op 📖 | CompOp | 1059 mathmath: CategoryTheory.Functor.IsDenseSubsite.mapPreimage_map_of_fac, HomotopicalAlgebra.fibration_op_iff, CategoryTheory.LocalizerMorphism.LeftResolution.opFunctor_map_f, AlgebraicGeometry.Γ_map_morphismRestrict, CategoryTheory.Limits.pushoutIsoOpPullback_inr_hom_assoc, CategoryTheory.CommSq.LiftStruct.op_l, CategoryTheory.GrothendieckTopology.overMapPullbackId_hom_app_val_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_eq, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π, AlgebraicGeometry.Scheme.Modules.pushforward_obj_presheaf_map, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_hom_right, CategoryTheory.PreOneHypercover.forkOfIsColimit_ι_map_inj_assoc, Bicategory.Opposite.op2_associator, CategoryTheory.ShortComplex.LeftHomologyData.op_g', AlgebraicGeometry.Proj.awayMap_awayToSection_assoc, CategoryTheory.Equivalence.leftOp_unitIso_hom_app, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_hom_app_val_app, CategoryTheory.Pseudofunctor.DescentData.ofObj_hom, CategoryTheory.kernelUnopOp_inv, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.Equivalence.sheafCongr.counitIso_hom_app_val_app, CategoryTheory.opHom_apply, LightProfinite.Extend.functorOp_obj, CategoryTheory.Limits.colimitHomIsoLimitYoneda_hom_comp_π, AlgebraicGeometry.IsAffineOpen.isLocalization_of_eq_basicOpen, CategoryTheory.DinatTrans.dinaturality_assoc, CategoryTheory.ShortComplex.HomologyData.ofIso_right_p, CategoryTheory.regularTopology.EqualizerCondition.bijective_mapToEqualizer_pullback', CategoryTheory.Functor.leftOpRightOpEquiv_functor_obj_map, TopCat.Sheaf.interUnionPullbackCone_snd, LightCondensed.isoFinYonedaComponents_hom_apply, CategoryTheory.ShortComplex.Splitting.op_r, CategoryTheory.ShortComplex.SnakeInput.op_δ, CategoryTheory.Limits.isLimitConeRightOpOfCocone_lift, CategoryTheory.ShortComplex.cyclesOpIso_inv_op_iCycles_assoc, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_snd, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_hom_app_eq, CategoryTheory.op_hom_leftUnitor, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app, CategoryTheory.Limits.coconeEquivalenceOpConeOp_unitIso, CategoryTheory.ShortComplex.homologyOpIso_hom_naturality, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_inv_app_val_app, AlgebraicGeometry.Scheme.Hom.app_invApp'_assoc, Bicategory.Opposite.op2_associator_inv, AlgebraicGeometry.Scheme.app_eq, HomotopicalAlgebra.instWeakEquivalenceOppositeOp, CategoryTheory.Pseudofunctor.DescentData.pullFunctorCompIso_inv_app_hom, CategoryTheory.GrothendieckTopology.Cover.index_fst, CategoryTheory.op_comp, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_unitIso, CategoryTheory.Functor.sheafPushforwardContinuousComp'_inv_app_val_app, TopCat.Presheaf.germ_eq_of_isBasis, CategoryTheory.Functor.rightOp_map, SSet.Subcomplex.mem_ofSimplex_obj_iff, CondensedMod.IsSolid.isIso_solidification_map, CategoryTheory.eqToHom_comp_homOfLE_op, AlgebraicGeometry.Spec_Γ_naturality, CategoryTheory.MorphismProperty.LeftFraction.op_map, CategoryTheory.WithInitial.opEquiv_unitIso_inv_app, CategoryTheory.Limits.pushoutIsoOpPullback_inl_hom, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top, CategoryTheory.op_inv_associator, CategoryTheory.Limits.walkingParallelPairOp_left, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_counit_app_app, CategoryTheory.ShortComplex.op_g, CategoryTheory.Limits.ι_comp_colimitOpIsoOpLimit_hom_assoc, commBialgCatEquivComonCommAlgCat_unitIso_inv_app, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_app_apply, CategoryTheory.Limits.parallelPairOpIso_inv_app_zero, CategoryTheory.PreOneHypercover.forkOfIsColimit_pt, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_eq_iff', CategoryTheory.eval_map, Profinite.Extend.functorOp_map, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_hom_app_app, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHomRight, CategoryTheory.op_tensorHom, Bicategory.Opposite.op2_whiskerLeft, CategoryTheory.Equivalence.rightOp_counitIso_inv_app, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp, CategoryTheory.Functor.PullbackObjObj.mapArrowRight_right, HomologicalComplex.op_d, LightCondensed.ihomPoints_symm_comp, CategoryTheory.Retract.op_i, CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map', CategoryTheory.Functor.WellOrderInductionData.map_succ, HomologicalComplex.opSymm_d, AlgebraicGeometry.Scheme.Opens.topIso_inv, CategoryTheory.GrothendieckTopology.overMapPullbackId_inv_app_val_app, CategoryTheory.Equivalence.leftOp_unitIso_inv_app, CategoryTheory.op_mono_of_epi, CategoryTheory.Functor.WellOrderInductionData.Extension.ofLE_val, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHomRight, CategoryTheory.ShortComplex.RightHomologyMapData.op_φH, CategoryTheory.Pretriangulated.shiftFunctorZero_op_inv_app, CategoryTheory.HasLiftingProperty.op, AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id_assoc, CategoryTheory.Presieve.isSeparatedFor_singleton, CategoryTheory.Functor.leftOpRightOpEquiv_counitIso_inv_app_app, SSet.spine_map_subinterval, CategoryTheory.Equivalence.rightOp_functor_map, CategoryTheory.ParametrizedAdjunction.whiskerLeft_map_counit, AlgebraicGeometry.Scheme.inv_app, CategoryTheory.Functor.RepresentableBy.homEquiv_eq, CategoryTheory.PreOneHypercover.multicospanIndex_fst, CategoryTheory.ShortComplex.opMap_τ₁, CategoryTheory.simplicialCosimplicialEquiv_counitIso_inv_app_app, CategoryTheory.Limits.PushoutCocone.unop_π_app, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app, CategoryTheory.op_whiskerRight, CategoryTheory.simplicialCosimplicialEquiv_inverse_map, CategoryTheory.IsPullback.op, CategoryTheory.Functor.WellOrderInductionData.Extension.map_zero, CategoryTheory.Pseudofunctor.DescentData.pullFunctor_map_hom, HomologicalComplex.opcyclesOpIso_inv_naturality_assoc, unop_op, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_map, CategoryTheory.OverPresheafAux.YonedaCollection.map₂_yonedaEquivFst, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one, CategoryTheory.opOp_map, CategoryTheory.Limits.limitOpIsoOpColimit_hom_comp_ι_assoc, CategoryTheory.Limits.pushoutIsoUnopPullback_inr_hom, HomotopicalAlgebra.instFibrationOppositeOpOfCofibration, AlgebraicGeometry.Scheme.IdealSheafData.ideal_le_comap_ideal, CategoryTheory.Functor.PullbackObjObj.π_fst, HomologicalComplex.extend_op_d_assoc, CategoryTheory.Square.op_f₁₂, CategoryTheory.cokernelUnopUnop_inv, AlgebraicGeometry.StructureSheaf.exists_const, CategoryTheory.Limits.desc_op_comp_opCoproductIsoProduct'_hom, CategoryTheory.WithInitial.opEquiv_functor_map, CategoryTheory.Iso.op_inv, AlgebraicGeometry.Scheme.congr_app, SimplicialObject.opFunctor_obj_map, CategoryTheory.kernelOpUnop_hom, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHomRight, CategoryTheory.ShortComplex.Homotopy.op_h₀, SSet.Truncated.Edge.CompStruct.d₂, CategoryTheory.Limits.pushoutIsoUnopPullback_inl_hom_assoc, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app', CategoryTheory.Pseudofunctor.CoGrothendieck.map_map_fiber, HomologicalComplex.unopInverse_map, CategoryTheory.WithInitial.opEquiv_counitIso_hom_app, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_hom_app, CategoryTheory.CostructuredArrow.unop_left_comp_ofMkLEMk_unop, CategoryTheory.Limits.multicospanIndexEnd_snd, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_hom_app_val_app, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app_assoc, CategoryTheory.ShortComplex.unopFunctor_map, CategoryTheory.Limits.pushoutIsoUnopPullback_inr_hom_assoc, HomotopicalAlgebra.cofibration_op_iff, CategoryTheory.ShortComplex.Homotopy.op_h₂, TopCat.Sheaf.interUnionPullbackCone_fst, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map, imageToKernel_op, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app, CategoryTheory.op_epi_iff, CategoryTheory.Presieve.FamilyOfElements.compatible_singleton_iff, SimplicialObject.Splitting.cofan_inj_eq, CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inr_assoc, SSet.exists_nonDegenerate, CategoryTheory.Limits.PushoutCocone.op_snd, CategoryTheory.Limits.coend.condition, TopCat.Presheaf.germ_res_apply, CochainComplex.homotopyUnop_hom_eq, CategoryTheory.uliftYonedaEquiv_symm_apply_app, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₂, CategoryTheory.Limits.inr_opProdIsoCoprod_inv_assoc, CategoryTheory.Limits.isLimitOfCoconeOfConeRightOp_lift, AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimage, HomologicalComplex.opcyclesOpIso_inv_naturality, CategoryTheory.Groupoid.invFunctor_map, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality, HomologicalComplex.extend.XOpIso_hom_d_op, CategoryTheory.Limits.parallelPairOpIso_inv_app_one, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app', CategoryTheory.Limits.colimitHomIsoLimitYoneda'_hom_comp_π_assoc, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_left, CategoryTheory.Limits.compYonedaSectionsEquiv_apply_app, CategoryTheory.cokernelOpOp_hom, CategoryTheory.ShortComplex.op_pOpcycles_opcyclesOpIso_hom, CategoryTheory.SimplicialObject.