheory.Monad.algebraFunctorOfMonadHomComp_hom_app_f, CategoryTheory.Limits.CatCospanTransform.leftIso_hom, SSet.stdSimplex.objMk₁_apply, CategoryTheory.Limits.IsColimit.isIso_colimMap_ι, whiskerLeft_comp_whiskerRight_assoc, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_right_app, CategoryTheory.Limits.Fork.unop_ι_app_one, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π_assoc, CategoryTheory.evaluation_obj_map, CategoryTheory.GrothendieckTopology.isoToPlus_hom, CategoryTheory.Linear.smulOfRingMorphism_smul_eq, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_map_app_app, CategoryTheory.MonoidalCategory.DayFunctor.equiv_functor_map, CategoryTheory.coyoneda_preservesLimits, CategoryTheory.Limits.Cone.equivCostructuredArrow_inverse, CategoryTheory.Sheaf.classifier_Ω₀, CategoryTheory.TwistShiftData.shiftFunctorZero_hom_app, SheafOfModules.pushforwardComp_inv_app_val_app, CategoryTheory.Equivalence.changeFunctor_trans, CategoryTheory.Sheaf.instHasSubobjectClassifierTypeOfEssentiallySmall, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp_hom_app, CategoryTheory.Abelian.SpectralObject.cokernelSequenceE_g, AddCommGrpCat.HasLimit.productLimitCone_isLimit_lift, CategoryTheory.GrothendieckTopology.Point.toPresheafFiberMap_naturality_assoc, Monoidal.transport_ε, CategoryTheory.Limits.pointwiseCocone_ι_app_app, CategoryTheory.Adjunction.homEquiv_ofNatIsoLeft_apply, leftDerived_fac_assoc, CategoryTheory.Limits.Cocone.functoriality_obj_ι_app, CategoryTheory.endofunctorMonoidalCategory_associator_inv_app, SSet.id_app, CategoryTheory.MorphismProperty.underEquivOfIsTerminal_counitIso, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_app_fst_app, currying_counitIso_inv_app_app, ihom_ev_app, IsCoverDense.sheafIso_inv_hom, CategoryTheory.WithTerminal.inclLift_hom_app, CategoryTheory.Sheaf.isConstant_iff_forget, CategoryTheory.ShiftedHom.map_naturality_2, CategoryTheory.Quotient.liftCommShift_compatibility, SSet.instFiniteTensorObj, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality_assoc, CategoryTheory.Limits.FormalCoproduct.eval_map_app, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_inv_app_hom, CategoryTheory.shrinkYonedaObjObjEquiv_map_app, CategoryTheory.Adjunction.mapGrp_unit, leftKanExtensionCompIsoOfPreserves_hom_fac_assoc, CategoryTheory.uliftYonedaEquiv_naturality, OneHypercoverDenseData.essSurj.presheafObjObjIso.hom_map_assoc, Rep.coindFunctorIso_inv_app_hom_toFun_coe, OneHypercoverDenseData.isEquivalence, CategoryTheory.functorProdFunctorEquiv_functor, CategoryTheory.Limits.opHomCompWhiskeringLimYonedaIsoCocones_hom_app_app_app, SSet.stdSimplex.δ_objEquiv_symm_apply, curry₃_obj_map_app_app, coreId_inv_app_iso_hom, CategoryTheory.Presheaf.classifier_χ, CategoryTheory.Limits.hasLimitsOfShape_iff_isLeftAdjoint_const, CategoryTheory.Under.mapId_inv, isoShift_hom_naturality, CategoryTheory.Adjunction.map_restrictFullyFaithful_unit_app_assoc, CategoryTheory.CatCenter.app_add, CategoryTheory.Triangulated.TStructure.eTruncLTLTIsoLT_inv_hom_id_app_eTruncLT_obj_assoc, CategoryTheory.Localization.instFaithfulFunctorWhiskeringLeftFunctor', CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_inv, CategoryTheory.GradedObject.ι_mapTrifunctorMapMap_assoc, CategoryTheory.conjugateEquiv_counit_symm, CategoryTheory.instHasImagesSheafType, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_base, CategoryTheory.Sheaf.hasFilteredColimitsOfSize, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.ev_naturality_app, flip₂₃_obj_obj_obj, CategoryTheory.Idempotents.functorExtension₂_obj_map_f, CategoryTheory.GrothendieckTopology.toSheafification_app, CategoryTheory.Limits.FormalCoproduct.powerBifunctor_obj, CategoryTheory.Triangulated.TStructure.truncLEIsoTruncLT_inv_ι_app, CommShift.isoZero'_inv_app, CategoryTheory.Grothendieck.ιCompMap_inv_app_fiber, CategoryTheory.Abelian.SpectralObject.kernelSequenceE_g, typeToPartialFunIsoPartialFunToPointed_hom_app_toFun, CategoryTheory.plusPlusSheaf_map_hom, AlgebraicTopology.DoldKan.map_Hσ, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_obj_obj_mor₁, TopCat.Sheaf.extend_hom_app, SSet.stdSimplex.toSSetObj_app_const_zero, CategoryTheory.OverPresheafAux.YonedaCollection.yonedaEquivFst_eq, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_shift, CategoryTheory.SimplicialObject.Augmented.whiskering_obj, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₁, CategoryTheory.presheaf_mono_of_mono, CategoryTheory.Limits.opParallelPairIso_hom_app_zero, PartOrdEmb.Limits.CoconePt.fac_apply, CategoryTheory.Triangulated.TStructure.eTruncGEIsoGEGE_inv_hom_id_app_assoc, CategoryTheory.Limits.map_id_left_eq_curry_map, HomologicalComplex.singleMapHomologicalComplex_inv_app_self, CategoryTheory.NatTrans.CommShift.of_isIso, CategoryTheory.TwoSquare.guitartExact_id, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_snd_obj, CategoryTheory.PreGaloisCategory.autIsoFibers_inv_app, Initial.extendCone_obj_π_app', CategoryTheory.Subfunctor.equalizer.ι_ι_assoc, CategoryTheory.MorphismProperty.IsStableUnderColimitsOfShape.functorCategory, CategoryTheory.instPreservesFiniteLimitsFunctorOppositeSheafReflectorSheafToPresheaf, CategoryTheory.Abelian.SpectralObject.toCycles_cyclesMap_assoc, MulEquiv.toSingleObjEquiv_unitIso_hom, CategoryTheory.GrothendieckTopology.instFullSheafTypeUliftYoneda, CategoryTheory.Enriched.FunctorCategory.coneFunctorEnrichedHom_π_app, SSet.stdSimplex.ι₀_whiskerLeft_toSSetObjI_μ_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_map_left, CategoryTheory.evaluationAdjunctionRight_counit_app_app, coreprW_hom_app, LaxMonoidal.ofBifunctor.bottomMapᵣ_app, CategoryTheory.Pseudofunctor.ObjectProperty.mapId_inv_app, CategoryTheory.Limits.ColimitPresentation.map_ι, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_counitIso, CategoryTheory.Limits.Cocone.toCostructuredArrowCompToOverCompForget_inv_app, CategoryTheory.MorphismProperty.Comma.mapRightEq_hom_app_left, CategoryTheory.Nerve.instIsStrictSegalObjCatTruncatedOfNatNatNerveFunctor₂, AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTrans, SSet.Augmented.stdSimplex_map_right, CategoryTheory.Abelian.SpectralObject.exact₂', PresheafOfModules.toSheaf_map_sheafificationAdjunction_counit_app, CategoryTheory.Limits.cospanUnop_inv_app, CategoryTheory.Adjunction.leftAdjointUniq_hom_counit, CategoryTheory.Subfunctor.equivalenceMonoOver_inverse_map, CategoryTheory.Adjunction.isIso_counit_of_iso, CategoryTheory.Limits.Cowedge.condition_assoc, CategoryTheory.NatTrans.CommShift.rightUnitor, HomologicalComplex.mapBifunctor₁₂.d₂_eq_zero, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_left, CategoryTheory.sheafification_map, CategoryTheory.Limits.DiagramOfCocones.coconePoints_map, natTransEquiv_symm_apply_app, CategoryTheory.CatCommSq.hId_iso_inv_app, CategoryTheory.GrothendieckTopology.PreservesSheafification.le, homEquivOfIsLeftKanExtension_symm_apply, SSet.PtSimplex.MulStruct.δ_succ_succ_map, CategoryTheory.Limits.Cone.functorialityEquivalence_counitIso, CategoryTheory.δ_μ_app, CategoryTheory.WithTerminal.equivComma_functor_map_right, CategoryTheory.Localization.Monoidal.map_hexagon_forward, CategoryTheory.Limits.limCompFlipIsoWhiskerLim_inv_app_app, CategoryTheory.MorphismProperty.Comma.mapLeftComp_inv_app_left, CategoryTheory.Coyoneda.colimitCocone_ι_app, whiskeringLeft₂_obj_obj_obj_map_app, CategoryTheory.Pretriangulated.instIsHomologicalOppositeAddCommGrpCatObjFunctorPreadditiveYoneda, SheafOfModules.pushforwardNatTrans_id, topCatToSheafCompHausLike_map_hom_app, mapAddMonFunctor_map_app_hom, CategoryTheory.Presheaf.functorEnrichedHomCoyonedaObjEquiv_naturality, CategoryTheory.Monoidal.whiskerRight_app, commShiftOfLocalization_iso_inv_app, leftDerivedZeroIsoSelf_hom_inv_id_app, SSet.Subcomplex.homOfLE_comp_assoc, uncurry_map_app, whiskeringLeft₂_obj_obj_obj_obj_obj, CategoryTheory.Adjunction.map_restrictFullyFaithful_counit_app, CategoryTheory.Limits.piConst_obj_map, CategoryTheory.Limits.diagramIsoParallelPair_hom_app, CommMonCat.coyonedaForget_inv_app_app, CategoryTheory.Iso.coreId, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₁, CategoryTheory.GrothendieckTopology.plusFunctor_obj, CategoryTheory.Subfunctor.equalizer.lift_ι'_assoc, SSet.prodStdSimplex.objEquiv_apply_snd, CategoryTheory.PreGaloisCategory.functorToContAction_map, SSet.Subcomplex.unionProd.symmIso_hom, CategoryTheory.WithInitial.coconeEquiv_counitIso_inv_app_hom, Rep.coinvariantsTensorIndIso_hom, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₃, CategoryTheory.Equivalence.mapMon_unitIso, AlgebraicGeometry.PresheafedSpace.colimitCocone_ι_app_base, CategoryTheory.Monoidal.monFunctorCategoryEquivalence_functor, SSet.Subcomplex.instEpiToImage, CategoryTheory.Triangulated.TStructure.natTransTruncLEOfLE_ι, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinset_obj_map, CategoryTheory.Abelian.SpectralObject.homologyDataIdId_right_p, SSet.hoFunctor.unitHomEquiv_eq, commShiftOfLocalization.iso_inv_app, HomologicalComplex.mapBifunctor₁₂.ιOrZero_eq_zero, CategoryTheory.flipCompEvaluation_hom_app, SheafOfModules.restrictScalars_obj_val, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁'_obj_obj_obj, CategoryTheory.NatTrans.removeOp_id, LaxMonoidal.ofBifunctor.topMapₗ_app, CategoryTheory.ComposableArrows.whiskerLeftFunctor_obj_map, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom, instIsIsoAppLanUnit, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_naturality_right_assoc, CategoryTheory.Localization.lift₃NatIso_hom, CategoryTheory.WithInitial.mkCommaMorphism_left, CategoryTheory.Limits.coend.map_comp_assoc, CategoryTheory.sheafifyMap_id, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_inv_assoc, AlgebraicTopology.DoldKan.Γ₀_obj_map, CategoryTheory.instFaithfulMonFunctorOppositeMonCatYonedaMon, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_hom_app_hom_app, CategoryTheory.cosimplicialSimplicialEquiv_functor_obj_obj, instPreservesFiniteCoproductsSheafTypeUliftYonedaOfPreservesFiniteProductsOppositeObjFunctorIsSheaf, CategoryTheory.PreGaloisCategory.continuous_mapAut_whiskeringRight, SheafOfModules.instSmallElemForallObjCompModuleCatCarrierOppositeRingCatObjFunctorIsSheafPresheafOfModulesForgetEvaluationForgetLinearMapIdCarrierSections, AlgebraicGeometry.ExistsHomHomCompEqCompAux.exists_index, CategoryTheory.WithInitial.commaFromUnder_map_left, mapArrowFunctor_obj, Action.resId_inv_app_hom, CategoryTheory.NatTrans.instIsClosedUnderColimitsOfShapeUnderFunctorCoequifiberedHomDiscretePUnitOfHasProductsOfShapeHom, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_whiskerLeft_app, CategoryTheory.SimplicialObject.Augmented.const_map_left, CategoryTheory.simplicialCosimplicialEquiv_unitIso_hom_app, CategoryTheory.Adjunction.leftAdjointUniq_hom_app_counit, CategoryTheory.Abelian.SpectralObject.p_opcyclesToE, CategoryTheory.Triangulated.SpectralObject.triangle_obj₂, LeftExtension.postcompose₂ObjMkIso_inv_right_app, CategoryTheory.Monoidal.tensorUnit_obj, CategoryTheory.NatTrans.instCommShiftOppositeShiftHomFunctorNatIsoId, CommShift.comp_commShiftIso_inv_app, CategoryTheory.Abelian.SpectralObject.rightHomologyDataShortComplex_H, CategoryTheory.Limits.CompleteLattice.finiteColimitCocone_cocone_ι_app, AlgebraicTopology.DoldKan.N₁Γ₀_hom_app_f_f, CategoryTheory.Limits.sigmaFunctor_obj_map, SSet.Augmented.stdSimplex_obj_left, sheafPushforwardContinuousCompSheafToPresheafIso_inv_app_app, CategoryTheory.Mon.limit_mon_mul, CategoryTheory.MorphismProperty.Over.mapId_inv_app_left, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_left, CategoryTheory.Limits.colimitYonedaHomIsoLimit_π_apply, CategoryTheory.NatTrans.rightOpWhiskerRight, CategoryTheory.Limits.Cotrident.condition_assoc, Monoidal.transport_δ, CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_inv_π_π, CategoryTheory.CosimplicialObject.Augmented.whiskering_map_app_left, inlCompSum'_hom_app, SSet.instIsStableUnderCoproductsMonomorphismsOfHasCoproductsType, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w, CategoryTheory.ExponentiableMorphism.pushforwardId_hom_counit_assoc, CategoryTheory.GradedObject.ι_mapBifunctorRightUnitor_hom_apply, SSet.stdSimplex.σ_objMk₁_of_le, HomologicalComplex.instIsCorepresentableCompEvalObjOppositeFunctorTypeCoyonedaOp, CategoryTheory.Quotient.natTransLift_id, Rep.coinvariantsTensorIndNatIso_inv_app, CategoryTheory.Limits.walkingCospanOpEquiv_unitIso_inv_app, CategoryTheory.Join.mapPairComp_hom_app_right, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_hom, CategoryTheory.Abelian.SpectralObject.cyclesIsoH_inv_hom_id, CategoryTheory.bifunctorComp₁₂_map_app_app, CategoryTheory.prodFunctor_map, CategoryTheory.Limits.coconeUnopOfConeEquiv_counitIso, AlgebraicGeometry.StructureSheaf.isLocalizedModule_toPushforwardStalkAlgHom_aux, sumIsoExt_inv_app_inr, CategoryTheory.Presheaf.coherentExtensiveEquivalence_functor_obj_obj, AddCommGrpCat.binaryProductLimitCone_cone_π_app_left, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.faithful_ι, CategoryTheory.SimplicialObject.Augmented.const_obj_right, CategoryTheory.GrothendieckTopology.W_adj_unit_app, CategoryTheory.Sheaf.cartesianMonoidalCategorySnd_hom, CategoryTheory.Limits.CoconeMorphism.w_assoc, CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan_inj, CategoryTheory.comp_toNatTrans, CategoryTheory.Limits.coneOfCoconeLeftOp_π_app, CategoryTheory.MorphismProperty.presheaf_mono_of_le, CategoryTheory.Limits.LimitPresentation.reindex_π, CategoryTheory.SmallObject.SuccStruct.extendToSuccRestrictionLEIso_hom_app, CategoryTheory.Sheaf.instHasFunctorialFactorizationLocallySurjectiveLocallyInjective, OneHypercoverDenseData.essSurj.presheafObj_condition_assoc, CategoryTheory.Limits.coneOfCoconeUnop_π, AlgebraicGeometry.StructureSheaf.algebraMap_self_map, PresheafOfModules.limitCone_π_app_app, AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInfty_assoc, CategoryTheory.WithInitial.liftStar_lift_map, CategoryTheory.PreGaloisCategory.instPreservesIsConnectedActionFintypeCatAutFunctorFunctorToAction, CategoryTheory.additive_yonedaObj', CategoryTheory.MonoidalCategory.tensoringRight_δ, CategoryTheory.Idempotents.functorExtension_obj_obj, CategoryTheory.yonedaAddMonObjIsoOfRepresentableBy_inv_app_hom_apply, CategoryTheory.Iso.coreLeftUnitor, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.secondMap₂_app_app_app, CategoryTheory.Limits.Types.isLimitEquivSections_apply, CategoryTheory.GradedObject.ι_mapBifunctorBifunctor₂₃Desc, leftOpRightOpIso_hom_app, leftKanExtensionCompIsoOfPreserves_inv_fac_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_obj, ranCompIsoOfPreserves_inv_app, CategoryTheory.OverPresheafAux.counitForward_val_snd, CategoryTheory.Sheaf.isLocallySurjective_iff_epi', CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one_assoc, CategoryTheory.MonoidalOpposite.mopEquiv_unitIso, CategoryTheory.SimplicialObject.augmentOfIsTerminal_hom_app, CategoryTheory.Comma.mapLeftComp_inv_app_left, SSet.stdSimplex.faceSingletonIso_zero_hom_comp_ι_eq_δ_assoc, CategoryTheory.shiftFunctorComm_hom_app_comp_shift_shiftFunctorAdd_hom_app_assoc, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_star, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv_assoc, CategoryTheory.CosimplicialObject.Truncated.whiskering_map_app_app, CategoryTheory.Mat_.embeddingLiftIso_hom_app, CategoryTheory.Idempotents.instIsIdempotentCompleteSimplicialObject, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_map_fst_app, CategoryTheory.MorphismProperty.Comma.mapLeftIso_inverse_obj_hom, CategoryTheory.TwoSquare.isIso_lanBaseChange_app, CategoryTheory.Limits.CompleteLattice.colimitCocone_cocone_ι_app, CategoryTheory.ProjectiveResolution.extMk_hom, CategoryTheory.Subfunctor.equivalenceMonoOver_functor_map, CategoryTheory.NatTrans.rightDerived_comp, CategoryTheory.Projective.projective_iff_preservesEpimorphisms_coyoneda_obj, SheafOfModules.instAdditiveSheafAddCommGrpCatToSheaf, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_neg_assoc, instIsEquivalenceRightExtensionPostcomp₁OfIsIso, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_obj_X₃, CategoryTheory.Idempotents.DoldKan.equivalence_counitIso, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_whiskerLeft, shiftIso_add_hom_app, CategoryTheory.Under.liftCocone_ι_app, CategoryTheory.AdditiveFunctor.forget_obj_of, CategoryTheory.Bicategory.postcomposing₂_map_as_app_toNatTrans_app, mapMonNatIso_hom_app_hom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_app_fst_app, CategoryTheory.shiftFunctorAdd_inv_app_obj_of_induced, CategoryTheory.conjugateEquiv_symm_iso, OneHypercoverDenseData.essSurj.presheafObjObjIso_inv_naturality, HomologicalComplex.instHasMapProdObjGradedObjectFunctorMapBifunctorXMapBifunctorMapObjπ, mapTriangleIso_hom_app_hom₂, CondensedMod.epi_iff_surjective_on_stonean, CategoryTheory.Join.mapWhiskerLeft_whiskerRight_assoc, CategoryTheory.Limits.opParallelPairIso_hom_app_one, CategoryTheory.typeEquiv_unitIso_hom_app, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_hom_assoc, CategoryTheory.Equivalence.symmEquivFunctor_map, SSet.instFiniteObjOppositeSimplexCategoryTensorObj, Rep.instAdditiveModuleCatObjFunctorCoinvariantsTensor, CategoryTheory.Presheaf.instPreservesFiniteProductsOppositeObjFunctorIsSheafCoherentTopology, CategoryTheory.Limits.cospanCompIso_inv_app_left, mapTriangleCompIso_inv_app_hom₃, preservesZeroMorphisms_evaluation_obj, rightOpId_inv_app, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_inv_app_hom_app, CategoryTheory.faithful_preadditiveCoyoneda, CategoryTheory.WithInitial.inclLiftToInitial_inv_app, SSet.horn₃₁.desc.multicofork_π_two_assoc, CategoryTheory.TwistShiftData.shift_z_app, IsOpenMap.pullbackIso_inv_app_app, CategoryTheory.Ind.isIndObject_inclusion_obj, CategoryTheory.Limits.yonedaCompLimIsoCocones_hom_app_app, CategoryTheory.Abelian.SpectralObject.ιE_δFromOpcycles_assoc, SSet.ι₁_app_snd_apply, CategoryTheory.Over.starPullbackIsoStar_hom_app_left, CategoryTheory.Limits.PushoutCocone.ofCocone_ι, CategoryTheory.Over.postEquiv_inverse, CategoryTheory.TwoSquare.equivalenceJ_counitIso, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_obj_obj_map, AlgebraicTopology.DoldKan.Γ₂N₂ToKaroubiIso_hom_app, CategoryTheory.StructuredArrow.mapNatIso_unitIso_hom_app_right, CategoryTheory.Limits.coend.condition_assoc, rightDerivedNatTrans_comp, AlgebraicGeometry.Spec.map_appLE, postcompose₃_obj_obj_obj_obj_map, CategoryTheory.Pi.evalCompEqToEquivalenceFunctor_hom, CategoryTheory.Abelian.Ext.mapExactFunctor_hom, CategoryTheory.AdditiveFunctor.forget_obj, SSet.stdSimplex.objMk₁_injective, rightDerivedZeroIsoSelf_hom_inv_id, CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_hom_apply, CategoryTheory.Localization.whiskeringLeftFunctor'_eq, CategoryTheory.Limits.spanUnop_hom_app, CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_hom_apply, smoothSheafCommRing.ι_evalHom, CategoryTheory.shrinkYonedaObjObjEquiv_map_app_assoc, CategoryTheory.Adjunction.conjugateEquiv_leftAdjointIdIso_hom, CategoryTheory.Abelian.SpectralObject.isIso_toCycles, CategoryTheory.Subfunctor.ofSection_eq_range', CategoryTheory.simplicialCosimplicialEquiv_counitIso_hom_app_app, LightCondMod.LocallyConstant.instFullModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf, CategoryTheory.faithful_preadditiveYoneda, CategoryTheory.Yoneda.yoneda_faithful, CategoryTheory.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCocone_π_app_eq_sum, CategoryTheory.Sheaf.cartesianMonoidalCategorySnd_val, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.isIso_f, CategoryTheory.ComposableArrows.isoMk₄_hom, CategoryTheory.Limits.ι_colimitCompWhiskeringLeftIsoCompColimit_hom, mapTriangleCompIso_hom_app_hom₃, CategoryTheory.Limits.coneOfIsSplitMono_π_app, CategoryTheory.Sheaf.χ_hom, CategoryTheory.Limits.ι_comp_sigmaObjIso_hom, CategoryTheory.coreFunctor_obj_obj_of, CategoryTheory.Localization.Monoidal.map_hexagon_reverse, CategoryTheory.Limits.parallelPairIsoMk_hom_app, CategoryTheory.GradedObject.mapBifunctorObjSingle₀ObjIso_hom, CategoryTheory.Triangulated.Octahedron.map_m₃, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_inv_app_hom_app_hom_hom, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone_cocone_ι_app, CategoryTheory.NatTrans.CommShift.comp, CategoryTheory.Triangulated.TStructure.triangleω₁δ_map_hom₃, CategoryTheory.linearYoneda_map_app, CategoryTheory.SimplicialObject.augmentOfIsTerminal_left, CategoryTheory.Localization.faithful_whiskeringLeft, CategoryTheory.Join.isoMkFunctor_inv_app, isoWhiskerLeft_right, CategoryTheory.Sheaf.classifier_Ω, CategoryTheory.OverPresheafAux.yonedaCollectionFunctor_obj, CategoryTheory.Triangulated.TStructure.natTransTruncLTOfLE_refl, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_μ, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransId_inv_app_f, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_hom_app_app, PrincipalSeg.cocone_ι_app, CategoryTheory.Limits.end_.condition, SSet.horn.spineId_map_hornInclusion, CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_comp_assoc, CategoryTheory.WithTerminal.coneEquiv_functor_obj_π_app_of, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_map_app_snd, CategoryTheory.Paths.liftNatIso_hom_app, CategoryTheory.WithInitial.coconeEquiv_unitIso_hom_app_hom_right, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_right, CategoryTheory.Sheaf.instMonoAppArrowPLocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, SSet.instFiniteCoprod, CompHausLike.LocallyConstant.counit_app_hom_app, CategoryTheory.Localization.lift₂_iso_hom_app_app₂, CategoryTheory.Over.forgetMapTerminal_inv_app, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_hom_app, sheafAdjunctionCocontinuous_counit_app_hom, CategoryTheory.Limits.Concrete.isColimit_exists_rep, CategoryTheory.Pi.optionEquivalence_unitIso, CategoryTheory.MorphismProperty.Over.mapCongr_hom_app_left, shiftIso_add'_hom_app, SSet.horn₃₁.desc.multicofork_π_zero_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app, CategoryTheory.Join.mapIsoWhiskerRight_inv, Monoidal.transport_μ_assoc, CategoryTheory.endofunctorMonoidalCategory_whiskerRight_app, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app, CategoryTheory.Limits.spanExt_hom_app_zero, SSet.horn_obj, CategoryTheory.sectionsFunctorNatIsoCoyoneda_inv_app_coe, CategoryTheory.NatIso.op_isoWhiskerRight, CategoryTheory.instMonoFunctorOppositeHomFullSubcategoryIsSheafOfHasWeakSheafifyOfSheaf, CategoryTheory.Abelian.SpectralObject.shortComplexMap_id, ModuleCat.directLimitIsColimit_desc, CategoryTheory.BraidedCategory.ofBifunctor.Forward.secondMap₂_app_app_app, CategoryTheory.LeftExactFunctor.whiskeringLeft_obj_obj_obj, CategoryTheory.Abelian.SpectralObject.liftE_ιE_fromOpcycles, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_obj_obj_map, CondensedSet.epi_iff_surjective_on_stonean, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app, SSet.finite_of_isColimit, CategoryTheory.ShortComplex.SnakeInput.composableArrowsFunctor_map, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_inv_app_app, CategoryTheory.Limits.functorCategoryHasColimit, CategoryTheory.PreGaloisCategory.toAutHomeo_apply, CategoryTheory.FunctorToTypes.binaryCoproductCocone_pt_map, CategoryTheory.ULift.equivalence_unitIso_inv, CategoryTheory.ComposableArrows.opEquivalence_functor_obj_map, CategoryTheory.Subfunctor.homOfLe_ι_assoc, CategoryTheory.Presheaf.coherentExtensiveEquivalence_inverse_obj_obj, CategoryTheory.Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor, CategoryTheory.Subfunctor.homOfLe_ι, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_one_app, SSet.leftUnitor_inv_app_apply, CategoryTheory.NatTrans.naturality_app_app_assoc, CategoryTheory.TwoSquare.GuitartExact.vComp'_iff_of_equivalences, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₁, SSet.ι₀_fst_assoc, SSet.ι₁_comp, CategoryTheory.Subobject.inf_eq_map_pullback', CategoryTheory.Preadditive.commGrpEquivalenceAux_hom_app_hom_hom_hom, CategoryTheory.Presheaf.restrictedULiftYoneda_map_app, CategoryTheory.Abelian.LeftResolution.instEpiKaroubiAppπ', CategoryTheory.PreGaloisCategory.exists_set_ker_evaluation_subset_of_isOpen, SSet.Subcomplex.yonedaEquiv_coe, CategoryTheory.Sum.natTransOfWhiskerLeftInlInr_id, CategoryTheory.Abelian.SpectralObject.isZero_H_obj_mk₁_i₀_le, CategoryTheory.NatIso.prod_inv, CategoryTheory.hoFunctor.preservesFiniteProducts, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.ι_map_tensorHom_eq, CommShift.ofComp_compatibility, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan_inv_app_app_apply_eq_id, CategoryTheory.CosimplicialObject.Augmented.leftOp_left_map, CategoryTheory.Discrete.functorComp_hom_app, CategoryTheory.Localization.liftNatIso_inv, CategoryTheory.Limits.spanOp_inv_app, CategoryTheory.Presheaf.isSeparated_iff_subsingleton, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom, CategoryTheory.right_unitality_app_assoc, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_hom_app_hom_app, Action.functorCategoryEquivalence_functor, PresheafOfModules.instReflectsIsomorphismsSheafOfModulesSheafAddCommGrpCatToSheaf_1, CategoryTheory.GrothendieckTopology.toSheafify_comp_sheafifyCompIso_inv_assoc, LightCondensed.isColimitLocallyConstantPresheafDiagram_desc_apply, AlgebraicGeometry.StructureSheaf.IsLocalization.to_basicOpen, CategoryTheory.Equivalence.rightOp_unitIso_hom_app, CategoryTheory.Over.conePostIso_hom_app_hom, CategoryTheory.Join.pseudofunctorLeft_mapComp_inv_toNatTrans_app, SSet.OneTruncation₂.ofNerve₂.natIso_hom_app_obj, CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_cancel_hom_app, SSet.Subcomplex.homOfLE_ι_assoc, CategoryTheory.SheafOfTypes.finitary_extensive, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descAddMonoidHom_quotMk, CategoryTheory.Sheaf.instIsGrothendieckAbelian, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom, CategoryTheory.Limits.reflexivePair.compRightIso_hom_app, CategoryTheory.preservesLimits_preadditiveCoyoneda_obj, shiftIso_inv_naturality, OplaxMonoidal.ofBifunctor.secondMap₃_app_app_app, CategoryTheory.η_app_obj, IsCoverDense.restrictHomEquivHom_naturality_left_assoc, CategoryTheory.bifunctorComp₂₃Obj_obj_obj, CategoryTheory.MonoidalCategory.endofunctorMonoidalCategory.evaluationRightAction_actionHomRight, TopCat.Sheaf.objSupIsoProdEqLocus_hom_fst, TopCat.nonempty_isLimit_iff_eq_induced, leibnizPushout_obj_map, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_whiskerRight_app, CategoryTheory.linearYoneda_obj_obj_isAddCommGroup, CategoryTheory.Limits.ker.condition, CategoryTheory.MonoidalCategory.DayFunctor.equiv_counitIso_hom_app, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInrIso_inv_app_app, CategoryTheory.Limits.colimitLimitToLimitColimitCone_hom, CategoryTheory.NatIso.mapHomologicalComplex_hom_app_f, CategoryTheory.GrothendieckTopology.plusMap_plusLift, CategoryTheory.Sheaf.toImage_hom, CategoryTheory.isIso_iff_isIso_yoneda_map, isDenseAt_eq_isPointwiseLeftKanExtensionAt, RightExtension.coneAtFunctor_obj, CategoryTheory.Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor_assoc, CategoryTheory.MonoidalCategory.Limits.preservesCoLimit_curriedTensor, CategoryTheory.GrothendieckTopology.Point.skyscraperSheafAdjunction_homEquiv_symm_apply, whiskeringLeft₃ObjMap_app, CategoryTheory.MorphismProperty.instHasFunctorialFactorizationFunctorFunctorCategory, CategoryTheory.essImage_yonedaGrp, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_three, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃'_obj_obj_map, CategoryTheory.leftExactFunctor_le_additiveFunctor, mapBifunctorHomologicalComplexObj_obj_X_X, essImage.liftFunctorCompIso_hom_app, CategoryTheory.Sheaf.natTransΓRes_app, PushoutObjObj.mapArrowLeft_id, CategoryTheory.Limits.Cocone.precomposeComp_hom_app_hom, CategoryTheory.shiftFunctorAdd'_zero_add_inv_app, OneHypercoverDenseData.essSurj.presheafObjObjIso.hom_mapPreimage, CategoryTheory.cosimplicialSimplicialEquiv_inverse_obj, CategoryTheory.PreGaloisCategory.exists_lift_of_continuous, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_mapIso_mkNatIso_eq_mkIso, CategoryTheory.Limits.Multicofork.π_eq_app_right, CategoryTheory.Abelian.Preradical.instEpiFunctorColonπ, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_fst_map, CategoryTheory.Limits.instPreservesFiniteLimitsFunctorObjEvaluationOfHasFiniteLimits, curry₃ObjProdComp_hom_app_app_app, rightDerivedNatIso_hom, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality', whiskeringLeftObjIdIso_hom_app_app, CategoryTheory.Sheaf.image_obj, CategoryTheory.BraidedCategory.curriedBraidingNatIso_hom_app_app, CategoryTheory.equivYoneda'_hom_hom, CategoryTheory.Limits.Cocone.functoriality_map_hom, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_uliftYoneda_map, OplaxMonoidal.ofBifunctor.secondMap_app_app_app, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap_assoc, CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_snd_apply, CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_hom_app, mapMonNatIso_inv_app_hom, CategoryTheory.Adjunction.shift_counit_app, CategoryTheory.SimplicialObject.isoCoskOfIsCoskeletal_hom, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso_hom_app_hom_hom_app, CategoryTheory.Limits.Cone.ofPullbackCone_π, CategoryTheory.FunctorToTypes.coprod.desc_inl, LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom, map_shift_unop, CategoryTheory.NatTrans.toCatHom₂_id, SSet.prod_map_fst, CategoryTheory.PreGaloisCategory.toAut_surjective_isGalois, CategoryTheory.GradedObject.ι_mapBifunctorComp₂₃MapObjIso_hom, CategoryTheory.Adjunction.Quadruple.epi_leftTriple_rightToLeft_iff_mono_rightTriple_leftToRight, CategoryTheory.Presieve.FamilyOfElements.Compatible.functorPushforward, IsCoverDense.presheafIso_hom_app, AlgebraicGeometry.exists_appTop_π_eq_of_isAffine_of_isLimit, CategoryTheory.Abelian.Preradical.toColon_hom_left_colonπ_assoc, CategoryTheory.Limits.ConeMorphism.map_w, CategoryTheory.FunctorToTypes.binaryProductEquiv_symm_apply, SheafOfModules.Presentation.quasicoherentData_presentation, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_counitIso, TopCat.Presheaf.app_surjective_of_injective_of_locally_surjective, CategoryTheory.sheafifyMap_sheafifyLift, CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_base, CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_inv_app, CategoryTheory.SmallObject.succStruct_prop_le_propArrow, SSet.Truncated.id_app, CategoryTheory.GradedObject.comapEquiv_unitIso, CategoryTheory.curryingIso_inv_toFunctor_obj_map_app, CategoryTheory.Limits.pointwiseBinaryBiproductData_isBilimit, CategoryTheory.Triangulated.TStructure.instIsGEObjEIntFunctorETruncGE, CategoryTheory.Adjunction.leftAdjointUniq_trans_assoc, CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcyclesEIso_hom_τ₃, ihom_map, mapCommMonFunctor_map_app, AlgebraicGeometry.StructureSheaf.const_mul_cancel, HomologicalComplex.mapBifunctor₂₃.ι_D₁, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_app, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_map_τ₁, CategoryTheory.Limits.ColimitPresentation.self_diag, CategoryTheory.Adjunction.map_restrictFullyFaithful_counit_app_assoc, CategoryTheory.Iso.inv_hom_id_app_app, CategoryTheory.endofunctorMonoidalCategory_tensorMap_app, CategoryTheory.Discrete.productEquiv_counitIso_hom_app, CategoryTheory.instHasExactColimitsOfShapeFunctorOfHasFiniteLimits, IsDenseSubsite.sheafifyHomEquivOfIsEquivalence_naturality_left, CategoryTheory.Limits.limit.isoLimitCone_hom_π, CategoryTheory.Abelian.SpectralObject.isZero₁_of_isFirstQuadrant, CategoryTheory.Limits.LimitPresentation.ofIso_π, LeftExtension.postcompose₂_map_right_app, CategoryTheory.typeEquiv_counitIso_hom_app_hom_app, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.mk₀_f_comp_biprodAddEquiv_symm_biprodIsoProd_hom, CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatIso_hom, SSet.whiskerRight_app_apply, CategoryTheory.Triangulated.TStructure.eTruncGEπ_top, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functor_obj, HomologicalComplex.mapBifunctor₂₃.ι_mapBifunctor₂₃Desc_assoc, IsDenseSubsite.mapPreimage_comp_map, CategoryTheory.δ_app, instIsRepresentableCompOppositeOpObjTypeYonedaObjRightAdjointObjIsDefined, CategoryTheory.Limits.pullbackConeOfRightIso_π_app_right, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_map_app_app, CategoryTheory.Presheaf.functorToRepresentables_obj, CategoryTheory.SpectralSequence.pageHomologyNatIso_hom_app, CategoryTheory.Join.mapIsoWhiskerRight_hom_app, CategoryTheory.PreGaloisCategory.instIsPretransitiveAutObjFiniteVFintypeCatFunctorObjActionFunctorToActionOfIsGalois, CategoryTheory.PreGaloisCategory.toAutMulEquiv_apply, CategoryTheory.Idempotents.app_p_comp_assoc, CategoryTheory.Equivalence.CommShift.instCommShiftHomFunctorCounitIso, final_const_of_isTerminal, CategoryTheory.Limits.Fork.ofι_π_app, CategoryTheory.Equivalence.congrLeft_functor, Monoidal.whiskeringLeft_ε_app, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_iso_inv_app, CategoryTheory.ComposableArrows.δ₀Functor_obj_map, CategoryTheory.ULift.equivalence_counitIso_hom_app, CategoryTheory.Ind.exists_nonempty_arrow_mk_iso_ind_lim, CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcycles_X₂, op_commShiftIso_hom_app_assoc, CategoryTheory.Monad.monadToMon_map_hom, CategoryTheory.Limits.preservesLimitsOfShape_colim_grothendieck, CategoryTheory.WithInitial.mkCommaObject_hom_app, FullyFaithful.compYonedaCompWhiskeringLeftMaxRight_inv_app_app, SSet.Subcomplex.unionProd.ι₂_ι, CategoryTheory.instLocallySmallFullSubcategoryFunctorOppositeTypeIsIndObject, SSet.rightUnitor_inv_app_apply, CategoryTheory.pullbackShiftFunctorZero'_hom_app, CategoryTheory.yoneda_obj_obj, CategoryTheory.GrothendieckTopology.Point.toPresheafFiberMap_w, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_inv_app, CategoryTheory.uliftYonedaEquiv_comp, CategoryTheory.CostructuredArrow.map_map_right, SSet.stdSimplex.face_obj, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app_assoc, CategoryTheory.Limits.IsLimit.hom_lift, SheafOfModules.pushforwardCongr_hom_app_val_app, SSet.stdSimplex.nonDegenerateEquiv_apply_apply, CategoryTheory.Abelian.SpectralObject.kernelSequenceCyclesE_g, CategoryTheory.Limits.coconePointwiseProduct_ι_app, CategoryTheory.ExactFunctor.whiskeringLeft_map_app, SSet.Truncated.HomotopyCategory.BinaryProduct.left_unitality, CategoryTheory.Monoidal.tensorObj_obj, CategoryTheory.μ_naturality, CategoryTheory.FinitaryExtensive.mono_inr_of_isColimit, CategoryTheory.GrothendieckTopology.Point.presheafFiberMapCocone_pt, sectionsEquivHom_naturality, CategoryTheory.sheafifyLift_id_toSheafify, SSet.modelCategoryQuillen.horn_ι_mem_J, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_leftUnitor, CategoryTheory.hoFunctor.isIso_prodComparison_of_stdSimplex, CategoryTheory.Limits.PullbackCone.mk_π_app_right, CategoryTheory.Limits.Cofork.op_π_app_zero, ModuleCat.restrictScalarsCongr_hom_app, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.instIsIsoAppIncl, CategoryTheory.Limits.DiagramOfCones.mkOfHasLimits_map_hom, CategoryTheory.pullbackShiftFunctorZero_hom_app, CategoryTheory.GrothendieckTopology.Point.presheafFiberOfIsCofilteredCocone_pt, CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_obj_right_as, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerLeft_assoc, CategoryTheory.Presheaf.freeYoneda_map, CategoryTheory.GrothendieckTopology.pointBotFunctor_map_hom, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.inverseObj_comon_counit_app, CategoryTheory.Limits.instHasCofilteredLimitsOfSizeFunctor, PresheafOfModules.pullback_assoc, TopologicalSpace.Opens.mapIso_inv_app, CategoryTheory.Limits.opSpan_hom_app, CategoryTheory.PreGaloisCategory.toAut_isHomeomorph, groupHomology.isoShortComplexH1_hom, CategoryTheory.GrothendieckTopology.Point.instIsIsoδFunctorOppositePresheafFiber, CategoryTheory.GrothendieckTopology.instIsIsoFunctorOppositeSheafSheafComposeNatTransPlusPlusAdjunction, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃'_obj_map_app, CategoryTheory.obj_zero_map_μ_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionActionOfMonoidalFunctorToEndofunctorMopIso_inv_app_unmop_app, CategoryTheory.Iso.compInverseIso_inv_app, CategoryTheory.Limits.CatCospanTransform.isIso_base, CategoryTheory.ComposableArrows.isoMkSucc_inv, CategoryTheory.Adjunction.restrictFullyFaithful_homEquiv_apply, CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_hom, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac, CategoryTheory.curryingIso_hom_toFunctor_obj_obj, SSet.stdSimplex.map_apply, CategoryTheory.CatCenter.smul_iso_hom_eq'_assoc, CategoryTheory.instIsMonoidalFunctorCongrLeft, CategoryTheory.Limits.piObjIso_inv_comp_π, CategoryTheory.GrothendieckTopology.overMapPullback_assoc_assoc, rightDerivedZeroIsoSelf_hom_inv_id_app, CategoryTheory.Abelian.SpectralObject.fromOpcyles_δ_assoc, CategoryTheory.Limits.ColimitPresentation.Total.Hom.w, CategoryTheory.Limits.coneOfConeCurry_π_app, HomologicalComplex.mapBifunctorAssociatorX_hom_D₃_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_snd_obj, CategoryTheory.Sheaf.isSheaf_of_isLimit, AlgebraicTopology.AlternatingFaceMapComplex.ε_app_f_zero, Monoidal.whiskeringLeft_μ_app, ContAction.resCongr_hom, CategoryTheory.Comma.equivProd_unitIso_hom_app_right, CategoryTheory.Equivalence.sheafCongr.unitIso_hom_app_hom_app, CategoryTheory.DifferentialObject.shiftZero_inv_app_f, CategoryTheory.whiskering_linearYoneda, TopCat.Presheaf.presheafEquivOfIso_unitIso_hom_app_app, zero_obj, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom, mapCochainComplexPlusCompι_inv_app_f, CategoryTheory.TwoSquare.GuitartExact.whiskerVertical_iff, CategoryTheory.conjugateEquiv_whiskerRight, isLeftDerivedFunctor_iff_of_inverts, CategoryTheory.NatTrans.op_whiskerRight, CategoryTheory.Abelian.Preradical.ι_π, CategoryTheory.Discrete.sumEquiv_unitIso_hom_app, mapTriangle_map_hom₁, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι, CategoryTheory.BraidedCategory.ofBifunctor.Forward.secondMap₁_app_app_app, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.inverse_map_app, CategoryTheory.Sheaf.cartesianMonoidalCategoryWhiskerLeft_hom, CategoryTheory.FunctorToTypes.rightAdj_map_app, CategoryTheory.Enriched.Functor.associator_hom_apply, mapAddMonCompIso_inv_app_hom, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_inv_π_π, AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, CategoryTheory.GrothendieckTopology.Point.tensorHom_comp_toPresheafFiber_μ, CategoryTheory.Monad.algebraFunctorOfMonadHomEq_inv_app_f, CategoryTheory.NatTrans.CommShiftCore.shift_app, CategoryTheory.Triangulated.TStructure.natTransTruncLEOfLE_trans, sheafPushforwardContinuousId_hom_app_hom_app, homObjFunctor_map_app, SSet.ι₀_snd, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy₂'_homEquiv, CategoryTheory.SingleFunctors.isoMk_inv_hom, CategoryTheory.Abelian.SpectralObject.cokernelSequenceCycles_X₂, whiskeringLeft₃_obj_obj_obj_obj_obj_obj_obj, PartOrdEmb.Limits.cocone_ι_app, CategoryTheory.Limits.DiagramOfCocones.mkOfHasColimits_obj, CategoryTheory.Sheaf.instHasFiniteColimits, CategoryTheory.Limits.Types.limitCone_π_app, CategoryTheory.CatCommSq.vInv_iso_hom_app, ShiftSequence.induced_shiftIso_hom_app_obj, CategoryTheory.sheafToPresheaf_δ, CategoryTheory.Limits.lim_ε_π_assoc, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.inverseObj_X, SSet.Truncated.Edge.CompStruct.tensor_simplex_fst, CategoryTheory.Sheaf.Hom.mono_iff_presheaf_mono, CategoryTheory.Adjunction.whiskerRight_counit_iso_of_L_fully_faithful, CategoryTheory.Sum.natIsoOfWhiskerLeftInlInr_eq, CategoryTheory.NatTrans.shift_comm, SSet.PtSimplex.MulStruct.δ_succ_castSucc_map, ranCompIsoOfPreserves_hom_app, CategoryTheory.Abelian.SpectralObject.sc₂_g, CategoryTheory.Limits.PushoutCocone.condition_zero, LightCondensed.instPreservesEpimorphismsFunctorDiscreteNatLightCondModLim, TopCat.Sheaf.existsUnique_gluing, SSet.Homotopy.h₀, CategoryTheory.Abelian.SpectralObject.cyclesIsoH_inv_hom_id_assoc, CategoryTheory.Enriched.FunctorCategory.homEquiv_comp, CategoryTheory.whiskeringRightCompEvaluation_inv_app, associator_inv_app, RightExtension.postcomp₁_obj_left_obj, CategoryTheory.Limits.whiskeringLimYonedaIsoCones_inv_app_app, CategoryTheory.whiskering_linearCoyoneda₂, instCommShiftCochainComplexIntDerivedCategoryHomMapDerivedCategoryFactors, CategoryTheory.ObjectProperty.SerreClassLocalization.instFaithfulExactFunctorWhiskeringLeft, CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp, CategoryTheory.Limits.Cone.whiskeringEquivalence_unitIso, CategoryTheory.LocalizerMorphism.homMap_apply, CategoryTheory.Hom.addEquivCongrRight_symm_apply, CategoryTheory.CostructuredArrow.mapNatIso_functor_obj_hom, CategoryTheory.typeEquiv_unitIso_inv_app, functorialityCompPrecompose_hom_app_hom, CategoryTheory.NatTrans.unop_whiskerRight, CategoryTheory.Subfunctor.lift_ι, CategoryTheory.Limits.Cone.postcompose_obj_π, CategoryTheory.Over.mapId_inv_app_left, AlgebraicGeometry.AffineSpace.functor_obj_map, CategoryTheory.hoFunctor.instIsLeftAdjointSSetCatHoFunctor, CategoryTheory.Triangulated.TStructure.instIsIsoFunctorETruncLTιTopEInt, CategoryTheory.NatTrans.op_comp_assoc, CategoryTheory.Limits.endFunctor_obj, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left_assoc, CategoryTheory.Sigma.natIso_inv, CategoryTheory.Limits.FormalCoproduct.cechIsoCechNerve_inv_app, CategoryTheory.GrothendieckTopology.Cover.multicospanComp_inv_app, CategoryTheory.Abelian.SpectralObject.toCycles_Ψ_assoc, CategoryTheory.MorphismProperty.Over.pullbackComp_inv_app_left, CategoryTheory.Comma.mapRightIso_functor_obj_hom, CategoryTheory.Limits.Cone.toStructuredArrowCone_π_app, isoWhiskerRight_left_assoc, TwoP.swapEquiv_unitIso_hom_app_hom_toFun, CategoryTheory.Adjunction.instIsIsoFunctorUnitOfIsEquivalence_1, flipping_counitIso_hom_app_app_app, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_inv_app, leftDerivedNatTrans_comp, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_map_snd_app, CategoryTheory.Comma.toIdPUnitEquiv_unitIso_inv_app_right, CategoryTheory.Limits.pointwiseCocone_pt, CategoryTheory.Abelian.SpectralObject.isZero₁_of_isThirdQuadrant, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_inv_app_app, Condensed.isColimitLocallyConstantPresheaf_desc_apply, isoWhiskerRight_twice, leftOpRightOpEquiv_functor_obj_obj, CategoryTheory.Limits.colimitCoyonedaHomIsoLimitUnop_π_apply, CategoryTheory.shiftFunctorZero_hom_app_obj_of_induced, SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_inv_app, CompHausLike.LocallyConstant.functorToPresheaves_map_app, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_hom_app, CategoryTheory.Comma.toPUnitIdEquiv_unitIso_inv_app_left, CategoryTheory.Equivalence.congrRight_functor, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_right, instIsEquivalenceLeftExtensionPostcomp₁OfIsIso, CategoryTheory.isRegularEpiCategory_sheaf, Profinite.instEpiAppDiscreteQuotientCarrierToTopTotallyDisconnectedSpaceπAsLimitCone, CategoryTheory.TransfiniteCompositionOfShape.fac, CategoryTheory.PreGaloisCategory.exists_lift_of_mono_of_isConnected, isIso_ranAdjunction_unit_app_iff, CategoryTheory.SimplicialObject.instHasLimitsOfShape, CategoryTheory.FunctorToTypes.rightAdj_map_app_app, CategoryTheory.LeftExactFunctor.ofExact_map_hom, CategoryTheory.ObjectProperty.SerreClassLocalization.whiskeringLeft_obj_obj, CategoryTheory.Join.mkFunctorLeft_hom_app, curryingEquiv_apply_obj, CategoryTheory.GrothendieckTopology.uliftYonedaCompSheafToPresheaf_inv_app_app, CategoryTheory.CostructuredArrow.CreatesConnected.natTransInCostructuredArrow_app, CategoryTheory.Adjunction.comp_counit, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans, CategoryTheory.Limits.multispanIndexCoend_snd, CategoryTheory.CatCommSq.iso_hom_naturality, CategoryTheory.NatIso.op_symm, CategoryTheory.Sieve.sieveOfUliftSubfunctor_apply, CategoryTheory.yonedaEquiv_yoneda_map, CategoryTheory.Limits.Cocone.toStructuredArrow_obj, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_inv_app_unmop, CategoryTheory.Cat.exp_map, SSet.RelativeMorphism.botEquiv_apply, CategoryTheory.Limits.FormalCoproduct.eval_obj_map, CategoryTheory.Equivalence.changeFunctor_counitIso_hom_app, CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_app_fac'_assoc, CategoryTheory.Abelian.SpectralObject.H_map_twoδ₂Toδ₁_toCycles, CategoryTheory.Subfunctor.equivalenceMonoOver_inverse_obj, CategoryTheory.Localization.Monoidal.map_hexagon_reverse_assoc, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_snd_obj, CommMonCat.coyonedaType_obj_obj_coe, CategoryTheory.CatCenter.mul_app_assoc, LeftExtension.postcompose₂_obj_hom_app, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerLeftIso_hom_app, CategoryTheory.Limits.instPreservesWellOrderContinuousOfShapeFunctorObjEvaluationOfHasIterationOfShape, whiskeringRight₂_obj_obj_obj_obj, CategoryTheory.Limits.CatCospanTransform.category_comp_left, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s₀_comp_δ₁_assoc, CategoryTheory.GlueData.diagramIso_inv_app_left, CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc, pentagonIso, CategoryTheory.Equivalence.refl_counitIso, CategoryTheory.Iso.map_inv_hom_id_app, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app_assoc, CategoryTheory.Subfunctor.Subpresheaf.image_comp, CategoryTheory.WithInitial.liftFromUnder_obj_obj, CategoryTheory.Limits.colim_map, CategoryTheory.Iso.hom_inv_id_app, CategoryTheory.Iso.app_hom, CategoryTheory.Limits.HasLimit.isoOfEquivalence_hom_π, CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_app_fac_assoc, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_counitIso, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π, CategoryTheory.Limits.limitConstTerminal_inv_π, CategoryTheory.NatIso.naturality_1_assoc, CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_hom, CategoryTheory.unit_conjugateEquiv_symm, CategoryTheory.Adjunction.mapMon_counit, CategoryTheory.GrothendieckTopology.Point.Hom.sheafFiber_comp, CategoryTheory.shrinkYonedaMon_obj, AlgebraicTopology.inclusionOfMooreComplex_app, CategoryTheory.IsPushout.of_isColimit_binaryCofan_of_isInitial, CategoryTheory.preservesLimitNatIso_inv_app, shiftIso_zero, PresheafOfModules.sheafification_map, CategoryTheory.Limits.opCompYonedaSectionsEquiv_apply_app, CategoryTheory.Pretriangulated.preadditiveYoneda_homologySequenceδ_apply, instFaithfulProdUncurry, AlgebraicTopology.DoldKan.