Functor 📖 | CompData | 6719 mathmath: Equivalence.adjointify_η_ε_assoc, Sheaf.cartesianMonoidalCategoryLift_val, GrothendieckTopology.coneCompEvaluationOfConeCompDiagramFunctorCompEvaluation_pt, Limits.Trident.condition_assoc, Pretriangulated.rotCompInvRot_hom_app_hom₃, shiftFunctorZero_inv_app_obj_of_induced, Limits.Cones.postcomposeId_hom_app_hom, Presheaf.instIsCardinalPresentableFunctorOppositeFreeYonedaOfHasColimitsOfSize, GrothendieckTopology.isoSheafify_hom, Limits.instPreservesMonomorphismsObjFunctorTypeSigmaConst, Action.resCongr_inv, MorphismProperty.LeftFraction.map_compatibility, Limits.Cocones.precompose_obj_ι, GrothendieckTopology.overMapPullbackId_hom_app_val_app, Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_eq, SingleFunctors.shiftIso_add, Functor.whiskeringRightObjIdIso_hom_app_app, Limits.colimitHomIsoLimitYoneda'_hom_comp_π, ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₁, TopCat.binaryCofan_isColimit_iff, Functor.LeftExtension.coconeAtFunctor_map_hom, Functor.functorHomEquiv_apply_app, sum.inrCompInverseAssociator_hom_app, Functor.FullyFaithful.homNatIsoMaxRight_inv_app, MorphismProperty.exists_isPushout_of_isFiltered, GrothendieckTopology.W_sheafToPresheaf_map_iff_isIso, prodComonad_ε_app, LeftExactFunctor.ofExact_map, Functor.CommShift.isoAdd_hom_app, PresheafOfModules.instIsRightAdjointPushforwardCompFunctorOppositeRingCatWhiskerLeftOp, Adjunction.compUliftCoyonedaIso_hom_app_app_down, Monoidal.tensorHom_app, Tor'_obj_obj, sheafBotEquivalence_functor, GrothendieckTopology.plusFunctorWhiskerLeftIso_inv_app, whiskeringLeft_comp_evaluation, Enriched.Functor.associator_inv_apply, LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_map, Adjunction.Triple.isIso_unit_iff_isIso_counit, Limits.walkingParallelPairOpEquiv_unitIso_hom_app_zero, uliftCoyonedaEquiv_apply, Limits.DiagramOfCones.id, GrothendieckTopology.Point.Hom.presheafFiber_app, PreOneHypercover.forkOfIsColimit_ι_map_inj_assoc, TwoSquare.equivNatTrans_symm_apply, Sum.natTransOfWhiskerLeftInlInr_app, SheafOfModules.pushforward_assoc, MonoidalCategory.MonoidalLeftAction.actionUnitNatIso_inv_app, instSmallOppositeObjFunctorTypeYoneda, Monoidal.MonFunctorCategoryEquivalence.inverse_obj, LaxBraidedFunctor.isoMk_inv, Functor.rightKanExtensionCompIsoOfPreserves_inv_fac_app, Limits.CategoricalPullback.CatCommSqOver.sndFunctor_map, Functor.PushoutObjObj.inr_ι, Functor.isoSum_inv_app_inl, Limits.IndizationClosedUnderFilteredColimitsAux.exists_nonempty_limit_obj_of_isColimit, AddCommGrpCat.coyoneda_obj_obj_coe, Equivalence.leftOp_unitIso_hom_app, linearCoyoneda_obj_additive, Monad.ForgetCreatesColimits.commuting, Equivalence.sheafCongrPrecoherent_counitIso_hom_app_val_app, WithTerminal.coneEquiv_unitIso_hom_app_hom_left, Functor.mapTriangleIdIso_inv_app_hom₃, SimplicialObject.whiskering_obj_map_app, Monad.monadMonEquiv_unitIso_inv_app_toNatTrans_app, Limits.limitConeOfUnique_cone_π, ComposableArrows.opEquivalence_counitIso_inv_app_app, MonoidalCategory.DayConvolution.braidingHomCorepresenting_app, PreGaloisCategory.instT2SpaceAutFunctorFintypeCat, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_apply, Functor.OplaxMonoidal.ofBifunctor.firstMap₂_app_app_app, Functor.coreComp_hom_app_iso_inv, Functor.natTransEquiv_apply_app, uliftCoyonedaIsoCoyoneda_hom_app_app, Discrete.sumEquiv_counitIso_inv_app, WithTerminal.mkCommaObject_right, Limits.IsLimit.ofConeEquiv_symm_apply_desc, coyonedaEquiv_symm_app_apply, Functor.isZero, Limits.pushoutCoconeOfLeftIso_ι_app_right, HomologicalComplex.singleMapHomologicalComplex_hom_app_ne, StructuredArrow.map_map_right, NatTrans.hcomp_id_app, CommMon.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon_map, Pi.eqToEquivalenceFunctorIso_hom, PreGaloisCategory.mulAction_def, shiftFunctorAdd'_assoc_inv_app, Functor.leibnizPullback_obj_map, Sheaf.ΓHomEquiv_naturality_left_symm, isIso_sheafificationAdjunction_counit, Functor.isIso_of_isRightDerivedFunctor_of_inverts, Adjunction.toEquivalence_counitIso_hom_app, Limits.reflexivePair.diagramIsoReflexivePair_hom_app, typeToPartialFunIsoPartialFunToPointed_inv_app_toFun, AlgebraicTopology.DoldKan.Compatibility.equivalence₀_unitIso_hom_app, ObjectProperty.ColimitOfShape.toCostructuredArrow_obj, Sheaf.isLocallySurjective_sheafToPresheaf_map_iff, Idempotents.app_idem_assoc, Functor.homObjEquiv_apply_app, ParametrizedAdjunction.homEquiv_symm_naturality_three_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_left, WithInitial.equivComma_functor_obj_right_obj, Functor.sheafPushforwardContinuousIso_inv, Abelian.FunctorCategory.coimageImageComparison_app', MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_associator_hom_eq_associator_hom, NatIso.mapHomologicalComplex_inv_app_f, GrothendieckTopology.MayerVietorisSquare.shortComplex_X₃, SingleFunctors.Hom.comm, preservesFiniteLimits_iff_lan_preservesFiniteLimits, Pretriangulated.shiftFunctorCompIsoId_op_hom_app, whiskeringRightPreservesLimits, GrothendieckTopology.toPlus_plusLift_assoc, Adjunction.whiskerLeftLCounitIsoOfIsIsoUnit_hom_app, Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app, Equivalence.sheafCongr.counitIso_hom_app_val_app, shift_shiftFunctorCompIsoId_hom_app, GrothendieckTopology.liftToDiagramLimitObjAux_fac, Functor.liftOfIsRightKanExtension_fac, endofunctorMonoidalCategory_tensorUnit_obj, Endofunctor.Coalgebra.functorOfNatTransComp_inv_app_f, ULiftYoneda.instFullFunctorOppositeTypeUliftYoneda, yoneda_preservesLimit, evaluationLeftAdjoint_map_app, Limits.CategoricalPullback.catCommSq_iso_hom_app, Join.inlCompFromSum_hom_app, LightProfinite.Extend.functorOp_obj, Limits.colimitHomIsoLimitYoneda_hom_comp_π, AlgebraicGeometry.Scheme.Modules.pushforwardId_inv_app_app, AddCommMonCat.coyoneda_obj_obj_coe, Idempotents.KaroubiFunctorCategoryEmbedding.obj_map_f, conjugateEquiv_iso, DinatTrans.dinaturality_assoc, Functor.rightKanExtensionUniqueOfIso_hom, Limits.diagramIsoPair_hom_app, obj_ε_app_assoc, Action.instIsEquivalenceFunctorSingleObjInverse, SSet.stdSimplex.coe_triangle_down_toOrderHom, equivOfTensorIsoUnit_unitIso, Presheaf.isSheaf_of_isTerminal, Functor.mapHomologicalComplexIdIso_hom_app_f, Limits.CategoricalPullback.CatCommSqOver.precompose_map_associator, Join.mapPairId_hom_app, Limits.Bicone.toCocone_ι_app_mk, Functor.leftOpRightOpEquiv_functor_obj_map, linearCoyoneda_map_app, MorphismProperty.instIsStableUnderTransfiniteCompositionOfShapeFunctorMonomorphismsOfHasPullbacksOfHasIterationOfShape, Adjunction.whiskerLeftLCounitIsoOfIsIsoUnit_inv_app, linearCoyoneda_obj_obj_carrier, HomotopicalAlgebra.FibrantObject.instIsIsoFunctorWhiskerRightHoCatιCompResolutionNatTransOfIsLocalizationWeakEquivalences, MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionHomLeft, Functor.rightDerivedNatTrans_id, ObjectProperty.instCommShiftHomFunctorLiftCompιIso, Limits.WalkingMultispan.functorExt_hom_app, CosimplicialObject.whiskering_obj_obj_obj, Core.forgetFunctorToCore_map_app, Comma.mapLeftEq_inv_app_right, Functor.shiftIso_add_inv_app, Limits.colimitIsoFlipCompColim_inv_app, Functor.Monoidal.μNatIso_inv_app, Comma.mapLeftIso_inverse_map_right, Equivalence.mapGrp_counitIso, CategoryOfElements.costructuredArrowYonedaEquivalenceInverseπ_hom_app, Pretriangulated.opShiftFunctorEquivalence_add_unitIso_hom_app_eq, shiftFunctorComm_zero_hom_app, SSet.OneTruncation₂.ofNerve₂.natIso_hom_app_map, MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionAssocIso_hom, Grothendieck.ιCompMap_hom_app_fiber, shrinkYoneda_map, isSeparator_iff_faithful_preadditiveCoyoneda, Functor.flip₂₃Functor_obj_obj_obj_obj, NatTrans.rightDerived_comp_assoc, Functor.leftExtensionEquivalenceOfIso₁_functor_map_left, Equivalence.comp_asNatTrans, Functor.isoWhiskerRight_twice_assoc, MonoidalCategory.DayConvolutionUnit.leftUnitor_naturality_assoc, HomologicalComplex.singleMapHomologicalComplex_hom_app_self, Over.iteratedSliceForwardNaturalityIso_hom_app, ParametrizedAdjunction.homEquiv_naturality_two, Functor.Monoidal.rightUnitor_inv_app, GrothendieckTopology.yonedaOpCompCoyoneda_hom_app_app_down, Functor.LeftExtension.precomp₂_obj_hom_app, PresheafOfModules.pullback_id_comp, Limits.Types.binaryCofan_isColimit_iff, Equivalence.sheafCongrPreregular_counitIso_inv_app_val_app, Limits.Cotrident.ofCocone_ι, NatTrans.unop_whiskerLeft, sheafOver_val, Limits.colimit.isoColimitCocone_ι_inv, Functor.CommShift.isoAdd_inv_app, ReflQuiv.adj_homEquiv, MonadIso.toNatIso_hom, Idempotents.toKaroubi_comp_karoubiFunctorCategoryEmbedding, Join.pseudofunctorRight_mapComp_inv_toNatTrans_app, Limits.multicospanIndexEnd_fst, Functor.opUnopIso_hom_app, WithTerminal.equivComma_functor_obj_left_obj, ModuleCat.restrictScalarsCongr_symm, Limits.diagramIsoCospan_inv_app, MonoidalOpposite.tensorLeftMopIso_hom_app_unmop, NatTrans.rightDerivedToHomotopyCategory_id, Functor.instIsIsoAppCounitRanAdjunctionOfHasPointwiseRightKanExtension, equivEssImageOfReflective_unitIso, Limits.Trident.app_zero, Limits.IsColimit.fac, shrinkYonedaEquiv_comp, Functor.whiskeringRight₂_obj_obj_map_app, GrothendieckTopology.toSheafify_naturality_assoc, OverPresheafAux.costructuredArrowPresheafToOver_map, Subfunctor.Subpresheaf.range_eq_ofSection', GrothendieckTopology.Point.toPresheafFiber_presheafFiberDesc, ExactFunctor.forget_map, LocalizerMorphism.natTransCommShift_hom, Functor.Monoidal.commTensorLeft_hom_app, ObjectProperty.preservesLimitsOfShape_eq_iSup, Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_hom, Limits.map_id_right_eq_curry_swap_map, AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_inv_app, Monad.ofMon_η, HasShift.Induced.add_inv_app_obj, Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_ι_presheafHom, Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_inv_app_hom, AlgebraicGeometry.opensCone_pt, Adjunction.Localization.ε_app, Pseudofunctor.DescentData.pullFunctorCompIso_inv_app_hom, Limits.Cone.unop_ι, MonoidalCategory.MonoidalLeftAction.actionUnitNatIso_hom_app, FunctorToTypes.coprod.desc_inr, Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_isLimit_lift, Functor.curryingEquiv_symm_apply_obj_obj, Adjunction.rightAdjointUniq_trans, Limits.colimitLimitToLimitColimit_isIso, Functor.mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app_assoc, PullbackShift.adjunction_counit, CategoryOfElements.costructuredArrowYonedaEquivalence_functor, Equivalence.unitIso_hom_app_comp_inverse_map_η_functor_assoc, Square.mapFunctor_obj, MonoOver.congr_unitIso, Limits.colimitObjIsoColimitCompEvaluation_ι_app_hom_assoc, WithTerminal.equivComma_counitIso_hom_app_left_app, Functor.Monoidal.whiskerLeft_app_fst_assoc, iterated_mateEquiv_conjugateEquiv, FunctorToTypes.prodMk_fst, Limits.Cone.ofTrident_π, Functor.mapCommGrpCompIso_inv_app_hom_hom_hom, LeftExactFunctor.forget_map, Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse, Sum.functorEquivFunctorCompFstIso_inv_app_app, Functor.mapCommMonNatIso_inv_app_hom_hom, Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₁, functor_skeletal, OverPresheafAux.unitAux_hom, Limits.Cones.equivalenceOfReindexing_inverse, Limits.fiberwiseColimit_map, Quotient.natIsoLift_inv, cocones_map_app_app, Functor.LeftExtension.precomp₂_map_right, CategoryOfElements.costructuredArrowULiftYonedaEquivalence_unitIso, IndParallelPairPresentation.hf, IsGrothendieckAbelian.IsPresentable.injectivity₀.F_obj, Monoidal.leftUnitor_hom_app, Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_app_snd_app, whiskeringRightPreservesColimits, Functor.mapTriangleIso_inv_app_hom₁, Subfunctor.Subpresheaf.range_eq_ofSection, Functor.IsEventuallyConstantFrom.cocone_ι_app, Limits.CategoricalPullback.CatCommSqOver.precompose_map_whiskerRight, Discrete.sumEquiv_unitIso_inv_app, Limits.ReflexiveCofork.app_one_eq_π, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_π_app, NatIso.cancel_natIso_hom_right, MonoidalSingleObj.endMonoidalStarFunctorEquivalence_counitIso, Functor.sheafPushforwardContinuousComp'_inv_app_val_app, MonoidalCategory.externalProductBifunctor_obj_obj, ReflQuiv.adj.homEquiv_symm_apply, Functor.flip₁₃_map_app_app, Functor.instIsRightDerivedFunctorLiftInvFac, CondensedMod.IsSolid.isIso_solidification_map, Limits.DiagramOfCocones.mkOfHasColimits_coconePoints, instFullMonFunctorOppositeMonCatYonedaMon, Functor.leftDerivedNatTrans_fac_assoc, NonemptyParallelPairPresentationAux.hf, AlgebraicGeometry.ΓSpec.isIso_adjunction_counit, MonoidalCategory.endofunctorMonoidalCategory.evaluationRightAction_actionHomLeft, sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_hom_app_app_val, instLocallySmallFunctor, FunctorToTypes.functorHomEquiv_symm_apply_app_app, PresheafOfModules.toPresheaf_preservesFiniteLimits, StructuredArrow.commaMapEquivalenceInverse_map, MonoidalCategory.tensorRightTensor_hom_app, Pretriangulated.Triangle.invRotate_mor₃, iterated_mateEquiv_conjugateEquiv_symm, MonoidalCategory.tensorLeftTensor_inv_app, NatTrans.IsMonoidal.instHomFunctorAssociator, Limits.spanCompIso_inv_app_zero, Adjunction.LeftAdjointCommShift.iso_hom_app_assoc, Functor.Monoidal.natTransIsMonoidal_of_transport, WithInitial.opEquiv_unitIso_inv_app, Limits.Cocone.toOver_ι_app, Equivalence.counitIso_inv_app_comp_functor_map_η_inverse, NatTrans.flipApp_app, Endofunctor.Algebra.equivOfNatIso_functor, Functor.mapTriangleIso_inv_app_hom₃, ShortComplex.π₁Toπ₂_comp_π₂Toπ₃_assoc, Under.postComp_inv_app_right, orderDualEquivalence_unitIso, Limits.Multicofork.ofπ_ι_app, AddCommMonCat.equivalence_unitIso, Idempotents.instIsEquivalenceFunctorKaroubiFunctorExtension₂, AlgebraicGeometry.Scheme.restrictFunctorΓ_inv_app, FunctorToTypes.instHasImagesFunctorType, partialFunEquivPointed_counitIso_inv_app_toFun, Functor.isoSum_inv_app_inr, ran_isSheaf_of_isCocontinuous, shrinkYonedaEquiv_symm_map_assoc, Limits.cospanIsoMk_inv_app, MonoidalCategory.MonoidalRightAction.curriedAction_obj_obj, Functor.mapCocone_ι_app, TwistShiftData.z_zero_zero, Pretriangulated.rotCompInvRot_inv_app_hom₂, MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_incl_app, Functor.full_whiskeringRight_obj, commBialgCatEquivComonCommAlgCat_unitIso_inv_app, lan_preservesFiniteLimits_of_flat, TopCat.Presheaf.generateEquivalenceOpensLe_unitIso, partialFunEquivPointed_unitIso_hom_app, MonoidalCategory.DayConvolution.braiding_naturality_left_assoc, Limits.CategoricalPullback.CatCommSqOver.transform_obj_map_snd_app, Limits.parallelPairOpIso_inv_app_zero, Limits.HasColimit.isoOfEquivalence_inv_π, CatCenter.app_sub, Functor.shiftIso_add', SheafOfModules.pushforwardNatIso_inv, FreeMonoidalCategory.normalizeIsoAux_inv_app, Comonad.ComonadicityInternal.unitFork_π_app, ProdPreservesConnectedLimits.γ₂_app, Functor.CorepresentableBy.uniqueUpToIso_inv, Limits.pullbackConeOfLeftIso_π_app_left, SingleFunctors.id_hom, Idempotents.functorExtension₁CompWhiskeringLeftToKaroubiIso_inv_app_app_f, GrothendieckTopology.Point.toPresheafFiber_eq_iff', Limits.ι_colimitCompWhiskeringLeftIsoCompColimit_hom_assoc, GrothendieckTopology.liftToDiagramLimitObjAux_fac_assoc, Limits.colimit.cocone_ι, NatIso.pi_hom, Functor.instIsLeftAdjointDiscreteTensorLeftCompIncl, Monad.mul_def, Enriched.FunctorCategory.functorHomEquiv_comp, sum.inlCompInrCompInverseAssociator_hom_app_down_down, Functor.uliftCoyonedaCoreprXIso_hom_app, NatTrans.removeLeftOp_id, Functor.isLimitConeOfIsRightKanExtension_lift, Limits.Pi.cone_π, ModuleCat.extendScalarsId_hom_app_one_tmul, Adjunction.mapMon_unit, isCoseparator_iff_faithful_preadditiveYoneda, Profinite.Extend.functorOp_map, Functor.Monoidal.tensorHom_app_fst_assoc, Iso.core_inv_app_iso_hom, GrothendieckTopology.W_eq_inverseImage_isomorphisms, instAdditiveObjFunctorAdditiveFunctor, AlgebraicTopology.singularChainComplexFunctor_exactAt_of_totallyDisconnectedSpace, WithTerminal.equivComma_counitIso_inv_app_left_app, Under.forgetMapInitial_inv_app, IsGrothendieckAbelian.IsPresentable.surjectivity.hf, Enriched.Functor.whiskerLeft_app_apply, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_hom_app_app, instMonoFunctorWhiskerRightOfPreservesMonomorphisms, Limits.HasLimit.isoOfNatIso_inv_π_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_map_app, NatIso.op_rightUnitor, NatTrans.CommShiftCore.shift_app_comm, Functor.map_shiftFunctorComm_hom_app, WithInitial.isColimitEquiv_apply_desc_right, Join.mapPairEquiv_unitIso, Comma.map_final, AlgebraicGeometry.exists_isAffineOpen_preimage_eq, Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_hom_app_snd_app, MorphismProperty.instIsStableUnderTransfiniteCompositionOfShapeFunctorFunctorCategoryOfHasIterationOfShape, Idempotents.functorExtension₂_map_app_f, Pretriangulated.Triangle.shiftFunctor_map_hom₁, Join.mapPairEquiv_counitIso, Limits.Fork.π_comp_hom, PreGaloisCategory.endEquivSectionsFibers_π, Paths.liftNatIso_inv_app, Functor.sumIsoExt_hom_app_inl, Functor.isoWhiskerRight_trans, Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app, Limits.CoconeMorphism.w, Limits.colimitUncurryIsoColimitCompColim_ι_ι_inv, Equivalence.rightOp_counitIso_inv_app, WithInitial.liftToInitialUnique_hom_app, Cat.Hom.inv_hom_id_toNatTrans_assoc, RightExactFunctor.whiskeringRight_obj_obj_obj, Functor.PullbackObjObj.mapArrowRight_right, TopologicalSpace.OpenNhds.inclusionMapIso_hom, shiftFunctorAdd'_zero_add, Functor.curryObjCompIso_hom_app_app, Functor.unopOpIso_inv_app, GrothendieckTopology.overMapPullback_comp_id, Functor.uncurryObjFlip_hom_app, Functor.PushoutObjObj.mapArrowRight_id, NatTrans.epi_iff_epi_app, Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_fst, Functor.PullbackObjObj.mapArrowLeft_id, Subobject.inf_le_left, Limits.BinaryBicone.toCone_π_app_right, yoneda_map_app, Limits.HasLimit.lift_isoOfNatIso_hom, Pseudofunctor.DescentData.pullFunctorIso_inv_app_hom, AlgebraicTopology.DoldKan.N₂Γ₂ToKaroubiIso_inv_app, WithInitial.coconeEquiv_functor_obj_pt, MonoidalClosed.ofEquiv_uncurry_def, Sum.functorEquiv_functor_map, Limits.MultispanIndex.toLinearOrderMultispanIso_inv_app, shiftFunctorComm_eq_refl, OverPresheafAux.restrictedYoneda_map, curryingIso_hom_toFunctor_obj_map, instReflectsIsomorphismsMonadFunctorMonadToFunctor, CatCommSq.hInv_iso_inv_app, whiskering_linearCoyoneda, Functor.isDense_iff_nonempty_isPointwiseLeftKanExtension, GrothendieckTopology.overMapPullbackId_inv_app_val_app, Limits.ColimitPresentation.changeDiag_ι, Equivalence.leftOp_unitIso_inv_app, PreGaloisCategory.autEmbedding_injective, Limits.Cone.equiv_inv_pt, PresheafOfModules.pullback_comp_id, shift_shiftFunctorCompIsoId_add_neg_cancel_hom_app, yonedaGrp_obj, Functor.Monoidal.RepresentableBy.tensorObj_homEquiv, Functor.descOfIsLeftKanExtension_fac_assoc, Limits.BinaryBicone.ofColimitCocone_inl, Functor.sectionsFunctor_obj, Subfunctor.Subpresheaf.equalizer.fork_ι, Functor.mapTriangleRotateIso_inv_app_hom₂, Limits.CatCospanTransform.leftIso_inv, Limits.CategoricalPullback.functorEquiv_inverse_obj_obj_iso_inv, Limits.PushoutCocone.mk_ι_app_zero, AlgebraicTopology.DoldKan.identity_N₂, Functor.whiskeringLeft₃ObjObjObj_obj_map_app_app, conjugateEquiv_symm_id, PreGaloisCategory.instContinuousMulAutFunctorFintypeCat, Functor.shiftIso_hom_app_comp, Limits.FormalCoproduct.cosimplicialObjectFunctor_obj_obj, Functor.postcompose₂_obj_obj_obj_map, Functor.Monoidal.commTensorRight_inv_app, Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom_assoc, Limits.CategoricalPullback.CatCommSqOver.sndFunctor_obj, SSet.opFunctorCompOpFunctorIso_inv_app_app, Pretriangulated.shiftFunctorZero_op_inv_app, Limits.MultispanIndex.multicoforkEquivSigmaCofork_functor_obj_ι_app, Idempotents.instIsEquivalenceFunctorKaroubiObjWhiskeringLeftToKaroubi, Adjunction.instIsIsoFunctorCounitOfIsEquivalence_1, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₂, Under.postCongr_inv_app_right, Rep.indCoindNatIso_hom_app, Functor.instIsIsoAppRanCounit, Functor.isColimitCoconeOfIsLeftKanExtension_desc, Join.inclRightCompOpEquivInverse_inv_app_op, Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_inv_app_hom, Localization.liftNatTrans_add, Limits.IsLimit.map_π, GrothendieckTopology.plusFunctorWhiskerRightIso_hom_app, Presheaf.coconeOfRepresentable_pt, Limits.Cocone.whisker_ι, Limits.end_.map_π, SimplicialObject.Truncated.whiskering_obj_obj_obj, cosimplicialSimplicialEquiv_counitIso_hom_app_app, MonoidalCategory.externalProductBifunctor_map_app, sum.inrCompInrCompInverseAssociator_hom_app_down, preservesFiniteColimits_liftToFinset, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₃, GrothendieckTopology.sheafifyMap_sheafifyLift_assoc, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left, Functor.mapTriangleCompIso_inv_app_hom₂, Limits.CategoricalPullback.CatCommSqOver.transform_map_leftUnitor, Functor.RightExtension.postcompose₂_obj_left_map, Functor.pi'CompEval_hom_app, BraidedCategory.Hexagon.functor₁₂₃_obj_obj_obj, Iso.app_inv, Limits.mono_of_isLimit_parallelFamily, GrothendieckTopology.plusCompIso_whiskerRight, Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app, GrothendieckTopology.Point.id_hom, Functor.FullyFaithful.homNatIsoMaxRight_hom_app_down, Functor.leftOpRightOpEquiv_counitIso_inv_app_app, Limits.IsLimit.conePointUniqueUpToIso_hom_comp_assoc, Adjunction.compCoyonedaIso_inv_app_app, Endofunctor.Adjunction.algebraCoalgebraEquiv_unitIso_hom_app_f, Subfunctor.Subpresheaf.equalizer.condition, IsPullback.of_isLimit_binaryFan_of_isTerminal, Grothendieck.map_comp_eq, Adjunction.LeftAdjointCommShift.iso_inv_app_assoc, Monad.algebraFunctorOfMonadHomId_inv_app_f, IsSifted.colim_preservesBinaryProducts_of_isSifted, bifunctorComp₁₂FunctorMap_app_app_app_app, Over.forgetMapTerminal_hom_app, DerivedCategory.instCommShiftHomologicalComplexIntUpHomFunctorQuotientCompQhIso, sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_inv_app_app, Limits.IsIndObject.isFiltered, Adjunction.leftAdjointUniq_refl, Functor.fullyFaithfulCancelRight_inv_app, ParametrizedAdjunction.whiskerLeft_map_counit, Limits.CategoricalPullback.functorEquiv_inverse_obj_map_snd, GrothendieckTopology.preservesLimitsOfShape_plusFunctor, OverPresheafAux.restrictedYoneda_obj, NatTrans.CommShift.leftUnitor, BraidedCategory.Hexagon.functor₂₃₁_map_app_app, GrothendieckTopology.ι_plusCompIso_hom_assoc, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_inv_app_hom_coe, Functor.mapTriangle_obj, Abelian.Ext.preadditiveYoneda_homologySequenceδ_singleTriangle_apply, LightCondensed.isoFinYoneda_inv_app, LocalizerMorphism.rightDerivedFunctorComparison_fac_app_assoc, BraidedCategory.ofBifunctor.Forward.secondMap₃_app_app_app, Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_hom_app, Comonad.ForgetCreatesLimits'.liftedCone_π_app_f, Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_one, Functor.RightExtension.postcompose₂_obj_right, CatCommSq.hId_iso_hom_app, linearYoneda_obj_map, Limits.coend.map_id, smoothSheafCommRing.ι_evalHom_apply, Functor.LeftExtension.postcomp₁_map_right_app, TopCat.uliftFunctorCompForgetIso_hom_app, NatIso.unop_rightUnitor, NatTrans.unop_comp_assoc, Functor.IsEventuallyConstantFrom.isIso_ι_of_isColimit', PresheafOfModules.homEquivOfIsLocallyBijective_symm_apply, Limits.PullbackCone.π_app_right, piEquivalenceFunctorDiscrete_inverse_obj, AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_hom_app, SingleObj.mapHom_id, Action.functorCategoryEquivalence_inverse, SingleFunctors.shiftIso_add', BraidedCategory.Hexagon.functor₂₁₃'_map_app_app, Limits.MultispanIndex.toLinearOrderMultispanIso_hom_app, Functor.commShiftOp_iso_eq, ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left, simplicialCosimplicialEquiv_counitIso_inv_app_app, Limits.PushoutCocone.unop_π_app, EnrichedFunctor.forgetComp_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_inv_app, comp_evaluation, GrothendieckTopology.plusMap_id, MonoidalCategory.DayFunctor.equiv_unitIso_hom_app, MonoidalCategory.tensorLeftTensor_hom_app, Subfunctor.range_le_equalizer_iff, Pretriangulated.shiftFunctorCompIsoId_op_inv_app, Limits.diagramIsoParallelFamily_inv_app, Presheaf.functorToRepresentables_map, Functor.mapGrpIdIso_hom_app_hom_hom, whiskeringLeft_preservesLimitsOfShape, Limits.functorCategoryHasLimitsOfSize, Linear.smulOfRingMorphism_smul_eq', NatIso.pi'_inv, simplicialCosimplicialEquiv_inverse_map, yonedaMonObjIsoOfRepresentableBy_hom_app_hom_apply, Limits.IndObjectPresentation.extend_ι_app_app, Join.mapWhiskerRight_leftUnitor_hom, Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv, Limits.Fork.unop_ι_app_zero, ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_inv_app, Limits.isClosedUnderLimitsOfShape_isIndObject_walkingParallelPair, Functor.inlCompSum'_inv_app, Limits.Cocone.ofCotrident_ι, Idempotents.KaroubiHomologicalComplexEquivalence.unitIso_inv_app_f_f, CochainComplex.mappingCone.homologySequenceδ_triangleh, Limits.SequentialProduct.cone_π_app_comp_Pi_π_pos_assoc, Limits.opCompYonedaSectionsEquiv_symm_apply_coe, Cat.Hom₂.eqToHom_toNatTrans, Yoneda.naturality, prodFunctorToFunctorProd_map, Functor.curry_obj_obj_obj, ObjectProperty.topEquivalence_counitIso, NatTrans.instCommShiftPullbackShiftHomFunctorNatIsoComp, GrothendieckTopology.yoneda_map_val, Functor.closedIhom_obj_map, SingleFunctors.Hom.comp_hom, Discrete.natIsoFunctor_hom_app, MonoidalCategory.externalProductCompDiagIso_hom_app_app, Limits.yonedaCompLimIsoCocones_inv_app, coyonedaEvaluation_map_down, SSet.Truncated.sk_coreflective, Limits.mapPairIso_inv_app, Limits.LimitPresentation.w, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_isModule, StructuredArrow.commaMapEquivalenceCounitIso_hom_app_left_right, Functor.shiftIso_zero_inv_app, Iso.isoInverseComp_inv_app, Limits.CategoricalPullback.CatCommSqOver.transformObjComp_hom_app_fst_app, PreGaloisCategory.toAutMulEquiv_isHomeomorph, Functor.Monoidal.coreMonoidalTransport_εIso_inv, Action.FunctorCategoryEquivalence.counitIso_inv_app_app, Profinite.Extend.cone_π_app, CompHausLike.LocallyConstant.adjunction_counit, IsGrothendieckAbelian.IsPresentable.injectivity₀.g_app, Functor.commShift₂_comm, Pretriangulated.Triangle.shiftFunctor_obj, δ_naturalityₗ_assoc, Comma.mapLeftIso_functor_map_left, Functor.OplaxMonoidal.ofBifunctor.bottomMapₗ_app, Iso.map_inv_hom_id_app_assoc, instFaithfulGrpFunctorOppositeGrpCatYonedaGrp, Functor.LaxMonoidal.ofBifunctor.secondMap₁_app_app_app, Functor.IsCoverDense.restrictHomEquivHom_naturality_left_symm_assoc, Square.mapFunctor_map, Functor.Fiber.fiberInclusionCompIsoConst_inv_app, Functor.whiskeringRight_obj_id, Limits.KernelFork.condition_assoc, Limits.Cocone.unop_π, AlgebraicTopology.DoldKan.instIsIsoFunctorSimplicialObjectKaroubiNatTrans, MonoidalCategory.associatorNatIso_hom_app, Action.functorCategoryEquivalence_unitIso, Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_map_app_fst, GrothendieckTopology.whiskerRight_toSheafify_sheafifyCompIso_hom_assoc, MorphismProperty.FunctorialFactorizationData.fac, Comma.mapLeftIso_unitIso_inv_app_left, Functor.IsLocalization.instDiscreteObjWhiskeringRightFunctorCategoryOfFiniteOfContainsIdentities, Functor.pentagon, Presheaf.isSeparating, Limits.reflexivePair.mkNatIso_hom_app, Grothendieck.grothendieckTypeToCat_counitIso_inv_app_coe, sheafificationNatIso_inv_app_val, Limits.colimitCoyonedaHomIsoLimit'_π_apply, Endofunctor.Coalgebra.equivOfNatIso_inverse, NatIso.cancel_natIso_inv_right_assoc, evaluationRightAdjoint_obj_map, Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, Action.leftUnitor_inv_hom, η_naturality_assoc, Functor.leftExtensionEquivalenceOfIso₁_functor_obj_left, endofunctorMonoidalCategory_tensorObj_obj, WithTerminal.coneEquiv_inverse_obj_π_app_left, yonedaMonObjIsoOfRepresentableBy_inv_app_hom_apply, Functor.cones_map_app, Pretriangulated.invRotCompRot_inv_app_hom₃, MonObj.mopEquivCompForgetIso_hom_app_unmop, Monoidal.CommMonFunctorCategoryEquivalence.counitIso_inv_app_app_hom_hom, Functor.instIsIsoAppUnitLanAdjunctionOfHasPointwiseLeftKanExtension, ComonadIso.toNatIso_inv, μ_δ_app_assoc, Cat.Hom.isoMk_hom, Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_inv_app_snd_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_left, Functor.IsRightKanExtension.nonempty_isUniversal, Monoidal.associator_hom_app, Localization.Construction.natTransExtension_hcomp, Join.isoMkFunctor_hom_app, MonoidalCategory.DayConvolution.corepresentableBy₂_homEquiv, Equivalence.leftOp_counitIso_inv_app, TransfiniteCompositionOfShape.fac_assoc, η_ε_app_assoc, NatTrans.unop_whiskerLeft_assoc, conjugateEquiv_symm_comp_assoc, Limits.coyonedaCompLimIsoCones_inv_app, Subfunctor.ofSection_eq_range, Limits.Cofork.ofCocone_ι, GrothendieckTopology.MayerVietorisSquare.shortComplex_X₁, MorphismProperty.Over.pullbackComp_hom_app_left, Localization.SmallHom.equiv_equiv_symm, Functor.CommShift.isoZero_hom_app, Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.isIso_hom_app, Limits.walkingParallelPairOpEquiv_counitIso_inv_app_op_zero, Presheaf.instIsLeftKanExtensionFunctorOppositeTypeLanOpHomCompULiftYonedaIsoULiftYonedaCompLan, Limits.CategoricalPullback.functorEquiv_functor_obj_fst_map, LocalizerMorphism.commShift_iso_hom_app, Cat.Hom.toNatIso_hom, Limits.inl_comp_pushoutObjIso_hom, Comma.mapRightIso_counitIso_inv_app_left, AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_hom_app, Functor.whiskeringLeft_obj_id, Limits.multispanIndexCoend_right, Limits.IsLimit.conePointsIsoOfNatIso_hom, Abelian.LeftResolution.karoubi.π_app_toKaroubi_obj, Presheaf.compULiftYonedaIsoULiftYonedaCompLan.natTrans_app_uliftYoneda_obj, Limits.MonoCoprod.binaryCofan_inl, Bicategory.associatorNatIsoLeft_inv_app, Limits.pushoutCoconeEquivBinaryCofan_inverse_obj, ParametrizedAdjunction.homEquiv_symm_naturality_one, SimplicialObject.Truncated.whiskering_map_app_app, Condensed.discrete_map, Functor.rightDerivedNatIso_inv, Limits.CatCospanTransformMorphism.right_coherence_assoc, Limits.limitConstTerminal_inv_π_assoc, StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_right, Limits.Fork.isoForkOfι_hom_hom, GradedObject.mapBifunctorObjObjSingle₀Iso_hom, Functor.Monoidal.whiskerRight_app_fst_assoc, ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₂, Limits.colimitObjIsoColimitCompEvaluation_ι_inv_assoc, Limits.Cocones.precomposeEquivalence_functor, Functor.RightExtension.coneAt_pt, Comma.mapRightEq_hom_app_right, Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_inv_app_snd_app, BraidedCategory.ofBifunctor.Reverse.secondMap₁_app_app_app, yonedaEquiv_apply, WithInitial.coconeEquiv_inverse_obj_pt_right, Monad.beckCoequalizer_desc, coprodMonad_μ_app, Functor.currying_inverse_obj_obj_obj, ChosenPullbacksAlong.unit_pullbackComp_hom_assoc, Limits.IndObjectPresentation.instFinalICostructuredArrowFunctorOppositeTypeYonedaToCostructuredArrow, SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_inv_app, Functor.opInv_obj, Functor.PullbackObjObj.π_fst, Functor.LeftExtension.postcomp₁_obj_left, Comma.mapRightIso_counitIso_inv_app_right, Enriched.FunctorCategory.isLimitConeFunctorEnrichedHom.fac, Functor.Monoidal.transport_μ, Limits.Fork.IsLimit.mono, instIsIsoFunctorOppositeValAppSheafCounitSheafificationAdjunction, sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_inv_app_app, instIsLeftKanExtensionSimplexCategoryTopCatSSetToTopInvFunctorToTopSimplex, IsFiltered.iff_nonempty_limit, Limits.pushoutCoconeEquivBinaryCofan_unitIso, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_hom_app, FreeGroupoid.functorEquiv_apply, sum.inlCompInrCompInverseAssociator_inv_app_down_down, sheafificationNatIso_hom_app_val, TopologicalSpace.OpenNhds.inclusionMapIso_inv, Functor.commShiftIso_comp_hom_app, instAdditiveObjFunctorAdditiveFunctor_1, Comma.mapLeftEq_hom_app_left, Functor.coreId_hom_app_iso_hom, ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₂_app, Monad.monadMonEquiv_counitIso_hom_app_hom, Limits.Cone.fromCostructuredArrow_map_hom, MonoOver.mapIso_unitIso, exactFunctor_le_additiveFunctor, Functor.equivCatHom_symm_apply, Limits.Cone.toCostructuredArrow_obj, PreGaloisCategory.instEssSurjContActionFintypeCatHomCarrierAutFunctorFunctorToContAction, Functor.Monoidal.tensorObj_map, constantCommuteCompose_hom_app_val, CatCenter.smul_iso_inv_eq', WithTerminal.mapComp_hom_app, Limits.coconeOfCoconeCurry_pt, Equivalence.congrFullSubcategory_counitIso, Functor.mapTriangleCommShiftIso_inv_app_hom₁, MonoidalCategory.curriedAssociatorNatIso_hom_app_app_app, Limits.colimitObjIsoColimitCompEvaluation_inv_colimit_map_assoc, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right, CondensedSet.instIsIsoFunctorCompactlyGeneratedCounitCompactlyGeneratedAdjunction, Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_fac_app_assoc, Limits.colimit.homIso_hom, MonadHom.comp_toNatTrans, Limits.WidePullbackShape.functorExt_hom_app, Functor.reflective', Functor.PullbackObjObj.π_iso_of_iso_left_inv, Functor.flipping_functor_map_app_app, Functor.leftDerivedNatIso_inv, Functor.Monoidal.tensorObjComp_hom_app, Join.mapWhiskerLeft_whiskerRight, Endofunctor.Algebra.functorOfNatTransId_inv_app_f, GrothendieckTopology.preservesLimitsOfShape_diagramFunctor, Functor.flip₂₃_obj_obj_map, MonoidalCategory.instFaithfulFunctorTensoringRight, GradedObject.mapTrifunctor_map_app_app, Monad.algebraFunctorOfMonadHomId_hom_app_f, Functor.IsEventuallyConstantTo.cone_π_app, commGroupAddCommGroupEquivalence_counitIso, Functor.IsCoverDense.isoOver_hom_app, IsGrothendieckAbelian.IsPresentable.surjectivity.F_map, AlgebraicGeometry.Scheme.SpecΓIdentity_hom_app, Functor.currying₃_unitIso_hom_app_app_app_app, Comma.coneOfPreserves_π_app_right, Functor.FullyFaithful.compUliftCoyonedaCompWhiskeringLeft_hom_app_app_down, Limits.limitIsoLimitCurryCompLim_hom_π_π_assoc, Adjunction.instIsIsoFunctorUnitOfIsEquivalence, Limits.prodComparisonNatIso_hom, Idempotents.karoubiUniversal_functor_eq, Limits.limitObjIsoLimitCompEvaluation_inv_π_app, Coyoneda.objOpOp_inv_app, GradedObject.comapEquiv_counitIso, toOverPullbackIsoToOver_inv_app_left, Functor.opComp_inv_app, Idempotents.functorExtension_map_app, partialFunEquivPointed_unitIso_inv_app, Functor.curry_obj_uncurry_obj, WithInitial.ofCommaObject_obj, Limits.CatCospanTransform.inv_left, FunctorToTypes.binaryProductEquiv_apply, Functor.LeftExtension.precomp_map_right, WithTerminal.equivComma_inverse_obj_obj, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_π_app_walkingParallelPair_one, SSet.opFunctorCompOpFunctorIso_hom_app_app, sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_app_app, Limits.coprodComparisonNatTrans_app, Limits.CategoricalPullback.CatCommSqOver.fstFunctor_obj, FinitaryExtensive.mono_ι, instIsClosedUnderLimitsOfShapeFunctorOppositeTypeIsIndObjectDiscreteOfHasLimitsOfShape, Functor.LeftExtension.precomp₂_obj_left, Limits.CatCospanTransform.category_id_left, HasExactLimitsOfShape.preservesFiniteColimits, Limits.colimitCurrySwapCompColimIsoColimitCurryCompColim_ι_ι_hom, FreeGroupoid.mapComp_hom_app, Equivalence.instPreservesFiniteLimitsFunctorOppositeSheafTransportAndSheafify, FinitaryExtensive.isPullback_initial_to_binaryCofan, BraidedCategory.curriedBraidingNatIso_inv_app_app, Functor.RightExtension.coneAt_π_app, Action.whiskerRight_hom, SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_hom_app, ModuleCat.restrictScalarsComp'_inv_app, Comma.mapRightIso_functor_map_left, μ_naturality₂_assoc, TwoSquare.guitartExact_id', Comma.mapLeftIso_counitIso_inv_app_right, WithTerminal.equivComma_counitIso_hom_app_right, Functor.prod'CompSnd_inv_app, Idempotents.KaroubiKaroubi.counitIso_inv_app_f_f, Presheaf.freeYonedaHomEquiv_comp, NatTrans.epi_of_epi_app, PresheafOfModules.free_map_app, MonoidalCategory.externalProductBifunctorCurried_obj_obj_obj_map, ShortComplex.functorEquivalence_counitIso, Limits.lim_map, Pi.equivalenceOfEquiv_unitIso, ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd_assoc, CochainComplex.shiftShortComplexFunctorIso_add'_hom_app, Limits.IsColimit.homIso_hom, WithInitial.opEquiv_counitIso_hom_app, Adjunction.id_counit, Pretriangulated.shiftFunctorAdd'_op_hom_app, NatIso.ofComponents_inv_app, prodComonad_δ_app, WithInitial.isColimitEquiv_symm_apply_desc, uliftCoyonedaIsoCoyoneda_inv_app_app_down, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_hom_app_hom, Quotient.comp_natTransLift_assoc, GrothendieckTopology.sheafificationWhiskerRightIso_hom_app, Quotient.lift.isLift_hom, CostructuredArrow.mapNatIso_inverse_map_right, HomologicalComplex.natIsoSc'_inv_app_τ₂, Limits.Cocone.underPost_ι_app, DerivedCategory.singleFunctorsPostcompQIso_inv_hom, Limits.multicospanIndexEnd_snd, functorProdFunctorEquiv_inverse, GrothendieckTopology.diagramCompIso_hom_ι, CommMon.EquivLaxBraidedFunctorPUnit.unitIso_hom_app_hom_hom_app, Limits.colimitIsoSwapCompColim_hom_app, Localization.HasProductsOfShapeAux.adj_counit_app, Monad.algebraEquivOfIsoMonads_unitIso, Equivalence.sheafCongrPreregular_unitIso_hom_app_val_app, Limits.coneOfDiagramTerminal_π_app, Functor.mapTriangleCompIso_hom_app_hom₂, Subfunctor.Subpresheaf.preimage_id, Functor.RightExtension.postcomp₁_obj_left_map, Adjunction.compYonedaIso_hom_app_app, Pi.equivalenceOfEquiv_counitIso, PresheafOfModules.freeYonedaEquiv_symm_app, CommRingCat.coyoneda_map_app, Functor.currying_counitIso_hom_app_app, zero_map, Functor.mapContActionCongr_inv, MorphismProperty.Over.mapCongr_inv_app_left, MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.associator_hom_unit_unit, Limits.Cotrident.