δ_def, commBialgCatEquivComonCommAlgCat_unitIso_hom_app, CategoryTheory.Limits.Cofork.unop_op_π, CategoryTheory.WithTerminal.opEquiv_counitIso_inv_app, CategoryTheory.Equivalence.sheafCongrPreregular_inverse_obj_val_map, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app, CategoryTheory.ShortComplex.RightHomologyMapData.op_φK, CategoryTheory.ShortComplex.LeftHomologyMapData.op_φH, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_map, SimplexCategory.II_σ, CategoryTheory.Limits.PullbackCone.op_pt, CategoryTheory.oppositeShiftFunctorAdd_inv_app, CategoryTheory.Limits.pushoutIsoUnopPullback_inv_snd, HomologicalComplex.extend.XOpIso_hom_d_op_assoc, CategoryTheory.image_ι_op_comp_imageUnopOp_hom, CategoryTheory.Limits.inl_opProdIsoCoprod_inv_assoc, LightCondSet.topCatAdjunctionUnit_val_app_apply, AlgebraicGeometry.RingedSpace.exists_res_eq_zero_of_germ_eq_zero, CategoryTheory.Presieve.isSheafFor_singleton, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality_assoc, Bicategory.Opposite.unop2_id_bop, SSet.spine_vertex, CategoryTheory.Limits.pushoutIsoUnopPullback_inv_fst, AlgebraicGeometry.Scheme.Hom.appLE_map', CategoryTheory.instIsSplitMonoOppositeOpOfIsSplitEpi, HomologicalComplex.instQuasiIsoAtMapOppositeSymmUnopFunctorOp, CategoryTheory.ShortComplex.leftHomologyMap_op, op_inj, CategoryTheory.Limits.opCoproductIsoProduct'_hom_comp_proj, CategoryTheory.Functor.shift_map_op_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality, CategoryTheory.Functor.IsCoverDense.Types.pushforwardFamily_def, CategoryTheory.ShortComplex.homologyOpIso_inv_naturality, HomologicalComplex.cyclesOpIso_inv_naturality_assoc, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app_assoc, CategoryTheory.Limits.fst_opProdIsoCoprod_hom_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_inv_app, CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullback, Condensed.isoFinYonedaComponents_hom_apply, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_inv_toNatTrans_app_val_app, CategoryTheory.ShortComplex.cyclesOpIso_hom_naturality, CategoryTheory.Iso.op_hom, CategoryTheory.Functor.RepresentableBy.comp_homEquiv_symm, CategoryTheory.Pseudofunctor.DescentData.iso_hom, CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inl, CategoryTheory.Limits.spanOp_hom_app, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_hom_comp_π_assoc, CategoryTheory.Join.opEquiv_inverse_map_inclRight_op, Profinite.Extend.functorOp_obj, AlgebraicGeometry.Scheme.Hom.congr_app, CategoryTheory.Over.opEquivOpUnder_inverse_obj, CategoryTheory.Limits.ι_comp_colimitRightOpIsoUnopLimit_hom_assoc, AlgebraicGeometry.Scheme.ofRestrict_appLE, Bicategory.Opposite.op2_whiskerRight, AlgebraicGeometry.IsAffineOpen.isoSpec_inv, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_left, CategoryTheory.op_whiskerLeft, CategoryTheory.Pseudofunctor.presheafHom_obj, CompHausLike.LocallyConstant.incl_of_counitAppApp, CategoryTheory.WithTerminal.opEquiv_unitIso_hom_app, AlgebraicGeometry.Scheme.Hom.app_appIso_inv_assoc, CategoryTheory.Functor.leftOpRightOpEquiv_unitIso_inv_app, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_assoc, CategoryTheory.WithTerminal.opEquiv_counitIso_hom_app, SSet.prodStdSimplex.objEquiv_naturality, CategoryTheory.ComposableArrows.opEquivalence_unitIso_inv_app, CategoryTheory.PreOneHypercover.multifork_ι, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₃, CategoryTheory.NatTrans.removeLeftOp_app, CategoryTheory.op_tensor_op, CategoryTheory.CommSq.HasLift.iff_op, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app', CategoryTheory.homOfLE_op_comp_eqToHom_assoc, HomotopicalAlgebra.weakEquivalences_op_iff, CategoryTheory.Pseudofunctor.DescentData.iso_inv, CategoryTheory.Abelian.subobjectIsoSubobjectOp_apply, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π, CategoryTheory.RetractArrow.op_r_right, Alexandrov.principals_map, CategoryTheory.Limits.PullbackCone.op_inr, op_unop, CategoryTheory.Limits.parallelPairOpIso_hom_app_one, CategoryTheory.ShortComplex.opMap_τ₃, CategoryTheory.PreOneHypercover.multicospanIndex_snd, CategoryTheory.Limits.PullbackCone.op_ι_app, CategoryTheory.ShortComplex.opcyclesOpIso_hom_naturality_assoc, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_hom_app, SSet.Truncated.spine_map_subinterval, TopCat.Presheaf.presheafEquivOfIso_inverse_obj_map, AlgebraicGeometry.Scheme.fromSpecStalk_appTop, CategoryTheory.Square.op_f₂₄, CategoryTheory.Limits.opCoproductIsoProduct_hom_comp_π, CategoryTheory.Equivalence.inverseFunctor_map, AlgebraicGeometry.PresheafedSpace.Γ_map_op, CategoryTheory.simplicialToCosimplicialAugmented_map_left, CategoryTheory.OverPresheafAux.YonedaCollection.map₂_snd, CategoryTheory.kernelOpUnop_inv, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π_assoc, CategoryTheory.Comon.ComonToMonOpOp_map, AlgebraicGeometry.Scheme.Spec_map_presheaf_map_eqToHom, CategoryTheory.ShortComplex.homologyMap'_op, SSet.spine_arrow, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality_assoc, CategoryTheory.OverPresheafAux.OverArrows.map₂_val, HomologicalComplex.instQuasiIsoMapOppositeSymmUnopFunctorOp, CategoryTheory.Limits.Fork.unop_op_ι, CategoryTheory.op_inv_braiding, CategoryTheory.Limits.opParallelPairIso_hom_app_zero, TopCat.Presheaf.map_germ_eq_Γgerm, CategoryTheory.Limits.Cowedge.condition_assoc, AlgebraicGeometry.IsAffineOpen.algebraMap_Spec_obj, CategoryTheory.Presheaf.functorEnrichedHomCoyonedaObjEquiv_naturality, CategoryTheory.NatTrans.removeUnop_app, CategoryTheory.ShortComplex.LeftHomologyMapData.op_φQ, CategoryTheory.Localization.isoOfHom_op_inv, CategoryTheory.ShortComplex.op_pOpcycles_opcyclesOpIso_hom_assoc, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top_assoc, SSet.S.mk_map_eq_iff_of_mono, AlgebraicGeometry.liftCoborder_app, CategoryTheory.simplicialCosimplicialEquiv_unitIso_hom_app, CategoryTheory.Limits.pullbackIsoOpPushout_inv_fst_assoc, CategoryTheory.MorphismProperty.MapFactorizationData.op_Z, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_left, CategoryTheory.cokernelUnopOp_hom, CategoryTheory.Equivalence.sheafCongrPrecoherent_functor_obj_val_map, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w, AlgebraicGeometry.Spec_map_localization_isIso, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_assoc, CategoryTheory.Pseudofunctor.DescentData.instIsIsoαCategoryObjLocallyDiscreteOppositeCatMkOpHom, CategoryTheory.Limits.coneOfCoconeLeftOp_π_app, AlgebraicGeometry.ΓSpec.adjunction_counit_app, SSet.S.le_iff, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj_condition_assoc, CategoryTheory.Limits.SequentialProduct.functorMap_commSq_aux, ModuleCat.Tilde.toOpen_res, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one_assoc, CategoryTheory.Over.opEquivOpUnder_inverse_map, CategoryTheory.Equalizer.Presieve.isSheafFor_singleton_iff, CategoryTheory.presheafHom_map_app, CategoryTheory.Limits.opParallelPairIso_hom_app_one, CategoryTheory.Iso.op2_hom_unop2, CategoryTheory.Equivalence.symmEquivFunctor_map, CategoryTheory.Limits.isLimitConeOfCoconeUnop_lift, CategoryTheory.Equivalence.sheafCongrPreregular_functor_obj_val_map, CategoryTheory.Limits.isColimitOfConeUnopOfCocone_desc, CategoryTheory.Limits.coend.condition_assoc, CategoryTheory.simplicialCosimplicialEquiv_counitIso_hom_app_app, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_presheafMap, AlgebraicGeometry.Scheme.Hom.app_eq, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_hom_app_app, CategoryTheory.Limits.end_.condition, TopCat.Presheaf.germ_res_assoc, HomologicalComplex.opcyclesOpIso_hom_naturality_assoc, CategoryTheory.Limits.opCoproductIsoProduct'_inv_comp_inj, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_inv_app_app, CategoryTheory.ComposableArrows.opEquivalence_functor_obj_map, SSet.Truncated.StrictSegal.spine_δ_arrow_lt, CategoryTheory.SimplicialObject.