Γ₂_obj_X_map, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_unitIso_hom_app_hom_app, NatTrans.hcomp_eq_whiskerLeft_comp_whiskerRight, Action.instIsEquivalenceFunctorSingleObjFunctor, CategoryTheory.toPresheafToSheafCompComposeAndSheafify_app, SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁_inv_f_f, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_map_hom, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp_assoc, CategoryTheory.Limits.BinaryFan.rightUnitor_inv, CategoryTheory.Subfunctor.Subpresheaf.range_comp, TopCat.Presheaf.stalk_mono_of_mono, SSet.Subcomplex.image_comp, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app_assoc, SSet.Truncated.Edge.map_associator_hom, mapMonFunctor_obj, CategoryTheory.Triangulated.TStructure.eTruncLT_obj_coe, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_inverse, HomologicalComplex.mapBifunctor.d₂_eq, CategoryTheory.SimplicialObject.augment_right, CategoryTheory.Limits.isIndObject_iff, whiskeringLeft₃_obj_obj_map_app_app_app_app, MulEquiv.toSingleObjEquiv_counitIso_hom, CategoryTheory.unit_conjugateEquiv, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_ι_inv_assoc, SSet.stdSimplex.yonedaEquiv_symm_app_objEquiv_symm, CategoryTheory.NatIso.trans_app, CategoryTheory.SimplicialObject.augment_hom_zero, CategoryTheory.Limits.PullbackCone.mk_π_app_one, CategoryTheory.isSeparator_iff_faithful_coyoneda_obj, CategoryTheory.GradedObject.mapBifunctorObjSingle₀ObjIso_inv, CategoryTheory.Iso.coreAssociator, mapGrpNatIso_hom_app_hom_hom, CategoryTheory.NatTrans.rightDerivedToHomotopyCategory_comp_assoc, CategoryTheory.Limits.BinaryCofan.isColimit_iff_isIso_inl, CategoryTheory.Under.postEquiv_counitIso, CategoryTheory.MonoidalSingleObj.endMonoidalStarFunctorEquivalence_unitIso, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone_ι_app, whiskeringLeft₃Map_app_app, CategoryTheory.Adjunction.toEquivalence_unitIso_hom_app, TopCat.Presheaf.app_surjective_of_stalkFunctor_map_bijective, CategoryTheory.Sieve.uliftNatTransOfLe_comm, CategoryTheory.Abelian.SpectralObject.δToCycles_πE_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionActionOfMonoidalFunctorToEndofunctorIso_hom_app_app, SSet.horn₂₀.sq, CategoryTheory.ShortComplex.mapNatIso_hom, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_left, CategoryTheory.TransfiniteCompositionOfShape.map_isColimit, CategoryTheory.Join.mapWhiskerLeft_associator_hom, CategoryTheory.uliftYoneda_obj_map, LeibnizAdjunction.adj_counit_app_right, TopCat.Sheaf.interUnionPullbackConeLift_right, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_inv_app_app, LightProfinite.Extend.functor_map, CategoryTheory.instPreservesFiniteProductsFunctorColimOfPreadditive, CategoryTheory.Enriched.FunctorCategory.homEquiv_id, CategoryTheory.Limits.CompleteLattice.limitCone_isLimit_lift, CategoryTheory.Abelian.SpectralObject.sc₁_X₁, CategoryTheory.Presheaf.final_toCostructuredArrow_comp_pre, CategoryTheory.ComposableArrows.whiskerLeftFunctor_obj_obj, CategoryTheory.Limits.PushoutCocone.ι_app_left, HomologicalComplex.ι_mapBifunctorFlipIso_inv_assoc, CategoryTheory.GrothendieckTopology.uliftYonedaCompSheafToPresheaf_hom_app_app, CompHausLike.LocallyConstant.functor_map_hom, CategoryTheory.instPreservesFiniteLimitsFunctorOppositeSheafLeftAdjointSheafToPresheaf, mapTriangleRotateIso_hom_app_hom₂, SheafOfModules.pullback_comp_id, CategoryTheory.yoneda_preservesLimitsOfShape, CategoryTheory.GradedObject.mapTrifunctorMap_map_app_app, CategoryTheory.Over.conePost_map_hom, CategoryTheory.piEquivalenceFunctorDiscrete_unitIso, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedAction_obj_map, CategoryTheory.Under.postComp_hom_app_right, SSet.horn₃₂.exists_desc, CategoryTheory.ComposableArrows.opEquivalence_functor_map_app, CategoryTheory.shiftFunctorAdd'_add_zero_inv_app, CategoryTheory.FunctorToTypes.binaryProductIso_hom_comp_snd, HomologicalComplex.mapBifunctor.d₁_eq_zero, mapGrpFunctor_map_app, mapCommMonCompIso_inv_app_hom_hom, CategoryTheory.GrothendieckTopology.map_yonedaEquiv', CategoryTheory.GrothendieckTopology.W_inverseImage_whiskeringLeft, CategoryTheory.Limits.colimit_obj_ext_iff, CategoryTheory.Adjunction.Triple.rightToLeft_eq_counits, CategoryTheory.sheafBotEquivalence_unitIso, CategoryTheory.bifunctorComp₁₂Functor_map, CategoryTheory.FreeMonoidalCategory.tensorFunc_map_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_right_unitality, CategoryTheory.WithTerminal.mkCommaObject_left_map, CategoryTheory.PreGaloisCategory.instIsFundamentalGroupAutFunctorFintypeCat, rightDerivedZeroIsoSelf_hom_inv_id_app_assoc, CategoryTheory.Sieve.natTransOfLe_comm, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τl, curry₃_obj_obj_obj_map, SSet.stdSimplex.mem_face_iff, CategoryTheory.SimplicialObject.Augmented.rightOp_right_map, CategoryTheory.Subfunctor.preimage_id, AlgebraicGeometry.StructureSheaf.const_one, SSet.hoFunctor.preservesTerminal, SSet.Truncated.rightExtensionInclusion_right_as, mapComposableArrowsObjMk₂Iso_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.LocalizerMorphism.commShift_iso_hom_app_assoc, CategoryTheory.WithInitial.coconeEquiv_functor_map_hom, flip₂₃Functor_obj_obj_obj_map, CategoryTheory.NatTrans.op_whiskerLeft_assoc, CategoryTheory.Equivalence.unop_counitIso, CategoryTheory.Monoidal.rightUnitor_inv_app, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_right, CategoryTheory.FinitaryPreExtensive.hasPullbacks_of_is_coproduct, RightExtension.coneAtWhiskerRightIso_inv_hom, CategoryTheory.eHomFunctor_map_app, CategoryTheory.instHasExactLimitsOfShapeFunctorOfHasFiniteColimits, CategoryTheory.Idempotents.DoldKan.equivalence_inverse, CategoryTheory.EnrichedCat.comp_whiskerRight, HomotopyCategory.instFullFunctorHomologicalComplexObjWhiskeringLeftQuotient, CategoryTheory.Comma.mapLeftIso_unitIso_inv_app_right, AlgebraicGeometry.StructureSheaf.globalSectionsIso_hom, shiftIso_add, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInlIso_hom_app_app, CategoryTheory.SimplicialThickening.functor_map, CategoryTheory.WithTerminal.ofCommaMorphism_app, SheafOfModules.instPreservesFiniteLimitsFunctorOppositeAddCommGrpCatCompSheafToSheafSheafToPresheaf, CategoryTheory.Over.lift_obj, CategoryTheory.uliftYoneda_obj_obj, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_inv_app_left, CategoryTheory.OverPresheafAux.counitAuxAux_inv, pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, LeftExtension.postcomp₁_obj_hom_app, CategoryTheory.ComposableArrows.sc'MapIso_hom, mapCommMonIdIso_hom_app_hom_hom, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_δ_assoc, whiskerLeft_comp, CategoryTheory.Abelian.SpectralObject.cokernelSequenceCycles_f, TopologicalSpace.Opens.overEquivalence_unitIso_hom_app_left, SSet.stdSimplex.coe_edge_down_toOrderHom, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.section_app_comp_hom_app, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_left, CategoryTheory.Iso.inv_hom_id_app_app_app, CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod_fac₂, CategoryTheory.ExactFunctor.whiskeringLeft_obj_obj_obj, CategoryTheory.WithTerminal.liftToTerminalUnique_inv_app, IsDenseSubsite.sheafifyHomEquivOfIsEquivalence_naturality_right, CategoryTheory.ComposableArrows.opEquivalence_inverse_obj, flippingEquiv_symm_apply_map_app, CategoryTheory.Limits.Fork.ofCone_π, CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_left, CategoryTheory.Monoidal.commMonFunctorCategoryEquivalence_counitIso, CategoryTheory.Limits.preservesLimit_of_evaluation, CategoryTheory.Equivalence.mapCommGrp_unitIso, HomologicalComplex.mapBifunctor₂₃.ι_D₂, AlgebraicTopology.DoldKan.N₂Γ₂_inv_app_f_f, SSet.Subcomplex.unionProd.ι₁_ι, CategoryTheory.Limits.CompleteLattice.finiteLimitCone_isLimit_lift, CategoryTheory.WithTerminal.mapComp_inv_app, SimplexCategory.toTopHomeo_symm_naturality_apply, SSet.stdSimplex.faceSingletonIso_one_hom_comp_ι_eq_δ, CategoryTheory.Equivalence.invFunIdAssoc_hom_app, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_X, CategoryTheory.Limits.Cocone.precomposeId_hom_app_hom, CategoryTheory.WithTerminal.mkCommaMorphism_right, rightKanExtension_hom_ext_iff, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.functor_map_hom_app, commShiftPullback_iso_eq, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinset_obj_map, CategoryTheory.Limits.DiagramOfCocones.comp, SSet.instIsStableUnderCobaseChangeMonomorphisms, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.functorObjObj_comon_counit, ContinuousCohomology.MultiInd.d_comp_d_assoc, Action.FunctorCategoryEquivalence.inverse_obj_ρ_apply, CategoryTheory.yonedaMon_map_app, CategoryTheory.Limits.pullbackConeEquivBinaryFan_inverse_obj, CategoryTheory.Abelian.SpectralObject.zero₂, CategoryTheory.SimplicialObject.Homotopy.precomp_h, CategoryTheory.shrinkYonedaEquiv_naturality, CategoryTheory.Limits.Cone.postcomposeEquivalence_counitIso, CategoryTheory.instPreservesLimitsOfShapeFunctorIndLimOfFinCategoryOfHasLimitsOfShape, CategoryTheory.Triangulated.TStructure.natTransTruncGEOfLE_refl, CategoryTheory.Equivalence.unitIso_hom_app_comp_inverse_map_η_functor, CategoryTheory.CostructuredArrow.mapIso_counitIso_hom_app_left, LightCondensed.isoLocallyConstantOfIsColimit_inv, fullyFaithfulCancelRight_hom_app, CategoryTheory.ExactFunctor.whiskeringLeft_obj_map, CategoryTheory.GrothendieckTopology.plusFunctorWhiskerRightIso_inv_app, HomotopyCategory.composableArrowsFunctor_obj, whiskeringLeft₃_obj_map_app_app_app_app_app, opUnopEquiv_functor, AlgebraicGeometry.exists_preimage_eq, AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInfty, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_zero_apply, CategoryTheory.Triangulated.TStructure.eTruncLTLTIsoLT_hom_inv_id_app, CategoryTheory.Limits.IsIndObject.finallySmall, CategoryTheory.GrothendieckTopology.toPlus_comp_plusCompIso_inv, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.right_triangle_components, CategoryTheory.Enriched.FunctorCategory.functorEnriched_id_comp, CategoryTheory.Limits.coprod.functor_map_app, CategoryTheory.Iso.compInverseIso_hom_app, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_hom_app_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_inv_app_fst_app, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_hom_assoc, CategoryTheory.yonedaEquiv_naturality', Condensed.comp_val, CategoryTheory.Idempotents.karoubiFunctorCategoryEmbedding_obj, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_hom_app_snd_app, instIsRepresentableObjOppositeTypeYoneda, CategoryTheory.WithInitial.equivComma_functor_map_left, AlgebraicGeometry.ΓSpec.left_triangle, CategoryTheory.FunctorToTypes.prod.lift_fst, CategoryTheory.Subfunctor.eq_top_iff_isIso, mapCommGrpNatIso_inv_app_hom_hom_hom, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app_assoc, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_add_apply, CategoryTheory.Adjunction.toEquivalence_counitIso_inv_app, pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac, CategoryTheory.OverPresheafAux.restrictedYonedaObj_map, CategoryTheory.Triangulated.TStructure.spectralObjectFunctor_map_hom, CategoryTheory.Enriched.Functor.whiskerRight_app_apply, CategoryTheory.Limits.colimitIsoSwapCompColim_inv_app, CondensedMod.hom_naturality_apply, CategoryTheory.Localization.full_whiskeringLeft, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_pt_left_as, SimplexCategory.revCompRevIso_inv_app, CategoryTheory.isDetector_iff_reflectsIsomorphisms_coyoneda_obj, CategoryTheory.Equivalence.changeFunctor_refl, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app, CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj_inv_app, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_functor_obj, CategoryTheory.Adjunction.toEquivalence_unitIso_inv_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_hom_app_fst_app, SSet.ι₁_snd_assoc, SimplicialObject.Splitting.ofIso_isColimit', PresheafOfModules.toSheaf_map_sheafificationHomEquiv_symm, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₂, CategoryTheory.Limits.walkingSpanOpEquiv_counitIso_hom_app, postcomposeWhiskerLeftMapCone_inv_hom, CategoryTheory.SimplicialObject.Truncated.sk.full, SSet.horn.edge_coe, CategoryTheory.Limits.Types.Colimit.ι_map_apply, map₂HomologicalComplex_map_app, CategoryTheory.PreGaloisCategory.instPreservesColimitsOfShapeActionFintypeCatAutFunctorSingleObjFunctorToActionOfFinite, TopCat.uliftFunctorCompForgetIso_inv_app, CategoryTheory.GrothendieckTopology.plusMap_comp_assoc, CategoryTheory.ComposableArrows.scMapIso_inv, PushoutObjObj.isPushout, cocones_obj, CategoryTheory.shiftFunctorCompIsoId_naturality_1_assoc, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₃, CategoryTheory.Limits.compCoyonedaSectionsEquiv_symm_apply_coe, OplaxMonoidal.whiskeringRight_δ_app, CategoryTheory.Enriched.Functor.functorHom_whiskerLeft_natTransEquiv_symm_app, flippingEquiv_symm_apply_obj_obj, CategoryTheory.Limits.coker.condition, constCompWhiskeringLeftIso_hom_app_app, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app_assoc, CategoryTheory.Limits.Types.limitConeIsLimit_lift_coe, CategoryTheory.Adjunction.corepresentableBy_homEquiv, CategoryTheory.Limits.Cocone.precomposeEquivalence_counitIso, CategoryTheory.Over.postComp_inv_app_left, CategoryTheory.Monad.toMon_mon, CochainComplex.shiftFunctorAdd'_inv_app_f', CategoryTheory.Limits.coneOfAdj_pt, CategoryTheory.Limits.Cocone.equivStructuredArrow_unitIso, CategoryTheory.SimplicialObject.Homotopy.singularChainComplexFunctor_map_homology_eq_of_simplicialHomotopy, CategoryTheory.NatTrans.app_zero, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_app, TopCat.toSheafCompHausLike_obj_obj, CategoryTheory.cosimplicialSimplicialEquiv_functor_map_app, curryingFlipEquiv_apply_obj, SSet.horn₃₁.ι₂_desc, CategoryTheory.NatIso.unop_symm, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_right, CategoryTheory.Limits.isIndObject_colimit, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_fst, CategoryTheory.Equivalence.congrFullSubcategory_unitIso, mapBifunctorHomologicalComplex_map_app_f_f, ShiftSequence.induced.shiftIso_hom_app_obj, CategoryTheory.IsSifted.colim_preservesFiniteProducts_of_isSifted, CategoryTheory.Equivalence.inverseFunctorObjIso_inv, AlgebraicGeometry.StructureSheaf.smul_const, CategoryTheory.Abelian.SpectralObject.toCycles_πE_descE_assoc, coreCompInclusionIso_hom_app, AlgebraicTopology.DoldKan.N₂Γ₂ToKaroubiIso_hom_app, CategoryTheory.Equivalence.changeInverse_counitIso_inv_app, SSet.modelCategoryQuillen.cofibration_of_mono, Monoidal.coreMonoidalTransport_μIso_inv, CategoryTheory.SingleFunctors.postcompIsoOfIso_hom_hom_app, CategoryTheory.NatTrans.isIso_iff_isIso_app, commShiftIso_hom_naturality_assoc, CategoryTheory.Limits.IndObjectPresentation.yoneda_isColimit_desc, CategoryTheory.Comma.mapRightEq_inv_app_left, CategoryTheory.Iso.inv_hom_id_app_app_assoc, CategoryTheory.GrothendieckTopology.Point.skyscraperSheafFunctor_map_hom, CategoryTheory.flippingIso_inv_toFunctor_map_app_app, SSet.OneTruncation₂.nerveEquiv_symm_apply_map, CategoryTheory.Presheaf.tautologicalCocone'_pt, CategoryTheory.Triangulated.TStructure.eTruncGEπ_app_eTruncGE_map_app_assoc, CategoryTheory.shiftFunctorAdd'_zero_add_hom_app, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_inv_f_f, CategoryTheory.whiskering_preadditiveYoneda, CategoryTheory.MonadIso.toNatIso_inv, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app, lanCompColimIso_inv_app, CategoryTheory.Limits.opCospan_hom_app, mapTriangleCommShiftIso_hom_app_hom₃, Profinite.exists_isClopen_of_cofiltered, FundamentalGroupoidFunctor.instIsIsoFunctorFundamentalGroupoidHomotopicMapsNatIso, CategoryTheory.isPullback_initial_to_of_cofan_isVanKampen, CategoryTheory.Limits.Bicone.ofColimitCocone_ι, uncurry_obj_obj, CategoryTheory.Grothendieck.map_id_eq, CategoryTheory.isSheaf_pointwiseColimit, flip₁₃Functor_obj_obj_obj_obj, CategoryTheory.SingleFunctors.shiftIso_add_inv_app, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π, isLeftDerivedFunctor_of_inverts, CategoryTheory.lan_preservesFiniteLimits_of_preservesFiniteLimits, CategoryTheory.GrothendieckTopology.Point.toPresheafFiberOfIsCofiltered_naturality_assoc, unopOpIso_hom_app, CategoryTheory.uliftYonedaEquiv_uliftYoneda_map, ShiftSequence.induced_shiftIso_hom_app_obj_assoc, CategoryTheory.Localization.SmallShiftedHom.equiv_shift', CategoryTheory.functorProdToProdFunctor_obj, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂'_map_app_app, CategoryTheory.instFaithfulFunctorOppositeTypeShrinkYoneda, CategoryTheory.yoneda_obj_map, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.functorToInterchangeIso_hom_app_app, SSet.stdSimplex.isoNerve_hom_app_apply, CategoryTheory.Cat.opFunctorInvolutive_hom_app_toFunctor_map, mapCommMonFunctor_obj, AlgebraicGeometry.ΓSpec.unop_locallyRingedSpaceAdjunction_counit_app', OneHypercoverDenseData.essSurj.presheafMap_presheafObjObjIso_hom, TopCat.Presheaf.app_bijective_of_stalkFunctor_map_bijective, CategoryTheory.GradedObject.HasGoodTrifunctor₁₂Obj.hasMap, CategoryTheory.full_linearCoyoneda, CategoryTheory.LaxBraidedFunctor.isoMk_hom, CategoryTheory.functorProdFunctorEquivUnitIso_hom_app, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_inv_app_hom, CategoryTheory.SmallObject.ιFunctorObj_eq, CategoryTheory.PreGaloisCategory.toAut_surjective_of_isPretransitive, commShiftIso_comp_inv_app, TwoP.swapEquiv_counitIso_inv_app_hom_toFun, CategoryTheory.Limits.FormalCoproduct.cechFunctor_obj, leftExtensionEquivalenceOfIso₁_inverse_map_right, sumIsoExt_hom_app_inr, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocNatIso_inv_app_app_app, equiv_functor_obj, AlgebraicTopology.DoldKan.compatibility_N₂_N₁_karoubi, CategoryTheory.IsGrothendieckAbelian.preservesColimit_coyoneda_obj_of_mono, topCatToSheafCompHausLike_obj, Monoidal.whiskerRight_app_fst, Condensed.epi_iff_locallySurjective_on_compHaus, op_comp_isSheaf_of_types, CategoryTheory.Cat.opFunctorInvolutive_hom_app_toFunctor_obj, CategoryTheory.Limits.spanCompIso_inv_app_right, CategoryTheory.GlueData.diagramIso_inv_app_right, CategoryTheory.Limits.limit.conePointUniqueUpToIso_hom_comp_assoc, CategoryTheory.Limits.Cofan.mk_ι_app, CategoryTheory.EnrichedFunctor.forgetId_inv_app, CategoryTheory.Abelian.SpectralObject.opcyclesIsoH_hom, CategoryTheory.Abelian.SpectralObject.cyclesIsoH_hom_EIsoH_inv_assoc, CategoryTheory.Limits.isIndObject_limit_of_discrete_of_hasLimitsOfShape, CategoryTheory.WithTerminal.lift_map_liftStar, CategoryTheory.GrothendieckTopology.Point.W_isInvertedBy_presheafFiber, CategoryTheory.GradedObject.mapBifunctorRightUnitor_hasMap, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_symm_app, CategoryTheory.WithTerminal.inclLiftToTerminal_inv_app, SSet.stdSimplex.faceSingletonComplIso_hom_ι, CategoryTheory.Limits.HasLimit.isoOfNatIso_inv_π, CategoryTheory.Adjunction.leftAdjointCompIso_inv_app, CategoryTheory.Triangulated.TStructure.natTransTruncLEOfLE_refl, CategoryTheory.Sheaf.adjunction_counit_app_val, CategoryTheory.Equivalence.mapCommMon_unitIso, CategoryTheory.CatCommSq.vComp_iso_hom_app, mapCochainComplexShiftIso_inv_app_f, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_hom_app, CategoryTheory.Under.mapCongr_hom_app, CategoryTheory.LocalizerMorphism.commShift_iso_inv_app_assoc, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_ε, CategoryTheory.MorphismProperty.Comma.mapRightComp_hom_app_right, CategoryTheory.LocalizerMorphism.equiv_smallHomMap', map_shiftFunctorCompIsoId_inv_app_assoc, CategoryTheory.SheafOfTypes.adhesive, CochainComplex.shiftFunctorAdd'_inv_app_f, CategoryTheory.Presheaf.isLeftKanExtension_along_uliftYoneda_iff, CategoryTheory.coyonedaEquiv_naturality, CategoryTheory.Limits.BinaryCofan.isColimit_iff_isIso_inr, SheafOfModules.id_val, SSet.instHasDimensionLETensorObjHAddNat, CategoryTheory.CategoryOfElements.fromCostructuredArrow_obj_snd, CategoryTheory.SingleFunctors.inv_hom_id_hom_assoc, HomologicalComplexUpToQuasiIso.homologyFunctorFactorsh_inv_app_quotient_obj, SSet.ι₁_app_fst, CategoryTheory.Sigma.descUniq_inv_app, LightCondensed.isLocallySurjective_iff_locallySurjective_on_lightProfinite, CategoryTheory.GrothendieckTopology.yonedaEquiv_comp, CategoryTheory.preservesColimitNatIso_hom_app, CategoryTheory.oppositeShiftFunctorZero_inv_app, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.instEpiSheafAddCommGrpCatGShortComplex, CategoryTheory.MonoidalCategory.externalProductCompDiagIso_inv_app_app, LeftExtension.postcompose₂_obj_right_obj, prod'CompFst_inv_app, CategoryTheory.Limits.PushoutCocone.mk_ι_app, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_naturality_left_symm_assoc, CategoryTheory.coyonedaEquiv_apply, CategoryTheory.Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom_assoc, whiskeringLeft₂_obj_map_app_app_app, CategoryTheory.Sieve.EffectiveEpimorphic.iff_forall_isSheafFor_yoneda, mapMonFunctor_map_app_hom, mapTriangleCommShiftIso_inv_app_hom₃, AlgebraicGeometry.StructureSheaf.isLocalizedModule_toPushforwardStalkAlgHom, CategoryTheory.CostructuredArrow.mapIso_functor_map_right, CategoryTheory.Comonad.comparisonForget_inv_app, CategoryTheory.Equivalence.mkIso_hom, CategoryTheory.Equivalence.changeInverse_unitIso_inv_app, PresheafOfModules.instIsIsoFunctorSheafOfModulesCounitSheafificationAdjunction, CategoryTheory.Equivalence.sheafCongr.inverse_obj_obj_obj, CategoryTheory.Equivalence.sheafCongrPreregular_inverse_obj_obj_obj, CategoryTheory.prod.rightUnitorEquivalence_counitIso, CategoryTheory.endofunctorMonoidalCategory_tensorObj_map, CategoryTheory.Limits.compCoyonedaSectionsEquiv_apply_app, SSet.ι₁_snd, isoSum_hom_app_inl, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_hom_app, pentagonIso_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompPointIso_inv_app, CategoryTheory.WithTerminal.equivComma_functor_obj_hom_app, CategoryTheory.Subfunctor.Subpresheaf.toRange_ι, isZero_iff, rightOpLeftOpIso_inv_app, CategoryTheory.Triangulated.TStructure.eTruncLT_obj_map_eTruncLTι_app, CategoryTheory.Limits.Cocone.precompose_map_hom, CategoryTheory.shrinkYonedaMon_map_app_shrinkYonedaObjObjEquiv_symm, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso_inv_app_f, CategoryTheory.Enriched.FunctorCategory.enrichedComp_π_assoc, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂, CategoryTheory.DinatTrans.compNatTrans_app, pointedToBipointedCompBipointedToPointedSnd_hom_app_toFun, mapMonIdIso_hom_app_hom, CategoryTheory.SimplicialObject.Augmented.hom_ext_iff, LightCondensed.forget_map_hom_app, CategoryTheory.NatIso.prod_hom, CategoryTheory.Mono.cofanInr_of_binaryCoproductDisjoint, CategoryTheory.Join.mapPairComp_inv_app_right, HomologicalComplex.mapBifunctor₁₂.ι_D₁, CategoryTheory.Abelian.extFunctor_obj, CategoryTheory.Limits.PushoutCocone.ι_app_right, map_shiftFunctorComm_assoc, CategoryTheory.WithInitial.equivComma_inverse_map_app, coconeOfIsLeftKanExtension_ι, CategoryTheory.Limits.isIndObject_pi, CategoryTheory.Limits.coneRightOpOfCocone_π, CategoryTheory.Sheaf.isSeparating, CategoryTheory.Sheaf.isGrothendieckAbelian_of_essentiallySmall, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_right_assoc, CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_hom_app_coe, ShiftSequence.induced_isoShiftZero_hom_app_obj_assoc, CategoryTheory.MorphismProperty.FunctorsInverting.comp_hom_assoc, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompYoneda, CategoryTheory.Limits.comp_lim_obj_ext_iff, SSet.stdSimplex.objMk₁_of_castSucc_lt, CategoryTheory.Abelian.SpectralObject.opcyclesMap_fromOpcycles, SSet.hasDimensionLT_of_isColimit, CategoryTheory.Limits.LimitPresentation.self_diag, IsCoverDense.Types.appHom_restrict, CategoryTheory.Limits.DiagramOfCones.conePoints_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.e_hom_app, CategoryTheory.instReflectsLimitsOfShapeFunctorObjWhiskeringRightOfHasLimitsOfShapeOfReflectsIsomorphismsOfPreservesLimitsOfShape, CategoryTheory.OverPresheafAux.counitBackward_counitForward, AlgebraicTopology.DoldKan.map_PInfty_f, CategoryTheory.Abelian.SpectralObject.shortComplexMap_comp_assoc, CategoryTheory.Triangulated.TStructure.eTruncLTLTIsoLT_inv_hom_id_app_assoc, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_map_hom_hom, CategoryTheory.Sheaf.cond, CategoryTheory.Idempotents.instFullKaroubiFunctorKaroubiFunctorCategoryEmbedding, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd, CategoryTheory.Limits.colimitHomIsoLimitYoneda_hom_comp_π_assoc, CategoryTheory.Limits.Types.binaryProductFunctor_map_app, CategoryTheory.MorphismProperty.Comma.mapRightEq_inv_app_right, CategoryTheory.faithful_linearCoyoneda, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_inv_left_app, functorHom_ext_iff, CategoryTheory.ObjectProperty.IsConservativeFamilyOfPoints.jointlyReflectIsomorphisms_type, CategoryTheory.Over.iteratedSliceEquivOverMapIso_inv_app_left_left, SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁_hom_app_f_f, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_map, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_functor_map, map_shiftFunctorCompIsoId_hom_app_assoc, CategoryTheory.ShiftMkCore.assoc_inv_app_assoc, IsDenseSubsite.sheafEquiv_inverse, ModuleCat.smulNatTrans_apply_app, CategoryTheory.Limits.PullbackCone.π_app_left, TopCat.Sheaf.existsUnique_gluing', CategoryTheory.CostructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₁, CategoryTheory.Over.iteratedSliceEquivOverMapIso_hom_app_left_left, CategoryTheory.whiskeringRight_preservesColimitsOfShape, CategoryTheory.Comma.mapLeftComp_inv_app_right, TopCat.isClosed_iff_of_isColimit, CategoryTheory.Comma.equivProd_counitIso_inv_app, CategoryTheory.WithTerminal.isLimitEquiv_symm_apply_lift, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functor_map_app_hom, CategoryTheory.Comma.coconeOfPreserves_ι_app_right, CategoryTheory.endofunctorMonoidalCategory_rightUnitor_inv_app, CategoryTheory.pre_id, CategoryTheory.Comma.toIdPUnitEquiv_unitIso_hom_app_right, CategoryTheory.Localization.instIsEquivalenceFunctorFunctorsInvertingWhiskeringLeftFunctor, CategoryTheory.Limits.Wedge.condition, CategoryTheory.Bicategory.leftUnitorNatIso_hom_app, CategoryTheory.Sheaf.ΓObjEquivSections_naturality_symm, CategoryTheory.FunctorToTypes.binaryProductLimit_lift, CategoryTheory.Limits.spanExt_inv_app_zero, CategoryTheory.Abelian.extFunctor_map_app, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_map_app_app, CategoryTheory.WithInitial.equivComma_counitIso_hom_app_left, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_map_app_hom₁, OneHypercoverDenseData.essSurj.presheafObjObjIso.hom_mapPreimage_assoc, CategoryTheory.Abelian.SpectralObject.cokernelSequenceE_X₂, 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, CategoryTheory.Iso.unop_hom_inv_id_app, CategoryTheory.Coyoneda.naturality, MulEquiv.toSingleObjEquiv_unitIso_inv, CategoryTheory.GrothendieckTopology.sheafification_obj, mapAddMonIdIso_hom_app_hom, Condensed.isoLocallyConstantOfIsColimit_inv, CategoryTheory.Mono.cofanInl_of_binaryCoproductDisjoint, CategoryTheory.Sheaf.mono_of_isLocallyInjective, CategoryTheory.NatTrans.IsMonoidal.comp, CategoryTheory.WithTerminal.liftFromOver_obj_obj, CategoryTheory.Join.mapPairLeft_inv_app, CategoryTheory.Sheaf.isLocallyInjective_iff_injective, CategoryTheory.cosimplicialSimplicialEquiv_counitIso_inv_app_app, CategoryTheory.Codiscrete.natIsoFunctor_inv_app, commShiftIso_hom_naturality, CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_obj_left, ModuleCat.uliftFunctorForgetIso_inv_app, CommShift.comp_commShiftIso_hom_app, CategoryTheory.Abelian.SpectralObject.instEpiToCycles, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_functor_map_hom, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatTrans_comp, HomologicalComplex.ι_mapBifunctorAssociatorX_hom_assoc, precomposeWhiskerLeftMapCocone_hom_hom, CategoryTheory.ComposableArrows.opEquivalence_unitIso_hom_app, CategoryTheory.Equivalence.congrLeftFunctor_obj, CategoryTheory.Presheaf.isSeparator, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.firstMap₂_app_app_app, CategoryTheory.ComposableArrows.mapFunctorArrows_app, CategoryTheory.PreGaloisCategory.FibreFunctor.end_isIso, CategoryTheory.SimplicialObject.augment_hom_app, W_map_of_adjunction_of_isContinuous, CategoryTheory.Sheaf.classifier_χ₀, CategoryTheory.bifunctorComp₁₂_obj, AlgebraicGeometry.StructureSheaf.const_zero, HomologicalComplex.ιOrZero_mapBifunctorAssociatorX_hom, initial_const_of_isInitial, CategoryTheory.ShortComplex.mapToComposableArrows_comp, CategoryTheory.Subfunctor.equivalenceMonoOver_functor_obj, CategoryTheory.Limits.CatCospanTransform.rightIso_hom, CategoryTheory.SimplicialObject.isCoskeletal_iff, mapComposableArrowsObjMk₁Iso_hom_app, CategoryTheory.Limits.Multifork.app_left_eq_ι, CategoryTheory.Limits.Cocone.fromStructuredArrow_obj_pt, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_left_app, CategoryTheory.Abelian.SpectralObject.cokernelSequenceCyclesE_X₁, sheafPushforwardContinuous_obj_obj_obj, CategoryTheory.η_naturality, mapBifunctorHomologicalComplex_obj_obj_X_d, opUnopEquiv_inverse, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverse_map_hom_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_map_bijective, CategoryTheory.Abelian.LeftResolution.karoubi_F, AddCommMonCat.coyoneda_map_app, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_hom_app_app_hom_hom, CategoryTheory.functorProdFunctorEquiv_unitIso, CategoryTheory.Sheaf.ΓRes_map_assoc, isoCopyObj_inv_app, instIsCardinalAccessibleObjConst, mapComposableArrows_obj_map, AlgebraicTopology.DoldKan.N₂Γ₂_compatible_with_N₁Γ₀, CategoryTheory.Abelian.SpectralObject.Ψ_fromOpcycles_assoc, CategoryTheory.Abelian.SpectralObject.homologyDataIdId_right_ι, SSet.whiskerLeft_app_apply, CategoryTheory.Limits.coconeOfConeRightOp_ι, CategoryTheory.Abelian.SpectralObject.exact₃', CategoryTheory.Limits.piObjIso_hom_comp_π_assoc, AlgebraicGeometry.Scheme.restrictFunctorΓ_hom_app, CategoryTheory.Abelian.SpectralObject.p_fromOpcycles_assoc, CategoryTheory.Limits.limit.conePointUniqueUpToIso_inv_comp_assoc, uncurryObjFlip_inv_app, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_inv_app_hom, CategoryTheory.conjugateEquiv_symm_of_iso, CategoryTheory.Abelian.SpectralObject.πE_EIsoH_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedAction_map_app, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_hom_app_app, CategoryTheory.Adjunction.mapAddMon_counit, CategoryTheory.Limits.sigmaFunctor_obj_obj, CategoryTheory.PreGaloisCategory.continuousSMul_aut_fiber, CategoryTheory.CatCommSq.iso_inv_naturality_assoc, CategoryTheory.Under.liftCone_π_app, CategoryTheory.Limits.Cocone.ofCofork_ι, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τr, CategoryTheory.TwoSquare.isIso_lanBaseChange_app_iff, CategoryTheory.TwoSquare.instIsIsoFunctorLanBaseChangeOfGuitartExact, CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_left, CategoryTheory.tensoringLeft_linear, IsCoverDense.Types.pushforwardFamily_compatible, CategoryTheory.SmallObject.instIsIsoRightAppArrowMapToTypeOrdFunctorIterationFunctor, CategoryTheory.Limits.isFiltered_costructuredArrow_yoneda_of_preservesFiniteLimits, CategoryTheory.Pairwise.cocone_ι_app, CategoryTheory.ComposableArrows.isoMk₂_inv, TopCat.Sheaf.comp_app, rightDerivedNatTrans_fac, CategoryTheory.Localization.liftNatTrans_app, CategoryTheory.NatTrans.naturality_app_assoc, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_inv_app_app, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_left, CategoryTheory.Abelian.Preradical.toColon_hom_left_colonπ, CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod_fac₁, CategoryTheory.ULift.equivalence_unitIso_hom, CategoryTheory.Limits.CatCospanTransform.inv_base, CategoryTheory.GrothendieckTopology.W.monoidal, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.F_map, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.counitIso_hom_app_app_hom, CategoryTheory.Mat_.embeddingLiftIso_inv_app, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_counitIso_inv_app_f, CategoryTheory.Under.forgetMapInitial_hom_app, Condensed.lanPresheafNatIso_hom_app, CategoryTheory.Limits.FormalCoproduct.cochainComplexFunctor_obj_d, CategoryTheory.Limits.fiberwiseColim_map_app, CategoryTheory.Abelian.SpectralObject.isZero₂_of_isFirstQuadrant, triangle, instIsLeftDerivedFunctorLiftHomFac, CategoryTheory.sum.inrCompInrCompInverseAssociator_inv_app_down, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_hom_π, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_pt, CategoryTheory.Limits.colimCompFlipIsoWhiskerColim_hom_app_app, mapHomologicalComplexIdIso_inv_app_f, CategoryTheory.conjugateEquiv_symm_comp, CategoryTheory.Discrete.sumEquiv_counitIso_hom_app, CategoryTheory.Sheaf.ab5ofSize, CategoryTheory.Limits.DiagramOfCocones.mkOfHasColimits_map_hom, CategoryTheory.Comma.mapRightIso_functor_map_right, leftKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, CategoryTheory.Sieve.functorInclusion_app, CategoryTheory.GradedObject.mapBifunctor₁₂BifunctorMapObj_ext_iff, CategoryTheory.Triangulated.TStructure.π_truncGTIsoTruncGE_inv_ι_app_assoc, isoWhiskerLeft_right_assoc, CategoryTheory.ShortComplex.opEquiv_counitIso, CategoryTheory.Pretriangulated.shiftFunctorZero_op_hom_app, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_app_apply, SSet.comp_app, AlgebraicGeometry.Scheme.Modules.pushforwardComp_hom_app_app, Rep.Tor_map, CategoryTheory.Mon.limitCone_π_app_hom, CategoryTheory.Comma.limitAuxiliaryCone_π_app, CategoryTheory.Abelian.SpectralObject.IsFirstQuadrant.isZero₁, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι_assoc, CategoryTheory.Triangulated.TStructure.eTruncLT_ι_top, CategoryTheory.prodOpEquiv_unitIso_inv_app, CategoryTheory.Localization.comp_liftNatTrans_assoc, CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj_obj_X, HomologicalComplex.tensor_unit_d₂, CategoryTheory.nerveFunctor_map, CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_map_left, postcompose₃_map_app_app_app_app, CategoryTheory.Sheaf.ΓObjEquivHom_naturality_symm, SSet.stdSimplex.σ_objEquiv_symm_apply, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_iso_hom_app, CategoryTheory.WithInitial.equivComma_functor_map_right_app, PresheafOfModules.inverseImage_W_toPresheaf_eq_inverseImage_isomorphisms, CategoryTheory.frobeniusMorphism_iso_of_preserves_binary_products, CategoryTheory.GradedObject.mapBifunctorRightUnitor_inv_apply, CategoryTheory.GradedObject.ι_mapBifunctorComp₁₂MapObjIso_inv, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply, TopCat.Sheaf.IsFlasque.epi_of_shortExact, SSet.Augmented.stdSimplex_obj_right, CategoryTheory.DifferentialObject.shiftFunctorAdd_hom_app_f, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_hom, CategoryTheory.Over.postEquiv_counitIso, CategoryTheory.Limits.coconeRightOpOfConeEquiv_unitIso, CategoryTheory.WithInitial.coconeEquiv_inverse_obj_ι_app_right, LightCondensed.forget_obj_obj_map, CategoryTheory.ChosenPullbacksAlong.pullbackId_hom_counit, CategoryTheory.Limits.multispanIndexCoend_left, CategoryTheory.ι_colimitCompWhiskeringRightIsoColimitComp_hom, CategoryTheory.Subfunctor.orderIsoSubobject_apply, AlgebraicTopology.normalizedMooreComplex_objD, CategoryTheory.Over.ConstructProducts.conesEquivCounitIso_hom_app_hom_left, CategoryTheory.Limits.coneOpEquiv_counitIso, ranObjObjIsoLimit_inv_π_assoc, SheafOfModules.toSheaf_obj_obj, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_hom_f_f, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_hom_app_app, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π_assoc, precomposeWhiskerLeftMapCocone_inv_hom, CategoryTheory.GradedObject.ι_mapBifunctorMapObjDesc_assoc, SheafOfModules.pushforwardCongr_inv_app_val_app, PullbackObjObj.ofHasPullback_π, CategoryTheory.Triangulated.TStructure.eTruncLT_obj_bot, CategoryTheory.MorphismProperty.Comma.mapRightId_inv_app_left, CategoryTheory.Limits.Cocone.functorialityEquivalence_inverse, CategoryTheory.Monoidal.comonFunctorCategoryEquivalence_unitIso, CategoryTheory.Limits.colim.mapShortComplex_X₃, CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_ω₁, FullyFaithful.whiskeringRight_preimage_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_map_right, ContAction.resComp_hom, RightExtension.precomp_obj_right, CategoryTheory.preservesLimits_preadditiveYoneda_obj, CategoryTheory.instPreservesFiniteLimitsFunctorOppositeSheafPresheafToSheaf, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_inv_π_assoc, SSet.Subcomplex.prod_obj, CochainComplex.shiftFunctorZero'_hom_app_f, CategoryTheory.Limits.fiberwiseColimitLimitIso_inv_app, CategoryTheory.whiskeringLeft_preservesLimits, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatIso_hom, IsCoverDense.Types.appIso_inv, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv_desc_assoc, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_inverse, CategoryTheory.Abelian.Preradical.isRadical_iff_isIso, CategoryTheory.MonoidalOpposite.tensorRightUnmopIso_inv_app, pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_assoc, HomologicalComplex₂.flipEquivalenceUnitIso_inv_app_f_f, CategoryTheory.CosimplicialObject.Truncated.whiskering_obj_map_app, SimplicialObject.Splitting.ofIso_ι, PresheafOfModules.Sheafify.smul_add, mapCochainComplexPlusCompι_hom_app_f, CategoryTheory.isCodetector_iff_reflectsIsomorphisms_yoneda_obj, PushoutObjObj.ι_iso_of_iso_right_hom, CategoryTheory.Idempotents.whiskeringLeft_obj_preimage_app, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy_homEquiv_symm_apply, CategoryTheory.Limits.cospanCompIso_inv_app_right, CategoryTheory.Cat.freeMapCompIso_hom_app, OneHypercoverDenseData.essSurj.presheafMap_presheafObjObjIso_hom_assoc, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.isoAux_hom_app, CategoryTheory.Triangulated.TStructure.ω₁_obj, Monoidal.tensorObjComp_inv_app, CategoryTheory.Hom.mulEquivCongrRight_symm_apply, CategoryTheory.MonoidalCategory.DayFunctor.equiv_functor_obj, SSet.Truncated.Edge.map_whiskerLeft, CategoryTheory.Iso.map_hom_inv_id_app, op_commShiftIso_inv_app_assoc, CategoryTheory.Abelian.SpectralObject.liftOpcycles_fromOpcycles, HomologicalComplex.mapBifunctorAssociatorX_hom_D₂_assoc, OplaxMonoidal.ofBifunctor.topMapᵣ_app, Profinite.Extend.functor_obj, ModuleCat.matrixEquivalence_unitIso, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₂, CategoryTheory.Abelian.Preradical.shortComplex_X₂, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_id, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_hom_app_snd_app, SSet.horn₃₂.ι₃_desc, AlgebraicGeometry.ΓSpec.isIso_locallyRingedSpaceAdjunction_counit, CategoryTheory.Abelian.LeftResolution.instEpiKaroubiAppπObjToKaroubi, CategoryTheory.prod.prodFunctorToFunctorProdAssociator_inv_app_app, SSet.comp_const, mapGrpCompIso_hom_app_hom_hom, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_map_mkHom_homMk_id, CategoryTheory.Sheaf.hasSeparator, CategoryTheory.Abelian.SpectralObject.IsThirdQuadrant.isZero₂, map_shiftFunctorCompIsoId_hom_app, CategoryTheory.additive_coyonedaObj', LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocNatIso_inv_app_app_app, CategoryTheory.Subfunctor.range_eq_ofSection', SimplicialObject.opFunctor_obj_δ, CategoryTheory.instFaithfulSheafSheafCompose, CategoryTheory.MorphismProperty.Comma.mapRightIso_unitIso_inv_app_left, mapTriangleInvRotateIso_inv_app_hom₂, FullyFaithful.homNatIso'_hom_app_down, CategoryTheory.SimplicialObject.Augmented.const_map_right, CategoryTheory.Limits.sigmaConst_obj_map, CategoryTheory.GrothendieckTopology.Point.instIsMonoidalFunctorOppositeHomPresheafToSheafCompSheafFiberIso, leftExtensionEquivalenceOfIso₁_inverse_obj_right, leftOpId_inv_app, HomotopyCategory.instFaithfulFunctorHomologicalComplexObjWhiskeringLeftQuotient, CategoryTheory.Limits.IsColimit.coconePointsIsoOfEquivalence_inv, Initial.extendCone_map_hom, CategoryTheory.Comonad.comparisonForget_hom_app, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_obj_X₁, SheafOfModules.conjugateEquiv_pullbackComp_inv, CategoryTheory.Limits.Cone.toCostructuredArrow_map, CategoryTheory.NatTrans.CommShiftCore.shift_app_assoc, CategoryTheory.Triangulated.TStructure.