π_eq_app_one, Limits.CategoricalPullback.CatCommSqOver.w_app, Grothendieck.grothendieckTypeToCat_unitIso_hom_app_fiber, Limits.CatCospanTransform.baseIso_inv, Functor.RightExtension.postcomp₁_map_right, CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompCoyoneda, GrothendieckTopology.Point.Hom.presheafFiber_comp, Limits.colimit.ι_map, Functor.prod'CompSnd_hom_app, Limits.cospanIsoMk_hom_app, FunctorToTypes.binaryProductCone_pt_obj, MonoidalCategory.endofunctorMonoidalCategory.evaluationRightAction_actionUnitIso, Iso.isoInverseComp_hom_app, Over.opEquivOpUnder_unitIso, Functor.mapActionComp_hom, AdditiveFunctor.ofExact_obj_fst, MonoidalCategory.MonoidalRightAction.curriedActionActionOfMonoidalFunctorToEndofunctorIso_inv_app_app, Limits.constCone_pt, Profinite.NobelingProof.spanFunctorIsoIndexFunctor_hom_app_hom_hom_apply_coe, Limits.piObjIso_hom_comp_π, Action.FunctorCategoryEquivalence.functor_obj_obj, Functor.LeibnizAdjunction.adj_unit_app_left, Pretriangulated.Opposite.OpOpCommShift.iso_inv_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_map_app, Over.iteratedSliceForwardIsoPost_inv_app, Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, Functor.whiskeringLeft₃Obj_map, IsSifted.factorization_prodComparison_colim, NatIso.naturality_1, NatIso.inv_map_inv_app, MorphismProperty.FunctorialFactorizationData.functorCategory.Z_map_app, Limits.Cone.whisker_π, Comma.mapRightIso_inverse_map_right, Equivalence.core_unitIso_hom_app_iso_inv, DifferentialObject.shiftZero_hom_app_f, Functor.ranCompLimIso_inv_app, PreGaloisCategory.instTotallyDisconnectedSpaceAutFunctorFintypeCat, Limits.colimitIsoColimitCurryCompColim_ι_hom_assoc, Limits.Cocones.whiskeringEquivalence_unitIso, Sheaf.comp_val, Functor.ShiftSequence.induced.isoZero_hom_app_obj, Sum.functorEquiv_unit_app_app_inr, Limits.PreservesColimit₂.map_ι_comp_isoColimitUncurryWhiskeringLeft₂_inv_assoc, Limits.colimitCurrySwapCompColimIsoColimitCurryCompColim_ι_ι_inv, Limits.Cocone.toCostructuredArrow_map, Limits.hasColimitCompEvaluation, Functor.Fiber.fiberInclusion_comp_eq_const, WithTerminal.equivComma_functor_obj_left_map, Functor.whiskeringLeft₃_map_app_app_app_app_app_app, SimplexCategory.revEquivalence_unitIso, MonoidalCategory.DayFunctor.id_natTrans, NatTrans.vcomp_app', LightCondensed.discrete_map, Adjunction.Triple.rightToLeft_eq_units, CostructuredArrow.mapNatIso_unitIso_inv_app_left, HasShift.Induced.zero_inv_app_obj, Limits.Types.pUnitCocone_ι_app, NatTrans.instCommShiftPullbackShiftHomFunctorNatIsoId, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_single, Functor.curry₃_obj_obj_map_app, WithTerminal.mkCommaMorphism_left_app, shift_shift_neg', SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_quotMk, Limits.parallelPairIsoMk_inv_app, Limits.IsColimit.mono_ι_app_of_isFiltered, Functor.LaxMonoidal.ofBifunctor.firstMap₃_app_app_app, NatTrans.CommShift.shift_comm, evaluationAdjunctionLeft_unit_app_app, MonoidalCategory.MonoidalLeftAction.actionAssocNatIso_hom_app_app_app, Limits.colimMap_eq, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_inv_app, Sum.functorEquiv_unitIso_inv_app_app_inl, LocalizerMorphism.commShift_iso_inv_app, Sheaf.isPullback_square_op_map_yoneda_presheafToSheaf_yoneda_iff, GrothendieckTopology.Point.toPresheafFiber_naturality_assoc, NatIso.op_trans, MonoOver.mapIso_counitIso, HasShift.Induced.add_hom_app_obj, ComonadIso.toNatIso_hom, Functor.rightKanExtensionCompIsoOfPreserves_hom_fac_app, TwoSquare.equivalenceJ_unitIso, Limits.coend.condition, IsSifted.instIsIsoObjFunctorTypeColimTensorObjProdComparison, Pi.sum_obj_obj, sheafToPresheaf_μ, NatTrans.mapHomologicalComplex_id, GradedObject.mapTrifunctorObj_obj_obj, HomologicalComplex.asFunctor_obj_X, ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₁_app, GrothendieckTopology.toSheafify_sheafifyLift_assoc, Functor.whiskeringLeft_obj_comp, CatCommSq.hComp_iso_hom_app, pullbackShiftFunctorZero_inv_app, Functor.mapTriangleRotateIso_inv_app_hom₁, Under.liftCone_pt, GrothendieckTopology.isIso_toSheafify, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompPointIso_hom_app, NatTrans.rightOp_comp, Cat.Hom.inv_hom_id_toNatTrans, Discrete.compNatIsoDiscrete_hom_app, uliftCoyonedaEquiv_uliftCoyoneda_map, Functor.leftKanExtensionCompIsoOfPreserves_hom_fac_app, Functor.RepresentableBy.coyoneda_homEquiv, Square.flipEquivalence_unitIso, CostructuredArrow.mapIso_unitIso_hom_app_left, TwoSquare.equivNatTrans_apply, CatCommSq.iso_inv_naturality, Functor.PullbackObjObj.mapArrowLeft_comp, coyonedaEquiv_comp, uliftYonedaEquiv_symm_apply_app, flippingIso_inv_toFunctor_obj_obj_obj, Functor.mapProjectiveResolution_π, Limits.Cocones.whiskeringEquivalence_inverse, Adjunction.localization_unit_app, WithTerminal.equivComma_functor_obj_right, Pretriangulated.TriangleOpEquivalence.functor_map_hom₂, NatTrans.app_naturality, Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π, ParametrizedAdjunction.arrowHomEquiv_apply_left, Adjunction.colim_preservesColimits, Limits.closedUnderLimitsOfShape_walkingParallelPair_isIndObject, HomologicalComplex.complexOfFunctorsToFunctorToComplex_obj, Limits.PushoutCocone.isoMk_inv_hom, Limits.colimitYonedaHomIsoLimit'_π_apply, Prod.symmetry_hom_app, WithInitial.liftFromUnderComp_inv_app, sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_hom_app_app_val, NatTrans.Equifibered.comp, preservesColimitNatIso_inv_app, conjugateEquiv_symm_apply_app, Presheaf.isLocallyInjective_presheafToSheaf_map_iff, MonoidalCategory.MonoidalLeftAction.curriedActionActionOfMonoidalFunctorToEndofunctorMopIso_hom_app_unmop_app, bifunctorComp₂₃_obj, Functor.IsRepresentedBy.of_natIso, Comma.mapRightIso_unitIso_inv_app_right, Join.mapWhiskerLeft_whiskerLeft, Limits.Cone.toStructuredArrowCompProj_inv_app, Limits.parallelPairOpIso_inv_app_one, Functor.instFullOppositeTypeRestrictedULiftYonedaOfIsDense, ε_η_app_assoc, Limits.PullbackCone.mk_π_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_right_unitality_assoc, Join.inrCompFromSum_hom_app, CartesianMonoidalCategory.prodComparisonBifunctorNatIso_inv, Functor.PreservesRightKanExtension.preserves, Functor.flipping_inverse_obj_obj_map, CommMonCat.coyonedaType_obj_map, OppositeShift.adjunction_unit, plusPlusSheaf_obj_val, ε_naturality_assoc, limitCompWhiskeringRightIsoLimitComp_hom_whiskerRight_π_assoc, ModuleCat.restrictScalarsComp'_hom_app, MonoidalCategory.DayFunctor.η_comp_tensorDec, LightProfinite.Extend.cocone_ι_app, Comma.toPUnitIdEquiv_counitIso_hom_app, Functor.sheafAdjunctionCocontinuous_counit_app_val, MonoidalCategory.prodCompExternalProduct_inv_app, Equivalence.mkHom_id_inverse, Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.functorToInterchangeIso_inv_app_app, Functor.LeftExtension.precomp_obj_hom_app, FreeGroupoid.mapId_hom_app, Rep.homEquiv_apply_hom, GrothendieckTopology.MayerVietorisSquare.biprodAddEquiv_symm_biprodIsoProd_hom_toBiprod_apply, Limits.IsColimit.ι_map, WithTerminal.ofCommaObject_obj, Functor.mapMatComp_hom_app, Limits.colimitHomIsoLimitYoneda'_hom_comp_π_assoc, Limits.Types.binaryCoproductCocone_ι_app, Sigma.mapComp_hom_app, conjugateEquiv_apply_app, BinaryCofan.isVanKampen_iff, Functor.LeibnizAdjunction.adj_counit_app_left, CatCenter.mul_app, Limits.CategoricalPullback.functorEquiv_unitIso_inv_app_app_fst, TransfiniteCompositionOfShape.ofOrderIso_incl, Functor.isoWhiskerLeft_trans_isoWhiskerRight, Idempotents.app_p_comp, toSheafify_sheafifyLift_assoc, Limits.MultispanIndex.multicoforkEquivSigmaCofork_counitIso_hom_app_hom, Limits.compYonedaSectionsEquiv_apply_app, Functor.isRightDerivedFunctor_iff_of_inverts, Endofunctor.Algebra.functorOfNatTransComp_hom_app_f, Comma.mapSnd_inv_app, GradedObject.mapBifunctor_obj_obj, MorphismProperty.functorCategory_isomorphisms, Condensed.lanPresheafExt_inv, Limits.IsLimit.conePointsIsoOfNatIso_inv_comp, HomologicalComplex.forgetEval_hom_app, Functor.rightKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, Functor.compConstIso_hom_app_app, Limits.CatCospanTransformMorphism.left_coherence_app_assoc, NatIso.op_isoWhiskerLeft, Preadditive.commGrpEquivalence_unitIso_inv_app, commBialgCatEquivComonCommAlgCat_unitIso_hom_app, Functor.coreComp_hom_app_iso_hom, CatCommSq.vId_iso_hom_app, Limits.CategoricalPullback.functorEquiv_counitIso_inv_app_snd_app, evaluationRightAdjoint_map_app, Rep.coindFunctorIso_hom_app_hom_hom_apply_hom_hom_apply, Functor.imageSieve_eq_imageSieve, WithTerminal.opEquiv_counitIso_inv_app, frobeniusMorphism_mate, Idempotents.karoubiUniversal₁_functor, Limits.Multicofork.ofSigmaCofork_ι_app_right', Localization.liftNatTrans_zero, Monad.monadToMon_obj, Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_fst, toOverIsoToOverUnit_inv_app_left, MonoidalCategory.DayFunctor.equiv_inverse_obj_functor, Cat.Hom.isoMk_inv, GrothendieckTopology.preserveFiniteLimits_plusFunctor, Over.ConstructProducts.conesEquivCounitIso_inv_app_hom_left, Codiscrete.natIsoFunctor_hom_app, Functor.flipping_counitIso_inv_app_app_app, Pretriangulated.commShiftIso_opOp_inv_app, Under.mapCongr_inv_app, Presheaf.compULiftYonedaIsoULiftYonedaCompLan.presheafHom_naturality, Equivalence.congrLeft_counitIso_inv_app, Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_snd, Localization.Lifting.compLeft_iso, Over.conePost_obj_π_app, Functor.instFaithfulProdCurry, Functor.initial_const_initial, Limits.multicospanIndexEnd_right, Limits.Cocone.w_assoc, BraidedCategory.Hexagon.functor₂₃₁'_map_app_app, Adjunction.conjugateEquiv_leftAdjointCompIso_inv, Functor.isoWhiskerLeft_twice, AlgebraicGeometry.Scheme.Modules.instIsIsoFunctorCounitRestrictAdjunction, limitCompWhiskeringRightIsoLimitComp_inv_π_assoc, TwoSquare.GuitartExact.vComp_iff_of_equivalences, Functor.curryObjProdComp_hom_app_app, RightExactFunctor.whiskeringLeft_map_app, AlgebraicGeometry.Scheme.Modules.pushforwardComp_inv_app_app, GrothendieckTopology.preservesLimitsOfShape_sheafification, oppositeShiftFunctorAdd_inv_app, Idempotents.app_p_comm, Functor.associator_hom_app, Functor.shiftIso_zero_hom_app, Presheaf.restrictedULiftYoneda_obj_map, Limits.inr_comp_pushoutObjIso_hom_assoc, ModuleCat.HasLimit.productLimitCone_cone_π, MonoidalClosedFunctor.comparison_iso, CommRingCat.coyoneda_obj_obj_carrier, Functor.rightOpComp_hom_app, Functor.rightAdjointObjIsDefined_iff, obj_zero_map_μ_app_assoc, Functor.comp_flip_uncurry_eq, BraidedCategory.Hexagon.functor₃₁₂_map_app_app, NatTrans.instIsClosedUnderLimitsOfShapeOverFunctorEquifiberedHomDiscretePUnitOfHasCoproductsOfShapeHom, Functor.isoShift_inv_naturality_assoc, ModuleCat.HasColimit.colimitCocone_ι_app, ExactFunctor.forget_obj, LeftExactFunctor.forget_obj, Presheaf.comp_isLocallySurjective_iff, Limits.HasColimit.isoOfEquivalence_hom_π, Limits.CokernelCofork.π_mapOfIsColimit, Equivalence.inverseFunctor_obj, Functor.mapContActionComp_inv, AlgebraicTopology.DoldKan.instIsIsoFunctorKaroubiSimplicialObjectNatTrans, Limits.Cofork.unop_π_app_one, AddCommGrpCat.Colimits.colimitCocone_ι_app, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_obj_obj, PresheafOfModules.toPresheaf_map_toSheafify, Functor.mapGrpFunctor_obj, Functor.rightOpLeftOpIso_hom_app, Discrete.monoidalFunctorComp_isMonoidal, Functor.rightDerived_fac_assoc, TopCat.sigmaCofan_ι_app, Functor.uncurry_obj_curry_obj, Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_fst_map, HomologicalComplex.natIsoSc'_inv_app_τ₃, Subfunctor.Subpresheaf.ofSection_eq_range', AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap, Preadditive.commGrpEquivalence_unitIso_hom_app, ParametrizedAdjunction.arrowHomEquiv_apply_right_snd, Comonad.ForgetCreatesColimits'.newCocone_ι_app, Functor.LaxMonoidal.ofBifunctor.bottomMapₗ_app, MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app, CatCenter.smul_iso_inv_eq'_assoc, CommRingCat.coyoneda_obj_map, yonedaFunctor_reflectsLimits, Functor.postcompose₃_obj_obj_obj_map_app, Limits.piConst_map_app, Functor.mapMonCompIso_hom_app_hom, BraidedCategory.Hexagon.functor₁₂₃'_obj_map_app, isIso_toSheafify, Limits.Cofork.IsColimit.epi, ParametrizedAdjunction.arrowHomEquiv_symm_apply_right, Limits.Cocone.fromCostructuredArrow_ι_app, Grothendieck.grothendieckTypeToCat_unitIso_inv_app_fiber, Functor.LeftExtension.coconeAtWhiskerRightIso_inv_hom, Limits.Cone.fromStructuredArrow_π_app, Equivalence.symm_unitIso, Cat.exp_obj, WithTerminal.commaFromOver_map_left, Limits.pullbackConeOfLeftIso_π_app_right, Adjunction.mapCommMon_unit, Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality_assoc, MonoidalCategory.MonoidalRightAction.curriedAction_map_app, WithInitial.equivComma_functor_obj_right_map, Functor.RightExtension.precomp_map_left, Limits.FormalCoproduct.cochainComplexFunctor_map_f, μ_naturalityᵣ_assoc, Join.mapIsoWhiskerLeft_hom, GrothendieckTopology.MayerVietorisSquare.isPushout, Limits.Cocone.toCostructuredArrowCompProj_hom_app, Functor.LeftExtension.IsPointwiseLeftKanExtension.isLeftKanExtension, Limits.pullbackObjIso_inv_comp_fst_assoc, Iso.hom_inv_id_app_app_assoc, Functor.functorialityCompPostcompose_hom_app_hom, Profinite.exists_locallyConstant_finite_aux, preservesFiniteLimits_liftToFinset, Equivalence.mapHomologicalComplex_unitIso, Limits.Cone.fromCostructuredArrow_obj_π, NatTrans.epi_iff_epi_app', Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app_assoc, FunctorToTypes.binaryCoproductEquiv_apply, Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_mul_app, Limits.instHasFiniteLimitsFunctor, WithInitial.equivComma_counitIso_hom_app_right_app, MonoidalCategory.DayConvolutionInternalHom.left_triangle_components, MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_μ_unmop_app, Functor.FullyFaithful.homNatIso_inv_app_down, MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionUnitIso_inv, Functor.isIso_whiskerRight, Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_app, Functor.ranCounit_app_whiskerLeft_ranAdjunction_unit_app_assoc, Limits.HasColimit.isoOfNatIso_ι_inv, Over.mapCongr_inv_app_left, IsCofiltered.iff_nonempty_limit, FunctorToTypes.instHasStrongEpiMonoFactorisationsFunctorType, Limits.IsLimit.conePointUniqueUpToIso_hom_comp, Limits.Types.FilteredColimit.colimit_eq_iff_aux, sheafificationIso_inv_val, Limits.CategoricalPullback.CatCommSqOver.fstFunctor_map, HomologicalComplex.natIsoSc'_hom_app_τ₃, RightExactFunctor.whiskeringRight_map_app, BraidedCategory.Hexagon.functor₁₂₃'_obj_obj_obj, Cat.freeMapIdIso_hom_app, Functor.curryingFlipEquiv_symm_apply_map_app, Localization.comp_liftNatTrans, Functor.CommShift₂.commShift_flip_map, Functor.Final.extendCocone_obj_ι_app, Idempotents.instIsEquivalenceFunctorKaroubiFunctorExtension, ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom, uliftCoyonedaEquiv_symm_apply_app, Limits.instIsRightAdjointFunctorLim, NatIso.isIso_of_isIso_app, Functor.opId_hom_app, Core.forgetFunctorToCore_obj_obj, Under.lift_obj, Limits.PreservesColimit₂.map_ι_comp_isoColimitUncurryWhiskeringLeft₂_inv, Limits.CategoricalPullback.CatCommSqOver.transformObjId_hom_app_fst_app, HasExactColimitsOfShape.preservesFiniteLimits, Over.mapCongr_hom_app_left, Coyoneda.ULiftCoyoneda.instFullOppositeFunctorTypeUliftCoyoneda, ProdPreservesConnectedLimits.forgetCone_π, Functor.shift_map_op_assoc, PresheafOfModules.instFaithfulFunctorOppositeAbToPresheaf, Limits.coker.condition_assoc, MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isColimit_desc, GrothendieckTopology.Point.toPresheafFiber_jointly_surjective, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_π_app, FunctorToTypes.prodMk_snd, Equivalence.funInvIdAssoc_hom_app, Limits.ConeMorphism.w, Over.postCongr_inv_app_left, LocalizerMorphism.LeftResolution.opEquivalence_unitIso, Adjunction.leftAdjointCompNatTrans₀₁₃_eq_conjugateEquiv_symm, Localization.Monoidal.lifting_isMonoidal, Functor.opUnopIso_inv_app, MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_η_app, monadToFunctor_obj, GrothendieckTopology.diagramCompIso_hom_ι_assoc, GrothendieckTopology.sheafifyCompIso_inv_eq_sheafifyLift, Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality, WithInitial.coconeEquiv_inverse_obj_pt_hom, Limits.LimitPresentation.self_π, AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_inv_app, Limits.pushoutCoconeEquivBinaryCofan_inverse_map_hom, GrothendieckTopology.sheafifyMap_id, CostructuredArrow.ιCompGrothendieckProj_inv_app, Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app', AddCommMonCat.coyonedaType_obj_map, Limits.ι_comp_sigmaObjIso_inv, eqToHom_app, Limits.ι_colimitLimitIso_limit_π, Functor.mapContActionCongr_hom, MonoidalOpposite.mopMopEquivalence_unitIso_hom_app_unmop_unmop, WithInitial.inclLift_hom_app, OverPresheafAux.counitForward_naturality₁, Over.mapComp_hom_app_left, TransfiniteCompositionOfShape.ici_F, Limits.Cocones.precomposeEquivalence_unitIso, Functor.triangleIso, CategoryOfElements.structuredArrowEquivalence_counitIso, linearYoneda_obj_obj_carrier, Limits.walkingCospanOpEquiv_counitIso_hom_app, TopologicalSpace.Opens.mapId_hom_app, CosimplicialObject.Truncated.whiskering_obj_obj_obj, Rep.instLinearModuleCatObjFunctorCoinvariantsTensor, Limits.LimitPresentation.changeDiag_π, Bicategory.postcomposing_obj, Functor.mapTriangleInvRotateIso_inv_app_hom₃, Pretriangulated.commShiftIso_opOp_hom_app_assoc, Comma.equivProd_unitIso_hom_app_left, FunctorToTypes.binaryCoproductEquiv_symm_apply, TopologicalSpace.Opens.mapComp_hom_app, MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionUnitIso_hom, Adjunction.mapCommMon_counit, Limits.ι_colimitLimitToLimitColimit_π, SimplicialObject.Truncated.rightExtensionInclusion_hom_app, Coyoneda.objOpOp_hom_app, SmallObject.SuccStruct.ofNatTrans_X₀, Functor.mapCommGrpFunctor_obj, MorphismProperty.Over.pullbackCongr_hom_app_left_fst, Functor.PushoutObjObj.mapArrowRight_left, Abelian.FunctorCategory.coimageImageComparison_app, Functor.unopId_inv_app, Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_inv, Monad.algebraFunctorOfMonadHomEq_hom_app_f, OrderHom.equivalenceFunctor_counitIso_inv_app_app, Cat.ihom_obj, Action.FunctorCategoryEquivalence.unitIso_inv_app_hom, Functor.mapCommGrpCompIso_hom_app_hom_hom_hom, Limits.BinaryBicone.toCocone_ι_app_right, Limits.Types.binaryProductFunctor_obj_map, MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_map, Localization.Lifting.ofIsos_iso, Limits.colimit.toOver_ι_app, Functor.whiskeringRight₂_obj_obj_obj_map, sheafComposeIso_hom_fac, Functor.instIsLeftKanExtensionObjLanAppLanUnit, Over.postAdjunctionLeft_unit_app_left, Limits.Types.FilteredColimit.isColimit_eq_iff, Limits.Cone.extend_π, Functor.mapActionComp_inv, obj_μ_app, Action.FunctorCategoryEquivalence.functor_map_app, Idempotents.functorExtension₂CompWhiskeringLeftToKaroubiIso_hom_app_app_f, Limits.Multicofork.snd_app_right_assoc, Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality, μ_naturalityₗ, MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_tensorHom_app, Limits.Bicone.toCone_π_app_mk, Limits.coneOfCoconeRightOp_π, extensiveTopology.isSheaf_yoneda_obj, GrothendieckTopology.sheafifyMap_sheafifyLift, Pretriangulated.shiftFunctorAdd'_op_inv_app, Limits.limitConstTerminal_hom, CompHausLike.LocallyConstant.counitApp_app, Functor.leftDerivedNatTrans_comp_assoc, Cat.rightUnitor_hom_toNatTrans, Limits.spanCompIso_hom_app_zero, Limits.fiberwiseColim_obj, Functor.homObjEquiv_symm_apply_app, Functor.const.opObjUnop_hom_app, CommMonCat.coyoneda_obj_map, ModuleCat.uliftFunctorForgetIso_hom_app, Functor.prod'CompFst_hom_app, Functor.coreId_inv_app_iso_inv, eHomFunctor_obj_obj, instReflectsIsomorphismsFunctorObjWhiskeringRight, PullbackShift.adjunction_unit, Bipointed.swapEquiv_counitIso_hom_app_toFun, Monoidal.CommMonFunctorCategoryEquivalence.unitIso_inv_app_hom_hom_app, Functor.leftDerivedZeroIsoSelf_inv_hom_id, Functor.LeftExtension.postcompose₂_obj_right_map, Rep.MonoidalClosed.linearHomEquivComm_hom, LaxMonoidalFunctor.isoMk_inv, GradedObject.singleCompEval_hom_app, MonoidalOpposite.tensorLeftUnmopIso_inv_app, Limits.Trident.condition, GrothendieckTopology.pseudofunctorOver_mapComp_inv_toNatTrans_app_val_app, FreeGroupoid.liftNatIso_hom_app, compEvaluation_hom_app, Limits.limitFlipCompLimIsoLimitCompLim_hom_π_π, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, MonoidalCategory.DayFunctor.equiv_inverse_map_natTrans, flippingIso_inv_toFunctor_obj_map_app, AdditiveFunctor.ofLeftExact_map, NatTrans.mapHomotopyCategory_comp, RightExactFunctor.ofExact_map_hom, Functor.equivCatHom_apply, CompHausLike.LocallyConstantModule.functor_map_val, Limits.Cofork.condition_assoc, Functor.PullbackObjObj.π_iso_of_iso_right_hom, LightCondSet.instIsIsoFunctorSequentialCounitSequentialAdjunction, CompHausLike.LocallyConstant.functor_map_val, Localization.Construction.WhiskeringLeftEquivalence.functor_obj_obj_map, Sheaf.instIsIsoAppCounitConstantSheafAdjOfFaithfulOfFullConstantSheafOfIsConstant, Limits.IsColimit.comp_coconePointUniqueUpToIso_inv, WithTerminal.commaFromOver_obj_right, Limits.CategoricalPullback.functorEquiv_functor_obj_iso_inv_app, NatTrans.app_nsmul, Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_hom, Enriched.FunctorCategory.enrichedId_π_assoc, δ_naturalityᵣ_assoc, bifunctorComp₂₃_map_app_app, AddMonCat.equivalence_counitIso, Functor.opUnopEquiv_counitIso, Functor.PushoutObjObj.mapArrowRight_comp_assoc, AddCommMonCat.coyonedaType_map_app, EnrichedFunctor.category_id_out, LeftExactFunctor.whiskeringRight_map_app, NatTrans.op_id, CatCenter.mul_app', FreeGroupoid.mapCompLift_inv_app, Limits.Fork.ι_postcompose, GrothendieckTopology.Point.instPreservesColimitsOfSizeFunctorOppositePresheafFiber, MorphismProperty.FunctorsInverting.id_hom, Limits.BinaryBicone.toCone_π_app_left, Limits.spanOp_hom_app, Limits.limitIsoSwapCompLim_hom_app, Presheaf.isLimit_iff_isSheafFor_presieve, faithful_linearYoneda, Limits.Fork.equivOfIsos_functor_obj_ι, Presheaf.coherentExtensiveEquivalence_counitIso, Abelian.Ext.preadditiveCoyoneda_homologySequenceδ_singleTriangle_apply, Limits.coyonedaOpColimitIsoLimitCoyoneda_hom_comp_π_assoc, WithTerminal.coneEquiv_functor_obj_π_app_star, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_inv_app, Limits.limitIsoFlipCompLim_hom_app, Prod.braiding_unitIso, NatTrans.shift_comm_assoc, Profinite.Extend.functorOp_obj, Subfunctor.preimage_comp, Adjunction.mapCommGrp_unit, MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app, Limits.coneOfDiagramInitial_π_app, Functor.curry₃ObjProdComp_inv_app_app_app, coreFunctor_obj_map_iso_inv, Limits.colimitObjIsoColimitCompEvaluation_inv_colimit_map, conjugateEquiv_leftUnitor_hom, Sum.functorEquiv_inverse_map, Functor.PullbackObjObj.mapArrowRight_comp_assoc, WithTerminal.coneEquiv_counitIso_inv_app_hom, shiftFunctorCompIsoId_add'_inv_app, ShortComplex.functorEquivalence_functor, ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₃_app, shiftFunctorAdd_zero_add_hom_app, Abelian.LeftResolution.karoubi_π, Idempotents.functorExtension₁CompWhiskeringLeftToKaroubiIso_hom_app_app_f, Rep.coinvariantsTensorIndIso_inv, Functor.instCommShiftHomotopyCategoryIntUpDerivedCategoryHomMapDerivedCategoryFactorsh, Limits.limitCompCoyonedaIsoCone_hom_app, Functor.IsCoverDense.restrictHomEquivHom_naturality_right_symm, MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionAssocIso_inv, uliftYonedaEquiv_apply, Limits.instHasColimitObjFunctorConstInitial, HomologicalComplex₂.flipEquivalenceUnitIso_hom_app_f_f, Limits.WidePullbackShape.mkCone_π_app, prod.associativity_counitIso, Functor.sheafPushforwardContinuous_map_val_app, isZero_Tor'_succ_of_projective, Adjunction.leftAdjointUniq_hom_app_counit_assoc, Monad.ForgetCreatesLimits.newCone_π_app, Limits.spanExt_hom_app_right, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_map, NatTrans.comp_app_assoc, ModuleCat.binaryProductLimitCone_cone_π_app_right, CochainComplex.shiftFunctorZero_inv_app_f, WithInitial.mkCommaMorphism_right_app, shiftFunctorAdd'_assoc, SingleFunctors.Hom.comm_assoc, Limits.FormalCoproduct.powerBifunctor_map_app, CostructuredArrow.mapIso_functor_map_left, HasLiftingProperty.transfiniteComposition.hasLiftingProperty_ι_app_bot, Localization.Construction.WhiskeringLeftEquivalence.functor_obj_obj_obj, shiftFunctorComm_hom_app_comp_shift_shiftFunctorAdd_hom_app, Monad.monToMonad_obj, HasSheafify.isLeftExact, Functor.currying_inverse_obj_obj_map, Monoidal.MonFunctorCategoryEquivalence.functorObjObj_mon_one, Limits.CategoricalPullback.functorEquiv_functor_obj_fst_obj, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_left, Presheaf.isSheaf_yoneda', NatTrans.CommShift₂.commShift_flipApp, piEquivalenceFunctorDiscrete_functor_obj, Limits.Types.FilteredColimit.jointly_surjective_of_isColimit₂, left_unitality_app_assoc, GrothendieckTopology.Point.Hom.sheafFiber_comp_assoc, Limits.Cocones.equivalenceOfReindexing_functor_obj, μ_naturality₂, Sigma.mapComp_inv_app, LeftExactFunctor.whiskeringRight_obj_map, PresheafOfModules.toPresheaf_preservesLimit, Functor.RightExtension.mk_hom, PresheafOfModules.toPresheaf_obj_coe, Functor.flip₁₃_obj_map_app, Functor.mapCommMonNatIso_hom_app_hom_hom, Localization.instFullFunctorWhiskeringLeftFunctor', AdditiveFunctor.ofRightExact_map, Functor.leftExtensionEquivalenceOfIso₁_inverse_map_left, Functor.OplaxMonoidal.ofBifunctor.secondMap₂_app_app_app, Over.coprod_obj, Limits.Cone.toStructuredArrowCompToUnderCompForget_hom_app, Comma.equivProd_counitIso_hom_app, BraidedCategory.Hexagon.functor₁₃₂'_obj_map_app, Subfunctor.image_comp, Limits.PullbackCone.combine_π_app, ShortComplex.FunctorEquivalence.inverse_obj_X₂, Limits.spanCompIso_inv_app_left, Action.FunctorCategoryEquivalence.functor_δ, MorphismProperty.colimitsOfShape.of_isColimit, Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone_isColimit_desc, Localization.homEquiv_eq, CategoryOfElements.CreatesLimitsAux.liftedCone_π_app_coe, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_id, Limits.colimitUncurryIsoColimitCompColim_ι_hom_assoc, GrothendieckTopology.whiskerRight_toPlus_comp_plusCompIso_hom, prodOpEquiv_unitIso_hom_app, NatTrans.op_whiskerRight_assoc, Adjunction.leftAdjointUniq_trans_app_assoc, preadditiveYoneda_obj, bifunctorComp₁₂Obj_obj_obj, LightProfinite.lightToProfinite_map_proj_eq, Functor.rightUnitor_hom_app, Comma.mapRightId_inv_app_left, PreGaloisCategory.toAut_surjective_isGalois_finite_family, preservesColimitsOfShape_of_isCardinalPresentable_of_essentiallySmall, SingleFunctors.comp_hom_assoc, isFinitelyPresentable_iff_preservesFilteredColimitsOfSize, linearCoyoneda_obj_obj_isAddCommGroup, Functor.FullyFaithful.compUliftYonedaCompWhiskeringLeft_inv_app_app_down, ShortComplex.π₁Toπ₂_comp_π₂Toπ₃, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_inverse_obj_obj, GrothendieckTopology.preservesSheafification_iff_of_adjunctions, Limits.IsColimit.ι_map_assoc, AdditiveFunctor.ofExact_map, Functor.leftOpId_hom_app, WithTerminal.opEquiv_unitIso_hom_app, Limits.CatCospanTransform.category_id_right, Rep.standardComplex.εToSingle₀_comp_eq, Functor.OplaxMonoidal.ofBifunctor.firstMap₁_app_app_app, PreGaloisCategory.toAut_hom_app_apply, Limits.CokernelCofork.IsColimit.isIso_π, Functor.isoShift_inv_naturality, GrothendieckTopology.Point.toPresheafFiber_naturality_apply, Functor.leftExtensionEquivalenceOfIso₁_inverse_obj_left, Comma.mapLeftId_hom_app_right, tensoringRight_linear, Limits.Concrete.isColimit_rep_eq_iff_exists, Over.postCongr_hom_app_left, Functor.PushoutObjObj.ofHasPushout_pt, Functor.postcompose₃_obj_obj_map_app_app, μ_naturalityᵣ, Adjunction.compPreadditiveYonedaIso_inv_app_app_apply, Join.mapWhiskerRight_comp, ShortComplex.FunctorEquivalence.counitIso_inv_app_app_τ₃, MonoidalCategory.DayConvolution.hexagon_forward, Functor.leftOpRightOpEquiv_unitIso_inv_app, Functor.map_opShiftFunctorEquivalence_unitIso_inv_app_unop, ObjectProperty.fullSubcategoryCongr_unitIso, GradedObject.singleCompEval_inv_app, Adjunction.Triple.whiskerRight_rightToLeft_assoc, Equivalence.changeFunctor_unitIso_hom_app, WithTerminal.opEquiv_counitIso_hom_app, HasFibers.comp_const, Sheaf.tensorProd_isSheaf, ComposableArrows.opEquivalence_unitIso_inv_app, Functor.instFullProdCurry₃, Idempotents.KaroubiHomologicalComplexEquivalence.counitIso_inv, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_inv_app, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompPointIso_hom_app, ParametrizedAdjunction.hasLiftingProperty_iff, Pretriangulated.TriangleOpEquivalence.functor_map_hom₃, Functor.sectionsFunctor_map_coe, CommGrpCat.coyonedaType_map_app, instIsIsoFunctorOppositeSheafSheafComposeNatTrans, Limits.Multiequalizer.multifork_π_app_left, Cat.HasLimits.limitCone_π_app, MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app_assoc, MonoidalCategory.DayConvolution.associator_inv_unit_unit, Limits.colimitUncurryIsoColimitCompColim_ι_hom, Join.pseudofunctorLeft_mapComp_hom_toNatTrans_app, StructuredArrow.mapNatIso_functor_obj_hom, CostructuredArrow.mapIso_unitIso_inv_app_left, MonadIso.mk_hom_toNatTrans, MonoidalCategory.DayConvolution.hexagon_reverse, Functor.IsCoverDense.restrictHomEquivHom_naturality_left, Monoidal.MonFunctorCategoryEquivalence.functorObjObj_mon_mul, uliftYonedaEquiv_symm_map, GrothendieckTopology.W.transport_isMonoidal, Limits.ConeMorphism.map_w_assoc, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_hom_app, Enriched.FunctorCategory.homEquiv_apply_π, HomologicalComplex.cyclesOpNatIso_inv_app, Functor.cones_obj, Monoidal.monFunctorCategoryEquivalence_unitIso, preadditiveYonedaMap_app, Functor.postcompose₃_obj_obj_obj_obj_obj, MonoidalCategory.DayFunctor.equiv_counitIso_inv_app, WithInitial.mkCommaObject_right_obj, shrinkYoneda_obj, prod.associativity_unitIso, AddCommGrpCat.coyonedaForget_inv_app_app, instPreservesFiniteColimitsSheafExtensiveTopologyFunctorOppositeSheafToPresheafOfPreadditiveOfHasFiniteColimits, bifunctorComp₁₂Functor_obj, Adjunction.unit_app_shift_commShiftIso_inv_app, Comma.mapRightComp_inv_app_right, HomologicalComplex.quasiIso_iff_evaluation, SingleFunctors.Hom.id_hom, Limits.coprodComparisonNatIso_hom, SmallObject.SuccStruct.restrictionLTOfCoconeIso_inv_app, Functor.mapTriangleIso_hom_app_hom₁, TwistShiftData.assoc, Functor.whiskerRight_id', ModuleCat.restrictScalarsId'_inv_app, NatTrans.CommShift.associator, Adjunction.unit_rightAdjointUniq_hom, Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π, StructuredArrow.mapNatIso_inverse_map_right, Functor.compFlipUncurryIso_inv_app, Functor.CommShift.ofIso_commShiftIso_hom_app, NatTrans.leftOp_id, Limits.limit.isoLimitCone_hom_π_assoc, Quotient.LiftCommShift.iso_hom_app, Enriched.FunctorCategory.diagram_map_app, SimplicialObject.Augmented.whiskering_map_app_right, Functor.CommShift₂.commShift_map, LeftExactFunctor.whiskeringLeft_map_app, Functor.Monoidal.coreMonoidalTransport_μIso_hom, IsSifted.colim_preservesLimits_pair_of_sSifted, Functor.lanUnit_app_app_lanAdjunction_counit_app_app, PreGaloisCategory.instFaithfulActionFintypeCatAutFunctorFunctorToAction, Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_snd, Adjunction.compUliftCoyonedaIso_inv_app_app_down, presheafHom_obj, Limits.IsColimit.homEquiv_apply, ModuleCat.extendScalars_assoc_assoc, ObjectProperty.topEquivalence_unitIso, Functor.pointwiseLeftKanExtension_map, NatTrans.app_add, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_π_app, AlgebraicTopology.DoldKan.Γ₂_obj_p_app, Functor.lanUnit_app_whiskerLeft_lanAdjunction_counit_app, NatIso.unop_trans, Functor.whiskerLeft_obj_map_bijective_of_isCoverDense, Limits.parallelPairOpIso_hom_app_one, Limits.walkingCospanOpEquiv_counitIso_inv_app, Functor.mapTriangleInvRotateIso_hom_app_hom₃, Limits.HasColimit.isoOfNatIso_inv_desc_assoc, comonadToFunctor_obj, ThinSkeleton.map₂_obj, Endofunctor.Adjunction.AlgCoalgEquiv.counitIso_inv_app_f, WithInitial.mapId_inv_app, AlgebraicGeometry.isBasis_preimage_isAffineOpen, Adjunction.instIsIsoFunctorCounitOfIsEquivalence, Limits.PullbackCone.op_ι_app, Functor.whiskeringLeft₃ObjObjMap_app, Functor.Monoidal.coreMonoidalTransport_εIso_hom, Pretriangulated.TriangleOpEquivalence.unitIso_hom_app, Functor.constComp_inv_app, Bipointed.swapEquiv_unitIso_inv_app_toFun, RightExactFunctor.forget_map, TopCat.Presheaf.presheafEquivOfIso_inverse_obj_map, ComonadHom.id_toNatTrans, Limits.HasColimit.isoOfNatIso_hom_desc, Equivalence.symmEquivInverse_obj_counitIso_hom, Limits.evaluationPreservesLimits, essImage_yonedaMon, Join.mapWhiskerRight_whiskerRight, Presheaf.isLocallySurjective_comp_iff, FunctorToTypes.inv_hom_id_app_apply, Adjunction.Quadruple.epi_leftTriple_leftToRight_iff_mono_rightTriple_rightToLeft, ShiftMkCore.add_zero_hom_app, FinitaryExtensive.mono_inl_of_isColimit, Idempotents.DoldKan.N₂_map_isoΓ₀_hom_app_f, Limits.pullbackConeEquivBinaryFan_counitIso, Sum.swapCompInl_hom_app, Equivalence.inverseFunctor_map, Limits.CatCospanTransform.rightIso_inv, StructuredArrow.mapNatIso_functor_map_right, Equivalence.functor_map_μ_inverse_comp_counitIso_hom_app_tensor_assoc, MonoidalCategory.DayConvolution.pentagon, Limits.coneOfConeCurry_pt, GrothendieckTopology.W_iff_isIso_map_of_adjunction, Limits.MultispanIndex.multispanMapIso_inv_app, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_hom_app_f, Bicategory.precomposing_map_app, flipFunctor_obj, Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc_assoc, Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_snd_snd, Limits.diagramIsoCospan_hom_app, NatTrans.leftDerivedToHomotopyCategory_comp_assoc, AddCommGrpCat.coyonedaForget_hom_app_app_hom, GradedObject.mapTrifunctorMapIso_hom, Idempotents.karoubiCochainComplexEquivalence_unitIso_hom_app_f_f, Monad.comparisonForget_hom_app, GrothendieckTopology.W_isInvertedBy_whiskeringRight_presheafToSheaf, Monoidal.tensorUnit_map, OverPresheafAux.YonedaCollection.map₂_snd, MonoidalOpposite.tensorIso_hom_app_unmop, Functor.isDense_iff_fullyFaithful_restrictedULiftYoneda, Sheaf.ΓHomEquiv_naturality_left, SimplicialObject.Truncated.rightExtensionInclusion_left, NatTrans.mapHomologicalComplex_comp, Monad.algebraFunctorOfMonadHomComp_hom_app_f, Limits.CatCospanTransform.leftIso_hom, Limits.IsColimit.isIso_colimMap_ι, Functor.whiskerLeft_comp_whiskerRight_assoc, WithInitial.equivComma_counitIso_inv_app_right_app, Limits.Fork.unop_ι_app_one, Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π_assoc, evaluation_obj_map, GrothendieckTopology.isoToPlus_hom, Linear.smulOfRingMorphism_smul_eq, BraidedCategory.Hexagon.functor₁₃₂_map_app_app, MonoidalCategory.DayFunctor.equiv_functor_map, coyoneda_preservesLimits, Limits.Cone.equivCostructuredArrow_inverse, TwistShiftData.shiftFunctorZero_hom_app, SheafOfModules.pushforwardComp_inv_app_val_app, Equivalence.changeFunctor_trans, AddCommGrpCat.HasLimit.productLimitCone_isLimit_lift, Functor.Monoidal.transport_ε, Limits.pointwiseCocone_ι_app_app, Limits.Cones.whiskeringEquivalence_inverse, Functor.leftDerived_fac_assoc, endofunctorMonoidalCategory_associator_inv_app, Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_app_fst_app, PreGaloisCategory.instFullContActionFintypeCatHomCarrierAutFunctorFunctorToContAction, Functor.currying_counitIso_inv_app_app, Functor.ihom_ev_app, Limits.Types.Colimit.