σ_def, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac, CategoryTheory.Limits.spanOp_inv_app, HomologicalComplex.quasiIsoAt_unopFunctor_map_iff, CategoryTheory.RanIsSheafOfIsCocontinuous.fac_assoc, AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zero, AlgebraicGeometry.Scheme.Modules.restrict_map, TopCat.Sheaf.objSupIsoProdEqLocus_hom_fst, CategoryTheory.Limits.Fork.op_pt, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_map_assoc, CategoryTheory.cokernel.π_unop, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHom, CategoryTheory.Functor.map_shift_unop, Bicategory.Opposite.op2_rightUnitor_inv, CategoryTheory.Presheaf.app_localPreimage, HomologicalComplex.opcyclesOpIso_hom_toCycles_op, CategoryTheory.Pseudofunctor.DescentData.Hom.comm_assoc, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_comp_map, CategoryTheory.Functor.op_commShiftIso_hom_app_assoc, CategoryTheory.isIso_op, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_inv_app, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app_assoc, CategoryTheory.Limits.Cofork.op_π_app_zero, AlgebraicGeometry.Scheme.kerAdjunction_counit_app, CategoryTheory.Limits.opSpan_hom_app, LightCondensed.isoFinYonedaComponents_inv_comp, HomologicalComplex.opFunctor_map_f, SSet.Truncated.spine_map_vertex, AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, CategoryTheory.Functor.isRepresentedBy_iff, CategoryTheory.instIsSplitEpiOppositeOpOfIsSplitMono, CategoryTheory.ShortComplex.fromOpcycles_op_cyclesOpIso_inv_assoc, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_fst, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app'_assoc, CategoryTheory.ShortComplex.rightHomologyMap'_op, CategoryTheory.ShortComplex.opcyclesOpIso_hom_toCycles_op_assoc, CategoryTheory.factorThruImage_comp_imageUnopOp_inv, CondensedSet.topCatAdjunctionUnit_val_app_apply, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_right, CategoryTheory.Limits.limitRightOpIsoOpColimit_hom_comp_ι, CategoryTheory.ShortComplex.opcyclesOpIso_hom_naturality, CategoryTheory.OverPresheafAux.unitForward_naturality₂, CategoryTheory.Limits.isLimitOfCoconeLeftOpOfCone_lift, CategoryTheory.Pseudofunctor.CoGrothendieck.Hom.congr, AlgebraicGeometry.SheafedSpace.ofRestrict_hom_c_app, SSet.StrictSegal.spineToSimplex_interval, AlgebraicGeometry.Scheme.Hom.appIso_inv_app, CategoryTheory.MorphismProperty.LeftFraction.op_f, TopCat.Presheaf.map_germ_eq_Γgerm_assoc, HomologicalComplex.instQuasiIsoAtOppositeMapSymmOpFunctorOp, CategoryTheory.Limits.BinaryFan.op_mk, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_right, TopCat.Sheaf.interUnionPullbackConeLift_right, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_inv_app_app, CategoryTheory.regularTopology.mapToEqualizer_eq_comp, CategoryTheory.Groupoid.invEquivalence_functor_map, CategoryTheory.ComposableArrows.opEquivalence_functor_map_app, SSet.Truncated.Edge.src_eq, CategoryTheory.kernelUnopOp_hom, CategoryTheory.SimplicialObject.Augmented.rightOp_right_map, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.ShortComplex.homologyOpIso_hom_naturality_assoc, CategoryTheory.op_id_unop, AlgebraicGeometry.Scheme.Hom.map_appLE'_assoc, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map, CategoryTheory.Limits.π_comp_colimitOpIsoOpLimit_inv_assoc, CategoryTheory.shrinkYonedaEquiv_naturality, AlgebraicGeometry.Scheme.zeroLocus_map, AlgebraicGeometry.Scheme.AffineZariskiSite.coequifibered_iff_forall_isLocalizationAway, CategoryTheory.Presheaf.imageSieve_apply, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app_assoc, CategoryTheory.cokernel.π_op, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app_assoc, AlgebraicGeometry.Scheme.homOfLE_appTop, CategoryTheory.cosimplicialSimplicialEquiv_functor_map_app, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self, AlgebraicGeometry.Spec.toPresheafedSpace_map_op, CategoryTheory.Limits.opCospan_hom_app, CategoryTheory.Presheaf.FamilyOfElementsOnObjects.IsCompatible.familyOfElements_apply, SSet.Truncated.StrictSegal.spine_δ_arrow_gt, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app'_assoc, CategoryTheory.Pseudofunctor.DescentData.ofObj_obj, instIsMonHomOppositeCommAlgCatOpOfHomToAlgHomBialgHom, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv, HomologicalComplex.fromOpcycles_op_cyclesOpIso_inv_assoc, CategoryTheory.cokernelOpUnop_inv, CategoryTheory.coyonedaEquiv_naturality, CategoryTheory.oppositeShiftFunctorZero_inv_app, PresheafOfModules.pushforward_obj_map_apply, CategoryTheory.op_comp_assoc, AlgebraicGeometry.Scheme.Hom.app_invApp', CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_hom_app, HomologicalComplex.homologyOp_hom_naturality_assoc, CategoryTheory.StructuredArrow.toCostructuredArrow_map, CategoryTheory.Pseudofunctor.DescentData.hom_comp_assoc, CategoryTheory.ShortComplex.cyclesOpIso_inv_naturality, CategoryTheory.kernel.ι_unop, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp, CategoryTheory.Limits.colimitHomIsoLimitYoneda_hom_comp_π_assoc, AlgebraicGeometry.RingedSpace.isUnit_res_of_isUnit_germ, CategoryTheory.Limits.Wedge.condition, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHomLeft_op, CategoryTheory.regularTopology.parallelPair_pullback_initial, CategoryTheory.Limits.pushoutIsoUnopPullback_inl_hom, Bicategory.Opposite.opFunctor_obj, CategoryTheory.ComposableArrows.opEquivalence_unitIso_hom_app, HomologicalComplex.cyclesOpIso_inv_naturality, CategoryTheory.Limits.Fork.op_π, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_hom_app_app, AlgebraicGeometry.Scheme.Γ_map_op, HomologicalComplex.opcyclesOpIso_hom_naturality, CategoryTheory.Presieve.FamilyOfElements.isAmalgamation_iff_ofArrows, Bicategory.Opposite.bicategory_whiskerRight_unop2, CategoryTheory.Functor.sheafPushforwardContinuous_obj_val_map, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_inv_app_app, CategoryTheory.Pseudofunctor.CoGrothendieck.ι_map_fiber, AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id, CategoryTheory.Pretriangulated.shiftFunctorZero_op_hom_app, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_app_apply, CategoryTheory.Join.opEquiv_inverse_map_inclLeft_op, fintypeToFinBoolAlgOp_map, CategoryTheory.MorphismProperty.LeftFraction.op_s, CategoryTheory.Functor.PullbackObjObj.ofHasPullback_π, CategoryTheory.Limits.pullbackIsoOpPushout_inv_fst, CategoryTheory.Equivalence.sheafCongr.unitIso_hom_app_val_app, typeToBoolAlgOp_map, CategoryTheory.op_inv_leftUnitor, CategoryTheory.Functor.op_commShiftIso_inv_app_assoc, CategoryTheory.RetractArrow.op_i_right, CategoryTheory.Limits.pullbackIsoOpPushout_inv_snd, SSet.const_app, CategoryTheory.MorphismProperty.MapFactorizationData.op_i, CategoryTheory.leftDualFunctor_map, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₂, CategoryTheory.Presieve.FamilyOfElements.singletonEquiv_symm_apply, CategoryTheory.Functor.ofOpSequence_map_homOfLE_succ, SheafOfModules.pushforwardPushforwardAdj_unit_app_val_app, HomologicalComplex.extend_op_d, CategoryTheory.Pseudofunctor.DescentData.pullFunctorObj_obj, CategoryTheory.NatTrans.op_app, CategoryTheory.Limits.PushoutCocone.op_π_app, AlgebraicGeometry.Scheme.Hom.appIso_inv_appLE_assoc, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp, Bicategory.Opposite.op2_rightUnitor, CategoryTheory.rightDualFunctor_map, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_assoc, CategoryTheory.Limits.