π_natTransTruncGEOfLE_assoc, AlgebraicGeometry.Spec.sheafedSpaceMap_hom_c_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_inv_app_snd_app, AlgebraicTopology.DoldKan.whiskerLeft_toKaroubi_N₂Γ₂_hom, TopCat.toSSetObj₀Equiv_apply, CategoryTheory.WithTerminal.liftFromOverComp_hom_app, CategoryTheory.regularTopology.isSheaf_yoneda_obj, CategoryTheory.Triangulated.TStructure.eTruncLTι_naturality, whiskeringLeft₃Obj_obj, CategoryTheory.Limits.colimit.map_post, CategoryTheory.Equivalence.sheafCongrPreregular_inverse_map_hom_app, CategoryTheory.WithInitial.coconeEquiv_functor_obj_ι_app_of, CategoryTheory.Sheaf.Hom.mono_of_presheaf_mono, CategoryTheory.Sheaf.instHasExactColimitsOfShapeOfHasFiniteLimitsOfPreservesColimitsOfShapeFunctorOppositeSheafToPresheaf, SSet.Truncated.HomotopyCategory.BinaryProduct.mapHomotopyCategory_prod_id_comp_inverse, CategoryTheory.shiftFunctorAdd'_add_zero, RepresentableBy.equivUliftYonedaIso_symm_apply_homEquiv, CategoryTheory.Idempotents.functorExtension₂_obj_obj_X, CategoryTheory.Limits.BinaryFan.π_app_right, CategoryTheory.shiftFunctorCompIsoId_add'_hom_app, CategoryTheory.MonoidalPreadditive.instAdditiveFunctorCurriedTensor, CategoryTheory.MonoidalCategory.DayConvolution.triangle, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_comp, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_iso_hom_app, AlgebraicGeometry.opensCone_π_app, CategoryTheory.Limits.colimitFlipIsoCompColim_hom_app, CategoryTheory.bifunctorComp₂₃Functor_map, CategoryTheory.Equivalence.invFunIdAssoc_inv_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_inv_app_snd_app, CategoryTheory.Limits.coendFunctor_obj, CategoryTheory.Limits.colimit.isoColimitCocone_ι_inv_assoc, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_obj_map_hom₃, SSet.Truncated.Edge.map_snd, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.leftUnitor_hom_unit_app, CategoryTheory.SimplicialObject.instIsIsoAppUnitTruncatedCoskAdj, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_app_app, CategoryTheory.Triangulated.TStructure.π_truncGTIsoTruncGE_inv_assoc, CategoryTheory.Limits.end_.map_id, CategoryTheory.StructuredArrow.commaMapEquivalenceInverse_obj, SheafOfModules.inl_freeSumIso_hom_assoc, CategoryTheory.Limits.BinaryCofan.ι_app_right, CategoryTheory.MorphismProperty.Comma.mapRightId_hom_app_right, CategoryTheory.MorphismProperty.Over.mapComp_hom_app_left, CategoryTheory.Triangulated.TStructure.π_truncGTIsoTruncGE_hom, SSet.stdSimplex.instFiniteObjOppositeSimplexCategory, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₂, CategoryTheory.GrothendieckTopology.sheafToPresheaf_map_sheafComposeNatTrans_eq_sheafifyCompIso_inv, CategoryTheory.Triangulated.TStructure.isIso_eTruncLT_obj_map_truncLTπ_app, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_inv_app_zero, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_two, CategoryTheory.Idempotents.app_p_comm_assoc, CategoryTheory.toOverIteratedSliceForwardIsoPullback_hom_app_left, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.unitIso_hom_app_hom_app, CategoryTheory.plusPlusSheaf_obj_obj, CommShift₂.comm, CategoryTheory.Triangulated.SpectralObject.triangle_mor₂, MonObj.mopEquiv_counitIso_hom_app_hom_unmop, CategoryTheory.pullbackShiftFunctorAdd'_hom_app, CategoryTheory.Limits.IsColimit.homEquiv_symm_naturality, CategoryTheory.Abelian.SpectralObject.cokernelIsoCycles_hom_fac_assoc, Accessible.Limits.isColimitMapCocone.surjective, CategoryTheory.instSmallCarrierObjOppositeMonCatMonFunctorYonedaMon, CategoryTheory.Limits.CatCospanTransform.mkIso_hom_right, CategoryTheory.Under.mapComp_hom, CategoryTheory.GrothendieckTopology.toPlusNatTrans_app, CategoryTheory.ε_naturality, RightExtension.IsPointwiseRightKanExtension.isIso_hom, RightExtension.mk_right_as, AlgebraicTopology.normalizedMooreComplex_map, LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv_assoc, CategoryTheory.TwistShiftData.z_zero_left, CategoryTheory.MonoidalCategory.curriedTensorPreFunctor_obj, coconeTypesEquiv_symm_apply_ι, TopologicalSpace.Opens.mapId_inv_app, CategoryTheory.shrinkYonedaObjObjEquiv_obj_map_assoc, CategoryTheory.NatTrans.mono_iff_mono_app, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_inv_app, leftExtensionEquivalenceOfIso₁_counitIso_inv_app_right_app, flip₁₃Functor_obj_map_app_app, CategoryTheory.MorphismProperty.PreIndSpreads.exists_isPushout, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_map_left_app, CategoryTheory.Subfunctor.Subpresheaf.epi_iff_range_eq_top, isIso_ranAdjunction_homEquiv_iff, CategoryTheory.Limits.lim_obj, isoWhiskerLeft_inv, CategoryTheory.WithInitial.mkCommaObject_right_map, isIso_of_isLeftDerivedFunctor_of_inverts, CategoryTheory.shiftFunctorZero_inv_app_shift, CategoryTheory.ObjectProperty.fullSubcategoryCongr_counitIso, CategoryTheory.sheafComposeNatTrans_app_uniq, CategoryTheory.Sieve.shrinkFunctorUliftFunctorIso_inv_ι, CategoryTheory.Abelian.SpectralObject.iCycles_δ, CategoryTheory.Presheaf.coherentExtensiveEquivalence_functor_map_hom, CategoryTheory.WithInitial.equivComma_functor_obj_hom_app, CategoryTheory.PreGaloisCategory.FiberFunctor.isPretransitive_of_isConnected, CategoryTheory.OverPresheafAux.OverArrows.yonedaArrow_val, CategoryTheory.Limits.WalkingMultispan.functorExt_inv_app, CategoryTheory.Adjunction.commShiftIso_inv_app_counit_app_assoc, CategoryTheory.Limits.Multicofork.map_ι_app, SSet.Truncated.HomotopyCategory.BinaryProduct.functor_comp_inverse, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_map, CategoryTheory.instIsClosedUnderIsomorphismsFunctorRightExactFunctor, leftKanExtension_hom_ext_iff, CategoryTheory.Enriched.Functor.natTransEquiv_symm_app_app_apply, CategoryTheory.instIsClosedUnderIsomorphismsFunctorExactFunctor, CategoryTheory.MorphismProperty.instIsStableUnderCoproductsOfShapeFunctorMonomorphismsOfHasCoproductsOfShapeOfHasPullbacks, CommShift.id_commShiftIso_inv_app, CategoryTheory.Limits.isIndObject_limit_comp_yoneda, CategoryTheory.Tor_obj, CategoryTheory.Sheaf.instHasFiniteLimits, CategoryTheory.Localization.lift₂NatIso_inv, curryingFlipEquiv_symm_apply_obj_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_app_snd_app, CategoryTheory.TransfiniteCompositionOfShape.ici_isoBot, CategoryTheory.StructuredArrow.mapNatIso_inverse_obj_hom, SheafOfModules.pushforwardPushforwardAdj_unit_app_val_app, commShiftIso_inv_naturality_assoc, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₃, SSet.Truncated.HomotopyCategory.descOfTruncation_map_homMk, HomotopicalAlgebra.CofibrantObject.instIsIsoFunctorWhiskerRightHoCatιCompResolutionNatTransOfIsLocalizationWeakEquivalences, CategoryTheory.Endofunctor.Algebra.functorOfNatTransEq_inv_app_f, CategoryTheory.NatTrans.IsMonoidal.id, whiskerLeft_twice, MulEquiv.toSingleObjEquiv_counitIso_inv, TopCat.coinduced_of_isColimit, AlgebraicTopology.DoldKan.Γ₀_map_app, CategoryTheory.Limits.Cocone.toCostructuredArrowCocone_ι_app, CategoryTheory.Limits.isFiltered_costructuredArrow_yoneda_iff_nonempty_preservesFiniteLimits, whiskeringLeft₃ObjObjObj_obj_obj_obj_obj, CategoryTheory.uliftYoneda_obj_map_down, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence, CategoryTheory.SimplicialObject.comp_left_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_right, CategoryTheory.Limits.PushoutCocone.op_π_app, CategoryTheory.Triangulated.TStructure.eTruncGE_obj_map_eTruncGEπ_app_assoc, CategoryTheory.Equivalence.congrLeft_unitIso_inv_app, CategoryTheory.Limits.Cofork.coequalizer_ext, CategoryTheory.NatTrans.op_comp, CategoryTheory.shiftFunctorAdd'_assoc_inv_app_assoc, LeftExtension.postcompose₂ObjMkIso_hom_right_app, SSet.Subcomplex.prod_le_unionProd, curry₃_map_app_app_app, CategoryTheory.MonoidalOpposite.unmopEquiv_counitIso_hom_app, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_map_mkHom_homMk_homMk, CategoryTheory.Comonad.ForgetCreatesLimits'.newCone_π, CategoryTheory.mateEquiv_symm_apply, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap_assoc, CategoryTheory.Monoidal.commMonFunctorCategoryEquivalence_unitIso, Elements.instHasInitialObjOppositeTypeFlipShrinkYonedaOp, CategoryTheory.Limits.limit.lift_π_app, CategoryTheory.Limits.limit_obj_ext_iff, SSet.RelativeMorphism.comm_assoc, CategoryTheory.Limits.Cone.equiv_inv_π, CategoryTheory.biconeMk_map, CategoryTheory.Idempotents.DoldKan.N_obj, CategoryTheory.Equivalence.sheafCongrPreregular_inverse_obj_obj_map, CategoryTheory.instFinitaryExtensiveSheafOfHasPullbacksOfHasSheafify, CategoryTheory.WithInitial.commaFromUnder_obj_hom_app, rightDerivedNatTrans_comp_assoc, CompHausLike.LocallyConstant.adjunction_left_triangle, ranCounit_app_app_ranAdjunction_unit_app_app_assoc, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_app, AlgebraicGeometry.StructureSheaf.algebraMap_obj_top_bijective, AlgebraicTopology.DoldKan.toKaroubiCompN₂IsoN₁_hom_app, CategoryTheory.extensiveTopology.isLocallySurjective_iff, CategoryTheory.Limits.sigmaFunctor_map_app, mapTriangleInvRotateIso_inv_app_hom₁, SSet.Subcomplex.instMonoToRange, CategoryTheory.Equivalence.mapGrp_unitIso, CategoryTheory.Limits.hasColimitsOfShape_iff_isRightAdjoint_const, CategoryTheory.Limits.Cocone.isColimit_iff_isIso_colimMap_ι, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_left, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_hom_app_app_snd, CategoryTheory.Abelian.SpectralObject.cokernelSequenceCyclesEIso_inv_τ₁, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIso_hom_app_hom, HomologicalComplex.complexOfFunctorsToFunctorToComplex_map_app_f, CategoryTheory.NatIso.unop_whiskerRight, CategoryTheory.Abelian.SpectralObject.Hom.comm, curryingEquiv_symm_apply_map_app, leftOpRightOpEquiv_inverse_map, CategoryTheory.Equivalence.functorFunctor_obj, TopCat.Sheaf.pushforward_obj_val, CategoryTheory.WithTerminal.inclLift_inv_app, CategoryTheory.MorphismProperty.Comma.mapRightIso_counitIso_hom_app_left, CategoryTheory.SimplicialObject.Truncated.trunc_obj_map, CategoryTheory.Join.InclLeftCompRightOpOpEquivFunctor_hom_app, CategoryTheory.PreGaloisCategory.FibreFunctor.end_isUnit, CategoryTheory.Iso.isoFunctorOfIsoInverse_inv_app, CategoryTheory.Cat.opFunctorInvolutive_inv_app_toFunctor_map, leftOpRightOpEquiv_unitIso_hom_app, CategoryTheory.CostructuredArrow.mapNatIso_inverse_obj_hom, SheafOfModules.fullyFaithfulForget_preimage_val, HomotopicalAlgebra.CofibrantObject.instIsIsoFunctorHoCatAdjCounit', SSet.Subcomplex.unionProd.ι₁_ι_assoc, Final.extendCocone_obj_ι_app', CategoryTheory.Presheaf.uliftYonedaAdjunction_homEquiv_app, CategoryTheory.Sheaf.isLocallyInjective_forget, CategoryTheory.WithInitial.commaFromUnder_obj_right, CategoryTheory.MonoidalCategory.DayConvolution.symmetry, CategoryTheory.Adjunction.leftAdjointUniq_trans_app, CategoryTheory.flippingIso_hom_toFunctor_obj_obj_map, PresheafOfModules.instReflectsIsomorphismsSheafOfModulesSheafAddCommGrpCatToSheaf, CategoryTheory.Limits.parallelPair.ext_hom_app, SheafOfModules.pullback_id_comp, CategoryTheory.Abelian.SpectralObject.kernelSequenceE_f, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w, TopCat.Sheaf.sections_exact_of_left_exact, CategoryTheory.Sheaf.truth_hom, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIso_inv_app_hom, CategoryTheory.SmallObject.SuccStruct.restrictionLTOfCoconeIso_hom_app, CategoryTheory.WithInitial.equivComma_inverse_obj_map, elementsFunctor_map, SSet.modelCategoryQuillen.cofibration_iff, CategoryTheory.Limits.lim_ε_π, CategoryTheory.Adjunction.whiskerLeft_counit_iso_of_L_fully_faithful, CategoryTheory.Join.mapWhiskerRight_associator_hom, CategoryTheory.full_preadditiveCoyoneda, leftKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, IsCoverDense.restrictHomEquivHom_naturality_right_assoc, CategoryTheory.SimplicialObject.whiskering_map_app_app, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst_assoc, SheafOfModules.restrictScalars_map_val, CategoryTheory.PreGaloisCategory.nhds_one_has_basis_stabilizers, CategoryTheory.SimplicialObject.Augmented.rightOp_right_obj, CategoryTheory.Limits.reflexivePair.mkNatIso_inv_app, CategoryTheory.toOverPullbackIsoToOver_hom_app_left, SSet.Truncated.hoFunctor₂_naturality, flip₁₃_obj_obj_map, RightExtension.postcomp₁_map_left_app, CategoryTheory.cones_obj_map_app, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π_assoc, CategoryTheory.shiftFunctorAdd'_add_zero_hom_app, CategoryTheory.Limits.Types.Small.limitCone_π_app, CategoryTheory.ComonadIso.mk_hom_toNatTrans, SSet.instHasDimensionLTTensorObjHAddNat, CategoryTheory.Limits.instIsIPCFunctor, CategoryTheory.Limits.sigmaConst_map_app, CategoryTheory.Comma.toIdPUnitEquiv_counitIso_hom_app, CategoryTheory.Limits.walkingSpanOpEquiv_unitIso_inv_app, CategoryTheory.ComposableArrows.isoMk_inv, SSet.horn₃₂.ι₀_desc, CategoryTheory.Limits.PushoutCocone.coequalizer_ext, CategoryTheory.MonoidalCategory.curriedTensor_obj_map, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_μIso_inv, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_X_obj, CategoryTheory.instReflectsIsomorphismsSheafSheafCompose, CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_right, HomologicalComplex.natIsoSc'_hom_app_τ₂, CategoryTheory.sheafificationNatIso_inv_app_hom, CategoryTheory.IsPullback.of_forall_isPullback_app, CategoryTheory.LocalizerMorphism.homMap_apply_assoc, CategoryTheory.toSheafify_plusPlusIsoSheafify_hom, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_right_assoc, pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.AddMon.EquivLaxMonoidalFunctorPUnit.counitIso_hom_app_hom, CategoryTheory.WithTerminal.ofCommaObject_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_obj_iso_inv, AlgebraicGeometry.Scheme.LocalRepresentability.yoneda_toGlued_yonedaGluedToSheaf_assoc, HomotopicalAlgebra.CofibrantObject.instIsIsoFunctorHoCatCounitHoCatAdj, CategoryTheory.Limits.opCospan_inv_app, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_hom, CategoryTheory.Equivalence.congrLeft_unitIso_hom_app, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv, SSet.Truncated.HomotopyCategory.mkNatIso_inv_app_mk, CategoryTheory.Limits.Cone.overPost_pt, CategoryTheory.Comma.mapRightComp_hom_app_left, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_left, CategoryTheory.BinaryCofan.mono_inr_of_isVanKampen, commAlgCatEquivUnder_counitIso, CategoryTheory.ExponentiableMorphism.pushforwardComp_hom_counit_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_inv_app_snd_app, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_app, CategoryTheory.Monoidal.leftUnitor_inv_app, CategoryTheory.sum.inlCompAssociator_hom_app, SSet.Subcomplex.homOfLE_ι, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₂, mapTriangleRotateIso_hom_app_hom₃, CategoryTheory.conjugateEquiv_counit, CategoryTheory.NatTrans.CommShiftCore.shift_app_comm_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_ε_app, CategoryTheory.SimplicialObject.Truncated.rightExtensionInclusion_right_as, CategoryTheory.whiskerRight_ι_colimitCompWhiskeringRightIsoColimitComp_inv_assoc, CategoryTheory.Abelian.SpectralObject.kernelSequenceCycles_X₂, CategoryTheory.EnrichedFunctor.category_comp_out, Initial.limit_cone_comp_aux, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_left, sheafPushforwardCocontinuousCompSheafToPresheafIso_inv, CategoryTheory.Sheaf.coneΓ_pt, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂'_map_app_app, SSet.face_le_horn, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_whiskerLeft, CategoryTheory.Adjunction.unit_isIso_of_L_fully_faithful, LaxMonoidal.ofBifunctor.topMapᵣ_app, PullbackObjObj.mapArrowRight_comp, flippingEquiv_symm_apply_obj_map, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_X, instIsEquivalenceObjWhiskeringLeft, HomotopicalAlgebra.CofibrantObject.instIsIsoFunctorResolutionCompToLocalizationNatTrans, LeftExtension.postcomp₁_obj_right_map, CategoryTheory.Over.liftCone_π_app, CategoryTheory.Subfunctor.instEpiFunctorTypeToRange, CategoryTheory.Limits.Cocone.precomposeId_inv_app_hom, CategoryTheory.Adjunction.rightAdjointUniq_trans_app_assoc, CategoryTheory.Limits.pointwiseProductCompEvaluation_inv_app, CategoryTheory.bifunctorComp₁₂Obj_obj_map, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_counitIso_hom, ranObjObjIsoLimit_hom_π_assoc, CategoryTheory.ExactFunctor.whiskeringRight_obj_obj_obj, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatTrans_id, flip₂₃Functor_obj_obj_map_app, CategoryTheory.Limits.isLimitConeOfAdj_lift, CochainComplex.shiftFunctorAdd_inv_app_f, CategoryTheory.Adjunction.compPreadditiveYonedaIso_hom_app_app_apply, CategoryTheory.Limits.ι_colimitLimitIso_limit_π_assoc, CategoryTheory.Limits.IndObjectPresentation.yoneda_ι_app, TopologicalSpace.Opens.overEquivalence_counitIso_inv_app, CategoryTheory.Triangulated.Octahedron.map_m₁, CategoryTheory.Limits.colimIsoFlipCompWhiskerColim_hom_app_app, CategoryTheory.AdditiveFunctor.ofLeftExact_obj_fst, CategoryTheory.Limits.Types.Limit.lift_π_apply, CategoryTheory.Equivalence.ext_iff, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_nsmul_apply, CategoryTheory.sum.inrCompInlCompAssociator_inv_app_down_down, PreservesPointwiseLeftKanExtensionAt.preserves, AddCommGrpCat.coyonedaType_obj_map, CategoryTheory.Monoidal.comonFunctorCategoryEquivalence_functor, CategoryTheory.whiskeringRightCompEvaluation_hom_app, CategoryTheory.shiftFunctorAdd_assoc_hom_app_assoc, CategoryTheory.hoFunctor.preservesBinaryProducts, CategoryTheory.Limits.cospanExt_inv_app_one, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_right, CategoryTheory.instPreservesColimitsOfShapeSheafExtensiveTopologyFunctorOppositeSheafToPresheafOfPreservesFiniteProductsColim, flip₂₃Functor_map_app_app_app, PullbackObjObj.π_iso_of_iso_right_inv, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₁, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₂, CategoryTheory.Limits.Cone.functoriality_obj_π_app, CategoryTheory.NatTrans.CommShiftCore.shift_comm, CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_obj, CategoryTheory.Limits.end_.hom_ext_iff, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst, PresheafOfModules.toPresheaf_map_app_apply, CategoryTheory.Equivalence.symmEquivInverse_obj_counitIso_inv, CategoryTheory.yonedaCommGrpGrp_obj, CategoryTheory.Limits.ConeMorphism.w_assoc, CategoryTheory.ShortComplex.FunctorEquivalence.functor_obj_map, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₁, CategoryTheory.Limits.FormalCoproduct.cechFunctor_map_app, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_inv_π, CategoryTheory.conjugateEquiv_rightUnitor_hom, CategoryTheory.endofunctorMonoidalCategory_whiskerLeft_app, CategoryTheory.LocalizerMorphism.equiv_smallShiftedHomMap, AddCommGrpCat.coyonedaType_obj_obj_coe, CategoryTheory.FreeGroupoid.mapComp_inv_app, CondensedSet.continuous_coinducingCoprod, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₁, CategoryTheory.Adjunction.unit_app_shift_commShiftIso_inv_app_assoc, commShiftIso_map₂CochainComplex_inv_app, CategoryTheory.Limits.IsIndObject.instIsClosedUnderIsomorphismsFunctorOppositeType, commShiftOfLocalization.iso_inv_app_assoc, CategoryTheory.Sieve.sieveOfSubfunctor_apply, CategoryTheory.Limits.PullbackCone.unop_ι_app, CategoryTheory.Triangulated.SpectralObject.Hom.comm_assoc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_inv_app_hom, isDenseAt_iff, Monoidal.whiskeringLeft_η_app, AlgebraicGeometry.Proj.zero_apply, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_naturality_right, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality_assoc, CategoryTheory.instFaithfulMonFunctorOppositeMonCatyonedaAddMon, CategoryTheory.Abelian.SpectralObject.p_opcyclesMap_assoc, CategoryTheory.Idempotents.functorExtension₂_obj_obj_p, CategoryTheory.Triangulated.TStructure.natTransTruncGEOfLE_trans, CategoryTheory.Limits.FormalCoproduct.evalOp_map_app, instReflectsIsomorphismsDiscreteObjWhiskeringLeftIncl, CategoryTheory.SmallObject.SuccStruct.arrowMap_ofCocone_to_top, CategoryTheory.Limits.Multifork.toPiFork_π_app_one, CategoryTheory.Abelian.SpectralObject.d_ιE_fromOpcycles_assoc, CategoryTheory.SingleFunctors.hom_inv_id_hom, CategoryTheory.Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_inv_app, IsCoverDense.Types.presheafIso_inv_app, CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_none, CategoryTheory.GrothendieckTopology.overMapPullbackComp_inv_app_hom_app, OrderHom.equivalenceFunctor_functor_obj_obj, CategoryTheory.cosimplicialSimplicialEquiv_unitIso_hom_app, CategoryTheory.Join.inclRightCompOpEquivInverse_hom_app_op, CategoryTheory.instReflectsLimitsOfShapeFunctorObjWhiskeringRightOfHasLimitsOfShape, AddCommGrpCat.Colimits.toCocone_ι_app, CategoryTheory.Limits.coconeOfDiagramTerminal_ι_app, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₂, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_comp_functor, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_map_fst_app, CategoryTheory.Limits.pullbackObjIso_hom_comp_fst, LaxMonoidal.ofBifunctor.firstMap₁_app_app_app, AddCommGrpCat.Colimits.Quot.ι_desc, CategoryTheory.GrothendieckTopology.uliftYoneda_obj_obj_map_down, Preorder.coconeOfUpperBound_ι_app, CategoryTheory.Limits.cospanOp_hom_app, CategoryTheory.Sheaf.isConstant_iff_isIso_counit_app', CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w_apply, CategoryTheory.shiftFunctorZero_hom_app_shift, CategoryTheory.NatIso.op_associator, CategoryTheory.SheafOfTypes.balanced, CategoryTheory.whiskeringLeft_preservesColimit, CategoryTheory.Limits.asEmptyCocone_ι_app, SSet.stdSimplex.objMk₁_of_le_castSucc, CategoryTheory.coherentTopology.isSheaf_yoneda_obj, ModuleCat.homEquiv_extendScalarsComp, CategoryTheory.Equivalence.changeFunctor_unitIso_inv_app, TopCat.Sheaf.objSupIsoProdEqLocus_inv_snd, CategoryTheory.unitOfTensorIsoUnit_inv_app, CategoryTheory.Limits.Concrete.to_product_injective_of_isLimit, TopologicalSpace.Opens.overEquivalence_unitIso_inv_app_left, AlgebraicGeometry.StructureSheaf.const_algebraMap, SimplexCategory.toTopHomeo_naturality, CategoryTheory.preservesFiniteLimits_presheafToSheaf, CategoryTheory.NatTrans.naturality_app, CategoryTheory.Triangulated.TStructure.eTruncLT_obj_map_eTruncLTι_app_assoc, CategoryTheory.Limits.coend.ι_desc, CategoryTheory.sum.inlCompInlCompAssociator_inv_app_down, CategoryTheory.Triangulated.TStructure.isIso_eTruncLTLTIsoLT, CategoryTheory.Subfunctor.Subpresheaf.range_le_equalizer_iff, CategoryTheory.Sieve.uliftFunctorInclusion_app, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_counitIso, skyscraperPresheafCocone_ι_app, CategoryTheory.Adjunction.CommShift.compatibilityCounit_left, LeftExtension.coconeAtFunctor_obj, AlgebraicTopology.DoldKan.map_P, flipping_unitIso_hom_app_app_app, CategoryTheory.Triangulated.SpectralObject.id_hom, CategoryTheory.MonoidalCategory.externalProductBifunctorCurried_map_app_app_app, CategoryTheory.Equivalence.inverseFunctorObj'_hom_app, CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_obj_hom, CategoryTheory.Presheaf.hasSeparator, CategoryTheory.MorphismProperty.Comma.mapRightIso_inverse_obj_hom, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τr, CategoryTheory.GrothendieckTopology.pointBotPresheafFiberIso_inv, op_commShiftIso_inv_app, CategoryTheory.Arrow.augmentedCechNerve_left, CategoryTheory.Comma.unopFunctorCompSnd_inv_app, PresheafOfModules.map_comp, CategoryTheory.conjugateEquiv_mateEquiv_vcomp, CategoryTheory.cocones_obj_map_app, SSet.Subcomplex.image_eq_range, PresheafOfModules.instPreservesLimitsOfShapeFunctorOppositeAbToPresheaf, CategoryTheory.obj_η_app_assoc, CategoryTheory.coyonedaPreservesLimitsOfShape, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃'_map_app_app, HomologicalComplex.mapBifunctor₂₃.d₁_eq, instIsRightKanExtensionObjRanAppRanCounit, SSet.RelativeMorphism.comm, CategoryTheory.typeEquiv_counitIso_inv_app_hom_app, CategoryTheory.LocalizerMorphism.guitartExact_of_isLeftDerivabilityStructure', CategoryTheory.ShiftedHom.opEquiv'_symm_apply, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_neg_apply, SheafOfModules.inr_freeSumIso_hom_assoc, CategoryTheory.Limits.colimitPointwiseProductToProductColimit_app, CategoryTheory.yonedaFunctor_preservesLimits, CategoryTheory.Idempotents.DoldKan.η_inv_app_f, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_counitIso_hom_app_f, mapTriangleIdIso_hom_app_hom₃, CategoryTheory.Abelian.SpectralObject.sc₂_X₁, CategoryTheory.typeEquiv_inverse_map, CategoryTheory.Limits.PullbackCone.isoMk_inv_hom, rightDerivedZeroIsoSelf_inv_hom_id_app_assoc, CategoryTheory.IsFinitelyPresentable.exists_hom_of_isColimit, CategoryTheory.MorphismProperty.functorCategory_monomorphisms, CategoryTheory.Limits.colim_obj, CategoryTheory.Over.opEquivOpUnder_counitIso, CategoryTheory.Limits.FormalCoproduct.cechIsoAugmentedCechNerve_hom_right, CategoryTheory.NatTrans.mono_iff_mono_app', CategoryTheory.SimplicialObject.Augmented.whiskering_map_app_left, SSet.PtSimplex.MulStruct.δ_map_of_lt, CategoryTheory.AdditiveFunctor.forget_map, mapCone₂_pt, AddCommGrpCat.HasLimit.productLimitCone_cone_π, CategoryTheory.Comma.coconeOfPreserves_ι_app_left, closedUnit_app_app, CategoryTheory.ProdPreservesConnectedLimits.forgetCone_pt, CategoryTheory.Limits.filtered_colim_preservesFiniteLimits, LeftExtension.coconeAtWhiskerRightIso_hom_hom, CategoryTheory.OverPresheafAux.counitAux_hom, SheafOfModules.pushforward_map_val, RightExtension.IsPointwiseRightKanExtensionAt.isIso_hom_app, CategoryTheory.instPreservesFilteredColimitsOfSizeObjOppositeFunctorTypeCoyonedaOpOfIsFinitelyPresentable, CategoryTheory.CostructuredArrow.mapNatIso_unitIso_hom_app_left, CategoryTheory.SmallObject.SuccStruct.extendToSuccRestrictionLEIso_inv_app, CategoryTheory.MonoidalCategory.Limits.preservesLimit_curriedTensor, CategoryTheory.Abelian.SpectralObject.opcyclesIsoH_inv_hom_id_assoc, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_σ, instIsEquivalenceLeftExtensionCompPrecomp, CategoryTheory.NatTrans.CommShiftCore.shift_comm_assoc, equiv_unitIso, CategoryTheory.Limits.PreservesLimit₂.nonempty_isLimit_mapCone₂, CategoryTheory.mateEquiv_conjugateEquiv_vcomp, CategoryTheory.MonoidalCategory.tensoringRight_ε, CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_hom_app_app_hom, CategoryTheory.GrothendieckTopology.Point.instIsLeftAdjointSheafSheafFiber, CategoryTheory.Limits.coconeOfDiagramInitial_ι_app, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_eq_eqToIso, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_app, HomologicalComplex.ι_mapBifunctorMap_assoc, mapHomologicalComplex_commShiftIso_inv_app_f, HomologicalComplex.ιMapBifunctorOrZero_eq_zero, leftExtensionEquivalenceOfIso₁_inverse_obj_hom_app, CategoryTheory.CategoryOfElements.fromCostructuredArrow_map_coe, SSet.stdSimplex.instHasDimensionLEObjSimplexCategoryMk, CategoryTheory.GradedObject.mapBifunctor_map_app, sheafPushforwardCocontinuousCompSheafToPresheafIso_hom, CategoryTheory.Limits.coconeFiberwiseColimitOfCocone_ι_app, CategoryTheory.Limits.limit.isoLimitCone_inv_π_assoc, whiskeringLeft₃_obj_obj_obj_map_app_app_app, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_inv_apply, CategoryTheory.Equivalence.inverseFunctorMapIso_symm_eq_isoInverseOfIsoFunctor, CategoryTheory.CatCenter.smul_iso_inv_eq_assoc, SSet.stdSimplex.monotone_apply, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_μIso_hom, CategoryTheory.Idempotents.KaroubiUniversal₁.counitIso_hom_app_app_f, CommShift.id_commShiftIso_hom_app, groupHomology.isoShortComplexH1_inv, CategoryTheory.isoSheafify_hom, CategoryTheory.Sheaf.cartesianMonoidalCategoryFst_hom, CategoryTheory.Abelian.Preradical.isIso_toColon_hom_left_app_iff, CategoryTheory.Monad.monToMonad_map_toNatTrans, SSet.horn.faceι_ι, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_tensorHom_hom_eq_tensorHom, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₃, CategoryTheory.Adjunction.commShiftIso_hom_app_counit_app_shift_assoc, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_ε_assoc, Monoidal.transport_η_assoc, CategoryTheory.Limits.Cotrident.IsColimit.homIso_symm_apply, CategoryTheory.Limits.ColimitPresentation.w_assoc, SheafOfModules.pushforwardComp_hom_app_val_app, flipping_functor_obj_map_app, CategoryTheory.Bicategory.postcomposing_map_app, CategoryTheory.Limits.Cocone.precompose_obj_ι, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_inv_app, AlgebraicTopology.DoldKan.toKaroubiCompN₂IsoN₁_inv_app, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_unitIso_inv_app_f, CategoryTheory.Idempotents.KaroubiUniversal₁.counitIso_inv_app_app_f, LaxMonoidal.whiskeringRight_μ_app, CategoryTheory.Subfunctor.Subpresheaf.range_id, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app, CategoryTheory.StructuredArrow.map_map_left, CategoryTheory.GradedObject.mapBifunctorObjObjSingle₀Iso_inv, CategoryTheory.GrothendieckTopology.Point.instIsIsoMapFunctorOppositePresheafFiberToSheafify, PullbackObjObj.mapArrowLeft_left, CategoryTheory.eHomFunctor_obj_map, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_hom_app_hom₂, instPreservesLimitOfIsCoreflexivePairDiscreteObjWhiskeringLeftIncl, CategoryTheory.Adjunction.rightAdjointUniq_hom_counit_assoc, CategoryTheory.Presheaf.isLocallySurjective_comp, CategoryTheory.Localization.Monoidal.isInvertedBy₂, CategoryTheory.instPreservesFiniteLimitsObjFunctorLeftExactFunctor, isoWhiskerLeft_trans_isoWhiskerRight_assoc, triangleIso_assoc, CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_id, CategoryTheory.Bicategory.rightUnitorNatIso_inv_app, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd, flipIsoCurrySwapUncurry_hom_app_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso_hom_app_app, CondensedMod.LocallyConstant.instFaithfulSheafCompHausCoherentTopologyTypeConstantSheaf, CategoryTheory.Limits.CategoricalPullback.mkNatIso_hom_app_snd, CategoryTheory.SingleFunctors.postcomp_shiftIso_inv_app, CategoryTheory.shiftFunctorAdd_assoc_inv_app_assoc, mapCone₂_π_app, AlgebraicGeometry.Scheme.LocalRepresentability.glueData_V, CategoryTheory.yonedaGrpObjIsoOfRepresentableBy_hom, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.functor_obj, DerivedCategory.instFaithfulFunctorHomotopyCategoryIntUpObjWhiskeringLeftQh, instFullProdUncurry, SheafOfModules.unit_val, CategoryTheory.Subfunctor.lift_ι_assoc, CategoryTheory.FreeGroupoid.mapId_inv_app, LeftExtension.precomp_obj_right, CategoryTheory.Limits.limitFlipIsoCompLim_inv_app, CategoryTheory.shiftFunctorAdd_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_hom_app, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_app_hom, CategoryTheory.toOverIsoToOverUnit_hom_app_left, CategoryTheory.Adjunction.compYonedaIso_inv_app_app, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f, CategoryTheory.GrothendieckTopology.preservesSheafification_iff_of_adjunctions_of_hasSheafCompose, CategoryTheory.yonedaGrpObjIsoOfRepresentableBy_inv, CategoryTheory.Equivalence.changeInverse_counitIso_hom_app, CategoryTheory.Limits.CokernelCofork.isColimitMapBifunctor.exists_desc, LightCondSet.topCatAdjunctionUnit_hom_app_apply, leftUnitor_inv_app, CategoryTheory.Limits.HasLimit.isoOfNatIso_hom_π_assoc, mapTriangleRotateIso_hom_app_hom₁, SheafOfModules.Presentation.map_relations_I, CategoryTheory.SimplicialObject.Augmented.drop_obj, coreCompInclusionIso_inv_app, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_obj_map_app, CategoryTheory.BraidedCategory.tensorLeftIsoTensorRight_hom_app, PresheafOfModules.instPreservesLimitsOfSizeFunctorOppositeAbToPresheaf, CategoryTheory.Equivalence.sheafCongrPreregular_functor_map_hom_app, CategoryTheory.Sheaf.adjunction_unit_app_val, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.sq, SSet.Truncated.HomotopyCategory.homToNerveMk_app_one, CategoryTheory.FreeGroupoid.liftNatIso_inv_app, CategoryTheory.FunctorToTypes.shrinkCompUliftFunctorIso_hom_app, CategoryTheory.Coyoneda.colimitCoconeIsColimit_desc, CategoryTheory.Limits.instHasFiniteProductsFunctor, CategoryTheory.Comma.mapLeftEq_hom_app_right, SSet.stdSimplex.δ_one_toSSetObjI, TopCat.Presheaf.app_injective_of_stalkFunctor_map_injective, CategoryTheory.SimplicialObject.equivalenceRightToLeft_right, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_pos, const_map_app, CategoryTheory.Endofunctor.Algebra.functorOfNatTransId_hom_app_f, PullbackObjObj.mapArrowLeft_comp_assoc, CategoryTheory.GradedObject.ι_mapBifunctorMapMap_assoc, opInv_map, CategoryTheory.Limits.isIndObject_yoneda, CategoryTheory.Subfunctor.toRange_ι_assoc, TopCat.Presheaf.generateEquivalenceOpensLe_counitIso, CategoryTheory.MorphismProperty.Comma.mapLeftId_inv_app_right, CategoryTheory.StructuredArrow.mapIso_unitIso_inv_app_right, whiskeringRight₂_map_app_app_app, CategoryTheory.Cat.leftUnitor_hom_toNatTrans, CategoryTheory.FunctorToTypes.binaryCoproductColimit_desc, CategoryTheory.Cat.ihom_map, SSet.prodStdSimplex.objEquiv_map_apply, CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_left, SheafOfModules.instIsLeftAdjointOverOverRingCatPushforwardIdSheafOver, CategoryTheory.Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π_assoc, mapTriangleIso_hom_app_hom₃, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_π_app, CategoryTheory.MonoidalOpposite.tensorLeftUnmopIso_hom_app, CategoryTheory.Limits.DiagramOfCones.mkOfHasLimits_obj, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.flipFunctorToInterchange_inv_app_app, CategoryTheory.GradedObject.ι_mapBifunctor₁₂BifunctorDesc_assoc, CategoryTheory.Limits.spanCompIso_hom_app_right, SSet.stdSimplex.objEquiv_symm_mem_nonDegenerate_iff_mono, CategoryTheory.Subfunctor.Subpresheaf.homOfLe_ι, CategoryTheory.conjugateEquiv_comm, CategoryTheory.Abelian.SpectralObject.zero₁, lanUnit_app_whiskerLeft_lanAdjunction_counit_app_assoc, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_three, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatIso_inv, CategoryTheory.Presheaf.instIsLeftKanExtensionOppositeObjFunctorTypeYonedaYonedaMap, HomologicalComplex.mapBifunctor₂₃.ι_eq, isoWhiskerLeft_trans_assoc, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_hom_π_π_assoc, ihom_coev_app, LightProfinite.Extend.functorOp_map, CategoryTheory.Limits.pointwiseBinaryBicone_pt_map, TopCat.Sheaf.interUnionPullbackConeLift_left, PushoutObjObj.ι_iso_of_iso_left_inv, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality_assoc, CategoryTheory.NatIso.unop_leftUnitor, const.opObjOp_hom_app, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₂, MonObj.mopEquivCompForgetIso_inv_app_unmop, CategoryTheory.Subfunctor.instIsIsoFunctorTypeιTop, LeftExtension.postcompose₂_obj_left, CategoryTheory.Sieve.yonedaFamily_fromCocone_compatible, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_counitIso, CategoryTheory.NatIso.unop_associator, isIso_lanAdjunction_homEquiv_symm_iff, instIsRightAdjointSSetTopCatToSSet, CategoryTheory.GrothendieckTopology.W.whiskerLeft, sumIsoExt_inv_app_inl, CategoryTheory.MonoidalCategory.externalProductFlip_hom_app_app_app_app, CategoryTheory.RightExactFunctor.ofExact_map, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s₀_comp_δ₁, CategoryTheory.GrothendieckTopology.uliftYoneda_obj_obj_obj, CategoryTheory.LeftExactFunctor.ofExact_obj, CategoryTheory.toSheafification_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_hom_app_fst_app, CategoryTheory.TransfiniteCompositionOfShape.ici_isColimit, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app_assoc, CategoryTheory.Abelian.SpectralObject.δ_naturality_assoc, CategoryTheory.MorphismProperty.functorCategory_epimorphisms, CategoryTheory.ComposableArrows.δlastFunctor_obj_obj, CategoryTheory.SimplicialObject.cechNerve_obj, CategoryTheory.Limits.colimit.ι_desc_apply, Alexandrov.lowerCone_π_app, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_fst, CategoryTheory.Limits.IndObjectPresentation.ofCocone_I, CategoryTheory.extendCofan_ι_app, CategoryTheory.Limits.colimitLimitToLimitColimitCone_iso, CategoryTheory.MonoidalCategory.externalProductBifunctorCurried_obj_obj_map_app, instPreservesColimitSheafTypeYonedaOfPreservesLimitOppositeOpObjFunctorIsSheaf, CategoryTheory.Join.mapWhisker_exchange, CategoryTheory.Triangulated.TStructure.eTruncLTGELTSelfToGELT_app, CategoryTheory.Comma.opFunctorCompSnd_hom_app, LeftExtension.IsPointwiseLeftKanExtension.isIso_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionObj, CategoryTheory.MonoidalClosed.pre_id, CategoryTheory.NatTrans.IsMonoidal.instHomFunctorRightUnitor, RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π, CategoryTheory.Localization.SmallShiftedHom.equiv_shift, LeftExtension.precomp_obj_left, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.inverse_obj_map, CategoryTheory.Subfunctor.instIsIsoFunctorTypeToRangeOfMono, shiftIso_hom_naturality_assoc, CategoryTheory.opOpEquivalence_unitIso, instPreservesFiniteLimitsFunctorAddCommGrpCatColim, instPreservesColimitsOfShapeSheafTypeYonedaOfPreservesLimitsOfShapeOppositeObjFunctorIsSheaf, CategoryTheory.Triangulated.TStructure.truncLEIsoTruncLT_inv_ι_assoc, CategoryTheory.WithInitial.opEquiv_counitIso_inv_app, CategoryTheory.ShiftMkCore.add_zero_inv_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_obj, CategoryTheory.Limits.CatCospanTransform.inv_right, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_inv_app_hom_app, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_snd_coe, sectionsEquivHom_naturality_symm, CategoryTheory.hoFunctor.isIso_prodComparison_stdSimplex, CategoryTheory.HasShift.Induced.zero_hom_app_obj, Bipointed.swapEquiv_counitIso_inv_app_toFun, CategoryTheory.NatTrans.unop_id, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_two_assoc, Monoidal.tensorHom_app_fst, CategoryTheory.Limits.coneLeftOpOfCocone_π_app, AlgebraicTopology.DoldKan.natTransP_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.mkIso_inv_snd, PresheafOfModules.Elements.fromFreeYoneda_app_apply, CategoryTheory.StructuredArrow.mapIso_functor_map_left, CategoryTheory.Equivalence.congrLeftFunctor_map, CategoryTheory.Localization.Monoidal.lifting₂CurriedTensorPost_iso, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.e_inv_app, ModuleCat.binaryProductLimitCone_cone_π_app_left, flipping_unitIso_inv_app_app_app, SSet.Truncated.comp_app_assoc, CategoryTheory.Coyoneda.colimitCocone_pt, SSet.Subcomplex.homOfLE_comp, CategoryTheory.liftedLimitMapsToOriginal_inv_map_π, SSet.Truncated.Edge.map_tensorHom, CategoryTheory.Adjunction.CoreUnitCounit.right_triangle, CategoryTheory.PreGaloisCategory.functorToAction_map, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_inv_app_one, CategoryTheory.Adjunction.shift_unit_app, CategoryTheory.Join.inclLeftCompOpEquivInverse_inv_app_op, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_fst_obj, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃'_obj_obj_obj, PushoutObjObj.inl_ι_assoc, CategoryTheory.Quotient.natIsoLift_hom, SSet.horn.edge₃_coe_down, SheafOfModules.Presentation.mapRelations_mapGenerators, CategoryTheory.Limits.Cone.equivalenceOfReindexing_functor, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app_assoc, CategoryTheory.ChosenPullbacksAlong.pullbackId_hom_counit_assoc, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_map_hom_hom_app, CategoryTheory.Adjunction.unit_app_commShiftIso_hom_app_assoc, TopCat.continuous_iff_of_isColimit, LaxMonoidal.ofBifunctor.secondMap₂_app_app_app, CategoryTheory.MorphismProperty.instIsStableUnderBaseChangeFunctorFunctorCategoryOfHasPullbacks, AlgebraicTopology.DoldKan.N₁_obj_X, CategoryTheory.shrinkYonedaGrp_obj_map_shrinkYonedaGrpObjObjEquiv_symm, CategoryTheory.Abelian.SpectralObject.δ_naturality, CategoryTheory.Abelian.SpectralObject.d_EIsoH_hom_assoc, CategoryTheory.Limits.instPreservesFiniteLimitsFunctorColimOfPreservesColimitsOfShapeOfHasFiniteLimitsOfReflectsIsomorphismsForget, SSet.Truncated.rightExtensionInclusion_left, FundamentalGroupoid.punitEquivDiscretePUnit_unitIso, map₂HomologicalComplex_obj_obj, CategoryTheory.Monad.algebraEquivOfIsoMonads_counitIso, CategoryTheory.Sigma.inclCompMap_hom_app, CategoryTheory.Limits.KernelFork.app_one, RepresentableBy.uniqueUpToIso_hom, CategoryTheory.Abelian.SpectralObject.sc₃_X₁, PreOneHypercoverDenseData.multicospanMapIso_inv, AlgebraicTopology.map_alternatingFaceMapComplex, leftKanExtensionCompIsoOfPreserves_hom_fac, preservesFilteredColimits_coyoneda, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso_hom_app_f, CategoryTheory.NatIso.hom_app_isIso, LightCondensed.hom_ext_iff, coneOfIsRightKanExtension_π, CategoryTheory.Limits.Fork.app_zero_eq_ι, CategoryTheory.uliftYoneda_map_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiberMap_presheafFiberMapObjIso_hom, CategoryTheory.Yoneda.yoneda_full, CategoryTheory.sheafificationIso_inv_hom, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_carrier, CategoryTheory.Preadditive.commGrpEquivalenceAux_inv_app_hom_hom_hom, CategoryTheory.Limits.limit.cone_π, leftExtensionEquivalenceOfIso₁_functor_obj_hom_app, CategoryTheory.Comma.mapLeftIso_inverse_obj_hom, CategoryTheory.Limits.IsLimit.isIso_limMap_π, map_opShiftFunctorEquivalence_counitIso_hom_app_unop, CategoryTheory.Limits.CatCospanTransform.category_id_base, CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_naturality_app_assoc, CategoryTheory.SimplicialThickening.SimplicialCategory.assoc, Monoidal.whiskerLeft_app_snd, CategoryTheory.Limits.Types.Colimit.ι_desc_apply, whiskerRight_zero, SSet.stdSimplex.const_down_toOrderHom, CategoryTheory.Cat.Hom.hom_inv_id_toNatTrans_assoc, uliftYonedaReprXIso_hom_app, CategoryTheory.ComposableArrows.scMapIso_hom, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_unitIso, SSet.Subcomplex.topIso_inv_ι_assoc, CategoryTheory.NatIso.op_leftUnitor, whiskeringLeft₂_map_app_app_app_app, CategoryTheory.ComposableArrows.opEquivalence_functor_obj_obj, CategoryTheory.Equivalence.mapCommMon_counitIso, HomologicalComplex.mapBifunctor₁₂.