ι_desc_apply', WithTerminal.inclLift_hom_app, Quotient.liftCommShift_compatibility, Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality_assoc, Limits.FormalCoproduct.eval_map_app, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_inv_app_hom, Adjunction.mapGrp_unit, Functor.leftKanExtensionCompIsoOfPreserves_hom_fac_assoc, uliftYonedaEquiv_naturality, functorProdFunctorEquiv_functor, Limits.opHomCompWhiskeringLimYonedaIsoCocones_hom_app_app_app, Functor.curry₃_obj_map_app_app, Functor.coreId_inv_app_iso_hom, Limits.hasLimitsOfShape_iff_isLeftAdjoint_const, Under.mapId_inv, Functor.isoShift_hom_naturality, Adjunction.map_restrictFullyFaithful_unit_app_assoc, CatCenter.app_add, Localization.instFaithfulFunctorWhiskeringLeftFunctor', MonoidalCategory.DayConvolution.unit_uniqueUpToIso_inv, Limits.CokernelCofork.condition, conjugateEquiv_counit_symm, Limits.isIso_limit_cone_parallelPair_of_epi, Grothendieck.grothendieckTypeToCat_unitIso_inv_app_base, MonoidalCategory.DayConvolutionInternalHom.ev_naturality_app, Functor.flip₂₃_obj_obj_obj, Idempotents.functorExtension₂_obj_map_f, GrothendieckTopology.toSheafification_app, Limits.FormalCoproduct.powerBifunctor_obj, Functor.CommShift.isoZero'_inv_app, Grothendieck.ιCompMap_inv_app_fiber, typeToPartialFunIsoPartialFunToPointed_hom_app_toFun, AlgebraicTopology.DoldKan.map_Hσ, TopCat.Sheaf.extend_hom_app, OverPresheafAux.YonedaCollection.yonedaEquivFst_eq, Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_shift, SimplicialObject.Augmented.whiskering_obj, Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₁, presheaf_mono_of_mono, Limits.opParallelPairIso_hom_app_zero, PartOrdEmb.Limits.CoconePt.fac_apply, Limits.map_id_left_eq_curry_map, HomologicalComplex.singleMapHomologicalComplex_inv_app_self, NatTrans.CommShift.of_isIso, TwoSquare.guitartExact_id, Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_snd_obj, PreGaloisCategory.autIsoFibers_inv_app, Functor.Initial.extendCone_obj_π_app', Subfunctor.equalizer.ι_ι_assoc, MorphismProperty.IsStableUnderColimitsOfShape.functorCategory, instPreservesFiniteLimitsFunctorOppositeSheafReflectorSheafToPresheaf, MulEquiv.toSingleObjEquiv_unitIso_hom, Enriched.FunctorCategory.coneFunctorEnrichedHom_π_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_map_left, evaluationAdjunctionRight_counit_app_app, Functor.coreprW_hom_app, Functor.LaxMonoidal.ofBifunctor.bottomMapᵣ_app, Pseudofunctor.ObjectProperty.mapId_inv_app, Limits.ColimitPresentation.map_ι, TwoSquare.structuredArrowRightwardsOpEquivalence_counitIso, Limits.Cocone.toCostructuredArrowCompToOverCompForget_inv_app, Adjunction.leftAdjointUniq_hom_counit, Subfunctor.equivalenceMonoOver_inverse_map, Adjunction.isIso_counit_of_iso, Limits.Cowedge.condition_assoc, NatTrans.CommShift.rightUnitor, Limits.Cofork.app_zero_eq_comp_π_left, sheafification_map, Limits.DiagramOfCocones.coconePoints_map, Functor.natTransEquiv_symm_apply_app, CatCommSq.hId_iso_inv_app, GrothendieckTopology.PreservesSheafification.le, Functor.homEquivOfIsLeftKanExtension_symm_apply, δ_μ_app, WithTerminal.equivComma_functor_map_right, Localization.Monoidal.map_hexagon_forward, Limits.limCompFlipIsoWhiskerLim_inv_app_app, Coyoneda.colimitCocone_ι_app, Functor.whiskeringLeft₂_obj_obj_obj_map_app, Pretriangulated.instIsHomologicalOppositeAddCommGrpCatObjFunctorPreadditiveYoneda, SheafOfModules.pushforwardNatTrans_id, Presheaf.functorEnrichedHomCoyonedaObjEquiv_naturality, Monoidal.whiskerRight_app, Functor.commShiftOfLocalization_iso_inv_app, Functor.leftDerivedZeroIsoSelf_hom_inv_id_app, Functor.uncurry_map_app, Functor.whiskeringLeft₂_obj_obj_obj_obj_obj, Adjunction.map_restrictFullyFaithful_counit_app, Limits.piConst_obj_map, Limits.diagramIsoParallelPair_hom_app, CommMonCat.coyonedaForget_inv_app_app, Iso.coreId, GrothendieckTopology.plusFunctor_obj, PreGaloisCategory.functorToContAction_map, plusPlusSheaf_map_val, WithInitial.coconeEquiv_counitIso_inv_app_hom, Rep.coinvariantsTensorIndIso_hom, Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₃, Equivalence.mapMon_unitIso, AlgebraicGeometry.PresheafedSpace.colimitCocone_ι_app_base, Monoidal.monFunctorCategoryEquivalence_functor, Limits.CoproductsFromFiniteFiltered.liftToFinset_obj_map, SSet.hoFunctor.unitHomEquiv_eq, Functor.commShiftOfLocalization.iso_inv_app, flipCompEvaluation_hom_app, BraidedCategory.Hexagon.functor₂₃₁'_obj_obj_obj, NatTrans.removeOp_id, Functor.LaxMonoidal.ofBifunctor.topMapₗ_app, Limits.IsColimit.coconePointsIsoOfNatIso_hom, Functor.instIsIsoAppLanUnit, Localization.lift₃NatIso_hom, WithInitial.mkCommaMorphism_left, Limits.coend.map_comp_assoc, sheafifyMap_id, Limits.colimit.comp_coconePointUniqueUpToIso_inv_assoc, instFaithfulMonFunctorOppositeMonCatYonedaMon, cosimplicialSimplicialEquiv_functor_obj_obj, PreGaloisCategory.continuous_mapAut_whiskeringRight, AlgebraicGeometry.ExistsHomHomCompEqCompAux.exists_index, WithInitial.commaFromUnder_map_left, Functor.mapArrowFunctor_obj, Action.resId_inv_app_hom, NatTrans.instIsClosedUnderColimitsOfShapeUnderFunctorCoequifiberedHomDiscretePUnitOfHasProductsOfShapeHom, MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_whiskerLeft_app, simplicialCosimplicialEquiv_unitIso_hom_app, Adjunction.leftAdjointUniq_hom_app_counit, Functor.LeftExtension.postcompose₂ObjMkIso_inv_right_app, Monoidal.tensorUnit_obj, NatTrans.instCommShiftOppositeShiftHomFunctorNatIsoId, Functor.CommShift.comp_commShiftIso_inv_app, Limits.CompleteLattice.finiteColimitCocone_cocone_ι_app, AlgebraicTopology.DoldKan.N₁Γ₀_hom_app_f_f, Functor.sheafPushforwardContinuousCompSheafToPresheafIso_inv_app_app, Mon.limit_mon_mul, MorphismProperty.Over.mapId_inv_app_left, Limits.colimitYonedaHomIsoLimit_π_apply, NatTrans.rightOpWhiskerRight, Limits.Cotrident.condition_assoc, equivYoneda'_inv_val, Functor.Monoidal.transport_δ, Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_inv_π_π, CosimplicialObject.Augmented.whiskering_map_app_left, Functor.inlCompSum'_hom_app, GrothendieckTopology.Point.toPresheafFiber_w, ExponentiableMorphism.pushforwardId_hom_counit_assoc, HomologicalComplex.instIsCorepresentableCompEvalObjOppositeFunctorTypeCoyonedaOp, Quotient.natTransLift_id, Rep.coinvariantsTensorIndNatIso_inv_app, Limits.walkingCospanOpEquiv_unitIso_inv_app, Join.mapPairComp_hom_app_right, Limits.colimitIsoColimitCurryCompColim_ι_hom, bifunctorComp₁₂_map_app_app, prodFunctor_map, Functor.sumIsoExt_inv_app_inr, AddCommGrpCat.binaryProductLimitCone_cone_π_app_left, MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.faithful_ι, GrothendieckTopology.W_adj_unit_app, Limits.CoconeMorphism.w_assoc, comp_toNatTrans, Limits.coneOfCoconeLeftOp_π_app, Limits.LimitPresentation.reindex_π, SmallObject.SuccStruct.extendToSuccRestrictionLEIso_hom_app, Limits.coneOfCoconeUnop_π, sheafToPresheaf_obj, PresheafOfModules.limitCone_π_app_app, WithInitial.liftStar_lift_map, PreGaloisCategory.instPreservesIsConnectedActionFintypeCatAutFunctorFunctorToAction, additive_yonedaObj', MonoidalCategory.tensoringRight_δ, Idempotents.functorExtension_obj_obj, Iso.coreLeftUnitor, BraidedCategory.ofBifunctor.Reverse.secondMap₂_app_app_app, sheafToPresheaf_map, Limits.Types.isLimitEquivSections_apply, Functor.leftOpRightOpIso_hom_app, Functor.leftKanExtensionCompIsoOfPreserves_inv_fac_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_obj, Functor.ranCompIsoOfPreserves_inv_app, OverPresheafAux.counitForward_val_snd, ParametrizedAdjunction.homEquiv_symm_naturality_one_assoc, MonoidalOpposite.mopEquiv_unitIso, Comma.mapLeftComp_inv_app_left, shiftFunctorComm_hom_app_comp_shift_shiftFunctorAdd_hom_app_assoc, WithInitial.coconeEquiv_functor_obj_ι_app_star, Limits.IsColimit.comp_coconePointUniqueUpToIso_inv_assoc, CosimplicialObject.Truncated.whiskering_map_app_app, Mat_.embeddingLiftIso_hom_app, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj_assoc, Limits.CategoricalPullback.functorEquiv_functor_map_fst_app, TwoSquare.isIso_lanBaseChange_app, Limits.CompleteLattice.colimitCocone_cocone_ι_app, ProjectiveResolution.extMk_hom, Subfunctor.equivalenceMonoOver_functor_map, NatTrans.rightDerived_comp, Projective.projective_iff_preservesEpimorphisms_coyoneda_obj, Limits.SequentialProduct.cone_π_app_comp_Pi_π_neg_assoc, Functor.instIsEquivalenceRightExtensionPostcomp₁OfIsIso, ShortComplex.FunctorEquivalence.inverse_obj_X₃, Limits.CategoricalPullback.CatCommSqOver.transform_map_whiskerLeft, Functor.shiftIso_add_hom_app, AdditiveFunctor.forget_obj_of, Functor.mapMonNatIso_hom_app_hom, Limits.CategoricalPullback.CatCommSqOver.transform_map_app_fst_app, shiftFunctorAdd_inv_app_obj_of_induced, conjugateEquiv_symm_iso, Functor.mapTriangleIso_hom_app_hom₂, Join.mapWhiskerLeft_whiskerRight_assoc, Limits.opParallelPairIso_hom_app_one, typeEquiv_unitIso_hom_app, Limits.colimit.comp_coconePointUniqueUpToIso_hom_assoc, Equivalence.symmEquivFunctor_map, Limits.Cofork.IsColimit.homIso_apply_coe, Rep.instAdditiveModuleCatObjFunctorCoinvariantsTensor, Limits.cospanCompIso_inv_app_left, Functor.mapTriangleCompIso_inv_app_hom₃, Functor.preservesZeroMorphisms_evaluation_obj, CompHausLike.LocallyConstant.functor_obj_val, Functor.rightOpId_inv_app, faithful_preadditiveCoyoneda, WithInitial.inclLiftToInitial_inv_app, TwistShiftData.shift_z_app, Ind.isIndObject_inclusion_obj, Limits.yonedaCompLimIsoCocones_hom_app_app, Over.starPullbackIsoStar_hom_app_left, Limits.PushoutCocone.ofCocone_ι, Over.postEquiv_inverse, TwoSquare.equivalenceJ_counitIso, BraidedCategory.Hexagon.functor₃₁₂_obj_obj_map, AlgebraicTopology.DoldKan.Γ₂N₂ToKaroubiIso_hom_app, StructuredArrow.mapNatIso_unitIso_hom_app_right, Limits.coend.condition_assoc, Functor.rightDerivedNatTrans_comp, Functor.postcompose₃_obj_obj_obj_obj_map, Pi.evalCompEqToEquivalenceFunctor_hom, Abelian.Ext.mapExactFunctor_hom, AdditiveFunctor.forget_obj, Functor.rightDerivedZeroIsoSelf_hom_inv_id, FunctorToTypes.inr_comp_binaryCoproductIso_hom_apply, Localization.whiskeringLeftFunctor'_eq, FunctorToTypes.inl_comp_binaryCoproductIso_hom_apply, smoothSheafCommRing.ι_evalHom, Adjunction.conjugateEquiv_leftAdjointIdIso_hom, Subfunctor.ofSection_eq_range', simplicialCosimplicialEquiv_counitIso_hom_app_app, faithful_preadditiveYoneda, Yoneda.yoneda_faithful, Limits.ProductsFromFiniteCofiltered.finiteSubproductsCocone_π_app_eq_sum, Sheaf.cartesianMonoidalCategorySnd_val, IsGrothendieckAbelian.IsPresentable.surjectivity.isIso_f, Limits.ι_colimitCompWhiskeringLeftIsoCompColimit_hom, Functor.mapTriangleCompIso_hom_app_hom₃, Limits.coneOfIsSplitMono_π_app, Limits.ι_comp_sigmaObjIso_hom, coreFunctor_obj_obj_of, Localization.Monoidal.map_hexagon_reverse, Limits.parallelPairIsoMk_hom_app, GradedObject.mapBifunctorObjSingle₀ObjIso_hom, Triangulated.Octahedron.map_m₃, Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone_cocone_ι_app, NatTrans.CommShift.comp, linearYoneda_map_app, Localization.faithful_whiskeringLeft, Join.isoMkFunctor_inv_app, Functor.isoWhiskerLeft_right, OverPresheafAux.yonedaCollectionFunctor_obj, Localization.Monoidal.functorMonoidalOfComp_μ, Endofunctor.Coalgebra.functorOfNatTransId_inv_app_f, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_hom_app_app, PrincipalSeg.cocone_ι_app, CommRingCat.instIsLocalHomCarrierObjWalkingParallelPairFunctorConstPtEqualizerForkZeroParallelPairRingHomHomι, Limits.end_.condition, GrothendieckTopology.Point.Hom.presheafFiber_comp_assoc, WithTerminal.coneEquiv_functor_obj_π_app_of, Limits.Multicofork.ofSigmaCofork_π, Limits.CategoricalPullback.functorEquiv_inverse_map_app_snd, Paths.liftNatIso_hom_app, WithInitial.coconeEquiv_unitIso_hom_app_hom_right, Localization.lift₂_iso_hom_app_app₂, Over.forgetMapTerminal_inv_app, Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_hom_app, Limits.Concrete.isColimit_exists_rep, Pi.optionEquivalence_unitIso, MorphismProperty.Over.mapCongr_hom_app_left, Functor.shiftIso_add'_hom_app, Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app, Join.mapIsoWhiskerRight_inv, Functor.Monoidal.transport_μ_assoc, endofunctorMonoidalCategory_whiskerRight_app, ChosenPullbacksAlong.unit_pullbackId_hom_app, Limits.spanExt_hom_app_zero, sectionsFunctorNatIsoCoyoneda_inv_app_coe, NatIso.op_isoWhiskerRight, ModuleCat.directLimitIsColimit_desc, BraidedCategory.ofBifunctor.Forward.secondMap₂_app_app_app, LeftExactFunctor.whiskeringLeft_obj_obj_obj, BraidedCategory.Hexagon.functor₂₃₁_obj_obj_map, Limits.IsLimit.homEquiv_symm_π_app, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_inv_app_app, PreGaloisCategory.toAutHomeo_apply, FunctorToTypes.binaryCoproductCocone_pt_map, ULift.equivalence_unitIso_inv, ComposableArrows.opEquivalence_functor_obj_map, Subfunctor.homOfLe_ι_assoc, Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor, Subfunctor.homOfLe_ι, Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_one_app, NatTrans.naturality_app_app_assoc, TwoSquare.GuitartExact.vComp'_iff_of_equivalences, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₁, Subobject.inf_eq_map_pullback', Preadditive.commGrpEquivalenceAux_hom_app_hom_hom_hom, Presheaf.restrictedULiftYoneda_map_app, Abelian.LeftResolution.instEpiKaroubiAppπ', Sum.natTransOfWhiskerLeftInlInr_id, NatIso.prod_inv, MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.ι_map_tensorHom_eq, Functor.CommShift.ofComp_compatibility, Presheaf.compULiftYonedaIsoULiftYonedaCompLan_inv_app_app_apply_eq_id, Discrete.functorComp_hom_app, Localization.liftNatIso_inv, Limits.spanOp_inv_app, Presheaf.isSeparated_iff_subsingleton, Limits.IsColimit.comp_coconePointsIsoOfNatIso_hom, right_unitality_app_assoc, Action.functorCategoryEquivalence_functor, GrothendieckTopology.toSheafify_comp_sheafifyCompIso_inv_assoc, LightCondensed.isColimitLocallyConstantPresheafDiagram_desc_apply, Equivalence.rightOp_unitIso_hom_app, Over.conePostIso_hom_app_hom, fullyFaithfulSheafToPresheaf_preimage_val, Join.pseudofunctorLeft_mapComp_inv_toNatTrans_app, PreGaloisCategory.instIsEquivalenceContActionFintypeCatHomCarrierAutFunctorFunctorToContAction, Limits.Cones.functoriality_obj_π_app, SSet.OneTruncation₂.ofNerve₂.natIso_hom_app_obj, shift_shiftFunctorCompIsoId_neg_add_cancel_hom_app, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descAddMonoidHom_quotMk, Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom, Limits.reflexivePair.compRightIso_hom_app, preservesLimits_preadditiveCoyoneda_obj, Functor.shiftIso_inv_naturality, Functor.OplaxMonoidal.ofBifunctor.secondMap₃_app_app_app, enrichedFunctorTypeEquivFunctor_symm_apply_obj, η_app_obj, Functor.IsCoverDense.restrictHomEquivHom_naturality_left_assoc, bifunctorComp₂₃Obj_obj_obj, MonoidalCategory.endofunctorMonoidalCategory.evaluationRightAction_actionHomRight, TopCat.nonempty_isLimit_iff_eq_induced, Functor.leibnizPushout_obj_map, MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit_comp_ι_map_whiskerRight_app, linearYoneda_obj_obj_isAddCommGroup, Limits.ker.condition, MonoidalCategory.DayFunctor.equiv_counitIso_hom_app, Sum.functorEquivInverseCompWhiskeringLeftInrIso_inv_app_app, Limits.colimitLimitToLimitColimitCone_hom, NatIso.mapHomologicalComplex_hom_app_f, GrothendieckTopology.plusMap_plusLift, isIso_iff_isIso_yoneda_map, Functor.isDenseAt_eq_isPointwiseLeftKanExtensionAt, Functor.RightExtension.coneAtFunctor_obj, Equivalence.unitIso_hom_app_tensor_comp_inverse_map_δ_functor_assoc, MonoidalCategory.Limits.preservesCoLimit_curriedTensor, Functor.whiskeringLeft₃ObjMap_app, MorphismProperty.instHasFunctorialFactorizationFunctorFunctorCategory, essImage_yonedaGrp, ParametrizedAdjunction.homEquiv_symm_naturality_three, BraidedCategory.Hexagon.functor₁₂₃'_obj_obj_map, leftExactFunctor_le_additiveFunctor, Functor.essImage.liftFunctorCompIso_hom_app, Sheaf.natTransΓRes_app, Functor.PushoutObjObj.mapArrowLeft_id, shiftFunctorAdd'_zero_add_inv_app, cosimplicialSimplicialEquiv_inverse_obj, PreGaloisCategory.exists_lift_of_continuous, Limits.Multicofork.π_eq_app_right, Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_fst_map, Limits.instPreservesFiniteLimitsFunctorObjEvaluationOfHasFiniteLimits, Functor.curry₃ObjProdComp_hom_app_app_app, Functor.rightDerivedNatIso_hom, Functor.whiskeringLeftObjIdIso_hom_app_app, BraidedCategory.curriedBraidingNatIso_hom_app_app, Functor.OplaxMonoidal.ofBifunctor.secondMap_app_app_app, FunctorToTypes.binaryProductIso_inv_comp_snd_apply, Pseudofunctor.ObjectProperty.mapComp_hom_app, Functor.mapMonNatIso_inv_app_hom, Adjunction.shift_counit_app, Monoidal.CommMonFunctorCategoryEquivalence.unitIso_hom_app_hom_hom_app, Limits.Cone.ofPullbackCone_π, FunctorToTypes.coprod.desc_inl, Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom, Functor.map_shift_unop, NatTrans.toCatHom₂_id, PreGaloisCategory.toAut_surjective_isGalois, Adjunction.Quadruple.epi_leftTriple_rightToLeft_iff_mono_rightTriple_leftToRight, Functor.IsCoverDense.presheafIso_hom_app, AlgebraicGeometry.exists_appTop_π_eq_of_isAffine_of_isLimit, Limits.ConeMorphism.map_w, FunctorToTypes.binaryProductEquiv_symm_apply, Limits.Cones.equivalenceOfReindexing_counitIso, Endofunctor.Coalgebra.equivOfNatIso_counitIso, sheafifyMap_sheafifyLift, Grothendieck.grothendieckTypeToCat_unitIso_hom_app_base, CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_inv_app, SmallObject.succStruct_prop_le_propArrow, GradedObject.comapEquiv_unitIso, curryingIso_inv_toFunctor_obj_map_app, Adjunction.leftAdjointUniq_trans_assoc, Functor.ihom_map, Functor.mapCommMonFunctor_map_app, Adjunction.unit_rightAdjointUniq_hom_app, ShortComplex.FunctorEquivalence.inverse_map_τ₁, Limits.ColimitPresentation.self_diag, Adjunction.map_restrictFullyFaithful_counit_app_assoc, Iso.inv_hom_id_app_app, endofunctorMonoidalCategory_tensorMap_app, Discrete.productEquiv_counitIso_hom_app, instHasExactColimitsOfShapeFunctorOfHasFiniteLimits, Limits.limit.isoLimitCone_hom_π, Limits.LimitPresentation.ofIso_π, Functor.LeftExtension.postcompose₂_map_right_app, GrothendieckTopology.MayerVietorisSquare.mk₀_f_comp_biprodAddEquiv_symm_biprodIsoProd_hom, CartesianMonoidalCategory.prodComparisonBifunctorNatIso_hom, Monoidal.MonFunctorCategoryEquivalence.functor_obj, δ_app, Functor.instIsRepresentableCompOppositeOpObjTypeYonedaObjRightAdjointObjIsDefined, Limits.pullbackConeOfRightIso_π_app_right, BraidedCategory.Hexagon.functor₁₂₃_map_app_app, Presheaf.functorToRepresentables_obj, Join.mapIsoWhiskerRight_hom_app, PreGaloisCategory.toAutMulEquiv_apply, Idempotents.app_p_comp_assoc, CompHausLike.LocallyConstantModule.functor_obj_val, Equivalence.CommShift.instCommShiftHomFunctorCounitIso, Functor.final_const_of_isTerminal, Limits.Fork.ofι_π_app, Equivalence.congrLeft_functor, Functor.Monoidal.whiskeringLeft_ε_app, Limits.CategoricalPullback.toCatCommSqOver_obj_iso_inv_app, ULift.equivalence_counitIso_hom_app, Ind.exists_nonempty_arrow_mk_iso_ind_lim, Functor.op_commShiftIso_hom_app_assoc, Monad.monadToMon_map_hom, WithInitial.mkCommaObject_hom_app, Functor.FullyFaithful.compYonedaCompWhiskeringLeftMaxRight_inv_app_app, instLocallySmallFullSubcategoryFunctorOppositeTypeIsIndObject, pullbackShiftFunctorZero'_hom_app, yoneda_obj_obj, Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_inv_app, uliftYonedaEquiv_comp, CostructuredArrow.map_map_right, Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app_assoc, Limits.IsLimit.hom_lift, SheafOfModules.pushforwardCongr_hom_app_val_app, Limits.coconePointwiseProduct_ι_app, ExactFunctor.whiskeringLeft_map_app, Monoidal.tensorObj_obj, μ_naturality, FinitaryExtensive.mono_inr_of_isColimit, Functor.sectionsEquivHom_naturality, sheafifyLift_id_toSheafify, Limits.CategoricalPullback.CatCommSqOver.precompose_map_leftUnitor, SheafOfModules.toSheaf_map_val, Limits.PullbackCone.mk_π_app_right, Limits.Cofork.op_π_app_zero, ModuleCat.restrictScalarsCongr_hom_app, MorphismProperty.TransfiniteCompositionOfShape.instIsIsoAppIncl, Limits.DiagramOfCones.mkOfHasLimits_map_hom, pullbackShiftFunctorZero_hom_app, Limits.IndObjectPresentation.toCostructuredArrow_obj_right_as, GrothendieckTopology.plusCompIso_whiskerLeft_assoc, Presheaf.freeYoneda_map, Monoidal.ComonFunctorCategoryEquivalence.inverseObj_comon_counit_app, Limits.instHasCofilteredLimitsOfSizeFunctor, PresheafOfModules.pullback_assoc, TopologicalSpace.Opens.mapIso_inv_app, Limits.opSpan_hom_app, PreGaloisCategory.toAut_isHomeomorph, groupHomology.isoShortComplexH1_hom, GrothendieckTopology.instIsIsoFunctorOppositeSheafSheafComposeNatTransPlusPlusAdjunction, BraidedCategory.Hexagon.functor₂₁₃'_obj_map_app, obj_zero_map_μ_app, MonoidalCategory.MonoidalLeftAction.curriedActionActionOfMonoidalFunctorToEndofunctorMopIso_inv_app_unmop_app, Iso.compInverseIso_inv_app, Limits.CatCospanTransform.isIso_base, Adjunction.restrictFullyFaithful_homEquiv_apply, MonoidalCategory.DayConvolution.unit_uniqueUpToIso_hom, Limits.Cofork.IsColimit.π_desc_assoc, LocalizerMorphism.rightDerivedFunctorComparison_fac, curryingIso_hom_toFunctor_obj_obj, CatCenter.smul_iso_hom_eq'_assoc, instIsMonoidalFunctorCongrLeft, Limits.piObjIso_inv_comp_π, GrothendieckTopology.overMapPullback_assoc_assoc, Functor.rightDerivedZeroIsoSelf_hom_inv_id_app, Limits.ColimitPresentation.Total.Hom.w, Limits.coneOfConeCurry_π_app, Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_snd_obj, Sheaf.isSheaf_of_isLimit, Functor.Monoidal.whiskeringLeft_μ_app, ContAction.resCongr_hom, Comma.equivProd_unitIso_hom_app_right, DifferentialObject.shiftZero_inv_app_f, whiskering_linearYoneda, TopCat.Presheaf.presheafEquivOfIso_unitIso_hom_app_app, Functor.zero_obj, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom, TwoSquare.GuitartExact.whiskerVertical_iff, conjugateEquiv_whiskerRight, Functor.isLeftDerivedFunctor_iff_of_inverts, NatTrans.op_whiskerRight, Discrete.sumEquiv_unitIso_hom_app, Functor.mapTriangle_map_hom₁, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι, BraidedCategory.ofBifunctor.Forward.secondMap₁_app_app_app, Localization.Construction.WhiskeringLeftEquivalence.inverse_map_app, FunctorToTypes.rightAdj_map_app, Enriched.Functor.associator_hom_apply, Limits.limitFlipCompLimIsoLimitCompLim_inv_π_π, Monad.algebraFunctorOfMonadHomEq_inv_app_f, NatTrans.CommShiftCore.shift_app, Functor.homObjFunctor_map_app, MonoidalCategory.DayConvolution.corepresentableBy₂'_homEquiv, Functor.whiskeringLeft₃_obj_obj_obj_obj_obj_obj_obj, PartOrdEmb.Limits.cocone_ι_app, Limits.DiagramOfCocones.mkOfHasColimits_obj, Limits.Types.limitCone_π_app, CatCommSq.vInv_iso_hom_app, Functor.ShiftSequence.induced_shiftIso_hom_app_obj, sheafToPresheaf_δ, Limits.lim_ε_π_assoc, Monoidal.ComonFunctorCategoryEquivalence.inverseObj_X, Sheaf.Hom.mono_iff_presheaf_mono, Adjunction.whiskerRight_counit_iso_of_L_fully_faithful, Sum.natIsoOfWhiskerLeftInlInr_eq, NatTrans.shift_comm, Functor.ranCompIsoOfPreserves_hom_app, Limits.PushoutCocone.condition_zero, LightCondensed.instPreservesEpimorphismsFunctorDiscreteNatLightCondModLim, sheafBotEquivalence_inverse_map_val, Enriched.FunctorCategory.homEquiv_comp, whiskeringRightCompEvaluation_inv_app, Functor.associator_inv_app, Functor.RightExtension.postcomp₁_obj_left_obj, Limits.whiskeringLimYonedaIsoCones_inv_app_app, whiskering_linearCoyoneda₂, Functor.instCommShiftCochainComplexIntDerivedCategoryHomMapDerivedCategoryFactors, Presheaf.freeYonedaHomEquiv_symm_comp, LocalizerMorphism.homMap_apply, CostructuredArrow.mapNatIso_functor_obj_hom, typeEquiv_unitIso_inv_app, Functor.functorialityCompPrecompose_hom_app_hom, NatTrans.unop_whiskerRight, Subfunctor.lift_ι, Over.mapId_inv_app_left, Action.diagonalSuccIsoTensorTrivial_inv_hom_apply, AlgebraicGeometry.AffineSpace.functor_obj_map, NatTrans.op_comp_assoc, Limits.endFunctor_obj, ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left_assoc, Sigma.natIso_inv, GrothendieckTopology.Cover.multicospanComp_inv_app, MorphismProperty.Over.pullbackComp_inv_app_left, Comma.mapRightIso_functor_obj_hom, Limits.Cone.toStructuredArrowCone_π_app, Functor.isoWhiskerRight_left_assoc, TwoP.swapEquiv_unitIso_hom_app_hom_toFun, Adjunction.instIsIsoFunctorUnitOfIsEquivalence_1, Functor.flipping_counitIso_hom_app_app_app, Limits.walkingParallelFamilyEquivWalkingParallelPair_counitIso_inv_app, Functor.leftDerivedNatTrans_comp, Limits.CategoricalPullback.functorEquiv_functor_map_snd_app, Comma.toIdPUnitEquiv_unitIso_inv_app_right, Limits.pointwiseCocone_pt, GrothendieckTopology.yonedaOpCompCoyoneda_inv_app_app, Limits.Cones.whiskeringEquivalence_unitIso, Functor.isoWhiskerRight_twice, Functor.leftOpRightOpEquiv_functor_obj_obj, Limits.colimitCoyonedaHomIsoLimitUnop_π_apply, shiftFunctorZero_hom_app_obj_of_induced, SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_inv_app, CompHausLike.LocallyConstant.functorToPresheaves_map_app, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_hom_app, Comma.toPUnitIdEquiv_unitIso_inv_app_left, Equivalence.congrRight_functor, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_right, Functor.instIsEquivalenceLeftExtensionPostcomp₁OfIsIso, Profinite.instEpiAppDiscreteQuotientCarrierToTopTotallyDisconnectedSpaceπAsLimitCone, TransfiniteCompositionOfShape.fac, PreGaloisCategory.exists_lift_of_mono_of_isConnected, Functor.isIso_ranAdjunction_unit_app_iff, FunctorToTypes.rightAdj_map_app_app, LeftExactFunctor.ofExact_map_hom, Join.mkFunctorLeft_hom_app, Functor.curryingEquiv_apply_obj, GrothendieckTopology.uliftYonedaCompSheafToPresheaf_inv_app_app, CostructuredArrow.CreatesConnected.natTransInCostructuredArrow_app, Adjunction.comp_counit, Cat.Hom.hom_inv_id_toNatTrans, Limits.multispanIndexCoend_snd, CatCommSq.iso_hom_naturality, NatIso.op_symm, Sieve.sieveOfUliftSubfunctor_apply, yonedaEquiv_yoneda_map, Limits.Cocone.toStructuredArrow_obj, MonoidalOpposite.unmopEquiv_unitIso_inv_app_unmop, Cat.exp_map, Limits.FormalCoproduct.eval_obj_map, Equivalence.changeFunctor_counitIso_hom_app, Subfunctor.equivalenceMonoOver_inverse_obj, Localization.Monoidal.map_hexagon_reverse_assoc, Limits.CategoricalPullback.toCatCommSqOver_obj_snd_obj, CommMonCat.coyonedaType_obj_obj_coe, CatCenter.mul_app_assoc, Functor.LeftExtension.postcompose₂_obj_hom_app, GrothendieckTopology.plusFunctorWhiskerLeftIso_hom_app, Limits.instPreservesWellOrderContinuousOfShapeFunctorObjEvaluationOfHasIterationOfShape, Functor.whiskeringRight₂_obj_obj_obj_obj, Limits.CatCospanTransform.category_comp_left, GlueData.diagramIso_inv_app_left, Limits.IsLimit.ofConeEquiv_apply_desc, Functor.pentagonIso, Equivalence.refl_counitIso, Iso.map_inv_hom_id_app, Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app_assoc, Subfunctor.Subpresheaf.image_comp, WithInitial.liftFromUnder_obj_obj, Limits.colim_map, Iso.hom_inv_id_app, Iso.app_hom, Limits.HasLimit.isoOfEquivalence_hom_π, CategoryOfElements.costructuredArrowYonedaEquivalence_counitIso, Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π, Limits.limitConstTerminal_inv_π, NatIso.naturality_1_assoc, FunctorToTypes.inl_comp_binaryCoproductIso_hom, unit_conjugateEquiv_symm, Adjunction.mapMon_counit, GrothendieckTopology.Point.Hom.sheafFiber_comp, IsPushout.of_isColimit_binaryCofan_of_isInitial, preservesLimitNatIso_inv_app, Functor.shiftIso_zero, PresheafOfModules.sheafification_map, Limits.opCompYonedaSectionsEquiv_apply_app, Pretriangulated.preadditiveYoneda_homologySequenceδ_apply, Functor.instFaithfulProdUncurry, Functor.NatTrans.hcomp_eq_whiskerLeft_comp_whiskerRight, Action.instIsEquivalenceFunctorSingleObjFunctor, toPresheafToSheafCompComposeAndSheafify_app, Over.ConstructProducts.conesEquivFunctor_map_hom, Limits.IsLimit.conePointsIsoOfNatIso_hom_comp_assoc, Limits.BinaryFan.rightUnitor_inv, Subfunctor.Subpresheaf.range_comp, MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app_assoc, Functor.mapMonFunctor_obj, Limits.Types.Colimit.ι_map_apply', CategoryOfElements.costructuredArrowYonedaEquivalence_inverse, Limits.isIndObject_iff, Functor.whiskeringLeft₃_obj_obj_map_app_app_app_app, MulEquiv.toSingleObjEquiv_counitIso_hom, unit_conjugateEquiv, Limits.colimitIsoColimitCurryCompColim_ι_ι_inv_assoc, NatIso.trans_app, Limits.PullbackCone.mk_π_app_one, isSeparator_iff_faithful_coyoneda_obj, GradedObject.mapBifunctorObjSingle₀ObjIso_inv, Iso.coreAssociator, Functor.mapGrpNatIso_hom_app_hom_hom, NatTrans.rightDerivedToHomotopyCategory_comp_assoc, Limits.BinaryCofan.isColimit_iff_isIso_inl, Under.postEquiv_counitIso, MonoidalSingleObj.endMonoidalStarFunctorEquivalence_unitIso, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone_ι_app, Functor.whiskeringLeft₃Map_app_app, Adjunction.toEquivalence_unitIso_hom_app, Sieve.uliftNatTransOfLe_comm, MonoidalCategory.MonoidalRightAction.curriedActionActionOfMonoidalFunctorToEndofunctorIso_hom_app_app, ShortComplex.mapNatIso_hom, WithTerminal.coneEquiv_inverse_obj_pt_left, TransfiniteCompositionOfShape.map_isColimit, Join.mapWhiskerLeft_associator_hom, uliftYoneda_obj_map, Functor.LeibnizAdjunction.adj_counit_app_right, Quiv.adj_homEquiv, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_inv_app_app, LightProfinite.Extend.functor_map, instPreservesFiniteProductsFunctorColimOfPreadditive, Enriched.FunctorCategory.homEquiv_id, Limits.CompleteLattice.limitCone_isLimit_lift, Presheaf.final_toCostructuredArrow_comp_pre, Limits.PushoutCocone.ι_app_left, GrothendieckTopology.uliftYonedaCompSheafToPresheaf_hom_app_app, instPreservesFiniteLimitsFunctorOppositeSheafLeftAdjointSheafToPresheaf, Functor.mapTriangleRotateIso_hom_app_hom₂, SheafOfModules.pullback_comp_id, yoneda_preservesLimitsOfShape, Over.conePost_map_hom, piEquivalenceFunctorDiscrete_unitIso, MonoidalCategory.MonoidalRightAction.curriedAction_obj_map, Under.postComp_hom_app_right, ComposableArrows.opEquivalence_functor_map_app, shiftFunctorAdd'_add_zero_inv_app, FunctorToTypes.binaryProductIso_hom_comp_snd, Functor.mapGrpFunctor_map_app, Functor.mapCommMonCompIso_inv_app_hom_hom, GrothendieckTopology.W_inverseImage_whiskeringLeft, Limits.colimit_obj_ext_iff, Adjunction.Triple.rightToLeft_eq_counits, sheafBotEquivalence_unitIso, bifunctorComp₁₂Functor_map, FreeMonoidalCategory.tensorFunc_map_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_right_unitality, WithTerminal.mkCommaObject_left_map, PreGaloisCategory.instIsFundamentalGroupAutFunctorFintypeCat, Functor.rightDerivedZeroIsoSelf_hom_inv_id_app_assoc, Sieve.natTransOfLe_comm, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_left_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τl, Functor.curry₃_obj_obj_obj_map, Subfunctor.preimage_id, SSet.Truncated.rightExtensionInclusion_right_as, Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app, LocalizerMorphism.commShift_iso_hom_app_assoc, WithInitial.coconeEquiv_functor_map_hom, Functor.flip₂₃Functor_obj_obj_obj_map, NatTrans.op_whiskerLeft_assoc, Equivalence.unop_counitIso, Monoidal.rightUnitor_inv_app, MonoidalCategory.DayConvolution.braiding_naturality_right, FinitaryPreExtensive.hasPullbacks_of_is_coproduct, Functor.RightExtension.coneAtWhiskerRightIso_inv_hom, eHomFunctor_map_app, instHasExactLimitsOfShapeFunctorOfHasFiniteColimits, EnrichedCat.comp_whiskerRight, HomotopyCategory.instFullFunctorHomologicalComplexObjWhiskeringLeftQuotient, Comma.mapLeftIso_unitIso_inv_app_right, Functor.shiftIso_add, Sum.functorEquivInverseCompWhiskeringLeftInlIso_hom_app_app, WithTerminal.ofCommaMorphism_app, SheafOfModules.instPreservesFiniteLimitsFunctorOppositeAddCommGrpCatCompSheafToSheafSheafToPresheaf, Over.lift_obj, uliftYoneda_obj_obj, typeEquiv_counitIso_inv_app_val_app, CostructuredArrow.mapNatIso_counitIso_inv_app_left, OverPresheafAux.counitAuxAux_inv, Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, Functor.LeftExtension.postcomp₁_obj_hom_app, Functor.mapCommMonIdIso_hom_app_hom_hom, Functor.whiskerLeft_comp, TopologicalSpace.Opens.overEquivalence_unitIso_hom_app_left, SSet.stdSimplex.coe_edge_down_toOrderHom, Comma.mapLeftIso_unitIso_hom_app_left, Iso.inv_hom_id_app_app_app, Localization.StrictUniversalPropertyFixedTarget.prod_fac₂, ExactFunctor.whiskeringLeft_obj_obj_obj, WithTerminal.liftToTerminalUnique_inv_app, ComposableArrows.opEquivalence_inverse_obj, enrichedFunctorTypeEquivFunctor_apply_map, Functor.flippingEquiv_symm_apply_map_app, Limits.Fork.ofCone_π, Limits.pushoutCoconeOfLeftIso_ι_app_left, Monoidal.commMonFunctorCategoryEquivalence_counitIso, Equivalence.mapCommGrp_unitIso, AlgebraicTopology.DoldKan.N₂Γ₂_inv_app_f_f, Limits.CompleteLattice.finiteLimitCone_isLimit_lift, WithTerminal.mapComp_inv_app, Equivalence.invFunIdAssoc_hom_app, Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_X, WithTerminal.mkCommaMorphism_right, Functor.rightKanExtension_hom_ext_iff, Localization.Construction.WhiskeringLeftEquivalence.functor_map_hom_app, Functor.commShiftPullback_iso_eq, Limits.ProductsFromFiniteCofiltered.liftToFinset_obj_map, Limits.DiagramOfCocones.comp, Monoidal.ComonFunctorCategoryEquivalence.functorObjObj_comon_counit, ContinuousCohomology.MultiInd.d_comp_d_assoc, Action.FunctorCategoryEquivalence.inverse_obj_ρ_apply, yonedaMon_map_app, Limits.pullbackConeEquivBinaryFan_inverse_obj, Limits.Cones.postcomposeEquivalence_unitIso, shrinkYonedaEquiv_naturality, instPreservesLimitsOfShapeFunctorIndLimOfFinCategoryOfHasLimitsOfShape, Equivalence.unitIso_hom_app_comp_inverse_map_η_functor, CostructuredArrow.mapIso_counitIso_hom_app_left, LightCondensed.isoLocallyConstantOfIsColimit_inv, Functor.fullyFaithfulCancelRight_hom_app, ExactFunctor.whiskeringLeft_obj_map, GrothendieckTopology.plusFunctorWhiskerRightIso_inv_app, Functor.whiskeringLeft₃_obj_map_app_app_app_app_app, Functor.opUnopEquiv_functor, AlgebraicGeometry.exists_preimage_eq, Limits.IsIndObject.finallySmall, GrothendieckTopology.toPlus_comp_plusCompIso_inv, MonoidalCategory.DayConvolutionInternalHom.right_triangle_components, Enriched.FunctorCategory.functorEnriched_id_comp, Limits.coprod.functor_map_app, Iso.compInverseIso_hom_app, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_hom_app_app, Limits.KernelFork.IsLimit.isIso_ι, Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_inv_app_fst_app, yonedaEquiv_naturality', Condensed.comp_val, Idempotents.karoubiFunctorCategoryEmbedding_obj, Limits.CategoricalPullback.CatCommSqOver.transformObjComp_hom_app_snd_app, Functor.instIsRepresentableObjOppositeTypeYoneda, WithInitial.equivComma_functor_map_left, AlgebraicGeometry.ΓSpec.left_triangle, FunctorToTypes.prod.lift_fst, Subfunctor.eq_top_iff_isIso, Functor.mapCommGrpNatIso_inv_app_hom_hom_hom, sheafBotEquivalence_inverse_obj_val, Adjunction.toEquivalence_counitIso_inv_app, Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac, OverPresheafAux.restrictedYonedaObj_map, Enriched.Functor.whiskerRight_app_apply, Limits.colimitIsoSwapCompColim_inv_app, Localization.full_whiskeringLeft, WithInitial.coconeEquiv_inverse_obj_pt_left_as, Limits.Cones.postcomposeEquivalence_counitIso, SimplexCategory.revCompRevIso_inv_app, isDetector_iff_reflectsIsomorphisms_coyoneda_obj, Equivalence.changeFunctor_refl, MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app, CostructuredArrow.mapCompιCompGrothendieckProj_inv_app, CategoryOfElements.costructuredArrowULiftYonedaEquivalence_functor_obj, Adjunction.toEquivalence_unitIso_inv_app, Limits.CategoricalPullback.functorEquiv_counitIso_hom_app_fst_app, PresheafOfModules.toSheaf_map_sheafificationHomEquiv_symm, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₂, Limits.walkingSpanOpEquiv_counitIso_hom_app, Functor.postcomposeWhiskerLeftMapCone_inv_hom, Limits.Types.Colimit.ι_map_apply, PreGaloisCategory.instPreservesColimitsOfShapeActionFintypeCatAutFunctorSingleObjFunctorToActionOfFinite, TopCat.uliftFunctorCompForgetIso_inv_app, GrothendieckTopology.plusMap_comp_assoc, Limits.Cofork.