π_comp_colimitOpIsoOpLimit_inv, CategoryTheory.Functor.leftOpRightOpEquiv_inverse_map, CategoryTheory.SimplicialObject.Truncated.trunc_obj_map, CategoryTheory.Cat.opFunctorInvolutive_inv_app_toFunctor_map, CategoryTheory.Functor.leftOpRightOpEquiv_unitIso_hom_app, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_hom_app_val_app, CochainComplex.homotopyOp_hom_eq, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π_assoc, CategoryTheory.OverPresheafAux.MakesOverArrow.map₂, CategoryTheory.Square.opFunctor_map_τ₁, CategoryTheory.Limits.opCospan_inv_app, Bicategory.Opposite.op2_rightUnitor_hom, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_hom_app_left, CategoryTheory.Limits.limitRightOpIsoOpColimit_hom_comp_ι_assoc, CategoryTheory.Functor.WellOrderInductionData.Extension.map_succ, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_inv_app_val_app, Condensed.isoFinYonedaComponents_inv_comp, AlgebraicGeometry.Scheme.Opens.ι_appTop, HomologicalComplex.cyclesOpIso_hom_naturality_assoc, CategoryTheory.Functor.RepresentableBy.homEquiv_comp, AlgebraicGeometry.Scheme.map_basicOpen, CategoryTheory.Limits.PullbackCone.unop_ι_app, SSet.Truncated.StrictSegal.spineToSimplex_vertex, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality_assoc, CategoryTheory.Limits.FormalCoproduct.evalOp_map_app, CategoryTheory.ShortComplex.opMap_τ₂, CategoryTheory.cosimplicialSimplicialEquiv_unitIso_hom_app, CategoryTheory.Limits.cospanOp_hom_app, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w_apply, TopCat.Sheaf.objSupIsoProdEqLocus_inv_snd, CategoryTheory.op_hom_braiding, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_counitIso, CategoryTheory.Functor.op_commShiftIso_inv_app, SSet.Truncated.StrictSegal.spine_δ_vertex_ge, SSet.StrictSegal.spineToSimplex_edge, CategoryTheory.Over.opEquivOpUnder_counitIso, TopCat.Presheaf.SheafConditionEqualizerProducts.res_π, TopCat.Presheaf.germ_res, SSet.Truncated.StrictSegal.spineToSimplex_edge, CategoryTheory.CommSq.LiftStruct.opEquiv_symm_apply, SSet.Truncated.spine_arrow, CategoryTheory.CategoryOfElements.fromCostructuredArrow_map_coe, CategoryTheory.Equivalence.leftOp_inverse_map, CategoryTheory.Square.opFunctor_map_τ₂, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₃, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionRight_op, AlgebraicTopology.DoldKan.degeneracy_comp_PInfty_assoc, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_inv_app, Bicategory.Opposite.op2_comp, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_left, CategoryTheory.Functor.unop_map, TopCat.Presheaf.pullback_obj_obj_ext_iff, CategoryTheory.MorphismProperty.RightFraction.op_f, AlgebraicGeometry.Scheme.IdealSheafData.isLocalization_away, Bicategory.Opposite.op2_leftUnitor_hom, SSet.N.le_iff_exists_mono, AlgebraicGeometry.Scheme.ofRestrict_toLRSHom_c_app, CategoryTheory.regularTopology.equalizerCondition_iff_isIso_lift, SSet.Truncated.HomotopyCategory.homToNerveMk_app_one, CategoryTheory.Functor.opInv_map, SSet.prodStdSimplex.objEquiv_map_apply, SSet.Truncated.Edge.mk'_edge, SimplicialObject.Splitting.cofan_inj_comp_app, CategoryTheory.Limits.limitOpIsoOpColimit_inv_comp_π_assoc, LightProfinite.Extend.functorOp_map, TopCat.Sheaf.interUnionPullbackConeLift_left, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality_assoc, CategoryTheory.MorphismProperty.RightFraction.op_map, CategoryTheory.ShortComplex.opcyclesOpIso_inv_naturality, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_assoc, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app_assoc, CategoryTheory.Limits.ι_comp_colimitRightOpIsoUnopLimit_hom, CategoryTheory.op_hom_associator, topToLocale_map, CategoryTheory.WithInitial.opEquiv_counitIso_inv_app, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac', CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_obj, AlgebraicGeometry.Scheme.homOfLE_app, CategoryTheory.Equivalence.congrLeftFunctor_map, SSet.Truncated.StrictSegal.spineToSimplex_arrow, AlgebraicGeometry.Scheme.Hom.naturality_assoc, CategoryTheory.op_mono_iff, HomologicalComplex.cyclesOpIso_hom_naturality, Bicategory.Opposite.op2_id, CategoryTheory.op_hom_rightUnitor, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.sheafCondition_iff_bijective_toPullbackObj, CondensedSet.topCatAdjunctionUnit_val_app, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac'_assoc, CategoryTheory.eqToHom_op, AlgebraicGeometry.Scheme.homOfLE_appLE, CategoryTheory.Functor.sheafPushforwardContinuousId'_inv_app_val_app, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop, CategoryTheory.Functor.uliftYonedaReprXIso_hom_app, TopCat.Presheaf.pushforward_obj_map, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop_assoc, CategoryTheory.Limits.pushoutIsoOpPullback_inr_hom, AlgebraicGeometry.morphismRestrict_appTop, AlgebraicGeometry.Scheme.IdealSheafData.ofIdealTop_ideal, CategoryTheory.ShortComplex.LeftHomologyData.op_p, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_inv_comp_π, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality, CategoryTheory.cosimplicialSimplicialEquiv_unitIso_inv_app, SSet.Truncated.spine_vertex, CategoryTheory.Limits.BinaryCofan.op_mk, CategoryTheory.Functor.IsCoverDense.Types.naturality_apply, CategoryTheory.Equivalence.sheafCongr.functor_obj_val_map, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj_condition, CategoryTheory.PresheafOfGroups.OneCochain.ev_precomp, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_inv_app_val_app, CategoryTheory.kernelUnopUnop_hom, CategoryTheory.ShortComplex.homologyOpIso_inv_naturality_assoc, CategoryTheory.regularTopology.equalizerCondition_w', CategoryTheory.oppositeShiftFunctorZero_hom_app, AlgebraicGeometry.IsOpenImmersion.app_eq_appIso_inv_app_of_comp_eq, CategoryTheory.Limits.Fork.op_ι_app, CategoryTheory.ShortComplex.rightHomologyMap_op, AlgebraicGeometry.LocallyRingedSpace.restrict_presheaf_map, CategoryTheory.coyonedaEquiv_coyoneda_map, CategoryTheory.ShortComplex.Homotopy.op_h₃, CategoryTheory.op_add, CategoryTheory.CostructuredArrow.toStructuredArrow_obj, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.fac_assoc, SSet.Truncated.Edge.id_edge, CategoryTheory.ParametrizedAdjunction.unit_whiskerRight_map_assoc, CategoryTheory.simplicialCosimplicialEquiv_functor_map_app, CategoryTheory.Functor.leftOpRightOpEquiv_counitIso_hom_app_app, ContinuousMap.piComparison_fac, CategoryTheory.Limits.isColimitOfConeLeftOpOfCocone_desc, CategoryTheory.Presieve.FamilyOfElements.isAmalgamation_singleton_iff, CategoryTheory.orderDualEquivalence_counitIso, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_assoc, CategoryTheory.CommSq.op, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.fromBiprod_biprodIsoProd_inv_apply, CategoryTheory.ShiftedHom.opEquiv_symm_apply_comp, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app, AlgebraicGeometry.Scheme.toOpen_eq, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_assoc, SSet.Truncated.Path.arrow_src, SSet.spine_map_vertex, CategoryTheory.Equivalence.rightOp_counitIso_hom_app, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_unit_app_app, CategoryTheory.op_sum, TopCat.Presheaf.restrictOpenCommRingCat_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality, CategoryTheory.ShortComplex.Splitting.op_s, CategoryTheory.Limits.Fork.op_ι_app_one, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_comp_map_assoc, AlgebraicGeometry.ΓSpecIso_inv_ΓSpec_adjunction_homEquiv, AlgebraicGeometry.StructureSheaf.res_apply, CategoryTheory.Presieve.Arrows.toCompatible_coe, CategoryTheory.Limits.PullbackCone.op_inl, CategoryTheory.NatTrans.rightOp_app, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv, AlgebraicGeometry.Scheme.Hom.map_appLE', CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inl_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionRight_op, CategoryTheory.ShiftedHom.opEquiv'_symm_op_opShiftFunctorEquivalence_counitIso_inv_app_op_shift, AugmentedSimplexCategory.equivAugmentedSimplicialObjectFunctorCompToArrowIso_inv_app_right, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp_assoc, CategoryTheory.Functor.IsRepresentedBy.map_bijective, CategoryTheory.Functor.PullbackObjObj.ofHasPullback_snd, CategoryTheory.Functor.shift_map_op, CategoryTheory.Limits.