ι_D₃, CategoryTheory.Limits.FormalCoproduct.cochainComplexFunctor_obj_X, rightKanExtensionCompIsoOfPreserves_hom_fac, CategoryTheory.Equivalence.Equivalence_mk'_unit, AddCommGrpCat.leftExactFunctorForgetEquivalence.instPreservesFiniteLimitsObjLeftExactFunctorTypeFunctorInverseAux, CategoryTheory.Limits.limit.lift_π_apply, CategoryTheory.Limits.DiagramOfCones.conePoints_obj, pointedToBipointedCompBipointedToPointedSnd_inv_app_toFun, CategoryTheory.Hom.addEquivCongrRight_apply, CategoryTheory.equivYoneda_hom_app, AlgebraicGeometry.Scheme.GlueData.sheafValGluedMk_val, CategoryTheory.Equivalence.sheafCongr_counitIso, CategoryTheory.NatTrans.mapHomotopyCategory_id, CategoryTheory.Presheaf.instIsCardinalPresentableFunctorOppositeTypeObjUliftYonedaOfHasColimitsOfSize, TopCat.Presheaf.presheafEquivOfIso_unitIso_inv_app_app, CategoryTheory.Limits.coend.map_comp, PresheafOfModules.instFaithfulSheafOfModulesCompObjFunctorOppositeRingCatIsSheafForgetRestrictScalars, SSet.horn₂₁.isPushout, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_map_right, CategoryTheory.Enriched.FunctorCategory.functorEnrichedComp_app, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁'_obj_map_app, CategoryTheory.Comma.mapLeftId_hom_app_left, CategoryTheory.Cat.associator_inv_toNatTrans, CategoryTheory.Limits.pullbackConeOfRightIso_π_app_left, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_left_assoc, CategoryTheory.MonoidalOpposite.mopMopEquivalence_counitIso_inv_app, CategoryTheory.GrothendieckTopology.uliftYonedaIsoYoneda_hom_app_hom_app, CategoryTheory.Abelian.SpectralObject.leftHomologyDataShortComplex_π, SheafOfModules.relationsOfIsCokernelFree_I, ProfiniteGrp.cone_π_app, CategoryTheory.Limits.preservesColimits_const, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd, CategoryTheory.Limits.Cone.toStructuredArrowCompProj_hom_app, CategoryTheory.Limits.Trident.ofCone_π, CategoryTheory.Triangulated.SpectralObject.distinguished', CategoryTheory.Limits.instIsLeftAdjointFunctorColim, map_opShiftFunctorEquivalence_counitIso_inv_app_unop_assoc, curryingEquiv_apply_map, CategoryTheory.Presieve.FamilyOfElements.compPresheafMap_comp, AlgebraicGeometry.Scheme.LocalRepresentability.instIsIsoSheafZariskiTopologyTypeYonedaGluedToSheaf, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₂, CompHausLike.pullback.cone_π, CategoryTheory.Adjunction.isIso_unit_of_iso, AlgebraicGeometry.Scheme.LocalRepresentability.glueData_f, CategoryTheory.Limits.Cocone.w, CategoryTheory.NatTrans.app_sum, CategoryTheory.MonoOver.congr_inverse, flip₁₃Functor_obj_obj_map_app, CategoryTheory.monadToFunctor_mapIso_monad_iso_mk, CategoryTheory.Cat.leftUnitor_inv_toNatTrans, Monoidal.commTensorLeft_inv_app, Rep.isZero_Tor_succ_of_projective, CategoryTheory.Limits.Types.Small.limitConeIsLimit_lift, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_naturality_assoc, leibnizPushout_obj_obj, CategoryTheory.Join.mapPairId_inv_app, const.opObjOp_inv_app, CategoryTheory.tensoringLeft_additive, HomologicalComplex.mapBifunctorAssociatorX_hom_D₁, AlgebraicGeometry.structureSheafInType.add_apply, CategoryTheory.Presheaf.isLocallyInjective_comp_iff, CategoryTheory.MonoidalCategory.Functor.curriedTensorPreIsoPost_hom_app_app, CorepresentableBy.equivUliftCoyonedaIso_symm_apply_homEquiv, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ_assoc, CategoryTheory.Triangulated.TStructure.eTruncGE_obj_map_eTruncGEπ_app, CategoryTheory.Adjunction.rightAdjointUniq_hom_counit, CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj, CategoryTheory.Iso.core_hom_app_iso_inv, AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap, CategoryTheory.ObjectProperty.IsDetecting.isIso_iff_of_mono, CategoryTheory.FunctorToTypes.functorHomEquiv_apply_app, CategoryTheory.Comma.mapLeftId_inv_app_left, SSet.horn_eq_iSup, commShiftOfLocalization.iso_hom_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_δ, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_right, sheafPushforwardContinuous_obj_obj_map, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_map_fst_app, mapMonIdIso_inv_app_hom, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π, SSet.Subcomplex.unionProd.ι₂_ι_assoc, CategoryTheory.Limits.piConst_obj_obj, AlgebraicTopology.DoldKan.Γ₀_obj_obj, CategoryTheory.Iso.isoCompInverse_inv_app, CategoryTheory.NatTrans.app_shift_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality, postcompose₂_obj_map_app_app, CategoryTheory.Tor'_obj_map, LightCondensed.underlying_obj, CategoryTheory.Presieve.IsSheafFor.functorInclusion_comp_extend, CategoryTheory.Limits.evaluation_preservesColimits, CategoryTheory.GradedObject.comapEq_hom_app, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_unitIso, CategoryTheory.sum.inrCompAssociator_hom_app_down_down, CategoryTheory.Limits.limit.conePointUniqueUpToIso_hom_comp, CategoryTheory.cosimplicialSimplicialEquiv_unitIso_inv_app, HomologicalComplex.mapBifunctor₂₃.ι_D₁_assoc, CategoryTheory.Limits.pullbackObjIso_hom_comp_fst_assoc, AlgebraicGeometry.Scheme.LocalRepresentability.glueData_t', CategoryTheory.MonoidalCategory.curriedTensor_obj_obj, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_limit_map, CategoryTheory.Triangulated.SpectralObject.triangle_mor₁, mapCone_π_app, CategoryTheory.yonedaMap_app_apply, CategoryTheory.ε_app_obj, toSheafify_pullbackSheafificationCompatibility, CategoryTheory.ComposableArrows.isoMk₃_hom, CategoryTheory.Adjunction.homEquiv_ofNatIsoRight_symm_apply, CategoryTheory.Equivalence.mapMon_counitIso, CategoryTheory.Sheaf.Ω_obj, CategoryTheory.Sheaf.ΓHomEquiv_naturality_right_symm, SSet.yonedaEquiv_const, CategoryTheory.Pseudofunctor.toDescentDataAsCoalgebraCompCoalgebraEquivalenceFunctorIso_hom_app_f, CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_right_assoc, SimplexCategory.revCompRevIso_hom_app, CategoryTheory.Triangulated.TStructure.π_natTransTruncGEOfLE, CategoryTheory.Limits.Cone.equivCostructuredArrow_functor, IsCoverDense.Types.naturality_apply, SSet.stdSimplex.obj₀Equiv_symm_mem_face_iff, CategoryTheory.Iso.hom_inv_id_app_assoc, CategoryTheory.MonoidalOpposite.tensorRightIso_hom_app_unmop, SimplicialObject.opFunctorCompOpFunctorIso_hom_app_app, CategoryTheory.Limits.limit_map_limitObjIsoLimitCompEvaluation_hom_assoc, SSet.prodStdSimplex.nonDegenerateEquiv₁_fst, CategoryTheory.GrothendieckTopology.preservesLimitsOfSize_yoneda, SSet.range_eq_iSup_sigma_ι, SSet.Subcomplex.BicartSq.isPushout, CategoryTheory.AdditiveFunctor.ofRightExact_obj_fst, CategoryTheory.Arrow.augmentedCechNerve_right, CategoryTheory.Limits.WidePushoutShape.mkCocone_ι_app, CategoryTheory.Limits.Cone.whiskeringEquivalence_counitIso, CategoryTheory.ShiftedHom.map_naturality_1, MonObj.mopEquiv_unitIso_hom_app_hom, CategoryTheory.Pseudofunctor.ObjectProperty.mapId_hom_app, CategoryTheory.Abelian.SpectralObject.p_opcyclesIso_inv_assoc, CategoryTheory.NatTrans.rightOpWhiskerRight_assoc, pointedToBipointedCompBipointedToPointedFst_inv_app_toFun, CategoryTheory.Iso.isoInverseOfIsoFunctor_inv_app, CategoryTheory.SmallObject.SuccStruct.ofCocone_map_to_top, SSet.Subcomplex.range_comp, CategoryTheory.SpectralSequence.pageHomologyNatIso_inv_app, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_π_app, commShiftIso_id_hom_app, CategoryTheory.Grothendieck.ιCompMap_inv_app_base, lanAdjunction_unit, CategoryTheory.ComposableArrows.whiskerLeftFunctor_map_app, CategoryTheory.Over.conePostIso_inv_app_hom, CategoryTheory.Abelian.SpectralObject.shortComplexMap_τ₂, CategoryTheory.Limits.Types.binaryProductFunctor_obj_obj, CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair_inv_app, leftDerivedZeroIsoSelf_inv_hom_id_app, CategoryTheory.Limits.pointwiseBinaryBicone_pt_obj, PreservesPointwiseRightKanExtensionAt.preserves, shiftIso_hom_app_comp_assoc, CategoryTheory.Sheaf.coneΓ_π_app, CategoryTheory.SimplicialObject.Truncated.trunc_map_app, SSet.prodStdSimplex.instFiniteTensorObjObjSimplexCategoryStdSimplexMk, CategoryTheory.prod.leftUnitorEquivalence_counitIso, CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_hom_π_π, SSet.stdSimplex.objEquiv_symm_comp, CategoryTheory.SimplicialObject.Augmented.w₀_assoc, Fiber.inducedFunctorCompIsoSelf_hom_app, OneHypercoverDenseData.essSurj.presheafObj_condition, curryObjCompIso_inv_app_app, CategoryTheory.Equivalence.core_counitIso_hom_app_iso_hom, CategoryTheory.ChosenPullbacksAlong.pullbackComp_hom_counit, TopCat.subsheafToTypes_obj, CategoryTheory.Limits.FormalCoproduct.instPreservesLimitOppositeDiscreteFunctorCompOpObjFunctorEvalOp, CategoryTheory.GradedObject.mapBifunctorMap_map_app, CategoryTheory.SimplicialObject.cechNerve_map, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_symm_apply, CategoryTheory.Discrete.natIso_hom_app, CategoryTheory.shrinkYoneda_obj_map_shrinkYonedaObjObjEquiv_symm, CategoryTheory.GrothendieckTopology.Cover.multicospanComp_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_snd_map, mapCommGrpIdIso_hom_app_hom_hom_hom, CategoryTheory.instHasSubobjectClassifierFunctorOppositeTypeOfEssentiallySmall, HomotopicalAlgebra.CofibrantObject.HoCat.adjCounitIso_inv_app, TopCat.Presheaf.presheafEquivOfIso_functor_obj_obj, CategoryTheory.WithTerminal.commaFromOver_obj_hom_app, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransEq_hom_app_f, AlgebraicGeometry.AffineSpace.functor_obj_obj, SSet.Subcomplex.eqToIso_inv, CategoryTheory.Sheaf.ΓObjEquivHom_naturality, CategoryTheory.obj_μ_inv_app, CategoryTheory.Limits.colimit.ι_desc, CategoryTheory.NatTrans.appHom_apply, CategoryTheory.Limits.coneOfConeUncurry_π_app, CategoryTheory.SimplicialObject.whiskering_obj_obj_obj, IsRepresentedBy.uliftYonedaIso_hom, CategoryTheory.Limits.end_.map_comp, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_σ_assoc, CategoryTheory.GrothendieckTopology.isoToPlus_inv, CategoryTheory.Sheaf.ΓRes_map, CategoryTheory.NatTrans.leftDerived_comp_assoc, SimplicialObject.opEquivalence_unitIso, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinset_map_app, CategoryTheory.functorProdToProdFunctor_map, SheafOfModules.pushforwardCongr_symm, CategoryTheory.Idempotents.DoldKan.Γ_obj_map, RightExtension.IsPointwiseRightKanExtension.isRightKanExtension, CategoryTheory.NatTrans.CommShift₂.instCompFunctor, const.unop_functor_op_obj_map, rightKanExtensionCompIsoOfPreserves_inv_fac, leftOpComp_inv_app, CategoryTheory.Limits.MonoCoprod.mono_inl_iff, CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj_obj_p, instIsCorepresentableCompObjOppositeTypeCoyonedaOpObjLeftAdjointObjIsDefined, Rep.coinvariantsTensorIndNatIso_hom_app, CommShift.ofIso_commShiftIso_inv_app, CategoryTheory.Comma.opFunctorCompFst_hom_app, CategoryTheory.Sieve.shrinkFunctorUliftFunctorIso_inv_ι_assoc, CategoryTheory.GrothendieckTopology.Point.sheafFiberComapIso_hom_app, CategoryTheory.Limits.Types.jointly_surjective_of_isColimit, LightCondSet.hom_naturality_apply, CategoryTheory.Limits.evaluation_preservesColimitsOfShape, CategoryTheory.GrothendieckTopology.Point.toPresheafFiberMap_naturality_apply, CategoryTheory.Equivalence.trans_counitIso, CategoryTheory.evaluationRightAdjoint_obj_obj, CategoryTheory.ComposableArrows.δlastFunctor_map_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMop_map_unmop_app, CategoryTheory.CatCenter.mul_app'_assoc, CategoryTheory.Comma.toPUnitIdEquiv_unitIso_hom_app_left, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₃, CategoryTheory.CatCommSq.vInv_iso_inv_app, LaxMonoidal.whiskeringRight_ε_app, leftDerivedNatIso_hom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_naturality₂, CochainComplex.shiftFunctorZero'_inv_app_f, SSet.Subcomplex.prod_monotone, CategoryTheory.MorphismProperty.Comma.mapRightComp_inv_app_left, CategoryTheory.Limits.Multicofork.fst_app_right, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse_assoc, SSet.ι₀_comp_assoc, CommGrpCat.coyonedaForget_hom_app_app_hom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.mkIso_hom_fst, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv', constCompEvaluationObj_inv_app, CategoryTheory.oppositeShiftFunctorZero_hom_app, CategoryTheory.Comma.mapRightIso_unitIso_hom_app_left, CategoryTheory.Abelian.SpectralObject.homologyDataIdId_left_K, CategoryTheory.Limits.limitCompYonedaIsoCocone_inv, HomologicalComplex.singleMapHomologicalComplex_inv_app_ne, CategoryTheory.WithInitial.equivComma_unitIso_inv_app_app, CategoryTheory.MonoidalOpposite.tensorRightIso_inv_app_unmop, SSet.Subcomplex.instMonoι, CategoryTheory.Limits.asEmptyCone_π_app, CategoryTheory.Limits.fiberwiseColimCompEvaluationIso_hom_app, CategoryTheory.Limits.Fork.op_ι_app, AlgebraicGeometry.AffineSpace.functor_map_app, instIsEquivalenceObjWhiskeringRight, CategoryTheory.prod.rightUnitorEquivalence_unitIso, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_obj_f, CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counitIso_hom_app_assoc, SheafOfModules.add_val, CategoryTheory.SimplicialObject.Augmented.const_obj_left, CategoryTheory.Limits.pointwiseBinaryBicone.isBilimit_isLimit, CategoryTheory.functorProdFunctorEquivCounitIso_inv_app_app, CategoryTheory.RelCat.opEquivalence_counitIso, CategoryTheory.Limits.pointwiseBinaryBicone_inl_app, AlgebraicGeometry.Scheme.LocalRepresentability.yoneda_toGlued_yonedaGluedToSheaf, CategoryTheory.Abelian.SpectralObject.δ_pOpcycles_assoc, Monoidal.tensorHom_app_snd, CategoryTheory.conjugateEquiv_comp_assoc, CategoryTheory.instFullGrpFunctorOppositeGrpCatYonedaGrp, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.iso_hom_naturality_assoc, CategoryTheory.CartesianMonoidalCategory.instIsIsoFunctorProdComparisonNatTransOfProdComparison, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_incl, IsEventuallyConstantTo.isIso_π_of_isLimit, OplaxMonoidal.ofBifunctor.bottomMapᵣ_app, CategoryTheory.associativity_app_assoc, CategoryTheory.WithInitial.commaFromUnder_map_right, CategoryTheory.coyonedaEquiv_coyoneda_map, CategoryTheory.Limits.ColimitPresentation.Total.Hom.w_assoc, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv_desc, CategoryTheory.ThinSkeleton.map₂_map, CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_cancel_inv_app, CategoryTheory.CatCenter.smul_iso_hom_eq_assoc, CategoryTheory.IsPreconnected.iso_constant, CategoryTheory.endofunctorMonoidalCategory_leftUnitor_hom_app, CategoryTheory.CategoryOfElements.costructuredArrow_yoneda_equivalence_naturality, CategoryTheory.evaluationIsLeftAdjoint, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₁, CategoryTheory.Limits.Bicone.toCocone_ι_app, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_naturality, lanCompIsoOfPreserves_inv_app, CategoryTheory.WithInitial.equivComma_functor_obj_left, SSet.horn₃₂.ι₁_desc_assoc, CategoryTheory.Cat.Hom.instIsIsoFunctorαCategoryToNatTransInvHom, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_app, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_assoc, CategoryTheory.Sheaf.cartesianMonoidalCategoryWhiskerRight_val, isoWhiskerLeft_refl, CategoryTheory.Limits.Trident.ofι_π_app, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_distinguished, AlgebraicGeometry.Proj.add_apply, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_inv_comp_π, CategoryTheory.sheafifyMap_comp, CategoryTheory.GrothendieckTopology.plusFunctor_map, HomologicalComplex.ι_mapBifunctorDesc_assoc, CategoryTheory.Presieve.EffectiveEpimorphic.iff_forall_isSheafFor_yoneda, CategoryTheory.Limits.coneOfSectionCompYoneda_π, instFaithfulOppositeTypeRestrictedULiftYonedaOfIsDense, CategoryTheory.shrinkYonedaObjObjEquiv_symm_comp, CategoryTheory.Comma.opFunctorCompFst_inv_app, CategoryTheory.Abelian.SpectralObject.id_hom, CategoryTheory.Limits.cospanExt_hom_app_one, CategoryTheory.Limits.coend.ι_map, PresheafOfModules.sheafifyMap_val, mapActionCongr_inv, CategoryTheory.LocalizerMorphism.guitartExact_of_isRightDerivabilityStructure, CategoryTheory.SimplicialObject.augmentOfIsTerminal_right, CategoryTheory.GrothendieckTopology.sheafifyMap_comp, CategoryTheory.Localization.lift₂NatIso_hom, SheafOfModules.instFaithfulSheafAddCommGrpCatToSheaf, CategoryTheory.WithInitial.inclLift_inv_app, CategoryTheory.ObjectProperty.IsConservativeFamilyOfPoints.jointlyFaithful, HomotopyCategory.composableArrowsFunctor_map, NatTrans.hcomp_eq_whiskerRight_comp_whiskerLeft, CategoryTheory.Presheaf.classifier_truth, CategoryTheory.Limits.ι_comp_sigmaObjIso_hom_assoc, flip_obj_map, CategoryTheory.Triangulated.TStructure.isLE_eTruncLT_obj_obj, CategoryTheory.Limits.diagramIsoParallelFamily_hom_app, coreId_hom_app_iso_inv, CategoryTheory.Presheaf.isStrongGenerator, CategoryTheory.Abelian.instAdditiveOppositeFunctorAddCommGrpCatExtFunctor, CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_hom, CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ, CategoryTheory.ParametrizedAdjunction.unit_whiskerRight_map_assoc, CategoryTheory.Presheaf.isPullback_χ_truth, mapTriangleCompIso_inv_app_hom₁, CategoryTheory.simplicialCosimplicialEquiv_inverse_obj, CategoryTheory.Limits.Concrete.surjective_π_app_zero_of_surjective_map, SSet.ι₀_comp, pi'CompEval_inv_app, CategoryTheory.MonoidalCategory.DayFunctor.comp_natTrans, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_app_assoc, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_unitIso, CategoryTheory.Limits.IndObjectPresentation.ofCocone_isColimit, CategoryTheory.Join.mapWhiskerRight_whiskerLeft, AlgebraicTopology.DoldKan.natTransPInfty_f_app, CategoryTheory.Bicategory.associatorNatIsoMiddle_hom_app, CondensedSet.isDiscrete_tfae, isLeftKanExtensionId, CategoryTheory.Idempotents.DoldKan.Γ_obj_obj, SSet.horn₃₂.desc.multicofork_π_zero_assoc, CategoryTheory.linearCoyoneda_obj_map, pointedToBipointedCompBipointedToPointedFst_hom_app_toFun, CategoryTheory.Limits.CatCospanTransform.category_comp_base, Profinite.exists_locallyConstant, CategoryTheory.Limits.CatCospanTransform.isIso_left, CategoryTheory.simplicialCosimplicialEquiv_functor_map_app, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.functor_map_app_hom, leftOpRightOpEquiv_counitIso_hom_app_app, SSet.Homotopy.h₀_assoc, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isModule_smul_apply, CategoryTheory.CatCommSq.hComp_iso_inv_app, CategoryTheory.OverPresheafAux.restrictedYonedaObj_obj, CategoryTheory.Limits.Trident.equalizer_ext, CategoryTheory.OverPresheafAux.MakesOverArrow.app, isLeftKanExtension_iff_postcomp₁, AlgebraicGeometry.stalkMap_toStalk_apply, CategoryTheory.Triangulated.TStructure.π_truncGTIsoTruncGE_hom_assoc, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_inr, CategoryTheory.Subfunctor.equalizer.condition, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_π_app, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp, CategoryTheory.ExactFunctor.whiskeringRight_map_app, CategoryTheory.DifferentialObject.shiftFunctorAdd_inv_app_f, CategoryTheory.shiftFunctorAdd_add_zero_inv_app, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_unitIso, CategoryTheory.Adjunction.leftAdjointUniq_hom_counit_assoc, CategoryTheory.PreGaloisCategory.instPreservesFiniteCoproductsActionFintypeCatAutFunctorFunctorToAction, PresheafOfModules.comp_toPresheaf_map_sheafifyHomEquiv'_symm_hom, CategoryTheory.extendFan_π_app, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInrIso_hom_app_app, CategoryTheory.ShortComplex.rightHomologyFunctorOpNatIso_hom_app, CategoryTheory.Equivalence.sheafCongr.counitIso_inv_app_hom_app, CategoryTheory.Limits.lim_μ_π_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_μ_app, CategoryTheory.Limits.CatCospanTransform.category_comp_right, currying_unitIso_inv_app_app_app, CategoryTheory.coreFunctor_map_app_iso_inv, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_hom_app_hom, CategoryTheory.Subobject.le_inf, CategoryTheory.OverPresheafAux.OverArrows.app_val, coconeTypesEquiv_apply_ι_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_δ_unmop_app, CategoryTheory.IsDetecting.isIso_iff_of_mono, opHom_obj, CategoryTheory.Equivalence.mapAddMon_counitIso, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_obj_obj_map, currying_unitIso_hom_app_app_app, CategoryTheory.Abelian.SpectralObject.shortComplexMap_τ₃, CategoryTheory.Subfunctor.range_eq_ofSection, CategoryTheory.evaluationUncurried_map, CategoryTheory.orderDualEquivalence_counitIso, CategoryTheory.coprodMonad_η_app, CategoryTheory.Discrete.productEquiv_counitIso_inv_app, CategoryTheory.linearYoneda_obj_additive, CategoryTheory.Equivalence.counitIso_inv_app_comp_functor_map_η_inverse_assoc, Rep.indCoindNatIso_inv_app, CategoryTheory.Join.pseudofunctorRight_mapComp_hom_toNatTrans_app, CategoryTheory.Limits.preservesLimits_const, CategoryTheory.sheafBotEquivalence_inverse_obj_obj, CategoryTheory.MonoidalCategory.curriedAssociatorNatIso_inv_app_app_app, CategoryTheory.Iso.unop_hom_inv_id_app_assoc, CategoryTheory.Subobject.lowerEquivalence_counitIso, CategoryTheory.Idempotents.karoubiUniversal₁_counitIso, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_assoc, CategoryTheory.Adjunction.Triple.leftToRight_eq_counits, CategoryTheory.Limits.Cocone.w_apply, CategoryTheory.Abelian.SpectralObject.map_comp, CategoryTheory.Limits.colimit.pre_map', AlgebraicGeometry.Scheme.Modules.pushforwardId_hom_app_app, CategoryTheory.Equivalence.mapHomologicalComplex_counitIso, CategoryTheory.Limits.BinaryBicone.ofLimitCone_snd, rightDerivedZeroIsoSelf_inv_hom_id_app, SSet.opEquivalence_unitIso, CategoryTheory.WithInitial.inclLiftToInitial_hom_app, CategoryTheory.Abelian.SpectralObject.sc₂_X₂, mapCocone₂_pt, CategoryTheory.Pi.sum_obj_map, CategoryTheory.LocalizerMorphism.isRightDerivabilityStructure_iff, CategoryTheory.Adjunction.counit_isIso_of_R_fully_faithful, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_inv_assoc, TopCat.Sheaf.IsFlasque.structured_arrows_elements_sheaf_chains_bounded, CategoryTheory.η_app, CategoryTheory.ShiftedHom.opEquiv_symm_apply_comp, CategoryTheory.yonedaPairing_map, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_obj_map_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app, AlgebraicGeometry.ExistsHomHomCompEqCompAux.ha, AlgebraicTopology.DoldKan.Γ₂N₂ToKaroubiIso_inv_app, Action.functorCategoryEquivalence_counitIso, CategoryTheory.GradedObject.mapBifunctorMapObj_ext_iff, AlgebraicTopology.DoldKan.instMonoChainComplexNatInclusionOfMooreComplexMap, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_rightUnitor_hom_eq_rightUnitor_hom, CategoryTheory.GrothendieckTopology.toSheafify_comp_sheafifyCompIso_inv, RightExtension.mk_left, closedIhom_obj_obj, CategoryTheory.Sigma.inclCompMap_inv_app, CategoryTheory.Sheaf.instHasLimitsOfShape, SSet.Augmented.stdSimplex_obj_hom_app, CategoryTheory.Join.mapWhiskerRight_whiskerLeft_assoc, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_map_fst, IsCoverDense.iso_of_restrict_iso, CategoryTheory.GrothendieckTopology.overMapPullback_comp_id_assoc, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_π, rightOpComp_inv_app, CategoryTheory.Limits.cospanCompIso_inv_app_one, CategoryTheory.bifunctorComp₂₃FunctorObj_map_app_app_app, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₁, CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_inv_apply, CategoryTheory.Monad.monadMonEquiv_inverse, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_inv_app_hom_hom_hom, CategoryTheory.Limits.functorCategoryHasLimitsOfShape, CategoryTheory.SimplicialObject.whiskering_obj_obj_map, CategoryTheory.Abelian.DoldKan.equivalence_inverse, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_inv_app_fst_app, CategoryTheory.Over.conePost_obj_pt, CategoryTheory.Abelian.SpectralObject.cokernelIsoCycles_hom_fac, FullyFaithful.hasShift.map_add_hom_app, isoWhiskerRight_hom, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_g, SSet.horn.faceι_ι_assoc, CategoryTheory.Cat.Hom.toNatIso_rightUnitor, CategoryTheory.GrothendieckTopology.Point.comp_hom, CategoryTheory.uliftYoneda_map_app_down, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_inv_app_app, CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_none, mapAddMonNatIso_hom_app_hom, CategoryTheory.Join.mapPairComp_hom_app_left, SSet.Homotopy.h₁, opId_inv_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom.w_assoc, CategoryTheory.plusPlusSheaf_preservesZeroMorphisms, SSet.stdSimplex.δ_objMk₁_of_le, CategoryTheory.Triangulated.TStructure.truncGEδLT_comp_truncLTι_assoc, CategoryTheory.conjugateEquiv_associator_hom, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.isPushoutAddCommGrpFreeSheaf, mapTriangle_map_hom₃, CategoryTheory.Limits.limitConeOfUnique_isLimit_lift, CategoryTheory.coherentTopology.epi_π_app_zero_of_epi, CategoryTheory.Abelian.SpectralObject.δToCycles_cyclesIso_inv, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₃, CategoryTheory.sum.inrCompInlCompAssociator_hom_app_down_down, CategoryTheory.OverPresheafAux.restrictedYonedaObjMap₁_app, CategoryTheory.Limits.spanCompIso_hom_app_left, OrderHom.equivalenceFunctor_counitIso_hom_app_app, CategoryTheory.Sheaf.instIsLocallyInjectiveAppArrowPLocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, HomologicalComplex.mapBifunctor₁₂.d₃_eq_zero, CategoryTheory.Limits.FormalCoproduct.evalOpCompInlIsoId_hom_app_app, whiskeringLeft_obj_map, SSet.prodStdSimplex.le_orderHomOfSimplex, leftKanExtensionUniqueOfIso_inv, CategoryTheory.Comma.mapLeftIso_unitIso_hom_app_right, CategoryTheory.endofunctorMonoidalCategory_associator_hom_app, PresheafOfModules.free_obj, IsCoverDense.presheafIso_inv, CategoryTheory.instPreservesLimitsOfShapeMonFunctorOppositeMonCatShrinkYonedaMon, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom, CategoryTheory.Under.mapId_hom, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_inv_app_app_snd, CategoryTheory.Abelian.SpectralObject.p_descOpcycles, CategoryTheory.Limits.Cocone.fromStructuredArrow_map_hom, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_hom_assoc, const.opObjUnop_inv_app, CategoryTheory.Over.postComp_hom_app_left, CategoryTheory.flat_iff_lan_flat, flipping_inverse_obj_map_app, groupHomology.isoShortComplexH2_hom, SSet.RelativeMorphism.Homotopy.h₁_assoc, CategoryTheory.IndParallelPairPresentation.hg, CategoryTheory.Abelian.Preradical.instEpiFunctorGShortComplex, HomologicalComplex.singleCompEvalIsoSelf_inv_app, CategoryTheory.Equivalence.rightOp_counitIso_hom_app, CategoryTheory.FunctorToTypes.colimit.map_ι_apply, CategoryTheory.curryingIso_inv_toFunctor_obj_obj_obj, CategoryTheory.monadToFunctor_map, CategoryTheory.Sheaf.isConstant_iff_mem_essImage, CategoryTheory.Limits.Trident.ι_eq_app_zero, CategoryTheory.Subfunctor.fromPreimage_ι, Monoidal.whiskerLeft_app_fst, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinset_map_app, RightExtension.postcomp₁_obj_right, CategoryTheory.Sheaf.instPreservesFiniteLimitsFunctorOppositeSheafToPresheafOfHasFiniteLimits, HomologicalComplex.asFunctor_obj_d, CategoryTheory.yonedaPairingExt_iff, CategoryTheory.Idempotents.app_comp_p, CategoryTheory.GradedObject.mapTrifunctorMapFunctorObj_obj_obj, CategoryTheory.sheafCompose_map_hom, CategoryTheory.evaluationLeftAdjoint_obj_obj, SSet.Subcomplex.prodIso_inv, CategoryTheory.Abelian.SpectralObject.cokernelSequenceOpcyclesE_X₁, CategoryTheory.Limits.limIsoFlipCompWhiskerLim_hom_app_app, AlgebraicGeometry.StructureSheaf.comapₗ_const, CategoryTheory.Limits.MultispanIndex.multispanMapIso_hom_app, CategoryTheory.isCoseparator_iff_faithful_yoneda_obj, CategoryTheory.nerveFunctor.full, CategoryTheory.instPresheafIsFiniteObjFunctorOppositeTypeYoneda, CategoryTheory.SmallObject.πFunctorObj_eq, CategoryTheory.μ_δ_app, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerRight_assoc, CategoryTheory.MonoidalOpposite.unmopEquiv_unitIso_hom_app_unmop, CategoryTheory.StructuredArrow.mapNatIso_counitIso_hom_app_right, HasCardinalLT.Set.cocone_ι_app, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality, CategoryTheory.Presheaf.isLeftKanExtension_of_preservesColimits, CategoryTheory.MonoOver.inf_map_app, CategoryTheory.Sum.functorEquivFunctorCompSndIso_inv_app_app, SSet.Subcomplex.unionProd.preimage_β_inv, CategoryTheory.Limits.evaluation_preservesColimit, CategoryTheory.sheafificationAdjunction_unit_app, CategoryTheory.Discrete.compNatIsoDiscrete_inv_app, flipping_functor_obj_obj_obj, CategoryTheory.Limits.Fork.op_ι_app_one, CategoryTheory.Abelian.SpectralObject.πE_ιE_assoc, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafFunctor_obj_map, CategoryTheory.Under.postEquiv_inverse, CategoryTheory.equivOfTensorIsoUnit_functor, CategoryTheory.CategoryOfElements.toCostructuredArrow_obj, CategoryTheory.Limits.colimIsoFlipCompWhiskerColim_inv_app_app, CategoryTheory.OverPresheafAux.yonedaCollectionFunctor_map, CategoryTheory.Abelian.Preradical.toColon_hom_left_app_colonπ_app_assoc, CategoryTheory.Comma.mapRightId_hom_app_right, CategoryTheory.Subfunctor.instMonoFunctorTypeHomOfLe, instFaithfulProdUncurry₃, CategoryTheory.Limits.Cone.w, IsDenseSubsite.mapPreimage_comp_map_assoc, CategoryTheory.Presheaf.uliftYonedaAdjunction_unit_app_app, CategoryTheory.functorProdFunctorEquiv_counitIso, CategoryTheory.Triangulated.TStructure.triangleω₁δ_obj_obj₁, CategoryTheory.sheafificationIso_hom_hom, commShiftIso_map₂CochainComplex_flip_inv_app, opUnopEquiv_unitIso, SSet.Truncated.HomotopyCategory.BinaryProduct.associativity'Iso_hom_app, CategoryTheory.Sum.functorEquiv_unitIso_inv_app_app_inr, CategoryTheory.Presheaf.imageSieve_cofanIsColimitDesc_shrinkYoneda_map, CategoryTheory.left_unitality_app, FullyFaithful.compYonedaCompWhiskeringLeftMaxRight_hom_app_app_down, CategoryTheory.BasedNatTrans.forgetful_map, CategoryTheory.Limits.PullbackCone.ofCone_π, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app, AlgebraicGeometry.StructureSheaf.algebraMap_germ_assoc, ModuleCat.restrictScalarsId'_hom_app, AlgebraicGeometry.StructureSheaf.res_apply, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₃, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.isConnected, CategoryTheory.OverPresheafAux.YonedaCollection.mk_snd, CategoryTheory.Limits.inl_comp_pushoutObjIso_inv, LeftExtension.postcompose₂_map_left, CategoryTheory.Limits.pullbackObjIso_inv_comp_fst, uncurry_obj_map, LightCondensed.equalizerCondition, CategoryTheory.MonoidalCategory.externalProductBifunctorCurried_obj_obj_obj_obj, CategoryTheory.bifunctorComp₁₂FunctorObj_obj, AlgebraicGeometry.Scheme.LocalRepresentability.instIsLocallyInjectiveHomYonedaGluedToSheaf, CategoryTheory.lan_flat_of_flat, CategoryTheory.Limits.BinaryFan.isLimit_iff_isIso_fst, CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc_assoc, CategoryTheory.Limits.LimitPresentation.map_π, CategoryTheory.NatTrans.id_hcomp_app, SSet.stdSimplex.yonedaEquiv_map, CategoryTheory.shift_shiftFunctorCompIsoId_inv_app, CategoryTheory.Join.inclLeftCompOpEquivInverse_hom_app_op, CategoryTheory.Presheaf.coconeOfRepresentable_naturality, postcompose₂_obj_obj_obj_obj, CategoryTheory.Comma.mapLeftIso_counitIso_inv_app_left, CategoryTheory.GrothendieckTopology.Point.presheafFiberMapCocone_ι_app, CategoryTheory.instFaithfulSheafFunctorOppositeCompSheafComposeSheafToPresheaf, Monoidal.snd_app, LeftExtension.postcomp₁_obj_right_obj, CategoryTheory.NatTrans.app_naturality_assoc, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_zsmul_apply, Action.FunctorCategoryEquivalence.inverse_obj_V, CategoryTheory.NatIso.op_refl, CategoryTheory.GradedObject.comapEq_trans, CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcycles_g, Monoidal.fst_app, SSet.RelativeMorphism.Homotopy.ofEq_h, CategoryTheory.Enriched.Functor.natTransEquiv_symm_whiskerRight_functorHom_app, CategoryTheory.Adjunction.compCoyonedaIso_hom_app_app, CategoryTheory.GrothendieckTopology.Point.Hom.sheafFiber_id, SSet.horn_obj_zero, currying₃_unitIso_inv_app_app_app_app, AlgebraicTopology.DoldKan.instReflectsIsomorphismsSimplicialObjectKaroubiChainComplexNatN₁, CategoryTheory.NatTrans.instRespectsIsoFunctorCoequifibered, CategoryTheory.Limits.Cone.equivCostructuredArrow_counitIso, closedIhom_map_app, CategoryTheory.Cat.Hom.toNatTrans_id, instFullProdUncurry₃, CategoryTheory.instIsIsoFunctorOppositeHomFullSubcategoryIsSheafAppSheafCounitSheafificationAdjunction, rightKanExtensionCompIsoOfPreserves_hom_fac_assoc, whiskeringLeftObjIdIso_inv_app_app, CategoryTheory.Sheaf.instHasExactLimitsOfShapeOfHasFiniteColimitsOfPreservesFiniteColimitsFunctorOppositeSheafToPresheaf, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_inv_app_app, CategoryTheory.Triangulated.TStructure.eTruncLT_map_app_eTruncLTι_app_assoc, CategoryTheory.Cat.opFunctorInvolutive_inv_app_toFunctor_obj, CategoryTheory.Limits.Cocone.toCostructuredArrowCompToOverCompForget_hom_app, CategoryTheory.WithTerminal.mkCommaObject_hom_app, LightCondMod.hom_naturality_apply, pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac, OrderHom.equivalenceFunctor_unitIso_hom_app, AlgebraicGeometry.ExistsHomHomCompEqCompAux.hab, Monoidal.transport_η, CategoryTheory.MorphismProperty.Comma.mapLeftIso_counitIso_inv_app_right, CategoryTheory.MonoidalCategory.associatorNatIso_inv_app, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_counitIso_hom_app_hom, CategoryTheory.WithTerminal.mkCommaObject_left_obj, mapCocone₂_ι_app, PresheafOfModules.forgetToPresheafModuleCat_obj, CategoryTheory.instSmallCarrierObjOppositeGrpCatGrpFunctorYonedaGrp, CategoryTheory.MonoidalCategory.endofunctorMonoidalCategory.evaluationRightAction_actionObj, RightExtension.postcompose₂_obj_hom_app, CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv', CategoryTheory.ObjectProperty.ColimitOfShape.toCostructuredArrow_map, SheafOfModules.unitToPushforwardObjUnit_val_app_apply, CategoryTheory.NatTrans.leftOpWhiskerRight, CategoryTheory.Limits.limitCompCoyonedaIsoCone_inv, CategoryTheory.Comma.mapRightIso_counitIso_hom_app_left, CategoryTheory.Limits.Cofork.unop_π_app_zero, Action.resComp_inv_app_hom, CategoryTheory.Subobject.inf_def, CategoryTheory.WithInitial.equivComma_unitIso_hom_app_app, CategoryTheory.Bicategory.precomposing_obj, CategoryTheory.Triangulated.TStructure.truncLEIsoTruncLT_inv_ι, RightExtension.precomp_obj_hom_app, CategoryTheory.Cat.rightUnitor_inv_toNatTrans, CategoryTheory.Localization.lift₃NatTrans_app_app_app, CategoryTheory.ShiftedHom.opEquiv'_zero_add_symm, whiskerLeft_comp_assoc, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_hom_app_right_right, SheafOfModules.pullback_assoc, ranCounit_app_app_ranAdjunction_unit_app_app, CategoryTheory.OverPresheafAux.MakesOverArrow.of_yoneda_arrow, PresheafOfModules.Finite.toPresheaf_preservesFiniteColimits, CategoryTheory.Comma.mapRightId_hom_app_left, CategoryTheory.Limits.IsColimit.hom_desc, Final.colimit_cocone_comp_aux, SSet.horn.spineId_vertex_coe, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_unitIso_hom_app_hom, CategoryTheory.ShiftedHom.opEquiv'_symm_op_opShiftFunctorEquivalence_counitIso_inv_app_op_shift, CategoryTheory.LaxMonoidalFunctor.comp_hom, RightExtension.precomp_map_right, SSet.rightUnitor_hom_app_apply, CategoryTheory.prod.leftUnitorEquivalence_unitIso, CategoryTheory.full_preadditiveYoneda, CategoryTheory.shiftEquiv'_unitIso, CategoryTheory.FunctorToTypes.jointly_surjective, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_leftUnitor_hom_eq_leftUnitor_hom, CategoryTheory.Equivalence.comp_asNatTrans_assoc, CategoryTheory.Under.postCongr_hom_app_right, CategoryTheory.Over.mapId_hom_app_left, CategoryTheory.Comma.mapLeftEq_inv_app_left, AddCommMonCat.coyonedaForget_inv_app_app, CategoryTheory.SimplicialObject.instHasColimitsOfShape, CategoryTheory.Limits.colimit.pre_id, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_right, map_opShiftFunctorEquivalence_unitIso_hom_app_unop_assoc, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_apply, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_hom_π_π_assoc, CategoryTheory.CompatiblePreserving.apply_map, whiskeringLeft₃ObjObj_map, CategoryTheory.Limits.combineCocones_pt_obj, HomologicalComplex.coconeOfHasColimitEval_ι_app_f, instPreservesColimitSheafTypeYonedaOfPreservesLimitOppositeOpObjFunctorIsSheaf_1, CategoryTheory.NatTrans.CommShift₂.instIdFunctor, SheafOfModules.forget_map, CategoryTheory.Limits.Cone.toStructuredArrow_obj, CategoryTheory.NatTrans.rightDerivedToHomotopyCategory_comp, leftDerivedZeroIsoSelf_inv_hom_id_assoc, CategoryTheory.WithTerminal.commaFromOver_map_right, essImage.liftFunctorCompIso_inv_app, CategoryTheory.PreGaloisCategory.endEquivAutGalois_mul, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_hom_app_hom_app_apply, CommRingCat.coproductCoconeIsColimit_desc, CategoryTheory.Comma.mapLeftIso_counitIso_hom_app_right, CategoryTheory.Limits.Cotrident.app_one, CategoryTheory.Monoidal.rightUnitor_hom_app, CategoryTheory.CostructuredArrow.map_map_left, CategoryTheory.Limits.CategoricalPullback.mkNatIso_inv_app_fst, CategoryTheory.sectionsFunctorNatIsoCoyoneda_hom_app_app, CategoryTheory.Limits.CatCospanTransform.mkIso_inv_base, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_hom_app_app_down, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom.w, CategoryTheory.Triangulated.TStructure.eTruncGEIsoGEGE_hom_inv_id_app, CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_hom_assoc, PullbackObjObj.ofHasPullback_snd, CategoryTheory.evaluationUncurried_obj, CategoryTheory.bifunctorComp₂₃Functor_obj, HomologicalComplex.quasiIsoAt_iff_evaluation, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε_assoc, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_presheafHom_uliftYoneda_obj, CommGrpCat.coyoneda_obj_obj_coe, CategoryTheory.ComposableArrows.instIsIsoOfNatNatTwoδ₁Toδ₀, CategoryTheory.presheafToSheaf_additive, CategoryTheory.WithInitial.equivComma_inverse_obj_obj, groupAddGroupEquivalence_unitIso, shift_map_op, Elements.shrinkYoneda_map_app_coconeπOpCompShrinkYonedaObj_ι_app, CategoryTheory.Limits.limitIsoSwapCompLim_inv_app, mapTriangleCommShiftIso_inv_app_hom₂, CategoryTheory.ε_η_app, CategoryTheory.Over.isPullback_of_binaryFan_isLimit, CategoryTheory.CosimplicialObject.whiskering_obj_map_app, Action.FunctorCategoryEquivalence.unitIso_hom_app_hom, CategoryTheory.Limits.colimit.pre_map, LightCondensed.ihomPoints_symm_apply, CategoryTheory.LocalizerMorphism.isIso_iff_of_hasRightResolutions, CategoryTheory.LeftExactFunctor.of_fst, CategoryTheory.Sum.swapCompInl_inv_app, CategoryTheory.Pi.optionEquivalence_counitIso, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_inv_app_fst_app, CorepresentableBy.equivUliftCoyonedaIso_apply, CategoryTheory.EnrichedFunctor.forgetId_hom_app, CategoryTheory.comonadToFunctor_map, LightCondensed.discrete_obj, DerivedCategory.homologyFunctorFactorsh_hom_app_quotient_obj, Elements.shrinkYonedaCompWhiskeringLeftObjπCompColimIso_inv_app_apply, CategoryTheory.NatTrans.id_comm, SSet.Truncated.tensor_map_apply_fst, CategoryTheory.InjectiveResolution.extMk_hom, CategoryTheory.Limits.inr_comp_pushoutObjIso_inv, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_obj_obj_obj, CategoryTheory.Limits.IsLimit.fac_assoc, groupCohomology.isoShortComplexH1_hom, CategoryTheory.MonoidalPreadditive.instAdditiveFunctorFlipCurriedTensor, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy_homEquiv_apply_app, SSet.Truncated.HomotopyCategory.BinaryProduct.functor_obj, CategoryTheory.Pretriangulated.shiftFunctor_op_map, CategoryTheory.Triangulated.TStructure.π_truncGTIsoTruncGE_inv, CategoryTheory.Idempotents.functorExtension₂CompWhiskeringLeftToKaroubiIso_inv_app_app_f, CategoryTheory.Abelian.SpectralObject.Hom.comm_assoc, CategoryTheory.SimplicialObject.Homotopy.congr_homologyMap_singularChainComplexFunctor, SSet.horn.multicoequalizerDiagram, CategoryTheory.CatCenter.smul_iso_inv_eq, CategoryTheory.Abelian.SpectralObject.opcyclesIsoKernel_hom_fac, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_whiskerRight, currying_functor_obj_obj, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_map_snd, CategoryTheory.Limits.cospanCompIso_hom_app_left, CategoryTheory.uliftYonedaEquiv_symm_comp_assoc, SheafOfModules.forgetPreservesLimitsOfSize, CategoryTheory.Sieve.uliftFunctorInclusion_is_mono, CategoryTheory.Limits.BinaryFan.assoc_snd, CategoryTheory.Iso.coreRightUnitor, CategoryTheory.Endofunctor.Algebra.equivOfNatIso_unitIso, CategoryTheory.Adjunction.rightAdjointUniq_trans_app, instPreservesZeroMorphismsObjFlip, SSet.horn.spineId_arrow_coe, CategoryTheory.SimplicialObject.equivalenceRightToLeft_left, CategoryTheory.ComposableArrows.isoMk₅_hom, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceFunctorProj_hom_app, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₁, CategoryTheory.uliftCoyonedaEquiv_naturality, CategoryTheory.MorphismProperty.FunctorsInverting.ext_iff, HomologicalComplex.homologyFunctorSingleIso_inv_app, pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_assoc, CategoryTheory.Sheaf.Hom.epi_of_presheaf_epi, RightExtension.postcompose₂ObjMkIso_inv_left_app, SimplicialObject.opFunctorCompOpFunctorIso_inv_app_app, CategoryTheory.Limits.spanExt_hom_app_left, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMop_obj_unmop_obj, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π_assoc, isLeftKanExtensionAlongEquivalence, CategoryTheory.Limits.end_.lift_π, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_snd_obj, CategoryTheory.OverPresheafAux.YonedaCollection.map₁_comp, CategoryTheory.instFaithfulMonadFunctorMonadToFunctor, CategoryTheory.Endofunctor.Algebra.functorOfNatTransEq_hom_app_f, CategoryTheory.Join.mapWhiskerLeft_associator_hom_assoc, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_X_map, CategoryTheory.Equivalence.unit_app_tensor_comp_inverse_map_δ_functor_assoc, CategoryTheory.NatTrans.shift_app_assoc, Action.tensorHom_hom, CategoryTheory.Sheaf.isLocallyInjective_sheafToPresheaf_map_iff, PresheafOfModules.pullbackObjIsDefined_free_yoneda, AlgebraicTopology.DoldKan.Compatibility.υ_hom_app, CategoryTheory.CatCenter.app_neg_one_zpow, SheafOfModules.instFaithfulPresheafOfModulesObjFunctorOppositeRingCatIsSheafForget, CategoryTheory.FunctorToTypes.jointly_surjective', CategoryTheory.NatIso.cancel_natIso_inv_right, CategoryTheory.GradedObject.ι_mapBifunctorLeftUnitor_hom_apply, CategoryTheory.sheafComposeIso_inv_fac_assoc, SSet.iSup_range_eq_top_of_isColimit, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_inv_app_eq, Rep.coinvariantsTensor_hom_ext_iff, Action.associator_hom_hom, CategoryTheory.SimplicialObject.IsCoskeletal.isRightKanExtension, CategoryTheory.MonoidalOpposite.mopMopEquivalence_unitIso_inv_app_unmop_unmop, IsCoverDense.sheafCoyonedaHom_app, SSet.stdSimplex.objEquiv_toOrderHom_apply, sheafPullbackConstruction.preservesFiniteLimits, PresheafOfModules.toPresheaf_preservesColimitsOfShape, inrCompSum'_inv_app, constComp_hom_app, mapAddMonFunctor_obj, CategoryTheory.Abelian.SpectralObject.sc₁_X₃, CategoryTheory.Abelian.SpectralObject.δ_toCycles_assoc, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_left, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.inverse_obj_obj, CategoryTheory.instIsIsoFunctorToRightDerivedZero, CategoryTheory.DinatTrans.precompNatTrans_app, CategoryTheory.equivOfTensorIsoUnit_inverse, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s_comp_δ₀, AlgebraicGeometry.Scheme.SpecΓIdentity_inv_app, CategoryTheory.CatCenter.localization_zero, SSet.ι₁_fst, SSet.const_comp, instPreservesColimitSheafTypeUliftYonedaOfPreservesLimitOppositeOpObjFunctorIsSheaf, CategoryTheory.Abelian.LeftResolution.instEpiKaroubiAppπ, CategoryTheory.Adjunction.rightAdjointUniq_hom_app_counit, homEquivOfIsRightKanExtension_symm_apply, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.const_s, CategoryTheory.simplicialCosimplicialEquiv_unitIso_inv_app, CategoryTheory.instFullFunctorConstOfIsConnected, CategoryTheory.Triangulated.TStructure.truncLEIsoTruncLT_hom_ι_app_assoc, reflective, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_inv_comp_π_assoc, CategoryTheory.opOpEquivalence_counitIso, CategoryTheory.NatTrans.toCatHom₂_comp, CategoryTheory.Subobject.lowerEquivalence_unitIso, whiskeringRight_obj_map, RightExtension.postcompose₂_map_left_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_snd_map, CategoryTheory.ComposableArrows.isoMk₀_inv_app, CategoryTheory.isoSheafify_inv, CategoryTheory.Limits.limit.homIso_hom, CategoryTheory.Limits.colimitConstInitial_inv, CategoryTheory.sum.inrCompAssociator_inv_app_down_down, CategoryTheory.Iso.hom_inv_id_app_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_hom_app_app, AlgebraicGeometry.StructureSheaf.algebraMap_germ, CategoryTheory.Presieve.shrinkFunctor_ι_comp_eq_iff_isAmalgamation, ModuleCat.FilteredColimits.