π_precompose, Functor.PushoutObjObj.isPushout, Functor.cocones_obj, Limits.Cones.functorialityEquivalence_unitIso, Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₃, Limits.compCoyonedaSectionsEquiv_symm_apply_coe, Functor.OplaxMonoidal.whiskeringRight_δ_app, Enriched.Functor.functorHom_whiskerLeft_natTransEquiv_symm_app, Functor.flippingEquiv_symm_apply_obj_obj, Limits.coker.condition, Functor.constCompWhiskeringLeftIso_hom_app_app, Pretriangulated.Opposite.OpOpCommShift.iso_hom_app_assoc, Limits.Types.limitConeIsLimit_lift_coe, Adjunction.corepresentableBy_homEquiv, Over.postComp_inv_app_left, Monad.toMon_mon, CochainComplex.shiftFunctorAdd'_inv_app_f', Limits.coneOfAdj_pt, Limits.Cocone.equivStructuredArrow_unitIso, NatTrans.app_zero, LocalizerMorphism.rightDerivedFunctorComparison_fac_app, cosimplicialSimplicialEquiv_functor_map_app, Functor.curryingFlipEquiv_apply_obj, NatIso.unop_symm, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_right, Sum.associativityFunctorEquivNaturalityFunctorIso_inv_app_fst, Equivalence.congrFullSubcategory_unitIso, Functor.ShiftSequence.induced.shiftIso_hom_app_obj, IsSifted.colim_preservesFiniteProducts_of_isSifted, Equivalence.inverseFunctorObjIso_inv, Functor.coreCompInclusionIso_hom_app, AlgebraicTopology.DoldKan.N₂Γ₂ToKaroubiIso_hom_app, Equivalence.changeInverse_counitIso_inv_app, Functor.Monoidal.coreMonoidalTransport_μIso_inv, SingleFunctors.postcompIsoOfIso_hom_hom_app, NatTrans.isIso_iff_isIso_app, Functor.commShiftIso_hom_naturality_assoc, Limits.IndObjectPresentation.yoneda_isColimit_desc, Comma.mapRightEq_inv_app_left, Iso.inv_hom_id_app_app_assoc, Limits.KernelFork.condition, flippingIso_inv_toFunctor_map_app_app, Presheaf.tautologicalCocone'_pt, shiftFunctorAdd'_zero_add_hom_app, whiskering_preadditiveYoneda, MonadIso.toNatIso_inv, Pretriangulated.commShiftIso_unopUnop_inv_app, Functor.lanCompColimIso_inv_app, Limits.opCospan_hom_app, Functor.mapTriangleCommShiftIso_hom_app_hom₃, Profinite.exists_isClopen_of_cofiltered, FundamentalGroupoidFunctor.instIsIsoFunctorFundamentalGroupoidHomotopicMapsNatIso, isPullback_initial_to_of_cofan_isVanKampen, Limits.Bicone.ofColimitCocone_ι, Functor.uncurry_obj_obj, Grothendieck.map_id_eq, isSheaf_pointwiseColimit, Functor.flip₁₃Functor_obj_obj_obj_obj, SingleFunctors.shiftIso_add_inv_app, Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π, Functor.isLeftDerivedFunctor_of_inverts, lan_preservesFiniteLimits_of_preservesFiniteLimits, Functor.unopOpIso_hom_app, uliftYonedaEquiv_uliftYoneda_map, Functor.ShiftSequence.induced_shiftIso_hom_app_obj_assoc, Localization.SmallShiftedHom.equiv_shift', functorProdToProdFunctor_obj, BraidedCategory.Hexagon.functor₃₁₂'_map_app_app, instFaithfulFunctorOppositeTypeShrinkYoneda, yoneda_obj_map, Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.functorToInterchangeIso_hom_app_app, Cat.opFunctorInvolutive_hom_app_toFunctor_map, Functor.mapCommMonFunctor_obj, full_linearCoyoneda, LaxBraidedFunctor.isoMk_hom, functorProdFunctorEquivUnitIso_hom_app, Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_inv_app_hom, SmallObject.ιFunctorObj_eq, PreGaloisCategory.toAut_surjective_of_isPretransitive, Functor.commShiftIso_comp_inv_app, TwoP.swapEquiv_counitIso_inv_app_hom_toFun, Functor.leftExtensionEquivalenceOfIso₁_inverse_map_right, Functor.sumIsoExt_hom_app_inr, MonoidalCategory.MonoidalLeftAction.actionAssocNatIso_inv_app_app_app, Functor.equiv_functor_obj, AlgebraicTopology.DoldKan.compatibility_N₂_N₁_karoubi, IsGrothendieckAbelian.preservesColimit_coyoneda_obj_of_mono, Functor.Monoidal.whiskerRight_app_fst, Cat.opFunctorInvolutive_hom_app_toFunctor_obj, Limits.spanCompIso_inv_app_right, GlueData.diagramIso_inv_app_right, Limits.limit.conePointUniqueUpToIso_hom_comp_assoc, Limits.Cofan.mk_ι_app, EnrichedFunctor.forgetId_inv_app, WithTerminal.lift_map_liftStar, GrothendieckTopology.Point.W_isInvertedBy_presheafFiber, PreGaloisCategory.autMulEquivAutGalois_symm_app, WithTerminal.inclLiftToTerminal_inv_app, Limits.HasLimit.isoOfNatIso_inv_π, Adjunction.leftAdjointCompIso_inv_app, Sheaf.adjunction_counit_app_val, Equivalence.mapCommMon_unitIso, CatCommSq.vComp_iso_hom_app, Functor.mapCochainComplexShiftIso_inv_app_f, Under.mapCongr_hom_app, LocalizerMorphism.commShift_iso_inv_app_assoc, Localization.Monoidal.functorMonoidalOfComp_ε, LocalizerMorphism.equiv_smallHomMap', Functor.map_shiftFunctorCompIsoId_inv_app_assoc, CochainComplex.shiftFunctorAdd'_inv_app_f, coyonedaEquiv_naturality, Limits.BinaryCofan.isColimit_iff_isIso_inr, CategoryOfElements.fromCostructuredArrow_obj_snd, SingleFunctors.inv_hom_id_hom_assoc, Sigma.descUniq_inv_app, preservesColimitNatIso_hom_app, oppositeShiftFunctorZero_inv_app, MonoidalCategory.externalProductCompDiagIso_inv_app_app, Functor.LeftExtension.postcompose₂_obj_right_obj, Functor.prod'CompFst_inv_app, Limits.PushoutCocone.mk_ι_app, coyonedaEquiv_apply, Limits.PreservesColimit₂.map_ι_comp_isoObjConePointsOfIsColimit_hom_assoc, Functor.whiskeringLeft₂_obj_map_app_app_app, Functor.mapMonFunctor_map_app_hom, Functor.mapTriangleCommShiftIso_inv_app_hom₃, CostructuredArrow.mapIso_functor_map_right, Comonad.comparisonForget_inv_app, Equivalence.mkIso_hom, Equivalence.changeInverse_unitIso_inv_app, prod.rightUnitorEquivalence_counitIso, endofunctorMonoidalCategory_tensorObj_map, Limits.compCoyonedaSectionsEquiv_apply_app, Functor.isoSum_hom_app_inl, Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_hom_app, Limits.Multicofork.ofSigmaCofork_ι_app_right, Functor.pentagonIso_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompPointIso_inv_app, WithTerminal.equivComma_functor_obj_hom_app, Subfunctor.Subpresheaf.toRange_ι, Functor.isZero_iff, Functor.rightOpLeftOpIso_inv_app, Endofunctor.Adjunction.AlgCoalgEquiv.unitIso_inv_app_f, Enriched.FunctorCategory.enrichedComp_π_assoc, DinatTrans.compNatTrans_app, pointedToBipointedCompBipointedToPointedSnd_hom_app_toFun, Functor.mapMonIdIso_hom_app_hom, NatIso.prod_hom, Mono.cofanInr_of_binaryCoproductDisjoint, Join.mapPairComp_inv_app_right, Abelian.extFunctor_obj, Limits.PushoutCocone.ι_app_right, Functor.map_shiftFunctorComm_assoc, WithInitial.equivComma_inverse_map_app, Functor.coconeOfIsLeftKanExtension_ι, Limits.coneRightOpOfCocone_π, MonoidalCategory.DayConvolution.braiding_naturality_right_assoc, Grothendieck.grothendieckTypeToCat_counitIso_hom_app_coe, Functor.ShiftSequence.induced_isoShiftZero_hom_app_obj_assoc, MorphismProperty.FunctorsInverting.comp_hom_assoc, CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompYoneda, Limits.comp_lim_obj_ext_iff, Limits.LimitPresentation.self_diag, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, Limits.DiagramOfCones.conePoints_map, Limits.CategoricalPullback.CatCommSqOver.e_hom_app, OverPresheafAux.counitBackward_counitForward, AlgebraicTopology.DoldKan.map_PInfty_f, Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_map_hom_hom, Idempotents.instFullKaroubiFunctorKaroubiFunctorCategoryEmbedding, Limits.Multifork.app_right_eq_ι_comp_snd, Limits.colimitHomIsoLimitYoneda_hom_comp_π_assoc, Limits.Types.binaryProductFunctor_map_app, faithful_linearCoyoneda, Functor.functorHom_ext_iff, Over.iteratedSliceEquivOverMapIso_inv_app_left_left, SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁_hom_app_f_f, CategoryOfElements.costructuredArrowULiftYonedaEquivalence_functor_map, Functor.map_shiftFunctorCompIsoId_hom_app_assoc, ShiftMkCore.assoc_inv_app_assoc, ModuleCat.smulNatTrans_apply_app, Limits.PullbackCone.π_app_left, CostructuredArrow.mapNatIso_inverse_map_left, Pretriangulated.Triangle.invRotate_mor₁, Over.iteratedSliceEquivOverMapIso_hom_app_left_left, whiskeringRight_preservesColimitsOfShape, Comma.mapLeftComp_inv_app_right, TopCat.isClosed_iff_of_isColimit, Comma.equivProd_counitIso_inv_app, WithTerminal.isLimitEquiv_symm_apply_lift, Monoidal.MonFunctorCategoryEquivalence.functor_map_app_hom, Comma.coconeOfPreserves_ι_app_right, endofunctorMonoidalCategory_rightUnitor_inv_app, pre_id, Comma.toIdPUnitEquiv_unitIso_hom_app_right, Localization.instIsEquivalenceFunctorFunctorsInvertingWhiskeringLeftFunctor, Limits.Wedge.condition, Bicategory.leftUnitorNatIso_hom_app, Sheaf.ΓObjEquivSections_naturality_symm, FunctorToTypes.binaryProductLimit_lift, Limits.spanExt_inv_app_zero, Abelian.extFunctor_map_app, BraidedCategory.Hexagon.functor₂₁₃_map_app_app, WithInitial.equivComma_counitIso_hom_app_left, Limits.isIso_colimit_cocone_parallelPair_of_eq, BraidedCategory.ofBifunctor.Forward.firstMap₂_app_app_app, Equivalence.functor_map_ε_inverse_comp_counitIso_hom_app, Iso.unop_hom_inv_id_app, Coyoneda.naturality, MulEquiv.toSingleObjEquiv_unitIso_inv, GrothendieckTopology.sheafification_obj, Condensed.isoLocallyConstantOfIsColimit_inv, Mono.cofanInl_of_binaryCoproductDisjoint, NatTrans.IsMonoidal.comp, WithTerminal.liftFromOver_obj_obj, Join.mapPairLeft_inv_app, cosimplicialSimplicialEquiv_counitIso_inv_app_app, Codiscrete.natIsoFunctor_inv_app, Functor.commShiftIso_hom_naturality, Limits.IndObjectPresentation.toCostructuredArrow_obj_left, ModuleCat.uliftFunctorForgetIso_inv_app, Functor.CommShift.comp_commShiftIso_hom_app, CartesianMonoidalCategory.prodComparisonNatTrans_comp, Functor.precomposeWhiskerLeftMapCocone_hom_hom, ComposableArrows.opEquivalence_unitIso_hom_app, Equivalence.congrLeftFunctor_obj, Presheaf.isSeparator, BraidedCategory.ofBifunctor.Reverse.firstMap₂_app_app_app, PreGaloisCategory.FibreFunctor.end_isIso, bifunctorComp₁₂_obj, Functor.initial_const_of_isInitial, Subfunctor.equivalenceMonoOver_functor_obj, Limits.CatCospanTransform.rightIso_hom, SimplicialObject.isCoskeletal_iff, Limits.Multifork.app_left_eq_ι, Limits.Cocone.fromStructuredArrow_obj_pt, η_naturality, Functor.opUnopEquiv_inverse, Monoidal.MonFunctorCategoryEquivalence.inverse_map_hom_app, GrothendieckTopology.Point.toPresheafFiber_map_bijective, Abelian.LeftResolution.karoubi_F, AddCommMonCat.coyoneda_map_app, Monoidal.CommMonFunctorCategoryEquivalence.counitIso_hom_app_app_hom_hom, functorProdFunctorEquiv_unitIso, Functor.isoCopyObj_inv_app, Functor.instIsCardinalAccessibleObjConst, AlgebraicTopology.DoldKan.N₂Γ₂_compatible_with_N₁Γ₀, Limits.coconeOfConeRightOp_ι, Limits.Fork.op_π, Limits.piObjIso_hom_comp_π_assoc, AlgebraicGeometry.Scheme.restrictFunctorΓ_hom_app, Limits.limit.conePointUniqueUpToIso_inv_comp_assoc, Functor.uncurryObjFlip_inv_app, Over.ConstructProducts.conesEquivUnitIso_inv_app_hom, conjugateEquiv_symm_of_iso, MonoidalCategory.MonoidalLeftAction.curriedAction_map_app, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_hom_app_app, PreGaloisCategory.continuousSMul_aut_fiber, CatCommSq.iso_inv_naturality_assoc, Under.liftCone_π_app, Limits.Cocone.ofCofork_ι, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τr, TwoSquare.isIso_lanBaseChange_app_iff, TwoSquare.instIsIsoFunctorLanBaseChangeOfGuitartExact, Comma.mapLeftIso_counitIso_hom_app_left, Limits.Cones.postcomposeEquivalence_functor, tensoringLeft_linear, SmallObject.instIsIsoRightAppArrowMapToTypeOrdFunctorIterationFunctor, Limits.isFiltered_costructuredArrow_yoneda_of_preservesFiniteLimits, Pairwise.cocone_ι_app, Functor.rightDerivedNatTrans_fac, Localization.liftNatTrans_app, NatTrans.naturality_app_assoc, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_inv_app_app, Limits.Fork.app_one_eq_ι_comp_left, Localization.StrictUniversalPropertyFixedTarget.prod_fac₁, ULift.equivalence_unitIso_hom, Limits.CatCospanTransform.inv_base, GrothendieckTopology.W.monoidal, IsGrothendieckAbelian.IsPresentable.injectivity₀.F_map, Monoidal.ComonFunctorCategoryEquivalence.counitIso_hom_app_app_hom, Mat_.embeddingLiftIso_inv_app, Endofunctor.Adjunction.algebraCoalgebraEquiv_counitIso_inv_app_f, Under.forgetMapInitial_hom_app, Condensed.lanPresheafNatIso_hom_app, Limits.FormalCoproduct.cochainComplexFunctor_obj_d, Limits.fiberwiseColim_map_app, Functor.triangle, Functor.instIsLeftDerivedFunctorLiftHomFac, sum.inrCompInrCompInverseAssociator_inv_app_down, Limits.limitObjIsoLimitCompEvaluation_hom_π, CostructuredArrow.CreatesConnected.raiseCone_pt, Limits.colimCompFlipIsoWhiskerColim_hom_app_app, Functor.mapHomologicalComplexIdIso_inv_app_f, conjugateEquiv_symm_comp, Discrete.sumEquiv_counitIso_hom_app, Limits.DiagramOfCocones.mkOfHasColimits_map_hom, Comma.mapRightIso_functor_map_right, Functor.leftKanExtensionCompIsoOfPreserves_hom_fac_app_assoc, Sieve.functorInclusion_app, Functor.isoWhiskerLeft_right_assoc, ShortComplex.opEquiv_counitIso, Pretriangulated.shiftFunctorZero_op_hom_app, AlgebraicGeometry.Scheme.Modules.pushforwardComp_hom_app_app, Rep.Tor_map, Mon.limitCone_π_app_hom, Comma.limitAuxiliaryCone_π_app, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ι_assoc, prodOpEquiv_unitIso_inv_app, Localization.comp_liftNatTrans_assoc, Idempotents.KaroubiFunctorCategoryEmbedding.obj_obj_X, Limits.IndObjectPresentation.toCostructuredArrow_map_left, Functor.postcompose₃_map_app_app_app_app, Limits.CategoricalPullback.toCatCommSqOver_obj_iso_hom_app, WithInitial.equivComma_functor_map_right_app, frobeniusMorphism_iso_of_preserves_binary_products, Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply, DifferentialObject.shiftFunctorAdd_hom_app_f, WithTerminal.coneEquiv_inverse_obj_pt_hom, Over.postEquiv_counitIso, WithInitial.coconeEquiv_inverse_obj_ι_app_right, ChosenPullbacksAlong.pullbackId_hom_counit, Limits.multispanIndexCoend_left, ι_colimitCompWhiskeringRightIsoColimitComp_hom, Subfunctor.orderIsoSubobject_apply, Over.ConstructProducts.conesEquivCounitIso_hom_app_hom_left, Functor.ranObjObjIsoLimit_inv_π_assoc, MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_hom_app_app, Limits.PreservesLimit₂.isoObjConePointsOfIsColimit_inv_comp_map_π_assoc, Functor.precomposeWhiskerLeftMapCocone_inv_hom, SheafOfModules.pushforwardCongr_inv_app_val_app, Functor.PullbackObjObj.ofHasPullback_π, Monoidal.comonFunctorCategoryEquivalence_unitIso, Functor.FullyFaithful.whiskeringRight_preimage_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_map_right, ContAction.resComp_hom, Functor.RightExtension.precomp_obj_right, preservesLimits_preadditiveYoneda_obj, instPreservesFiniteLimitsFunctorOppositeSheafPresheafToSheaf, Limits.limitCompWhiskeringLeftIsoCompLimit_inv_π_assoc, CochainComplex.shiftFunctorZero'_hom_app_f, whiskeringLeft_preservesLimits, CartesianMonoidalCategory.prodComparisonNatIso_hom, Functor.IsCoverDense.Types.appIso_inv, Limits.IsColimit.coconePointsIsoOfNatIso_inv_desc_assoc, Endofunctor.Algebra.equivOfNatIso_inverse, MonoidalOpposite.tensorRightUnmopIso_inv_app, Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_assoc, HomologicalComplex₂.flipEquivalenceUnitIso_inv_app_f_f, CosimplicialObject.Truncated.whiskering_obj_map_app, isCodetector_iff_reflectsIsomorphisms_yoneda_obj, Functor.PushoutObjObj.ι_iso_of_iso_right_hom, Idempotents.whiskeringLeft_obj_preimage_app, MonoidalCategory.DayConvolution.corepresentableBy_homEquiv_symm_apply, Limits.cospanCompIso_inv_app_right, Cat.freeMapCompIso_hom_app, Equivalence.sheafCongr.unitIso_hom_app_val_app, Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.isoAux_hom_app, Functor.Monoidal.tensorObjComp_inv_app, MonoidalCategory.DayFunctor.equiv_functor_obj, Iso.map_hom_inv_id_app, Functor.op_commShiftIso_inv_app_assoc, Functor.OplaxMonoidal.ofBifunctor.topMapᵣ_app, Profinite.Extend.functor_obj, ModuleCat.matrixEquivalence_unitIso, Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₂, Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_id, Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_hom_app_snd_app, AlgebraicGeometry.ΓSpec.isIso_locallyRingedSpaceAdjunction_counit, Abelian.LeftResolution.instEpiKaroubiAppπObjToKaroubi, prod.prodFunctorToFunctorProdAssociator_inv_app_app, Functor.mapGrpCompIso_hom_app_hom_hom, Functor.map_shiftFunctorCompIsoId_hom_app, additive_coyonedaObj', Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom_assoc, MonoidalCategory.MonoidalRightAction.actionAssocNatIso_inv_app_app_app, Subfunctor.range_eq_ofSection', Functor.mapTriangleInvRotateIso_inv_app_hom₂, Functor.FullyFaithful.homNatIso'_hom_app_down, Limits.sigmaConst_obj_map, Functor.leftExtensionEquivalenceOfIso₁_inverse_obj_right, Functor.leftOpId_inv_app, HomotopyCategory.instFaithfulFunctorHomologicalComplexObjWhiskeringLeftQuotient, Limits.IsColimit.coconePointsIsoOfEquivalence_inv, Functor.Initial.extendCone_map_hom, Comonad.comparisonForget_hom_app, ShortComplex.FunctorEquivalence.inverse_obj_X₁, SheafOfModules.conjugateEquiv_pullbackComp_inv, Limits.Cone.toCostructuredArrow_map, NatTrans.CommShiftCore.shift_app_assoc, Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_inv_app_snd_app, AlgebraicTopology.DoldKan.whiskerLeft_toKaroubi_N₂Γ₂_hom, WithTerminal.liftFromOverComp_hom_app, regularTopology.isSheaf_yoneda_obj, Functor.whiskeringLeft₃Obj_obj, Limits.colimit.map_post, WithInitial.coconeEquiv_functor_obj_ι_app_of, shiftFunctorAdd'_add_zero, Functor.RepresentableBy.equivUliftYonedaIso_symm_apply_homEquiv, Idempotents.functorExtension₂_obj_obj_X, Limits.BinaryFan.π_app_right, shiftFunctorCompIsoId_add'_hom_app, MonoidalCategory.DayConvolution.triangle, Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_comp, Limits.CategoricalPullback.functorEquiv_functor_obj_iso_hom_app, AlgebraicGeometry.opensCone_π_app, Limits.colimitFlipIsoCompColim_hom_app, bifunctorComp₂₃Functor_map, Equivalence.invFunIdAssoc_inv_app, Limits.CategoricalPullback.CatCommSqOver.transformObjId_inv_app_snd_app, Functor.IsCoverDense.Types.sheafIso_hom_val, Limits.coendFunctor_obj, Limits.colimit.isoColimitCocone_ι_inv_assoc, MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.leftUnitor_hom_unit_app, sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_app_app, Limits.end_.map_id, StructuredArrow.commaMapEquivalenceInverse_obj, Limits.BinaryCofan.ι_app_right, MorphismProperty.Over.mapComp_hom_app_left, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₂, GrothendieckTopology.sheafToPresheaf_map_sheafComposeNatTrans_eq_sheafifyCompIso_inv, Limits.walkingParallelPairOpEquiv_unitIso_inv_app_zero, ParametrizedAdjunction.homEquiv_symm_naturality_two, Idempotents.app_p_comm_assoc, toOverIteratedSliceForwardIsoPullback_hom_app_left, Mon.EquivLaxMonoidalFunctorPUnit.unitIso_hom_app_hom_app, Functor.CommShift₂.comm, Limits.Fork.π_comp_hom_assoc, MonObj.mopEquiv_counitIso_hom_app_hom_unmop, pullbackShiftFunctorAdd'_hom_app, Limits.IsColimit.homEquiv_symm_naturality, Functor.Accessible.Limits.isColimitMapCocone.surjective, Under.mapComp_hom, GrothendieckTopology.toPlusNatTrans_app, ε_naturality, Functor.RightExtension.IsPointwiseRightKanExtension.isIso_hom, Functor.RightExtension.mk_right_as, Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv_assoc, TwistShiftData.z_zero_left, MonoidalCategory.curriedTensorPreFunctor_obj, Functor.coconeTypesEquiv_symm_apply_ι, TopologicalSpace.Opens.mapId_inv_app, NatTrans.mono_iff_mono_app, MonoidalCategory.DayConvolution.unit_app_braiding_inv_app, Functor.leftExtensionEquivalenceOfIso₁_counitIso_inv_app_right_app, Functor.flip₁₃Functor_obj_map_app_app, MorphismProperty.PreIndSpreads.exists_isPushout, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_map_left_app, Subfunctor.Subpresheaf.epi_iff_range_eq_top, Functor.isIso_ranAdjunction_homEquiv_iff, Limits.lim_obj, Functor.isoWhiskerLeft_inv, WithInitial.mkCommaObject_right_map, Functor.isIso_of_isLeftDerivedFunctor_of_inverts, shiftFunctorZero_inv_app_shift, ObjectProperty.fullSubcategoryCongr_counitIso, WithInitial.equivComma_functor_obj_hom_app, PreGaloisCategory.FiberFunctor.isPretransitive_of_isConnected, Limits.WalkingMultispan.functorExt_inv_app, Adjunction.commShiftIso_inv_app_counit_app_assoc, Limits.Multicofork.map_ι_app, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_map, Functor.leftKanExtension_hom_ext_iff, Enriched.Functor.natTransEquiv_symm_app_app_apply, Limits.Cones.whiskeringEquivalence_counitIso, MorphismProperty.instIsStableUnderCoproductsOfShapeFunctorMonomorphismsOfHasCoproductsOfShapeOfHasPullbacks, Functor.CommShift.id_commShiftIso_inv_app, Limits.isIndObject_limit_comp_yoneda, Tor_obj, Localization.lift₂NatIso_inv, Functor.curryingFlipEquiv_symm_apply_obj_map, Limits.CategoricalPullback.CatCommSqOver.transform_map_app_snd_app, TransfiniteCompositionOfShape.ici_isoBot, StructuredArrow.mapNatIso_inverse_obj_hom, Functor.commShiftIso_inv_naturality_assoc, Pretriangulated.rotCompInvRot_inv_app_hom₃, HomotopicalAlgebra.CofibrantObject.instIsIsoFunctorWhiskerRightHoCatιCompResolutionNatTransOfIsLocalizationWeakEquivalences, Endofunctor.Algebra.functorOfNatTransEq_inv_app_f, NatTrans.IsMonoidal.id, Functor.whiskerLeft_twice, GrothendieckTopology.uliftYonedaIsoYoneda_hom_app_val_app, MulEquiv.toSingleObjEquiv_counitIso_inv, TopCat.coinduced_of_isColimit, Limits.Cocone.toCostructuredArrowCocone_ι_app, Limits.isFiltered_costructuredArrow_yoneda_iff_nonempty_preservesFiniteLimits, Functor.whiskeringLeft₃ObjObjObj_obj_obj_obj_obj, uliftYoneda_obj_map_down, Limits.CatCospanTransformMorphism.left_coherence, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_right, Limits.PushoutCocone.op_π_app, Equivalence.congrLeft_unitIso_inv_app, NatTrans.op_comp, shiftFunctorAdd'_assoc_inv_app_assoc, Functor.LeftExtension.postcompose₂ObjMkIso_hom_right_app, Functor.curry₃_map_app_app_app, MonoidalOpposite.unmopEquiv_counitIso_hom_app, Comonad.ForgetCreatesLimits'.newCone_π, mateEquiv_symm_apply, Functor.sheafPushforwardContinuousComp_inv_app_val_app, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap_assoc, Monoidal.commMonFunctorCategoryEquivalence_unitIso, Limits.limit.lift_π_app, Limits.limit_obj_ext_iff, Limits.Cone.equiv_inv_π, biconeMk_map, WithInitial.commaFromUnder_obj_hom_app, Functor.rightDerivedNatTrans_comp_assoc, CompHausLike.LocallyConstant.adjunction_left_triangle, Functor.ranCounit_app_app_ranAdjunction_unit_app_app_assoc, Adjunction.LeftAdjointCommShift.iso_inv_app, AlgebraicTopology.DoldKan.toKaroubiCompN₂IsoN₁_hom_app, Functor.mapTriangleInvRotateIso_inv_app_hom₁, Equivalence.mapGrp_unitIso, Limits.hasColimitsOfShape_iff_isRightAdjoint_const, Limits.Cocone.isColimit_iff_isIso_colimMap_ι, StructuredArrow.commaMapEquivalenceFunctor_obj_left, Limits.CategoricalPullback.functorEquiv_unitIso_hom_app_app_snd, Pseudofunctor.DescentData.pullFunctorIso_hom_app_hom, HomologicalComplex.complexOfFunctorsToFunctorToComplex_map_app_f, NatIso.unop_whiskerRight, Functor.curryingEquiv_symm_apply_map_app, Functor.leftOpRightOpEquiv_inverse_map, Equivalence.functorFunctor_obj, WithTerminal.inclLift_inv_app, Join.InclLeftCompRightOpOpEquivFunctor_hom_app, PreGaloisCategory.FibreFunctor.end_isUnit, Iso.isoFunctorOfIsoInverse_inv_app, Cat.opFunctorInvolutive_inv_app_toFunctor_map, Functor.leftOpRightOpEquiv_unitIso_hom_app, CostructuredArrow.mapNatIso_inverse_obj_hom, HomotopicalAlgebra.CofibrantObject.instIsIsoFunctorHoCatAdjCounit', Functor.Final.extendCocone_obj_ι_app', WithInitial.commaFromUnder_obj_right, MonoidalCategory.DayConvolution.symmetry, Adjunction.leftAdjointUniq_trans_app, flippingIso_hom_toFunctor_obj_obj_map, Limits.parallelPair.ext_hom_app, SheafOfModules.pullback_id_comp, HasLiftingProperty.transfiniteComposition.SqStruct.w, Mon.EquivLaxMonoidalFunctorPUnit.counitIso_inv_app_hom, SmallObject.SuccStruct.restrictionLTOfCoconeIso_hom_app, WithInitial.equivComma_inverse_obj_map, Functor.elementsFunctor_map, Equivalence.sheafCongrPreregular_counitIso_hom_app_val_app, Limits.lim_ε_π, Adjunction.whiskerLeft_counit_iso_of_L_fully_faithful, Join.mapWhiskerRight_associator_hom, full_preadditiveCoyoneda, Functor.leftKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, Functor.IsCoverDense.restrictHomEquivHom_naturality_right_assoc, SimplicialObject.whiskering_map_app_app, ParametrizedAdjunction.arrowHomEquiv_apply_right_fst_assoc, PreGaloisCategory.nhds_one_has_basis_stabilizers, Limits.reflexivePair.mkNatIso_inv_app, toOverPullbackIsoToOver_hom_app_left, Functor.flip₁₃_obj_obj_map, Functor.RightExtension.postcomp₁_map_left_app, cones_obj_map_app, Limits.colimitHomIsoLimitYoneda'_inv_comp_π_assoc, shiftFunctorAdd'_add_zero_hom_app, Limits.Types.Small.limitCone_π_app, ComonadIso.mk_hom_toNatTrans, Limits.instIsIPCFunctor, Limits.sigmaConst_map_app, Comma.toIdPUnitEquiv_counitIso_hom_app, Limits.walkingSpanOpEquiv_unitIso_inv_app, Limits.PushoutCocone.coequalizer_ext, MonoidalCategory.curriedTensor_obj_map, Localization.Monoidal.functorCoreMonoidalOfComp_μIso_inv, Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_X_obj, HomologicalComplex.natIsoSc'_hom_app_τ₂, LocalizerMorphism.homMap_apply_assoc, toSheafify_plusPlusIsoSheafify_hom, Limits.Fork.app_one_eq_ι_comp_right_assoc, Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac_app, WithTerminal.ofCommaObject_map, Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_obj_iso_inv, HomotopicalAlgebra.CofibrantObject.instIsIsoFunctorHoCatCounitHoCatAdj, Limits.Cocones.functoriality_obj_ι_app, Limits.opCospan_inv_app, Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc, Equivalence.congrLeft_unitIso_hom_app, Limits.IsLimit.conePointsIsoOfNatIso_inv, SSet.Truncated.HomotopyCategory.mkNatIso_inv_app_mk, Limits.Cone.overPost_pt, Comma.mapRightComp_hom_app_left, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_left, BinaryCofan.mono_inr_of_isVanKampen, commAlgCatEquivUnder_counitIso, ExponentiableMorphism.pushforwardComp_hom_counit_assoc, Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_inv_app_snd_app, Limits.CatCospanTransformMorphism.left_coherence_app, Monoidal.leftUnitor_inv_app, sum.inlCompAssociator_hom_app, Pretriangulated.invRotCompRot_hom_app_hom₂, Equivalence.sheafCongrPrecoherent_counitIso_inv_app_val_app, Functor.mapTriangleRotateIso_hom_app_hom₃, ReflQuiv.adj.homEquiv_naturality_left_symm, conjugateEquiv_counit, NatTrans.CommShiftCore.shift_app_comm_assoc, MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_ε_app, SimplicialObject.Truncated.rightExtensionInclusion_right_as, whiskerRight_ι_colimitCompWhiskeringRightIsoColimitComp_inv_assoc, EnrichedFunctor.category_comp_out, Functor.Initial.limit_cone_comp_aux, StructuredArrow.commaMapEquivalenceFunctor_map_left, Functor.sheafPushforwardCocontinuousCompSheafToPresheafIso_inv, BraidedCategory.Hexagon.functor₁₃₂'_map_app_app, Limits.CategoricalPullback.CatCommSqOver.precompose_map_whiskerLeft, Adjunction.unit_isIso_of_L_fully_faithful, Functor.LaxMonoidal.ofBifunctor.topMapᵣ_app, Functor.PullbackObjObj.mapArrowRight_comp, Functor.flippingEquiv_symm_apply_obj_map, Monoidal.MonFunctorCategoryEquivalence.inverseObj_X, Functor.instIsEquivalenceObjWhiskeringLeft, HomotopicalAlgebra.CofibrantObject.instIsIsoFunctorResolutionCompToLocalizationNatTrans, Functor.LeftExtension.postcomp₁_obj_right_map, Subfunctor.instEpiFunctorTypeToRange, Adjunction.rightAdjointUniq_trans_app_assoc, Limits.pointwiseProductCompEvaluation_inv_app, bifunctorComp₁₂Obj_obj_map, Idempotents.karoubiCochainComplexEquivalence_counitIso_hom, Functor.ranObjObjIsoLimit_hom_π_assoc, Functor.sheafPushforwardContinuousComp_hom_app_val_app, ExactFunctor.whiskeringRight_obj_obj_obj, CartesianMonoidalCategory.prodComparisonNatTrans_id, instReflectsIsomorphismsSheafFunctorOppositeSheafToPresheaf, Functor.flip₂₃Functor_obj_obj_map_app, Limits.isLimitConeOfAdj_lift, CochainComplex.shiftFunctorAdd_inv_app_f, Adjunction.compPreadditiveYonedaIso_hom_app_app_apply, Limits.ι_colimitLimitIso_limit_π_assoc, Limits.IndObjectPresentation.yoneda_ι_app, TopologicalSpace.Opens.overEquivalence_counitIso_inv_app, Triangulated.Octahedron.map_m₁, Limits.colimIsoFlipCompWhiskerColim_hom_app_app, AdditiveFunctor.ofLeftExact_obj_fst, Functor.Monoidal.whiskerRight_app_snd_assoc, Limits.Types.Limit.lift_π_apply, Equivalence.ext_iff, sum.inrCompInlCompAssociator_inv_app_down_down, Functor.PreservesPointwiseLeftKanExtensionAt.preserves, AddCommGrpCat.coyonedaType_obj_map, Limits.Cofork.condition, Monoidal.comonFunctorCategoryEquivalence_functor, whiskeringRightCompEvaluation_hom_app, shiftFunctorAdd_assoc_hom_app_assoc, Limits.cospanExt_inv_app_one, Limits.Cofork.app_zero_eq_comp_π_right, instPreservesColimitsOfShapeSheafExtensiveTopologyFunctorOppositeSheafToPresheafOfPreservesFiniteProductsColim, Functor.flip₂₃Functor_map_app_app_app, Functor.PullbackObjObj.π_iso_of_iso_right_inv, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₁, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₂, NatTrans.CommShiftCore.shift_comm, MorphismProperty.FunctorialFactorizationData.functorCategory.Z_obj_obj, Limits.end_.hom_ext_iff, ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst, PresheafOfModules.toPresheaf_map_app_apply, Equivalence.symmEquivInverse_obj_counitIso_inv, yonedaCommGrpGrp_obj, Limits.ConeMorphism.w_assoc, ShortComplex.FunctorEquivalence.functor_obj_map, ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₁, Limits.limitUncurryIsoLimitCompLim_inv_π, conjugateEquiv_rightUnitor_hom, endofunctorMonoidalCategory_whiskerLeft_app, LocalizerMorphism.equiv_smallShiftedHomMap, AddCommGrpCat.coyonedaType_obj_obj_coe, FreeGroupoid.mapComp_inv_app, Pretriangulated.invRotCompRot_inv_app_hom₁, Adjunction.unit_app_shift_commShiftIso_inv_app_assoc, Limits.IsIndObject.instIsClosedUnderIsomorphismsFunctorOppositeType, Functor.commShiftOfLocalization.iso_inv_app_assoc, Sieve.sieveOfSubfunctor_apply, Limits.PullbackCone.unop_ι_app, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_inv_app_hom, Functor.isDenseAt_iff, Functor.Monoidal.whiskeringLeft_η_app, Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality_assoc, Idempotents.functorExtension₂_obj_obj_p, Limits.FormalCoproduct.evalOp_map_app, Functor.instReflectsIsomorphismsDiscreteObjWhiskeringLeftIncl, SmallObject.SuccStruct.arrowMap_ofCocone_to_top, Limits.Multifork.toPiFork_π_app_one, SingleFunctors.hom_inv_id_hom, Limits.walkingParallelFamilyEquivWalkingParallelPair_unitIso_inv_app, Functor.IsCoverDense.Types.presheafIso_inv_app, Limits.pullbackConeOfLeftIso_π_app_none, OrderHom.equivalenceFunctor_functor_obj_obj, cosimplicialSimplicialEquiv_unitIso_hom_app, Join.inclRightCompOpEquivInverse_hom_app_op, AddCommGrpCat.Colimits.toCocone_ι_app, Limits.coconeOfDiagramTerminal_ι_app, Limits.CategoricalPullback.CatCommSqOver.precompose_obj_map_fst_app, Limits.pullbackObjIso_hom_comp_fst, Functor.LaxMonoidal.ofBifunctor.firstMap₁_app_app_app, AddCommGrpCat.Colimits.Quot.ι_desc, Preorder.coconeOfUpperBound_ι_app, Limits.cospanOp_hom_app, Sheaf.isConstant_iff_isIso_counit_app', GrothendieckTopology.Point.toPresheafFiber_w_apply, shiftFunctorZero_hom_app_shift, NatIso.op_associator, whiskeringLeft_preservesColimit, Limits.asEmptyCocone_ι_app, coherentTopology.isSheaf_yoneda_obj, ModuleCat.homEquiv_extendScalarsComp, Equivalence.changeFunctor_unitIso_inv_app, unitOfTensorIsoUnit_inv_app, Limits.Concrete.to_product_injective_of_isLimit, TopologicalSpace.Opens.overEquivalence_unitIso_inv_app_left, preservesFiniteLimits_presheafToSheaf, NatTrans.naturality_app, sum.inlCompInlCompAssociator_inv_app_down, Limits.isIso_limit_cone_parallelPair_of_eq, Subfunctor.Subpresheaf.range_le_equalizer_iff, Sieve.uliftFunctorInclusion_app, CategoryOfElements.costructuredArrowULiftYonedaEquivalence_counitIso, skyscraperPresheafCocone_ι_app, Adjunction.CommShift.compatibilityCounit_left, Functor.LeftExtension.coconeAtFunctor_obj, AlgebraicTopology.DoldKan.map_P, Functor.flipping_unitIso_hom_app_app_app, Triangulated.SpectralObject.id_hom, MonoidalCategory.externalProductBifunctorCurried_map_app_app_app, Equivalence.inverseFunctorObj'_hom_app, Limits.IndObjectPresentation.toCostructuredArrow_obj_hom, Presheaf.hasSeparator, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τr, Functor.op_commShiftIso_inv_app, Comma.unopFunctorCompSnd_inv_app, PresheafOfModules.map_comp, conjugateEquiv_mateEquiv_vcomp, cocones_obj_map_app, PresheafOfModules.instPreservesLimitsOfShapeFunctorOppositeAbToPresheaf, obj_η_app_assoc, coyonedaPreservesLimitsOfShape, BraidedCategory.Hexagon.functor₁₂₃'_map_app_app, Functor.instIsRightKanExtensionObjRanAppRanCounit, LocalizerMorphism.guitartExact_of_isLeftDerivabilityStructure', ShiftedHom.opEquiv'_symm_apply, Limits.colimitPointwiseProductToProductColimit_app, yonedaFunctor_preservesLimits, Idempotents.DoldKan.η_inv_app_f, Functor.mapTriangleIdIso_hom_app_hom₃, Limits.PullbackCone.isoMk_inv_hom, Functor.rightDerivedZeroIsoSelf_inv_hom_id_app_assoc, IsFinitelyPresentable.exists_hom_of_isColimit, MorphismProperty.functorCategory_monomorphisms, Limits.colim_obj, Over.opEquivOpUnder_counitIso, NatTrans.mono_iff_mono_app', SimplicialObject.Augmented.whiskering_map_app_left, AdditiveFunctor.forget_map, Functor.mapCone₂_pt, AddCommGrpCat.HasLimit.productLimitCone_cone_π, Comma.coconeOfPreserves_ι_app_left, Functor.closedUnit_app_app, ProdPreservesConnectedLimits.forgetCone_pt, Limits.filtered_colim_preservesFiniteLimits, Functor.LeftExtension.coconeAtWhiskerRightIso_hom_hom, OverPresheafAux.counitAux_hom, Functor.RightExtension.IsPointwiseRightKanExtensionAt.isIso_hom_app, instPreservesFilteredColimitsOfSizeObjOppositeFunctorTypeCoyonedaOpOfIsFinitelyPresentable, CostructuredArrow.mapNatIso_unitIso_hom_app_left, plusPlusAdjunction_counit_app_val, SmallObject.SuccStruct.extendToSuccRestrictionLEIso_inv_app, MonoidalCategory.Limits.preservesLimit_curriedTensor, Functor.instIsEquivalenceLeftExtensionCompPrecomp, NatTrans.CommShiftCore.shift_comm_assoc, Functor.equiv_unitIso, Limits.PreservesLimit₂.nonempty_isLimit_mapCone₂, mateEquiv_conjugateEquiv_vcomp, MonoidalCategory.tensoringRight_ε, Limits.coconeOfDiagramInitial_ι_app, GrothendieckTopology.overMapPullbackCongr_eq_eqToIso, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_app, Functor.mapHomologicalComplex_commShiftIso_inv_app_f, Functor.leftExtensionEquivalenceOfIso₁_inverse_obj_hom_app, CategoryOfElements.fromCostructuredArrow_map_coe, GradedObject.mapBifunctor_map_app, Functor.sheafPushforwardCocontinuousCompSheafToPresheafIso_hom, Limits.coconeFiberwiseColimitOfCocone_ι_app, Limits.limit.isoLimitCone_inv_π_assoc, Functor.whiskeringLeft₃_obj_obj_obj_map_app_app_app, Equivalence.inverseFunctorMapIso_symm_eq_isoInverseOfIsoFunctor, CatCenter.smul_iso_inv_eq_assoc, Localization.Monoidal.functorCoreMonoidalOfComp_μIso_hom, Idempotents.KaroubiUniversal₁.counitIso_hom_app_app_f, Functor.CommShift.id_commShiftIso_hom_app, groupHomology.isoShortComplexH1_inv, isoSheafify_hom, Monad.monToMonad_map_toNatTrans, MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_tensorHom_hom_eq_tensorHom, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₃, Adjunction.commShiftIso_hom_app_counit_app_shift_assoc, Localization.Monoidal.functorMonoidalOfComp_ε_assoc, Functor.Monoidal.transport_η_assoc, Limits.Cotrident.IsColimit.homIso_symm_apply, Limits.ColimitPresentation.w_assoc, SheafOfModules.pushforwardComp_hom_app_val_app, instSmallFunctorOfLocallySmall, Functor.flipping_functor_obj_map_app, Bicategory.postcomposing_map_app, Limits.Cones.postcompose_obj_π, Pretriangulated.TriangleOpEquivalence.unitIso_inv_app, AlgebraicTopology.DoldKan.toKaroubiCompN₂IsoN₁_inv_app, Endofunctor.Adjunction.algebraCoalgebraEquiv_unitIso_inv_app_f, Idempotents.KaroubiUniversal₁.counitIso_inv_app_app_f, Functor.LaxMonoidal.whiskeringRight_μ_app, Subfunctor.Subpresheaf.range_id, MonoidalCategory.DayConvolution.unit_app_braiding_hom_app, StructuredArrow.map_map_left, GradedObject.mapBifunctorObjObjSingle₀Iso_inv, GrothendieckTopology.Point.instIsIsoMapFunctorOppositePresheafFiberToSheafify, Functor.PullbackObjObj.mapArrowLeft_left, eHomFunctor_obj_map, Functor.instPreservesLimitOfIsCoreflexivePairDiscreteObjWhiskeringLeftIncl, Adjunction.rightAdjointUniq_hom_counit_assoc, Presheaf.isLocallySurjective_comp, Localization.Monoidal.isInvertedBy₂, instPreservesFiniteLimitsObjFunctorLeftExactFunctor, Functor.isoWhiskerLeft_trans_isoWhiskerRight_assoc, Functor.triangleIso_assoc, GrothendieckTopology.Point.Hom.presheafFiber_id, Bicategory.rightUnitorNatIso_inv_app, ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd, Functor.flipIsoCurrySwapUncurry_hom_app_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso_hom_app_app, SingleFunctors.postcomp_shiftIso_inv_app, shiftFunctorAdd_assoc_inv_app_assoc, Functor.mapCone₂_π_app, yonedaGrpObjIsoOfRepresentableBy_hom, SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc, Monoidal.ComonFunctorCategoryEquivalence.functor_obj, DerivedCategory.instFaithfulFunctorHomotopyCategoryIntUpObjWhiskeringLeftQh, Limits.Cones.functoriality_map_hom, Functor.instFullProdUncurry, Subfunctor.lift_ι_assoc, FreeGroupoid.mapId_inv_app, Functor.LeftExtension.precomp_obj_right, Limits.limitFlipIsoCompLim_inv_app, shiftFunctorAdd_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_hom_app, Limits.colimitObjIsoColimitCompEvaluation_ι_app_hom, toOverIsoToOverUnit_hom_app_left, Adjunction.compYonedaIso_inv_app_app, GrothendieckTopology.preservesSheafification_iff_of_adjunctions_of_hasSheafCompose, yonedaGrpObjIsoOfRepresentableBy_inv, Equivalence.changeInverse_counitIso_hom_app, Functor.leftUnitor_inv_app, Limits.HasLimit.isoOfNatIso_hom_π_assoc, Functor.mapTriangleRotateIso_hom_app_hom₁, SheafOfModules.Presentation.map_relations_I, Functor.coreCompInclusionIso_inv_app, BraidedCategory.Hexagon.functor₂₃₁_obj_map_app, BraidedCategory.tensorLeftIsoTensorRight_hom_app, PresheafOfModules.instPreservesLimitsOfSizeFunctorOppositeAbToPresheaf, Sheaf.adjunction_unit_app_val, HasLiftingProperty.transfiniteComposition.SqStruct.sq, FreeGroupoid.liftNatIso_inv_app, Coyoneda.colimitCoconeIsColimit_desc, Limits.instHasFiniteProductsFunctor, Comma.mapLeftEq_hom_app_right, Limits.SequentialProduct.cone_π_app_comp_Pi_π_pos, Functor.const_map_app, Endofunctor.Algebra.functorOfNatTransId_hom_app_f, Functor.PullbackObjObj.mapArrowLeft_comp_assoc, Functor.opInv_map, Limits.isIndObject_yoneda, Subfunctor.toRange_ι_assoc, TopCat.Presheaf.generateEquivalenceOpensLe_counitIso, StructuredArrow.mapIso_unitIso_inv_app_right, Functor.whiskeringRight₂_map_app_app_app, Cat.leftUnitor_hom_toNatTrans, FunctorToTypes.binaryCoproductColimit_desc, Cat.ihom_map, Limits.pushoutCoconeOfRightIso_ι_app_left, Limits.PreservesLimit₂.isoObjConePointsOfIsLimit_hom_comp_π_assoc, Functor.mapTriangleIso_hom_app_hom₃, Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_π_app, MonoidalOpposite.tensorLeftUnmopIso_hom_app, MonoidalCategory.DayConvolution.braidingInvCorepresenting_app, Limits.DiagramOfCones.mkOfHasLimits_obj, Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.flipFunctorToInterchange_inv_app_app, Limits.spanCompIso_hom_app_right, Subfunctor.Subpresheaf.homOfLe_ι, Functor.lanUnit_app_whiskerLeft_lanAdjunction_counit_app_assoc, ParametrizedAdjunction.homEquiv_naturality_three, CartesianMonoidalCategory.prodComparisonNatIso_inv, Presheaf.instIsLeftKanExtensionOppositeObjFunctorTypeYonedaYonedaMap, Functor.isoWhiskerLeft_trans_assoc, Limits.limitFlipCompLimIsoLimitCompLim_hom_π_π_assoc, Functor.ihom_coev_app, LightProfinite.Extend.functorOp_map, Functor.PushoutObjObj.