ι_comp_colimitOpIsoOpLimit_hom, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHom_op, CategoryTheory.Pretriangulated.shiftFunctor_op_map, CategoryTheory.ShortComplex.RightHomologyData.op_f', CategoryTheory.uliftCoyonedaEquiv_naturality, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_inv_comp_π_assoc, CategoryTheory.op_inv_rightUnitor, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_inv_app_eq, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_left, CategoryTheory.simplicialCosimplicialEquiv_unitIso_inv_app, HomotopicalAlgebra.instCofibrationOppositeOpOfFibration, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_val_map, CategoryTheory.GrothendieckTopology.overMapPullbackComp_inv_app_val_app, CategoryTheory.IsCodetecting.isIso_iff_of_epi, CategoryTheory.RetractArrow.op_r_left, CategoryTheory.Limits.isLimitConeOfCoconeLeftOp_lift, CategoryTheory.uliftCoyonedaEquiv_symm_map_assoc, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app, CategoryTheory.op_inv, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_fst_assoc, CategoryTheory.HasLiftingProperty.iff_op, CategoryTheory.Presieve.FamilyOfElements.comp_of_compatible, AlgebraicGeometry.Scheme.Opens.toScheme_presheaf_map, CategoryTheory.orderDualEquivalence_functor_map, CategoryTheory.Limits.pushoutIsoOpPullback_inl_hom_assoc, TopCat.Sheaf.objSupIsoProdEqLocus_hom_snd, SSet.Truncated.StrictSegal.spine_δ_arrow_eq, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHomRight, CategoryTheory.imageUnopOp_hom_comp_image_ι, TopCat.Sheaf.objSupIsoProdEqLocus_inv_eq_iff, CategoryTheory.Limits.isColimitCoconeRightOpOfCone_desc, HomologicalComplex.instQuasiIsoOppositeMapSymmOpFunctorOp, CategoryTheory.Limits.desc_op_comp_opCoproductIsoProduct_hom, CategoryTheory.Equivalence.sheafCongrPrecoherent_inverse_obj_val_map, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_hom_app_val_app, CategoryTheory.Pseudofunctor.toDescentData_map_hom, AlgebraicGeometry.Proj.awayMap_awayToSection, CategoryTheory.Groupoid.invEquivalence_counitIso, CategoryTheory.Square.opFunctor_map_τ₃, CategoryTheory.homOfLE_op_comp_eqToHom, CategoryTheory.Limits.π_comp_colimitRightOpIsoUnopLimit_inv, AlgebraicGeometry.isIso_SpecMap_stakMap_localization, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHomLeft, Bicategory.Opposite.op2_leftUnitor_inv, AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit_map, CategoryTheory.Pseudofunctor.DescentData.pullFunctorObjHom_eq_assoc, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanIndex_fst, AlgebraicGeometry.ΓSpec.right_triangle, SSet.Truncated.Path₁.arrow_tgt, CategoryTheory.Square.op_f₁₃, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_of_eq, AlgebraicGeometry.StructureSheaf.comap_id_eq_map, AlgebraicGeometry.Scheme.Hom.appIso_hom, CategoryTheory.ShiftedHom.opEquiv'_symm_comp, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_apply, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHom, InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj, CategoryTheory.cokernelOpUnop_hom, AlgebraicGeometry.tilde.toOpen_res, AlgebraicGeometry.tilde.toOpen_res_assoc, Bicategory.Opposite.unop2_op2, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda_hom_comp_π, CategoryTheory.kernel.ι_op, CategoryTheory.Meq.mk_apply, CategoryTheory.SimplicialObject.Augmented.rightOp_hom_app, CategoryTheory.yonedaEquiv_naturality, SSet.Truncated.StrictSegal.spineToSimplex_interval, SheafOfModules.pushforwardNatTrans_app_val_app, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app_assoc, CategoryTheory.Limits.FormalCoproduct.cosimplicialObjectFunctor_obj_map, CategoryTheory.ComposableArrows.opEquivalence_inverse_map, CategoryTheory.LocalizerMorphism.LeftResolution.op_w, CategoryTheory.Limits.PushoutCocone.op_pt, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_apply, CategoryTheory.Iso.op2_inv_unop2, Bicategory.Opposite.op2_leftUnitor, AlgebraicGeometry.Spec_Γ_naturality_assoc, AlgebraicGeometry.Scheme.Hom.appLE_map'_assoc, AlgebraicGeometry.RingedSpace.isUnit_res_basicOpen, AlgebraicGeometry.Scheme.Opens.ι_app_self, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHomLeft, CategoryTheory.Functor.WellOrderInductionData.Extension.compatibility, CategoryTheory.Functor.map_shift_unop_assoc, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality, AlgebraicGeometry.Scheme.Hom.naturality, CategoryTheory.regularTopology.equalizerCondition_w, SSet.Truncated.Path.arrow_tgt, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_assoc, CategoryTheory.RetractArrow.op_i_left, CategoryTheory.ShortComplex.op_f, SSet.mem_degenerate_iff, CategoryTheory.Equivalence.sheafCongr.inverse_obj_val_map, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_assoc, CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda'_hom_comp_π_assoc, AlgebraicGeometry.Scheme.restrict_presheaf_map, HomologicalComplex.quasiIso_opFunctor_map_iff, CategoryTheory.map_yonedaEquiv, CategoryTheory.op_zsmul, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv, CategoryTheory.ShortComplex.homologyMap_op, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen', CategoryTheory.op_epi_of_mono, CategoryTheory.Limits.FormalCoproduct.evalOp_obj_map, CategoryTheory.RanIsSheafOfIsCocontinuous.fac, CategoryTheory.Limits.Cofork.op_unop_π, CategoryTheory.Limits.limitOpIsoOpColimit_inv_comp_π, TopCat.Sheaf.objSupIsoProdEqLocus_inv_fst, CategoryTheory.Limits.isColimitOfConeOfCoconeRightOp_desc, CategoryTheory.PresheafHom.IsSheafFor.app_cond, CategoryTheory.prodOpEquiv_functor_map, CategoryTheory.Comon.ComonToMonOpOpObj_mon_mul, CategoryTheory.ShortComplex.Homotopy.op_h₁, CategoryTheory.isIso_iff_isIso_coyoneda_map, AlgebraicGeometry.Scheme.fromSpecStalk_app, CategoryTheory.ParametrizedAdjunction.unit_whiskerRight_map, CategoryTheory.BraidedCategory.op_tensorμ, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHom, AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_comp, SheafOfModules.pushforwardPushforwardEquivalence_unit_app_val_app, CategoryTheory.Functor.WellOrderInductionData.map_lift, CategoryTheory.Limits.inr_opProdIsoCoprod_inv, CategoryTheory.GrothendieckTopology.overMapPullbackComp_hom_app_val_app, CategoryTheory.GrothendieckTopology.Cover.index_snd, CategoryTheory.Limits.fst_opProdIsoCoprod_hom, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_right, CategoryTheory.Limits.coconeOfConeLeftOp_ι_app, CategoryTheory.Functor.IsRepresentedBy.iff_of_isoObj, CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.map_eq_pullHom_assoc, AlgebraicTopology.DoldKan.Γ₂N₁.natTrans_app_f_app, CategoryTheory.prodOpEquiv_counitIso_hom_app, CategoryTheory.Limits.coconeEquivalenceOpConeOp_counitIso, CategoryTheory.Limits.Fork.op_ι_app_zero, AlgebraicTopology.DoldKan.degeneracy_comp_PInfty, CategoryTheory.Limits.cospanOp_inv_app, CategoryTheory.kernelOpOp_inv, CategoryTheory.coyonedaPairing_map, CategoryTheory.Presheaf.equalizerSieve_apply, CategoryTheory.oppositeShiftFunctorAdd'_hom_app, PresheafOfModules.pushforward_obj_map_apply', CompHausLike.LocallyConstant.sigmaComparison_comp_sigmaIso, CategoryTheory.Limits.Cofork.op_π_app_one, SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₁, AlgebraicGeometry.Scheme.SpecMap_presheaf_map_eqToHom, CategoryTheory.CompatiblePreserving.compatible, CategoryTheory.IsPushout.op, CategoryTheory.Under.opEquivOpOver_inverse_obj, CategoryTheory.Limits.opProductIsoCoproduct'_inv_comp_lift, CategoryTheory.PresheafHom.IsSheafFor.exists_app, CategoryTheory.Limits.pullbackIsoOpPushout_inv_snd_assoc, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_hom_toNatTrans_app_val_app, CategoryTheory.Coyoneda.fullyFaithful_preimage, LightCondSet.topCatAdjunctionUnit_val_app, SSet.op_map, CategoryTheory.Limits.isColimitCoconeOfConeLeftOp_desc, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_app_apply, HomologicalComplex.fromOpcycles_op_cyclesOpIso_inv, CategoryTheory.cosimplicialToSimplicialAugmented_map, SSet.OneTruncation₂.nerveHomEquiv_apply, TopCat.Presheaf.Γgerm_res_apply, CategoryTheory.Limits.