ι_colimitDesc, CategoryTheory.Equivalence.functor_unitIso_comp, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_apply, CategoryTheory.Comma.mapFst_hom_app, curry_obj_obj_map, CategoryTheory.Limits.sigmaConst_obj_obj, CategoryTheory.Limits.Cocone.ofPushoutCocone_ι, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₃_app, SSet.horn₃₁.desc.multicofork_π_three_assoc, CategoryTheory.uliftYonedaIsoYoneda_hom_app_app, CategoryTheory.SingleFunctors.isoMk_hom_hom, CategoryTheory.IsCodetecting.isIso_iff_of_epi, flip_obj_obj, CategoryTheory.prodFunctor_obj, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv_assoc, CategoryTheory.Limits.CategoricalPullback.mkNatIso_hom_app_fst, CategoryTheory.Limits.limit.map_pre', CategoryTheory.Limits.ColimitPresentation.reindex_ι, CategoryTheory.instPreservesColimitsOfShapeFunctorIndLimOfFinCategoryOfHasColimitsOfShape, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app, Monoidal.tensorObj_obj, CategoryTheory.NatTrans.CommShiftCore.app_shift, CategoryTheory.PreGaloisCategory.instPreservesMonomorphismsActionFintypeCatAutFunctorFunctorToAction, CategoryTheory.Limits.FormalCoproduct.instPreservesColimitsOfShapeDiscreteObjFunctorEval, FullyFaithful.compUliftYonedaCompWhiskeringLeft_hom_app_app_down, SSet.Truncated.Edge.tensor_edge, CategoryTheory.Join.mapWhiskerLeft_rightUnitor_hom, whiskeringRightObjCompIso_hom_app_app, whiskerLeft_id', CategoryTheory.GrothendieckTopology.diagramFunctor_map, leftDerived_fac, CategoryTheory.Sheaf.isConstant_iff_of_equivalence, CategoryTheory.Limits.coconeOpEquiv_unitIso, RightExtension.postcompose₂_obj_left_obj, CategoryTheory.equivYoneda_inv_app, CategoryTheory.Sheaf.hasExactColimitsOfShape, instPreservesLimitsOfShapeSheafTypeUliftYoneda, PushoutObjObj.ofHasPushout_inl, CategoryTheory.uliftCoyonedaEquiv_symm_map_assoc, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_obj, CategoryTheory.ObjectProperty.IsConservativeFamilyOfPoints.W_iff, SSet.Truncated.HomotopyCategory.mkNatIso_hom_app_mk, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app, CategoryTheory.presheafToSheafCompComposeAndSheafifyIso_inv_app, CategoryTheory.Sheaf.instHasFiniteCoproducts, CategoryTheory.Iso.map_hom_inv_id_eval_app_assoc, isoWhiskerRight_symm, CategoryTheory.Triangulated.SpectralObject.comp_hom, CommMonCat.coyoneda_map_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_right, CategoryTheory.Limits.Cocone.whiskeringEquivalence_inverse, CategoryTheory.NatTrans.appLinearMap_apply, AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex_homotopyInvHomId, CategoryTheory.Subfunctor.equivalenceMonoOver_unitIso, CategoryTheory.Adjunction.localization_counit_app, mapGrpIdIso_inv_app_hom_hom, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₂, CategoryTheory.Comma.unopFunctorCompFst_inv_app, postcomposeWhiskerLeftMapCone_hom_hom, CategoryTheory.Limits.inl_comp_pushoutObjIso_inv_assoc, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.counitIso_hom_app_hom, OneHypercoverDenseData.essSurj.presheafMap_restriction, mapAddMonNatIso_inv_app_hom, CategoryTheory.Limits.Cocone.precomposeEquivalence_functor, CategoryTheory.Limits.Cotrident.coequalizer_ext, SSet.PtSimplex.MulStruct.δ_castSucc_castSucc_map_assoc, CategoryTheory.GradedObject.HasGoodTrifunctor₂₃Obj.hasMap, CategoryTheory.GrothendieckTopology.Point.instPreservesColimitsOfShapeOppositeElementsFiberObjFunctorFlipCurriedTensor, CategoryTheory.MorphismProperty.IsStableUnderLimitsOfShape.functorCategory, SSet.ι₀_app_snd_apply, CategoryTheory.Abelian.SpectralObject.opcyclesIsoH_inv_hom_id, SSet.Truncated.cosk.faithful, leftDerivedZeroIsoSelf_inv_hom_id_app_assoc, CategoryTheory.Limits.IndObjectPresentation.extend_isColimit_desc_app, CategoryTheory.Limits.IndObjectPresentation.ofCocone_ι, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.section_app_comp_hom_app_assoc, mapActionCongr_hom, CategoryTheory.ShortComplex.leftHomologyFunctorOpNatIso_hom_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiberMap_w_assoc, AddCommMonCat.coyonedaType_obj_obj_coe, TopCat.coneOfConeForget_π_app, CategoryTheory.ComposableArrows.isoMk_hom, CategoryTheory.FreeMonoidalCategory.normalizeIsoAux_hom_app, SSet.horn₃₁.desc.multicofork_π_zero, CategoryTheory.Limits.pullbackObjIso_hom_comp_snd_assoc, CategoryTheory.Pi.evalCompEqToEquivalenceFunctor_inv, PreservesLeftKanExtension.preserves, CategoryTheory.GradedObject.mapTrifunctorObj_obj_map, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon_map, CategoryTheory.Abelian.SpectralObject.p_descOpcycles_assoc, PushoutObjObj.ι_iso_of_iso_right_inv, CategoryTheory.Limits.colimitIsoFlipCompColim_hom_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_inv_app_app, CategoryTheory.Monad.algebraFunctorOfMonadHomComp_inv_app_f, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafAdjunction_homEquiv_apply, FullyFaithful.compUliftCoyonedaCompWhiskeringLeft_inv_app_app_down, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_obj_iso_hom, LightCondMod.LocallyConstant.instFaithfulModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf, CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_fst_apply, LightCondensed.lanPresheafNatIso_hom_app, CategoryTheory.Preadditive.DoldKan.equivalence_inverse, CategoryTheory.Sum.natTransOfWhiskerLeftInlInr_comp, CategoryTheory.ComposableArrows.isIso_iff₀, CategoryTheory.Limits.Bicone.ofLimitCone_π, CategoryTheory.Join.mapWhiskerRight_id, CategoryTheory.Limits.ι_comp_sigmaObjIso_inv_assoc, ModuleCat.extendScalars_id_comp_assoc, CategoryTheory.Limits.colimit.ι_coconeMorphism, CategoryTheory.GrothendieckTopology.instFaithfulSheafTypeYoneda, CategoryTheory.Comma.equivProd_unitIso_inv_app_right, CategoryTheory.AdditiveFunctor.of_obj, CategoryTheory.LocalizerMorphism.equiv_smallHomMap, CategoryTheory.NatTrans.IsMonoidal.instHomFunctorLeftUnitor, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.guitartExact', instFullProdCurry, CategoryTheory.Limits.CatCospanTransform.mkIso_inv_right, CategoryTheory.Monad.beckAlgebraCofork_ι_app, IsDenseSubsite.mapPreimage_comp, TopCat.Sheaf.objSupIsoProdEqLocus_hom_snd, CategoryTheory.Sheaf.instIsLocallySurjectiveHomMapTypeSheafComposeForget, CategoryTheory.Adjunction.CommShift.compatibilityUnit_right, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_inv_app_fst_app, IsDenseSubsite.sheafifyHomEquivOfIsEquivalence_naturality_right_assoc, CategoryTheory.WithInitial.commaFromUnder_obj_left, Monoidal.associator_inv_app, CommShift.isoAdd'_hom_app, CategoryTheory.flippingIso_hom_toFunctor_obj_map_app, AlgebraicGeometry.StructureSheaf.const_mul_cancel', instPreservesHomologyFunctorAddCommGrpCatColim, CategoryTheory.conjugateEquiv_symm_comm, CategoryTheory.WithTerminal.mapId_hom_app, IsCoverDense.homOver_app, groupAddGroupEquivalence_counitIso, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_inv_app_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w_assoc, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_mon_mul, CategoryTheory.Join.mapWhiskerRight_rightUnitor_hom, CategoryTheory.Abelian.SpectralObject.p_fromOpcycles, CategoryTheory.Limits.Cone.ofFork_π, CorepresentableBy.uniqueUpToIso_hom, CategoryTheory.Limits.colimit.ι_map_assoc, CategoryTheory.Limits.fiberwiseColimCompColimIso_hom_app, mapTriangleCompIso_hom_app_hom₁, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_iso_inv_app, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left_assoc, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_hom_app_f, CategoryTheory.FunctorToTypes.rightAdj_obj_map_app, TopCat.Sheaf.objSupIsoProdEqLocus_inv_eq_iff, CategoryTheory.Abelian.SpectralObject.Ψ_fromOpcycles, CategoryTheory.Pi.eqToEquivalenceFunctorIso_inv, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_associator, SSet.Subcomplex.unionProd.preimage_β_hom, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_comp, pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_app, CategoryTheory.PreGaloisCategory.autEmbedding_apply, CategoryTheory.Localization.lift₂NatTrans_app_app, AlgebraicGeometry.instIsScalarTowerObjOppositeOpensCarrierTopObjFunctorTypeIsSheafGrothendieckTopologyStructureSheafInType, CategoryTheory.MonoidalOpposite.tensorRightMopIso_inv_app_unmop, CategoryTheory.Sheaf.cohomologyFunctor_obj, ModuleCat.extendScalars_assoc', lightCondSetToTopCat_obj_carrier, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_id, AlgebraicTopology.DoldKan.map_Q, CategoryTheory.Sum.natIsoOfWhiskerLeftInlInr_hom, CategoryTheory.Equivalence.core_counitIso_hom_app_iso_inv, CategoryTheory.Sheaf.mono_of_injective, CategoryTheory.GrothendieckTopology.instIsLocalizationFunctorOppositeSheafPresheafToSheafW, Monoidal.instPreservesColimitsOfShapeTensorLeftOfHasColimitsOfShape, CategoryTheory.SimplicialObject.Truncated.whiskering_obj_obj_map, constCompEvaluationObj_hom_app, CategoryTheory.Limits.WalkingMulticospan.functorExt_hom_app, leftKanExtensionIsoFiberwiseColimit_hom_app, SheafOfModules.Finite.forgetPreservesFiniteLimits, CategoryTheory.SimplicialObject.Truncated.cosk_reflective, CategoryTheory.Monad.comparisonForget_inv_app, OrderHom.equivalenceFunctor_inverse_obj, CategoryTheory.NatIso.removeOp_inv, CategoryTheory.Abelian.SpectralObject.p_opcyclesMap, AlgebraicGeometry.Proj.sheafedSpaceMap_hom_c_app_hom_apply_coe, CategoryTheory.shiftFunctorAdd_add_zero_hom_app, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, CategoryTheory.StructuredArrow.mapIso_unitIso_hom_app_right, CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ', CategoryTheory.Sheaf.instIsClosedUnderLimitsOfShapeFunctorOppositeIsSheaf, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_app_app, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_fst, CategoryTheory.piEquivalenceFunctorDiscrete_inverse_map, CategoryTheory.Triangulated.TStructure.eTruncGEIsoGEGE_hom, CategoryTheory.Presheaf.map_comp_uliftYonedaEquiv_down_assoc, SSet.Subcomplex.liftPath_arrow_coe, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_obj, TopCat.induced_of_isLimit, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_hom, CategoryTheory.ShortComplex.FunctorEquivalence.functor_obj_obj, CategoryTheory.GrothendieckTopology.Point.instPreservesFiniteLimitsFunctorOppositePresheafFiberOfLocallySmallOfHasFiniteLimitsOfAB5OfSize, SheafOfModules.forget_obj, CategoryTheory.Abelian.SpectralObject.opcyclesIso_hom_δFromOpcycles_assoc, CategoryTheory.Coyoneda.instHasColimitObjOppositeFunctorTypeCoyoneda, CategoryTheory.TransfiniteCompositionOfShape.iic_incl_app, curryingFlipEquiv_apply_map, CategoryTheory.Presheaf.instIsCardinalLocallyPresentableFunctorOppositeOfHasPullbacks, CategoryTheory.Limits.Types.surjective_π_app_zero_of_surjective_map, IsCoverDense.Types.presheafIso_hom_app, CategoryTheory.Limits.coconeLeftOpOfCone_ι_app, CategoryTheory.MonoidalCategory.DayFunctor.ι_obj, CategoryTheory.GrothendieckTopology.preservesFiniteLimits_sheafification, CategoryTheory.EnrichedFunctor.forgetComp_hom_app, CategoryTheory.Equivalence.symm_counitIso, CategoryTheory.finitaryExtensive_functor, CategoryTheory.Equivalence.sheafCongrPrecoherent_functor_obj_obj_map, CategoryTheory.conjugateEquiv_id, CategoryTheory.GrothendieckTopology.diagramFunctor_obj, pointwiseLeftKanExtensionCompIsoOfPreserves_fac_app, constCompWhiskeringLeftIso_inv_app_app, RightExtension.postcompose₂_map_right, CategoryTheory.MorphismProperty.Comma.mapRightIso_unitIso_hom_app_left, AlgebraicTopology.DoldKan.N₂_obj_p_f, isoWhiskerRight_refl, AlgebraicGeometry.exists_mem_of_isClosed_of_nonempty', CategoryTheory.NatTrans.leftOpWhiskerRight_assoc, ModuleCat.extendScalars_id_comp, CategoryTheory.Equivalence.sheafCongrPrecoherent_inverse_obj_obj_obj, leftOpComp_hom_app, CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit_assoc, SSet.Truncated.HomotopyCategory.BinaryProduct.square, CategoryTheory.Limits.cospanCompIso_hom_app_one, CategoryTheory.Limits.pointwiseBinaryBicone_snd_app, CategoryTheory.Abelian.SpectralObject.isZero_H_obj_of_isIso, CategoryTheory.Limits.Cone.fromCostructuredArrow_obj_pt, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv, CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero, CategoryTheory.Idempotents.app_comp_p_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_app_snd_app, RepresentableBy.uniqueUpToIso_inv, CategoryTheory.coreFunctor_map_app_iso_hom, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_hom_comp_map_π, CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatTrans_app, CommShift.isoZero_inv_app, CategoryTheory.instPreservesFiniteLimitsFunctorObjWhiskeringLeftOfHasFiniteLimits, CategoryTheory.Subfunctor.equalizer.lift_ι, CategoryTheory.Limits.coend.hom_ext_iff, CategoryTheory.WithTerminal.inclLiftToTerminal_hom_app, sheafPushforwardContinuousCompSheafToPresheafIso_hom_app_app, RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_obj_snd, CommMonCat.coyoneda_obj_obj_coe, instIsCorepresentableObjOppositeTypeCoyoneda, CommRingCat.coyonedaUnique_inv_app_hom_apply, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_counitIso_hom_app_f, CategoryTheory.Limits.Cone.isLimit_iff_isIso_limMap_π, LightCondMod.epi_iff_locallySurjective_on_lightProfinite, CategoryTheory.Limits.pointwiseBinaryBicone.isBilimit_isColimit, commShiftIso_inv_naturality, CategoryTheory.expComparison_iso_of_frobeniusMorphism_iso, CategoryTheory.Limits.limitIsoLimitCurryCompLim_inv_π, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence_app, SSet.horn₂₀.isPushout, CategoryTheory.Limits.colimit.ι_desc_assoc, CategoryTheory.Adjunction.left_triangle, CategoryTheory.IsPushout.of_is_coproduct, SSet.stdSimplex.ofSimplex_yonedaEquiv_δ, SheafOfModules.comp_val_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_app_fst_app, CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_inv, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.secondMap₃_app_app_app, CategoryTheory.Sieve.forallYonedaIsSheaf_iff_colimit, CategoryTheory.Equivalence.sheafCongrPrecoherent_inverse_obj_obj_map, PullbackObjObj.mapArrowRight_id, CategoryTheory.Monoidal.comonFunctorCategoryEquivalence_counitIso, CategoryTheory.WithTerminal.liftFromOver_obj_map, CategoryTheory.Sheaf.epi_of_isLocallySurjective, CategoryTheory.GrothendieckTopology.Point.comp_hom_assoc, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_unitIso_inv_app_hom_app, CategoryTheory.NatIso.pi_inv, AlgebraicTopology.DoldKan.Compatibility.τ₁_hom_app, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj, LeftExtension.precomp_map_left, mapBifunctorHomologicalComplex_obj_obj_X_X, CategoryTheory.Comma.mapLeftIso_functor_obj_hom, leftKanExtensionCompIsoOfPreserves_inv_fac, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_η, LightCondensed.ihom_map_val_app, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_hom_f_f, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.unitIso_inv, CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_cancel_inv_app, inv_whiskerLeft, CategoryTheory.ShortComplex.SnakeInput.composableArrowsFunctor_obj, CategoryTheory.sheafToPresheaf_η, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_right, CategoryTheory.GradedObject.mapBifunctorRightUnitorCofan_inj_assoc, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_hom_app_app_hom, TopCat.Presheaf.presheafEquivOfIso_counitIso_inv_app_app, CategoryTheory.Iso.map_hom_inv_id_app_assoc, HomotopyCategory.homologyFunctor_shiftMap_assoc, whiskerRight_comp_assoc, CategoryTheory.CostructuredArrow.mapNatIso_counitIso_hom_app_left, CategoryTheory.ι_colimitCompWhiskeringRightIsoColimitComp_hom_assoc, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_app_assoc, Action.FunctorCategoryEquivalence.inverse_map_hom, CategoryTheory.Pretriangulated.Triangle.functorIsoMk_hom, CategoryTheory.Limits.coconeRightOpOfCone_ι, CategoryTheory.Triangulated.TStructure.truncGEπ_comp_truncGEδLT, CategoryTheory.Limits.Cocone.equivStructuredArrow_inverse, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.unitIso_hom_app_f_f, isRightKanExtensionId, CategoryTheory.exactFunctor_le_leftExactFunctor, CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso_functor, CategoryTheory.Abelian.SpectralObject.instEpiPOpcycles, AlgebraicGeometry.ΓSpec.right_triangle, CategoryTheory.MorphismProperty.Comma.mapRightIso_unitIso_hom_app_right, CategoryTheory.Enriched.FunctorCategory.functorEnriched_id_comp_assoc, CategoryTheory.Limits.colimit.ι_desc_app_assoc, CategoryTheory.Localization.liftNatTrans_id, CategoryTheory.PreGaloisCategory.stabilizer_normal_of_isGalois, CategoryTheory.Limits.Cocone.toCostructuredArrow_obj, CategoryTheory.Idempotents.KaroubiKaroubi.unitIso_hom_app_f, TopCat.Presheaf.app_isIso_of_stalkFunctor_map_iso, elementsFunctor_obj, CategoryTheory.TwistShiftData.shiftFunctorAdd'_inv_app, CategoryTheory.Localization.HasProductsOfShapeAux.inverts, CategoryTheory.Limits.PullbackCone.combine_pt_map, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_inv_app_hom_app, CategoryTheory.Quotient.full_whiskeringLeft_functor, CategoryTheory.RightExactFunctor.of_fst, CompHausLike.LocallyConstant.instIsIsoFunctorTypeUnitSheafCoherentTopologyAdjunction, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_unitIso, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₃, IsDenseSubsite.mapPreimage_of_eq, AlgebraicGeometry.StructureSheaf.toOpenₗ_top_bijective, CochainComplex.shiftFunctorZero_hom_app_f, CategoryTheory.MorphismProperty.Comma.mapLeftId_hom_app_left, CategoryTheory.Join.mapPairComp_inv_app_left, CategoryTheory.WithInitial.coconeEquiv_inverse_map_hom_right, AlgebraicGeometry.StructureSheaf.comap_id_eq_map, CategoryTheory.MonoidalClosed.internalHom_map, CategoryTheory.Quotient.faithful_whiskeringLeft_functor, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_inv_app_hom_coe', CategoryTheory.Sigma.mapId_hom_app, ContAction.resCongr_inv, CategoryTheory.Triangulated.TStructure.ω₁δ_app, CategoryTheory.toSheafify_sheafifyLift, Condensed.isColimitLocallyConstantPresheafDiagram_desc_apply, DerivedCategory.shiftMap_homologyFunctor_map_Q, CategoryTheory.ComposableArrows.isoMk₂_hom, CategoryTheory.Subfunctor.orderIsoSubobject_symm_apply, CategoryTheory.Bicategory.postcomposingCat_map, unopComp_inv_app, CategoryTheory.δ_naturality_assoc, CategoryTheory.CatCommSq.vComp_iso_inv_app, CategoryTheory.Limits.Types.jointly_surjective, CategoryTheory.Limits.PullbackCone.equalizer_ext, CategoryTheory.Abelian.SpectralObject.opcyclesIsoKernel_hom_fac_assoc, AlgebraicTopology.DoldKan.N₂_obj_X_X, CategoryTheory.Limits.multicospanIndexEnd_left, Action.whiskerLeft_hom, CategoryTheory.Equivalence.core_unitIso_hom_app_iso_hom, CategoryTheory.GradedObject.mapBifunctorLeftUnitor_hasMap, CategoryTheory.Monad.ofMon_μ, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd_assoc, CategoryTheory.Over.liftCocone_ι_app, CategoryTheory.Sieve.functorInclusion_top_isIso, SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_hom_app, final_const_terminal, LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm, CategoryTheory.Idempotents.DoldKan.isoN₁_hom_app_f, Preorder.coneOfLowerBound_π_app, AlgebraicTopology.DoldKan.N₁Γ₀_hom_app, CategoryTheory.instIsClosedUnderIsomorphismsFunctorLeftExactFunctor, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_εIso_inv, CategoryTheory.underEquivOfIsTerminal_counitIso, SheafOfModules.toSheaf_map_hom, CategoryTheory.MorphismProperty.Comma.mapLeftId_hom_app_right, CategoryTheory.Abelian.SpectralObject.ιE_δFromOpcycles, instPreservesZeroMorphismsFlipOfObj, HomologicalComplex.mapBifunctorMapHomotopy.comm₁_aux, CategoryTheory.MorphismProperty.FunctorsInverting.comp_hom, LeftExtension.precomp₂_obj_right, PullbackObjObj.π_snd_assoc, mapMonCompIso_inv_app_hom, SSet.prodStdSimplex.nonDegenerate_iff_injective_objEquiv, CategoryTheory.NatIso.naturality_2, CategoryTheory.MonoidalClosed.internalHom_obj, opComp_hom_app, CategoryTheory.ObjectProperty.IsConservativeFamilyOfPoints.jointlyReflectIsomorphisms, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_left, CategoryTheory.Limits.CategoricalPullback.catCommSq_iso_inv_app, CategoryTheory.Limits.coconeRightOpOfConeEquiv_counitIso, CategoryTheory.essImage_yonedaAddMon, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_fst, PushoutObjObj.mapArrowLeft_left, CategoryTheory.StructuredArrow.mapNatIso_unitIso_inv_app_right, CategoryTheory.Subfunctor.Subpresheaf.preimage_comp, CategoryTheory.Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone_ι_app, CategoryTheory.Limits.wideCoequalizer.cotrident_ι_app_one, CategoryTheory.Limits.limit.lift_π_assoc, ranObjObjIsoLimit_hom_π, CategoryTheory.WithTerminal.isLimitEquiv_apply_lift_left, CategoryTheory.Triangulated.TStructure.triangleω₁δ_obj_mor₃, CategoryTheory.Equivalence.rightOp_unitIso_inv_app, CategoryTheory.Coyoneda.coyoneda_full, mapTriangleCommShiftIso_hom_app_hom₁, CategoryTheory.ComposableArrows.isoMk₃_inv, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_map_app_fst, CategoryTheory.instPreservesLimitsOfShapeFunctorColim, TopCat.toSSet_map_const, OplaxMonoidal.ofBifunctor.secondMap₁_app_app_app, SSet.Quasicategory.hornFilling, ModuleCat.directLimitCocone_ι_app, CategoryTheory.curryingIso_inv_toFunctor_map_app_app, CategoryTheory.Adjunction.leftAdjointCompIso_hom, SSet.prodStdSimplex.nonDegenerate_max_dim_iff, AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap_assoc, rightKanExtensionUniqueOfIso_inv, CategoryTheory.GrothendieckTopology.plusFunctor_preservesZeroMorphisms, CategoryTheory.Abelian.SpectralObject.homologyDataIdId_right_H, SSet.stdSimplex.instFiniteObjSimplexCategory, CategoryTheory.Adjunction.Triple.whiskerRight_rightToLeft, CategoryTheory.Equivalence.id_asNatTrans, CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso_hom_app, commGroupAddCommGroupEquivalence_unitIso, SSet.Subcomplex.prod_le_top_prod, CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_two_symm, CategoryTheory.Limits.IndObjectPresentation.ofCocone_F, FullyFaithful.homNatIso'_inv_app_down, SSet.stdSimplex.objMk_apply, CategoryTheory.NatIso.op_hom, HomologicalComplex.mapBifunctor.ι_D₁, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.inverseObj_comon_comul_app, CategoryTheory.Limits.IsColimit.ι_smul, isoShift_hom_naturality_assoc, CategoryTheory.ShortComplex.quasiIso_iff_evaluation, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitNatIso_hom_app, CategoryTheory.Abelian.SpectralObject.δToCycles_iCycles_assoc, CategoryTheory.GrothendieckTopology.whiskerRight_toPlus_comp_plusCompIso_hom_assoc, CategoryTheory.NatTrans.leftDerivedToHomotopyCategory_comp, CategoryTheory.PreGaloisCategory.instReflectsIsomorphismsActionFintypeCatAutFunctorFunctorToAction, CategoryTheory.GrothendieckTopology.ofArrows_mem_iff_isLocallySurjective_cofanIsColimitDesc_shrinkYoneda_map, CategoryTheory.ObjectProperty.preservesColimitsOfShape_eq_iSup, SSet.horn₃₂.desc.multicofork_π_three, IsRepresentedBy.iff_isIso_uliftYonedaEquiv, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_hom_comp_π, SSet.Truncated.HomotopyCategory.homToNerveMk_app_edge, OneHypercoverDenseData.essSurj.presheafObj_hom_ext_iff, CategoryTheory.Bicategory.associatorNatIsoRight_hom_app, CategoryTheory.Join.InclLeftCompRightOpOpEquivFunctor_inv_app, CategoryTheory.ULift.equivalence_counitIso_inv_app, CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.functorObjObj_comon_comul, CategoryTheory.Sum.swapCompInr_hom_app, CategoryTheory.whiskeringLeft_preservesColimitsOfShape, CategoryTheory.Sheaf.instHasColimitsOfSize, isZero_Ext_succ_of_projective, CategoryTheory.SimplicialObject.Augmented.rightOp_hom_app, CategoryTheory.Over.postEquiv_unitIso, LeftExtension.coconeAt_pt, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂'_obj_obj_obj, CategoryTheory.yonedaEquiv_naturality, CategoryTheory.full_linearYoneda, CategoryTheory.Limits.colim.mapShortComplex_X₁, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_symm_apply, CategoryTheory.Subfunctor.instMonoFunctorTypeι_1, mapCommGrpFunctor_map, CategoryTheory.shrinkYonedaRepresentableBy_homEquiv, SheafOfModules.pushforwardNatTrans_app_val_app, CategoryTheory.Limits.IndObjectPresentation.ofCocone_ℐ, HomotopyCategory.spectralObjectMappingCone_ω₁, AddCommGrpCat.HasLimit.lift_hom_apply, CategoryTheory.Presheaf.instIsLocallyPresentableFunctorOppositeOfHasPullbacks, CategoryTheory.Limits.PullbackCone.combine_pt_obj, Profinite.Extend.cocone_ι_app, CategoryTheory.GrothendieckTopology.W_iff, CategoryTheory.Idempotents.functorExtension_obj_map, CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_assoc, CategoryTheory.Triangulated.TStructure.eTruncGEπ_app_eTruncGE_map_app, CategoryTheory.WithInitial.equivComma_counitIso_inv_app_left, CategoryTheory.SimplicialObject.Augmented.point_obj, instFaithfulConstOfNonempty, SimplicialObject.Split.natTransCofanInj_app, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_map_app_app, preservesColimit_coyoneda_of_finitePresentation, CategoryTheory.Endofunctor.Algebra.functorOfNatTransComp_inv_app_f, PresheafOfModules.Sheafify.one_smul, CategoryTheory.Limits.IsLimit.conePointsIsoOfEquivalence_hom, CategoryTheory.ExponentiableMorphism.pushforwardComp_hom_counit, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackId_hom, CategoryTheory.Limits.whiskeringLimYonedaIsoCones_hom_app_app_app, CategoryTheory.Iso.isoCompInverse_hom_app, CategoryTheory.NatTrans.CommShift.of_iso_symm, CategoryTheory.ULiftYoneda.instFaithfulFunctorOppositeTypeUliftYoneda, CategoryTheory.Limits.BinaryCofan.ι_app_left, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app_assoc, CategoryTheory.Limits.FormalCoproduct.cosimplicialObjectFunctor_obj_map, CategoryTheory.Iso.isoInverseOfIsoFunctor_hom_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app_assoc, CategoryTheory.Limits.ColimitPresentation.ofIso_ι, CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app, CategoryTheory.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCone_π_app, CategoryTheory.ComposableArrows.opEquivalence_inverse_map, TopCat.Homotopy.congr_homologyMap_singularChainComplexFunctor, CategoryTheory.GrothendieckTopology.W_eq_inverseImage_isomorphisms_of_adjunction, CategoryTheory.NatIso.inv_app_isIso, CategoryTheory.δ_naturality, CategoryTheory.MonoidalCategory.DayConvolution.associator_naturality, CategoryTheory.δ_iso_of_coreflective, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.counitIso_inv, CategoryTheory.Limits.BinaryBicone.toCocone_ι_app_left, CondensedMod.epi_iff_locallySurjective_on_compHaus, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_map, CategoryTheory.Idempotents.karoubiUniversal₁_unitIso, CategoryTheory.instPreservesFiniteColimitsObjFunctorRightExactFunctor, isInitialConst_to_app, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_inv_app_hom_app, CategoryTheory.Limits.WidePullbackShape.functorExt_inv_app, CategoryTheory.GrothendieckTopology.isoSheafify_inv, CategoryTheory.CatCenter.smul_iso_hom_eq', CochainComplex.shiftFunctorAdd'_hom_app_f', leftDerivedZeroIsoSelf_hom_inv_id, CategoryTheory.CosimplicialObject.Augmented.leftOp_left_obj, CategoryTheory.Monoidal.monFunctorCategoryEquivalence_counitIso, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_inv, CategoryTheory.Limits.Multifork.ofPiFork_π_app_right, SSet.RelativeMorphism.Homotopy.h₀, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberMapObjIso_inv_assoc, CategoryTheory.instReflectsIsomorphismsComonadFunctorComonadToFunctor, pointwiseRightKanExtension_map, CategoryTheory.SimplicialObject.Augmented.rightOp_left, CategoryTheory.Triangulated.TStructure.truncGEδLT_comp_whiskerRight_natTransTruncLTOfLE_assoc, CategoryTheory.Iso.map_inv_hom_id_eval_app, CategoryTheory.Limits.PushoutCocone.mk_ι_app_right, CategoryTheory.sheafOver_obj, CategoryTheory.GrothendieckTopology.toPlus_naturality_assoc, CategoryTheory.Idempotents.karoubiUniversal₂_functor_eq, CategoryTheory.Abelian.SpectralObject.shortComplexMap_τ₁, AlgebraicGeometry.Scheme.empty_presheaf, CategoryTheory.Limits.Multicofork.snd_app_right, CategoryTheory.Comma.mapRightId_inv_app_right, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.section_app_op_mk_zero, LeftExtension.postcomp₁_map_left, equiv_functor_map, CategoryTheory.Adjunction.rightAdjointUniq_trans_assoc, CategoryTheory.Limits.Cocone.precomposeEquivalence_unitIso, CategoryTheory.Abelian.Radical.instIsIsoPreradicalToColonObjIsRadical, LightCondensed.epi_π_app_zero_of_epi, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_π_app_assoc, RightExtension.coneAtFunctor_map_hom, CategoryTheory.Adjunction.CoreUnitCounit.left_triangle, CategoryTheory.prodFunctorToFunctorProd_obj, TopologicalSpace.Opens.mapComp_inv_app, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_symm_apply, CategoryTheory.Limits.Cotrident.condition, AlgebraicGeometry.ΓSpec.toSpecΓ_of, CategoryTheory.Preadditive.commGrpEquivalence_counitIso_hom_app_hom_hom_hom, CategoryTheory.Limits.spanIsoMk_hom_app, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackComp_inv, map_shift_unop_assoc, sheafPushforwardContinuousIso_hom, CategoryTheory.NatTrans.naturality_app_app, mapComposableArrows_obj_obj, IsCoverDense.Types.presheafHom_app, CategoryTheory.ShiftMkCore.zero_add_hom_app, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₁, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalence_unitIso, AlgebraicGeometry.StructureSheaf.toOpen_germ, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality, HomologicalComplex.mapBifunctor.d₁_eq', CategoryTheory.Square.isPullback_iff_map_coyoneda_isPullback, PresheafOfModules.instIsLocalizationSheafOfModulesSheafificationInverseImageFunctorOppositeAbWToPresheaf, CategoryTheory.Idempotents.karoubiFunctorCategoryEmbedding_map, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₁_app, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_snd_map, CategoryTheory.Comma.mapRightComp_hom_app_right, CategoryTheory.Comma.opFunctorCompSnd_inv_app, CochainComplex.shiftEval_hom_app, mapCommGrpIdIso_inv_app_hom_hom_hom, CategoryTheory.NatTrans.id_app, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app, CategoryTheory.Abelian.Preradical.toColon_hom_left_app_colon_ι_app, CategoryTheory.yonedaCommGrpGrp_map_app, whiskeringRightObjIdIso_inv_app_app, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_counitIso_inv, CategoryTheory.Subobject.inf_le_right, sheafPushforwardContinuousComp_inv_app_hom_app, CategoryTheory.RightExactFunctor.ofExact_obj, CategoryTheory.Subfunctor.equalizer.fork_pt, CategoryTheory.Iso.core_inv_app_iso_inv, whiskeringLeft₂_obj_obj_obj_obj_map, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_assoc, CategoryTheory.MorphismProperty.Comma.mapLeftIso_unitIso_inv_app_left, HomologicalComplex.singleCompEvalIsoSelf_hom_app, CategoryTheory.Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_hom_comp_map_π_assoc, AlgebraicGeometry.exists_appTop_π_eq_of_isLimit, SSet.horn₃₁.ι₀_desc_assoc, CategoryTheory.Join.mapIsoWhiskerRight_hom, CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_inv, SSet.nonDegenerateEquivOfIso_apply_coe, TopCat.Presheaf.isGluing_iff_pairwise, SSet.modelCategoryQuillen.boundary_ι_mem_I, flip₁₃_obj_obj_obj, CategoryTheory.CosimplicialObject.whiskering_map_app_app, CategoryTheory.SimplicialObject.Truncated.sk_coreflective, CategoryTheory.Monoidal.associator_inv_app, CochainComplex.instHasMapBifunctorObjIntShiftFunctor_1, CategoryTheory.LocalizerMorphism.guitartExact_of_isLeftDerivabilityStructure, SSet.Augmented.stdSimplex_map_left, isRightKanExtension_iff_precomp, TopCat.toSheafCompHausLike_obj_map, CategoryTheory.FunctorToTypes.rightAdj_obj_obj, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_assoc, CategoryTheory.GradedObject.mapTrifunctorMap_obj, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_obj_pt, CategoryTheory.Sheaf.cartesianMonoidalCategoryFst_val, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_cone_π_app, CategoryTheory.Bicategory.associatorNatIsoLeft_hom_app, CategoryTheory.Triangulated.TStructure.isIso_eTruncGEIsoGEGE, CategoryTheory.Discrete.addMonoidalFunctorComp_isMonoidal, HomologicalComplex.mapBifunctor.d₂_eq_zero, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π_assoc, CategoryTheory.Limits.colimit.isoColimitCocone_ι_hom_assoc, CategoryTheory.isCardinalPresentable_iff_isCardinalAccessible_coyoneda_obj, CategoryTheory.Limits.pullbackConeOfRightIso_π_app_none, CategoryTheory.Adjunction.rightAdjointUniq_hom_app_counit_assoc, RightExtension.coneAtWhiskerRightIso_hom_hom, HomologicalComplex.quasiIsoAt_π_of_isLimit_of_isEventuallyConstantTo, flipping_inverse_map_app_app, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_inv_assoc, SSet.Truncated.trunc_spine, CategoryTheory.Sieve.shrinkFunctorIsoFunctor_hom_app_coe, CategoryTheory.sheafification_obj, CategoryTheory.Comma.mapRightIso_inverse_obj_hom, SSet.stdSimplex.faceSingletonComplIso_hom_ι_assoc, CategoryTheory.TwistShiftData.shiftFunctorAdd'_hom_app, flip₁₃Functor_map_app_app_app, CategoryTheory.Limits.functorCategoryHasBinaryBiproducts, CategoryTheory.Abelian.SpectralObject.opcyclesMap_id, Action.FunctorCategoryEquivalence.counitIso_hom_app_app, CategoryTheory.Sheaf.ΓHomEquiv_naturality_right, CategoryTheory.Sheaf.instIsLeftAdjointComposeAndSheafify, SSet.RelativeMorphism.Homotopy.precomp_h, CategoryTheory.GradedObject.mapTrifunctorObj_map_app, CategoryTheory.MonoOver.commSqOfHasStrongEpiMonoFactorisation, CategoryTheory.GrothendieckTopology.Point.presheafFiber_map_shrinkYoneda_map_shrinkYonedaCompPresheafFiberIso_inv_app, CategoryTheory.Equivalence.sheafCongr.functor_map_hom_app, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_app_π_assoc, CategoryTheory.MonoidalCategory.externalProductSwap_inv_app_app, mapArrowFunctor_map_app_right, CategoryTheory.NatIso.op_inv, PresheafOfModules.pushforward_assoc, CategoryTheory.evaluation_obj_obj, CategoryTheory.Triangulated.TStructure.truncGEδLT_comp_whiskerRight_natTransTruncLTOfLE, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_hom_app_app, SSet.Finite.exists_epi_from_isCardinalPresentable, CategoryTheory.Limits.limMap_eq, CategoryTheory.map_yonedaEquiv, CategoryTheory.Subfunctor.range_subobjectMk_ι, CategoryTheory.Limits.inl_comp_pushoutObjIso_hom_assoc, CategoryTheory.GrothendieckTopology.Point.instIsRightAdjointSheafSkyscraperSheafFunctor, PresheafOfModules.map_id, AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf_map', CategoryTheory.ComonadIso.mk_inv_toNatTrans, CategoryTheory.Sheaf.isSeparator, CategoryTheory.Triangulated.TStructure.eTruncGEIsoGEGE_inv_hom_id_app, CommGrpCat.coyonedaForget_inv_app_app, CategoryTheory.Idempotents.DoldKan.equivalence_functor, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv, CategoryTheory.StructuredArrow.mapIso_inverse_map_right, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁_obj_obj_obj, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app_assoc, CategoryTheory.Limits.fiberwiseColimCompColimIso_inv_app, CategoryTheory.Presheaf.coherentExtensiveEquivalence_unitIso_inv_app_hom_app, CategoryTheory.sum.inlCompInverseAssociator_inv_app_down_down, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoColimitUncurryWhiskeringLeft₂_hom_assoc, shiftIso_hom_app_comp_shiftMap, CategoryTheory.Limits.preservesColimitsOfShape_of_evaluation, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_hom, CommRingCat.coyonedaUnique_hom_app_hom_apply, Condensed.isoFinYoneda_hom_app, CategoryTheory.Subfunctor.Subpresheaf.fromPreimage_ι, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.Limits.BinaryCofan.IsColimit.desc'_coe, CategoryTheory.Adjunction.Triple.whiskerLeft_leftToRight_assoc, isoWhiskerRight_left, shiftIso_add'_inv_app, CategoryTheory.Limits.ι_colimitLimitToLimitColimit_π_apply, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_naturality₂, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionHomRight, CategoryTheory.Limits.WalkingMulticospan.functorExt_inv_app, PushoutObjObj.mapArrowLeft_right, ModuleCat.HasLimit.lift_hom_apply, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, CategoryTheory.Limits.combineCocones_ι_app_app, CategoryTheory.FunctorToTypes.binaryProductCone_π_app, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right, ModuleCat.binaryProductLimitCone_isLimit_lift, CategoryTheory.LocalizerMorphism.guitartExact_of_isRightDerivabilityStructure', instAdditiveObjEvaluation, SSet.ι₀_fst, CategoryTheory.Limits.DiagramOfCocones.coconePoints_obj, TopCat.Sheaf.eq_app_of_locally_eq, CategoryTheory.GrothendieckTopology.preservesLimits_diagramFunctor, CategoryTheory.PreGaloisCategory.autEmbedding_range, CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom_assoc, CochainComplex.instHasMapBifunctorObjIntShiftFunctor, CategoryTheory.Equivalence.sheafCongrPrecoherent_functor_map_hom_app, CategoryTheory.Abelian.SpectralObject.liftCycles_i, AlgebraicGeometry.Scheme.Modules.pseudofunctor_left_unitality, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_hom_app_app, CategoryTheory.conjugateIsoEquiv_apply_hom, CategoryTheory.FunctorToTypes.shrinkCompUliftFunctorIso_inv_app_down, CategoryTheory.Idempotents.karoubiUniversal₁_inverse, CategoryTheory.SmallObject.transfiniteCompositionOfShapeSuccStructPropιIteration_F, CategoryTheory.GradedObject.ι_mapBifunctorBifunctor₂₃Desc_assoc, CategoryTheory.SimplicialObject.Truncated.sk.faithful, CategoryTheory.shrinkYonedaIsoYoneda_inv_app_app, mapTriangleIso_inv_app_hom₂, CategoryTheory.evaluationAdjunctionRight_unit_app, AlgebraicTopology.DoldKan.N₂_obj_X_d, CategoryTheory.Monoidal.commMonFunctorCategoryEquivalence_functor, CategoryTheory.Limits.FormalCoproduct.evalOp_obj_map, AlgebraicGeometry.Scheme.Modules.pseudofunctor_associativity_assoc, CategoryTheory.IsPushout.of_forall_isPushout_app, CategoryTheory.Abelian.SpectralObject.cyclesIsoH_hom_inv_id_assoc, CategoryTheory.whiskeringRight_preservesLimitsOfShape, Rep.coinvariantsTensorMk_apply, CategoryTheory.Abelian.SpectralObject.EToCycles_i, CategoryTheory.Abelian.SpectralObject.zero₃_assoc, CategoryTheory.WithTerminal.coneEquiv_unitIso_inv_app_hom_left, CategoryTheory.Abelian.SpectralObject.mono_H_map_twoδ₁Toδ₀', CategoryTheory.Limits.Multifork.ofι_π_app, CategoryTheory.Equivalence.sheafCongrPrecoherent_inverse_map_hom_app, CategoryTheory.MorphismProperty.Comma.mapLeftIso_functor_obj_hom, Profinite.NobelingProof.spanFunctorIsoIndexFunctor_inv_app, whiskeringLeft₃ObjObjObj_obj_obj_obj_map, CategoryTheory.GradedObject.mapBifunctorBifunctor₂₃MapObj_ext_iff, CategoryTheory.Abelian.Preradical.shortComplex_f, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_obj_obj_map, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_f, CategoryTheory.Pi.sum_map_app, CategoryTheory.Sheaf.isLocallyBijective_iff_isIso, mapMatId_hom_app, CategoryTheory.Equivalence.congrRightFunctor_obj, CategoryTheory.NatIso.ofComponents'_inv_app, CategoryTheory.Square.arrowArrowEquivalence'_unitIso, CategoryTheory.Join.InclRightCompRightOpOpEquivFunctor_inv_app, CategoryTheory.Sieve.shrinkFunctor_obj, mapHomologicalComplex_commShiftIso_hom_app_f, CategoryTheory.ShortComplex.functorEquivalence_unitIso, TopCat.nonempty_isColimit_iff_eq_coinduced, CategoryTheory.Limits.limit.isoLimitCone_inv_π, LeftExtension.mk_right, CategoryTheory.SimplicialObject.Augmented.toArrow_obj_hom, SimplicialObject.opEquivalence_inverse, CategoryTheory.GrothendieckTopology.toPlus_naturality, FullyFaithful.hasShift.map_add_inv_app, AlgebraicGeometry.Scheme.Modules.instFullPresheafOfModulesToPresheafOfModules, isRightDerivedFunctor_iff_isIso_rightDerivedDesc, CategoryTheory.Limits.Bicone.toCone_π_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberDesc_assoc, CategoryTheory.ComposableArrows.δ₀Functor_obj_obj, CategoryTheory.CostructuredArrow.mapCompιCompGrothendieckProj_hom_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_left, IsCoverDense.isoOver_inv_app, CategoryTheory.WithTerminal.equivComma_functor_map_left_app, CategoryTheory.Adjunction.whiskerLeftRUnitIsoOfIsIsoCounit_hom_app, CategoryTheory.HasLiftingProperty.transfiniteComposition.hasLiftingPropertyFixedBot_ι_app_bot, CategoryTheory.ExponentiableMorphism.unit_pushforwardId_hom, SheafOfModules.instReflectsIsomorphismsPresheafOfModulesObjFunctorOppositeRingCatIsSheafForget, SSet.stdSimplex.δ_one_eq_const, CategoryTheory.Limits.cospanExt_inv_app_left, CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_δ_app, CategoryTheory.Adjunction.RightAdjointCommShift.iso_inv_app_assoc, flipping_functor_obj_obj_map, CategoryTheory.MorphismProperty.Comma.mapLeftIso_counitIso_hom_app_left, CommMonCat.coyonedaForget_hom_app_app_hom, CategoryTheory.MonoidalCategory.endofunctorMonoidalCategory.evaluationRightAction_actionAssocIso, CategoryTheory.MonoidalCategory.DayConvolution.associator_inv_unit_unit_assoc, AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp, CategoryTheory.Triangulated.TStructure.eTruncLTLTIsoLT_hom_inv_id_app_assoc, TopologicalSpace.Opens.mapIso_hom_app, TopCat.Sheaf.objSupIsoProdEqLocus_inv_fst, CategoryTheory.instIsConstantObjSheafSheafCompose, smoothSheaf.ι_evalHom, CategoryTheory.OverPresheafAux.YonedaCollection.map₁_id, HomologicalComplex.coneOfHasLimitEval_π_app_f, CategoryTheory.linearYoneda_obj_obj_isModule, isoSum_hom_app_inr, postcompose₂_obj_obj_map_app, CategoryTheory.MorphismProperty.Comma.mapRightId_hom_app_left, CategoryTheory.conjugateIsoEquiv_apply_inv, CategoryTheory.CosimplicialObject.Augmented.whiskering_map_app_right, CategoryTheory.Monad.ForgetCreatesColimits.liftedCocone_ι_app_f, HomologicalComplex.mapBifunctor₂₃.d_eq, SSet.associator_hom_app_apply, CategoryTheory.instIsIsoFunctorOppositeSheafToPresheafToSheafCompComposeAndSheafify, CategoryTheory.Abelian.DoldKan.equivalence_functor, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τl, isRightKanExtension_iff_isIso, SSet.Truncated.cosk.full, CategoryTheory.Triangulated.TStructure.instIsIsoFunctorTruncGELTToLTGE, ModuleCat.extendScalarsComp_hom_app_one_tmul, CategoryTheory.Equivalence.mkHom_id_functor, whiskerLeft_comp_whiskerRight, CategoryTheory.Subobject.leInfCone_π_app_none, CategoryTheory.Limits.fiberwiseColimCompEvaluationIso_inv_app, RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π, CategoryTheory.WithInitial.liftFromUnderComp_hom_app, CategoryTheory.shrinkYonedaObjObjEquiv_obj_map, smoothSheafCommRing.ι_evalHom_assoc, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom_assoc, CommShift.OfComp.map_iso_hom_app_assoc, CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_hom_assoc, CategoryTheory.yonedaEvaluation_map_down, CategoryTheory.yoneda_preservesLimits, CategoryTheory.Limits.DiagramOfCones.comp, rightDerivedNatTrans_fac_assoc, CategoryTheory.Abelian.SpectralObject.isZero_H_obj_mk₁_i₃_le, CochainComplex.