ι_iso_of_iso_left_inv, Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality_assoc, NatIso.unop_leftUnitor, Functor.const.opObjOp_hom_app, Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₂, MonObj.mopEquivCompForgetIso_inv_app_unmop, Subfunctor.instIsIsoFunctorTypeιTop, Functor.LeftExtension.postcompose₂_obj_left, Sieve.yonedaFamily_fromCocone_compatible, Endofunctor.Algebra.equivOfNatIso_counitIso, NatIso.unop_associator, Functor.isIso_lanAdjunction_homEquiv_symm_iff, GrothendieckTopology.W.whiskerLeft, Functor.sumIsoExt_inv_app_inl, MonoidalCategory.externalProductFlip_hom_app_app_app_app, RightExactFunctor.ofExact_map, LeftExactFunctor.ofExact_obj, toSheafification_app, Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_hom_app_fst_app, TransfiniteCompositionOfShape.ici_isColimit, Pretriangulated.Opposite.OpOpCommShift.iso_inv_app_assoc, MorphismProperty.functorCategory_epimorphisms, Limits.colimit.ι_desc_apply, Alexandrov.lowerCone_π_app, OverPresheafAux.unitAuxAux_inv_app_fst, Limits.IndObjectPresentation.ofCocone_I, extendCofan_ι_app, Limits.colimitLimitToLimitColimitCone_iso, MonoidalCategory.externalProductBifunctorCurried_obj_obj_map_app, Join.mapWhisker_exchange, Comma.opFunctorCompSnd_hom_app, Functor.LeftExtension.IsPointwiseLeftKanExtension.isIso_hom, MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionObj, MonoidalClosed.pre_id, NatTrans.IsMonoidal.instHomFunctorRightUnitor, Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π, Localization.SmallShiftedHom.equiv_shift, Functor.LeftExtension.precomp_obj_left, Localization.Construction.WhiskeringLeftEquivalence.inverse_obj_map, Subfunctor.instIsIsoFunctorTypeToRangeOfMono, Functor.shiftIso_hom_naturality_assoc, opOpEquivalence_unitIso, instPreservesFiniteLimitsFunctorAddCommGrpCatColim, WithInitial.opEquiv_counitIso_inv_app, ShiftMkCore.add_zero_inv_app, Pretriangulated.TriangleOpEquivalence.functor_obj, Limits.CatCospanTransform.inv_right, Limits.Cones.functorialityEquivalence_inverse, OverPresheafAux.unitAuxAux_inv_app_snd_coe, Limits.Fork.condition, Functor.sectionsEquivHom_naturality_symm, HasShift.Induced.zero_hom_app_obj, Bipointed.swapEquiv_counitIso_inv_app_toFun, NatTrans.unop_id, ParametrizedAdjunction.homEquiv_symm_naturality_two_assoc, Functor.Monoidal.tensorHom_app_fst, Limits.coneLeftOpOfCocone_π_app, PresheafOfModules.Elements.fromFreeYoneda_app_apply, StructuredArrow.mapIso_functor_map_left, Equivalence.congrLeftFunctor_map, Localization.Monoidal.lifting₂CurriedTensorPost_iso, Limits.CategoricalPullback.CatCommSqOver.e_inv_app, Functor.sheafPushforwardContinuousId_hom_app_val_app, ModuleCat.binaryProductLimitCone_cone_π_app_left, Functor.flipping_unitIso_inv_app_app_app, Coyoneda.colimitCocone_pt, liftedLimitMapsToOriginal_inv_map_π, Adjunction.CoreUnitCounit.right_triangle, PreGaloisCategory.functorToAction_map, Limits.walkingParallelPairOpEquiv_unitIso_inv_app_one, Adjunction.shift_unit_app, Join.inclLeftCompOpEquivInverse_inv_app_op, Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_fst_obj, BraidedCategory.Hexagon.functor₂₁₃'_obj_obj_obj, Functor.PushoutObjObj.inl_ι_assoc, Quotient.natIsoLift_hom, SSet.horn.edge₃_coe_down, Adjunction.RightAdjointCommShift.iso_hom_app_assoc, ChosenPullbacksAlong.pullbackId_hom_counit_assoc, Monoidal.CommMonFunctorCategoryEquivalence.inverse_map_hom_hom_app, ReflQuiv.adj.homEquiv_apply, Adjunction.unit_app_commShiftIso_hom_app_assoc, TopCat.continuous_iff_of_isColimit, Functor.LaxMonoidal.ofBifunctor.secondMap₂_app_app_app, MorphismProperty.instIsStableUnderBaseChangeFunctorFunctorCategoryOfHasPullbacks, Limits.instPreservesFiniteLimitsFunctorColimOfPreservesColimitsOfShapeOfHasFiniteLimitsOfReflectsIsomorphismsForget, SSet.Truncated.rightExtensionInclusion_left, FundamentalGroupoid.punitEquivDiscretePUnit_unitIso, Monad.algebraEquivOfIsoMonads_counitIso, Sigma.inclCompMap_hom_app, Limits.KernelFork.app_one, Functor.RepresentableBy.uniqueUpToIso_hom, Functor.PreOneHypercoverDenseData.multicospanMapIso_inv, AlgebraicTopology.map_alternatingFaceMapComplex, Functor.sheafPushforwardContinuousId'_inv_app_val_app, Functor.leftKanExtensionCompIsoOfPreserves_hom_fac, preservesFilteredColimits_coyoneda, Endofunctor.Adjunction.AlgCoalgEquiv.counitIso_hom_app_f, NatIso.hom_app_isIso, Functor.coneOfIsRightKanExtension_π, Limits.Fork.app_zero_eq_ι, uliftYoneda_map_app, Yoneda.yoneda_full, Limits.Cones.postcomposeComp_inv_app_hom, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_carrier, Preadditive.commGrpEquivalenceAux_inv_app_hom_hom_hom, Limits.limit.cone_π, Functor.leftExtensionEquivalenceOfIso₁_functor_obj_hom_app, Comma.mapLeftIso_inverse_obj_hom, Limits.IsLimit.isIso_limMap_π, Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_hom_app_val_app_apply, Limits.CatCospanTransform.category_id_base, Functor.Monoidal.whiskerLeft_app_snd, Limits.Types.Colimit.ι_desc_apply, Functor.whiskerRight_zero, SSet.stdSimplex.const_down_toOrderHom, Cat.Hom.hom_inv_id_toNatTrans_assoc, Functor.uliftYonedaReprXIso_hom_app, TwoSquare.structuredArrowRightwardsOpEquivalence_unitIso, NatIso.op_leftUnitor, Functor.whiskeringLeft₂_map_app_app_app_app, ComposableArrows.opEquivalence_functor_obj_obj, Equivalence.mapCommMon_counitIso, Limits.FormalCoproduct.cochainComplexFunctor_obj_X, Functor.rightKanExtensionCompIsoOfPreserves_hom_fac, AddCommGrpCat.leftExactFunctorForgetEquivalence.instPreservesFiniteLimitsObjLeftExactFunctorTypeFunctorInverseAux, Limits.limit.lift_π_apply, Limits.DiagramOfCones.conePoints_obj, pointedToBipointedCompBipointedToPointedSnd_inv_app_toFun, equivYoneda_hom_app, NatTrans.mapHomotopyCategory_id, Presheaf.instIsCardinalPresentableFunctorOppositeTypeObjUliftYonedaOfHasColimitsOfSize, TopCat.Presheaf.presheafEquivOfIso_unitIso_inv_app_app, Limits.coend.map_comp, StructuredArrow.commaMapEquivalenceFunctor_map_right, Enriched.FunctorCategory.functorEnrichedComp_app, BraidedCategory.Hexagon.functor₂₃₁'_obj_map_app, Comma.mapLeftId_hom_app_left, Cat.associator_inv_toNatTrans, Limits.isKernelCompMono_lift, Limits.pullbackConeOfRightIso_π_app_left, Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_left_assoc, MonoidalOpposite.mopMopEquivalence_counitIso_inv_app, ProfiniteGrp.cone_π_app, Limits.preservesColimits_const, ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd, Limits.Cone.toStructuredArrowCompProj_hom_app, Limits.Trident.ofCone_π, Limits.instIsLeftAdjointFunctorColim, Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop_assoc, Functor.curryingEquiv_apply_map, Presieve.FamilyOfElements.compPresheafMap_comp, CompHausLike.pullback.cone_π, Adjunction.isIso_unit_of_iso, Limits.Cocone.w, NatTrans.app_sum, MonoOver.congr_inverse, Functor.flip₁₃Functor_obj_obj_map_app, Cat.leftUnitor_inv_toNatTrans, Functor.Monoidal.commTensorLeft_inv_app, Rep.isZero_Tor_succ_of_projective, Limits.Types.Small.limitConeIsLimit_lift, MonoidalCategory.DayConvolutionUnit.rightUnitor_naturality_assoc, Functor.leibnizPushout_obj_obj, Join.mapPairId_inv_app, Functor.const.opObjOp_inv_app, tensoringLeft_additive, Presheaf.isLocallyInjective_comp_iff, MonoidalCategory.Functor.curriedTensorPreIsoPost_hom_app_app, Functor.CorepresentableBy.equivUliftCoyonedaIso_symm_apply_homEquiv, Adjunction.rightAdjointUniq_hom_counit, Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj, Iso.core_hom_app_iso_inv, ObjectProperty.IsDetecting.isIso_iff_of_mono, FunctorToTypes.functorHomEquiv_apply_app, Comma.mapLeftId_inv_app_left, Functor.commShiftOfLocalization.iso_hom_app, Comma.mapRightIso_counitIso_hom_app_right, Limits.CategoricalPullback.toCatCommSqOver_map_fst_app, Functor.mapMonIdIso_inv_app_hom, Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π, Limits.piConst_obj_obj, Iso.isoCompInverse_inv_app, NatTrans.app_shift_assoc, Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality, Functor.postcompose₂_obj_map_app_app, Tor'_obj_map, Presieve.IsSheafFor.functorInclusion_comp_extend, Limits.evaluation_preservesColimits, GradedObject.comapEq_hom_app, Endofunctor.Coalgebra.equivOfNatIso_unitIso, sum.inrCompAssociator_hom_app_down_down, Limits.limit.conePointUniqueUpToIso_hom_comp, cosimplicialSimplicialEquiv_unitIso_inv_app, Limits.pullbackObjIso_hom_comp_fst_assoc, MonoidalCategory.curriedTensor_obj_obj, Limits.limitObjIsoLimitCompEvaluation_inv_limit_map, Limits.Cocones.functorialityEquivalence_counitIso, Functor.mapCone_π_app, yonedaMap_app_apply, ε_app_obj, Functor.toSheafify_pullbackSheafificationCompatibility, Equivalence.mapMon_counitIso, Sheaf.ΓHomEquiv_naturality_right_symm, Limits.Cofork.app_zero_eq_comp_π_right_assoc, SimplexCategory.revCompRevIso_hom_app, Limits.Cone.equivCostructuredArrow_functor, Iso.hom_inv_id_app_assoc, MonoidalOpposite.tensorRightIso_hom_app_unmop, SimplicialObject.opFunctorCompOpFunctorIso_hom_app_app, Limits.limit_map_limitObjIsoLimitCompEvaluation_hom_assoc, AdditiveFunctor.ofRightExact_obj_fst, Limits.WidePushoutShape.mkCocone_ι_app, MonObj.mopEquiv_unitIso_hom_app_hom, Pseudofunctor.ObjectProperty.mapId_hom_app, NatTrans.rightOpWhiskerRight_assoc, pointedToBipointedCompBipointedToPointedFst_inv_app_toFun, Iso.isoInverseOfIsoFunctor_inv_app, SmallObject.SuccStruct.ofCocone_map_to_top, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_π_app, Functor.commShiftIso_id_hom_app, Grothendieck.ιCompMap_inv_app_base, Functor.lanAdjunction_unit, Over.conePostIso_inv_app_hom, Limits.Types.binaryProductFunctor_obj_obj, Limits.reflexivePair.diagramIsoReflexivePair_inv_app, Functor.leftDerivedZeroIsoSelf_inv_hom_id_app, Functor.PreservesPointwiseRightKanExtensionAt.preserves, Functor.shiftIso_hom_app_comp_assoc, Sheaf.coneΓ_π_app, prod.leftUnitorEquivalence_counitIso, Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_hom_π_π, Limits.Fork.equivOfIsos_inverse_obj_ι, Functor.curryObjCompIso_inv_app_app, Equivalence.core_counitIso_hom_app_iso_hom, ChosenPullbacksAlong.pullbackComp_hom_counit, Limits.FormalCoproduct.instPreservesLimitOppositeDiscreteFunctorCompOpObjFunctorEvalOp, Discrete.natIso_hom_app, GrothendieckTopology.Cover.multicospanComp_hom_app, Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_snd_map, Functor.mapCommGrpIdIso_hom_app_hom_hom_hom, Equivalence.sheafCongrPrecoherent_unitIso_inv_app_val_app, HomotopicalAlgebra.CofibrantObject.HoCat.adjCounitIso_inv_app, TopCat.Presheaf.presheafEquivOfIso_functor_obj_obj, WithTerminal.commaFromOver_obj_hom_app, Endofunctor.Coalgebra.functorOfNatTransEq_hom_app_f, AlgebraicGeometry.AffineSpace.functor_obj_obj, obj_μ_inv_app, Limits.colimit.ι_desc, NatTrans.appHom_apply, Limits.coneOfConeUncurry_π_app, SimplicialObject.whiskering_obj_obj_obj, Functor.IsRepresentedBy.uliftYonedaIso_hom, Limits.end_.map_comp, GrothendieckTopology.isoToPlus_inv, NatTrans.leftDerived_comp_assoc, SimplicialObject.opEquivalence_unitIso, Limits.ProductsFromFiniteCofiltered.liftToFinset_map_app, functorProdToProdFunctor_map, SheafOfModules.pushforwardCongr_symm, Functor.RightExtension.IsPointwiseRightKanExtension.isRightKanExtension, NatTrans.CommShift₂.instCompFunctor, Functor.const.unop_functor_op_obj_map, Functor.rightKanExtensionCompIsoOfPreserves_inv_fac, Functor.leftOpComp_inv_app, Limits.MonoCoprod.mono_inl_iff, Idempotents.KaroubiFunctorCategoryEmbedding.obj_obj_p, Functor.instIsCorepresentableCompObjOppositeTypeCoyonedaOpObjLeftAdjointObjIsDefined, Rep.coinvariantsTensorIndNatIso_hom_app, Functor.CommShift.ofIso_commShiftIso_inv_app, Comma.opFunctorCompFst_hom_app, Limits.Types.jointly_surjective_of_isColimit, Limits.evaluation_preservesColimitsOfShape, Equivalence.trans_counitIso, evaluationRightAdjoint_obj_obj, MonoidalCategory.MonoidalLeftAction.curriedActionMop_map_unmop_app, CatCenter.mul_app'_assoc, Comma.toPUnitIdEquiv_unitIso_hom_app_left, Limits.CokernelCofork.π_mapOfIsColimit_assoc, Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₃, CatCommSq.vInv_iso_inv_app, Functor.LaxMonoidal.whiskeringRight_ε_app, Functor.leftDerivedNatIso_hom, Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_naturality₂, CochainComplex.shiftFunctorZero'_inv_app_f, Limits.Multicofork.fst_app_right, Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse_assoc, CommGrpCat.coyonedaForget_hom_app_app_hom, SingleObj.mapHom_comp, Functor.constCompEvaluationObj_inv_app, oppositeShiftFunctorZero_hom_app, Comma.mapRightIso_unitIso_hom_app_left, Limits.limitCompYonedaIsoCocone_inv, HomologicalComplex.singleMapHomologicalComplex_inv_app_ne, WithInitial.equivComma_unitIso_inv_app_app, MonoidalOpposite.tensorRightIso_inv_app_unmop, Limits.asEmptyCone_π_app, Limits.fiberwiseColimCompEvaluationIso_hom_app, Limits.Fork.op_ι_app, AlgebraicGeometry.AffineSpace.functor_map_app, Functor.instIsEquivalenceObjWhiskeringRight, prod.rightUnitorEquivalence_unitIso, ShortComplex.FunctorEquivalence.inverse_obj_f, Equivalence.functor_map_ε_inverse_comp_counitIso_hom_app_assoc, functorProdFunctorEquivCounitIso_inv_app_app, RelCat.opEquivalence_counitIso, Functor.Monoidal.tensorHom_app_snd, conjugateEquiv_comp_assoc, instFullGrpFunctorOppositeGrpCatYonedaGrp, Limits.CategoricalPullback.CatCommSqOver.iso_hom_naturality_assoc, CartesianMonoidalCategory.instIsIsoFunctorProdComparisonNatTransOfProdComparison, TransfiniteCompositionOfShape.ofArrowIso_incl, Functor.IsEventuallyConstantTo.isIso_π_of_isLimit, Functor.OplaxMonoidal.ofBifunctor.bottomMapᵣ_app, associativity_app_assoc, WithInitial.commaFromUnder_map_right, coyonedaEquiv_coyoneda_map, Limits.ColimitPresentation.Total.Hom.w_assoc, Limits.IsColimit.coconePointsIsoOfNatIso_inv_desc, ThinSkeleton.map₂_map, shift_shiftFunctorCompIsoId_add_neg_cancel_inv_app, CatCenter.smul_iso_hom_eq_assoc, IsPreconnected.iso_constant, endofunctorMonoidalCategory_leftUnitor_hom_app, CategoryOfElements.costructuredArrow_yoneda_equivalence_naturality, evaluationIsLeftAdjoint, Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₁, Limits.Bicone.toCocone_ι_app, MonoidalCategory.DayConvolutionUnit.leftUnitor_naturality, Functor.lanCompIsoOfPreserves_inv_app, WithInitial.equivComma_functor_obj_left, Cat.Hom.instIsIsoFunctorαCategoryToNatTransInvHom, Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_app, Adjunction.unit_leftAdjointUniq_hom_assoc, Sheaf.cartesianMonoidalCategoryWhiskerRight_val, Functor.isoWhiskerLeft_refl, Limits.Trident.ofι_π_app, Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_inv_comp_π, sheafifyMap_comp, GrothendieckTopology.plusFunctor_map, Limits.coneOfSectionCompYoneda_π, Functor.instFaithfulOppositeTypeRestrictedULiftYonedaOfIsDense, Comma.opFunctorCompFst_inv_app, Limits.cospanExt_hom_app_one, Limits.coend.ι_map, Functor.mapActionCongr_inv, LocalizerMorphism.guitartExact_of_isRightDerivabilityStructure, GrothendieckTopology.sheafifyMap_comp, Localization.lift₂NatIso_hom, WithInitial.inclLift_inv_app, Limits.ι_comp_sigmaObjIso_hom_assoc, Functor.flip_obj_map, Limits.diagramIsoParallelFamily_hom_app, Functor.coreId_hom_app_iso_inv, Presheaf.isStrongGenerator, Abelian.instAdditiveOppositeFunctorAddCommGrpCatExtFunctor, FunctorToTypes.inr_comp_binaryCoproductIso_hom, Triangulated.SpectralObject.mapTriangulatedFunctor_δ, ParametrizedAdjunction.unit_whiskerRight_map_assoc, Functor.mapTriangleCompIso_inv_app_hom₁, simplicialCosimplicialEquiv_inverse_obj, Limits.Concrete.surjective_π_app_zero_of_surjective_map, Functor.pi'CompEval_inv_app, MonoidalCategory.DayFunctor.comp_natTrans, Limits.CatCospanTransformMorphism.right_coherence_app_assoc, Limits.IndObjectPresentation.ofCocone_isColimit, Join.mapWhiskerRight_whiskerLeft, Bicategory.associatorNatIsoMiddle_hom_app, Functor.isLeftKanExtensionId, linearCoyoneda_obj_map, pointedToBipointedCompBipointedToPointedFst_hom_app_toFun, Limits.CatCospanTransform.category_comp_base, Profinite.exists_locallyConstant, Limits.CatCospanTransform.isIso_left, simplicialCosimplicialEquiv_functor_map_app, Monoidal.ComonFunctorCategoryEquivalence.functor_map_app_hom, Functor.leftOpRightOpEquiv_counitIso_hom_app_app, CatCommSq.hComp_iso_inv_app, OverPresheafAux.restrictedYonedaObj_obj, Limits.Trident.equalizer_ext, OverPresheafAux.MakesOverArrow.app, Functor.isLeftKanExtension_iff_postcomp₁, Limits.BinaryBicone.ofColimitCocone_inr, Subfunctor.equalizer.condition, CostructuredArrow.CreatesConnected.raiseCone_π_app, Limits.IsLimit.conePointUniqueUpToIso_inv_comp, ExactFunctor.whiskeringRight_map_app, DifferentialObject.shiftFunctorAdd_inv_app_f, shiftFunctorAdd_add_zero_inv_app, CategoryOfElements.costructuredArrowYonedaEquivalence_unitIso, Adjunction.leftAdjointUniq_hom_counit_assoc, PreGaloisCategory.instPreservesFiniteCoproductsActionFintypeCatAutFunctorFunctorToAction, PresheafOfModules.comp_toPresheaf_map_sheafifyHomEquiv'_symm_hom, extendFan_π_app, Sum.functorEquivInverseCompWhiskeringLeftInrIso_hom_app_app, ShortComplex.rightHomologyFunctorOpNatIso_hom_app, Limits.lim_μ_π_assoc, MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_μ_app, Limits.CatCospanTransform.category_comp_right, Functor.currying_unitIso_inv_app_app_app, coreFunctor_map_app_iso_inv, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_hom_app_hom, Subobject.le_inf, OverPresheafAux.OverArrows.app_val, Functor.coconeTypesEquiv_apply_ι_app, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map_val_app, MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_δ_unmop_app, IsDetecting.isIso_iff_of_mono, Functor.opHom_obj, BraidedCategory.Hexagon.functor₁₂₃_obj_obj_map, Functor.currying_unitIso_hom_app_app_app, Subfunctor.range_eq_ofSection, evaluationUncurried_map, orderDualEquivalence_counitIso, coprodMonad_η_app, Discrete.productEquiv_counitIso_inv_app, linearYoneda_obj_additive, Equivalence.counitIso_inv_app_comp_functor_map_η_inverse_assoc, Rep.indCoindNatIso_inv_app, Join.pseudofunctorRight_mapComp_hom_toNatTrans_app, Limits.preservesLimits_const, MonoidalCategory.curriedAssociatorNatIso_inv_app_app_app, Iso.unop_hom_inv_id_app_assoc, Subobject.lowerEquivalence_counitIso, Idempotents.karoubiUniversal₁_counitIso, Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_assoc, Adjunction.Triple.leftToRight_eq_counits, Limits.Cocone.w_apply, Limits.colimit.pre_map', AlgebraicGeometry.Scheme.Modules.pushforwardId_hom_app_app, Equivalence.mapHomologicalComplex_counitIso, Limits.BinaryBicone.ofLimitCone_snd, Functor.rightDerivedZeroIsoSelf_inv_hom_id_app, SSet.opEquivalence_unitIso, WithInitial.inclLiftToInitial_hom_app, Functor.mapCocone₂_pt, Pi.sum_obj_map, LocalizerMorphism.isRightDerivabilityStructure_iff, Adjunction.counit_isIso_of_R_fully_faithful, Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_inv_assoc, η_app, ShiftedHom.opEquiv_symm_apply_comp, yonedaPairing_map, BraidedCategory.Hexagon.functor₂₁₃_obj_map_app, Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app, AlgebraicGeometry.ExistsHomHomCompEqCompAux.ha, AlgebraicTopology.DoldKan.Γ₂N₂ToKaroubiIso_inv_app, Action.functorCategoryEquivalence_counitIso, MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_rightUnitor_hom_eq_rightUnitor_hom, OrderHom.equivFunctor_apply, GrothendieckTopology.toSheafify_comp_sheafifyCompIso_inv, Limits.splitEpiOfIdempotentOfIsColimitCofork_section_, Functor.RightExtension.mk_left, Functor.closedIhom_obj_obj, Sigma.inclCompMap_inv_app, Join.mapWhiskerRight_whiskerLeft_assoc, Limits.CategoricalPullback.functorEquiv_inverse_obj_map_fst, GrothendieckTopology.overMapPullback_comp_id_assoc, PreGaloisCategory.autMulEquivAutGalois_π, Functor.rightOpComp_inv_app, Limits.cospanCompIso_inv_app_one, bifunctorComp₂₃FunctorObj_map_app_app_app, Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₁, FunctorToTypes.inl_comp_binaryCoproductIso_inv_apply, Monad.monadMonEquiv_inverse, Preadditive.commGrpEquivalence_counitIso_inv_app_hom_hom_hom, Limits.functorCategoryHasLimitsOfShape, SimplicialObject.whiskering_obj_obj_map, Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_inv_app_fst_app, Over.conePost_obj_pt, Functor.FullyFaithful.hasShift.map_add_hom_app, Functor.isoWhiskerRight_hom, GrothendieckTopology.MayerVietorisSquare.shortComplex_g, Cat.Hom.toNatIso_rightUnitor, GrothendieckTopology.Point.comp_hom, uliftYoneda_map_app_down, SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_inv_app_app, Limits.pushoutCoconeOfLeftIso_ι_app_none, Join.mapPairComp_hom_app_left, Functor.opId_inv_app, Limits.CategoricalPullback.CatCommSqOver.Hom.w_assoc, plusPlusSheaf_preservesZeroMorphisms, conjugateEquiv_associator_hom, GrothendieckTopology.MayerVietorisSquare.isPushoutAddCommGrpFreeSheaf, Functor.mapTriangle_map_hom₃, Limits.limitConeOfUnique_isLimit_lift, coherentTopology.epi_π_app_zero_of_epi, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₃, sum.inrCompInlCompAssociator_hom_app_down_down, Limits.spanCompIso_hom_app_left, OrderHom.equivalenceFunctor_counitIso_hom_app_app, Limits.FormalCoproduct.evalOpCompInlIsoId_hom_app_app, Functor.whiskeringLeft_obj_map, Functor.leftKanExtensionUniqueOfIso_inv, Comma.mapLeftIso_unitIso_hom_app_right, endofunctorMonoidalCategory_associator_hom_app, PresheafOfModules.free_obj, Functor.IsCoverDense.presheafIso_inv, Limits.IsColimit.comp_coconePointUniqueUpToIso_hom, GrothendieckTopology.yoneda_obj_val, Under.mapId_hom, Limits.CategoricalPullback.functorEquiv_unitIso_inv_app_app_snd, Limits.Cocone.fromStructuredArrow_map_hom, Limits.HasColimit.isoOfNatIso_ι_hom_assoc, Functor.const.opObjUnop_inv_app, Over.postComp_hom_app_left, flat_iff_lan_flat, Functor.flipping_inverse_obj_map_app, groupHomology.isoShortComplexH2_hom, IndParallelPairPresentation.hg, HomologicalComplex.singleCompEvalIsoSelf_inv_app, Functor.IsCoverDense.Types.sheafIso_inv_val, Equivalence.rightOp_counitIso_hom_app, FunctorToTypes.colimit.map_ι_apply, curryingIso_inv_toFunctor_obj_obj_obj, monadToFunctor_map, Limits.Trident.ι_eq_app_zero, Subfunctor.fromPreimage_ι, Functor.Monoidal.whiskerLeft_app_fst, Limits.CoproductsFromFiniteFiltered.liftToFinset_map_app, Functor.RightExtension.postcomp₁_obj_right, Sheaf.instPreservesFiniteLimitsFunctorOppositeSheafToPresheafOfHasFiniteLimits, HomologicalComplex.asFunctor_obj_d, Limits.Cones.functorialityEquivalence_counitIso, yonedaPairingExt_iff, Idempotents.app_comp_p, evaluationLeftAdjoint_obj_obj, Limits.limIsoFlipCompWhiskerLim_hom_app_app, Limits.MultispanIndex.multispanMapIso_hom_app, isCoseparator_iff_faithful_yoneda_obj, instPresheafIsFiniteObjFunctorOppositeTypeYoneda, SmallObject.πFunctorObj_eq, μ_δ_app, GrothendieckTopology.plusCompIso_whiskerRight_assoc, MonoidalOpposite.unmopEquiv_unitIso_hom_app_unmop, StructuredArrow.mapNatIso_counitIso_hom_app_right, HasCardinalLT.Set.cocone_ι_app, ReflQuiv.adj.homEquiv_naturality_right, MonoOver.inf_map_app, Sum.functorEquivFunctorCompSndIso_inv_app_app, sheafificationAdjunction_unit_app, typeEquiv_counitIso_hom_app_val_app, Discrete.compNatIsoDiscrete_inv_app, Functor.flipping_functor_obj_obj_obj, Limits.Fork.op_ι_app_one, Under.postEquiv_inverse, equivOfTensorIsoUnit_functor, CategoryOfElements.toCostructuredArrow_obj, Limits.colimIsoFlipCompWhiskerColim_inv_app_app, OverPresheafAux.yonedaCollectionFunctor_map, Comma.mapRightId_hom_app_right, Subfunctor.instMonoFunctorTypeHomOfLe, Functor.instFaithfulProdUncurry₃, Limits.Cone.w, functorProdFunctorEquiv_counitIso, Functor.opUnopEquiv_unitIso, SSet.Truncated.HomotopyCategory.BinaryProduct.associativity'Iso_hom_app, Presheaf.coherentExtensiveEquivalence_unitIso, Sum.functorEquiv_unitIso_inv_app_app_inr, Limits.mono_of_isLimit_fork, left_unitality_app, Functor.FullyFaithful.compYonedaCompWhiskeringLeftMaxRight_hom_app_app_down, BasedNatTrans.forgetful_map, instFaithfulSheafFunctorOppositeSheafToPresheaf, Limits.PullbackCone.ofCone_π, Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_ι_app, ModuleCat.restrictScalarsId'_hom_app, Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₃, LocalizerMorphism.IsRightDerivabilityStructure.Constructor.isConnected, OverPresheafAux.YonedaCollection.mk_snd, Limits.inl_comp_pushoutObjIso_inv, Functor.LeftExtension.postcompose₂_map_left, Limits.pullbackObjIso_inv_comp_fst, Functor.uncurry_obj_map, MonoidalCategory.externalProductBifunctorCurried_obj_obj_obj_obj, bifunctorComp₁₂FunctorObj_obj, lan_flat_of_flat, Limits.BinaryFan.isLimit_iff_isIso_fst, Limits.HasColimit.isoOfNatIso_hom_desc_assoc, Limits.LimitPresentation.map_π, NatTrans.id_hcomp_app, shift_shiftFunctorCompIsoId_inv_app, Join.inclLeftCompOpEquivInverse_hom_app_op, Presheaf.coconeOfRepresentable_naturality, Functor.postcompose₂_obj_obj_obj_obj, Comma.mapLeftIso_counitIso_inv_app_left, instFaithfulSheafFunctorOppositeCompSheafComposeSheafToPresheaf, Functor.Monoidal.snd_app, Functor.LeftExtension.postcomp₁_obj_right_obj, NatTrans.app_naturality_assoc, Action.FunctorCategoryEquivalence.inverse_obj_V, NatIso.op_refl, GradedObject.comapEq_trans, Functor.Monoidal.fst_app, Enriched.Functor.natTransEquiv_symm_whiskerRight_functorHom_app, Adjunction.compCoyonedaIso_hom_app_app, GrothendieckTopology.Point.Hom.sheafFiber_id, Functor.currying₃_unitIso_inv_app_app_app_app, NatTrans.instRespectsIsoFunctorCoequifibered, Limits.Cone.equivCostructuredArrow_counitIso, Functor.closedIhom_map_app, Cat.Hom.toNatTrans_id, Functor.instFullProdUncurry₃, Functor.rightKanExtensionCompIsoOfPreserves_hom_fac_assoc, Functor.whiskeringLeftObjIdIso_inv_app_app, MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_inv_app_app, Cat.opFunctorInvolutive_inv_app_toFunctor_obj, Limits.Cocone.toCostructuredArrowCompToOverCompForget_hom_app, WithTerminal.mkCommaObject_hom_app, Functor.pointwiseRightKanExtensionCompIsoOfPreserves_inv_fac, OrderHom.equivalenceFunctor_unitIso_hom_app, AlgebraicGeometry.ExistsHomHomCompEqCompAux.hab, Functor.Monoidal.transport_η, MonoidalCategory.associatorNatIso_inv_app, WithTerminal.mkCommaObject_left_obj, Functor.mapCocone₂_ι_app, PresheafOfModules.forgetToPresheafModuleCat_obj, MonoidalCategory.endofunctorMonoidalCategory.evaluationRightAction_actionObj, Functor.RightExtension.postcompose₂_obj_hom_app, ObjectProperty.ColimitOfShape.toCostructuredArrow_map, NatTrans.leftOpWhiskerRight, Limits.limitCompCoyonedaIsoCone_inv, Comma.mapRightIso_counitIso_hom_app_left, Limits.Cofork.unop_π_app_zero, Action.resComp_inv_app_hom, Subobject.inf_def, WithInitial.equivComma_unitIso_hom_app_app, Bicategory.precomposing_obj, Functor.RightExtension.precomp_obj_hom_app, Cat.rightUnitor_inv_toNatTrans, Localization.lift₃NatTrans_app_app_app, ShiftedHom.opEquiv'_zero_add_symm, Functor.whiskerLeft_comp_assoc, StructuredArrow.commaMapEquivalenceCounitIso_hom_app_right_right, SheafOfModules.pullback_assoc, Functor.ranCounit_app_app_ranAdjunction_unit_app_app, PresheafOfModules.Finite.toPresheaf_preservesFiniteColimits, Comma.mapRightId_hom_app_left, Limits.IsColimit.hom_desc, Functor.Final.colimit_cocone_comp_aux, ShiftedHom.opEquiv'_symm_op_opShiftFunctorEquivalence_counitIso_inv_app_op_shift, LaxMonoidalFunctor.comp_hom, Functor.RightExtension.precomp_map_right, prod.leftUnitorEquivalence_unitIso, full_preadditiveYoneda, shiftEquiv'_unitIso, MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_leftUnitor_hom_eq_leftUnitor_hom, Equivalence.comp_asNatTrans_assoc, Under.postCongr_hom_app_right, Over.mapId_hom_app_left, Comma.mapLeftEq_inv_app_left, AddCommMonCat.coyonedaForget_inv_app_app, Limits.colimit.pre_id, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_right, Functor.map_opShiftFunctorEquivalence_unitIso_hom_app_unop_assoc, Limits.Cofork.IsColimit.existsUnique, Limits.limitUncurryIsoLimitCompLim_hom_π_π_assoc, Functor.whiskeringLeft₃ObjObj_map, Limits.combineCocones_pt_obj, HomologicalComplex.coconeOfHasColimitEval_ι_app_f, Functor.IsCoverDense.sheafIso_inv_val, NatTrans.CommShift₂.instIdFunctor, Pi.optionEquivalence_inverse, Limits.Cone.toStructuredArrow_obj, NatTrans.rightDerivedToHomotopyCategory_comp, Functor.leftDerivedZeroIsoSelf_inv_hom_id_assoc, WithTerminal.commaFromOver_map_right, Functor.essImage.liftFunctorCompIso_inv_app, PreGaloisCategory.endEquivAutGalois_mul, CommRingCat.coproductCoconeIsColimit_desc, Comma.mapLeftIso_counitIso_hom_app_right, Limits.Cotrident.app_one, Monoidal.rightUnitor_hom_app, CostructuredArrow.map_map_left, sectionsFunctorNatIsoCoyoneda_hom_app_app, GrothendieckTopology.uliftYonedaOpCompCoyoneda_hom_app_app_down, Limits.CategoricalPullback.CatCommSqOver.Hom.w, MonoidalCategory.DayConvolution.unit_uniqueUpToIso_hom_assoc, Functor.PullbackObjObj.ofHasPullback_snd, evaluationUncurried_obj, bifunctorComp₂₃Functor_obj, HomologicalComplex.quasiIsoAt_iff_evaluation, Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_presheafHom_uliftYoneda_obj, CommGrpCat.coyoneda_obj_obj_coe, presheafToSheaf_additive, WithInitial.equivComma_inverse_obj_obj, groupAddGroupEquivalence_unitIso, Functor.shift_map_op, Limits.limitIsoSwapCompLim_inv_app, Functor.mapTriangleCommShiftIso_inv_app_hom₂, ε_η_app, Over.isPullback_of_binaryFan_isLimit, CosimplicialObject.whiskering_obj_map_app, Action.FunctorCategoryEquivalence.unitIso_hom_app_hom, Limits.colimit.pre_map, sheafificationIso_hom_val, LocalizerMorphism.isIso_iff_of_hasRightResolutions, LeftExactFunctor.of_fst, Sum.swapCompInl_inv_app, Pi.optionEquivalence_counitIso, Limits.CategoricalPullback.CatCommSqOver.transformObjId_inv_app_fst_app, Functor.CorepresentableBy.equivUliftCoyonedaIso_apply, EnrichedFunctor.forgetId_hom_app, comonadToFunctor_map, LightCondensed.discrete_obj, NatTrans.id_comm, InjectiveResolution.extMk_hom, Limits.inr_comp_pushoutObjIso_inv, BraidedCategory.Hexagon.functor₂₁₃_obj_obj_obj, Limits.IsLimit.fac_assoc, groupCohomology.isoShortComplexH1_hom, MonoidalCategory.DayConvolution.corepresentableBy_homEquiv_apply_app, Pretriangulated.shiftFunctor_op_map, Idempotents.functorExtension₂CompWhiskeringLeftToKaroubiIso_inv_app_app_f, Limits.CokernelCofork.condition_assoc, CatCenter.smul_iso_inv_eq, Limits.CategoricalPullback.CatCommSqOver.transform_map_whiskerRight, Functor.currying_functor_obj_obj, Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_map_snd, Limits.cospanCompIso_hom_app_left, Sieve.uliftFunctorInclusion_is_mono, Limits.BinaryFan.assoc_snd, Iso.coreRightUnitor, Endofunctor.Algebra.equivOfNatIso_unitIso, Adjunction.rightAdjointUniq_trans_app, Functor.instPreservesZeroMorphismsObjFlip, CategoryOfElements.costructuredArrowYonedaEquivalenceFunctorProj_hom_app, Pretriangulated.rotCompInvRot_inv_app_hom₁, uliftCoyonedaEquiv_naturality, MorphismProperty.FunctorsInverting.ext_iff, HomologicalComplex.homologyFunctorSingleIso_inv_app, Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac_assoc, Functor.RightExtension.postcompose₂ObjMkIso_inv_left_app, SimplicialObject.opFunctorCompOpFunctorIso_inv_app_app, Limits.spanExt_hom_app_left, MonoidalCategory.MonoidalLeftAction.curriedActionMop_obj_unmop_obj, Limits.IsLimit.homEquiv_symm_π_app_assoc, Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π_assoc, Functor.isLeftKanExtensionAlongEquivalence, Limits.CategoricalPullback.functorEquiv_functor_obj_snd_obj, OverPresheafAux.YonedaCollection.map₁_comp, instFaithfulMonadFunctorMonadToFunctor, Endofunctor.Algebra.functorOfNatTransEq_hom_app_f, Join.mapWhiskerLeft_associator_hom_assoc, Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_X_map, Equivalence.unit_app_tensor_comp_inverse_map_δ_functor_assoc, NatTrans.shift_app_assoc, Action.tensorHom_hom, Sheaf.isLocallyInjective_sheafToPresheaf_map_iff, PresheafOfModules.pullbackObjIsDefined_free_yoneda, AlgebraicTopology.DoldKan.Compatibility.υ_hom_app, CatCenter.app_neg_one_zpow, NatIso.cancel_natIso_inv_right, Sheaf.id_val, sheafComposeIso_inv_fac_assoc, SSet.iSup_range_eq_top_of_isColimit, Pretriangulated.opShiftFunctorEquivalence_add_unitIso_inv_app_eq, Rep.coinvariantsTensor_hom_ext_iff, Action.associator_hom_hom, SimplicialObject.IsCoskeletal.isRightKanExtension, MonoidalOpposite.mopMopEquivalence_unitIso_inv_app_unmop_unmop, Functor.IsCoverDense.sheafCoyonedaHom_app, PresheafOfModules.toPresheaf_preservesColimitsOfShape, Functor.inrCompSum'_inv_app, Functor.constComp_hom_app, Localization.Construction.WhiskeringLeftEquivalence.inverse_obj_obj, instIsIsoFunctorToRightDerivedZero, DinatTrans.precompNatTrans_app, equivOfTensorIsoUnit_inverse, AlgebraicGeometry.Scheme.SpecΓIdentity_inv_app, CatCenter.localization_zero, Abelian.LeftResolution.instEpiKaroubiAppπ, Adjunction.rightAdjointUniq_hom_app_counit, Functor.homEquivOfIsRightKanExtension_symm_apply, simplicialCosimplicialEquiv_unitIso_inv_app, instFullFunctorConstOfIsConnected, Functor.reflective, Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_inv_comp_π_assoc, opOpEquivalence_counitIso, NatTrans.toCatHom₂_comp, Subobject.lowerEquivalence_unitIso, Functor.whiskeringRight_obj_map, Functor.RightExtension.postcompose₂_map_left_app, Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_snd_map, isoSheafify_inv, Limits.limit.homIso_hom, Limits.colimitConstInitial_inv, sum.inrCompAssociator_inv_app_down_down, Iso.hom_inv_id_app_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_hom_app_app, ModuleCat.FilteredColimits.