π_comp_colimitRightOpIsoUnopLimit_inv_assoc, SheafOfModules.pushforwardPushforwardAdj_counit_app_val_app, HomologicalComplex.quasiIso_unopFunctor_map_iff, SSet.StrictSegalCore.map_mkOfSucc_zero_spineToSimplex, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.SheafCondition.bijective_toPullbackObj, CategoryTheory.ShortComplex.RightHomologyData.op_i, CategoryTheory.Limits.isLimitOfCoconeUnopOfCone_lift, CategoryTheory.Functor.PullbackObjObj.mapArrowLeft_right, CategoryTheory.Under.opEquivOpOver_counitIso, CategoryTheory.Functor.IsDenseSubsite.map_eq_of_eq, AlgebraicGeometry.LocallyRingedSpace.Γ_map_op, CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanIndex_snd, AlgebraicGeometry.Scheme.Opens.ι_appLE, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHom_op, SSet.StrictSegal.spineToSimplex_arrow, CategoryTheory.coyonedaEquiv_symm_map, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ_assoc, CategoryTheory.Functor.opHom_map_app, CategoryTheory.Limits.opCoproductIsoProduct_hom_comp_π_assoc, CategoryTheory.Limits.proj_comp_opProductIsoCoproduct'_hom, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop, CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.map_eq_pullHom, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_hom_app_val_app, AlgebraicGeometry.ΓSpec_adjunction_homEquiv_eq, AlgebraicGeometry.Scheme.Opens.ι_app, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_inv_app_app, CategoryTheory.Limits.limitRightOpIsoOpColimit_inv_comp_π_assoc, SSet.Truncated.Edge.CompStruct.d₀, CompHausLike.LocallyConstant.incl_comap, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app_assoc, AlgebraicTopology.DoldKan.Γ₀.Obj.mapMono_on_summand_id_assoc, CategoryTheory.Pseudofunctor.DescentData.pullFunctorCompIso_hom_app_hom, CategoryTheory.Presieve.IsSheafFor.valid_glue, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHom, CategoryTheory.cosimplicialSimplicialEquiv_inverse_map, TopCat.Presheaf.germ_eq, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one, CategoryTheory.Pseudofunctor.DescentData.pullFunctorObjHom_eq, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHomLeft, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_inv_app', CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_left, CategoryTheory.eqToHom_comp_homOfLE_op_assoc, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₁, CategoryTheory.Pseudofunctor.DescentData.hom_self, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_hom, CategoryTheory.Functor.PullbackObjObj.ofHasPullback_pt, CategoryTheory.Limits.op_zero, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHomLeft_op, CategoryTheory.ShortComplex.opcyclesOpIso_hom_toCycles_op, SheafOfModules.pushforwardNatTrans_app_val_app_apply, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_apply, CategoryTheory.Pseudofunctor.CoGrothendieck.categoryStruct_comp_fiber, CategoryTheory.op_neg, CategoryTheory.LocalizerMorphism.RightResolution.op_w, CategoryTheory.Functor.op_commShiftIso_hom_app, CategoryTheory.Groupoid.invEquivalence_unitIso, CategoryTheory.op_sub, SSet.S.mk_map_le, CategoryTheory.Limits.SequentialProduct.functorMap_commSq_succ, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app, CategoryTheory.Functor.PullbackObjObj.π_fst_assoc, CategoryTheory.cokernelUnopOp_inv, CategoryTheory.Limits.Fork.op_unop_ι, CategoryTheory.Functor.IsRepresentedBy.of_isoObj, CategoryTheory.Limits.opProductIsoCoproduct_inv_comp_lift, AlgebraicGeometry.IsAffineOpen.app_basicOpen_eq_away_map, CategoryTheory.Functor.WellOrderInductionData.Extension.map_limit, CategoryTheory.Limits.Wedge.condition_assoc, CategoryTheory.opEquiv_symm_apply, CategoryTheory.Limits.multispanIndexCoend_fst, CategoryTheory.Limits.snd_opProdIsoCoprod_hom_assoc, AlgebraicGeometry.IsAffineOpen.ΓSpecIso_hom_fromSpec_app, CategoryTheory.kernelOpOp_hom, CategoryTheory.ShortComplex.cyclesOpIso_inv_op_iCycles, CategoryTheory.Limits.opCoproductIsoProduct'_hom_comp_proj_assoc, SSet.Truncated.Path₁.arrow_src, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp_assoc, AlgebraicGeometry.morphismRestrict_app, CategoryTheory.Functor.leftOpRightOpEquiv_functor_map_app, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_hom_app_app, TopCat.Sheaf.eq_of_locally_eq_iff, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι_assoc, AlgebraicTopology.DoldKan.Γ₀.Obj.map_epi_on_summand_id, SSet.Truncated.Edge.CompStruct.d₁, CategoryTheory.regularTopology.EqualizerCondition.bijective_mapToEqualizer_pullback, CategoryTheory.map_shrinkYonedaEquiv, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_inv_app_val_app, SSet.OneTruncation₂.id_edge, CategoryTheory.ShortComplex.cyclesOpIso_inv_naturality_assoc, CategoryTheory.Limits.coconeEquivalenceOpConeOp_functor_map, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_snd_assoc, CategoryTheory.Limits.opParallelPairIso_inv_app_zero, CategoryTheory.constantPresheafAdj_counit_app_app, CategoryTheory.Equivalence.sheafCongr.unitIso_inv_app_val_app, AlgebraicGeometry.Scheme.Opens.topIso_hom, CategoryTheory.GrothendieckTopology.map_yonedaEquiv, CategoryTheory.Functor.reprW_hom_app, CategoryTheory.uliftCoyonedaEquiv_symm_map, CategoryTheory.Limits.opParallelPairIso_inv_app_one, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π, AlgebraicGeometry.Scheme.ofRestrict_app, CategoryTheory.yonedaEquiv_symm_naturality_left, CategoryTheory.Limits.inl_opProdIsoCoprod_inv, CategoryTheory.Limits.snd_opProdIsoCoprod_hom, CategoryTheory.imageUnopOp_inv_comp_op_factorThruImage, CategoryTheory.ObjectProperty.IsCodetecting.isIso_iff_of_epi, CategoryTheory.Limits.isColimitCoconeOfConeUnop_desc, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop_assoc, AlgebraicGeometry.IsAffineOpen.fromSpec_app_of_le, AlgebraicGeometry.Scheme.Hom.app_appIso_inv, TopCat.Sheaf.interUnionPullbackCone_pt, HomologicalComplex.homologyOp_hom_naturality, CategoryTheory.Square.opFunctor_map_τ₄, CategoryTheory.ShortComplex.fromOpcycles_op_cyclesOpIso_inv, AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInfty_assoc, CategoryTheory.PreOneHypercover.forkOfIsColimit_ι_map_inj, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one_assoc, CategoryTheory.CostructuredArrow.unop_left_comp_underlyingIso_hom_unop, commBialgCatEquivComonCommAlgCat_counitIso_hom_app, CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inr, HomologicalComplex.opcyclesOpIso_hom_toCycles_op_assoc, CategoryTheory.Limits.opSpan_inv_app, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app, CategoryTheory.Functor.sheafPushforwardContinuousId'_hom_app_val_app, HomologicalComplex.quasiIsoAt_opFunctor_map_iff, SSet.Truncated.StrictSegal.spine_δ_vertex_lt, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.restriction_map, CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_ι, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_val_app, commBialgCatEquivComonCommAlgCat_functor_map_unop_hom, CategoryTheory.WithInitial.opEquiv_unitIso_hom_app, AlgebraicGeometry.Scheme.Opens.eq_presheaf_map_eqToHom, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_map, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ, AlgebraicGeometry.map_injective_of_isIntegral, CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map, CategoryTheory.OverPresheafAux.map_mkPrecomp_eqToHom, CategoryTheory.Limits.end_.condition_assoc, SimplicialObject.Splitting.cofan_inj_comp_app_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_eq, CategoryTheory.prodOpEquiv_counitIso_inv_app, CategoryTheory.Equalizer.Presieve.isSheafFor_singleton_iff_of_hasPullback, CategoryTheory.Limits.cokernelOrderHom_coe, CategoryTheory.Subfunctor.sieveOfSection_apply, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_map, CategoryTheory.Functor.rightOp_map_unop, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_val_app, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_inv_app'_assoc, CategoryTheory.cosimplicialSimplicialEquiv_functor_obj_map, CategoryTheory.DinatTrans.dinaturality, CategoryTheory.oppositeShiftFunctorAdd_hom_app, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map_assoc, CategoryTheory.Meq.condition, AlgebraicGeometry.Scheme.Hom.inv_app, CategoryTheory.CommSq.LiftStruct.opEquiv_apply, CategoryTheory.WithTerminal.opEquiv_unitIso_inv_app, CategoryTheory.Square