ι_mapBifunctorShift₁Iso_hom_f_assoc, groupCohomology.isoShortComplexH2_hom, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity, CategoryTheory.MonoidalCategory.DayConvolutionUnit.corepresentableByLeft_homEquiv, OneHypercoverDenseData.essSurj.presheafObjObjIso.inv_restriction, CategoryTheory.Monad.monadMonEquiv_counitIso_inv_app_hom, CategoryTheory.SimplicialObject.Homotopy.whiskerRight_h, CategoryTheory.Limits.FormalCoproduct.evalCompInclIsoId_inv_app_app, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w_assoc, SSet.Truncated.HomotopyCategory.BinaryProduct.associativity, PushoutObjObj.mapArrowLeft_comp_assoc, AlgebraicGeometry.StructureSheaf.instAwayObjOppositeOpensCarrierTopObjFunctorTypeIsSheafGrothendieckTopologyStructureSheafInTypeOpBasicOpen, CategoryTheory.sheafToPresheaf_ε, CategoryTheory.Limits.PullbackCone.condition_one, MonObj.mopEquiv_counitIso_inv_app_hom_unmop, CategoryTheory.NatTrans.app_smul, CategoryTheory.MonoidalCategory.curriedTensor_map_app, CategoryTheory.GrothendieckTopology.coneCompEvaluationOfConeCompDiagramFunctorCompEvaluation_π_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_right, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_functor_map_hom, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_inv_app_hom_app, CategoryTheory.FunctorToTypes.binaryCoproductCocone_ι_app, CategoryTheory.Subfunctor.range_comp, CategoryTheory.Limits.Sigma.cocone_ι, CategoryTheory.Adjunction.leftAdjointCompIso_id_comp, AddCommGrpCat.coyoneda_map_app, sectionsEquivHom_apply_app, CategoryTheory.Pseudofunctor.DescentData.exists_equivalence_of_sieve_eq, CategoryTheory.Limits.limitIsoLimitCurryCompLim_inv_π_assoc, CategoryTheory.Limits.Cone.equivalenceOfReindexing_counitIso, CategoryTheory.bifunctorComp₂₃FunctorObj_obj, CategoryTheory.CategoryOfElements.structuredArrowEquivalence_unitIso, CategoryTheory.Triangulated.TStructure.natTransTriangleLTGEOfLE_refl, CategoryTheory.ExactFunctor.forget_obj_of, CommRingCat.instIsRightAdjointOppositeObjFunctorTypeYoneda, SSet.OneTruncation₂.nerveEquiv_symm_apply_obj, AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp_assoc, CategoryTheory.IsSifted.colim_preservesLimitsOfShape_pempty_of_isSifted, AlgebraicGeometry.StructureSheaf.toOpenₗ_eq_const, CategoryTheory.PreGaloisCategory.mulAction_naturality, CategoryTheory.Limits.BinaryBicone.ofLimitCone_fst, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst, CategoryTheory.NatTrans.op_whiskerLeft, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app, CategoryTheory.sheafificationAdjunction_counit_app_val, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_inv_app_app, CategoryTheory.Limits.pullbackObjIso_inv_comp_snd_assoc, CategoryTheory.WithInitial.coconeEquiv_counitIso_hom_app_hom, CategoryTheory.ShortComplex.rightHomologyFunctorOpNatIso_inv_app, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_hom_whiskerLeft_π_assoc, CategoryTheory.preservesLimitsOfShape_presheafToSheaf, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_hom_app_hom_coe, LightCondensed.lanPresheafExt_inv, Action.FunctorCategoryEquivalence.functor_μ, CategoryTheory.Limits.Cone.toUnder_π_app, CategoryTheory.isIso_iff_isIso_coyoneda_map, Condensed.lanPresheafExt_hom, CategoryTheory.Limits.functorCategoryHasColimitsOfSize, AlgebraicGeometry.ofArrows_ι_mem_zariskiTopology_of_isColimit, CategoryTheory.Triangulated.TStructure.eTruncGE_obj_top, CategoryTheory.Limits.colimitCoyonedaHomIsoLimit_π_apply, CategoryTheory.Adjunction.ofNatIsoRight_counit, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_inv_f_f, CategoryTheory.Enriched.FunctorCategory.diagram_obj_map, CategoryTheory.Limits.CatCospanTransform.baseIso_hom, AlgebraicTopology.DoldKan.karoubi_PInfty_f, CategoryTheory.ParametrizedAdjunction.unit_whiskerRight_map, CategoryTheory.Adjunction.unit_app_commShiftIso_hom_app, SSet.Subcomplex.liftPath_vertex_coe, CategoryTheory.Equivalence.functor_map_μ_inverse_comp_counitIso_hom_app_tensor, SSet.modelCategoryQuillen.J_le_monomorphisms, whiskerRight_comp, CategoryTheory.CartesianMonoidalCategory.isLeftAdjoint_prod_functor, functorialityCompPrecompose_inv_app_hom, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₃, AlgebraicGeometry.StructureSheaf.res_const, CategoryTheory.Limits.FormalCoproduct.instPreservesColimitDiscreteFunctorObjFunctorEval, CategoryTheory.Limits.coneOfSectionCompCoyoneda_π, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isColimit, HomologicalComplex.mapBifunctorAssociatorX_hom_D₃, pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac, flip₂₃_obj_map_app, CategoryTheory.conjugateEquiv_whiskerLeft, HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_symm_apply, CategoryTheory.flippingIso_inv_toFunctor_obj_obj_map, CategoryTheory.GrothendieckTopology.sheafification_map, commShiftIso_id_inv_app, CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso_inv_app, CategoryTheory.Limits.DiagramOfCocones.id, op_comp_isSheaf, CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_comp_assoc, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_hom_π_assoc, CategoryTheory.Abelian.SpectralObject.shortComplex_X₁, mapGrpNatIso_inv_app_hom_hom, CategoryTheory.GrothendieckTopology.Point.instPreservesColimitsOfShapeOppositeElementsFiberObjFunctorCurriedTensor, CategoryTheory.LaxMonoidalFunctor.isoMk_hom, rightOpId_hom_app, CategoryTheory.Subfunctor.fromPreimage_ι_assoc, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_inv_app_hom_hom_app, HomotopicalAlgebra.FibrantObject.instIsIsoFunctorResolutionCompToLocalizationNatTrans, CategoryTheory.CostructuredArrow.mapNatIso_functor_map_left, CategoryTheory.Adjunction.whiskerLeft_unit_app_app, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_comp, CategoryTheory.Limits.CoconeMorphism.map_w_assoc, CategoryTheory.Over.ConstructProducts.conesEquivUnitIso_hom_app_hom, CategoryTheory.IsCardinalPresentable.exists_hom_of_isColimit, CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_app_fac', CategoryTheory.hoFunctor.instIsIsoCatProdComparisonSSetHoFunctorNerve, CategoryTheory.Comma.mapRightIso_unitIso_inv_app_left, CategoryTheory.Presieve.IsSheafFor.functorInclusion_comp_extend_assoc, HomotopyCategory.homologyShiftIso_hom_app, CategoryTheory.Presheaf.map_comp_uliftYonedaEquiv_down, CategoryTheory.Abelian.LeftResolution.instPreservesZeroMorphismsKaroubiFKaroubi, CategoryTheory.Limits.limCompFlipIsoWhiskerLim_hom_app_app, CategoryTheory.GrothendieckTopology.Point.skyscraperSheafAdjunction_homEquiv_apply_val, SSet.boundary_eq_iSup, CategoryTheory.Limits.limitIsoLimitCurryCompLim_hom_π_π, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_assoc, CategoryTheory.NatIso.removeOp_hom, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app, CochainComplex.shiftFunctorAdd_hom_app_f, AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_comp, SSet.Subcomplex.unionProd.bicartSq, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_apply, SheafOfModules.pushforwardPushforwardEquivalence_unit_app_val_app, CategoryTheory.Limits.hasLimitCompEvaluation, SSet.prod_σ_snd, CategoryTheory.WithInitial.liftFromUnder_map_app, CategoryTheory.obj_μ_app_assoc, HomologicalComplex.ι_mapBifunctorFlipIso_hom, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_left, CategoryTheory.SingleFunctors.evaluation_obj, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIdIso_inv_app_hom, SSet.RelativeMorphism.Homotopy.h₁, whiskeringRight_obj_obj, CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_hom_app, CategoryTheory.GrothendieckTopology.whiskerRight_toSheafify_sheafifyCompIso_hom, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.instMonoSheafAddCommGrpCatFShortComplex, Monoidal.whiskerRight_app_snd, CategoryTheory.Abelian.SpectralObject.isIso_H_map_twoδ₁Toδ₀', CategoryTheory.Sieve.functorInclusion_is_mono, CategoryTheory.Pretriangulated.Triangle.functorIsoMk_inv, CategoryTheory.hasColimitsEssentiallySmallSite, CategoryTheory.Quotient.lift.isLift_inv, CategoryTheory.Limits.IsColimit.isIso_ι_app_of_isTerminal, CategoryTheory.Sigma.mapId_inv_app, CategoryTheory.MorphismProperty.instIsStableUnderCoproductsFunctorMonomorphismsOfHasCoproductsOfHasPullbacks, CategoryTheory.Injective.injective_iff_preservesEpimorphisms_yoneda_obj, CategoryTheory.conjugateIsoEquiv_symm_apply_inv, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_germ, SSet.stdSimplex.spineId_vertex, CategoryTheory.Limits.limitCompYonedaIsoCocone_hom_app, lanCompIsoOfPreserves_hom_app, flip₂₃_map_app_app, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.F_obj, CategoryTheory.Iso.inverseCompIso_inv_app, CategoryTheory.Limits.Cocone.whiskeringEquivalence_unitIso, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_obj_map, CategoryTheory.GrothendieckTopology.Point.presheafFiberMapIso_inv_app, postcompose₃_obj_map_app_app_app, LeibnizAdjunction.adj_unit_app_right, CategoryTheory.Limits.coconeOfConeLeftOp_ι_app, Monoidal.μNatIso_hom_app, CategoryTheory.Abelian.SpectralObject.cokernelSequenceOpcycles_X₁, CondensedMod.LocallyConstant.instFullSheafCompHausCoherentTopologyTypeConstantSheaf, ContinuousCohomology.MultiInd.d_comp_d, SSet.Subcomplex.range_tensorHom, CategoryTheory.OverPresheafAux.unitAuxAux_hom_app, CategoryTheory.pullbackShiftFunctorZero'_inv_app, CategoryTheory.Limits.limit.coneMorphism_π, leftExtensionEquivalenceOfIso₁_unitIso_hom_app_right_app, CategoryTheory.simplicialCosimplicialEquiv_functor_obj_obj, CategoryTheory.Idempotents.KaroubiKaroubi.counitIso_hom_app_f_f, CategoryTheory.Limits.end_.map_comp_assoc, AlgebraicGeometry.Scheme.AffineZariskiSite.cocone_ι_app, SSet.stdSimplex.objMk₁_apply_eq_zero_iff, whiskeringLeft₃ObjObjObj_obj_obj_map_app, TopCat.Presheaf.presheafEquivOfIso_counitIso_hom_app_app, CategoryTheory.Abelian.FunctorCategory.imageObjIso_hom, CategoryTheory.Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv, CategoryTheory.Join.mkFunctorRight_inv_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_skyscraperPresheafHomEquiv_symm_assoc, CategoryTheory.Idempotents.DoldKan.Γ_map_app, CategoryTheory.Limits.Cocone.op_π, CategoryTheory.Limits.coneLeftOpOfCoconeEquiv_counitIso, CategoryTheory.endofunctorMonoidalCategory_rightUnitor_hom_app, SSet.Truncated.HomotopyCategory.BinaryProduct.right_unitality, CategoryTheory.NatIso.isIso_inv_app, CategoryTheory.Monad.ofMon_obj, CategoryTheory.Under.mapComp_inv, HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_apply, SheafOfModules.pushforward_comp_id, CategoryTheory.Limits.coend.ι_map_assoc, mapContActionComp_hom, CategoryTheory.Equivalence.sheafCongr_inverse, PushoutObjObj.ofHasPushout_inr, SSet.Truncated.cosk_reflective, CategoryTheory.Limits.coconeOfConeUnop_ι, CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.section_comp_hom, isRightDerivedFunctor_of_inverts, CategoryTheory.Enriched.FunctorCategory.homEquiv_apply_π_assoc, map₂HomologicalComplex_obj_map, CategoryTheory.MorphismProperty.Over.mapComp_inv_app_left, CategoryTheory.Limits.colimitYonedaHomIsoLimitOp_π_apply, CategoryTheory.coyoneda_preservesLimit, CategoryTheory.Pseudofunctor.CoGrothendieck.comp_const, ModuleCat.extendScalars_comp_id_assoc, CategoryTheory.Limits.Cone.equivalenceOfReindexing_unitIso, CategoryTheory.MonoidalCategory.tensorRightTensor_inv_app, CategoryTheory.Limits.epi_of_isColimit_parallelFamily, AlgebraicTopology.DoldKan.Γ₂N₁.natTrans_app_f_app, CommShift.ofIso_compatibility, CategoryTheory.SimplicialObject.id_right, CategoryTheory.hoFunctor.preservesBinaryProduct, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_inv_π, CategoryTheory.flip_comp_evaluation, CochainComplex.mapBifunctorShift₁Iso_trans_mapBifunctorShift₂Iso, CategoryTheory.NatIso.naturality_2_assoc, CategoryTheory.shiftFunctorComm_hom_app_of_add_eq_zero, CategoryTheory.nerve.functorOfNerveMap_nerveFunctor₂_map, CategoryTheory.Limits.PushoutCocone.isoMk_hom_hom, CategoryTheory.Limits.coconeOfCoconeUncurry_pt, CategoryTheory.endofunctorMonoidalCategory_tensorUnit_map, CategoryTheory.Iso.isoFunctorOfIsoInverse_hom_app, LightCondensed.isColimitLocallyConstantPresheaf_desc_apply, SheafOfModules.relationsOfIsCokernelFree_s, CategoryTheory.SimplicialObject.instIsLeftKanExtensionOppositeTruncatedSimplexCategoryObjSkAppTruncatedUnitSkAdjTruncation, CategoryTheory.bifunctorComp₂₃FunctorMap_app_app_app_app, CategoryTheory.ShiftedHom.opEquiv_symm_apply, AddMonCat.equivalence_unitIso, CategoryTheory.prodOpEquiv_counitIso_hom_app, CategoryTheory.Over.starPullbackIsoStar_inv_app_left, CategoryTheory.Comma.mapSnd_hom_app, CategoryTheory.Iso.instIsMonoidalInvFunctor, CategoryTheory.Join.mapWhiskerLeft_whiskerLeft_assoc, SSet.RelativeMorphism.Homotopy.postcomp_h, AlgebraicGeometry.exists_mem_of_isClosed_of_nonempty, CategoryTheory.Limits.FintypeCat.jointly_surjective, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_map_snd_app, CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero_assoc, CategoryTheory.Limits.Fork.op_ι_app_zero, CategoryTheory.instIsIsoFunctorFromLeftDerivedZero, CategoryTheory.Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_snd, CategoryTheory.Pseudofunctor.sheafHom_obj, HomologicalComplex.instHasMapProdObjGradedObjectFunctorMapBifunctorMapBifunctorMapObjπX, CategoryTheory.Limits.end_.map_π_assoc, CategoryTheory.Abelian.SpectralObject.opcyclesIsoH_hom_inv_id, HomologicalComplex₂.flipEquivalenceCounitIso_inv_app_f_f, mapTriangleIdIso_inv_app_hom₁, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left, HomologicalComplex.homologyFunctorIso_hom_app, CategoryTheory.simplicialToCosimplicialAugmented_map_right, CategoryTheory.Limits.coconeOfCoconeUncurry_ι_app, postcompose₂_map_app_app_app, HomologicalComplex.mapBifunctor₁₂.d₁_eq_zero, CategoryTheory.Triangulated.TStructure.π_truncGTIsoTruncGE_hom_ι_app, mapGrpCompIso_inv_app_hom_hom, CategoryTheory.Limits.cospanOp_inv_app, CategoryTheory.bifunctorComp₁₂FunctorObj_map_app_app_app, CategoryTheory.AddMon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToAddMon_map, CategoryTheory.Presheaf.freeYonedaHomEquiv_comp_assoc, CategoryTheory.GrothendieckTopology.overMapPullback_id_comp_assoc, SheafOfModules.forgetToSheafModuleCat_obj_obj, SSet.stdSimplex.σ_objMk₁_of_lt, CategoryTheory.coyonedaPairing_map, CategoryTheory.Limits.MonoCoprod.mono_binaryCofanSum_inr, CategoryTheory.CosimplicialObject.whiskering_obj_obj_map, CategoryTheory.Limits.ker.condition_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_hom_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionUnitIso_hom, CategoryTheory.Limits.cospanCompIso_hom_app_right, CategoryTheory.shiftFunctorComm_symm, AddCommMonCat.equivalence_counitIso, CategoryTheory.Abelian.SpectralObject.sc₃_X₃, CategoryTheory.MonoOver.inf_obj, CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_none, mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app, CategoryTheory.Presheaf.tautologicalCocone_ι_app, Rep.coinvariantsTensorIndHom_mk_tmul_indVMk, CategoryTheory.NatTrans.removeUnop_id, HomologicalComplex.mapBifunctor.d₂_eq_zero', CategoryTheory.Limits.zero_app, mapAddMonCompIso_hom_app_hom, CategoryTheory.Pseudofunctor.CoGrothendieck.compIso_inv_app, CategoryTheory.CosimplicialObject.Augmented.leftOp_hom_app, CategoryTheory.Limits.instHasFilteredColimitsOfSizeFunctor, HomologicalComplex.asFunctor_map_f, CategoryTheory.Pretriangulated.instIsHomologicalAddCommGrpCatObjOppositeFunctorPreadditiveCoyoneda, AlgebraicGeometry.Scheme.exists_π_app_comp_eq_of_locallyOfFinitePresentation, CategoryTheory.Abelian.SpectralObject.homologyDataIdId_right_Q, CategoryTheory.Abelian.Preradical.instMonoFunctorFShortComplex, CategoryTheory.Join.mapWhiskerLeft_id, CategoryTheory.ShiftedHom.opEquiv'_apply, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₁_assoc, SSet.stdSimplex.face_inter_face, CategoryTheory.WithInitial.mkCommaObject_left, RepresentableBy.equivUliftYonedaIso_apply, CategoryTheory.Adjunction.id_unit, CategoryTheory.Cat.HasLimits.limitConeLift_toFunctor, LightCondMod.LocallyConstant.instFullSheafLightProfiniteCoherentTopologyTypeConstantSheaf, CategoryTheory.Adjunction.leftAdjointCompNatTrans₀₂₃_eq_conjugateEquiv_symm, CategoryTheory.nerveFunctor_obj, CategoryTheory.CatCommSq.iso_hom_naturality_assoc, CategoryTheory.Prod.symmetry_inv_app, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_left, CategoryTheory.Equivalence.leftOp_counitIso_hom_app, CategoryTheory.Limits.Trident.app_zero_assoc, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id_hom_app, CategoryTheory.constantSheafAdj_counit_w, CategoryTheory.Limits.colimit_map_colimitObjIsoColimitCompEvaluation_hom, CategoryTheory.μ_iso_of_reflective, CategoryTheory.sheafCompose_id, SSet.stdSimplex.mem_nonDegenerate_iff_mono, CategoryTheory.oppositeShiftFunctorAdd'_hom_app, CategoryTheory.ComposableArrows.isoMk₁_inv_app, CategoryTheory.Presheaf.tautologicalCocone'_ι_app, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.presheafHom_naturality_assoc, CategoryTheory.sum.inlCompInlCompAssociator_hom_app_down, CategoryTheory.Limits.PushoutCocone.mk_ι_app_left, curry_obj_map_app, instPreservesFiniteCoproductsSheafTypeYonedaOfPreservesFiniteProductsOppositeObjFunctorIsSheaf, CategoryTheory.shiftFunctorComm_eq, CategoryTheory.Comma.toPUnitIdEquiv_counitIso_inv_app, CategoryTheory.mono_of_cofan_isVanKampen, CategoryTheory.SingleFunctors.hom_inv_id_hom_assoc, CategoryTheory.MonoidalCategory.leftUnitorNatIso_inv_app, closedCounit_app_app, CategoryTheory.toOverIteratedSliceForwardIsoPullback_inv_app_left, CategoryTheory.Join.mapWhiskerRight_whiskerRight_assoc, PullbackObjObj.π_snd, CategoryTheory.Presheaf.coconeOfRepresentable_ι_app, SSet.horn₃₂.desc.multicofork_pt, CategoryTheory.Limits.coconeOfCoconeFiberwiseColimit_ι_app, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂'_obj_obj_map, CategoryTheory.Abelian.SpectralObject.shortComplex_X₃, CategoryTheory.Limits.combineCones_pt_map, SSet.prodStdSimplex.strictMono_orderHomOfSimplex, CompHausLike.LocallyConstant.unit_app, CategoryTheory.MonoidalCategory.Functor.curriedTensorPreIsoPost_inv_app_app, HomologicalComplex.cyclesOpNatIso_hom_app, CategoryTheory.instPreservesLimitsOfSizeFunctorOppositeTypeShrinkYoneda, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₃, CategoryTheory.Pseudofunctor.DescentData.pullFunctorIdIso_hom_app_hom, CategoryTheory.Mon.limit_mon_one, CategoryTheory.PreGaloisCategory.exists_lift_of_mono, CochainComplex.shiftFunctorAdd'_hom_app_f, CategoryTheory.Limits.Cofork.op_π_app_one, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_right_app, CategoryTheory.Limits.Cocone.equivalenceOfReindexing_unitIso, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₁, leftDerivedZeroIsoSelf_hom, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceInverseπ_inv_app, CategoryTheory.Equivalence.mapCommGrp_counitIso, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp_assoc, CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm_assoc, CategoryTheory.Quotient.LiftCommShift.iso_inv_app, CategoryTheory.typeEquiv_functor_obj_obj_map, Action.resId_hom_app_hom, DerivedCategory.instFullFunctorHomotopyCategoryIntUpObjWhiskeringLeftQh, PullbackObjObj.mapArrowRight_left, CategoryTheory.pre_map, mapCommGrpNatIso_hom_app_hom_hom_hom, CategoryTheory.Triangulated.TStructure.instIsIsoFunctorETruncLTGELTSelfToLTGE, CategoryTheory.MorphismProperty.Comma.mapLeftId_inv_app_left, CategoryTheory.Limits.limit.conePointUniqueUpToIso_inv_comp, CategoryTheory.Join.mapWhiskerLeft_leftUnitor_hom, descOfIsLeftKanExtension_fac, HomologicalComplex.mapBifunctor.d₂_eq', CategoryTheory.Limits.IsLimit.map_π_assoc, CategoryTheory.Abelian.SpectralObject.sc₃_X₂, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_obj_iso_hom, curryingFlipEquiv_symm_apply_obj_obj, CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_naturality_app, uncurry_obj_curry_obj_flip_flip', CategoryTheory.Idempotents.karoubiChainComplexEquivalence_unitIso_inv_app_f_f, AlgebraicGeometry.Scheme.Modules.pseudofunctor_left_unitality_assoc, CategoryTheory.ProdPreservesConnectedLimits.γ₁_app, CategoryTheory.conjugateEquiv_adjunction_id_symm, SSet.Subcomplex.mono_homOfLE, CategoryTheory.Limits.ColimitPresentation.w, CategoryTheory.CompatiblePreserving.compatible, CategoryTheory.Localization.Monoidal.lifting₂CurriedTensorPre_iso, OplaxMonoidal.whiskeringRight_η_app, groupHomology.isoShortComplexH2_inv, SSet.Truncated.Path.mk₂_vertex, skyscraperPresheafCoconeOfSpecializes_ι_app, SSet.horn₂₂.isPushout, CategoryTheory.NatTrans.rightDerived_id, CategoryTheory.Limits.Cone.functoriality_map_hom, CategoryTheory.IsSifted.colim_preservesTerminal_of_isSifted, CategoryTheory.MonadIso.mk_inv_toNatTrans, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompCoyoneda, Action.rightUnitor_hom_hom, CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_app, CategoryTheory.Triangulated.TStructure.natTransTruncLTOfLE_ι, CategoryTheory.GrothendieckTopology.instIsIsoFunctorOppositeToPresheafFiberNatTransPointBotCoeEquivHomUnopOpObjTypeShrinkYonedaSymmShrinkYonedaObjObjEquivId, AlgebraicGeometry.Scheme.isZero_ellAdicSheaf_of_isEmpty, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_map_injective, CategoryTheory.Limits.BinaryFan.leftUnitor_inv, CategoryTheory.Equivalence.core_counitIso_inv_app_iso_hom, CategoryTheory.SmallObject.SuccStruct.ofNatTrans_succ, CategoryTheory.Limits.piObjIso_inv_comp_π_assoc, CategoryTheory.Iso.unop_inv_hom_id_app, CategoryTheory.instFaithfulComonadFunctorComonadToFunctor, isLeftKanExtension_iff_precomp, TopCat.Presheaf.presheafEquivOfIso_inverse_obj_obj, CategoryTheory.yoneda'_comp, AlgebraicTopology.DoldKan.N₁Γ₀_inv_app, SSet.prodStdSimplex.nonDegenerate_iff_strictMono_objEquiv, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₂, CategoryTheory.Coyoneda.fullyFaithful_preimage, ranObjObjIsoLimit_inv_π, CategoryTheory.Limits.Cone.postcomposeId_inv_app_hom, SSet.yonedaEquiv_comp, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_hom_app_hom_app, CategoryTheory.Sum.natIsoOfWhiskerLeftInlInr_inv, Elements.coconeπOpCompShrinkYonedaObj_ι_app, CategoryTheory.MonoidalOpposite.tensorLeftIso_hom_app_unmop, ShiftSequence.shiftIso_add, CategoryTheory.Limits.colimit_map_colimitObjIsoColimitCompEvaluation_hom_assoc, CategoryTheory.Iso.inverseCompIso_hom_app, CategoryTheory.Abelian.Preradical.isPullback_colon, CategoryTheory.GrothendieckTopology.toSheafify_naturality, CommGrpCat.coyonedaType_obj_map, CategoryTheory.Equivalence.congrLeft_counitIso_hom_app, CategoryTheory.Adjunction.right_triangle, CategoryTheory.Adjunction.leftAdjointUniq_inv_app, CategoryTheory.Sigma.descUniq_hom_app, CategoryTheory.Limits.instHasFiniteColimitsFunctor, CategoryTheory.coherentTopology.isLocallySurjective_π_app_zero_of_isLocallySurjective_map, CategoryTheory.Limits.Cocone.toCostructuredArrowCompProj_inv_app, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_app_apply, LightCondSet.topCatAdjunctionUnit_hom_app, CategoryTheory.Limits.Types.Pushout.cocone_ι_app, CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument.preservesColimit, SSet.stdSimplex.spineId_arrow_apply_one, PresheafOfModules.toPresheaf_preservesColimit, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_obj_fst, OneHypercoverDenseData.essSurj.presheafObjObjIso_inv_naturality_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_map_app_snd, SSet.Quasicategory.hornFilling', CategoryTheory.Limits.piFunctor_map_app, CategoryTheory.flipFunctor_map_app_app, CategoryTheory.Limits.functorCategoryHasColimitsOfShape, CategoryTheory.GrothendieckTopology.ι_plusCompIso_hom, CategoryTheory.WithTerminal.mapId_inv_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionUnitIso_inv, CategoryTheory.PreGaloisCategory.functorToContAction_obj_obj, CategoryTheory.Iso.coreComp, CategoryTheory.obj_μ_zero_app, AlgebraicTopology.DoldKan.Compatibility.τ₀_hom_app, CategoryTheory.adhesive_functor, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_right_map, mapTriangleIdIso_inv_app_hom₂, CategoryTheory.ExponentiableMorphism.unit_pushforwardId_hom_assoc, CategoryTheory.OverPresheafAux.MakesOverArrow.of_arrow, CategoryTheory.cosimplicialToSimplicialAugmented_map, flippingEquiv_apply_obj_map, CategoryTheory.typeEquiv_functor_obj_obj_obj, CategoryTheory.Monad.monadMonEquiv_functor, PresheafOfModules.freeAdjunction_unit_app, CategoryTheory.Abelian.SpectralObject.kernelSequenceCycles_X₃, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst_assoc, CategoryTheory.Comma.mapRightEq_hom_app_left, SSet.OneTruncation₂.nerveHomEquiv_apply, CategoryTheory.frobeniusMorphism_iso_of_expComparison_iso, CategoryTheory.Over.forgetCocone_ι_app, CategoryTheory.Limits.colimitIsoColimitCurryCompColim_ι_ι_inv, commShiftOfLocalization_iso_hom_app, CategoryTheory.StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_left, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₂, CategoryTheory.Join.inrCompFromSum_inv_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_hom_toNatTrans_app_hom_app, CategoryTheory.PreGaloisCategory.FiberFunctor.isPretransitive_of_isGalois, LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv, CategoryTheory.evaluationIsRightAdjoint, CategoryTheory.MorphismProperty.instIsStableUnderRetractsFunctorFunctorCategory, CategoryTheory.BasedNatTrans.instIsIsoFunctorObjOfBasedFunctor, CategoryTheory.WithTerminal.liftFromOverComp_inv_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_right, HomologicalComplex.mapBifunctor.d₁_eq_zero', CategoryTheory.Limits.hasLimit_const_of_isConnected, CategoryTheory.Comma.mapRightEq_inv_app_right, CategoryTheory.PreGaloisCategory.instIsEquivalenceContActionFintypeCatHomObjFiniteAutFunctorFunctorToContAction, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_jointly_surjective₂, CategoryTheory.isCardinalPresentable_iff_isCardinalAccessible_uliftCoyoneda_obj, CategoryTheory.SingleFunctors.evaluation_map, AlgebraicGeometry.StructureSheaf.comap_basicOpen, CategoryTheory.StructuredArrow.mapIso_functor_map_right, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_hom_assoc, CategoryTheory.Limits.ι_colimitConstInitial_hom, CategoryTheory.SingleFunctors.comp_hom, Condensed.underlying_obj, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τl, CategoryTheory.Adjunction.map_restrictFullyFaithful_unit_app, CategoryTheory.Limits.reflexivePair.compRightIso_inv_app, CategoryTheory.Limits.equalizer.fork_π_app_zero, partialFunEquivPointed_counitIso_hom_app_toFun, CategoryTheory.Sheaf.sheafifyCocone_ι_app_val_assoc, CategoryTheory.Core.forgetFunctorToCore_obj_map, CategoryTheory.LocalizerMorphism.LeftResolution.opEquivalence_counitIso, curryObjProdComp_inv_app_app, TwoP.swapEquiv_counitIso_hom_app_hom_toFun, SheafOfModules.pushforwardPushforwardAdj_counit_app_val_app, SheafOfModules.conjugateEquiv_pullbackId_hom, CategoryTheory.Sheaf.Hom.add_app, Monoidal.associator_hom_app, CategoryTheory.Limits.Cone.equivCostructuredArrow_unitIso, SSet.Subcomplex.instEpiToRange, CategoryTheory.PreGaloisCategory.endEquivAutGalois_π, CategoryTheory.Limits.coneOfConeUncurry_pt, CategoryTheory.Triangulated.SpectralObject.triangle_obj₃, LaxMonoidal.ofBifunctor.firstMap_app_app_app, CategoryTheory.NatTrans.app_units_zsmul, CategoryTheory.Prod.braiding_counitIso, CategoryTheory.Limits.Cocone.extend_ι, CategoryTheory.Presieve.extension_iff_amalgamation, CategoryTheory.GradedObject.instHasMapProdObjFunctorMapTrifunctorObjOfMapTrifunctor, CategoryTheory.Limits.prod.functor_obj_obj, CategoryTheory.Limits.prodComparisonNatTrans_app, CategoryTheory.MonoidalClosed.pre_map, CochainComplex.shiftFunctorComm_hom_app_f, CategoryTheory.EnrichedFunctor.isoMk_inv_out, CategoryTheory.Sheaf.hasLimitsOfSize, SSet.instFiniteSigmaObjOfFinite, CategoryTheory.Cat.Hom.toNatTrans_comp, CategoryTheory.PreGaloisCategory.instIsTopologicalGroupAutFunctorFintypeCat, const_obj_obj, CategoryTheory.Limits.Cocone.toStructuredArrow_map, CategoryTheory.Limits.Cone.equivalenceOfReindexing_inverse, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_left_map, CategoryTheory.MorphismProperty.Comma.mapLeftIso_counitIso_inv_app_left, CategoryTheory.WithTerminal.equivComma_inverse_map_app, CategoryTheory.NatTrans.instIsMultiplicativeFunctorEquifibered, CategoryTheory.Limits.coconeOpEquiv_counitIso, CategoryTheory.Idempotents.KaroubiKaroubi.unitIso_inv_app_f, CategoryTheory.GrothendieckTopology.diagramNatTrans_id, CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv, CategoryTheory.Sum.functorEquiv_unit_app_app_inl, CategoryTheory.Join.mkFunctorLeft_inv_app, CategoryTheory.ExactFunctor.of_fst, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₃, SSet.RelativeMorphism.Homotopy.rel, CategoryTheory.ComposableArrows.isoMk₄_inv, leftKanExtensionUniqueOfIso_hom, CategoryTheory.Limits.Cone.w_apply, CategoryTheory.Abelian.Preradical.shortComplex_X₃, TopCat.isOpen_iff_of_isColimit, AlgebraicGeometry.tilde.toOpen_map_app_assoc, CategoryTheory.MonoidalOpposite.unmopEquiv_counitIso_inv_app, faithful_whiskeringRight_obj, CategoryTheory.Limits.limitFlipIsoCompLim_hom_app, CategoryTheory.shiftFunctorAdd_assoc_hom_app, CategoryTheory.ShortComplex.FunctorEquivalence.functor_map_app, SSet.horn.primitiveEdge_coe_down, CategoryTheory.instPreservesFiniteColimitsObjFunctorExactFunctor, CategoryTheory.CategoryOfElements.fromCostructuredArrow_obj_mk, CategoryTheory.GrothendieckTopology.Point.shrinkYonedaCompPresheafFiberIso_inv_app_toPresheafFiber, CategoryTheory.Triangulated.TStructure.eTruncLT_obj_map_eTruncLTι_app_eTruncLT_map_app_assoc, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_hom_π_π, PullbackObjObj.mapArrowLeft_right, CategoryTheory.Limits.limIsoFlipCompWhiskerLim_inv_app_app, CategoryTheory.WithInitial.ofCommaObject_map, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_rightUnitor, CategoryTheory.Abelian.DoldKan.comparisonN_hom_app_f, CategoryTheory.constantCommuteCompose_hom_app_hom, CategoryTheory.MonoidalOpposite.tensorRightMopIso_hom_app_unmop, CategoryTheory.Limits.Cone.overPost_π_app, CategoryTheory.Under.opEquivOpOver_counitIso, mapTriangleRotateIso_inv_app_hom₃, isIso_whiskerLeft, IsDenseSubsite.map_eq_of_eq, HomologicalComplex.unit_tensor_d₁, CategoryTheory.WithTerminal.equivComma_inverse_obj_map, SSet.Truncated.HomotopyCategory.BinaryProduct.associativityIso_hom_app, CategoryTheory.Subfunctor.Subpresheaf.range_comp_le, CategoryTheory.GrothendieckTopology.plusCompIso_whiskerLeft, CategoryTheory.PreGaloisCategory.PointedGaloisObject.instHasColimitOppositeFunctorTypeCompOpInclCoyoneda, CategoryTheory.Triangulated.SpectralObject.comp_hom_assoc, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_inv_app_app, CategoryTheory.Limits.IndObjectPresentation.cocone_pt, IsCoverDense.sheaf_eq_amalgamation, toEssImageCompι_inv_app, localCohomology.hasColimitDiagram, CategoryTheory.Subfunctor.equalizer.lift_ι_assoc, CategoryTheory.conjugateEquiv_adjunction_id, CategoryTheory.Yoneda.fullyFaithful_preimage, monoidalClosed_closed_adj, OneHypercoverDenseData.essSurj.presheafMap_π, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_incl_app, CategoryTheory.Limits.limit.id_pre, CategoryTheory.CosimplicialObject.Augmented.whiskering_obj, SSet.stdSimplex.faceSingletonIso_one_hom_comp_ι_eq_δ_assoc, CategoryTheory.Limits.Cone.toStructuredArrow_map, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_fst_obj, HomologicalComplex.HomologySequence.composableArrows₃Functor_map, CategoryTheory.SimplicialObject.Augmented.drop_map, mapArrowFunctor_map_app_left, AlgebraicGeometry.ExistsHomHomCompEqCompAux.hb, CategoryTheory.coyonedaEquiv_symm_map, leftDerivedZeroIsoSelf_hom_inv_id_app_assoc, CategoryTheory.GradedObject.mapTrifunctor_obj, opHom_map_app, CategoryTheory.Comma.toIdPUnitEquiv_counitIso_inv_app, CategoryTheory.Abelian.FunctorCategory.functor_category_isIso_coimageImageComparison, SSet.Subcomplex.range_eq_top_iff, Action.associator_inv_hom, cocones_map_app, CategoryTheory.Idempotents.instFaithfulKaroubiFunctorKaroubiFunctorCategoryEmbedding, CategoryTheory.MonoidalCategory.DayFunctor.equiv_unitIso_inv_app, CategoryTheory.Enriched.FunctorCategory.functorEnriched_comp_id_assoc, CategoryTheory.Limits.coprod.functor_obj_map, CategoryTheory.instFaithfulIndFunctorOppositeTypeInclusion, CategoryTheory.ShiftMkCore.assoc_hom_app, RightExtension.postcomp₁_obj_hom_app, map_opShiftFunctorEquivalence_counitIso_inv_app_unop, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_map, CategoryTheory.Limits.Multicoequalizer.multicofork_ι_app_right, ModuleCat.extendScalars_comp_id, CategoryTheory.Abelian.SpectralObject.p_opcyclesToE_assoc, CategoryTheory.NatTrans.commShift_iso_hom_of_localization, CategoryTheory.functorProdFunctorEquivUnitIso_inv_app, SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁_inv_app_f_f, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_obj₂, flip₂₃Functor_obj_map_app_app, CategoryTheory.Sheaf.adjunction_counit_app_hom, CategoryTheory.overEquivOfIsInitial_counitIso, CategoryTheory.sheafToPresheaf_isRightAdjoint, LightCondensed.id_val, CategoryTheory.RightExactFunctor.whiskeringLeft_obj_obj_obj, leftDerivedNatTrans_id, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃'_obj_obj_map, CategoryTheory.Enriched.FunctorCategory.functorEnriched_assoc_assoc, commShiftOfLocalization.iso_hom_app_assoc, LightCondensed.ofSheafForgetLightProfinite_obj, CategoryTheory.Limits.SequentialProduct.cone_π_app, PresheafOfModules.freeYonedaEquiv_comp, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_hom_app_app_hom, CategoryTheory.instFullSheafFunctorOppositeCompSheafComposeSheafToPresheafOfFaithful, AddCommMonCat.coyoneda_obj_map, ranAdjunction_counit, CategoryTheory.SingleFunctors.instIsIsoFunctorHom, CategoryTheory.NatIso.unop_refl, PresheafOfModules.Sheafify.zero_smul, CategoryTheory.endofunctorMonoidalCategory_leftUnitor_inv_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMop_obj_unmop_map, CategoryTheory.toSheafify_naturality_assoc, CategoryTheory.WithInitial.liftFromUnder_obj_map, CategoryTheory.Equivalence.functorFunctor_map, CategoryTheory.flippingIso_hom_toFunctor_obj_obj_obj, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₂, CategoryTheory.Abelian.SpectralObject.δ_pOpcycles, CategoryTheory.Limits.limit.lift_π_app_assoc, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_inv_app_app, CategoryTheory.NatTrans.app_shift, CategoryTheory.Triangulated.TStructure.instIsLEObjEIntFunctorETruncGE, leftDerivedNatTrans_fac, whiskeringLeft₃_obj_obj_obj_obj_obj_map_app, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_mul_app, CategoryTheory.NatTrans.comp_app, instIsRegularEpiCategoryOfForallEpiHasPullbackOfHasPushouts, instIsIsoAppLanUnit_1, CategoryTheory.Limits.Cone.w_assoc, CategoryTheory.Equivalence.Equivalence_mk'_counitInv, CategoryTheory.CatCenter.localization_mul, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right_assoc, SSet.Truncated.HomotopyCategory.homToNerveMk_app_zero, CategoryTheory.Limits.limitIsoFlipCompLim_inv_app, CategoryTheory.Join.mapPairLeft_hom_app, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransId_hom_app_f, flipIsoCurrySwapUncurry_inv_app_app, CategoryTheory.cones_map_app_app, CategoryTheory.Triangulated.TStructure.instIsIsoFunctorETruncGEπBotEInt, CommGrpCat.coyoneda_obj_map, CategoryTheory.ShortComplex.functorEquivalence_inverse, CategoryTheory.GradedObject.Monoidal.instHasMapProdObjFunctorMapBifunctorCurriedTensorSingle₀TensorUnit_1, CategoryTheory.EnrichedFunctor.isoMk_hom_out, CategoryTheory.BraidedCategory.ofBifunctor.Reverse.firstMap₃_app_app_app, CategoryTheory.nat_trans_from_is_connected, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_app_snd_app, CategoryTheory.GrothendieckTopology.Point.sheafFiberComapIso_inv_app, CategoryTheory.WithTerminal.liftFromOver_map_app, CategoryTheory.whiskerRight_ι_colimitCompWhiskeringRightIsoColimitComp_inv, SSet.Truncated.Edge.map_whiskerRight, CategoryTheory.Sheaf.hom_ext_iff, AlgebraicGeometry.isAffineHom_π_app, DerivedCategory.singleFunctorsPostcompQIso_hom_hom, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₂, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_map_right_app, CategoryTheory.GradedObject.ιMapBifunctor₁₂BifunctorMapObj_eq, CategoryTheory.Presieve.FamilyOfElements.compPresheafMap_id, SSet.Truncated.comp_app, CategoryTheory.ChosenPullbacksAlong.unit_pullbackComp_hom, LightProfinite.Extend.functor_obj, LightCondensed.isoFinYoneda_hom_app, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app_assoc, CategoryTheory.coyonedaPairingExt_iff, CategoryTheory.Pseudofunctor.DescentData.pullFunctorCompIso_hom_app_hom, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₂, CategoryTheory.associativity_app, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_obj_obj_mor₃, CategoryTheory.Pretriangulated.preadditiveYoneda_shiftMap_apply, CategoryTheory.SmallObject.prop_iterationFunctor_map_succ, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_right, CategoryTheory.Enriched.FunctorCategory.homEquiv_comp_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformPrecomposeObjSquare_iso_hom_comp, CategoryTheory.Limits.parallelPair.eqOfHomEq_hom_app, CategoryTheory.Limits.coconeLeftOpOfConeEquiv_counitIso, CategoryTheory.Limits.limit.map_pre, CategoryTheory.WithTerminal.coneEquiv_inverse_map_hom_left, CategoryTheory.Iso.inv_hom_id_app_app_app_assoc, FundamentalGroupoid.punitEquivDiscretePUnit_counitIso, mapCochainComplexShiftIso_hom_app_f, CategoryTheory.shrinkYonedaMon_obj_map_shrinkYonedaMonObjObjEquiv_symm, map_opShiftFunctorEquivalence_unitIso_inv_app_unop_assoc, CategoryTheory.Triangulated.TStructure.eTruncLTι_naturality_assoc, CategoryTheory.instPreservesFiniteProductsOppositeObjFunctorIsSheafExtensiveTopology, CategoryTheory.Triangulated.TStructure.isZero_eTruncLT_obj_obj, HomologicalComplexUpToQuasiIso.homologyFunctorFactorsh_hom_app_quotient_obj, CategoryTheory.Iso.inv_hom_id_app, CategoryTheory.SingleFunctors.shiftIso_add_hom_app, CategoryTheory.flippingIso_hom_toFunctor_map_app_app, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_apply_app, SSet.Subcomplex.fromPreimage_ι, CategoryTheory.GrothendieckTopology.Point.presheafFiberCocone_ι_app, CategoryTheory.AdditiveFunctor.of_fst, CategoryTheory.Equivalence.unop_unitIso, CategoryTheory.instFullFunctorOppositeTypeShrinkYoneda, CategoryTheory.cosimplicialSimplicialEquiv_inverse_map, CategoryTheory.OppositeShift.adjunction_counit, CategoryTheory.Triangulated.TStructure.eTruncGE_obj_coe, bifunctorComp₁₂Iso_inv_app_app_app, CategoryTheory.Presheaf.classifier_Ω₀, PresheafOfModules.sheafificationAdjunction_homEquiv_apply, Condensed.comp_hom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_inv_app, CategoryTheory.Adjunction.representableBy_homEquiv, CategoryTheory.shiftFunctorCompIsoId_zero_zero_hom_app, sheafPushforwardContinuousComp'_inv_app_hom_app, CategoryTheory.GradedObject.ι_mapBifunctorComp₂₃MapObjIso_inv, PushoutObjObj.inr_ι_assoc, CategoryTheory.Equivalence.inverseFunctorObjIso_hom, CategoryTheory.MonoidalCategory.externalProductBifunctorCurried_obj_map_app_app, CategoryTheory.Limits.coequalizer.cofork_ι_app_one, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one, SheafOfModules.instPreservesFiniteLimitsSheafAddCommGrpCatToSheaf, CategoryTheory.obj_μ_inv_app_assoc, rightDerivedZeroIsoSelf_inv, CategoryTheory.Limits.prod.functor_map_app, toEssImageCompι_hom_app, CategoryTheory.shrinkYonedaIsoYoneda_hom_app_app, CategoryTheory.GrothendieckTopology.W_eq_isLocal_range_sheafToPresheaf_obj, whiskeringLeft₃_obj_obj_obj_obj_obj_obj_map, CategoryTheory.δ_naturalityₗ, CochainComplex.shiftEval_inv_app, HomologicalComplex.mapBifunctor₂₃.ι_D₃_assoc, CategoryTheory.Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_as_app_toNatTrans_app, CategoryTheory.GrothendieckTopology.instIsIsoSheafAppFunctorOppositeSheafComposeNatTransPlusPlusAdjunction, CategoryTheory.Monad.ForgetCreatesLimits.liftedCone_π_app_f, whiskeringRight_obj_comp, PushoutObjObj.hom_ext_iff, DerivedCategory.shiftMap_homologyFunctor_map_Qh, CategoryTheory.Abelian.SpectralObject.EIsoH_hom_opcyclesIsoH_inv, CategoryTheory.IsPullback.iff_app, CategoryTheory.Limits.combineCones_pt_obj, PushoutObjObj.mapArrowRight_comp, CategoryTheory.FunctorToTypes.hom_inv_id_app_apply, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionUnitNatIso_inv_app, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁, CategoryTheory.TwoSquare.vComp'_app, HomologicalComplexUpToQuasiIso.homologyFunctorFactorsh_hom_app_quotient_obj_assoc, CategoryTheory.Equivalence.congrLeft_inverse, CategoryTheory.Limits.walkingSpanOpEquiv_unitIso_hom_app, CategoryTheory.Join.mapIsoWhiskerLeft_inv_app, CategoryTheory.Triangulated.TStructure.truncLTι_comp_truncGEπ, CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app_assoc, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_left, TopCat.Presheaf.presheafEquivOfIso_functor_map_app, SSet.stdSimplex.face_le_face_iff, CategoryTheory.Equivalence.inverseFunctorObj'_inv_app, CategoryTheory.Limits.CatCospanTransform.mkIso_hom_base, CategoryTheory.Enriched.FunctorCategory.enrichedComp_π, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_X₂, SSet.Finite.instIsFinitelyPresentable, CategoryTheory.Abelian.SpectralObject.δ_eq_zero_of_isIso₁, rightUnitor_inv_app, CategoryTheory.Subfunctor.Subpresheaf.subobjectMk_range_arrow, CategoryTheory.Adjunction.ofNatIsoLeft_counit, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_map_surjective, leftUnitor_hom_app, flippingEquiv_apply_map_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality, CategoryTheory.Grothendieck.ιCompMap_hom_app_base, AlgebraicTopology.DoldKan.Γ₂_obj_X_obj, SSet.RelativeMorphism.Homotopy.refl_h, CategoryTheory.Iso.core_hom_app_iso_hom, CategoryTheory.Over.ConstructProducts.conesEquivInverseObj_π_app, CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_inv, SSet.horn₃₁.ι₃_desc, CategoryTheory.Abelian.SpectralObject.cokernelSequenceE_X₁, CategoryTheory.GradedObject.comapEq_inv_app, SSet.truncation_spine, CategoryTheory.GrothendieckTopology.liftToPlusObjLimitObj_fac, CategoryTheory.LaxMonoidalFunctor.comp_hom_assoc, PresheafOfModules.toPresheaf_preservesColimitsOfSize, CategoryTheory.Equivalence.refl_unitIso, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_hom_app, CategoryTheory.TransfiniteCompositionOfShape.map_incl, CategoryTheory.GradedObject.mapBifunctor_obj_map, homEquivOfIsRightKanExtension_apply_app, CategoryTheory.Limits.CompleteLattice.limitCone_cone_π_app, CategoryTheory.ParametrizedAdjunction.homEquiv_eq, CategoryTheory.Equivalence.symmEquivInverse_obj_unitIso_inv, CategoryTheory.Limits.combineCocones_pt_map, CategoryTheory.Adjunction.comp_unit, CategoryTheory.ExponentiableMorphism.unit_pushforwardComp_hom, CategoryTheory.Limits.IsLimit.homEquiv_symm_naturality, CategoryTheory.MonoidalCategory.curriedTensorPreFunctor_map_app_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₁, CategoryTheory.Limits.pointwiseProductCompEvaluation_hom_app, CategoryTheory.conjugateIsoEquiv_symm_apply_hom, CategoryTheory.toSheafify_plusPlusIsoSheafify_hom_assoc, IsDenseSubsite.sheafifyHomEquivOfIsEquivalence_naturality_left_assoc, sheafPushforwardContinuousId'_inv_app_hom_app, ranCounit_app_whiskerLeft_ranAdjunction_unit_app, CategoryTheory.Limits.Cotrident.ofπ_ι_app, AlgebraicGeometry.Scheme.LocalRepresentability.glueData_t, shiftIso_inv_naturality_assoc, SSet.PtSimplex.RelStruct.δ_succ_map, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_obj_obj_obj₂, CategoryTheory.instAdditiveAdditiveFunctorFunctorForget, IsEventuallyConstantTo.isIso_π_of_isLimit', PullbackObjObj.ofHasPullback_pt, SheafOfModules.forgetPreservesLimitsOfShape, CategoryTheory.Triangulated.SpectralObject.triangle_obj₁, CategoryTheory.Abelian.SpectralObject.toCycles_Ψ, CategoryTheory.Iso.unop_inv_hom_id_app_assoc, CategoryTheory.GrothendieckTopology.yoneda_map_hom, CategoryTheory.CosimplicialObject.Truncated.whiskering_obj_obj_map, LeftExtension.coconeAt_ι_app, CategoryTheory.Limits.coconeOfIsSplitEpi_ι_app, CategoryTheory.Presheaf.isLimit_iff_isSheafFor, SheafOfModules.Presentation.IsFinite.finite_relations, CategoryTheory.CatCenter.instIsMulCommutative, Action.functorCategoryEquivalence_linear, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_one_app, CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcyclesEIso_inv_τ₃, LightProfinite.instEpiAppOppositeNatπAsLimitCone, CategoryTheory.Abelian.SpectralObject.kernelSequenceE_X₂, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst_assoc, CategoryTheory.FunctorToTypes.binaryProductCone_pt_map, CategoryTheory.Monoidal.comonFunctorCategoryEquivalence_inverse, mapTriangleCommShiftIso_hom_app_hom₂, CategoryTheory.Limits.Cocone.precomposeEquivalence_inverse, CategoryTheory.PreGaloisCategory.exists_lift_of_quotient_openSubgroup, CategoryTheory.Adjunction.leftAdjointCompIso_hom_app, CategoryTheory.RightExactFunctor.forget_obj_of, CategoryTheory.NatTrans.shift_app_comm_assoc, CategoryTheory.Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₂, CategoryTheory.ComposableArrows.δ₀Functor_map_app, SSet.stdSimplex.δ_objMk₁_of_lt, CategoryTheory.Sheaf.instIsRightAdjointSheafComposeOfHasWeakSheafify, CategoryTheory.MorphismProperty.instIsStableUnderCobaseChangeFunctorFunctorCategoryOfHasPushouts, whiskerRight_twice, CategoryTheory.NatIso.pi'_hom, CategoryTheory.LocalizerMorphism.instCommShiftLocalizationHomFunctorIsoFunctorQLocalizedFunctor, SheafOfModules.pushforwardNatTrans_app_val_app_apply, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_id, CategoryTheory.piEquivalenceFunctorDiscrete_functor_map, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_obj_snd, CategoryTheory.Equivalence.congrRight_inverse, flip₁₃Functor_obj_obj_obj_map, CategoryTheory.Sieve.uliftFunctorInclusion_top_isIso, CategoryTheory.GrothendieckTopology.Point.instIsIsoηFunctorOppositePresheafFiber, PresheafOfModules.colimitCocone_ι_app_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiberNatTrans_app, AlgebraicTopology.DoldKan.Γ₂_map_f_app, CategoryTheory.Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone_ι_app_eq_sum, Monoidal.whiskeringLeft_δ_app, CategoryTheory.NatTrans.shift_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app, CategoryTheory.whiskering_linearYoneda₂, CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_naturality_app, SSet.Truncated.HomotopyCategory.homToNerveMk_comp, SSet.Truncated.HomotopyCategory.BinaryProduct.functor_map, CategoryTheory.NatTrans.mono_of_mono_app, isoWhiskerLeft_trans, CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_counitIso, CategoryTheory.Limits.inr_comp_pushoutObjIso_inv_assoc, ShiftSequence.induced_shiftMap, LeftExtension.mk_left_as, commShiftIso_eq_ofInduced, CategoryTheory.SmallObject.coconeOfLE_ι_app, AddCommMonCat.coyonedaForget_hom_app_app_hom, CategoryTheory.Square.arrowArrowEquivalence'_counitIso, CategoryTheory.Monad.toMon_X, CategoryTheory.Limits.IndizationClosedUnderFilteredColimitsAux.isFiltered, CategoryTheory.Limits.inr_comp_pushoutObjIso_hom, CategoryTheory.Idempotents.KaroubiHomologicalComplexEquivalence.counitIso_hom, CategoryTheory.Abelian.SpectralObject.opcyclesIsoH_hom_inv_id_assoc, CategoryTheory.Limits.colimitCoconeOfUnique_cocone_ι, CategoryTheory.Sum.functorEquiv_inverse_obj, CategoryTheory.Subfunctor.Subpresheaf.equalizer.ι_ι, CategoryTheory.Pseudofunctor.DescentData.pullFunctorEquivalence_counitIso, CategoryTheory.μ_naturality_assoc, mapCommMonIdIso_inv_app_hom_hom, CategoryTheory.ShortComplex.leftHomologyFunctorOpNatIso_inv_app, CategoryTheory.Limits.BinaryFan.assocInv_snd, CategoryTheory.shiftFunctorAdd_hom_app_obj_of_induced, CategoryTheory.Presheaf.preservesColimitsOfSize_leftKanExtension, LightCondMod.LocallyConstant.instFaithfulSheafLightProfiniteCoherentTopologyTypeConstantSheaf, CategoryTheory.Comma.mapLeftIso_inverse_map_left, isoWhiskerRight_trans_assoc, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₂, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left_assoc, map_shiftFunctorComm, CategoryTheory.MonoOver.congr_counitIso, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.unitIso_hom, LaxMonoidal.ofBifunctor.firstMap₂_app_app_app, op_commShiftIso_hom_app, CategoryTheory.Triangulated.TStructure.instIsGEObjEIntFunctorETruncLT, SheafOfModules.comp_val, flipping_inverse_obj_obj_obj, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_app_fst_app, CategoryTheory.instSmallHomFunctorOppositeTypeColimitCompYoneda, CategoryTheory.Equivalence.op_unitIso, CategoryTheory.GrothendieckTopology.Point.toPresheafFiberOfIsCofiltered_w, CategoryTheory.Adjunction.leftAdjointCompIso_comp_id, CategoryTheory.Limits.FormalCoproduct.eval_obj_obj, HomologicalComplex.mapBifunctor₁₂.ι_eq, CategoryTheory.RightExactFunctor.whiskeringLeft_obj_map, PushoutObjObj.inl_ι, HomotopyCategory.homologyFunctor_shiftMap, CategoryTheory.Bicategory.toNatTrans_conjugateEquiv, CategoryTheory.Adjunction.whiskerRight_counit_app_app, CategoryTheory.instPreservesColimitFunctorOppositeTypeObjCoyonedaOpYoneda, CategoryTheory.NatTrans.vcomp_eq_comp, bifunctorComp₁₂Iso_hom_app_app_app, CategoryTheory.GradedObject.ιMapBifunctorBifunctor₂₃MapObj_eq, PresheafOfModules.instReflectsFiniteLimitsSheafOfModulesSheafAddCommGrpCatToSheaf, CategoryTheory.Equivalence.mkHom_comp, CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm, CategoryTheory.Subfunctor.to_sheafifyLift, Fiber.inducedFunctorCompIsoSelf_inv_app, CategoryTheory.TwistShiftData.commShift, CategoryTheory.Limits.PullbackCone.isoMk_hom_hom, CategoryTheory.GrothendieckTopology.Point.presheafFiberMap_hom_ext_iff, AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf, CategoryTheory.Equivalence.sheafCongrPreregular_functor_obj_obj_map, CategoryTheory.CatCommSq.hInv_iso_hom_app, CategoryTheory.ObjectProperty.SerreClassLocalization.instFullExactFunctorWhiskeringLeft, CategoryTheory.SimplicialObject.isCoskeletal_iff_isIso, CategoryTheory.instIsRegularEpiCategorySheafTypeOfHasSheafify, CategoryTheory.Comma.mapLeftComp_hom_app_left, CategoryTheory.Comonad.ForgetCreatesLimits'.commuting, HomologicalComplex.HomologySequence.composableArrows₃Functor_obj, CategoryTheory.δ_naturalityᵣ, CategoryTheory.Presheaf.instIsLeftKanExtensionFunctorOppositeTypeIdCompUliftYonedaOfPreservesColimitsOfSizeOfHasPointwiseLeftKanExtension, CategoryTheory.ComposableArrows.isoMk₀_hom_app, CategoryTheory.Equivalence.mkIso_inv, CategoryTheory.Monad.MonadicityInternal.counitCofork_ι_app, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app, IsContinuous.op_comp_isSheaf_of_types, bifunctorComp₂₃Iso_hom_app_app_app, CategoryTheory.Equivalence.Equivalence_mk'_unitInv, PresheafOfModules.toPresheaf_map_sheafificationAdjunction_unit_app, PushoutObjObj.mapArrowRight_right, PullbackObjObj.π_fst_assoc, CategoryTheory.ShortComplex.opEquiv_unitIso, Action.functorCategoryEquivalence_preservesZeroMorphisms, CategoryTheory.LocalizerMorphism.rightDerivedFunctorComparison_fac_assoc, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₁, Initial.extendCone_obj_π_app, MonObj.mopEquiv_unitIso_inv_app_hom, CondensedSet.toTopCatMap_hom_apply, CategoryTheory.NatIso.cancel_natIso_hom_right_assoc, CategoryTheory.Localization.SmallHom.equiv_shift, CategoryTheory.FunctorToTypes.prod.lift_snd, CategoryTheory.ComposableArrows.functorArrows_map, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₃, CategoryTheory.Abelian.SpectralObject.liftCycles_i_assoc, CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp, AlgebraicGeometry.structurePresheafInCommRingCat_obj_carrier, CategoryTheory.nerveMap_app, CategoryTheory.Presieve.isSheaf_yoneda', CategoryTheory.Limits.prodComparisonNatIso_inv, CategoryTheory.SimplicialThickening.functor_id, CategoryTheory.FunctorToTypes.comp, CategoryTheory.SimplicialObject.augmentedCechNerve_obj_right, CochainComplex.shiftShortComplexFunctorIso_zero_add_hom_app, SSet.Subcomplex.top_prod_le_unionProd, CategoryTheory.Presheaf.classifier_χ₀, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv_assoc, CategoryTheory.sheafCompose_obj_obj, CategoryTheory.uliftYonedaMap_app_apply, CategoryTheory.Limits.diagramIsoSpan_inv_app, SheafOfModules.pushforward_id_comp, inrCompSum'_hom_app, whiskeringLeftObjCompIso_hom_app_app, SSet.modelCategoryQuillen.fibration_iff, mapTriangleInvRotateIso_hom_app_hom₁, CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.rightUnitor_hom_unit_app, functorialityCompPostcompose_inv_app_hom, LeftExtension.precomp₂_map_left, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_inv_app_assoc, CategoryTheory.Limits.HasLimit.isoOfNatIso_hom_π, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_inv_app_hom_hom, CategoryTheory.Localization.liftNatIso_hom, CategoryTheory.Limits.HasBiproductsOfShape.colimIsoLim_hom_app, CategoryTheory.OverPresheafAux.counitForward_counitBackward, CategoryTheory.Abelian.LeftResolution.karoubi.π'_app_f, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_obj_map_app, CategoryTheory.Under.lift_map, CategoryTheory.Limits.Wedge.condition_assoc, IsCoverDense.Types.appIso_hom, IsCoverDense.restrictHomEquivHom_naturality_right_symm_assoc, CategoryTheory.NatIso.unop_inv, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionAssocIso_inv, CategoryTheory.Limits.CokernelCofork.π_eq_zero, CategoryTheory.Triangulated.TStructure.eTruncLT_ι_bot, CategoryTheory.MonoidalCategory.rightUnitorNatIso_inv_app, CategoryTheory.OverPresheafAux.costructuredArrowPresheafToOver_obj, CategoryTheory.Triangulated.TStructure.triangleω₁δ_obj_mor₂, Final.extendCocone_map_hom, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.mkIso_hom_snd, CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso_inv_app, CategoryTheory.Limits.DiagramOfCones.mkOfHasLimits_conePoints, CategoryTheory.GrothendieckTopology.Point.presheafFiber_hom_ext_iff, CategoryTheory.CatCenter.localization_one, CategoryTheory.ObjectProperty.LimitOfShape.toStructuredArrow_obj, CategoryTheory.Abelian.SpectralObject.cokernelSequenceE_f, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_map_fst_app, CategoryTheory.Subfunctor.Subpresheaf.range_subobjectMk_ι, CategoryTheory.Sieve.equalizer_eq_equalizerSieve, SSet.Truncated.rightExtensionInclusion_hom_app, LightCondensed.comp_val, CategoryTheory.MonoidalClosed.ofEquiv_curry_def, CategoryTheory.Limits.multispanIndexCoend_fst, CategoryTheory.Idempotents.app_idem, Monoidal.leftUnitor_hom_app, LightCondensed.id_hom, CategoryTheory.LaxBraidedFunctor.id_hom, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_obj_map_app, CategoryTheory.Iso.coreWhiskerRight, CategoryTheory.Idempotents.functor_category_isIdempotentComplete, CategoryTheory.Equivalence.changeInverse_unitIso_hom_app, CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso_hom_app_f, CategoryTheory.Adjunction.rightAdjointUniq_refl, CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_tensor, CategoryTheory.Adjunction.homEquiv_symm_rightAdjointUniq_hom_app, CategoryTheory.Abelian.Radical.isZero, CategoryTheory.sheafBotEquivalence_counitIso, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_hom_app_hom_app, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₁, CategoryTheory.Limits.instPreservesFiniteColimitsFunctorObjEvaluationOfHasFiniteColimits, CategoryTheory.Limits.coconeUnopOfCone_ι, CategoryTheory.curryingIso_inv_toFunctor_obj_obj_map, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₃, Action.rightUnitor_inv_hom, CategoryTheory.unitOfTensorIsoUnit_hom_app, CategoryTheory.StructuredArrow.mapIso_inverse_map_left, CategoryTheory.preservesLimitNatIso_hom_app, CategoryTheory.cones_obj_obj, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_counitIso_inv, isoWhiskerLeft_hom, AlgebraicGeometry.Scheme.instIsGrothendieckAbelianSheafProEtTopologyAb, Bipointed.swapEquiv_unitIso_hom_app_toFun, CategoryTheory.Limits.MonoCoprod.mono_binaryCofanSum_inl, CategoryTheory.Abelian.SpectralObject.cyclesIsoH_hom_inv_id, CategoryTheory.Limits.whiskerLeft_ι_colimitCompWhiskeringLeftIsoCompColimit_inv, FullyFaithful.homNatIso_hom_app_down, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_obj_g, CategoryTheory.Abelian.SpectralObject.sc₁_X₂, CategoryTheory.AdditiveFunctor.ofExact_map_hom, CategoryTheory.Adjunction.commShiftIso_inv_app_counit_app, CategoryTheory.SimplicialObject.augmentedCechNerve_map_left_app, CategoryTheory.Limits.IndizationClosedUnderFilteredColimitsAux.exists_nonempty_limit_obj_of_colimit, CategoryTheory.Monad.monadMonEquiv_unitIso_hom_app_toNatTrans_app, PresheafOfModules.instIsLocallyInjectiveToSheafify, CategoryTheory.shrinkYoneda_map_app_shrinkYonedaObjObjEquiv_symm, CategoryTheory.nerve.functorOfNerveMap_obj, leftDerivedZeroIsoSelf_hom_inv_id_assoc, CategoryTheory.GrothendieckTopology.W_eq_W_range_sheafToPresheaf_obj, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst, CategoryTheory.CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompYoneda, AlgebraicTopology.DoldKan.Γ₂N₁_inv, CategoryTheory.Limits.BinaryFan.assocInv_fst, mapMatId_inv_app, CategoryTheory.CostructuredArrow.ιCompGrothendieckProj_hom_app, CategoryTheory.CostructuredArrow.initial_map₂_id, CategoryTheory.PreGaloisCategory.toAut_bijective, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionObj, CategoryTheory.MonoidalCategory.externalProductSwap_hom_app_app, coreflective', CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_naturality, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_inv_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionAssocNatIso_hom_app_app_app, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionHomRight, CategoryTheory.Limits.Cone.postcomposeId_hom_app_hom, CategoryTheory.shiftFunctorAdd'_assoc_hom_app_assoc, DerivedCategory.homologyFunctorFactorsh_inv_app_quotient_obj_assoc, CategoryTheory.Limits.BinaryFan.π_app_left, IsEventuallyConstantFrom.isIso_ι_of_isColimit, AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_fac, CategoryTheory.Monoidal.tensorObj_map, CategoryTheory.Limits.Cofork.ofπ_ι_app, CategoryTheory.Equivalence.congrRight_unitIso_hom_app, CategoryTheory.NatTrans.shift_app_comm, CategoryTheory.Join.mapPairRight_hom_app, CategoryTheory.Limits.evaluation_preservesLimit, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_hom_app_hom, CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_hom_app_one, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂'_obj_obj_map, CategoryTheory.sheafComposeIso_hom_fac_assoc, PullbackObjObj.hom_ext_iff, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, currying_functor_obj_map, CategoryTheory.SimplicialObject.augmentedCechNerve_obj_left_map, leftOpRightOpEquiv_functor_map_app, CategoryTheory.sheafification_reflective, CategoryTheory.yonedaGrp_map_app, CategoryTheory.Abelian.SpectralObject.shortComplexMap_comp, Monoidal.leftUnitor_inv_app, CategoryTheory.FunctorToTypes.monoFactorisation_m, AlgebraicTopology.DoldKan.instReflectsIsomorphismsKaroubiSimplicialObjectChainComplexNatN₂, AlgebraicGeometry.instIsIsoFunctorModuleCatCarrierUnitModulesSpecOfAdjunction, pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_assoc, SSet.hasDimensionLE_prod, CategoryTheory.FunctorToTypes.monoFactorisation_I, CategoryTheory.Limits.preservesColimits_of_evaluation, rightDerivedZeroIsoSelf_inv_hom_id_assoc, ShiftSequence.induced_isoShiftZero_hom_app_obj, SSet.ι₁_fst_assoc, CategoryTheory.sheafComposeIso_inv_fac, HomologicalComplex.mapBifunctor₁₂.d₁_eq, CategoryTheory.Limits.walkingSpanOpEquiv_counitIso_inv_app, SmallCategories.instPreservesFiniteLimitsSheafSheafPullbackOfRepresentablyFlat, OrderHom.equivalenceFunctor_unitIso_inv_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app_assoc, CategoryTheory.nerve.nerveFunctor₂_map_functorOfNerveMap, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality, equiv_inverse, CategoryTheory.Under.opEquivOpOver_unitIso, AlgebraicGeometry.Scheme.Modules.instIsRightAdjointPresheafOfModulesToPresheafOfModules, isoCopyObj_hom_app, CategoryTheory.SingleFunctors.shiftIso_zero_hom_app, CategoryTheory.sheafHomSectionsEquiv_symm_apply_coe_apply, CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_fst, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_hom_app_app, TopCat.Sheaf.eq_of_locally_eq_iff, flip_map_app, CategoryTheory.NatTrans.exchange, CategoryTheory.MorphismProperty.presheaf_monomorphisms_le_monomorphisms, CategoryTheory.Limits.isIndObject_limit_comp_yoneda_comp_colim, CategoryTheory.isVanKampenColimit_of_evaluation, OneHypercoverDenseData.essSurj.presheafObjObjIso.hom_map, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app_assoc, CategoryTheory.Bicategory.yoneda_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_toPrelaxFunctor_toPrelaxFunctorStruct_map₂_toNatTrans_app, isEquivalence_of_isOneHypercoverDense, LightCondensed.underlying_map, CategoryTheory.Adjunction.leftAdjointIdIso_inv_app, CategoryTheory.Limits.ι_colimitLimitToLimitColimit_π_assoc, map_shiftFunctorCompIsoId_inv_app, CategoryTheory.Abelian.SpectralObject.sc₂_f, CategoryTheory.Adjunction.leftAdjointUniq_trans, CategoryTheory.conjugateEquiv_of_iso, CategoryTheory.Triangulated.TStructure.eTruncGEδLT_coe, CategoryTheory.Abelian.SpectralObject.isZero₂_of_isThirdQuadrant, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_η_unmop_app, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv_def, SimplicialObject.opEquivalence_functor, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberMapObjIso_inv, CategoryTheory.Equivalence.core_unitIso_inv_app_iso_hom, CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_obj, CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.flipFunctorToInterchange_hom_app_app, groupCohomology.isoShortComplexH1_inv, CategoryTheory.NatTrans.unop_whiskerRight_assoc, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec, CategoryTheory.Limits.Cone.toStructuredArrowCompToUnderCompForget_inv_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_unitIso_hom_app_app_fst, AlgebraicTopology.DoldKan.identity_N₂_objectwise, FundamentalGroupoid.punitEquivDiscretePUnit_inverse, CategoryTheory.Iso.hom_inv_id_app_app_app_assoc, SSet.stdSimplex.objMk₁_apply_eq_one_iff, CategoryTheory.conjugateEquiv_comp, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_π_app_walkingParallelPair_zero, CategoryTheory.MonoidalOpposite.tensorRightUnmopIso_hom_app, CategoryTheory.Limits.preservesLimits_of_evaluation, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_iso_hom_app, CategoryTheory.coyonedaFunctor_preservesLimits, CategoryTheory.map_shrinkYonedaEquiv, CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan_inj_assoc, CategoryTheory.GrothendieckTopology.Point.sheafFiberCompIso_hom_app, Condensed.underlying_map, CategoryTheory.NatTrans.app_zsmul, CategoryTheory.OverPresheafAux.YonedaCollection.map₁_snd, SSet.Truncated.HomotopyCategory.BinaryProduct.id_prod_mapHomotopyCategory_comp_inverse, CategoryTheory.GrothendieckTopology.ofArrows_mem_iff_isLocallySurjective_sigmaDesc_uliftYoneda_map, CategoryTheory.CostructuredArrow.mapNatIso_functor_map_right, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.hf, CategoryTheory.BraidedCategory.Hexagon.functor₁₂₃_obj_map_app, CategoryTheory.Triangulated.TStructure.truncLEIsoTruncLT_hom_ι_app, CategoryTheory.Limits.prod.functor_obj_map, mapBifunctorHomologicalComplex_obj_map_f_f, CategoryTheory.Presieve.FamilyOfElements.map_comp, isTerminalConst_from_app, CategoryTheory.WithTerminal.coneEquiv_functor_obj_pt, CategoryTheory.ObjectProperty.LimitOfShape.toStructuredArrow_map, CategoryTheory.Abelian.SpectralObject.toCycles_πE_descE, IsRepresentedBy.iff_natIso, CategoryTheory.Abelian.SpectralObject.EIsoH_hom_naturality, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_ε_unmop_app, CategoryTheory.MonoidalOpposite.tensorLeftMopIso_inv_app_unmop, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₃, CategoryTheory.Adjunction.sheafPushforwardContinuous_counit_app_hom_app, CategoryTheory.NatTrans.leftDerived_comp, PresheafOfModules.instFullRestrictScalarsIdFunctorOppositeRingCat, SSet.Subcomplex.topIso_hom, CategoryTheory.Limits.diagramIsoPair_inv_app, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_unitIso, AlgebraicTopology.inclusionOfMooreComplexMap_f, CategoryTheory.ComposableArrows.instIsIsoOfNatNatTwoδ₂Toδ₁, CategoryTheory.Limits.coprod.functor_obj_obj, CategoryTheory.yonedaEquiv_symm_map, CategoryTheory.Limits.IsLimit.homIso_hom, CategoryTheory.Triangulated.TStructure.instAdditiveObjEIntFunctorETruncGE, CategoryTheory.Idempotents.DoldKan.hη, CategoryTheory.obj_ε_app, ModuleCat.FilteredColimits.ι_colimitDesc_assoc, CategoryTheory.GrothendieckTopology.yoneda_obj_obj, CategoryTheory.Square.arrowArrowEquivalence_unitIso, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCBasicOpens_app, ContinuousCohomology.MultiInd.d_succ, ModuleCat.extendScalarsId_inv_app_apply, SSet.stdSimplex.toSSetObj_app_const_one, OplaxMonoidal.ofBifunctor.firstMap₃_app_app_app, CategoryTheory.liftedLimitMapsToOriginal_hom_π, CategoryTheory.MorphismProperty.Comma.mapLeftEq_hom_app_right, CategoryTheory.SimplicialObject.augmentedCechNerve_obj_left_obj, CategoryTheory.Adjunction.whiskerRight_unit_iso_of_R_fully_faithful, CategoryTheory.NatTrans.leftDerivedToHomotopyCategory_id, SSet.Edge.toTruncated_id, SSet.horn.ι_ι_assoc, CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_assoc, IsDenseSubsite.isIso_ranCounit_app_of_isDenseSubsite, CategoryTheory.Cat.Hom.toNatIso_inv, CategoryTheory.Limits.opParallelPairIso_inv_app_zero, CategoryTheory.GradedObject.ι_mapBifunctorAssociator_inv, CategoryTheory.Abelian.SpectralObject.kernelSequenceE_X₃, Monoidal.rightUnitor_hom_app, AlgebraicGeometry.Proj.res_apply, CategoryTheory.Equivalence.trans_unitIso, CategoryTheory.Idempotents.karoubiCochainComplexEquivalence_unitIso_inv_app_f_f, CategoryTheory.Triangulated.TStructure.ω₁δ_naturality, CategoryTheory.NatTrans.leftDerived_id, CategoryTheory.Under.postEquiv_unitIso, Monoidal.commTensorRight_hom_app, TopCat.Presheaf.app_injective_iff_stalkFunctor_map_injective, AlgebraicGeometry.StructureSheaf.comapₗ_eq_localRingHom, CategoryTheory.Sieve.toFunctor_app_coe, HomologicalComplex.mapBifunctor₁₂.d₃_eq, CategoryTheory.isFinitelyPresentable_iff_preservesFilteredColimits, CategoryTheory.Limits.PullbackCone.mk_π_app_left, CategoryTheory.constantPresheafAdj_counit_app_app, CategoryTheory.Sum.functorEquivFunctorCompSndIso_hom_app_app, SheafOfModules.pushforwardSections_coe, DerivedCategory.homologyFunctorFactorsh_inv_app_quotient_obj, CategoryTheory.Abelian.SpectralObject.cokernelSequenceOpcyclesE_f, CategoryTheory.ObjectProperty.instIsClosedUnderColimitsOfShapeFunctorPreservesFiniteLimitsOfHasExactColimitsOfShape, CategoryTheory.Join.mapIsoWhiskerLeft_hom_app, CategoryTheory.Adjunction.mapAddMon_unit, AlgebraicTopology.DoldKan.N₁Γ₀_inv_app_f_f, CategoryTheory.GrothendieckTopology.map_yonedaEquiv, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τr, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_hom_app_fst_app, AlgebraicTopology.alternatingFaceMapComplex_obj_X, CategoryTheory.WithTerminal.commaFromOver_obj_left, PresheafOfModules.Sheafify.smul_zero, PresheafOfModules.fromFreeYonedaCoproduct_app_mk, CategoryTheory.rightExactFunctor_le_additiveFunctor, TopologicalSpace.Opens.overEquivalence_counitIso_hom_app, reprW_hom_app, CategoryTheory.Sheaf.isLocallySurjective_iff_isIso, CategoryTheory.FreeGroupoid.mapCompLift_hom_app, PresheafOfModules.Sheafify.map_smul, CategoryTheory.ComposableArrows.opEquivalence_counitIso_hom_app_app, CategoryTheory.uliftCoyonedaEquiv_symm_map, CategoryTheory.GrothendieckTopology.Point.presheafFiberMapIso_hom_app, CategoryTheory.Limits.CompleteLattice.colimitCocone_isColimit_desc, CategoryTheory.GrothendieckTopology.overMapPullback_assoc, CategoryTheory.MorphismProperty.Comma.mapLeftComp_hom_app_right, AlgebraicGeometry.StructureSheaf.toOpen_res, curry_map_app_app, CategoryTheory.Limits.opParallelPairIso_inv_app_one, CategoryTheory.ExponentiableMorphism.pushforwardId_hom_counit, CategoryTheory.TwoSquare.lanBaseChange_app, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π, CategoryTheory.Sum.functorEquivFunctorCompFstIso_hom_app_app, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.tensorHom_eq, CategoryTheory.GradedObject.ι_mapBifunctorComp₁₂MapObjIso_hom, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_ε, CategoryTheory.Linear.toCatCenter_apply_app, CategoryTheory.whiskeringLeftCompEvaluation_inv_app, CategoryTheory.Abelian.Preradical.isIso_toColon_iff, CategoryTheory.Limits.CatCospanTransform.isIso_right, CategoryTheory.Limits.CompleteLattice.finiteColimitCocone_isColimit_desc, CategoryTheory.coherentTopology.isLocallySurjective_iff, SSet.Truncated.sk.faithful, AlgebraicGeometry.structurePresheafInModuleCat_obj_carrier, SSet.opEquivalence_counitIso, CategoryTheory.Triangulated.TStructure.instIsIsoAppETruncLTιObjEIntFunctorETruncLT, CategoryTheory.CatCommSq.vId_iso_inv_app, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec_assoc, CategoryTheory.Comma.equivProd_unitIso_inv_app_left, HomologicalComplex.mapBifunctor₁₂.ι_D₂, CategoryTheory.Adjunction.lim_preservesLimits, CategoryTheory.yonedaYonedaColimit_app_inv, CategoryTheory.Sheaf.ΓObjEquivSections_naturality, CategoryTheory.Limits.Cone.extensions_app, CategoryTheory.yonedaEquiv_symm_naturality_left, CategoryTheory.Limits.pullbackConeEquivBinaryFan_unitIso, CategoryTheory.Presheaf.comp_isLocallyInjective_iff, SSet.leftUnitor_hom_app_apply, CategoryTheory.Limits.Cone.whiskeringEquivalence_inverse, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_spec, CategoryTheory.SmallObject.preservesColimit, CategoryTheory.CatCenter.app_neg, SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁_hom_f_f, CategoryTheory.Limits.HasLimitOfHasProductsOfHasEqualizers.buildLimit_π_app, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_inv_π, CategoryTheory.Limits.coneUnopOfCocone_π, CategoryTheory.Adjunction.homEquiv_ofNatIsoLeft_symm_apply, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransEq_inv_app_f, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionAssocIso_hom, CategoryTheory.ObjectProperty.IsCodetecting.isIso_iff_of_epi, CategoryTheory.NatIso.unop_whiskerLeft, CategoryTheory.Subfunctor.instMonoFunctorTypeι, instCommShiftCochainComplexIntMapMap₂CochainComplex, CategoryTheory.NatIso.hcomp_inv, CategoryTheory.Limits.Cotrident.app_one_assoc, CategoryTheory.Abelian.SpectralObject.cyclesIsoH_inv, LightCondSet.toTopCatMap_hom_apply, SimplicialObject.Split.id_F, CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_left, CategoryTheory.δ_μ_app_assoc, CategoryTheory.ComposableArrows.functorArrows_obj, CategoryTheory.Subfunctor.Subpresheaf.equalizer.lift_ι, map_opShiftFunctorEquivalence_counitIso_hom_app_unop_assoc, CategoryTheory.GrothendieckTopology.diagramNatTrans_zero, CategoryTheory.NatIso.unop_hom, CategoryTheory.Discrete.functorComp_inv_app, HomologicalComplex.mapBifunctor₁₂.ι_mapBifunctor₁₂Desc_assoc, mapBifunctorHomologicalComplexObj_obj_d_f, CondensedSet.epi_iff_locallySurjective_on_compHaus, CategoryTheory.Hom.mulEquivCongrRight_apply, shiftIso_hom_app_comp_shiftMap_of_add_eq_zero, AlgebraicGeometry.StructureSheaf.const_mul, CategoryTheory.GrothendieckTopology.toPlus_plusLift, CategoryTheory.GrothendieckTopology.ofArrows_mem_iff_isLocallySurjective_cofanIsColimitDesc_uliftYoneda_map, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₁, CategoryTheory.Limits.HasLimit.isoOfEquivalence_inv_π, CategoryTheory.Comma.unopFunctorCompSnd_hom_app, CommShift.OfComp.map_iso_inv_app, rightKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, CategoryTheory.Pretriangulated.preadditiveYoneda_map_distinguished, CategoryTheory.Limits.hasColimit_const_of_isConnected, CategoryTheory.Monad.one_def, whiskeringLeft_obj_obj, CategoryTheory.CatCenter.smul_iso_hom_eq, CategoryTheory.coyonedaFunctor_reflectsLimits, CategoryTheory.Limits.coconeOfCoconeCurry_ι_app, CategoryTheory.Triangulated.TStructure.isGE_eTruncGE_obj_obj, CategoryTheory.NatTrans.instCommShiftOppositeShiftHomFunctorNatIsoComp, CategoryTheory.Adjunction.whiskerLeftRUnitIsoOfIsIsoCounit_inv_app, flippingEquiv_apply_obj_obj, CategoryTheory.Triangulated.TStructure.eTruncLT_obj_top, sheafPushforwardContinuousComp'_hom_app_hom_app, LightCondensed.lanPresheafExt_hom, CategoryTheory.Triangulated.TStructure.instIsLEObjEIntFunctorETruncLT, CategoryTheory.Abelian.SpectralObject.cyclesMap_i_assoc, CategoryTheory.yonedaEquiv_symm_naturality_right, CategoryTheory.PreGaloisCategory.PointedGaloisObject.cocone_app, CategoryTheory.Adjunction.RightAdjointCommShift.iso_hom_app, CochainComplex.ShiftSequence.shiftIso_inv_app, compConstIso_inv_app_app, CategoryTheory.BasedNatTrans.instReflectsIsomorphismsBasedFunctorFunctorObjForgetful, ranCompLimIso_hom_app, mapTriangleInvRotateIso_hom_app_hom₂, CategoryTheory.constantSheafAdj_counit_app, PresheafOfModules.toSheafify_app_apply, leibnizPullback_map_app, CategoryTheory.GradedObject.ι_mapBifunctorRightUnitor_hom_apply_assoc, CategoryTheory.Limits.Cocone.precomposeComp_inv_app_hom, CategoryTheory.Over.mapCongr_rfl, CategoryTheory.ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₂_app, CategoryTheory.CommShift₂Setup.z_zero₂, CategoryTheory.NatTrans.rightOp_id, TopCat.Presheaf.isIso_iff_stalkFunctor_map_iso, rightDerivedZeroIsoSelf_hom_inv_id_assoc, Action.resComp_hom_app_hom, CategoryTheory.CommShift₂Setup.int_ε, CategoryTheory.Equivalence.funInvIdAssoc_inv_app, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_inv_app_f, TopCat.Sheaf.interUnionPullbackCone_pt, CategoryTheory.NatTrans.removeRightOp_id, CategoryTheory.GrothendieckTopology.uliftYoneda_map_hom_app_down, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_inv, Profinite.exists_locallyConstant_finite_nonempty, CategoryTheory.Limits.BinaryFan.assoc_fst, CategoryTheory.sheafSectionsNatIsoEvaluation_hom_app, CategoryTheory.Limits.MonoFactorisation.fac_apply, CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_app_assoc, CategoryTheory.Enriched.FunctorCategory.enrichedId_π, CategoryTheory.Sieve.shrinkFunctorIsoFunctor_inv_app_coe, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberCompIso_hom_app_assoc, CategoryTheory.GrothendieckTopology.preservesLimit_diagramFunctor, SSet.RelativeMorphism.comp_map, CategoryTheory.Equivalence.mkHom_comp_assoc, leftKanExtensionCompIsoOfPreserves_inv_fac_app, CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_naturality_assoc, SSet.prod_map_snd, CategoryTheory.Limits.colimCompFlipIsoWhiskerColim_inv_app_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_inverse_obj_obj_fst, CategoryTheory.Limits.parallelPair.eqOfHomEq_inv_app, SheafOfModules.instIsRightAdjointPushforwardIdSheafRingCat, SSet.horn₃₂.desc.multicofork_π_zero, CategoryTheory.Limits.FormalCoproduct.cosimplicialObjectFunctor_map_app, CategoryTheory.NatTrans.instIsMultiplicativeFunctorCoequifibered, CategoryTheory.GrothendieckTopology.overMapPullback_id_comp, CategoryTheory.sum.inlCompAssociator_inv_app, CategoryTheory.ExactFunctor.whiskeringRight_obj_map, instCommShiftCochainComplexIntMapFlipMap₂CochainComplex, unopId_hom_app, CategoryTheory.Limits.IndObjectPresentation.yoneda_I, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.sheafCondition_iff_comp_coyoneda, isoWhiskerRight_inv, CategoryTheory.Equivalence.Equivalence_mk'_counit, HomologicalComplex₂.flipEquivalenceCounitIso_hom_app_f_f, SSet.stdSimplex.objEquiv_symm_apply, commShift₂_comm_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjComp_inv_app_snd_app, CategoryTheory.Abelian.SpectralObject.liftE_ιE_fromOpcycles_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionHomLeft, CategoryTheory.NatIso.hcomp_hom, CategoryTheory.Triangulated.TStructure.eTruncLT_obj_map_eTruncLTι_app_eTruncLT_map_app, CategoryTheory.Limits.CompleteLattice.finiteLimitCone_cone_π_app, CategoryTheory.FinitaryExtensive.isPullback_initial_to, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinset_obj_obj, SSet.StrictSegal.instIsStrictSegalObjTruncatedHAddNatOfNatTruncationOfIsStrictSegal, CategoryTheory.Abelian.SpectralObject.sc₃_f, CategoryTheory.WithInitial.liftToInitialUnique_inv_app, CategoryTheory.prod.functorProdToProdFunctorAssociator_inv_app, CategoryTheory.WithInitial.mapComp_inv_app, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_hom_c_app, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv_assoc, CategoryTheory.Limits.Types.Limit.lift_π_apply', SSet.horn₃₂.desc.multicofork_π_three_assoc, CategoryTheory.OverPresheafAux.OverArrows.map_val, AddCommGrpCat.binaryProductLimitCone_cone_π_app_right, CategoryTheory.Abelian.SpectralObject.iCycles_δ_assoc, CategoryTheory.Triangulated.TStructure.eTruncGE_obj_bot, sheafAdjunctionCocontinuous_homEquiv_apply_val, SheafOfModules.instFullPresheafOfModulesObjFunctorOppositeRingCatIsSheafForget, whiskerRight_left, CondensedSet.topCatAdjunctionUnit_hom_app, isLeftDerivedFunctor_iff_isIso_leftDerivedLift, CategoryTheory.Iso.inv_hom_id_app_assoc, CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_unitIso_hom_app_hom_app, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one_assoc, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, Action.functorCategoryEquivalence_additive, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjId_hom_app_snd_app, CategoryTheory.PreservesFiniteLimitsOfFlat.fac, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_yonedaULift_map, CategoryTheory.Subfunctor.equalizer.condition_assoc, CategoryTheory.Limits.walkingCospanOpEquiv_unitIso_hom_app, AlgebraicTopology.DoldKan.map_hσ', FullyFaithful.hasShift.map_zero_inv_app, CategoryTheory.Abelian.SpectralObject.zero₁_assoc, AlgebraicTopology.DoldKan.N₂_map_f_f, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinset_obj_obj, curry_obj_comp_flip, CategoryTheory.Adjunction.leftAdjointIdIso_hom_app, CategoryTheory.Pseudofunctor.DescentData.pullFunctorEquivalence_unitIso, CategoryTheory.Comonad.ForgetCreatesColimits'.liftedCocone_ι_app_f, CategoryTheory.Limits.instHasIterationOfShapeFunctor, AlgebraicGeometry.Scheme.Cover.functorOfLocallyDirectedHomBase_app, CategoryTheory.CostructuredArrow.mapIso_inverse_map_right, SSet.horn₃₂.desc.multicofork_π_one_assoc, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₂, CategoryTheory.Presheaf.coherentExtensiveEquivalence_counitIso_inv_app_hom_app, CategoryTheory.Injective.injective_iff_preservesEpimorphisms_preadditiveYoneda_obj, CategoryTheory.uliftYonedaIsoYoneda_inv_app_app_down, CategoryTheory.NatTrans.leftOp_comp, ShiftSequence.shiftIso_zero, commShiftIso_map₂CochainComplex_hom_app, SSet.KanComplex.hornFilling, CategoryTheory.Localization.lift₂_iso_hom_app_app₁, CategoryTheory.uliftYonedaEquiv_symm_map_assoc, CategoryTheory.Abelian.Preradical.shortExact_shortComplex, CategoryTheory.Limits.constCone_π, Monoidal.transport_ε_assoc, HomologicalComplex.mapBifunctor₁₂.d₂_eq, ModuleCat.restrictScalarsCongr_inv_app, PushoutObjObj.mapArrowLeft_comp, commBialgCatEquivComonCommAlgCat_counitIso_hom_app, CategoryTheory.Limits.HasZeroObject.instFunctor, Monoidal.transport_δ_assoc, SSet.PtSimplex.RelStruct.δ_map_of_gt, curryingEquiv_symm_apply_obj_map, CategoryTheory.PreGaloisCategory.instFaithfulContActionFintypeCatHomObjFiniteAutFunctorFunctorToContAction, TopCat.Sheaf.isLocallySurjective_iff_epi, CategoryTheory.Adjunction.leftAdjointCompIso_assoc, CategoryTheory.Limits.opSpan_inv_app, CategoryTheory.SimplicialObject.instHasLimits, CategoryTheory.LeftExactFunctor.whiskeringLeft_obj_map, CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_neg, leftExtensionEquivalenceOfIso₁_counitIso_hom_app_right_app, CategoryTheory.SingleFunctors.shiftIso_add'_inv_app, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right_assoc, CategoryTheory.IsPullback.of_isLimit_cone, CategoryTheory.Limits.coendFunctor_map, CategoryTheory.Limits.CatCospanTransform.mkIso_hom_left, CategoryTheory.Limits.coyonedaCompLimIsoCones_hom_app_app, CategoryTheory.Limits.PreservesColimit₂.ι_comp_isoColimitUncurryWhiskeringLeft₂_hom, CategoryTheory.WithTerminal.equivComma_counitIso_inv_app_right, CategoryTheory.Limits.whiskerLeft_ι_colimitCompWhiskeringLeftIsoCompColimit_inv_assoc, CategoryTheory.Limits.colimitCoconeOfUnique_isColimit_desc, CategoryTheory.toOverUnitPullback_hom_app_left, CategoryTheory.Limits.mapPairIso_hom_app, Condensed.isoFinYoneda_inv_app, CategoryTheory.Limits.pullbackObjIso_inv_comp_snd, CategoryTheory.Limits.FormalCoproduct.evalOp_obj_obj, CategoryTheory.Limits.limit.lift_π, HomologicalComplex.mapBifunctor₂₃.d₁_eq_zero, CategoryTheory.NatTrans.instRespectsIsoFunctorEquifibered, OneHypercoverDenseData.essSurj.restriction_map, CategoryTheory.Limits.IsColimit.fac_assoc, CategoryTheory.Triangulated.TStructure.triangleω₁δ_obj_obj₃, AlgebraicGeometry.SheafedSpace.isColimit_exists_rep, CategoryTheory.tensoringRight_additive, AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_inv_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso_inv_app_app, CategoryTheory.compEvaluation_inv_app, leftAdjointObjIsDefined_iff, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafFunctor_obj_obj, AlgebraicGeometry.StructureSheaf.algebraMap_pushforward_stalk, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₂, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, PullbackObjObj.π_iso_of_iso_left_hom, CategoryTheory.instAdhesiveSheafOfHasPullbacksOfHasPushoutsOfHasSheafify, CategoryTheory.Sum.functorEquiv_unitIso, CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_right, PresheafOfModules.freeAdjunction_homEquiv, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_app_π, SSet.Truncated.HomotopyCategory.descOfTruncation_obj_mk, leftOpRightOpEquiv_inverse_obj, CategoryTheory.sheafifyMap_sheafifyLift_assoc, CategoryTheory.Cat.associator_hom_toNatTrans, Action.FunctorCategoryEquivalence.functor_obj_map, CategoryTheory.Limits.wideEqualizer.trident_π_app_zero, CategoryTheory.Limits.cospanExt_inv_app_right, CategoryTheory.Equivalence.op_counitIso, CategoryTheory.ShortComplex.mapToComposableArrows_id, CategoryTheory.Limits.BinaryFan.isLimit_iff_isIso_snd, CategoryTheory.Cat.Hom.instIsIsoFunctorαCategoryToNatTransHomHom, CategoryTheory.SimplicialObject.Homotopy.postcomp_h, CategoryTheory.TransfiniteCompositionOfShape.ici_incl, CategoryTheory.ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₃, CategoryTheory.Subfunctor.Subpresheaf.eq_top_iff_isIso, CategoryTheory.MonoidalOpposite.tensorLeftIso_inv_app_unmop, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_obj_obj_obj₃, CategoryTheory.Limits.LimitPresentation.w_assoc, CommGrpCat.coyoneda_map_app, CategoryTheory.exactFunctor_le_rightExactFunctor, CategoryTheory.Sum.swapCompInr_inv_app, CategoryTheory.cocones_obj_obj, const_obj_map, CategoryTheory.PreGaloisCategory.instCompactSpaceAutFunctorFintypeCat, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_hom, CategoryTheory.Limits.colimitYonedaHomIsoLimitRightOp_π_apply, CategoryTheory.WithInitial.opEquiv_unitIso_hom_app, CategoryTheory.obj_η_app, CategoryTheory.GrothendieckTopology.plusMap_zero, CategoryTheory.ChosenPullbacksAlong.pullbackComp_hom_counit_assoc, CategoryTheory.PreGaloisCategory.instReflectsMonomorphismsActionFintypeCatAutFunctorFunctorToAction, CategoryTheory.Triangulated.TStructure.eTruncLTLTIsoLT_hom, CategoryTheory.Limits.FormalCoproduct.evalCompInclIsoId_hom_app_app, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_map_τ₃, CategoryTheory.Comma.unopFunctorCompFst_hom_app, TopologicalSpace.OpenNhds.inclusionMapIso_inv_app, CategoryTheory.Sheaf.isConstant_iff_isIso_counit_app, CategoryTheory.NatTrans.Coequifibered.comp, CategoryTheory.Presheaf.tautologicalCocone_pt, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_rightUnitor, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_map, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_map_snd_app, CategoryTheory.Over.coprod_map_app, CorepresentableBy.coyoneda_homEquiv, CategoryTheory.Adjunction.homEquiv_leftAdjointUniq_hom_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_hom_app_hom_hom, CategoryTheory.Bicategory.associatorNatIsoMiddle_inv_app, CategoryTheory.ShiftMkCore.zero_add_inv_app, CategoryTheory.Abelian.SpectralObject.kernelSequenceCyclesE_X₃, SSet.associator_inv_app_apply, CategoryTheory.Limits.end_.lift_π_assoc, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_unitIso_hom_app_f_f, CategoryTheory.Limits.colimit.isoColimitCocone_ι_hom, CategoryTheory.CostructuredArrow.mapIso_inverse_map_left, CategoryTheory.Adjunction.whiskerRight_unit_app_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_obj_map, CategoryTheory.Limits.Cocone.equivStructuredArrow_functor, CategoryTheory.instIsLeftAdjointFunctorOppositeSheafPresheafToSheaf, SSet.stdSimplex.nonDegenerateEquiv_symm_apply_coe, AlgebraicTopology.DoldKan.homotopyEquivNormalizedMooreComplexAlternatingFaceMapComplex_hom, ranAdjunction_unit_app, CategoryTheory.Limits.Types.FilteredColimit.isColimit_eq_iff', CategoryTheory.prod_preservesConnectedLimits, CategoryTheory.pullbackShiftFunctorAdd'_inv_app, instFaithfulProdCurry₃, CategoryTheory.OverPresheafAux.map_mkPrecomp_eqToHom, CategoryTheory.SimplicialObject.Homotopy.map_homology_eq, CategoryTheory.LocalizerMorphism.isLeftDerivabilityStructure_iff, CategoryTheory.Limits.end_.condition_assoc, Profinite.exists_locallyConstant_fin_two, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_obj_obj_obj, CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_limit_map_assoc, CategoryTheory.StructuredArrow.mapNatIso_inverse_map_left, CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor, shiftIso_hom_naturality, CategoryTheory.Sheaf.cartesianMonoidalCategoryWhiskerLeft_val, CategoryTheory.WithInitial.ofCommaMorphism_app, SSet.horn.ι_ι, CategoryTheory.Limits.Cocone.fromStructuredArrow_obj_ι, CategoryTheory.Sheaf.ΓRes_naturality, coreComp_inv_app_iso_hom, CategoryTheory.Presheaf.coherentExtensiveEquivalence_counitIso_hom_app_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_eq, CategoryTheory.Limits.colim.mapShortComplex_X₂, CategoryTheory.AdditiveFunctor.ofLeftExact_map_hom, ModuleCat.HasLimit.productLimitCone_isLimit_lift, CategoryTheory.Limits.Cocone.equivStructuredArrow_counitIso, SheafOfModules.pushforwardNatIso_hom, AlgebraicGeometry.structureSheafInType.smul_apply, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app_assoc, HomologicalComplex.ι_mapBifunctorFlipIso_hom_assoc, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_obj₁, CategoryTheory.prodOpEquiv_counitIso_inv_app, CategoryTheory.TwistShiftData.shiftFunctor_map, CategoryTheory.Comonad.beckCoalgebraFork_π_app, CategoryTheory.MorphismProperty.Comma.mapLeftEq_hom_app_left, CategoryTheory.MonoidalOpposite.tensorIso_inv_app_unmop, CategoryTheory.MonoidalOpposite.mopMopEquivalence_counitIso_hom_app, CategoryTheory.Limits.CatCospanTransform.isIso_iff, CategoryTheory.GrothendieckTopology.diagramNatTrans_comp, CategoryTheory.Limits.pointwiseBinaryBiproductData_bicone, CategoryTheory.TwistShiftData.shiftFunctorZero_inv_app, CategoryTheory.uliftYonedaFunctor_preservesLimits, sheafPushforwardContinuousComp_hom_app_hom_app, AlgebraicTopology.DoldKan.N₁Γ₀_app, CategoryTheory.bifunctorComp₂₃Obj_map_app, CategoryTheory.Equivalence.core_unitIso_inv_app_iso_inv, CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp_hom_app_f, CategoryTheory.Limits.colimitLimitToLimitColimit_injective, CategoryTheory.Abelian.SpectralObject.opcyclesMap_fromOpcycles_assoc, lanAdjunction_counit_app, id_hcomp, CategoryTheory.MonoidalCategory.rightUnitorNatIso_hom_app, SSet.Subcomplex.prod_le_prod_top, CategoryTheory.Abelian.SpectralObject.pOpcycles_δFromOpcycles_assoc, PushoutObjObj.