ι_colimitDesc, Equivalence.functor_unitIso_comp, Adjunction.equivHomsetRightOfNatIso_apply, Comma.mapFst_hom_app, Functor.curry_obj_obj_map, Limits.sigmaConst_obj_obj, GrothendieckTopology.overMapPullbackComp_inv_app_val_app, Limits.Cocone.ofPushoutCocone_ι, ShortComplex.FunctorEquivalence.unitIso_inv_app_τ₃_app, uliftYonedaIsoYoneda_hom_app_app, IsCodetecting.isIso_iff_of_epi, Functor.flip_obj_obj, prodFunctor_obj, Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv_assoc, Limits.limit.map_pre', Limits.ColimitPresentation.reindex_ι, instPreservesColimitsOfShapeFunctorIndLimOfFinCategoryOfHasColimitsOfShape, MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app, Functor.Monoidal.tensorObj_obj, NatTrans.CommShiftCore.app_shift, PreGaloisCategory.instPreservesMonomorphismsActionFintypeCatAutFunctorFunctorToAction, Limits.FormalCoproduct.instPreservesColimitsOfShapeDiscreteObjFunctorEval, Functor.FullyFaithful.compUliftYonedaCompWhiskeringLeft_hom_app_app_down, Join.mapWhiskerLeft_rightUnitor_hom, Functor.whiskeringRightObjCompIso_hom_app_app, Functor.whiskerLeft_id', GrothendieckTopology.diagramFunctor_map, Functor.leftDerived_fac, Functor.RightExtension.postcompose₂_obj_left_obj, equivYoneda_inv_app, Functor.PushoutObjObj.ofHasPushout_inl, uliftCoyonedaEquiv_symm_map_assoc, Pretriangulated.TriangleOpEquivalence.inverse_obj, SSet.Truncated.HomotopyCategory.mkNatIso_hom_app_mk, Pretriangulated.commShiftIso_opOp_hom_app, presheafToSheafCompComposeAndSheafifyIso_inv_app, Iso.map_hom_inv_id_eval_app_assoc, Functor.isoWhiskerRight_symm, Triangulated.SpectralObject.comp_hom, CommMonCat.coyoneda_map_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_inv_app_right, enrichedFunctorTypeEquivFunctor_apply_obj, NatTrans.appLinearMap_apply, Subfunctor.equivalenceMonoOver_unitIso, Adjunction.localization_counit_app, Functor.mapGrpIdIso_inv_app_hom_hom, Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₂, Comma.unopFunctorCompFst_inv_app, Functor.postcomposeWhiskerLeftMapCone_hom_hom, Limits.inl_comp_pushoutObjIso_inv_assoc, Mon.EquivLaxMonoidalFunctorPUnit.counitIso_hom_app_hom, MorphismProperty.IsStableUnderLimitsOfShape.functorCategory, yoneda'_obj_val, Functor.leftDerivedZeroIsoSelf_inv_hom_id_app_assoc, Limits.IndObjectPresentation.extend_isColimit_desc_app, Limits.IndObjectPresentation.ofCocone_ι, Functor.mapActionCongr_hom, ShortComplex.leftHomologyFunctorOpNatIso_hom_app, AddCommMonCat.coyonedaType_obj_obj_coe, TopCat.coneOfConeForget_π_app, FreeMonoidalCategory.normalizeIsoAux_hom_app, Limits.pullbackObjIso_hom_comp_snd_assoc, Pi.evalCompEqToEquivalenceFunctor_inv, Functor.PreservesLeftKanExtension.preserves, GradedObject.mapTrifunctorObj_obj_map, Mon.EquivLaxMonoidalFunctorPUnit.laxMonoidalToMon_map, Functor.PushoutObjObj.ι_iso_of_iso_right_inv, Limits.colimitIsoFlipCompColim_hom_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_inv_app_app, Monad.algebraFunctorOfMonadHomComp_inv_app_f, Functor.FullyFaithful.compUliftCoyonedaCompWhiskeringLeft_inv_app_app_down, Limits.CategoricalPullback.functorEquiv_inverse_obj_obj_iso_hom, FunctorToTypes.binaryProductIso_inv_comp_fst_apply, LightCondensed.lanPresheafNatIso_hom_app, Sum.natTransOfWhiskerLeftInlInr_comp, Limits.Bicone.ofLimitCone_π, Join.mapWhiskerRight_id, Limits.ι_comp_sigmaObjIso_inv_assoc, ModuleCat.extendScalars_id_comp_assoc, Limits.colimit.ι_coconeMorphism, Comma.equivProd_unitIso_inv_app_right, AdditiveFunctor.of_obj, LocalizerMorphism.equiv_smallHomMap, NatTrans.IsMonoidal.instHomFunctorLeftUnitor, LocalizerMorphism.IsRightDerivabilityStructure.guitartExact', Functor.instFullProdCurry, Monad.beckAlgebraCofork_ι_app, Functor.Monoidal.tensorHom_app_snd_assoc, plusPlusAdjunction_unit_app, Adjunction.CommShift.compatibilityUnit_right, Limits.CategoricalPullback.CatCommSqOver.transformObjComp_inv_app_fst_app, WithInitial.commaFromUnder_obj_left, Functor.Monoidal.associator_inv_app, Functor.CommShift.isoAdd'_hom_app, flippingIso_hom_toFunctor_obj_map_app, instPreservesHomologyFunctorAddCommGrpCatColim, WithTerminal.mapId_hom_app, Functor.IsCoverDense.homOver_app, groupAddGroupEquivalence_counitIso, MonoidalCategory.DayConvolution.associatorCorepresentingIso_inv_app_app, GrothendieckTopology.Point.toPresheafFiber_w_assoc, Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_mon_mul, Join.mapWhiskerRight_rightUnitor_hom, PreGaloisCategory.instFaithfulContActionFintypeCatHomCarrierAutFunctorFunctorToContAction, Limits.Cone.ofFork_π, Functor.CorepresentableBy.uniqueUpToIso_hom, Limits.colimit.ι_map_assoc, Limits.fiberwiseColimCompColimIso_hom_app, Functor.mapTriangleCompIso_hom_app_hom₁, ChosenPullbacksAlong.unit_pullbackId_hom, Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_iso_inv_app, ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left_assoc, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_hom_app_f, FunctorToTypes.rightAdj_obj_map_app, Pi.eqToEquivalenceFunctorIso_inv, Limits.CategoricalPullback.CatCommSqOver.transform_map_associator, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_comp, Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_app, PreGaloisCategory.autEmbedding_apply, Localization.lift₂NatTrans_app_app, Limits.CokernelCofork.map_condition, MonoidalOpposite.tensorRightMopIso_inv_app_unmop, ModuleCat.extendScalars_assoc', Limits.CategoricalPullback.CatCommSqOver.precomposeObjTransformObjSquare_iso_hom_id, AlgebraicTopology.DoldKan.map_Q, Sum.natIsoOfWhiskerLeftInlInr_hom, Equivalence.core_counitIso_hom_app_iso_inv, Equivalence.sheafCongrPrecoherent_unitIso_hom_app_val_app, GrothendieckTopology.instIsLocalizationFunctorOppositeSheafPresheafToSheafW, Functor.Monoidal.instPreservesColimitsOfShapeTensorLeftOfHasColimitsOfShape, SimplicialObject.Truncated.whiskering_obj_obj_map, Functor.constCompEvaluationObj_hom_app, Limits.WalkingMulticospan.functorExt_hom_app, Functor.leftKanExtensionIsoFiberwiseColimit_hom_app, SimplicialObject.Truncated.cosk_reflective, Monad.comparisonForget_inv_app, OrderHom.equivalenceFunctor_inverse_obj, NatIso.removeOp_inv, shiftFunctorAdd_add_zero_hom_app, Monoidal.ComonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, StructuredArrow.mapIso_unitIso_hom_app_right, Triangulated.SpectralObject.mapTriangulatedFunctor_δ', GrothendieckTopology.uliftYonedaOpCompCoyoneda_app_app, Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_fst, piEquivalenceFunctorDiscrete_inverse_map, Presheaf.map_comp_uliftYonedaEquiv_down_assoc, CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_obj, TopCat.induced_of_isLimit, Limits.colimit.comp_coconePointUniqueUpToIso_hom, ShortComplex.FunctorEquivalence.functor_obj_obj, GrothendieckTopology.Point.instPreservesFiniteLimitsFunctorOppositePresheafFiberOfLocallySmallOfHasFiniteLimitsOfAB5OfSize, Coyoneda.instHasColimitObjOppositeFunctorTypeCoyoneda, TransfiniteCompositionOfShape.iic_incl_app, Functor.curryingFlipEquiv_apply_map, Presheaf.instIsCardinalLocallyPresentableFunctorOppositeOfHasPullbacks, Limits.Types.surjective_π_app_zero_of_surjective_map, Functor.IsCoverDense.Types.presheafIso_hom_app, Limits.coconeLeftOpOfCone_ι_app, MonoidalCategory.DayFunctor.ι_obj, GrothendieckTopology.preservesFiniteLimits_sheafification, EnrichedFunctor.forgetComp_hom_app, Equivalence.symm_counitIso, finitaryExtensive_functor, conjugateEquiv_id, GrothendieckTopology.diagramFunctor_obj, Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_fac_app, Functor.constCompWhiskeringLeftIso_inv_app_app, Functor.RightExtension.postcompose₂_map_right, Functor.isoWhiskerRight_refl, AlgebraicGeometry.exists_mem_of_isClosed_of_nonempty', NatTrans.leftOpWhiskerRight_assoc, ModuleCat.extendScalars_id_comp, Functor.leftOpComp_hom_app, MonoidalCategory.DayConvolution.associator_hom_unit_unit_assoc, Limits.cospanCompIso_hom_app_one, Limits.Cone.fromCostructuredArrow_obj_pt, Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv, shiftFunctorComm_inv_app_of_add_eq_zero, Idempotents.app_comp_p_assoc, Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_app_snd_app, Functor.RepresentableBy.uniqueUpToIso_inv, coreFunctor_map_app_iso_hom, Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_hom_comp_map_π, CartesianMonoidalCategory.prodComparisonBifunctorNatTrans_app, Functor.CommShift.isoZero_inv_app, instPreservesFiniteLimitsFunctorObjWhiskeringLeftOfHasFiniteLimits, Limits.coend.hom_ext_iff, WithTerminal.inclLiftToTerminal_hom_app, Functor.sheafPushforwardContinuousCompSheafToPresheafIso_hom_app_app, Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_inv_π_assoc, Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_obj_snd, CommMonCat.coyoneda_obj_obj_coe, Functor.instIsCorepresentableObjOppositeTypeCoyoneda, CommRingCat.coyonedaUnique_inv_app_hom_apply, Endofunctor.Adjunction.algebraCoalgebraEquiv_counitIso_hom_app_f, Limits.Cone.isLimit_iff_isIso_limMap_π, Functor.commShiftIso_inv_naturality, expComparison_iso_of_frobeniusMorphism_iso, Limits.limitIsoLimitCurryCompLim_inv_π, Limits.CatCospanTransformMorphism.right_coherence_app, Limits.colimit.ι_desc_assoc, Adjunction.left_triangle, IsPushout.of_is_coproduct, Limits.CategoricalPullback.CatCommSqOver.precompose_map_app_fst_app, FunctorToTypes.inl_comp_binaryCoproductIso_inv, BraidedCategory.ofBifunctor.Reverse.secondMap₃_app_app_app, Sieve.forallYonedaIsSheaf_iff_colimit, Functor.PullbackObjObj.mapArrowRight_id, Monoidal.comonFunctorCategoryEquivalence_counitIso, WithTerminal.liftFromOver_obj_map, GrothendieckTopology.Point.comp_hom_assoc, NatIso.pi_inv, AlgebraicTopology.DoldKan.Compatibility.τ₁_hom_app, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj, Functor.LeftExtension.precomp_map_left, Comma.mapLeftIso_functor_obj_hom, Functor.leftKanExtensionCompIsoOfPreserves_inv_fac, Localization.Construction.WhiskeringLeftEquivalence.unitIso_inv, shift_shiftFunctorCompIsoId_neg_add_cancel_inv_app, Functor.inv_whiskerLeft, sheafToPresheaf_η, StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_right, Monoidal.MonFunctorCategoryEquivalence.counitIso_hom_app_app_hom, TopCat.Presheaf.presheafEquivOfIso_counitIso_inv_app_app, Iso.map_hom_inv_id_app_assoc, HomotopyCategory.homologyFunctor_shiftMap_assoc, Functor.whiskerRight_comp_assoc, CostructuredArrow.mapNatIso_counitIso_hom_app_left, ι_colimitCompWhiskeringRightIsoColimitComp_hom_assoc, Adjunction.unit_leftAdjointUniq_hom_app_assoc, Action.FunctorCategoryEquivalence.inverse_map_hom, Limits.coconeRightOpOfCone_ι, Limits.Cocone.equivStructuredArrow_inverse, Idempotents.KaroubiHomologicalComplexEquivalence.unitIso_hom_app_f_f, Functor.isRightKanExtensionId, exactFunctor_le_leftExactFunctor, Endofunctor.Coalgebra.equivOfNatIso_functor, AlgebraicGeometry.ΓSpec.right_triangle, Enriched.FunctorCategory.functorEnriched_id_comp_assoc, Limits.colimit.ι_desc_app_assoc, Localization.liftNatTrans_id, PreGaloisCategory.stabilizer_normal_of_isGalois, Limits.Cocone.toCostructuredArrow_obj, Idempotents.KaroubiKaroubi.unitIso_hom_app_f, Functor.elementsFunctor_obj, TwistShiftData.shiftFunctorAdd'_inv_app, Localization.HasProductsOfShapeAux.inverts, Limits.PullbackCone.combine_pt_map, Quotient.full_whiskeringLeft_functor, RightExactFunctor.of_fst, CompHausLike.LocallyConstant.instIsIsoFunctorTypeUnitSheafCoherentTopologyAdjunction, Pretriangulated.Triangle.shiftFunctor_map_hom₃, CochainComplex.shiftFunctorZero_hom_app_f, Join.mapPairComp_inv_app_left, WithInitial.coconeEquiv_inverse_map_hom_right, MonoidalClosed.internalHom_map, Quotient.faithful_whiskeringLeft_functor, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_inv_app_hom_coe', Sigma.mapId_hom_app, ContAction.resCongr_inv, toSheafify_sheafifyLift, Condensed.isColimitLocallyConstantPresheafDiagram_desc_apply, Subfunctor.orderIsoSubobject_symm_apply, Functor.unopComp_inv_app, δ_naturality_assoc, CatCommSq.vComp_iso_inv_app, Limits.Types.jointly_surjective, Limits.PullbackCone.equalizer_ext, Limits.CokernelCofork.map_π, Limits.multicospanIndexEnd_left, Action.whiskerLeft_hom, Equivalence.core_unitIso_hom_app_iso_hom, Monad.ofMon_μ, Limits.Multifork.app_right_eq_ι_comp_snd_assoc, Over.liftCocone_ι_app, Sieve.functorInclusion_top_isIso, SSet.Truncated.HomotopyCategory.BinaryProduct.inverseCompFunctorIso_hom_app, Functor.final_const_terminal, Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm, Idempotents.DoldKan.isoN₁_hom_app_f, Preorder.coneOfLowerBound_π_app, AlgebraicTopology.DoldKan.N₁Γ₀_hom_app, Localization.Monoidal.functorCoreMonoidalOfComp_εIso_inv, MorphismProperty.FunctorsInverting.comp_hom, Functor.LeftExtension.precomp₂_obj_right, Functor.PullbackObjObj.π_snd_assoc, Functor.mapMonCompIso_inv_app_hom, NatIso.naturality_2, MonoidalClosed.internalHom_obj, Functor.opComp_hom_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_inv_app_left, Limits.CategoricalPullback.catCommSq_iso_inv_app, PreGaloisCategory.instEssSurjContActionFintypeCatHomCarrierAutFunctorFunctorToContActionOfFiberFunctor, Sum.Swap.equivalenceFunctorEquivFunctorIso_hom_app_fst, Functor.PushoutObjObj.mapArrowLeft_left, StructuredArrow.mapNatIso_unitIso_inv_app_right, Subfunctor.Subpresheaf.preimage_comp, Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone_ι_app, Limits.wideCoequalizer.cotrident_ι_app_one, Limits.limit.lift_π_assoc, Functor.ranObjObjIsoLimit_hom_π, WithTerminal.isLimitEquiv_apply_lift_left, Equivalence.rightOp_unitIso_inv_app, Coyoneda.coyoneda_full, Functor.mapTriangleCommShiftIso_hom_app_hom₁, Limits.CategoricalPullback.functorEquiv_inverse_map_app_fst, instPreservesLimitsOfShapeFunctorColim, Functor.OplaxMonoidal.ofBifunctor.secondMap₁_app_app_app, ModuleCat.directLimitCocone_ι_app, curryingIso_inv_toFunctor_map_app_app, Adjunction.leftAdjointCompIso_hom, Functor.rightKanExtensionUniqueOfIso_inv, GrothendieckTopology.plusFunctor_preservesZeroMorphisms, Adjunction.Triple.whiskerRight_rightToLeft, Equivalence.id_asNatTrans, GrothendieckTopology.sheafificationWhiskerLeftIso_hom_app, commGroupAddCommGroupEquivalence_unitIso, MonoidalClosed.FunctorCategory.homEquiv_naturality_two_symm, FreeGroupoid.functorEquiv_symm_apply, Limits.IndObjectPresentation.ofCocone_F, Functor.FullyFaithful.homNatIso'_inv_app_down, NatIso.op_hom, Monoidal.ComonFunctorCategoryEquivalence.inverseObj_comon_comul_app, Limits.IsColimit.ι_smul, Functor.isoShift_hom_naturality_assoc, ShortComplex.quasiIso_iff_evaluation, MonoidalCategory.MonoidalRightAction.actionUnitNatIso_hom_app, GrothendieckTopology.whiskerRight_toPlus_comp_plusCompIso_hom_assoc, NatTrans.leftDerivedToHomotopyCategory_comp, PreGaloisCategory.instReflectsIsomorphismsActionFintypeCatAutFunctorFunctorToAction, Rep.MonoidalClosed.linearHomEquiv_hom, ObjectProperty.preservesColimitsOfShape_eq_iSup, Functor.IsRepresentedBy.iff_isIso_uliftYonedaEquiv, Limits.coyonedaOpColimitIsoLimitCoyoneda_hom_comp_π, CompHausLike.LocallyConstant.counit_app_val, Bicategory.associatorNatIsoRight_hom_app, Join.InclLeftCompRightOpOpEquivFunctor_inv_app, ULift.equivalence_counitIso_inv_app, Monoidal.ComonFunctorCategoryEquivalence.functorObjObj_comon_comul, Sum.swapCompInr_hom_app, whiskeringLeft_preservesColimitsOfShape, isZero_Ext_succ_of_projective, Over.postEquiv_unitIso, Functor.LeftExtension.coconeAt_pt, BraidedCategory.Hexagon.functor₃₁₂'_obj_obj_obj, yonedaEquiv_naturality, full_linearYoneda, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_symm_apply, Subfunctor.instMonoFunctorTypeι_1, Functor.mapCommGrpFunctor_map, Limits.IndObjectPresentation.ofCocone_ℐ, AddCommGrpCat.HasLimit.lift_hom_apply, Presheaf.instIsLocallyPresentableFunctorOppositeOfHasPullbacks, Limits.PullbackCone.combine_pt_obj, Profinite.Extend.cocone_ι_app, GrothendieckTopology.W_iff, Idempotents.functorExtension_obj_map, Limits.CatCospanTransformMorphism.left_coherence_assoc, WithInitial.equivComma_counitIso_inv_app_left, Functor.instFaithfulConstOfNonempty, SimplicialObject.Split.natTransCofanInj_app, MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_map_app_app, preservesColimit_coyoneda_of_finitePresentation, Endofunctor.Algebra.functorOfNatTransComp_inv_app_f, Limits.IsLimit.conePointsIsoOfEquivalence_hom, ExponentiableMorphism.pushforwardComp_hom_counit, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackId_hom, Limits.whiskeringLimYonedaIsoCones_hom_app_app_app, Iso.isoCompInverse_hom_app, NatTrans.CommShift.of_iso_symm, ULiftYoneda.instFaithfulFunctorOppositeTypeUliftYoneda, Limits.BinaryCofan.ι_app_left, Pretriangulated.commShiftIso_opOp_inv_app_assoc, Limits.FormalCoproduct.cosimplicialObjectFunctor_obj_map, Iso.isoInverseOfIsoFunctor_hom_app, Pretriangulated.commShiftIso_unopUnop_inv_app_assoc, Limits.ColimitPresentation.ofIso_ι, Adjunction.RightAdjointCommShift.iso_inv_app, Limits.ProductsFromFiniteCofiltered.finiteSubproductsCone_π_app, ComposableArrows.opEquivalence_inverse_map, GrothendieckTopology.W_eq_inverseImage_isomorphisms_of_adjunction, NatIso.inv_app_isIso, δ_naturality, MonoidalCategory.DayConvolution.associator_naturality, δ_iso_of_coreflective, Localization.Construction.WhiskeringLeftEquivalence.counitIso_inv, Limits.BinaryBicone.toCocone_ι_app_left, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_map, IsFreeGroupoid.unique_lift, Idempotents.karoubiUniversal₁_unitIso, instPreservesFiniteColimitsObjFunctorRightExactFunctor, typeEquiv_functor_map_val_app, Limits.WidePullbackShape.functorExt_inv_app, GrothendieckTopology.isoSheafify_inv, CatCenter.smul_iso_hom_eq', CochainComplex.shiftFunctorAdd'_hom_app_f', Functor.leftDerivedZeroIsoSelf_hom_inv_id, Monoidal.monFunctorCategoryEquivalence_counitIso, Abelian.FunctorCategory.coimageObjIso_inv, Limits.Multifork.ofPiFork_π_app_right, instReflectsIsomorphismsComonadFunctorComonadToFunctor, Functor.pointwiseRightKanExtension_map, Iso.map_inv_hom_id_eval_app, Limits.PushoutCocone.mk_ι_app_right, GrothendieckTopology.toPlus_naturality_assoc, Idempotents.karoubiUniversal₂_functor_eq, AlgebraicGeometry.Scheme.empty_presheaf, Limits.Multicofork.snd_app_right, Comma.mapRightId_inv_app_right, Functor.LeftExtension.postcomp₁_map_left, Functor.equiv_functor_map, Adjunction.rightAdjointUniq_trans_assoc, LightCondensed.epi_π_app_zero_of_epi, Limits.limitObjIsoLimitCompEvaluation_inv_π_app_assoc, Functor.RightExtension.coneAtFunctor_map_hom, Adjunction.CoreUnitCounit.left_triangle, prodFunctorToFunctorProd_obj, TopologicalSpace.Opens.mapComp_inv_app, Adjunction.equivHomsetLeftOfNatIso_symm_apply, Limits.Cotrident.condition, Preadditive.commGrpEquivalence_counitIso_hom_app_hom_hom_hom, Limits.spanIsoMk_hom_app, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackComp_inv, Functor.map_shift_unop_assoc, Functor.sheafPushforwardContinuousIso_hom, NatTrans.naturality_app_app, ShiftMkCore.zero_add_hom_app, Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₁, Grothendieck.compAsSmallFunctorEquivalence_unitIso, Square.isPullback_iff_map_coyoneda_isPullback, Idempotents.karoubiFunctorCategoryEmbedding_map, ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₁_app, Limits.CategoricalPullback.toCatCommSqOver_obj_snd_map, Comma.mapRightComp_hom_app_right, Comma.opFunctorCompSnd_inv_app, CochainComplex.shiftEval_hom_app, Functor.mapCommGrpIdIso_inv_app_hom_hom_hom, NatTrans.id_app, Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app, yonedaCommGrpGrp_map_app, Limits.Multifork.ofPiFork_π_app_left, Functor.whiskeringRightObjIdIso_inv_app_app, Idempotents.karoubiChainComplexEquivalence_counitIso_inv, Subobject.inf_le_right, RightExactFunctor.ofExact_obj, Subfunctor.equalizer.fork_pt, Iso.core_inv_app_iso_inv, Functor.whiskeringLeft₂_obj_obj_obj_obj_map, Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_assoc, HomologicalComplex.singleCompEvalIsoSelf_hom_app, Limits.PreservesLimit₂.isoLimitUncurryWhiskeringLeft₂_hom_comp_map_π_assoc, AlgebraicGeometry.exists_appTop_π_eq_of_isLimit, Join.mapIsoWhiskerRight_hom, FunctorToTypes.inr_comp_binaryCoproductIso_inv, TopCat.Presheaf.isGluing_iff_pairwise, Functor.flip₁₃_obj_obj_obj, CosimplicialObject.whiskering_map_app_app, SimplicialObject.Truncated.sk_coreflective, Monoidal.associator_inv_app, LocalizerMorphism.guitartExact_of_isLeftDerivabilityStructure, Functor.isRightKanExtension_iff_precomp, FunctorToTypes.rightAdj_obj_obj, Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_assoc, Over.ConstructProducts.conesEquivFunctor_obj_pt, Sheaf.cartesianMonoidalCategoryFst_val, Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_cone_π_app, Bicategory.associatorNatIsoLeft_hom_app, Discrete.addMonoidalFunctorComp_isMonoidal, Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π_assoc, Limits.colimit.isoColimitCocone_ι_hom_assoc, isCardinalPresentable_iff_isCardinalAccessible_coyoneda_obj, Limits.pullbackConeOfRightIso_π_app_none, Adjunction.rightAdjointUniq_hom_app_counit_assoc, Functor.RightExtension.coneAtWhiskerRightIso_hom_hom, Functor.flipping_inverse_map_app_app, Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_inv_assoc, sheafification_obj, Comma.mapRightIso_inverse_obj_hom, TwistShiftData.shiftFunctorAdd'_hom_app, Functor.flip₁₃Functor_map_app_app_app, Action.FunctorCategoryEquivalence.counitIso_hom_app_app, Sheaf.ΓHomEquiv_naturality_right, GradedObject.mapTrifunctorObj_map_app, MonoOver.commSqOfHasStrongEpiMonoFactorisation, MonoidalCategory.externalProductSwap_inv_app_app, Functor.mapArrowFunctor_map_app_right, NatIso.op_inv, PresheafOfModules.pushforward_assoc, evaluation_obj_obj, MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_hom_app_app, Limits.limMap_eq, map_yonedaEquiv, Subfunctor.range_subobjectMk_ι, Limits.inl_comp_pushoutObjIso_hom_assoc, PresheafOfModules.map_id, ComonadIso.mk_inv_toNatTrans, CommGrpCat.coyonedaForget_inv_app_app, StructuredArrow.mapIso_inverse_map_right, BraidedCategory.Hexagon.functor₂₃₁_obj_obj_obj, MonoidalCategory.DayConvolution.unit_app_braiding_hom_app_assoc, Limits.fiberwiseColimCompColimIso_inv_app, sum.inlCompInverseAssociator_inv_app_down_down, Limits.PreservesColimit₂.ι_comp_isoColimitUncurryWhiskeringLeft₂_hom_assoc, Functor.shiftIso_hom_app_comp_shiftMap, Limits.HasColimit.isoOfNatIso_ι_hom, GrothendieckTopology.uliftYonedaIsoYoneda_inv_app_val_app_down, CommRingCat.coyonedaUnique_hom_app_hom_apply, Condensed.isoFinYoneda_hom_app, Subfunctor.Subpresheaf.fromPreimage_ι, Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_hom_app, Limits.BinaryCofan.IsColimit.desc'_coe, Adjunction.Triple.whiskerLeft_leftToRight_assoc, Functor.isoWhiskerRight_left, Functor.shiftIso_add'_inv_app, Limits.Cocones.functoriality_map_hom, Limits.ι_colimitLimitToLimitColimit_π_apply, Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_naturality₂, MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionHomRight, Limits.WalkingMulticospan.functorExt_inv_app, Functor.PushoutObjObj.mapArrowLeft_right, ModuleCat.HasLimit.lift_hom_apply, Monoidal.MonFunctorCategoryEquivalence.counitIso_inv_app_app_hom, Limits.combineCocones_ι_app_app, FunctorToTypes.binaryProductCone_π_app, SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right, ModuleCat.binaryProductLimitCone_isLimit_lift, LocalizerMorphism.guitartExact_of_isRightDerivabilityStructure', Comonad.beckEqualizer_lift, Functor.instAdditiveObjEvaluation, Limits.DiagramOfCocones.coconePoints_obj, GrothendieckTopology.preservesLimits_diagramFunctor, PreGaloisCategory.autEmbedding_range, Limits.IsColimit.comp_coconePointUniqueUpToIso_hom_assoc, AlgebraicGeometry.Scheme.Modules.pseudofunctor_left_unitality, MonoidalCategory.DayConvolution.associatorCorepresentingIso_hom_app_app, conjugateIsoEquiv_apply_hom, Idempotents.karoubiUniversal₁_inverse, SmallObject.transfiniteCompositionOfShapeSuccStructPropιIteration_F, Functor.mapTriangleIso_inv_app_hom₂, evaluationAdjunctionRight_unit_app, Monoidal.commMonFunctorCategoryEquivalence_functor, Limits.FormalCoproduct.evalOp_obj_map, AlgebraicGeometry.Scheme.Modules.pseudofunctor_associativity_assoc, whiskeringRight_preservesLimitsOfShape, Rep.coinvariantsTensorMk_apply, WithTerminal.coneEquiv_unitIso_inv_app_hom_left, Limits.Multifork.ofι_π_app, Profinite.NobelingProof.spanFunctorIsoIndexFunctor_inv_app, Functor.whiskeringLeft₃ObjObjObj_obj_obj_obj_map, MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_obj_obj_map, GrothendieckTopology.MayerVietorisSquare.shortComplex_f, Pi.sum_map_app, Functor.mapMatId_hom_app, Equivalence.congrRightFunctor_obj, Square.arrowArrowEquivalence'_unitIso, Join.InclRightCompRightOpOpEquivFunctor_inv_app, Functor.mapHomologicalComplex_commShiftIso_hom_app_f, ShortComplex.functorEquivalence_unitIso, TopCat.nonempty_isColimit_iff_eq_coinduced, Limits.limit.isoLimitCone_inv_π, Functor.LeftExtension.mk_right, GrothendieckTopology.toPlus_naturality, Functor.FullyFaithful.hasShift.map_add_inv_app, Functor.isRightDerivedFunctor_iff_isIso_rightDerivedDesc, Limits.Bicone.toCone_π_app, GrothendieckTopology.Point.toPresheafFiber_presheafFiberDesc_assoc, CostructuredArrow.mapCompιCompGrothendieckProj_hom_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_left, Functor.IsCoverDense.isoOver_inv_app, WithTerminal.equivComma_functor_map_left_app, Adjunction.whiskerLeftRUnitIsoOfIsIsoCounit_hom_app, ExponentiableMorphism.unit_pushforwardId_hom, Limits.cospanExt_inv_app_left, MonoidalCategory.MonoidalRightAction.curriedActionMonoidal_δ_app, Adjunction.RightAdjointCommShift.iso_inv_app_assoc, Functor.flipping_functor_obj_obj_map, CommMonCat.coyonedaForget_hom_app_app_hom, MonoidalCategory.endofunctorMonoidalCategory.evaluationRightAction_actionAssocIso, MonoidalCategory.DayConvolution.associator_inv_unit_unit_assoc, Rep.homEquiv_symm_apply_hom, TopologicalSpace.Opens.mapIso_hom_app, OverPresheafAux.YonedaCollection.map₁_id, HomologicalComplex.coneOfHasLimitEval_π_app_f, linearYoneda_obj_obj_isModule, Functor.isoSum_hom_app_inr, Functor.postcompose₂_obj_obj_map_app, conjugateIsoEquiv_apply_inv, CosimplicialObject.Augmented.whiskering_map_app_right, Monad.ForgetCreatesColimits.liftedCocone_ι_app_f, instIsIsoFunctorOppositeSheafToPresheafToSheafCompComposeAndSheafify, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τl, ModuleCat.extendScalarsComp_hom_app_one_tmul, Equivalence.mkHom_id_functor, Functor.whiskerLeft_comp_whiskerRight, Subobject.leInfCone_π_app_none, Limits.fiberwiseColimCompEvaluationIso_inv_app, Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π, WithInitial.liftFromUnderComp_hom_app, smoothSheafCommRing.ι_evalHom_assoc, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom_assoc, Functor.CommShift.OfComp.map_iso_hom_app_assoc, Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_hom_assoc, yonedaEvaluation_map_down, yoneda_preservesLimits, Limits.DiagramOfCones.comp, Functor.rightDerivedNatTrans_fac_assoc, groupCohomology.isoShortComplexH2_hom, IsGrothendieckAbelian.IsPresentable.surjectivity, MonoidalCategory.DayConvolutionUnit.corepresentableByLeft_homEquiv, Monad.monadMonEquiv_counitIso_inv_app_hom, Limits.FormalCoproduct.evalCompInclIsoId_inv_app_app, HasLiftingProperty.transfiniteComposition.SqStruct.w_assoc, Functor.PushoutObjObj.mapArrowLeft_comp_assoc, sheafToPresheaf_ε, Limits.PullbackCone.condition_one, MonObj.mopEquiv_counitIso_inv_app_hom_unmop, NatTrans.app_smul, MonoidalCategory.curriedTensor_map_app, GrothendieckTopology.coneCompEvaluationOfConeCompDiagramFunctorCompEvaluation_π_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_right, Monoidal.MonFunctorCategoryEquivalence.unitIso_inv_app_hom_app, FunctorToTypes.binaryCoproductCocone_ι_app, Subfunctor.range_comp, Limits.Sigma.cocone_ι, AddCommGrpCat.coyoneda_map_app, Functor.sectionsEquivHom_apply_app, Pseudofunctor.DescentData.exists_equivalence_of_sieve_eq, Limits.limitIsoLimitCurryCompLim_inv_π_assoc, bifunctorComp₂₃FunctorObj_obj, CategoryOfElements.structuredArrowEquivalence_unitIso, ExactFunctor.forget_obj_of, CommRingCat.instIsRightAdjointOppositeObjFunctorTypeYoneda, IsSifted.colim_preservesLimitsOfShape_pempty_of_isSifted, PreGaloisCategory.mulAction_naturality, Limits.BinaryBicone.ofLimitCone_fst, ParametrizedAdjunction.arrowHomEquiv_apply_right_fst, NatTrans.op_whiskerLeft, GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app, sheafificationAdjunction_counit_app_val, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompDropIso_inv_app_app, Limits.pullbackObjIso_inv_comp_snd_assoc, WithInitial.coconeEquiv_counitIso_hom_app_hom, ShortComplex.rightHomologyFunctorOpNatIso_inv_app, Limits.limitCompWhiskeringLeftIsoCompLimit_hom_whiskerLeft_π_assoc, preservesLimitsOfShape_presheafToSheaf, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_hom_app_hom_coe, LightCondensed.lanPresheafExt_inv, Action.FunctorCategoryEquivalence.functor_μ, Limits.Cone.toUnder_π_app, isIso_iff_isIso_coyoneda_map, Condensed.lanPresheafExt_hom, Limits.functorCategoryHasColimitsOfSize, Limits.colimitCoyonedaHomIsoLimit_π_apply, Enriched.FunctorCategory.diagram_obj_map, Limits.CatCospanTransform.baseIso_hom, AlgebraicTopology.DoldKan.karoubi_PInfty_f, ParametrizedAdjunction.unit_whiskerRight_map, Adjunction.unit_app_commShiftIso_hom_app, Equivalence.functor_map_μ_inverse_comp_counitIso_hom_app_tensor, Functor.whiskerRight_comp, Limits.Cones.equivalenceOfReindexing_unitIso, CartesianMonoidalCategory.isLeftAdjoint_prod_functor, Functor.functorialityCompPrecompose_inv_app_hom, Pretriangulated.invRotCompRot_hom_app_hom₃, Limits.FormalCoproduct.instPreservesColimitDiscreteFunctorObjFunctorEval, Limits.coneOfSectionCompCoyoneda_π, TransfiniteCompositionOfShape.ofArrowIso_isColimit, Functor.pointwiseRightKanExtensionCompIsoOfPreserves_hom_fac, Functor.flip₂₃_obj_map_app, conjugateEquiv_whiskerLeft, HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_symm_apply, flippingIso_inv_toFunctor_obj_obj_map, GrothendieckTopology.sheafification_map, Functor.commShiftIso_id_inv_app, GrothendieckTopology.sheafificationWhiskerLeftIso_inv_app, Limits.DiagramOfCocones.id, Limits.IsLimit.conePointUniqueUpToIso_inv_comp_assoc, Limits.limitObjIsoLimitCompEvaluation_hom_π_assoc, Functor.mapGrpNatIso_inv_app_hom_hom, LaxMonoidalFunctor.isoMk_hom, Functor.rightOpId_hom_app, Subfunctor.fromPreimage_ι_assoc, CommMon.EquivLaxBraidedFunctorPUnit.unitIso_inv_app_hom_hom_app, HomotopicalAlgebra.FibrantObject.instIsIsoFunctorResolutionCompToLocalizationNatTrans, CostructuredArrow.mapNatIso_functor_map_left, Adjunction.whiskerLeft_unit_app_app, Limits.CoconeMorphism.map_w_assoc, Over.ConstructProducts.conesEquivUnitIso_hom_app_hom, IsCardinalPresentable.exists_hom_of_isColimit, Comma.mapRightIso_unitIso_inv_app_left, Presieve.IsSheafFor.functorInclusion_comp_extend_assoc, HomotopyCategory.homologyShiftIso_hom_app, Presheaf.map_comp_uliftYonedaEquiv_down, Abelian.LeftResolution.instPreservesZeroMorphismsKaroubiFKaroubi, Limits.limCompFlipIsoWhiskerLim_hom_app_app, Limits.limitIsoLimitCurryCompLim_hom_π_π, Adjunction.unit_rightAdjointUniq_hom_assoc, NatIso.removeOp_hom, Localization.Monoidal.braidingNatIso_hom_app, CochainComplex.shiftFunctorAdd_hom_app_f, Adjunction.equivHomsetLeftOfNatIso_apply, Limits.hasLimitCompEvaluation, WithInitial.liftFromUnder_map_app, obj_μ_app_assoc, Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_left, SingleFunctors.evaluation_obj, Pseudofunctor.DescentData.pullFunctorIdIso_inv_app_hom, Functor.whiskeringRight_obj_obj, CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_hom_app, GrothendieckTopology.whiskerRight_toSheafify_sheafifyCompIso_hom, Functor.Monoidal.whiskerRight_app_snd, Sieve.functorInclusion_is_mono, GrothendieckTopology.overMapPullbackComp_hom_app_val_app, Quotient.lift.isLift_inv, Limits.IsColimit.isIso_ι_app_of_isTerminal, Sigma.mapId_inv_app, MorphismProperty.instIsStableUnderCoproductsFunctorMonomorphismsOfHasCoproductsOfHasPullbacks, Injective.injective_iff_preservesEpimorphisms_yoneda_obj, conjugateIsoEquiv_symm_apply_inv, Limits.limitCompYonedaIsoCocone_hom_app, Functor.lanCompIsoOfPreserves_hom_app, Functor.flip₂₃_map_app_app, IsGrothendieckAbelian.IsPresentable.surjectivity.F_obj, Iso.inverseCompIso_inv_app, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_obj_map, Functor.postcompose₃_obj_map_app_app_app, Functor.LeibnizAdjunction.adj_unit_app_right, Limits.coconeOfConeLeftOp_ι_app, Functor.Monoidal.μNatIso_hom_app, ContinuousCohomology.MultiInd.d_comp_d, OverPresheafAux.unitAuxAux_hom_app, pullbackShiftFunctorZero'_inv_app, Limits.limit.coneMorphism_π, Functor.leftExtensionEquivalenceOfIso₁_unitIso_hom_app_right_app, simplicialCosimplicialEquiv_functor_obj_obj, Idempotents.KaroubiKaroubi.counitIso_hom_app_f_f, Limits.end_.map_comp_assoc, AlgebraicGeometry.Scheme.AffineZariskiSite.cocone_ι_app, Functor.whiskeringLeft₃ObjObjObj_obj_obj_map_app, TopCat.Presheaf.presheafEquivOfIso_counitIso_hom_app_app, Abelian.FunctorCategory.imageObjIso_hom, Limits.IsColimit.comp_coconePointsIsoOfNatIso_inv, Join.mkFunctorRight_inv_app, Limits.Cocone.op_π, endofunctorMonoidalCategory_rightUnitor_hom_app, NatIso.isIso_inv_app, Limits.KernelFork.map_condition, Monad.ofMon_obj, Under.mapComp_inv, HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_apply, SheafOfModules.pushforward_comp_id, Limits.coend.ι_map_assoc, Functor.mapContActionComp_hom, Functor.PushoutObjObj.ofHasPushout_inr, SSet.Truncated.cosk_reflective, Limits.coconeOfConeUnop_ι, Functor.isRightDerivedFunctor_of_inverts, Enriched.FunctorCategory.homEquiv_apply_π_assoc, MorphismProperty.Over.mapComp_inv_app_left, Limits.colimitYonedaHomIsoLimitOp_π_apply, coyoneda_preservesLimit, Pseudofunctor.CoGrothendieck.comp_const, ModuleCat.extendScalars_comp_id_assoc, MonoidalCategory.tensorRightTensor_inv_app, Limits.epi_of_isColimit_parallelFamily, Functor.CommShift.ofIso_compatibility, Limits.limitCompWhiskeringLeftIsoCompLimit_inv_π, flip_comp_evaluation, NatIso.naturality_2_assoc, shiftFunctorComm_hom_app_of_add_eq_zero, Limits.PushoutCocone.isoMk_hom_hom, Limits.coconeOfCoconeUncurry_pt, endofunctorMonoidalCategory_tensorUnit_map, Iso.isoFunctorOfIsoInverse_hom_app, bifunctorComp₂₃FunctorMap_app_app_app_app, ShiftedHom.opEquiv_symm_apply, AddMonCat.equivalence_unitIso, prodOpEquiv_counitIso_hom_app, Over.starPullbackIsoStar_inv_app_left, Comma.mapSnd_hom_app, Iso.instIsMonoidalInvFunctor, Join.mapWhiskerLeft_whiskerLeft_assoc, AlgebraicGeometry.exists_mem_of_isClosed_of_nonempty, Limits.FintypeCat.jointly_surjective, Limits.CategoricalPullback.CatCommSqOver.precompose_obj_map_snd_app, shiftFunctorComm_inv_app_of_add_eq_zero_assoc, Limits.Fork.op_ι_app_zero, instIsIsoFunctorFromLeftDerivedZero, Sum.Swap.equivalenceFunctorEquivFunctorIso_inv_app_snd, Limits.Cocones.precomposeEquivalence_inverse, Limits.end_.map_π_assoc, HomologicalComplex₂.flipEquivalenceCounitIso_inv_app_f_f, Functor.mapTriangleIdIso_inv_app_hom₁, Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left, HomologicalComplex.homologyFunctorIso_hom_app, Limits.coconeOfCoconeUncurry_ι_app, Functor.postcompose₂_map_app_app_app, Functor.mapGrpCompIso_inv_app_hom_hom, Limits.cospanOp_inv_app, bifunctorComp₁₂FunctorObj_map_app_app_app, Presheaf.freeYonedaHomEquiv_comp_assoc, GrothendieckTopology.overMapPullback_id_comp_assoc, coyonedaPairing_map, Limits.MonoCoprod.mono_binaryCofanSum_inr, CosimplicialObject.whiskering_obj_obj_map, Limits.ker.condition_assoc, AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_hom_app, MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionUnitIso_hom, Limits.cospanCompIso_hom_app_right, shiftFunctorComm_symm, AddCommMonCat.equivalence_counitIso, MonoOver.inf_obj, Limits.pushoutCoconeOfRightIso_ι_app_none, Functor.mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app, Presheaf.tautologicalCocone_ι_app, Rep.coinvariantsTensorIndHom_mk_tmul_indVMk, NatTrans.removeUnop_id, Limits.zero_app, Pseudofunctor.CoGrothendieck.compIso_inv_app, Rep.ihom_coev_app_hom, Limits.instHasFilteredColimitsOfSizeFunctor, HomologicalComplex.asFunctor_map_f, Pretriangulated.instIsHomologicalAddCommGrpCatObjOppositeFunctorPreadditiveCoyoneda, Join.mapWhiskerLeft_id, ShiftedHom.opEquiv'_apply, WithInitial.mkCommaObject_left, Functor.RepresentableBy.equivUliftYonedaIso_apply, Adjunction.id_unit, Cat.HasLimits.limitConeLift_toFunctor, Adjunction.leftAdjointCompNatTrans₀₂₃_eq_conjugateEquiv_symm, CatCommSq.iso_hom_naturality_assoc, Prod.symmetry_inv_app, StructuredArrow.commaMapEquivalenceUnitIso_hom_app_right_left, Equivalence.leftOp_counitIso_hom_app, Limits.Trident.app_zero_assoc, constantSheafAdj_counit_w, Limits.colimit_map_colimitObjIsoColimitCompEvaluation_hom, μ_iso_of_reflective, sheafCompose_id, oppositeShiftFunctorAdd'_hom_app, Presheaf.tautologicalCocone'_ι_app, Presheaf.compULiftYonedaIsoULiftYonedaCompLan.presheafHom_naturality_assoc, sum.inlCompInlCompAssociator_hom_app_down, Limits.PushoutCocone.mk_ι_app_left, Functor.curry_obj_map_app, shiftFunctorComm_eq, Comma.toPUnitIdEquiv_counitIso_inv_app, mono_of_cofan_isVanKampen, SingleFunctors.hom_inv_id_hom_assoc, MonoidalCategory.leftUnitorNatIso_inv_app, Functor.closedCounit_app_app, toOverIteratedSliceForwardIsoPullback_inv_app_left, Join.mapWhiskerRight_whiskerRight_assoc, Functor.PullbackObjObj.