.op_f₃₄, CategoryTheory.ShortComplex.opcyclesOpIso_inv_naturality_assoc, SheafOfModules.pushforwardPushforwardEquivalence_counit_app_val_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app, AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_map, CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π_assoc, CategoryTheory.Functor.sheafPushforwardContinuousComp'_hom_app_val_app, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.lift_map, CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv, HomologicalComplex.opInverse_map, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_inv_app_val_app, CategoryTheory.MorphismProperty.RightFraction.op_s, CategoryTheory.GrothendieckTopology.Plus.toPlus_apply, CategoryTheory.Equivalence.sheafCongr.counitIso_inv_app_val_app, AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInfty, TopCat.Presheaf.presheafEquivOfIso_functor_obj_map, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.lift_map_assoc, CategoryTheory.oppositeShiftFunctorAdd'_inv_app, CategoryTheory.Under.opEquivOpOver_inverse_map, Bicategory.Opposite.op2_associator_hom, SimplicialObject.Splitting.cofan_inj_eq_assoc, SimplexCategory.II_δ, CategoryTheory.Limits.Cofork.op_ι, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal_basicOpen, CategoryTheory.MorphismProperty.MapFactorizationData.op_p, CategoryTheory.Functor.PullbackObjObj.ofHasPullback_fst, CategoryTheory.Functor.IsRepresentedBy.representableBy_homEquiv_apply, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHomLeft, CategoryTheory.Retract.op_r, CategoryTheory.op_comp_unop, CategoryTheory.Limits.walkingParallelPairOp_right, CategoryTheory.WithTerminal.opEquiv_functor_map, CategoryTheory.Limits.opCoproductIsoProduct_inv_comp_ι, CategoryTheory.CostructuredArrow.projectQuotient_mk, CategoryTheory.CostructuredArrow.toStructuredArrow_map, CategoryTheory.Functor.IsCoverDense.Types.pushforwardFamily_apply, commBialgCatEquivComonCommAlgCat_counitIso_inv_app, CategoryTheory.Pseudofunctor.DescentData.hom_comp, Alexandrov.projSup_map, CategoryTheory.SimplicialObject.equivalenceLeftToRight_left_app, TopCat.Presheaf.SheafConditionEqualizerProducts.res_π_apply, AlgebraicGeometry.Scheme.zeroLocus_map_of_eq, CategoryTheory.presheafHom_map_app_op_mk_id, CategoryTheory.cokernelOpOp_inv, CategoryTheory.Pseudofunctor.CoGrothendieck.Hom.ext_iff, CategoryTheory.isIso_op_iff, AlgebraicGeometry.IsOpenImmersion.lift_app, CategoryTheory.Limits.limitOpIsoOpColimit_hom_comp_ι, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.toBiprod_apply, Bicategory.Opposite.bicategory_whiskerLeft_unop2, CategoryTheory.Limits.PushoutCocone.op_fst, CategoryTheory.ShortComplex.LeftHomologyData.op_ι, CategoryTheory.ShortComplex.RightHomologyData.op_π, SSet.Truncated.Edge.CompStruct.idCompId_simplex, CategoryTheory.Limits.Cowedge.condition, CategoryTheory.op_id, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality, CategoryTheory.Limits.π_comp_opProductIsoCoproduct_hom, CategoryTheory.simplicialCosimplicialEquiv_functor_obj_map, AlgebraicGeometry.SheafedSpace.Γ_map_op, CategoryTheory.StructuredArrow.toCostructuredArrow_obj, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.liftAux_fac, AlgebraicGeometry.Scheme.Hom.appIso_inv_appLE, AlgebraicGeometry.Scheme.Modules.map_smul, CategoryTheory.ShortComplex.leftHomologyMap'_op, CategoryTheory.Functor.PullbackObjObj.isPullback, CategoryTheory.Limits.limitRightOpIsoOpColimit_inv_comp_π, CategoryTheory.Equivalence.symmEquivInverse_map_app, SSet.StrictSegal.spineToSimplex_vertex, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app_assoc, CategoryTheory.ShiftedHom.opEquiv'_add_symm, SSet.Truncated.Edge.tgt_eq, CategoryTheory.ParametrizedAdjunction.whiskerLeft_map_counit_assoc, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_apply, AlgebraicGeometry.PresheafedSpace.ofRestrict_c_app, CategoryTheory.Limits.SequentialProduct.functorMap_commSq, CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.fac, CategoryTheory.Functor.IsCoverDense.Types.naturality_assoc, CategoryTheory.yonedaEquiv_symm_app_apply, AlgebraicGeometry.exists_lift_of_germInjective, CategoryTheory.Functor.op_map, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_assoc, CategoryTheory.Limits.colimitHomIsoLimitYoneda'_inv_comp_π, CategoryTheory.ShortComplex.cyclesOpIso_hom_naturality_assoc, CategoryTheory.Pseudofunctor.DescentData.Hom.comm, CategoryTheory.Comon.ComonToMonOpOpObj_mon_one, CategoryTheory.Limits.parallelPairOpIso_hom_app_zero, CategoryTheory.Functor.IsCoverDense.Types.naturality
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unop 📖 | CompOp | 590 mathmath: CategoryTheory.Comon.tensorObj_comul', CategoryTheory.LocalizerMorphism.LeftResolution.opFunctor_map_f, CategoryTheory.Limits.pushoutIsoOpPullback_inr_hom_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_eq, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_hom_right, CategoryTheory.ComposableArrows.opEquivalence_counitIso_inv_app_app, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_adj, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionRight_unop, CategoryTheory.kernelUnopOp_inv, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.ShortComplex.HomologyData.ofIso_right_p, CategoryTheory.Limits.limitUnopIsoUnopColimit_hom_comp_ι, TopCat.presheafToType_map, CategoryTheory.linearCoyoneda_map_app, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_snd, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_hom_app_eq, Bicategory.Opposite.op2_unop2, CategoryTheory.Limits.coconeEquivalenceOpConeOp_unitIso, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, CategoryTheory.ShortComplex.LeftHomologyMapData.unop_φQ, CategoryTheory.ShortComplex.LeftHomologyData.unop_p, CategoryTheory.Localization.isoOfHom_unop, CategoryTheory.Groupoid.invEquivalence_inverse_map, CategoryTheory.cocones_map_app_app, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_unitIso, CategoryTheory.Limits.pushoutIsoOpPullback_inl_hom, imageToKernel_unop, CategoryTheory.shrinkYonedaEquiv_symm_map_assoc, commBialgCatEquivComonCommAlgCat_unitIso_inv_app, CategoryTheory.HasLiftingProperty.unop, CategoryTheory.Functor.CorepresentableBy.uniqueUpToIso_inv, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_left_hom, CategoryTheory.Functor.hom_map, Profinite.Extend.functorOp_map, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHomRight, SimplicialObject.Splitting.IndexSet.fac_pull_assoc, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app, CategoryTheory.yoneda_map_app, CategoryTheory.unop_tensorHom, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀', CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_inverse, CategoryTheory.yonedaCommGrpGrpObj_map, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHomRight, CategoryTheory.Limits.opProdIsoCoprod_hom_snd_assoc, CategoryTheory.Iso.unop2_op2, CategoryTheory.Functor.leftOpRightOpEquiv_counitIso_inv_app_app, CategoryTheory.isIso_unop_iff, CategoryTheory.unop_epi_of_mono, CategoryTheory.linearYoneda_obj_map, CategoryTheory.Limits.widePullbackShapeUnop_map, CategoryTheory.prodOpEquiv_inverse_map, CategoryTheory.simplicialCosimplicialEquiv_counitIso_inv_app_app, CategoryTheory.Limits.PushoutCocone.unop_π_app, CategoryTheory.Presheaf.functorToRepresentables_map, CategoryTheory.ShortComplex.Homotopy.unop_h₂, CategoryTheory.unop_inv_associator, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv, CategoryTheory.Limits.Fork.unop_ι_app_zero, unop_op, LightCondensed.finYoneda_map, CategoryTheory.Functor.cones_map_app, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inr_assoc, CategoryTheory.ShortComplex.LeftHomologyData.unop_ι, CategoryTheory.NatTrans.leftOp_app, CommRingCat.moduleCatRestrictScalarsPseudofunctor_mapComp, CategoryTheory.Equivalence.leftOp_counitIso_inv_app, CategoryTheory.Limits.pushoutIsoUnopPullback_inr_hom, CategoryTheory.unop_mono_iff, CategoryTheory.cokernelUnopUnop_inv, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_right_as, CategoryTheory.unop_tensor_unop, SimplicialObject.opFunctor_obj_map, CategoryTheory.kernelOpUnop_hom, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHomRight, CategoryTheory.Limits.isColimitCoconeLeftOpOfCone_desc, CategoryTheory.Limits.pushoutIsoUnopPullback_inl_hom_assoc, AlgebraicTopology.AlternatingCofaceMapComplex.d_eq_unop_d, CategoryTheory.OverPresheafAux.yonedaCollectionPresheaf_map, CategoryTheory.ShortComplex.RightHomologyData.unop_i, CategoryTheory.CostructuredArrow.unop_left_comp_ofMkLEMk_unop, CommRingCat.coyoneda_map_app, TopCat.Presheaf.germ_res', AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_l, CategoryTheory.Limits.pushoutIsoUnopPullback_inr_hom_assoc, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_left_right, CategoryTheory.Limits.isColimitOfConeRightOpOfCocone_desc, CategoryTheory.Limits.PullbackCone.unop_inl, CategoryTheory.uliftCoyonedaEquiv_uliftCoyoneda_map, CochainComplex.homotopyUnop_hom_eq, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₂, CategoryTheory.Limits.