ι_iso_of_iso_left_hom, RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π_assoc, CategoryTheory.coreFunctor_obj_map_iso_hom, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_obj_map_app, CategoryTheory.FunctorToTypes.binaryCoproductCocone_pt_obj, CategoryTheory.Equivalence.sheafCongr_unitIso, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_map, CategoryTheory.hoFunctor.isIso_prodComparison, CategoryTheory.Limits.Cone.postcomposeEquivalence_inverse, isIso_lanAdjunction_counit_app_iff, CategoryTheory.sheafifyLift_id_toSheafify_assoc, LaxMonoidal.ofBifunctor.secondMap₃_app_app_app, CategoryTheory.Limits.Cocone.tensor_pt, SSet.horn₃₁.ι₀_desc, groupCohomology.isoShortComplexH2_inv, CategoryTheory.Abelian.SpectralObject.instMonoICycles, CategoryTheory.shiftFunctorCompIsoId_zero_zero_inv_app, CategoryTheory.Limits.instHasLimitProdObjFunctorUncurryWhiskeringLeft₂OfPreservesLimit₂, CategoryTheory.Pseudofunctor.ObjectProperty.mapComp_inv_app, CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_inv, CategoryTheory.preadditiveCoyoneda_obj, CategoryTheory.Enriched.FunctorCategory.functorEnriched_assoc, CategoryTheory.WithTerminal.equivComma_unitIso_hom_app_app, PresheafOfModules.pushforward_id_comp, CategoryTheory.cosimplicialSimplicialEquiv_functor_obj_map, CategoryTheory.prod.prodFunctorToFunctorProdAssociator_hom_app_app, CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse_assoc, CategoryTheory.DinatTrans.dinaturality, CategoryTheory.Adjunction.leftAdjointCompNatTrans_assoc, CategoryTheory.Grothendieck.compAsSmallFunctorEquivalence_counitIso, TopCat.piFan_π_app, coreComp_inv_app_iso_inv, CategoryTheory.MorphismProperty.Comma.mapRightIso_functor_obj_hom, CategoryTheory.Adjunction.shift_unit_app_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionHom, HomologicalComplex.homologyFunctorIso_inv_app, CategoryTheory.oppositeShiftFunctorAdd_hom_app, commShiftUnop_commShiftIso, TopCat.coconeOfCoconeForget_ι_app, CategoryTheory.GrothendieckTopology.Point.instPreservesFiniteColimitsSheafSheafFiber, CochainComplex.liftCycles_shift_homologyπ_assoc, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_inv_app, CategoryTheory.Comma.colimitAuxiliaryCocone_ι_app, CategoryTheory.SimplicialThickening.functor_obj_as, CategoryTheory.Limits.Fan.mk_π_app, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map_assoc, CategoryTheory.Limits.piFunctor_obj_map, SSet.instIsRegularEpiCategory, CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLift, Condensed.isSheafProfinite, isRightKanExtension_iff_postcomp₁, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂, CategoryTheory.curryingIso_hom_toFunctor_map_app, CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_fst, HomologicalComplex.isIso_π_f_of_isLimit_of_isEventuallyConstantTo, ContAction.resComp_inv, CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatTrans_comp, leftOpRightOpIso_inv_app, mapTriangleIdIso_hom_app_hom₁, CategoryTheory.Limits.Cone.postcompose_map_hom, CategoryTheory.Sheaf.sheafifyCocone_ι_app_val, CategoryTheory.CartesianMonoidalCategory.prodComparisonNatTrans_app, CategoryTheory.SingleFunctors.inv_hom_id_hom, CategoryTheory.MonadHom.id_toNatTrans, CategoryTheory.MorphismProperty.Over.mapId_hom_app_left, CategoryTheory.Idempotents.DoldKan.N_map, CategoryTheory.Equivalence.mapAddMon_unitIso, instIsRepresentableObjOppositeTypeUliftYoneda, CategoryTheory.NonemptyParallelPairPresentationAux.hg, coreflective, CategoryTheory.Limits.evaluation_preservesLimitsOfShape, CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso_hom_app_hom_app, CategoryTheory.Adjunction.unit_leftAdjointUniq_hom_app, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_inv_app, mapTriangleIdIso_hom_app_hom₂, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop, CategoryTheory.SingleFunctors.postcompIsoOfIso_inv_hom_app, CategoryTheory.WithTerminal.opEquiv_unitIso_inv_app, CategoryTheory.PreGaloisCategory.toAut_injective_of_non_trivial, OneHypercoverDenseData.essSurj.restriction_eq_of_fac, CategoryTheory.Limits.functorCategoryHasLimit, CategoryTheory.Abelian.SpectralObject.fromOpcyles_δ, ShiftSequence.induced_shiftMap_assoc, CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom, CategoryTheory.ShortComplex.FunctorEquivalence.inverse_map_τ₂, CategoryTheory.LocalizerMorphism.isIso_iff_of_hasLeftResolutions, pushforwardContinuousSheafificationCompatibility_hom_app_val, CategoryTheory.Limits.diagramIsoParallelPair_inv_app, SSet.Truncated.HomotopyCategory.BinaryProduct.inverse_obj, CategoryTheory.Adjunction.commShiftIso_hom_app_counit_app_shift, CategoryTheory.equivYoneda'_inv_hom, CategoryTheory.MorphismProperty.Over.pullbackComp_left_fst_fst, Profinite.Extend.functor_map, CategoryTheory.Sheaf.isSeparated, SheafOfModules.pushforwardPushforwardEquivalence_counit_app_val_app, CategoryTheory.OverPresheafAux.counitAuxAux_hom, CategoryTheory.Enriched.FunctorCategory.functorEnrichedHom_map, CategoryTheory.Limits.coneOfAdj_π, CategoryTheory.Discrete.natIsoFunctor_inv_app, CategoryTheory.shrinkYonedaGrpObjObjEquiv_symm_comp, CategoryTheory.Bicategory.associatorNatIsoRight_inv_app, CategoryTheory.Limits.lim_μ_π, CategoryTheory.Limits.colimitCoyonedaHomIsoLimitLeftOp_π_apply, CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.convolutionUnitApp_eq, IsDenseSubsite.full_sheafPushforwardContinuous, IsCoverDense.restrictHomEquivHom_naturality_right, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app, Condensed.id_val, CategoryTheory.Abelian.SpectralObject.epi_H_map_twoδ₁Toδ₀, TopCat.Presheaf.mono_iff_stalk_mono, CategoryTheory.Limits.limitUncurryIsoLimitCompLim_inv_π_assoc, CategoryTheory.Limits.cospanExt_hom_app_right, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂'_obj_map_app, CategoryTheory.instIsIsoSSetProdComparisonCatCompNerveFunctorHoFunctorOf, CategoryTheory.Subfunctor.equalizer.ι_ι, SSet.PtSimplex.MulStruct.δ_succ_castSucc_map_assoc, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_hom_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_map, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π_assoc, CategoryTheory.PreGaloisCategory.endMulEquivAutGalois_pi, Condensed.locallyConstantIsoFinYoneda_hom_app, CategoryTheory.Pi.comapComp_hom_app, CategoryTheory.NatTrans.app_sub, hcomp_id, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_two_assoc, leibnizPullback_obj_obj, CategoryTheory.MorphismProperty.Comma.mapRightComp_inv_app_right, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_left_right, CategoryTheory.linearCoyoneda_obj_obj_isModule, CategoryTheory.GlueData.diagramIso_hom_app_right, CategoryTheory.Abelian.SpectralObject.toCycles_descCycles_assoc, ModuleCat.homEquiv_extendScalarsId, SSet.horn.const_val_apply, CategoryTheory.yoneda_obj_isGeneratedBy, CategoryTheory.Limits.coend.ι_desc_assoc, CategoryTheory.Limits.Concrete.isColimit_rep_eq_of_exists, CategoryTheory.MonoidalCategory.prodCompExternalProduct_hom_app, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_hom_app_snd_app, Condensed.instPreservesFiniteProductsOppositeCompHausObjFunctorIsSheafCoherentTopology, CategoryTheory.MonoidalCategory.DayFunctor.η_comp_isoPointwiseLeftKanExtension_hom, CategoryTheory.NatTrans.app_neg, CategoryTheory.toOverUnitPullback_inv_app_left, CategoryTheory.NatIso.cancel_natIso_hom_left, CategoryTheory.Comma.mapRightIso_inverse_map_left, CategoryTheory.NatIso.inv_hom_app, SSet.horn₃₁.desc.multicofork_π_three, OplaxMonoidal.ofBifunctor.firstMap_app_app_app, CategoryTheory.RightExactFunctor.forget_obj, CategoryTheory.nerveAdjunction.isIso_counit, CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv, CategoryTheory.Limits.Cofork.app_one_eq_π, CategoryTheory.Subfunctor.epi_iff_range_eq_top, CategoryTheory.Limits.constCocone_ι, OneHypercoverDenseData.essSurj.presheafObjObjIso.inv_restriction_assoc, CategoryTheory.Equivalence.CommShift.instCommShiftHomFunctorUnitIso, CategoryTheory.CommShift₂Setup.z_zero₁, CategoryTheory.functor_thin, CategoryTheory.Limits.spanIsoMk_inv_app, SSet.StrictSegal.isRightKanExtension, AlgebraicGeometry.Scheme.exists_isOpenCover_and_isAffine, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CategoryTheory.Subfunctor.equalizer.fork_ι, CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_assoc, CategoryTheory.GrothendieckTopology.pointBot_fiber, CategoryTheory.Subfunctor.Subpresheaf.ofSection_eq_range, CategoryTheory.piEquivalenceFunctorDiscrete_counitIso, CategoryTheory.Abelian.SpectralObject.IsThirdQuadrant.isZero₁, CategoryTheory.Join.mapIsoWhiskerLeft_inv, CategoryTheory.isZero_Tor_succ_of_projective, CategoryTheory.SingleFunctors.shiftIso_add'_hom_app, whiskeringLeft₃_obj_obj_obj_obj_map_app_app, CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc, CategoryTheory.Limits.instHasColimitProdObjFunctorUncurryWhiskeringLeft₂OfPreservesColimit₂, CommRingCat.preservesFilteredColimits_coyoneda, CategoryTheory.Limits.CatCospanTransformMorphism.right_coherence, CategoryTheory.Comma.mapLeftId_inv_app_right, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app_hom_app, SSet.horn₃₂.ι₃_desc_assoc, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_inv_app_op_one, mapMatComp_inv_app, HomologicalComplex.mapBifunctorAssociatorX_hom_D₁_assoc, CochainComplex.homologyFunctorFactors_hom_app_homologyδOfTriangle, CategoryTheory.Limits.opHomCompWhiskeringLimYonedaIsoCocones_inv_app_app, CategoryTheory.GrothendieckTopology.plusMap_comp, CategoryTheory.StructuredArrow.mapNatIso_functor_map_left, CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp_assoc, CategoryTheory.sheafSectionsNatIsoEvaluation_inv_app, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_isAddCommGroup, instIsAccessibleObjConst, CategoryTheory.Limits.HasColimitOfHasCoproductsOfHasCoequalizers.buildColimit_ι_app, CategoryTheory.OverPresheafAux.YonedaCollection.map₂_fst, CategoryTheory.Tor_map, CategoryTheory.Sheaf.IsConstant.mem_essImage, sheafPushforwardContinuousId_inv_app_hom_app, CategoryTheory.Presheaf.instIsIsoFunctorLeftKanExtensionUnitOppositeTypeUliftYoneda, CategoryTheory.GradedObject.ι_mapBifunctorLeftUnitor_hom_apply_assoc, CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd_assoc, CategoryTheory.FunctorToTypes.prod_ext'_iff, TopCat.Presheaf.presheafEquivOfIso_functor_obj_map, mapDerivedCategoryFactorsh_hom_app, SSet.horn₂₁.sq, CategoryTheory.Adjunction.Localization.η_app, AlgebraicTopology.isZero_singularHomologyFunctor_of_totallyDisconnectedSpace, CategoryTheory.Subpresheaf.to_sheafifyLift, CategoryTheory.Limits.CategoricalPullback.mkNatIso_eq, CategoryTheory.sum.inlCompInverseAssociator_hom_app_down_down, AlgebraicGeometry.StructureSheaf.algebraMap_germ_apply, CategoryTheory.SimplicialThickening.SimplicialCategory.id_comp, sheafAdjunctionCocontinuous_unit_app_val, rightDerivedZeroIsoSelf_inv_hom_id, CategoryTheory.Limits.HasBiproductsOfShape.colimIsoLim_inv_app, CategoryTheory.StructuredArrow.mapNatIso_counitIso_inv_app_right, map_opShiftFunctorEquivalence_unitIso_hom_app_unop, CategoryTheory.Sieve.toUliftFunctor_app_down_coe, homObjFunctor_obj, CategoryTheory.NatIso.cancel_natIso_inv_left, CategoryTheory.Abelian.SpectralObject.map_comp_assoc, CategoryTheory.Triangulated.TStructure.truncLEIsoTruncLT_inv_ι_app_assoc, CategoryTheory.MorphismProperty.Comma.mapLeftComp_inv_app_right, CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_zero, CategoryTheory.WithInitial.coconeEquiv_unitIso_inv_app_hom_right, CategoryTheory.Join.mapWhiskerLeft_comp, CategoryTheory.Tor'_map_app, CategoryTheory.yoneda'_obj_obj, CompHausLike.LocallyConstantModule.functor_map_hom_app_hom_apply_apply, SheafOfModules.pushforward_obj_val, CategoryTheory.Abelian.SpectralObject.isZero_H_map_mk₁_of_isIso, CategoryTheory.oppositeShiftFunctorAdd'_inv_app, CategoryTheory.Equivalence.symmEquivInverse_obj_unitIso_hom, CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit, whiskeringRight_map_app_app, CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_inv_assoc, lanUnit_app_app_lanAdjunction_counit_app_app_assoc, Rep.Tor_obj, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_obj_map_hom₂, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_right, Condensed.equalizerCondition_profinite, CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.counitIso_hom, CategoryTheory.GrothendieckTopology.isIso_toPlus_of_isSheaf, AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_toGlued, CategoryTheory.SimplicialObject.whiskering_obj_obj_δ, PresheafOfModules.Sheafify.mul_smul, CategoryTheory.GrothendieckTopology.Point.skyscraperSheafAdjunction_homEquiv_apply_hom, leftExtensionEquivalenceOfIso₁_functor_map_right, SSet.instFinitePullback, CategoryTheory.GrothendieckTopology.Point.sheafFiberCompIso_inv_app, Action.resCongr_hom, CategoryTheory.CommShift₂Setup.hε, CategoryTheory.Limits.Cocone.underPost_pt, CategoryTheory.ε_app, CategoryTheory.Limits.FormalCoproduct.evalOpCompInlIsoId_inv_app_app, CategoryTheory.Abelian.DoldKan.comparisonN_inv_app_f, CategoryTheory.Join.mkNatTransComp, whiskeringLeft₂_obj_obj_map_app_app, HomologicalComplex.homologyFunctorSingleIso_hom_app, CategoryTheory.right_unitality_app, CategoryTheory.Abelian.FunctorCategory.imageObjIso_inv, CommGrpCat.coyonedaType_obj_obj_coe, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_inv_app_fst_app, instIsIsoAppRanCounit_1, CategoryTheory.Enriched.FunctorCategory.functorEnriched_comp_id, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_hom_app, CommRingCat.coproductCocone_ι, CategoryTheory.Limits.cospanExt_hom_app_left, SSet.Truncated.HomotopyCategory.homToNerveMk_comp_assoc, Condensed.equalizerCondition, TopCat.Presheaf.presheafEquivOfIso_inverse_map_app, CategoryTheory.SimplicialThickening.functor_comp, CategoryTheory.Limits.filtered_colim_preservesFiniteLimits_of_types, CategoryTheory.Equivalence.adjointify_η_ε, CategoryTheory.Limits.Cocone.extensions_app, CategoryTheory.Limits.IndObjectPresentation.yoneda_F, CategoryTheory.MonoidalCategory.externalProductFlip_inv_app_app_app_app, CategoryTheory.Subfunctor.range_id, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₁, CommRingCat.preservesColimit_coyoneda_of_finitePresentation, HomologicalComplex.mapBifunctor.d₁_eq, CategoryTheory.Limits.ColimitPresentation.bind_ι_app, inv_whiskerRight, CategoryTheory.Under.forgetCone_π_app, PullbackObjObj.ofHasPullback_fst, instPreservesColimitsOfShapeSheafTypeUliftYonedaOfPreservesLimitsOfShapeOppositeObjFunctorIsSheaf, CategoryTheory.WithTerminal.liftToTerminalUnique_hom_app, CategoryTheory.Limits.diagramIsoSpan_hom_app, PresheafOfModules.instAdditiveFunctorOppositeAbToPresheaf, TopologicalSpace.OpenNhds.inclusionMapIso_hom_app, CategoryTheory.Sheaf.tensorUnit_isSheaf, CategoryTheory.Limits.Types.surjective_π_app_zero_of_surjective_map_aux, CategoryTheory.flipCompEvaluation_inv_app, FullyFaithful.hasShift.map_zero_hom_app, CategoryTheory.instEpiFunctorWhiskerRightOfPreservesEpimorphisms, Fiber.fiberInclusionCompIsoConst_hom_app, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_obj_map_hom₁, CategoryTheory.η_ε_app, leftKanExtensionIsoFiberwiseColimit_inv_app, CategoryTheory.GradedObject.mapTrifunctorMapNatTrans_app_app_app, CategoryTheory.shiftFunctorAdd_assoc_inv_app, SSet.horn.primitiveTriangle_coe, HomologicalComplex.isZero_single_comp_eval, CategoryTheory.NatTrans.CommShift.id, TopologicalSpace.Opens.mapIso_refl, CategoryTheory.Limits.endFunctor_map, CompHausLike.LocallyConstant.functorToPresheaves_obj_map, AlgebraicGeometry.PresheafedSpace.colimitCocone_ι_app_c, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₂_assoc, CategoryTheory.Equivalence.core_counitIso_inv_app_iso_inv, CategoryTheory.Join.InclRightCompRightOpOpEquivFunctor_hom_app, CategoryTheory.Equivalence.unit_app_tensor_comp_inverse_map_δ_functor, CategoryTheory.Join.mapPairRight_inv_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τl, RightExtension.postcompose₂ObjMkIso_hom_left_app, instPreservesLimitsOfShapeSheafTypeYoneda, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂_assoc, CategoryTheory.Limits.IsLimit.isIso_π_app_of_isInitial, CategoryTheory.Limits.Cotrident.IsColimit.homIso_apply_coe, CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₁, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_inv_app_f, leftKanExtensionUnique_inv, CategoryTheory.GradedObject.mapBifunctorMap_obj_obj, CategoryTheory.instPreservesFiniteLimitsObjFunctorExactFunctor, equiv_counitIso, CategoryTheory.WithTerminal.equivComma_unitIso_inv_app_app, CategoryTheory.Iso.map_hom_inv_id_eval_app, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_hom_app, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right, AlgebraicGeometry.Scheme.Modules.pseudofunctor_associativity, CategoryTheory.nerve.instFaithfulCatTruncatedOfNatNatNerveFunctor₂, CategoryTheory.Sheaf.instHasFiniteProducts, CategoryTheory.Idempotents.functorExtension₁_obj, CategoryTheory.NatTrans.CommShiftCore.app_shift_assoc, PresheafOfModules.map_comp_assoc, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.epi_f, CategoryTheory.Comma.mapLeftComp_hom_app_right, CategoryTheory.Adjunction.whiskerLeft_unit_iso_of_R_fully_faithful, CategoryTheory.Localization.Monoidal.functorMonoidalOfComp_μ_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedAction_obj_obj, whiskeringRight₂_obj_map_app_app, CategoryTheory.shiftFunctorAdd'_assoc_hom_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.iso_hom_naturality, CategoryTheory.yonedaMon_obj, CategoryTheory.Limits.CatCospanTransform.mkIso_inv_left, rightKanExtensionUnique_hom, CategoryTheory.Pi.comapId_inv_app, unopComp_hom_app, leibnizPushout_map_app, PresheafOfModules.Sheafify.SMulCandidate.h, CategoryTheory.IsPushout.isVanKampen_inl, rightDerived_fac, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberCompIso_hom_app, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₁, CategoryTheory.μ_naturalityₗ_assoc, CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_inv_π_π_assoc, AlgebraicTopology.DoldKan.Compatibility.υ_inv_app, compFlipUncurryIso_hom_app, CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_three, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_right_obj, CategoryTheory.OverPresheafAux.counitForward_val_fst, CategoryTheory.CatCenter.localization_add, CategoryTheory.Discrete.natIso_inv_app, CategoryTheory.LocalizerMorphism.IsLeftDerivabilityStructure.guitartExact', IsCoverDense.Types.pushforwardFamily_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_yoneda_map, CategoryTheory.SingleFunctors.postcomp_shiftIso_hom_app, CategoryTheory.Limits.CoconeMorphism.map_w, CategoryTheory.Equivalence.congrRightFunctor_map, commBialgCatEquivComonCommAlgCat_counitIso_inv_app, CategoryTheory.Pseudofunctor.CoGrothendieck.compIso_hom_app, CategoryTheory.whiskeringLeftCompEvaluation_hom_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map_hom_app, leftExtensionEquivalenceOfIso₁_unitIso_inv_app_right_app, CategoryTheory.Limits.coneUnopOfCoconeEquiv_unitIso, CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.map_app_f, whiskeringRightObjCompIso_inv_app_app, SSet.stdSimplex.ι₀_whiskerLeft_toSSetObjI_μ, AlgebraicGeometry.StructureSheaf.instIsLocalizedModuleObjOppositeOpensCarrierTopObjFunctorTypeIsSheafGrothendieckTopologyStructureSheafInTypeOpBasicOpenPowersToOpenₗ, HomologicalComplexUpToQuasiIso.homologyFunctorFactorsh_inv_app_quotient_obj_assoc, CategoryTheory.Join.mkFunctorRight_hom_app, CategoryTheory.Subfunctor.range_comp_le, CategoryTheory.Comma.mapFst_inv_app, CategoryTheory.Iso.coreWhiskerLeft, CategoryTheory.FunctorToTypes.binaryProductIso_hom_comp_fst, CategoryTheory.MonoidalCategory.instFaithfulFunctorTensoringLeft, HomologicalComplex.natIsoSc'_inv_app_τ₁, CategoryTheory.GrothendieckTopology.plusCompIso_inv_eq_plusLift, CategoryTheory.Adjunction.Triple.whiskerLeft_leftToRight, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_obj_obj_mor₂, CategoryTheory.SimplicialObject.equivalenceLeftToRight_left_app, mapAddMonIdIso_inv_app_hom, CategoryTheory.Over.liftCocone_pt, CategoryTheory.MonoidalCategory.DayConvolutionUnit.corepresentableByRight_homEquiv, CategoryTheory.Subfunctor.equivalenceMonoOver_counitIso, PresheafOfModules.forgetToPresheafModuleCat_map, CategoryTheory.WithTerminal.coneEquiv_counitIso_hom_app_hom, CategoryTheory.Abelian.SpectralObject.HasSpectralSequence.isZero_H_obj_mk₁_i₃_le, CategoryTheory.WithInitial.mapId_hom_app, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv, CategoryTheory.MonoidalCategory.tensoringRight_η, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τr, CategoryTheory.MorphismProperty.Comma.mapLeftIso_unitIso_hom_app_left, Condensed.discrete_obj, CategoryTheory.Abelian.coimIsoIm_hom_app, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_comp, CategoryTheory.LocalizerMorphism.instIsIsoFunctorRightDerivedFunctorComparison, CategoryTheory.Over.iteratedSliceForwardNaturalityIso_inv_app, CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_left, CategoryTheory.Limits.IndObjectPresentation.yoneda_ℐ, CategoryTheory.ShortComplex.mapNatIso_inv, CategoryTheory.Localization.essSurj_mapComposableArrows, CategoryTheory.whiskeringRight_comp_evaluation, SSet.stdSimplex.face_singleton_compl, TopCat.isTopologicalBasis_cofiltered_limit, PresheafOfModules.instIsRightAdjointPushforwardIdFunctorOppositeRingCat, CategoryTheory.CategoryOfElements.fromCostructuredArrow_obj_fst, SSet.ι₀_app_fst, CommShift.isoAdd'_inv_app, CategoryTheory.Limits.constCocone_pt, SSet.horn₃₂.ι₀_desc_assoc, CategoryTheory.ComposableArrows.isIso_iff₁, CategoryTheory.LaxMonoidalFunctor.id_hom, DerivedCategory.homologyFunctorFactors_hom_naturality_assoc, CategoryTheory.Localization.associator_hom_app_app_app, OplaxMonoidal.ofBifunctor.topMapₗ_app, CategoryTheory.Limits.instHasLimitObjFunctorConstTerminal, CommShift.OfComp.map_iso_hom_app, CategoryTheory.Limits.colimitUncurryIsoColimitCompColim_ι_ι_inv_assoc, CategoryTheory.IsPushout.iff_app, CommShift.OfComp.map_iso_inv_app_assoc, CommShift.isoZero'_hom_app, CategoryTheory.Bicategory.leftUnitorNatIso_inv_app, CategoryTheory.Equivalence.congrRight_counitIso_inv_app, pushforwardContinuousSheafificationCompatibility_hom_app_hom, CategoryTheory.IsPullback.of_is_product, CategoryTheory.Localization.Monoidal.map_hexagon_forward_assoc, CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_fst, CategoryTheory.BinaryCofan.isPullback_initial_to_of_isVanKampen, CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.unitIso_inv_app_hom_app, CategoryTheory.Limits.colimit.ι_desc_app, CategoryTheory.TwoSquare.GuitartExact.whiskerVertical, CategoryTheory.MonoidalCategory.leftUnitorNatIso_hom_app, CategoryTheory.Sigma.natIso_hom, CategoryTheory.Monoidal.monFunctorCategoryEquivalence_inverse, CategoryTheory.instPreservesFiniteColimitsFunctorObjWhiskeringLeftOfHasFiniteColimits, CategoryTheory.MonoidalCategory.externalProductBifunctor_obj_map, CategoryTheory.FunctorToTypes.monoFactorisation_e, CategoryTheory.sum.inrCompInverseAssociator_inv_app, CategoryTheory.RelCat.opEquivalence_unitIso, CategoryTheory.MonoidalCategory.DayFunctor.ι_map, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_mon_one, CategoryTheory.sheafComposeNatTrans_fac, CategoryTheory.toSheafify_naturality, Module.Flat.rTensor_shortComplex_exact, CategoryTheory.Limits.IsLimit.fac, CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_naturality, CategoryTheory.Abelian.SpectralObject.sc₁_g, CategoryTheory.Pi.comapEvalIsoEval_inv_app, CategoryTheory.CostructuredArrow.mapIso_counitIso_inv_app_left, CategoryTheory.Limits.widePushoutShapeOpEquiv_unitIso, rightKanExtensionCompIsoOfPreserves_inv_fac_assoc, CategoryTheory.PreGaloisCategory.functorToAction_full, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₁, CategoryTheory.ObjectProperty.IsConservativeFamilyOfPoints.jointlyReflectEpimorphisms, CategoryTheory.GrothendieckTopology.yonedaEquiv_apply, CategoryTheory.GrothendieckTopology.Point.toPresheafFiberMap_naturality, CategoryTheory.SimplicialObject.Truncated.whiskering_obj_map_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_left_obj, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst_assoc, CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor_map_app_hom_hom, CategoryTheory.Over.ConstructProducts.conesEquivFunctor_obj_π_app, CategoryTheory.BraidedCategory.Hexagon.functor₂₁₃_obj_obj_map, CategoryTheory.Monoidal.commMonFunctorCategoryEquivalence_inverse, pointwiseLeftKanExtensionCompIsoOfPreserves_inv_fac_assoc, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_obj_obj_obj, SheafOfModules.Finite.evaluationPreservesFiniteLimits, CategoryTheory.shrinkYonedaEquiv_symm_map, CategoryTheory.IsPushout.of_isColimit_cocone, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_η_assoc, CategoryTheory.GradedObject.comapEq_symm, HomologicalComplex.ι_mapBifunctorMap, CategoryTheory.Comma.mapLeftIso_functor_map_right, CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.epi_f, CategoryTheory.SimplicialObject.augmentedCechNerve_obj_hom_app, CategoryTheory.MonoidalCategory.DayFunctor.ι_comp_isoPointwiseLeftKanExtension_inv, currying_functor_map_app, CategoryTheory.GradedObject.ι_mapBifunctorComp₂₃MapObjIso_hom_assoc, CategoryTheory.map_coyonedaEquiv, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_map_fst, CategoryTheory.shiftFunctorAdd_zero_add_inv_app, CategoryTheory.Presieve.FamilyOfElements.map_id, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_inv_app_hom₁, CategoryTheory.Iso.hom_inv_id_app_app_app, Action.leftUnitor_hom_hom, CategoryTheory.shiftFunctorComm_hom_app_of_add_eq_zero_assoc, CategoryTheory.Cat.freeMapIdIso_inv_app, CategoryTheory.Limits.combineCones_π_app_app, AddCommGrpCat.coyonedaType_map_app, SSet.Edge.toTruncated_edge, bifunctorComp₂₃Iso_inv_app_app_app, CategoryTheory.instIsCardinalAccessibleObjOppositeFunctorTypeUliftCoyonedaOpOfIsCardinalPresentable, CategoryTheory.Join.mkNatIso_hom, CategoryTheory.Pretriangulated.Triangle.functorIsoMk'_inv_app_hom₃, CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_snd, HomologicalComplex.mapBifunctor₂₃.d₂_eq_zero, CategoryTheory.isMonoidalLeftDistrib.of_endofunctors, Action.FunctorCategoryEquivalence.functor_η, CategoryTheory.SimplicialObject.augmentedCechNerve_map_right, CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_hom_app_hom, CategoryTheory.Yoneda.obj_map_id, rightKanExtensionUnique_inv, CategoryTheory.Subfunctor.Subpresheaf.equalizer.lift_ι', CategoryTheory.Arrow.mapAugmentedCechNerve_right, CategoryTheory.NatTrans.CommShift.of_iso_inv, HomologicalComplex.ιOrZero_mapBifunctorAssociatorX_hom_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.w_app_assoc, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_inv_app, CategoryTheory.Limits.spanExt_inv_app_right, CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_naturality_left, CategoryTheory.Monoidal.whiskerLeft_app, CochainComplex.liftCycles_shift_homologyπ, AlgebraicGeometry.ΓSpec.toSpecΓ_unop, AlgebraicTopology.DoldKan.Γ₂N₂_inv, CategoryTheory.Sheaf.instIsMonoidalFunctorOppositeIsSheaf, CategoryTheory.map_yonedaEquiv', HomologicalComplex.natIsoSc'_hom_app_τ₁, CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionHom, SSet.stdSimplex.ι₁_whiskerLeft_toSSetObjI_μ_assoc, CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso_inv_app_right_right, CategoryTheory.bifunctorComp₂₃Obj_obj_map, CategoryTheory.prod.functorProdToProdFunctorAssociator_hom_app, CategoryTheory.StructuredArrow.mapIso_counitIso_hom_app_right, CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcycles_X₃, CategoryTheory.Limits.Cowedge.condition, CategoryTheory.GradedObject.ι_mapBifunctorComp₂₃MapObjIso_inv_assoc, CategoryTheory.MonoidalCategory.DayConvolution.unit_uniqueUpToIso_inv_assoc, CommMonCat.coyonedaType_map_app, costructuredArrowMapCocone_ι_app, SSet.range_eq_iSup_of_isColimit, CategoryTheory.AdditiveFunctor.ofRightExact_map_hom, CategoryTheory.Adjunction.mapCommGrp_counit, CategoryTheory.Over.iteratedSliceForwardIsoPost_hom_app, CategoryTheory.Limits.CategoricalPullback.toCatCommSqOver_obj_fst_map, LaxMonoidal.ofBifunctor.secondMap_app_app_app, CategoryTheory.Join.inlCompFromSum_inv_app, CategoryTheory.Abelian.Preradical.toColon_hom_left_app_colonπ_app, CategoryTheory.evaluation_map_app, CategoryTheory.Subfunctor.subobjectMk_range_arrow, CategoryTheory.CategoryOfElements.toCostructuredArrow_map, mapTriangle_map_hom₂, CategoryTheory.Pi.comapEvalIsoEval_hom_app, CategoryTheory.yoneda'_map_hom, CategoryTheory.shrinkYonedaGrp_map_app_shrinkYonedaObjObjEquiv_symm, CategoryTheory.evaluationLeftAdjoint_obj_map, CategoryTheory.Equivalence.sheafCongr.inverse_map_hom_app, CategoryTheory.instIsRepresentableObjFunctorOppositeTypeShrinkYoneda, PresheafOfModules.pushforward_comp_id, CategoryTheory.Equivalence.congrRight_counitIso_hom_app, CategoryTheory.PreGaloisCategory.toAut_continuous, CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceFunctorProj_inv_app, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop_assoc, homEquivOfIsLeftKanExtension_apply_app, CategoryTheory.Iso.map_inv_hom_id_eval_app_assoc, CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit_hom_whiskerLeft_π, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_right_app, CategoryTheory.ExponentiableMorphism.unit_pushforwardComp_hom_assoc, CategoryTheory.WithTerminal.coneEquiv_inverse_obj_pt_right_as, CategoryTheory.Subfunctor.Subpresheaf.lift_ι, CategoryTheory.Square.arrowArrowEquivalence_counitIso, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality, CategoryTheory.MorphismProperty.Comma.mapRightEq_inv_app_left, CategoryTheory.Sum.functorEquiv_counitIso, CategoryTheory.WithInitial.mapComp_hom_app, CategoryTheory.Idempotents.DoldKan.η_hom_app_f, AlgebraicTopology.normalizedMooreComplex_obj, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_right, SSet.Subcomplex.instIsIsoToRangeOfMono, CompHausLike.LocallyConstant.adjunction_unit, CategoryTheory.simplicialCosimplicialEquiv_functor_obj_map, CategoryTheory.Over.lift_map, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_left, Accessible.Limits.isColimitMapCocone.injective, CategoryTheory.instFullIndFunctorOppositeTypeInclusion, lanCompColimIso_hom_app, CategoryTheory.Limits.Fork.app_one_eq_ι_comp_right, CategoryTheory.GradedObject.ι_mapBifunctorComp₁₂MapObjIso_inv_assoc, CategoryTheory.ObjectProperty.instIsClosedUnderColimitsOfShapeFunctorPreservesLimitsOfShapeOfPreservesLimitsOfShapeColim, CategoryTheory.Pretriangulated.preadditiveCoyoneda_homologySequenceδ_apply, CategoryTheory.PreGaloisCategory.autEmbedding_isClosedEmbedding, Profinite.exists_hom, CategoryTheory.Idempotents.functorExtension₁_map, CategoryTheory.Limits.coneRightOpOfCoconeEquiv_counitIso, SSet.ι₁_comp_assoc, CategoryTheory.Presheaf.isLocallyInjective_comp, LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm_assoc, AlgebraicTopology.DoldKan.natTransQ_app, CategoryTheory.μ_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.curriedAction_obj_map, CategoryTheory.Sigma.inclDesc_hom_app, CategoryTheory.Triangulated.TStructure.eTruncGEToGEGE_app, CategoryTheory.Triangulated.TStructure.natTransTriangleLTGEOfLE_trans, CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_inv_apply, CategoryTheory.Limits.ι_colimitConstInitial_hom_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_hom_app_app, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_symm_apply, LightCondensed.instIsMonoidalFunctorOppositeLightProfiniteModuleCatWCoherentTopology, CategoryTheory.Comma.mapRightComp_inv_app_left, mapBifunctorHomologicalComplex_obj_obj_toGradedObject, CategoryTheory.Limits.pullbackConeEquivBinaryFan_inverse_map_hom, CategoryTheory.StructuredArrow.mapIso_counitIso_inv_app_right, CategoryTheory.ShiftMkCore.assoc_hom_app_assoc, CategoryTheory.Equivalence.changeFunctor_counitIso_inv_app, CategoryTheory.GradedObject.ι_mapTrifunctorMapMap, IsCoverDense.restrictHomEquivHom_naturality_left_symm, CategoryTheory.Limits.parallelPair.ext_inv_app, instAdditiveFunctorColim, CategoryTheory.Sum.functorEquiv_functor_obj, AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_app, CategoryTheory.SingleFunctors.shiftIso_zero_inv_app, HomologicalComplex.ι_mapBifunctorFlipIso_inv, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_three_assoc, CategoryTheory.SmallObject.SuccStruct.ofNatTrans_toSucc, SSet.PtSimplex.RelStruct.δ_succ_map_assoc, isoWhiskerLeft_symm, whiskeringLeft₃ObjObjObj_map_app_app_app, CategoryTheory.Abelian.Preradical.instMonoFunctorWhiskerLeftι, 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.GlueData.diagramIso_hom_app_left, CategoryTheory.SimplicialObject.instHasColimits, CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_inv_assoc, CategoryTheory.PreGaloisCategory.instContinuousInvAutFunctorFintypeCat, CategoryTheory.Abelian.SpectralObject.toCycles_i, IsDenseSubsite.faithful_sheafPushforwardContinuous, CategoryTheory.SimplicialObject.equivalenceLeftToRight_right, ModuleCat.extendScalars_assoc, CategoryTheory.Enriched.FunctorCategory.functorEnrichedId_app, TwoP.swapEquiv_unitIso_inv_app_hom_toFun, SSet.opEquivalence_functor, CategoryTheory.Equivalence.congrRight_unitIso_inv_app, CategoryTheory.NatIso.inv_inv_app, CategoryTheory.Presheaf.isLocallySurjective_presheafToSheaf_map_iff, CategoryTheory.Adjunction.shift_counit_app_assoc, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_right, whiskeringLeft₃ObjObj_obj, CategoryTheory.shift_neg_shift', CategoryTheory.Abelian.SpectralObject.toCycles_i_assoc, CategoryTheory.MonoidalOpposite.mopEquiv_counitIso, CategoryTheory.LeftExactFunctor.whiskeringRight_obj_obj_obj, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality_assoc, CategoryTheory.Limits.spanExt_inv_app_left, SheafOfModules.pushforwardNatTrans_comp, CategoryTheory.RightExactFunctor.whiskeringRight_obj_map, CategoryTheory.limitCompWhiskeringRightIsoLimitComp_hom_whiskerRight_π, CategoryTheory.shrinkYonedaEquiv_shrinkYoneda_map, CategoryTheory.Adjunction.mapGrp_counit, CategoryTheory.Idempotents.karoubiChainComplexEquivalence_counitIso_hom, CategoryTheory.NatTrans.CommShift₂.commShift_app, liftOfIsRightKanExtension_fac_assoc, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂'_obj_obj_obj, CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂_obj_obj_map, CategoryTheory.Limits.Fork.equalizer_ext, LeftExtension.mk_hom, CategoryTheory.Idempotents.DoldKan.equivalence_unitIso, CategoryTheory.Pi.comapComp_inv_app, CategoryTheory.Sheaf.instEpiAppArrowILocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, currying_inverse_map_app_app, PullbackObjObj.isPullback, CategoryTheory.Limits.CategoricalPullback.functorEquiv_counitIso_inv_app_fst_app, CategoryTheory.ShiftMkCore.assoc_inv_app, CategoryTheory.constantPresheafAdj_unit_app, CategoryTheory.Subfunctor.toRange_ι, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_hom_app, CategoryTheory.Triangulated.TStructure.natTransTruncLTOfLE_ι_assoc, CategoryTheory.Limits.instHasFiniteCoproductsFunctor, IsLeftKanExtension.nonempty_isUniversal, CategoryTheory.Presheaf.freeYoneda_obj, CategoryTheory.Limits.limit_map_limitObjIsoLimitCompEvaluation_hom, CategoryTheory.Equivalence.symmEquivInverse_map_app, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app_assoc, CategoryTheory.Mon.equivLaxMonoidalFunctorPUnit_unitIso_inv_app_hom_app, CategoryTheory.ShiftedHom.opEquiv'_add_symm, CategoryTheory.Sigma.inclDesc_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_hom_app, pointwiseLeftKanExtensionCompIsoOfPreserves_inv_fac, functorHomEquiv_symm_apply_app_app, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.mem_incl_app, CategoryTheory.Bicategory.rightUnitorNatIso_hom_app, CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor_obj_hom, PushoutObjObj.ofHasPushout_ι, CategoryTheory.MorphismProperty.Comma.mapRightEq_hom_app_right, CategoryTheory.Pi.comapId_hom_app, SSet.stdSimplex.isoNerve_inv_app_apply, HomologicalComplex.forgetEval_inv_app, CategoryTheory.colimitYonedaHomEquiv_π_apply, CategoryTheory.Enriched.FunctorCategory.diagram_obj_obj, CategoryTheory.Sheaf.cartesianMonoidalCategoryWhiskerRight_hom, CategoryTheory.Presheaf.instIsLeftKanExtensionOppositeObjFunctorTypeUliftYonedaUliftYonedaMap, CategoryTheory.GrothendieckTopology.ofArrows_mem_iff_isLocallySurjective_sigmaDesc_shrinkYoneda_map, CategoryTheory.Abelian.coimIsoIm_inv_app, CategoryTheory.ParametrizedAdjunction.whiskerLeft_map_counit_assoc, whiskeringLeft_map_app_app, CategoryTheory.LeftExactFunctor.forget_obj_of, PresheafOfModules.instPreservesFiniteLimitsSheafAddCommGrpCatCompSheafOfModulesSheafificationToSheaf, CategoryTheory.instMonoSheafTypeImageι, leftKanExtensionUnique_hom, CategoryTheory.Limits.MonoCoprod.binaryCofan_inr, CategoryTheory.Adjunction.whiskerLeft_counit_app_app, CategoryTheory.Sheaf.isSheaf_yoneda_obj, CategoryTheory.BasedNatTrans.forgetful_obj, CategoryTheory.CommShift₂Setup.int_z, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_iff, CategoryTheory.Limits.Types.isLimitEquivSections_symm_apply, CategoryTheory.Limits.pullbackObjIso_hom_comp_snd, CategoryTheory.MorphismProperty.Comma.mapLeftIso_unitIso_hom_app_right, Action.FunctorCategoryEquivalence.functor_ε, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_obj₃, CategoryTheory.Sheaf.isTerminalTerminal_from_hom, IsCoverDense.full_sheafPushforwardContinuous, CategoryTheory.BraidedCategory.Hexagon.functor₃₁₂_obj_obj_obj, CategoryTheory.FreeMonoidalCategory.tensorFunc_obj_map, CategoryTheory.uliftCoyonedaEquiv_comp, CategoryTheory.Localization.whiskeringLeftFunctor'_obj, CategoryTheory.Cat.freeMapCompIso_inv_app, IsCoverDense.Types.naturality_assoc, CategoryTheory.BraidedCategory.ofBifunctor.Forward.firstMap₃_app_app_app, CategoryTheory.Triangulated.TStructure.eTruncLT_map_eq_truncLTι, CompHausLike.LocallyConstant.functorToPresheaves_obj_obj, CategoryTheory.BraidedCategory.tensorLeftIsoTensorRight_inv_app, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit, CategoryTheory.Limits.Cone.op_ι, CategoryTheory.Abelian.SpectralObject.map_id, CategoryTheory.Limits.colimitFlipIsoCompColim_inv_app, CategoryTheory.yonedaEquiv_symm_app_apply, CategoryTheory.Square.flipEquivalence_counitIso, SSet.instFiniteInitial, AlgebraicGeometry.Spec.sheafedSpaceObj_presheaf, RightExtension.precomp_obj_left, CategoryTheory.PreGaloisCategory.instPreservesFiniteProductsActionFintypeCatAutFunctorFunctorToAction, CategoryTheory.Limits.CategoricalPullback.functorEquiv_functor_obj_snd_map, CategoryTheory.Limits.colimitLimitToLimitColimit_surjective, instIsEquivalenceRightExtensionCompPrecomp, CategoryTheory.ComposableArrows.δlastFunctor_obj_map, AlgebraicGeometry.Spec.map_app, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_hom_app, mapCommMonCompIso_hom_app_hom_hom, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_exact, CategoryTheory.preservesColimitsOfShape_of_isCardinalPresentable, CategoryTheory.evaluationAdjunctionLeft_counit_app, CategoryTheory.WithTerminal.coneEquiv_functor_map_hom, CategoryTheory.ObjectProperty.SerreClassLocalization.essImage_whiskeringLeft, SSet.PtSimplex.MulStruct.δ_castSucc_castSucc_map, CategoryTheory.TwistShiftData.z_zero_right, CategoryTheory.Limits.Cone.functorialityEquivalence_unitIso, HomologicalComplex.mapBifunctor₂₃.ι_D₂_assoc, CategoryTheory.Join.mapIsoWhiskerRight_inv_app, CategoryTheory.instIsClosedUnderColimitsOfShapeFunctorOppositeTypeIsIndObjectOfIsFiltered, mapBifunctorHomologicalComplex_obj_obj_d_f, CategoryTheory.Equivalence.sheafCongr.counitIso_hom_app_hom_app, CategoryTheory.functorProdFunctorEquivCounitIso_hom_app_app, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_right_assoc, CategoryTheory.Limits.PreservesColimit₂.nonempty_isColimit_mapCocone₂, CochainComplex.ι_mapBifunctorShift₁Iso_hom_f, SSet.RelativeMorphism.Homotopy.rel_assoc, CategoryTheory.yonedaAddMon_map_app, CategoryTheory.Adjunction.rightAdjointUniq_inv_app, leftExtensionEquivalenceOfIso₁_functor_obj_right, CategoryTheory.NatIso.ofComponents_hom_app, CategoryTheory.NatTrans.unop_comp, SheafOfModules.unitHomEquiv_apply_coe, CategoryTheory.Localization.lift₃NatIso_inv, CategoryTheory.instPreservesColimitsOfShapeFunctorLim, CochainComplex.ShiftSequence.shiftIso_hom_app, CategoryTheory.Limits.widePullbackShapeOpEquiv_unitIso, CategoryTheory.GrothendieckTopology.W.whiskerRight, CategoryTheory.MorphismProperty.FunctorsInverting.hom_ext_iff, CategoryTheory.Sum.functorEquivInverseCompWhiskeringLeftInlIso_inv_app_app, CategoryTheory.BraidedCategory.Hexagon.functor₂₃₁'_obj_obj_map, CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_counitIso_inv_app_f, CategoryTheory.MonoidalCategory.tensoringRight_μ, CategoryTheory.PreGaloisCategory.autEmbedding_range_isClosed, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_shift, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_assoc, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π, CategoryTheory.mateEquiv_apply, structuredArrowMapCone_π_app, whiskeringLeftObjCompIso_inv_app_app, CategoryTheory.sheafCompose_comp, CategoryTheory.Limits.IsLimit.homEquiv_apply, CategoryTheory.whiskering_preadditiveCoyoneda, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd_assoc, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_fst_obj, CategoryTheory.Coyoneda.ULiftCoyoneda.instFaithfulOppositeFunctorTypeUliftCoyoneda, uncurry_obj_curry_obj_flip_flip, CategoryTheory.GradedObject.mapTrifunctorMapIso_inv, CategoryTheory.CartesianMonoidalCategory.instIsIsoFunctorProdComparisonBifunctorNatTransOfProdComparison, CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_inv_app_fst_app, CategoryTheory.Limits.coprodComparisonNatIso_inv, CategoryTheory.GrothendieckTopology.Point.presheafFiberCocone_pt, CategoryTheory.Square.isPushout_iff_op_map_yoneda_isPullback, CategoryTheory.Discrete.instIsIsoFunctorNatTrans, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_map_app_app_app, CategoryTheory.Coyoneda.coyoneda_faithful, CategoryTheory.Quotient.comp_natTransLift, AlgebraicGeometry.tilde.toOpen_map_app, CategoryTheory.Limits.compYonedaSectionsEquiv_symm_apply_coe, PreOneHypercoverDenseData.multicospanMapIso_hom, CategoryTheory.yonedaEquiv_comp, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app_assoc, CategoryTheory.OverPresheafAux.counitForward_naturality₂, CategoryTheory.Limits.ColimitPresentation.self_ι, HomotopyCategory.instCommShiftHomologicalComplexIntUpHomFunctorMapHomotopyCategoryFactors, CategoryTheory.Comma.coneOfPreserves_π_app_left, CategoryTheory.Triangulated.TStructure.spectralObject_δ, CochainComplex.mappingCone.map_δ, AddCommGrpCat.coyoneda_obj_map, CategoryTheory.bifunctorComp₁₂Obj_map_app, CategoryTheory.sheafifyLift_comp, CategoryTheory.PreGaloisCategory.functorToAction_comp_forget₂_eq, CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp_εIso_hom, isRightKanExtensionAlongEquivalence, ChainComplex.linearYonedaObj_X, CategoryTheory.Monad.ForgetCreatesColimits.newCocone_ι, currying_inverse_obj_map_app, CategoryTheory.Limits.parallelPairOpIso_hom_app_zero, IsCoverDense.Types.naturality, mapComposableArrows_map_app, CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_hom, Rep.coindFunctorIso_hom_app_hom_toFun_hom_toFun
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