π_snd, Presheaf.coconeOfRepresentable_ι_app, Limits.coconeOfCoconeFiberwiseColimit_ι_app, BraidedCategory.Hexagon.functor₃₁₂'_obj_obj_map, Limits.combineCones_pt_map, CompHausLike.LocallyConstant.unit_app, MonoidalCategory.Functor.curriedTensorPreIsoPost_inv_app_app, HomologicalComplex.cyclesOpNatIso_hom_app, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₃, Pseudofunctor.DescentData.pullFunctorIdIso_hom_app_hom, Mon.limit_mon_one, PreGaloisCategory.exists_lift_of_mono, CochainComplex.shiftFunctorAdd'_hom_app_f, Limits.Cofork.op_π_app_one, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_right_app, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₁, Functor.leftDerivedZeroIsoSelf_hom, CategoryOfElements.costructuredArrowYonedaEquivalenceInverseπ_inv_app, Equivalence.mapCommGrp_counitIso, Limits.IsLimit.conePointsIsoOfNatIso_inv_comp_assoc, Limits.IsColimit.ι_app_homEquiv_symm_assoc, Quotient.LiftCommShift.iso_inv_app, Action.resId_hom_app_hom, DerivedCategory.instFullFunctorHomotopyCategoryIntUpObjWhiskeringLeftQh, Functor.PullbackObjObj.mapArrowRight_left, pre_map, Functor.mapCommGrpNatIso_hom_app_hom_hom_hom, Limits.limit.conePointUniqueUpToIso_inv_comp, Join.mapWhiskerLeft_leftUnitor_hom, Functor.descOfIsLeftKanExtension_fac, Limits.IsLimit.map_π_assoc, Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_obj_iso_hom, Functor.curryingFlipEquiv_symm_apply_obj_obj, Functor.uncurry_obj_curry_obj_flip_flip', Idempotents.karoubiChainComplexEquivalence_unitIso_inv_app_f_f, AlgebraicGeometry.Scheme.Modules.pseudofunctor_left_unitality_assoc, ProdPreservesConnectedLimits.γ₁_app, conjugateEquiv_adjunction_id_symm, Limits.ColimitPresentation.w, Localization.Monoidal.lifting₂CurriedTensorPre_iso, Limits.Cofork.IsColimit.π_desc, Functor.OplaxMonoidal.whiskeringRight_η_app, groupHomology.isoShortComplexH2_inv, Grothendieck.map_map_fiber, skyscraperPresheafCoconeOfSpecializes_ι_app, Sheaf.comp_val_assoc, NatTrans.rightDerived_id, IsSifted.colim_preservesTerminal_of_isSifted, MonadIso.mk_inv_toNatTrans, CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompCoyoneda, Action.rightUnitor_hom_hom, Adjunction.LeftAdjointCommShift.iso_hom_app, TopCat.isOpen_iff_of_isColimit_cofork, GrothendieckTopology.Point.toPresheafFiber_map_injective, Limits.BinaryFan.leftUnitor_inv, Equivalence.core_counitIso_inv_app_iso_hom, SmallObject.SuccStruct.ofNatTrans_succ, Limits.piObjIso_inv_comp_π_assoc, Iso.unop_inv_hom_id_app, GrothendieckTopology.pseudofunctorOver_mapComp_hom_toNatTrans_app_val_app, instFaithfulComonadFunctorComonadToFunctor, Functor.isLeftKanExtension_iff_precomp, TopCat.Presheaf.presheafEquivOfIso_inverse_obj_obj, yoneda'_comp, AlgebraicTopology.DoldKan.N₁Γ₀_inv_app, SheafOfModules.forgetToSheafModuleCat_map_val, Coyoneda.fullyFaithful_preimage, Functor.ranObjObjIsoLimit_inv_π, Sum.natIsoOfWhiskerLeftInlInr_inv, MonoidalOpposite.tensorLeftIso_hom_app_unmop, Functor.ShiftSequence.shiftIso_add, Limits.colimit_map_colimitObjIsoColimitCompEvaluation_hom_assoc, Iso.inverseCompIso_hom_app, GrothendieckTopology.toSheafify_naturality, CommGrpCat.coyonedaType_obj_map, Equivalence.congrLeft_counitIso_hom_app, Adjunction.right_triangle, Adjunction.leftAdjointUniq_inv_app, Sigma.descUniq_hom_app, Limits.instHasFiniteColimitsFunctor, coherentTopology.isLocallySurjective_π_app_zero_of_isLocallySurjective_map, Limits.Cocone.toCostructuredArrowCompProj_inv_app, Limits.Types.Pushout.cocone_ι_app, MorphismProperty.IsCardinalForSmallObjectArgument.preservesColimit, PresheafOfModules.toPresheaf_preservesColimit, Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_obj_fst, TopCat.isQuotientMap_of_isColimit_cofork, Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_map_app_snd, Limits.KernelFork.map_ι, flipFunctor_map_app_app, Limits.functorCategoryHasColimitsOfShape, GrothendieckTopology.ι_plusCompIso_hom, WithTerminal.mapId_inv_app, MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionUnitIso_inv, PreGaloisCategory.functorToContAction_obj_obj, Iso.coreComp, obj_μ_zero_app, AlgebraicTopology.DoldKan.Compatibility.τ₀_hom_app, adhesive_functor, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_right_map, Functor.mapTriangleIdIso_inv_app_hom₂, ExponentiableMorphism.unit_pushforwardId_hom_assoc, PresheafOfModules.instReflectsIsomorphismsSheafOfModulesFunctorOppositeAddCommGrpCatCompSheafToSheafSheafToPresheaf, Functor.flippingEquiv_apply_obj_map, Monad.monadMonEquiv_functor, PresheafOfModules.freeAdjunction_unit_app, ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst_assoc, Comma.mapRightEq_hom_app_left, frobeniusMorphism_iso_of_expComparison_iso, Over.forgetCocone_ι_app, Limits.colimitIsoColimitCurryCompColim_ι_ι_inv, Functor.commShiftOfLocalization_iso_hom_app, StructuredArrow.commaMapEquivalenceUnitIso_inv_app_right_left, Pretriangulated.rotCompInvRot_hom_app_hom₂, Join.inrCompFromSum_inv_app, PreGaloisCategory.FiberFunctor.isPretransitive_of_isGalois, Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_inv, evaluationIsRightAdjoint, MorphismProperty.instIsStableUnderRetractsFunctorFunctorCategory, BasedNatTrans.instIsIsoFunctorObjOfBasedFunctor, WithTerminal.liftFromOverComp_inv_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompToArrowIso_hom_app_right, Limits.hasLimit_const_of_isConnected, Comma.mapRightEq_inv_app_right, GrothendieckTopology.Point.toPresheafFiber_jointly_surjective₂, isCardinalPresentable_iff_isCardinalAccessible_uliftCoyoneda_obj, SingleFunctors.evaluation_map, StructuredArrow.mapIso_functor_map_right, Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_hom_assoc, Limits.ι_colimitConstInitial_hom, SingleFunctors.comp_hom, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_hom_τl, Adjunction.map_restrictFullyFaithful_unit_app, Limits.reflexivePair.compRightIso_inv_app, Limits.equalizer.fork_π_app_zero, partialFunEquivPointed_counitIso_hom_app_toFun, Sheaf.sheafifyCocone_ι_app_val_assoc, Core.forgetFunctorToCore_obj_map, LocalizerMorphism.LeftResolution.opEquivalence_counitIso, Functor.curryObjProdComp_inv_app_app, TwoP.swapEquiv_counitIso_hom_app_hom_toFun, SheafOfModules.conjugateEquiv_pullbackId_hom, Functor.Monoidal.associator_hom_app, Limits.Cone.equivCostructuredArrow_unitIso, PreGaloisCategory.endEquivAutGalois_π, Limits.coneOfConeUncurry_pt, Functor.LaxMonoidal.ofBifunctor.firstMap_app_app_app, NatTrans.app_units_zsmul, Prod.braiding_counitIso, Limits.Cocone.extend_ι, Limits.splitMonoOfIdempotentOfIsLimitFork_retraction, Presieve.extension_iff_amalgamation, Limits.prod.functor_obj_obj, Limits.Cocones.functorialityEquivalence_inverse, Limits.prodComparisonNatTrans_app, MonoidalClosed.pre_map, CochainComplex.shiftFunctorComm_hom_app_f, EnrichedFunctor.isoMk_inv_out, Cat.Hom.toNatTrans_comp, PreGaloisCategory.instIsTopologicalGroupAutFunctorFintypeCat, Functor.const_obj_obj, Limits.Cocone.toStructuredArrow_map, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_left_map, WithTerminal.equivComma_inverse_map_app, NatTrans.instIsMultiplicativeFunctorEquifibered, Idempotents.KaroubiKaroubi.unitIso_inv_app_f, GrothendieckTopology.diagramNatTrans_id, Limits.IsColimit.coconePointsIsoOfNatIso_inv, Sum.functorEquiv_unit_app_app_inl, Join.mkFunctorLeft_inv_app, ExactFunctor.of_fst, Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₃, Functor.leftKanExtensionUniqueOfIso_hom, Limits.Cone.w_apply, TopCat.isOpen_iff_of_isColimit, MonoidalOpposite.unmopEquiv_counitIso_inv_app, Functor.faithful_whiskeringRight_obj, Limits.limitFlipIsoCompLim_hom_app, shiftFunctorAdd_assoc_hom_app, ShortComplex.FunctorEquivalence.functor_map_app, SSet.horn.primitiveEdge_coe_down, instPreservesFiniteColimitsObjFunctorExactFunctor, CategoryOfElements.fromCostructuredArrow_obj_mk, Limits.limitUncurryIsoLimitCompLim_hom_π_π, Functor.PullbackObjObj.mapArrowLeft_right, Limits.limIsoFlipCompWhiskerLim_inv_app_app, WithInitial.ofCommaObject_map, Limits.CategoricalPullback.CatCommSqOver.precompose_map_rightUnitor, Abelian.DoldKan.comparisonN_hom_app_f, MonoidalOpposite.tensorRightMopIso_hom_app_unmop, Limits.Cone.overPost_π_app, Under.opEquivOpOver_counitIso, Functor.mapTriangleRotateIso_inv_app_hom₃, Functor.isIso_whiskerLeft, WithTerminal.equivComma_inverse_obj_map, SSet.Truncated.HomotopyCategory.BinaryProduct.associativityIso_hom_app, Subfunctor.Subpresheaf.range_comp_le, GrothendieckTopology.plusCompIso_whiskerLeft, PreGaloisCategory.PointedGaloisObject.instHasColimitOppositeFunctorTypeCompOpInclCoyoneda, Triangulated.SpectralObject.comp_hom_assoc, MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_inv_app_app, Limits.IndObjectPresentation.cocone_pt, Functor.toEssImageCompι_inv_app, localCohomology.hasColimitDiagram, conjugateEquiv_adjunction_id, Yoneda.fullyFaithful_preimage, Functor.monoidalClosed_closed_adj, TransfiniteCompositionOfShape.ofComposableArrows_incl_app, Limits.limit.id_pre, CosimplicialObject.Augmented.whiskering_obj, Limits.Cone.toStructuredArrow_map, Limits.CategoricalPullback.toCatCommSqOver_obj_fst_obj, Functor.mapArrowFunctor_map_app_left, AlgebraicGeometry.ExistsHomHomCompEqCompAux.hb, coyonedaEquiv_symm_map, Functor.leftDerivedZeroIsoSelf_hom_inv_id_app_assoc, GradedObject.mapTrifunctor_obj, Functor.opHom_map_app, ShortComplex.π_isoOpcyclesOfIsColimit_hom_assoc, Comma.toIdPUnitEquiv_counitIso_inv_app, Abelian.FunctorCategory.functor_category_isIso_coimageImageComparison, Action.associator_inv_hom, Functor.cocones_map_app, Idempotents.instFaithfulKaroubiFunctorKaroubiFunctorCategoryEmbedding, MonoidalCategory.DayFunctor.equiv_unitIso_inv_app, Enriched.FunctorCategory.functorEnriched_comp_id_assoc, Limits.coprod.functor_obj_map, instFaithfulIndFunctorOppositeTypeInclusion, ShiftMkCore.assoc_hom_app, Functor.RightExtension.postcomp₁_obj_hom_app, Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop, equivYoneda'_hom_val, Limits.Multicoequalizer.multicofork_ι_app_right, ModuleCat.extendScalars_comp_id, NatTrans.commShift_iso_hom_of_localization, functorProdFunctorEquivUnitIso_inv_app, SimplicialObject.Split.toKaroubiNondegComplexFunctorIsoN₁_inv_app_f_f, Functor.flip₂₃Functor_obj_map_app_app, GrothendieckTopology.overMapPullbackCongr_hom_app_val_app, sheafToPresheaf_isRightAdjoint, LightCondensed.id_val, RightExactFunctor.whiskeringLeft_obj_obj_obj, Functor.leftDerivedNatTrans_id, BraidedCategory.Hexagon.functor₂₁₃'_obj_obj_map, Enriched.FunctorCategory.functorEnriched_assoc_assoc, Functor.commShiftOfLocalization.iso_hom_app_assoc, Limits.SequentialProduct.cone_π_app, PresheafOfModules.freeYonedaEquiv_comp, instFullSheafFunctorOppositeCompSheafComposeSheafToPresheafOfFaithful, AddCommMonCat.coyoneda_obj_map, Functor.ranAdjunction_counit, SingleFunctors.instIsIsoFunctorHom, NatIso.unop_refl, endofunctorMonoidalCategory_leftUnitor_inv_app, MonoidalCategory.MonoidalLeftAction.curriedActionMop_obj_unmop_map, toSheafify_naturality_assoc, WithInitial.liftFromUnder_obj_map, Equivalence.functorFunctor_map, flippingIso_hom_toFunctor_obj_obj_obj, ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₂, Limits.limit.lift_π_app_assoc, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_inv_app_app, NatTrans.app_shift, Functor.leftDerivedNatTrans_fac, Functor.whiskeringLeft₃_obj_obj_obj_obj_obj_map_app, Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_mul_app, NatTrans.comp_app, Functor.instIsRegularEpiCategoryOfForallEpiHasPullbackOfHasPushouts, Functor.instIsIsoAppLanUnit_1, Limits.Cone.w_assoc, CatCenter.localization_mul, Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right_assoc, Limits.limitIsoFlipCompLim_inv_app, Join.mapPairLeft_hom_app, Endofunctor.Coalgebra.functorOfNatTransId_hom_app_f, Functor.flipIsoCurrySwapUncurry_inv_app_app, cones_map_app_app, CommGrpCat.coyoneda_obj_map, ShortComplex.functorEquivalence_inverse, EnrichedFunctor.isoMk_hom_out, BraidedCategory.ofBifunctor.Reverse.firstMap₃_app_app_app, nat_trans_from_is_connected, Limits.CategoricalPullback.CatCommSqOver.precompose_map_app_snd_app, WithTerminal.liftFromOver_map_app, whiskerRight_ι_colimitCompWhiskeringRightIsoColimitComp_inv, AlgebraicGeometry.isAffineHom_π_app, DerivedCategory.singleFunctorsPostcompQIso_hom_hom, Pretriangulated.Triangle.shiftFunctor_map_hom₂, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_map_right_app, Presieve.FamilyOfElements.compPresheafMap_id, Functor.sheafPushforwardContinuousId_inv_app_val_app, ChosenPullbacksAlong.unit_pullbackComp_hom, LightProfinite.Extend.functor_obj, LightCondensed.isoFinYoneda_hom_app, Pretriangulated.shiftFunctorCompIsoId_op_hom_app_assoc, coyonedaPairingExt_iff, Pseudofunctor.DescentData.pullFunctorCompIso_hom_app_hom, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₂, associativity_app, Pretriangulated.preadditiveYoneda_shiftMap_apply, SmallObject.prop_iterationFunctor_map_succ, Enriched.FunctorCategory.homEquiv_comp_assoc, Limits.CategoricalPullback.CatCommSqOver.transformPrecomposeObjSquare_iso_hom_comp, Limits.parallelPair.eqOfHomEq_hom_app, Limits.limit.map_pre, WithTerminal.coneEquiv_inverse_map_hom_left, Iso.inv_hom_id_app_app_app_assoc, FundamentalGroupoid.punitEquivDiscretePUnit_counitIso, Functor.mapCochainComplexShiftIso_hom_app_f, Functor.map_opShiftFunctorEquivalence_unitIso_inv_app_unop_assoc, Iso.inv_hom_id_app, SingleFunctors.shiftIso_add_hom_app, flippingIso_hom_toFunctor_map_app_app, Enriched.FunctorCategory.functorHomEquiv_apply_app, ShortComplex.exact_iff_of_forks, AdditiveFunctor.of_fst, Equivalence.unop_unitIso, instFullFunctorOppositeTypeShrinkYoneda, cosimplicialSimplicialEquiv_inverse_map, OppositeShift.adjunction_counit, Functor.bifunctorComp₁₂Iso_inv_app_app_app, Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_inv_app, Adjunction.representableBy_homEquiv, shiftFunctorCompIsoId_zero_zero_hom_app, Functor.PushoutObjObj.inr_ι_assoc, Equivalence.inverseFunctorObjIso_hom, MonoidalCategory.externalProductBifunctorCurried_obj_map_app_app, Limits.coequalizer.cofork_ι_app_one, ParametrizedAdjunction.homEquiv_naturality_one, obj_μ_inv_app_assoc, Functor.rightDerivedZeroIsoSelf_inv, Limits.prod.functor_map_app, Functor.toEssImageCompι_hom_app, GrothendieckTopology.W_eq_isLocal_range_sheafToPresheaf_obj, Functor.whiskeringLeft₃_obj_obj_obj_obj_obj_obj_map, δ_naturalityₗ, CochainComplex.shiftEval_inv_app, GrothendieckTopology.instIsIsoSheafAppFunctorOppositeSheafComposeNatTransPlusPlusAdjunction, Monad.ForgetCreatesLimits.liftedCone_π_app_f, Functor.whiskeringRight_obj_comp, Functor.PushoutObjObj.hom_ext_iff, Limits.combineCones_pt_obj, Functor.PushoutObjObj.mapArrowRight_comp, FunctorToTypes.hom_inv_id_app_apply, MonoidalCategory.MonoidalRightAction.actionUnitNatIso_inv_app, TwoSquare.vComp'_app, Equivalence.congrLeft_inverse, Limits.walkingSpanOpEquiv_unitIso_hom_app, Join.mapIsoWhiskerLeft_inv_app, Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app_assoc, TopCat.Presheaf.presheafEquivOfIso_functor_map_app, Equivalence.inverseFunctorObj'_inv_app, Enriched.FunctorCategory.enrichedComp_π, GrothendieckTopology.MayerVietorisSquare.shortComplex_X₂, Functor.rightUnitor_inv_app, Subfunctor.Subpresheaf.subobjectMk_range_arrow, GrothendieckTopology.Point.toPresheafFiber_map_surjective, Functor.leftUnitor_hom_app, Functor.flippingEquiv_apply_map_app, GrothendieckTopology.Point.toPresheafFiber_naturality, Grothendieck.ιCompMap_hom_app_base, Iso.core_hom_app_iso_hom, Over.ConstructProducts.conesEquivInverseObj_π_app, Limits.colimitObjIsoColimitCompEvaluation_ι_inv, GradedObject.comapEq_inv_app, GrothendieckTopology.liftToPlusObjLimitObj_fac, LaxMonoidalFunctor.comp_hom_assoc, PresheafOfModules.toPresheaf_preservesColimitsOfSize, Equivalence.refl_unitIso, Adjunction.unit_leftAdjointUniq_hom, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_hom_app, TransfiniteCompositionOfShape.map_incl, GradedObject.mapBifunctor_obj_map, Functor.homEquivOfIsRightKanExtension_apply_app, Limits.CompleteLattice.limitCone_cone_π_app, ParametrizedAdjunction.homEquiv_eq, Equivalence.symmEquivInverse_obj_unitIso_inv, Limits.combineCocones_pt_map, Adjunction.comp_unit, ExponentiableMorphism.unit_pushforwardComp_hom, Limits.IsLimit.homEquiv_symm_naturality, MonoidalCategory.curriedTensorPreFunctor_map_app_app, Pretriangulated.TriangleOpEquivalence.functor_map_hom₁, Limits.pointwiseProductCompEvaluation_hom_app, conjugateIsoEquiv_symm_apply_hom, toSheafify_plusPlusIsoSheafify_hom_assoc, Functor.ranCounit_app_whiskerLeft_ranAdjunction_unit_app, Limits.Cotrident.ofπ_ι_app, Functor.shiftIso_inv_naturality_assoc, instAdditiveAdditiveFunctorFunctorForget, Functor.IsEventuallyConstantTo.isIso_π_of_isLimit', Functor.PullbackObjObj.ofHasPullback_pt, Iso.unop_inv_hom_id_app_assoc, Limits.Cones.equivalenceOfReindexing_functor, CosimplicialObject.Truncated.whiskering_obj_obj_map, Functor.LeftExtension.coconeAt_ι_app, Limits.coconeOfIsSplitEpi_ι_app, Presheaf.isLimit_iff_isSheafFor, CatCenter.instIsMulCommutative, Action.functorCategoryEquivalence_linear, Monoidal.MonFunctorCategoryEquivalence.inverseObj_mon_one_app, LightProfinite.instEpiAppOppositeNatπAsLimitCone, ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst_assoc, FunctorToTypes.binaryProductCone_pt_map, Monoidal.comonFunctorCategoryEquivalence_inverse, Functor.mapTriangleCommShiftIso_hom_app_hom₂, PreGaloisCategory.exists_lift_of_quotient_openSubgroup, Adjunction.leftAdjointCompIso_hom_app, RightExactFunctor.forget_obj_of, NatTrans.shift_app_comm_assoc, Equivalence.counitIso_inv_app_tensor_comp_functor_map_δ_inverse, Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₂, MorphismProperty.instIsStableUnderCobaseChangeFunctorFunctorCategoryOfHasPushouts, Functor.whiskerRight_twice, NatIso.pi'_hom, LocalizerMorphism.instCommShiftLocalizationHomFunctorIsoFunctorQLocalizedFunctor, Enriched.FunctorCategory.functorHomEquiv_id, piEquivalenceFunctorDiscrete_functor_map, Limits.CategoricalPullback.functorEquiv_inverse_obj_obj_snd, Equivalence.congrRight_inverse, Functor.flip₁₃Functor_obj_obj_obj_map, Sieve.uliftFunctorInclusion_top_isIso, PresheafOfModules.colimitCocone_ι_app_app, GrothendieckTopology.Point.toPresheafFiberNatTrans_app, AlgebraicTopology.DoldKan.Γ₂_map_f_app, Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone_ι_app_eq_sum, Functor.Monoidal.whiskeringLeft_δ_app, NatTrans.shift_app, Pretriangulated.commShiftIso_unopUnop_hom_app, whiskering_linearYoneda₂, MonoidalCategory.DayConvolutionInternalHom.coev_naturality_app, NatTrans.mono_of_mono_app, Functor.isoWhiskerLeft_trans, Limits.pushoutCoconeEquivBinaryCofan_counitIso, Limits.inr_comp_pushoutObjIso_inv_assoc, Functor.ShiftSequence.induced_shiftMap, Functor.LeftExtension.mk_left_as, Limits.CokernelCofork.map_condition_assoc, Functor.commShiftIso_eq_ofInduced, SmallObject.coconeOfLE_ι_app, AddCommMonCat.coyonedaForget_hom_app_app_hom, Square.arrowArrowEquivalence'_counitIso, Monad.toMon_X, Limits.inr_comp_pushoutObjIso_hom, Idempotents.KaroubiHomologicalComplexEquivalence.counitIso_hom, Limits.colimitCoconeOfUnique_cocone_ι, Sum.functorEquiv_inverse_obj, Subfunctor.Subpresheaf.equalizer.ι_ι, Pseudofunctor.DescentData.pullFunctorEquivalence_counitIso, μ_naturality_assoc, Functor.mapCommMonIdIso_inv_app_hom_hom, ShortComplex.leftHomologyFunctorOpNatIso_inv_app, Limits.BinaryFan.assocInv_snd, shiftFunctorAdd_hom_app_obj_of_induced, Comma.mapLeftIso_inverse_map_left, Functor.isoWhiskerRight_trans_assoc, Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₂, Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left_assoc, Functor.map_shiftFunctorComm, MonoOver.congr_counitIso, Localization.Construction.WhiskeringLeftEquivalence.unitIso_hom, Functor.LaxMonoidal.ofBifunctor.firstMap₂_app_app_app, Functor.op_commShiftIso_hom_app, Functor.flipping_inverse_obj_obj_obj, Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_hom_app_fst_app, instSmallHomFunctorOppositeTypeColimitCompYoneda, Equivalence.op_unitIso, Limits.FormalCoproduct.eval_obj_obj, RightExactFunctor.whiskeringLeft_obj_map, Functor.PushoutObjObj.inl_ι, HomotopyCategory.homologyFunctor_shiftMap, Bicategory.toNatTrans_conjugateEquiv, Adjunction.whiskerRight_counit_app_app, instPreservesColimitFunctorOppositeTypeObjCoyonedaOpYoneda, NatTrans.vcomp_eq_comp, Functor.bifunctorComp₁₂Iso_hom_app_app_app, Equivalence.mkHom_comp, Limits.IsColimit.ι_app_homEquiv_symm, Subfunctor.to_sheafifyLift, TwistShiftData.commShift, Limits.PullbackCone.isoMk_hom_hom, CatCommSq.hInv_iso_hom_app, Comma.mapLeftComp_hom_app_left, Comonad.ForgetCreatesLimits'.commuting, δ_naturalityᵣ, Equivalence.mkIso_inv, Monad.MonadicityInternal.counitCofork_ι_app, Pretriangulated.Opposite.OpOpCommShift.iso_hom_app, Limits.Multifork.ofPiFork_ι, Functor.bifunctorComp₂₃Iso_hom_app_app_app, Limits.Cofork.IsColimit.homIso_symm_apply, PresheafOfModules.toPresheaf_map_sheafificationAdjunction_unit_app, Functor.PushoutObjObj.mapArrowRight_right, Functor.PullbackObjObj.π_fst_assoc, ShortComplex.opEquiv_unitIso, Action.functorCategoryEquivalence_preservesZeroMorphisms, LocalizerMorphism.rightDerivedFunctorComparison_fac_assoc, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₁, Functor.Initial.extendCone_obj_π_app, MonObj.mopEquiv_unitIso_inv_app_hom, NatIso.cancel_natIso_hom_right_assoc, Localization.SmallHom.equiv_shift, FunctorToTypes.prod.lift_snd, Limits.Fork.condition_assoc, Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₃, Limits.Cofork.IsColimit.π_desc', Limits.IsLimit.conePointsIsoOfNatIso_hom_comp, Presieve.isSheaf_yoneda', Limits.prodComparisonNatIso_inv, OrderHom.equivFunctor_symm_apply, FunctorToTypes.comp, CochainComplex.shiftShortComplexFunctorIso_zero_add_hom_app, Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv_assoc, uliftYonedaMap_app_apply, Limits.diagramIsoSpan_inv_app, SheafOfModules.pushforward_id_comp, Functor.inrCompSum'_hom_app, Functor.whiskeringLeftObjCompIso_hom_app_app, Functor.mapTriangleInvRotateIso_hom_app_hom₁, MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.rightUnitor_hom_unit_app, Functor.functorialityCompPostcompose_inv_app_hom, Functor.LeftExtension.precomp₂_map_left, MonoidalCategory.DayConvolution.unit_app_braiding_inv_app_assoc, Limits.HasLimit.isoOfNatIso_hom_π, CommMon.EquivLaxBraidedFunctorPUnit.counitIso_inv_app_hom_hom, Localization.liftNatIso_hom, Limits.HasBiproductsOfShape.colimIsoLim_hom_app, OverPresheafAux.counitForward_counitBackward, Abelian.LeftResolution.karoubi.π'_app_f, MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_obj_map_app, Under.lift_map, Limits.Wedge.condition_assoc, Functor.IsCoverDense.Types.appIso_hom, Functor.IsCoverDense.restrictHomEquivHom_naturality_right_symm_assoc, NatIso.unop_inv, MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionAssocIso_inv, Limits.CokernelCofork.π_eq_zero, ComposableArrows.IsComplex.cokerToKer'_fac_assoc, MonoidalCategory.rightUnitorNatIso_inv_app, OverPresheafAux.costructuredArrowPresheafToOver_obj, Functor.Final.extendCocone_map_hom, GrothendieckTopology.sheafificationWhiskerRightIso_inv_app, Limits.DiagramOfCones.mkOfHasLimits_conePoints, GrothendieckTopology.Point.presheafFiber_hom_ext_iff, CatCenter.localization_one, ObjectProperty.LimitOfShape.toStructuredArrow_obj, Limits.CategoricalPullback.CatCommSqOver.transform_obj_map_fst_app, Subfunctor.Subpresheaf.range_subobjectMk_ι, Sieve.equalizer_eq_equalizerSieve, SSet.Truncated.rightExtensionInclusion_hom_app, LightCondensed.comp_val, MonoidalClosed.ofEquiv_curry_def, Limits.isIso_colimit_cocone_parallelPair_of_self, Limits.multispanIndexCoend_fst, Idempotents.app_idem, Functor.Monoidal.leftUnitor_hom_app, LaxBraidedFunctor.id_hom, BraidedCategory.Hexagon.functor₃₁₂_obj_map_app, Iso.coreWhiskerRight, Idempotents.functor_category_isIdempotentComplete, Equivalence.changeInverse_unitIso_hom_app, Endofunctor.Adjunction.AlgCoalgEquiv.unitIso_hom_app_f, Adjunction.rightAdjointUniq_refl, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_inv_app_val_app_hom_hom, FreeMonoidalCategory.normalizeIsoApp_tensor, Adjunction.homEquiv_symm_rightAdjointUniq_hom_app, sheafBotEquivalence_counitIso, Limits.instPreservesFiniteColimitsFunctorObjEvaluationOfHasFiniteColimits, Limits.coconeUnopOfCone_ι, curryingIso_inv_toFunctor_obj_obj_map, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₃, Action.rightUnitor_inv_hom, unitOfTensorIsoUnit_hom_app, StructuredArrow.mapIso_inverse_map_left, preservesLimitNatIso_hom_app, cones_obj_obj, Idempotents.karoubiCochainComplexEquivalence_counitIso_inv, Functor.isoWhiskerLeft_hom, Bipointed.swapEquiv_unitIso_hom_app_toFun, Limits.MonoCoprod.mono_binaryCofanSum_inl, Limits.whiskerLeft_ι_colimitCompWhiskeringLeftIsoCompColimit_inv, Functor.FullyFaithful.homNatIso_hom_app_down, ShortComplex.FunctorEquivalence.inverse_obj_g, AdditiveFunctor.ofExact_map_hom, Adjunction.commShiftIso_inv_app_counit_app, Limits.IndizationClosedUnderFilteredColimitsAux.exists_nonempty_limit_obj_of_colimit, Monad.monadMonEquiv_unitIso_hom_app_toNatTrans_app, Functor.leftDerivedZeroIsoSelf_hom_inv_id_assoc, GrothendieckTopology.W_eq_W_range_sheafToPresheaf_obj, ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst, CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompYoneda, AlgebraicTopology.DoldKan.Γ₂N₁_inv, Limits.BinaryFan.assocInv_fst, Functor.mapMatId_inv_app, CostructuredArrow.ιCompGrothendieckProj_hom_app, CostructuredArrow.initial_map₂_id, Limits.Fork.isoForkOfι_inv_hom, PreGaloisCategory.toAut_bijective, MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionObj, MonoidalCategory.externalProductSwap_hom_app_app, Functor.coreflective', MonoidalCategory.DayConvolutionUnit.rightUnitor_naturality, MonoidalCategory.MonoidalRightAction.actionAssocNatIso_hom_app_app_app, MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionHomRight, shiftFunctorAdd'_assoc_hom_app_assoc, Limits.BinaryFan.π_app_left, Functor.IsEventuallyConstantFrom.isIso_ι_of_isColimit, AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_fac, Monoidal.tensorObj_map, Limits.Cofork.ofπ_ι_app, Equivalence.congrRight_unitIso_hom_app, NatTrans.shift_app_comm, Join.mapPairRight_hom_app, Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_hom_app_hom, Limits.walkingParallelPairOpEquiv_unitIso_hom_app_one, BraidedCategory.Hexagon.functor₁₃₂'_obj_obj_map, sheafComposeIso_hom_fac_assoc, Functor.PullbackObjObj.hom_ext_iff, SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, Functor.currying_functor_obj_map, Functor.leftOpRightOpEquiv_functor_map_app, sheafification_reflective, yonedaGrp_map_app, Functor.Monoidal.leftUnitor_inv_app, FunctorToTypes.monoFactorisation_m, AlgebraicGeometry.instIsIsoFunctorModuleCatCarrierUnitModulesSpecOfAdjunction, Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_hom_fac_assoc, FunctorToTypes.monoFactorisation_I, Functor.rightDerivedZeroIsoSelf_inv_hom_id_assoc, Functor.ShiftSequence.induced_isoShiftZero_hom_app_obj, sheafComposeIso_inv_fac, Limits.walkingSpanOpEquiv_counitIso_inv_app, OrderHom.equivalenceFunctor_unitIso_inv_app, Pretriangulated.commShiftIso_unopUnop_hom_app_assoc, Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality, Functor.equiv_inverse, Under.opEquivOpOver_unitIso, Functor.isoCopyObj_hom_app, SingleFunctors.shiftIso_zero_hom_app, Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_fst, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_hom_app_app, Functor.flip_map_app, NatTrans.exchange, MorphismProperty.presheaf_monomorphisms_le_monomorphisms, MonoidalCategory.DayConvolutionUnit.rightUnitor_inv_app_assoc, Adjunction.leftAdjointIdIso_inv_app, Limits.ι_colimitLimitToLimitColimit_π_assoc, Functor.map_shiftFunctorCompIsoId_inv_app, Adjunction.leftAdjointUniq_trans, conjugateEquiv_of_iso, MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_η_unmop_app, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv_def, Equivalence.core_unitIso_inv_app_iso_hom, LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_obj, Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.flipFunctorToInterchange_hom_app_app, Limits.Cofork.unop_ι, groupCohomology.isoShortComplexH1_inv, NatTrans.unop_whiskerRight_assoc, Limits.Cone.toStructuredArrowCompToUnderCompForget_inv_app, Limits.CategoricalPullback.functorEquiv_unitIso_hom_app_app_fst, AlgebraicTopology.DoldKan.identity_N₂_objectwise, FundamentalGroupoid.punitEquivDiscretePUnit_inverse, Iso.hom_inv_id_app_app_app_assoc, conjugateEquiv_comp, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_π_app_walkingParallelPair_zero, MonoidalOpposite.tensorRightUnmopIso_hom_app, Limits.CategoricalPullback.CatCommSqOver.precompose_obj_obj_iso_hom_app, coyonedaFunctor_preservesLimits, map_shrinkYonedaEquiv, GrothendieckTopology.Point.sheafFiberCompIso_hom_app, NatTrans.app_zsmul, OverPresheafAux.YonedaCollection.map₁_snd, CostructuredArrow.mapNatIso_functor_map_right, IsGrothendieckAbelian.IsPresentable.injectivity₀.hf, BraidedCategory.Hexagon.functor₁₂₃_obj_map_app, Limits.prod.functor_obj_map, Presieve.FamilyOfElements.map_comp, WithTerminal.coneEquiv_functor_obj_pt, ObjectProperty.LimitOfShape.toStructuredArrow_map, Functor.IsRepresentedBy.iff_natIso, MonoidalCategory.MonoidalLeftAction.curriedActionMopMonoidal_ε_unmop_app, MonoidalOpposite.tensorLeftMopIso_inv_app_unmop, Equivalence.sheafCongrPreregular_unitIso_inv_app_val_app, NatTrans.leftDerived_comp, PresheafOfModules.instFullRestrictScalarsIdFunctorOppositeRingCat, Limits.diagramIsoPair_inv_app, Limits.coprod.functor_obj_obj, yonedaEquiv_symm_map, Limits.IsLimit.homIso_hom, Cat.Hom.equivFunctor_apply, obj_ε_app, ModuleCat.FilteredColimits.ι_colimitDesc_assoc, Square.arrowArrowEquivalence_unitIso, ContinuousCohomology.MultiInd.d_succ, ModuleCat.extendScalarsId_inv_app_apply, Functor.OplaxMonoidal.ofBifunctor.firstMap₃_app_app_app, liftedLimitMapsToOriginal_hom_π, Adjunction.whiskerRight_unit_iso_of_R_fully_faithful, NatTrans.leftDerivedToHomotopyCategory_id, MorphismProperty.FunctorialFactorizationData.fac_assoc, Functor.IsDenseSubsite.isIso_ranCounit_app_of_isDenseSubsite, Cat.Hom.toNatIso_inv, Limits.opParallelPairIso_inv_app_zero, Functor.Monoidal.rightUnitor_hom_app, Equivalence.trans_unitIso, Idempotents.karoubiCochainComplexEquivalence_unitIso_inv_app_f_f, NatTrans.leftDerived_id, Under.postEquiv_unitIso, Functor.Monoidal.commTensorRight_hom_app, Sieve.toFunctor_app_coe, isFinitelyPresentable_iff_preservesFilteredColimits, Limits.PullbackCone.mk_π_app_left, constantPresheafAdj_counit_app_app, Equivalence.sheafCongr.unitIso_inv_app_val_app, Sum.functorEquivFunctorCompSndIso_hom_app_app, ObjectProperty.instIsClosedUnderColimitsOfShapeFunctorPreservesFiniteLimitsOfHasExactColimitsOfShape, Join.mapIsoWhiskerLeft_hom_app, AlgebraicTopology.DoldKan.N₁Γ₀_inv_app_f_f, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τr, Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_hom_app_fst_app, WithTerminal.commaFromOver_obj_left, PresheafOfModules.fromFreeYonedaCoproduct_app_mk, rightExactFunctor_le_additiveFunctor, TopologicalSpace.Opens.overEquivalence_counitIso_hom_app, Functor.reprW_hom_app, FreeGroupoid.mapCompLift_hom_app, ComposableArrows.opEquivalence_counitIso_hom_app_app, uliftCoyonedaEquiv_symm_map, Limits.CompleteLattice.colimitCocone_isColimit_desc, GrothendieckTopology.overMapPullback_assoc, Functor.curry_map_app_app, Limits.opParallelPairIso_inv_app_one, ExponentiableMorphism.pushforwardId_hom_counit, TwoSquare.lanBaseChange_app, Limits.colimitHomIsoLimitYoneda_inv_comp_π, Sum.functorEquivFunctorCompFstIso_hom_app_app, MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.tensorHom_eq, Linear.toCatCenter_apply_app, whiskeringLeftCompEvaluation_inv_app, Limits.CatCospanTransform.isIso_right, Limits.CompleteLattice.finiteColimitCocone_isColimit_desc, CatCommSq.vId_iso_inv_app, Comma.equivProd_unitIso_inv_app_left, Adjunction.lim_preservesLimits, yonedaYonedaColimit_app_inv, Sheaf.ΓObjEquivSections_naturality, Limits.Cone.extensions_app, yonedaEquiv_symm_naturality_left, Limits.pullbackConeEquivBinaryFan_unitIso, Presheaf.comp_isLocallyInjective_iff, SmallObject.preservesColimit, CatCenter.app_neg, limitCompWhiskeringRightIsoLimitComp_inv_π, Limits.coneUnopOfCocone_π, Endofunctor.Coalgebra.functorOfNatTransEq_inv_app_f, MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionAssocIso_hom, ObjectProperty.IsCodetecting.isIso_iff_of_epi, NatIso.unop_whiskerLeft, Subfunctor.instMonoFunctorTypeι, NatIso.hcomp_inv, Limits.Cotrident.app_one_assoc, Limits.Multicofork.ofSigmaCofork_ι_app_left, δ_μ_app_assoc, Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop_assoc, GrothendieckTopology.diagramNatTrans_zero, NatIso.unop_hom, Discrete.functorComp_inv_app, Functor.shiftIso_hom_app_comp_shiftMap_of_add_eq_zero, GrothendieckTopology.toPlus_plusLift, Limits.HasLimit.isoOfEquivalence_inv_π, Comma.unopFunctorCompSnd_hom_app, Functor.CommShift.OfComp.map_iso_inv_app, Functor.rightKanExtensionCompIsoOfPreserves_inv_fac_app_assoc, Pretriangulated.preadditiveYoneda_map_distinguished, Limits.hasColimit_const_of_isConnected, Monad.one_def, Functor.whiskeringLeft_obj_obj, CatCenter.smul_iso_hom_eq, coyonedaFunctor_reflectsLimits, Limits.coconeOfCoconeCurry_ι_app, NatTrans.instCommShiftOppositeShiftHomFunctorNatIsoComp, Adjunction.whiskerLeftRUnitIsoOfIsIsoCounit_inv_app, Functor.flippingEquiv_apply_obj_obj, LightCondensed.lanPresheafExt_hom, yonedaEquiv_symm_naturality_right, PreGaloisCategory.PointedGaloisObject.cocone_app, Adjunction.RightAdjointCommShift.iso_hom_app, CochainComplex.ShiftSequence.shiftIso_inv_app, Functor.compConstIso_inv_app_app, BasedNatTrans.instReflectsIsomorphismsBasedFunctorFunctorObjForgetful, Functor.ranCompLimIso_hom_app, Functor.mapTriangleInvRotateIso_hom_app_hom₂, constantSheafAdj_counit_app, Functor.leibnizPullback_map_app, Over.mapCongr_rfl, ShortComplex.FunctorEquivalence.unitIso_hom_app_τ₂_app, CommShift₂Setup.z_zero₂, NatTrans.rightOp_id, Functor.rightDerivedZeroIsoSelf_hom_inv_id_assoc, Action.resComp_hom_app_hom, CommShift₂Setup.int_ε, Equivalence.funInvIdAssoc_inv_app, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_inv_app_f, NatTrans.removeRightOp_id, Limits.HasLimit.lift_isoOfNatIso_inv, Profinite.exists_locallyConstant_finite_nonempty, Limits.BinaryFan.assoc_fst, sheafSectionsNatIsoEvaluation_hom_app, Limits.MonoFactorisation.fac_apply, Adjunction.unit_rightAdjointUniq_hom_app_assoc, Enriched.FunctorCategory.enrichedId_π, GrothendieckTopology.Point.toPresheafFiber_presheafFiberCompIso_hom_app_assoc, GrothendieckTopology.preservesLimit_diagramFunctor, Equivalence.mkHom_comp_assoc, Functor.leftKanExtensionCompIsoOfPreserves_inv_fac_app, Limits.colimCompFlipIsoWhiskerColim_inv_app_app, Limits.CategoricalPullback.functorEquiv_inverse_obj_obj_fst, Limits.parallelPair.eqOfHomEq_inv_app, Limits.FormalCoproduct.cosimplicialObjectFunctor_map_app, NatTrans.instIsMultiplicativeFunctorCoequifibered, GrothendieckTopology.overMapPullback_id_comp, sum.inlCompAssociator_inv_app, ExactFunctor.whiskeringRight_obj_map, Functor.unopId_hom_app, Limits.IndObjectPresentation.yoneda_I, GrothendieckTopology.MayerVietorisSquare.sheafCondition_iff_comp_coyoneda, Functor.isoWhiskerRight_inv, HomologicalComplex₂.flipEquivalenceCounitIso_hom_app_f_f, Functor.commShift₂_comm_assoc, Limits.CategoricalPullback.CatCommSqOver.transformObjComp_inv_app_snd_app, MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionHomLeft, NatIso.hcomp_hom, Limits.CompleteLattice.finiteLimitCone_cone_π_app, ComposableArrows.IsComplex.cokerToKer'_fac, FinitaryExtensive.isPullback_initial_to, Limits.CoproductsFromFiniteFiltered.liftToFinset_obj_obj, WithInitial.liftToInitialUnique_inv_app, prod.functorProdToProdFunctorAssociator_inv_app, WithInitial.mapComp_inv_app, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_hom_c_app, Limits.PreservesColimit₂.ι_comp_isoObjConePointsOfIsColimit_inv_assoc, Limits.Types.Limit.lift_π_apply', OverPresheafAux.OverArrows.map_val, AddCommGrpCat.binaryProductLimitCone_cone_π_app_right, Functor.sheafAdjunctionCocontinuous_homEquiv_apply_val, Functor.whiskerRight_left, Functor.isLeftDerivedFunctor_iff_isIso_leftDerivedLift, Iso.inv_hom_id_app_assoc, PreOneHypercover.forkOfIsColimit_ι_map_inj, ParametrizedAdjunction.homEquiv_naturality_one_assoc, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, Action.functorCategoryEquivalence_additive, Limits.CategoricalPullback.CatCommSqOver.transformObjId_hom_app_snd_app, PreservesFiniteLimitsOfFlat.fac, Subfunctor.equalizer.condition_assoc, Limits.walkingCospanOpEquiv_unitIso_hom_app, AlgebraicTopology.DoldKan.map_hσ', Functor.FullyFaithful.hasShift.map_zero_inv_app, Limits.ProductsFromFiniteCofiltered.liftToFinset_obj_obj, Functor.curry_obj_comp_flip, Adjunction.leftAdjointIdIso_hom_app, Pseudofunctor.DescentData.pullFunctorEquivalence_unitIso, Comonad.ForgetCreatesColimits'.liftedCocone_ι_app_f, Limits.instHasIterationOfShapeFunctor, AlgebraicGeometry.Scheme.Cover.functorOfLocallyDirectedHomBase_app, CostructuredArrow.mapIso_inverse_map_right, Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₂, Injective.injective_iff_preservesEpimorphisms_preadditiveYoneda_obj, uliftYonedaIsoYoneda_inv_app_app_down, NatTrans.leftOp_comp, Functor.ShiftSequence.shiftIso_zero, Localization.lift₂_iso_hom_app_app₁, Limits.Cocones.precompose_map_hom, uliftYonedaEquiv_symm_map_assoc, Limits.constCone_π, Functor.Monoidal.transport_ε_assoc, ModuleCat.restrictScalarsCongr_inv_app, Functor.PushoutObjObj.mapArrowLeft_comp, commBialgCatEquivComonCommAlgCat_counitIso_hom_app, Limits.HasZeroObject.instFunctor, Functor.Monoidal.transport_δ_assoc, Functor.curryingEquiv_symm_apply_obj_map, Limits.opSpan_inv_app, LeftExactFunctor.whiskeringLeft_obj_map, Limits.SequentialProduct.cone_π_app_comp_Pi_π_neg, Functor.leftExtensionEquivalenceOfIso₁_counitIso_hom_app_right_app, SingleFunctors.shiftIso_add'_inv_app, SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right_assoc, IsPullback.of_isLimit_cone, Limits.coendFunctor_map, Limits.coyonedaCompLimIsoCones_hom_app_app, Limits.PreservesColimit₂.ι_comp_isoColimitUncurryWhiskeringLeft₂_hom, WithTerminal.equivComma_counitIso_inv_app_right, Limits.whiskerLeft_ι_colimitCompWhiskeringLeftIsoCompColimit_inv_assoc, Limits.colimitCoconeOfUnique_isColimit_desc, toOverUnitPullback_hom_app_left, Limits.mapPairIso_hom_app, Functor.sheafPushforwardContinuousId'_hom_app_val_app, Condensed.isoFinYoneda_inv_app, Limits.pullbackObjIso_inv_comp_snd, Limits.FormalCoproduct.evalOp_obj_obj, Limits.limit.lift_π, Limits.Cofork.IsColimit.π_desc'_assoc, NatTrans.instRespectsIsoFunctorEquifibered, Limits.IsColimit.fac_assoc, AlgebraicGeometry.SheafedSpace.isColimit_exists_rep, tensoringRight_additive, AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_inv_app, AugmentedSimplexCategory.equivAugmentedCosimplicialObjectFunctorCompDropIso_inv_app_app, compEvaluation_inv_app, Functor.leftAdjointObjIsDefined_iff, Functor.IsCoverDense.sheafIso_hom_val, Pretriangulated.invRotCompRot_inv_app_hom₂, Functor.PullbackObjObj.π_iso_of_iso_left_hom, Sum.functorEquiv_unitIso, Limits.pushoutCoconeOfRightIso_ι_app_right, PresheafOfModules.freeAdjunction_homEquiv, GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_val_app, Functor.leftOpRightOpEquiv_inverse_obj, sheafifyMap_sheafifyLift_assoc, Cat.associator_hom_toNatTrans, Action.FunctorCategoryEquivalence.functor_obj_map, Limits.wideEqualizer.trident_π_app_zero, Limits.cospanExt_inv_app_right, Equivalence.op_counitIso, instFullSheafFunctorOppositeSheafToPresheaf, Limits.BinaryFan.isLimit_iff_isIso_snd, Cat.Hom.instIsIsoFunctorαCategoryToNatTransHomHom, TransfiniteCompositionOfShape.ici_incl, ShortComplex.FunctorEquivalence.counitIso_hom_app_app_τ₃, Subfunctor.Subpresheaf.eq_top_iff_isIso, MonoidalOpposite.tensorLeftIso_inv_app_unmop, Limits.LimitPresentation.w_assoc, CommGrpCat.coyoneda_map_app, exactFunctor_le_rightExactFunctor, Sum.swapCompInr_inv_app, cocones_obj_obj, Functor.const_obj_map, PreGaloisCategory.instCompactSpaceAutFunctorFintypeCat, Abelian.FunctorCategory.coimageObjIso_hom, Limits.colimitYonedaHomIsoLimitRightOp_π_apply, WithInitial.opEquiv_unitIso_hom_app, obj_η_app, GrothendieckTopology.plusMap_zero, ChosenPullbacksAlong.pullbackComp_hom_counit_assoc, PreGaloisCategory.instReflectsMonomorphismsActionFintypeCatAutFunctorFunctorToAction, Limits.FormalCoproduct.evalCompInclIsoId_hom_app_app, ShortComplex.FunctorEquivalence.inverse_map_τ₃, Comma.unopFunctorCompFst_hom_app, TopologicalSpace.OpenNhds.inclusionMapIso_inv_app, Sheaf.isConstant_iff_isIso_counit_app, NatTrans.Coequifibered.comp, Presheaf.tautologicalCocone_pt, Limits.CategoricalPullback.CatCommSqOver.transform_map_rightUnitor, Pretriangulated.TriangleOpEquivalence.inverse_map, Limits.CategoricalPullback.toCatCommSqOver_map_snd_app, Over.coprod_map_app, Functor.CorepresentableBy.coyoneda_homEquiv, SheafOfModules.forgetToSheafModuleCat_obj_val, yoneda'_map_val, Adjunction.homEquiv_leftAdjointUniq_hom_app, CommMon.EquivLaxBraidedFunctorPUnit.counitIso_hom_app_hom_hom, Bicategory.associatorNatIsoMiddle_inv_app, ShiftMkCore.zero_add_inv_app, Idempotents.karoubiChainComplexEquivalence_unitIso_hom_app_f_f, Limits.colimit.isoColimitCocone_ι_hom, CostructuredArrow.mapIso_inverse_map_left, Adjunction.whiskerRight_unit_app_app, Limits.Cocone.equivStructuredArrow_functor, instIsLeftAdjointFunctorOppositeSheafPresheafToSheaf, Functor.ranAdjunction_unit_app, Limits.Types.FilteredColimit.isColimit_eq_iff', prod_preservesConnectedLimits, pullbackShiftFunctorAdd'_inv_app, Functor.instFaithfulProdCurry₃, OverPresheafAux.map_mkPrecomp_eqToHom, MonoidalCategory.DayConvolutionInternalHom.coev_app_π, LocalizerMorphism.isLeftDerivabilityStructure_iff, Limits.end_.condition_assoc, Profinite.exists_locallyConstant_fin_two, BraidedCategory.Hexagon.functor₁₃₂_obj_obj_obj, Limits.limitObjIsoLimitCompEvaluation_inv_limit_map_assoc, StructuredArrow.mapNatIso_inverse_map_left, Presheaf.subsingleton_iff_isSeparatedFor, Functor.shiftIso_hom_naturality, Sheaf.cartesianMonoidalCategoryWhiskerLeft_val, WithInitial.ofCommaMorphism_app, Limits.Cocone.fromStructuredArrow_obj_ι, Functor.coreComp_inv_app_iso_hom, Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_eq, AdditiveFunctor.ofLeftExact_map_hom, ModuleCat.HasLimit.productLimitCone_isLimit_lift, Limits.Cocone.equivStructuredArrow_counitIso, SheafOfModules.pushforwardNatIso_hom, ChosenPullbacksAlong.unit_pullbackId_hom_app_assoc, prodOpEquiv_counitIso_inv_app, TwistShiftData.shiftFunctor_map, Comonad.beckCoalgebraFork_π_app, MonoidalOpposite.tensorIso_inv_app_unmop, MonoidalOpposite.mopMopEquivalence_counitIso_hom_app, Limits.CatCospanTransform.isIso_iff, GrothendieckTopology.diagramNatTrans_comp, TwistShiftData.shiftFunctorZero_inv_app, uliftYonedaFunctor_preservesLimits, bifunctorComp₂₃Obj_map_app, Equivalence.core_unitIso_inv_app_iso_inv, Endofunctor.Coalgebra.functorOfNatTransComp_hom_app_f, Limits.colimitLimitToLimitColimit_injective, Functor.lanAdjunction_counit_app, Functor.id_hcomp, MonoidalCategory.rightUnitorNatIso_hom_app, Functor.PushoutObjObj.ι_iso_of_iso_left_hom, Functor.RightExtension.IsPointwiseRightKanExtensionAt.isoLimit_hom_π_assoc, coreFunctor_obj_map_iso_hom, BraidedCategory.Hexagon.functor₁₃₂_obj_map_app, FunctorToTypes.binaryCoproductCocone_pt_obj, CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_map, Functor.isIso_lanAdjunction_counit_app_iff, sheafifyLift_id_toSheafify_assoc, Functor.LaxMonoidal.ofBifunctor.secondMap₃_app_app_app, GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_val_app, groupCohomology.isoShortComplexH2_inv, shiftFunctorCompIsoId_zero_zero_inv_app, Limits.instHasLimitProdObjFunctorUncurryWhiskeringLeft₂OfPreservesLimit₂, Pseudofunctor.ObjectProperty.mapComp_inv_app, Limits.colimit.comp_coconePointUniqueUpToIso_inv, preadditiveCoyoneda_obj, Enriched.FunctorCategory.functorEnriched_assoc, WithTerminal.equivComma_unitIso_hom_app_app, PresheafOfModules.pushforward_id_comp, cosimplicialSimplicialEquiv_functor_obj_map, prod.prodFunctorToFunctorProdAssociator_hom_app_app, Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse_assoc, DinatTrans.dinaturality, Grothendieck.compAsSmallFunctorEquivalence_counitIso, TopCat.piFan_π_app, Functor.coreComp_inv_app_iso_inv, Adjunction.shift_unit_app_assoc, MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop_actionHom, HomologicalComplex.homologyFunctorIso_inv_app, oppositeShiftFunctorAdd_hom_app, Functor.commShiftUnop_commShiftIso, TopCat.coconeOfCoconeForget_ι_app, CochainComplex.liftCycles_shift_homologyπ_assoc, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_inv_app, Comma.colimitAuxiliaryCocone_ι_app, Limits.Fan.mk_π_app, GrothendieckTopology.toSheafify_sheafifyLift, Functor.isRightKanExtension_iff_postcomp₁, HasLiftingProperty.transfiniteComposition.SqStruct.w₂, curryingIso_hom_toFunctor_map_app, Limits.Multifork.app_right_eq_ι_comp_fst, ContAction.resComp_inv, CartesianMonoidalCategory.prodComparisonBifunctorNatTrans_comp, Functor.leftOpRightOpIso_inv_app, Functor.mapTriangleIdIso_hom_app_hom₁, Sheaf.sheafifyCocone_ι_app_val, CartesianMonoidalCategory.prodComparisonNatTrans_app, SingleFunctors.inv_hom_id_hom, MonadHom.id_toNatTrans, MorphismProperty.Over.mapId_hom_app_left, NonemptyParallelPairPresentationAux.hg, Functor.coreflective, Limits.evaluation_preservesLimitsOfShape, Monoidal.MonFunctorCategoryEquivalence.unitIso_hom_app_hom_app, Adjunction.unit_leftAdjointUniq_hom_app, Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_inv_app, Functor.mapTriangleIdIso_hom_app_hom₂, Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop, SingleFunctors.postcompIsoOfIso_inv_hom_app, WithTerminal.opEquiv_unitIso_inv_app, PreGaloisCategory.toAut_injective_of_non_trivial, Functor.ShiftSequence.induced_shiftMap_assoc, Limits.MultispanIndex.multicoforkEquivSigmaCofork_unitIso_inv_app_hom, ShortComplex.FunctorEquivalence.inverse_map_τ₂, LocalizerMorphism.isIso_iff_of_hasLeftResolutions, Functor.pushforwardContinuousSheafificationCompatibility_hom_app_val, Limits.diagramIsoParallelPair_inv_app, Adjunction.commShiftIso_hom_app_counit_app_shift, MorphismProperty.Over.pullbackComp_left_fst_fst, Profinite.Extend.functor_map, OverPresheafAux.counitAuxAux_hom, Enriched.FunctorCategory.functorEnrichedHom_map, Limits.coneOfAdj_π, Discrete.natIsoFunctor_inv_app, Bicategory.associatorNatIsoRight_inv_app, Limits.lim_μ_π, Limits.colimitCoyonedaHomIsoLimitLeftOp_π_apply, MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.convolutionUnitApp_eq, Functor.IsCoverDense.restrictHomEquivHom_naturality_right, Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app, Condensed.id_val, Limits.limitUncurryIsoLimitCompLim_inv_π_assoc, Limits.cospanExt_hom_app_right, BraidedCategory.Hexagon.functor₃₁₂'_obj_map_app, Subfunctor.equalizer.ι_ι, Limits.HasLimit.lift_isoOfNatIso_hom_assoc, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_map, Limits.colimitHomIsoLimitYoneda_inv_comp_π_assoc, PreGaloisCategory.endMulEquivAutGalois_pi, Condensed.locallyConstantIsoFinYoneda_hom_app, Pi.comapComp_hom_app, NatTrans.app_sub, Functor.hcomp_id, ParametrizedAdjunction.homEquiv_naturality_two_assoc, Functor.leibnizPullback_obj_obj, Limits.isIso_limit_cone_parallelPair_of_self, StructuredArrow.commaMapEquivalenceCounitIso_inv_app_left_right, linearCoyoneda_obj_obj_isModule, GlueData.diagramIso_hom_app_right, ModuleCat.homEquiv_extendScalarsId, yoneda_obj_isGeneratedBy, Limits.Concrete.isColimit_rep_eq_of_exists, MonoidalCategory.prodCompExternalProduct_hom_app, Limits.CategoricalPullback.functorEquiv_counitIso_hom_app_snd_app, MonoidalCategory.DayFunctor.η_comp_isoPointwiseLeftKanExtension_hom, NatTrans.app_neg, toOverUnitPullback_inv_app_left, NatIso.cancel_natIso_hom_left, Comma.mapRightIso_inverse_map_left, Functor.sheafPushforwardContinuousComp'_hom_app_val_app, Functor.OplaxMonoidal.ofBifunctor.firstMap_app_app_app, RightExactFunctor.forget_obj, nerveAdjunction.isIso_counit, Limits.Cofork.app_one_eq_π, Subfunctor.epi_iff_range_eq_top, GrothendieckTopology.overMapPullbackCongr_inv_app_val_app, Limits.constCocone_ι, Equivalence.CommShift.instCommShiftHomFunctorUnitIso, CommShift₂Setup.z_zero₁, functor_thin, Limits.spanIsoMk_inv_app, SSet.StrictSegal.isRightKanExtension, AlgebraicGeometry.Scheme.exists_isOpenCover_and_isAffine, InjectiveResolution.extEquivCohomologyClass_symm_mk_hom, Subfunctor.equalizer.fork_ι, ChosenPullbacksAlong.unit_pullbackId_hom_assoc, Subfunctor.Subpresheaf.ofSection_eq_range, piEquivalenceFunctorDiscrete_counitIso, Join.mapIsoWhiskerLeft_inv, isZero_Tor_succ_of_projective, SingleFunctors.shiftIso_add'_hom_app, Functor.whiskeringLeft₃_obj_obj_obj_obj_map_app_app, ShortComplex.π_isoOpcyclesOfIsColimit_hom, Limits.HasColimit.isoOfNatIso_inv_desc, Limits.instHasColimitProdObjFunctorUncurryWhiskeringLeft₂OfPreservesColimit₂, CommRingCat.preservesFilteredColimits_coyoneda, Limits.CatCospanTransformMorphism.right_coherence, Comma.mapLeftId_inv_app_right, Limits.walkingParallelPairOpEquiv_counitIso_inv_app_op_one, Equivalence.sheafCongr.counitIso_inv_app_val_app, Functor.mapMatComp_inv_app, Limits.opHomCompWhiskeringLimYonedaIsoCocones_inv_app_app, GrothendieckTopology.plusMap_comp, StructuredArrow.mapNatIso_functor_map_left, Presheaf.freeYonedaHomEquiv_symm_comp_assoc, sheafSectionsNatIsoEvaluation_inv_app, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_isAddCommGroup, Functor.instIsAccessibleObjConst, OverPresheafAux.YonedaCollection.map₂_fst, Tor_map, ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd_assoc, FunctorToTypes.prod_ext'_iff, TopCat.Presheaf.presheafEquivOfIso_functor_obj_map, Functor.mapDerivedCategoryFactorsh_hom_app, Adjunction.Localization.η_app, AlgebraicTopology.isZero_singularHomologyFunctor_of_totallyDisconnectedSpace, Subpresheaf.to_sheafifyLift, sum.inlCompInverseAssociator_hom_app_down_down, Functor.sheafAdjunctionCocontinuous_unit_app_val, Functor.rightDerivedZeroIsoSelf_inv_hom_id, Limits.HasBiproductsOfShape.colimIsoLim_inv_app, StructuredArrow.mapNatIso_counitIso_inv_app_right, Functor.map_opShiftFunctorEquivalence_unitIso_hom_app_unop, Sieve.toUliftFunctor_app_down_coe, Functor.homObjFunctor_obj, NatIso.cancel_natIso_inv_left, Limits.walkingParallelPairOpEquiv_counitIso_hom_app_op_zero, WithInitial.coconeEquiv_unitIso_inv_app_hom_right, Join.mapWhiskerLeft_comp, Tor'_map_app, oppositeShiftFunctorAdd'_inv_app, Equivalence.symmEquivInverse_obj_unitIso_hom, MonoidalCategory.DayConvolution.associator_hom_unit_unit, Functor.whiskeringRight_map_app_app, Limits.HasColimit.isoOfNatIso_ι_inv_assoc, Functor.lanUnit_app_app_lanAdjunction_counit_app_app_assoc, Rep.Tor_obj, StructuredArrow.commaMapEquivalenceFunctor_obj_right, Localization.Construction.WhiskeringLeftEquivalence.counitIso_hom, GrothendieckTopology.isIso_toPlus_of_isSheaf, Functor.leftExtensionEquivalenceOfIso₁_functor_map_right, GrothendieckTopology.Point.sheafFiberCompIso_inv_app, Action.resCongr_hom, CommShift₂Setup.hε, Limits.Cocone.underPost_pt, ε_app, Limits.FormalCoproduct.evalOpCompInlIsoId_inv_app_app, Abelian.DoldKan.comparisonN_inv_app_f, Functor.whiskeringLeft₂_obj_obj_map_app_app, HomologicalComplex.homologyFunctorSingleIso_hom_app, Limits.Cofork.op_ι, right_unitality_app, Abelian.FunctorCategory.imageObjIso_inv, CommGrpCat.coyonedaType_obj_obj_coe, Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_inv_app_fst_app, Functor.instIsIsoAppRanCounit_1, Limits.Cones.postcomposeComp_hom_app_hom, Enriched.FunctorCategory.functorEnriched_comp_id, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_hom_app, CommRingCat.coproductCocone_ι, Limits.cospanExt_hom_app_left, PreGaloisCategory.instIsPretransitiveAutCarrierVFintypeCatFunctorObjActionFunctorToActionOfIsGalois, TopCat.Presheaf.presheafEquivOfIso_inverse_map_app, Limits.filtered_colim_preservesFiniteLimits_of_types, Equivalence.adjointify_η_ε, Limits.Cocone.extensions_app, Limits.IndObjectPresentation.yoneda_F, MonoidalCategory.externalProductFlip_inv_app_app_app_app, Subfunctor.range_id, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₁, CommRingCat.preservesColimit_coyoneda_of_finitePresentation, Limits.ColimitPresentation.bind_ι_app, Functor.inv_whiskerRight, Under.forgetCone_π_app, Functor.PullbackObjObj.ofHasPullback_fst, WithTerminal.liftToTerminalUnique_hom_app, Limits.diagramIsoSpan_hom_app, PresheafOfModules.instAdditiveFunctorOppositeAbToPresheaf, TopologicalSpace.OpenNhds.inclusionMapIso_hom_app, Sheaf.tensorUnit_isSheaf, Limits.Types.surjective_π_app_zero_of_surjective_map_aux, Functor.Monoidal.whiskerLeft_app_snd_assoc, flipCompEvaluation_inv_app, Functor.FullyFaithful.hasShift.map_zero_hom_app, instEpiFunctorWhiskerRightOfPreservesEpimorphisms, Functor.Fiber.fiberInclusionCompIsoConst_hom_app, η_ε_app, Functor.leftKanExtensionIsoFiberwiseColimit_inv_app, GradedObject.mapTrifunctorMapNatTrans_app_app_app, shiftFunctorAdd_assoc_inv_app, Limits.Cones.postcompose_map_hom, HomologicalComplex.isZero_single_comp_eval, NatTrans.CommShift.id, TopologicalSpace.Opens.mapIso_refl, Limits.endFunctor_map, CompHausLike.LocallyConstant.functorToPresheaves_obj_map, AlgebraicGeometry.PresheafedSpace.colimitCocone_ι_app_c, Equivalence.core_counitIso_inv_app_iso_inv, Join.InclRightCompRightOpOpEquivFunctor_hom_app, Equivalence.unit_app_tensor_comp_inverse_map_δ_functor, Join.mapPairRight_inv_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τl, Functor.RightExtension.postcompose₂ObjMkIso_hom_left_app, HasLiftingProperty.transfiniteComposition.SqStruct.w₂_assoc, Limits.IsLimit.isIso_π_app_of_isInitial, Limits.Cotrident.IsColimit.homIso_apply_coe, Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₁, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_inv_app_f, Functor.leftKanExtensionUnique_inv, instPreservesFiniteLimitsObjFunctorExactFunctor, Functor.equiv_counitIso, WithTerminal.equivComma_unitIso_inv_app_app, Limits.Cocones.whiskeringEquivalence_counitIso, Iso.map_hom_inv_id_eval_app, AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_hom_app, Limits.Cones.postcomposeEquivalence_inverse, Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right, AlgebraicGeometry.Scheme.Modules.pseudofunctor_associativity, Idempotents.functorExtension₁_obj, NatTrans.CommShiftCore.app_shift_assoc, PresheafOfModules.map_comp_assoc, Limits.Cocones.functorialityEquivalence_unitIso, Comma.mapLeftComp_hom_app_right, Adjunction.whiskerLeft_unit_iso_of_R_fully_faithful, Localization.Monoidal.functorMonoidalOfComp_μ_assoc, MonoidalCategory.MonoidalLeftAction.curriedAction_obj_obj, Functor.whiskeringRight₂_obj_map_app_app, shiftFunctorAdd'_assoc_hom_app, Limits.CategoricalPullback.CatCommSqOver.iso_hom_naturality, yonedaMon_obj, Functor.rightKanExtensionUnique_hom, Pi.comapId_inv_app, Functor.unopComp_hom_app, Functor.leibnizPushout_map_app, Functor.rightDerived_fac, GrothendieckTopology.Point.toPresheafFiber_presheafFiberCompIso_hom_app, Pretriangulated.rotCompInvRot_hom_app_hom₁, μ_naturalityₗ_assoc, Limits.limitFlipCompLimIsoLimitCompLim_inv_π_π_assoc, AlgebraicTopology.DoldKan.Compatibility.υ_inv_app, Functor.compFlipUncurryIso_hom_app, MonoidalClosed.FunctorCategory.homEquiv_naturality_three, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_functor_obj_right_obj, OverPresheafAux.counitForward_val_fst, CatCenter.localization_add, Discrete.natIso_inv_app, LocalizerMorphism.IsLeftDerivabilityStructure.guitartExact', SingleFunctors.postcomp_shiftIso_hom_app, Limits.CoconeMorphism.map_w, Equivalence.congrRightFunctor_map, commBialgCatEquivComonCommAlgCat_counitIso_inv_app, Pseudofunctor.CoGrothendieck.compIso_hom_app, whiskeringLeftCompEvaluation_hom_app, Functor.leftExtensionEquivalenceOfIso₁_unitIso_inv_app_right_app, Idempotents.KaroubiFunctorCategoryEmbedding.map_app_f, Functor.whiskeringRightObjCompIso_inv_app_app, Join.mkFunctorRight_hom_app, Subfunctor.range_comp_le, Comma.mapFst_inv_app, Limits.Cones.postcomposeId_inv_app_hom, Iso.coreWhiskerLeft, FunctorToTypes.binaryProductIso_hom_comp_fst, MonoidalCategory.instFaithfulFunctorTensoringLeft, HomologicalComplex.natIsoSc'_inv_app_τ₁, GrothendieckTopology.plusCompIso_inv_eq_plusLift, Adjunction.Triple.whiskerLeft_leftToRight, Limits.Fork.unop_π, Over.liftCocone_pt, Cat.Hom.equivFunctor_symm_apply, MonoidalCategory.DayConvolutionUnit.corepresentableByRight_homEquiv, Subfunctor.equivalenceMonoOver_counitIso, PresheafOfModules.forgetToPresheafModuleCat_map, WithTerminal.coneEquiv_counitIso_hom_app_hom, WithInitial.mapId_hom_app, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv, MonoidalCategory.tensoringRight_η, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapId_inv_τr, Condensed.discrete_obj, Abelian.coimIsoIm_hom_app, LocalizerMorphism.instIsIsoFunctorRightDerivedFunctorComparison, Over.iteratedSliceForwardNaturalityIso_inv_app, MonoidalCategory.DayConvolution.braiding_naturality_left, Limits.IndObjectPresentation.yoneda_ℐ, ShortComplex.mapNatIso_inv, whiskeringRight_comp_evaluation, TopCat.isTopologicalBasis_cofiltered_limit, PresheafOfModules.instIsRightAdjointPushforwardIdFunctorOppositeRingCat, CategoryOfElements.fromCostructuredArrow_obj_fst, Functor.CommShift.isoAdd'_inv_app, Limits.constCocone_pt, LaxMonoidalFunctor.id_hom, Localization.associator_hom_app_app_app, Functor.OplaxMonoidal.ofBifunctor.topMapₗ_app, Limits.instHasLimitObjFunctorConstTerminal, Functor.CommShift.OfComp.map_iso_hom_app, Limits.colimitUncurryIsoColimitCompColim_ι_ι_inv_assoc, Functor.CommShift.OfComp.map_iso_inv_app_assoc, Functor.CommShift.isoZero'_hom_app, Bicategory.leftUnitorNatIso_inv_app, Equivalence.congrRight_counitIso_inv_app, IsPullback.of_is_product, Localization.Monoidal.map_hexagon_forward_assoc, FunctorToTypes.binaryProductIso_inv_comp_fst, BinaryCofan.isPullback_initial_to_of_isVanKampen, Mon.EquivLaxMonoidalFunctorPUnit.unitIso_inv_app_hom_app, Limits.colimit.ι_desc_app, TwoSquare.GuitartExact.whiskerVertical, MonoidalCategory.leftUnitorNatIso_hom_app, Limits.Cocones.precomposeEquivalence_counitIso, Sigma.natIso_hom, Monoidal.monFunctorCategoryEquivalence_inverse, instPreservesFiniteColimitsFunctorObjWhiskeringLeftOfHasFiniteColimits, MonoidalCategory.externalProductBifunctor_obj_map, FunctorToTypes.monoFactorisation_e, sum.inrCompInverseAssociator_inv_app, RelCat.opEquivalence_unitIso, MonoidalCategory.DayFunctor.ι_map, Monoidal.CommMonFunctorCategoryEquivalence.functor_obj_obj_mon_one, sheafComposeNatTrans_fac, toSheafify_naturality, Limits.IsLimit.fac, Pi.comapEvalIsoEval_inv_app, CostructuredArrow.mapIso_counitIso_inv_app_left, Limits.widePushoutShapeOpEquiv_unitIso, Functor.rightKanExtensionCompIsoOfPreserves_inv_fac_assoc, PreGaloisCategory.functorToAction_full, Pretriangulated.invRotCompRot_hom_app_hom₁, SimplicialObject.Truncated.whiskering_obj_map_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_functor_obj_left_obj, MorphismProperty.Over.pullbackCongr_hom_app_left_fst_assoc, Monoidal.CommMonFunctorCategoryEquivalence.functor_map_app_hom_hom, Over.ConstructProducts.conesEquivFunctor_obj_π_app, BraidedCategory.Hexagon.functor₂₁₃_obj_obj_map, Monoidal.commMonFunctorCategoryEquivalence_inverse, Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_inv_fac_assoc, MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_obj_obj_obj, shrinkYonedaEquiv_symm_map, IsPushout.of_isColimit_cocone, GradedObject.comapEq_symm, Comma.mapLeftIso_functor_map_right, IsGrothendieckAbelian.IsPresentable.surjectivity.epi_f, MonoidalCategory.DayFunctor.ι_comp_isoPointwiseLeftKanExtension_inv, Functor.currying_functor_map_app, map_coyonedaEquiv, Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback_obj_map_fst, shiftFunctorAdd_zero_add_inv_app, Presieve.FamilyOfElements.map_id, Iso.hom_inv_id_app_app_app, Action.leftUnitor_hom_hom, shiftFunctorComm_hom_app_of_add_eq_zero_assoc, Cat.freeMapIdIso_inv_app, Limits.combineCones_π_app_app, Limits.isCokernelEpiComp_desc, AddCommGrpCat.coyonedaType_map_app, Functor.bifunctorComp₂₃Iso_inv_app_app_app, instIsCardinalAccessibleObjOppositeFunctorTypeUliftCoyonedaOpOfIsCardinalPresentable, Limits.isIso_limit_cocone_parallelPair_of_epi, FunctorToTypes.binaryProductIso_inv_comp_snd, isMonoidalLeftDistrib.of_endofunctors, Action.FunctorCategoryEquivalence.functor_η, Limits.MulticospanIndex.multiforkEquivPiFork_unitIso_hom_app_hom, Yoneda.obj_map_id, Limits.KernelFork.mapOfIsLimit_ι, Functor.rightKanExtensionUnique_inv, NatTrans.CommShift.of_iso_inv, Limits.CategoricalPullback.CatCommSqOver.w_app_assoc, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_inv_app, Limits.spanExt_inv_app_right, Monoidal.whiskerLeft_app, CochainComplex.liftCycles_shift_homologyπ, GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app_val_app, AlgebraicTopology.DoldKan.Γ₂N₂_inv, map_yonedaEquiv', HomologicalComplex.natIsoSc'_hom_app_τ₁, MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionHom, StructuredArrow.commaMapEquivalenceCounitIso_inv_app_right_right, bifunctorComp₂₃Obj_obj_map, prod.functorProdToProdFunctorAssociator_hom_app, StructuredArrow.mapIso_counitIso_hom_app_right, Limits.Cowedge.condition, MonoidalCategory.DayConvolution.unit_uniqueUpToIso_inv_assoc, CommMonCat.coyonedaType_map_app, Functor.costructuredArrowMapCocone_ι_app, SSet.range_eq_iSup_of_isColimit, AdditiveFunctor.ofRightExact_map_hom, Adjunction.mapCommGrp_counit, Over.iteratedSliceForwardIsoPost_hom_app, Limits.CategoricalPullback.toCatCommSqOver_obj_fst_map, Functor.LaxMonoidal.ofBifunctor.secondMap_app_app_app, Join.inlCompFromSum_inv_app, evaluation_map_app, Subfunctor.subobjectMk_range_arrow, CategoryOfElements.toCostructuredArrow_map, Functor.mapTriangle_map_hom₂, Pi.comapEvalIsoEval_hom_app, evaluationLeftAdjoint_obj_map, PresheafOfModules.pushforward_comp_id, Equivalence.congrRight_counitIso_hom_app, PreGaloisCategory.toAut_continuous, CategoryOfElements.costructuredArrowYonedaEquivalenceFunctorProj_inv_app, Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop_assoc, Functor.homEquivOfIsLeftKanExtension_apply_app, Iso.map_inv_hom_id_eval_app_assoc, Limits.limitCompWhiskeringLeftIsoCompLimit_hom_whiskerLeft_π, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_right_app, ExponentiableMorphism.unit_pushforwardComp_hom_assoc, WithTerminal.coneEquiv_inverse_obj_pt_right_as, Subfunctor.Subpresheaf.lift_ι, Square.arrowArrowEquivalence_counitIso, Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality, Sum.functorEquiv_counitIso, WithInitial.mapComp_hom_app, Idempotents.DoldKan.η_hom_app_f, CompHausLike.LocallyConstant.adjunction_unit, simplicialCosimplicialEquiv_functor_obj_map, Over.lift_map, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_inv_app_left, instFullIndFunctorOppositeTypeInclusion, Functor.lanCompColimIso_hom_app, Limits.Fork.app_one_eq_ι_comp_right, ObjectProperty.instIsClosedUnderColimitsOfShapeFunctorPreservesLimitsOfShapeOfPreservesLimitsOfShapeColim, Pretriangulated.preadditiveCoyoneda_homologySequenceδ_apply, PreGaloisCategory.autEmbedding_isClosedEmbedding, Profinite.exists_hom, Idempotents.functorExtension₁_map, Presheaf.isLocallyInjective_comp, Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm_assoc, μ_app, MonoidalCategory.MonoidalLeftAction.curriedAction_obj_map, Sigma.inclDesc_hom_app, FunctorToTypes.inr_comp_binaryCoproductIso_inv_apply, Limits.ι_colimitConstInitial_hom_assoc, AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_hom_app_app, Adjunction.equivHomsetRightOfNatIso_symm_apply, LightCondensed.instIsMonoidalFunctorOppositeLightProfiniteModuleCatWCoherentTopology, Comma.mapRightComp_inv_app_left, Limits.pullbackConeEquivBinaryFan_inverse_map_hom, StructuredArrow.mapIso_counitIso_inv_app_right, ShiftMkCore.assoc_hom_app_assoc, Equivalence.changeFunctor_counitIso_inv_app, Functor.IsCoverDense.restrictHomEquivHom_naturality_left_symm, Limits.parallelPair.ext_inv_app, instAdditiveFunctorColim, Sum.functorEquiv_functor_obj, AlgebraicTopology.DoldKan.Γ₂N₂.natTrans_app_f_app, SingleFunctors.shiftIso_zero_inv_app, ParametrizedAdjunction.homEquiv_naturality_three_assoc, SmallObject.SuccStruct.ofNatTrans_toSucc, Functor.isoWhiskerLeft_symm, Functor.whiskeringLeft₃ObjObjObj_map_app_app_app, Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply_assoc, Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_inv, Comma.mapRightIso_unitIso_hom_app_right, Over.mapComp_inv_app_left, GlueData.diagramIso_hom_app_left, Limits.HasLimit.lift_isoOfNatIso_inv_assoc, PreGaloisCategory.instContinuousInvAutFunctorFintypeCat, ModuleCat.extendScalars_assoc, Enriched.FunctorCategory.functorEnrichedId_app, TwoP.swapEquiv_unitIso_inv_app_hom_toFun, Equivalence.congrRight_unitIso_inv_app, NatIso.inv_inv_app, Presheaf.isLocallySurjective_presheafToSheaf_map_iff, Adjunction.shift_counit_app_assoc, Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_right, Functor.whiskeringLeft₃ObjObj_obj, shift_neg_shift', MonoidalOpposite.mopEquiv_counitIso, LeftExactFunctor.whiskeringRight_obj_obj_obj, Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality_assoc, Limits.spanExt_inv_app_left, SheafOfModules.pushforwardNatTrans_comp, RightExactFunctor.whiskeringRight_obj_map, limitCompWhiskeringRightIsoLimitComp_hom_whiskerRight_π, shrinkYonedaEquiv_shrinkYoneda_map, Adjunction.mapGrp_counit, Idempotents.karoubiChainComplexEquivalence_counitIso_hom, NatTrans.CommShift₂.commShift_app, Functor.liftOfIsRightKanExtension_fac_assoc, BraidedCategory.Hexagon.functor₁₃₂'_obj_obj_obj, BraidedCategory.Hexagon.functor₁₃₂_obj_obj_map, Limits.Fork.equalizer_ext, Functor.LeftExtension.mk_hom, Pi.comapComp_inv_app, Functor.currying_inverse_map_app_app, Functor.PullbackObjObj.isPullback, Limits.CategoricalPullback.functorEquiv_counitIso_inv_app_fst_app, ShiftMkCore.assoc_inv_app, constantPresheafAdj_unit_app, Subfunctor.toRange_ι, Limits.instHasFiniteCoproductsFunctor, Functor.IsLeftKanExtension.nonempty_isUniversal, Presheaf.freeYoneda_obj, Limits.limit_map_limitObjIsoLimitCompEvaluation_hom, Equivalence.symmEquivInverse_map_app, Pretriangulated.shiftFunctorCompIsoId_op_inv_app_assoc, ShiftedHom.opEquiv'_add_symm, Sigma.inclDesc_inv_app, AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_hom_app, Functor.pointwiseLeftKanExtensionCompIsoOfPreserves_inv_fac, Functor.functorHomEquiv_symm_apply_app_app, MorphismProperty.TransfiniteCompositionOfShape.mem_incl_app, Bicategory.rightUnitorNatIso_hom_app, StructuredArrow.commaMapEquivalenceFunctor_obj_hom, Functor.PushoutObjObj.ofHasPushout_ι, Pi.comapId_hom_app, HomologicalComplex.forgetEval_inv_app, colimitYonedaHomEquiv_π_apply, Enriched.FunctorCategory.diagram_obj_obj, Presheaf.instIsLeftKanExtensionOppositeObjFunctorTypeUliftYonedaUliftYonedaMap, Abelian.coimIsoIm_inv_app, ParametrizedAdjunction.whiskerLeft_map_counit_assoc, Functor.whiskeringLeft_map_app_app, LeftExactFunctor.forget_obj_of, Functor.leftKanExtensionUnique_hom, Limits.MonoCoprod.binaryCofan_inr, Adjunction.whiskerLeft_counit_app_app, Sheaf.isSheaf_yoneda_obj, BasedNatTrans.forgetful_obj, CommShift₂Setup.int_z, Limits.Types.isLimitEquivSections_symm_apply, Limits.pullbackObjIso_hom_comp_snd, Action.FunctorCategoryEquivalence.functor_ε, BraidedCategory.Hexagon.functor₃₁₂_obj_obj_obj, FreeMonoidalCategory.tensorFunc_obj_map, uliftCoyonedaEquiv_comp, Localization.whiskeringLeftFunctor'_obj, Cat.freeMapCompIso_inv_app, BraidedCategory.ofBifunctor.Forward.firstMap₃_app_app_app, enrichedFunctorTypeEquivFunctor_symm_apply_map, CompHausLike.LocallyConstant.functorToPresheaves_obj_obj, BraidedCategory.tensorLeftIsoTensorRight_inv_app, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit, Limits.Cone.op_ι, Limits.colimitFlipIsoCompColim_inv_app, yonedaEquiv_symm_app_apply, Square.flipEquivalence_counitIso, Functor.RightExtension.precomp_obj_left, PreGaloisCategory.instPreservesFiniteProductsActionFintypeCatAutFunctorFunctorToAction, Limits.CategoricalPullback.functorEquiv_functor_obj_snd_map, Limits.colimitLimitToLimitColimit_surjective, Functor.instIsEquivalenceRightExtensionCompPrecomp, Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_iso_hom_app, Functor.mapCommMonCompIso_hom_app_hom_hom, preservesColimitsOfShape_of_isCardinalPresentable, evaluationAdjunctionLeft_counit_app, WithTerminal.coneEquiv_functor_map_hom, TwistShiftData.z_zero_right, Join.mapIsoWhiskerRight_inv_app, instIsClosedUnderColimitsOfShapeFunctorOppositeTypeIsIndObjectOfIsFiltered, Limits.epi_of_isColimit_cofork, functorProdFunctorEquivCounitIso_hom_app_app, Localization.Monoidal.braidingNatIso_hom_app_naturality_μ_right_assoc, Limits.PreservesColimit₂.nonempty_isColimit_mapCocone₂, Adjunction.rightAdjointUniq_inv_app, Functor.leftExtensionEquivalenceOfIso₁_functor_obj_right, NatIso.ofComponents_hom_app, NatTrans.unop_comp, Localization.lift₃NatIso_inv, instPreservesColimitsOfShapeFunctorLim, CochainComplex.ShiftSequence.shiftIso_hom_app, Limits.widePullbackShapeOpEquiv_unitIso, GrothendieckTopology.W.whiskerRight, MorphismProperty.FunctorsInverting.hom_ext_iff, Sum.functorEquivInverseCompWhiskeringLeftInlIso_inv_app_app, BraidedCategory.Hexagon.functor₂₃₁'_obj_obj_map, MonoidalCategory.tensoringRight_μ, PreGaloisCategory.autEmbedding_range_isClosed, Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_shift, Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_assoc, Limits.colimitHomIsoLimitYoneda'_inv_comp_π, mateEquiv_apply, Functor.structuredArrowMapCone_π_app, Functor.whiskeringLeftObjCompIso_inv_app_app, sheafCompose_comp, Limits.IsLimit.homEquiv_apply, whiskering_preadditiveCoyoneda, ParametrizedAdjunction.arrowHomEquiv_apply_right_snd_assoc, Limits.CategoricalPullback.CatCommSqOver.transform_obj_obj_fst_obj, Coyoneda.ULiftCoyoneda.instFaithfulOppositeFunctorTypeUliftCoyoneda, Functor.uncurry_obj_curry_obj_flip_flip, GradedObject.mapTrifunctorMapIso_inv, CartesianMonoidalCategory.instIsIsoFunctorProdComparisonBifunctorNatTransOfProdComparison, Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp_inv_app_fst_app, Limits.coprodComparisonNatIso_inv, Square.isPushout_iff_op_map_yoneda_isPullback, Discrete.instIsIsoFunctorNatTrans, MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_map_app_app_app, Coyoneda.coyoneda_faithful, Quotient.comp_natTransLift, Limits.compYonedaSectionsEquiv_symm_apply_coe, Limits.KernelFork.map_condition_assoc, Functor.PreOneHypercoverDenseData.multicospanMapIso_hom, yonedaEquiv_comp, MonoidalCategory.DayConvolutionUnit.leftUnitor_inv_app_assoc, OverPresheafAux.counitForward_naturality₂, Limits.ColimitPresentation.self_ι, HomotopyCategory.instCommShiftHomologicalComplexIntUpHomFunctorMapHomotopyCategoryFactors, Comma.coneOfPreserves_π_app_left, CochainComplex.mappingCone.map_δ, AddCommGrpCat.coyoneda_obj_map, bifunctorComp₁₂Obj_map_app, PreGaloisCategory.functorToAction_comp_forget₂_eq, Localization.Monoidal.functorCoreMonoidalOfComp_εIso_hom, Functor.isRightKanExtensionAlongEquivalence, ChainComplex.linearYonedaObj_X, Monad.ForgetCreatesColimits.newCocone_ι, Functor.currying_inverse_obj_map_app, Limits.parallelPairOpIso_hom_app_zero, Limits.colimitFlipCompColimIsoColimitCompColim_ι_ι_hom
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