π_comp_colimitLeftOpIsoUnopLimit_inv, AlgebraicGeometry.PresheafedSpace.componentwiseDiagram_map, commBialgCatEquivComonCommAlgCat_unitIso_hom_app, CategoryTheory.Limits.Cofork.unop_op_π, CategoryTheory.Equivalence.sheafCongrPreregular_inverse_obj_val_map, CategoryTheory.Presheaf.restrictedULiftYoneda_obj_map, CategoryTheory.Iso.unop2_inv, CategoryTheory.image_ι_op_comp_imageUnopOp_hom, CategoryTheory.Limits.Cofork.unop_π_app_one, CategoryTheory.Limits.isLimitOfCoconeOfConeLeftOp_lift, Bicategory.Opposite.bicategory_associator_hom_unop2, CategoryTheory.Limits.piConst_map_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality_assoc, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app_assoc, topCatOpToFrm_map, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality', CategoryTheory.Functor.shift_map_op_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality, CategoryTheory.ShortComplex.Homotopy.unop_h₃, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_map, CategoryTheory.Limits.π_comp_colimitUnopIsoOpLimit_inv, CategoryTheory.MorphismProperty.RightFraction.unop_s, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality, HomotopicalAlgebra.instWeakEquivalenceUnopOfOpposite, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_inv_toNatTrans_app_val_app, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, CategoryTheory.StructuredArrow.functor_map, CategoryTheory.Limits.PullbackCone.unop_inr, AddCommMonCat.coyonedaType_map_app, CategoryTheory.Comon.MonOpOpToComon_map_hom, Bicategory.Opposite.bicategory_leftUnitor_hom_unop2, CategoryTheory.Limits.FormalCoproduct.powerBifunctor_map_app, Condensed.finYoneda_map, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality', CategoryTheory.Functor.leftOpRightOpEquiv_unitIso_inv_app, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_inv_app_unop, CategoryTheory.BraidedCategory.unop_tensorμ, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₃, CommGrpCat.coyonedaType_map_app, CategoryTheory.uliftYonedaEquiv_symm_map, CategoryTheory.Square.unop_f₁₂, CategoryTheory.kernelUnopUnop_inv, CategoryTheory.Enriched.FunctorCategory.diagram_map_app, op_unop, CategoryTheory.opEquiv_apply, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_hom_app, TopCat.Presheaf.presheafEquivOfIso_inverse_obj_map, CategoryTheory.ShortComplex.unop_f, CategoryTheory.simplicialToCosimplicialAugmented_map_left, CategoryTheory.kernelOpUnop_inv, CategoryTheory.Limits.Fork.unop_ι_app_one, CategoryTheory.yonedaMonObj_map, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality_assoc, CategoryTheory.uliftYonedaEquiv_naturality, CategoryTheory.Limits.Fork.unop_op_ι, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_val_obj, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_counitIso, CategoryTheory.Limits.piConst_obj_map, CategoryTheory.ShortComplex.unopMap_τ₁, unop_op', CategoryTheory.Localization.isoOfHom_op_inv, CategoryTheory.CostructuredArrow.toStructuredArrow'_obj, CategoryTheory.simplicialCosimplicialEquiv_unitIso_hom_app, CategoryTheory.Limits.pullbackIsoOpPushout_inv_fst_assoc, CategoryTheory.cokernelUnopOp_hom, CategoryTheory.Equivalence.sheafCongrPrecoherent_functor_obj_val_map, CategoryTheory.unop_whiskerRight, CommAlgCat.lift_unop_hom, CategoryTheory.Equivalence.rightOp_inverse_map, CategoryTheory.ShortComplex.RightHomologyMapData.unop_φK, CategoryTheory.Limits.isColimitOfConeOfCoconeLeftOp_desc, CategoryTheory.Over.opEquivOpUnder_inverse_map, CommAlgCat.mul_op_of_unop_hom, Bicategory.Opposite.bicategory_leftUnitor_inv_unop2, CategoryTheory.Equivalence.sheafCongrPreregular_functor_obj_val_map, CategoryTheory.simplicialCosimplicialEquiv_counitIso_hom_app_app, CategoryTheory.linearYoneda_map_app, CommRingCat.moduleCatRestrictScalarsPseudofunctor_map, AlgebraicGeometry.Spec.map_preimage_unop, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app, CategoryTheory.CosimplicialObject.Augmented.leftOp_left_map, CategoryTheory.Equivalence.rightOp_unitIso_hom_app, CommAlgCat.fst_unop_hom, CategoryTheory.cokernel.π_unop, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality', CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHom, CategoryTheory.Functor.map_shift_unop, CategoryTheory.unop_inv_leftUnitor, ContinuousMap.yonedaPresheaf_map, CategoryTheory.Functor.op_commShiftIso_hom_app_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_inv_app, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHom_unop, CategoryTheory.Limits.π_comp_colimitLeftOpIsoUnopLimit_inv_assoc, SSet.stdSimplex.map_apply, CategoryTheory.Limits.isColimitCoconeUnopOfCone_desc, HomologicalComplex.opFunctor_map_f, CategoryTheory.LocalizerMorphism.LeftResolution.unop_w, AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, CategoryTheory.Functor.homObjFunctor_map_app, CategoryTheory.MorphismProperty.LeftFraction.unop_f, CategoryTheory.Limits.limitUnopIsoUnopColimit_inv_comp_π_assoc, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_fst, classifyingSpaceUniversalCover_map, CompHausLike.LocallyConstant.functorToPresheaves_map_app, CategoryTheory.factorThruImage_comp_imageUnopOp_inv, CategoryTheory.Limits.opProdIsoCoprod_inv_inl, CategoryTheory.unop_comp, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app_assoc, CategoryTheory.Limits.BinaryFan.unop_mk, CategoryTheory.Limits.pushoutIsoOpPullback_inv_fst, CategoryTheory.ShortComplex.RightHomologyData.unop_f', CategoryTheory.uliftYoneda_obj_map, AlgebraicGeometry.Scheme.Hom.map_appLE_assoc, CategoryTheory.ComposableArrows.opEquivalence_functor_map_app, CategoryTheory.GrothendieckTopology.map_yonedaEquiv', AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τl, CategoryTheory.kernelUnopOp_hom, CategoryTheory.eHomFunctor_map_app, CategoryTheory.yonedaEquiv_naturality', CategoryTheory.OverPresheafAux.restrictedYonedaObj_map, CategoryTheory.cokernel.π_op, CategoryTheory.cosimplicialSimplicialEquiv_functor_map_app, CategoryTheory.Limits.isLimitConeUnopOfCocone_lift, CategoryTheory.RanIsSheafOfIsCocontinuous.fac', CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app, CategoryTheory.Comon.MonOpOpToComonObj_comon_comul, CategoryTheory.yoneda_obj_map, CategoryTheory.Cat.opFunctorInvolutive_hom_app_toFunctor_map, AlgebraicGeometry.ΓSpec.unop_locallyRingedSpaceAdjunction_counit_app', CategoryTheory.cokernelOpUnop_inv, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheaf_map, PresheafOfModules.pushforward_obj_map_apply, CategoryTheory.Limits.kernelOrderHom_coe, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_hom_app, CategoryTheory.StructuredArrow.toCostructuredArrow_map, CategoryTheory.kernel.ι_unop, CategoryTheory.ShortComplex.Splitting.unop_r, CategoryTheory.Comma.unopFunctor_obj, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_map, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_functor_map, CategoryTheory.unop_neg, CategoryTheory.Abelian.extFunctor_map_app, CategoryTheory.Iso.unop_hom_inv_id_app, CategoryTheory.Limits.pushoutIsoUnopPullback_inl_hom, TopCat.presheafToTypes_map, CategoryTheory.ShortComplex.unopMap_τ₂, AddCommMonCat.coyoneda_map_app, CategoryTheory.Under.mapFunctor_map, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τr, Bicategory.Opposite.bicategory_whiskerRight_unop2, Bicategory.Opposite.homCategory_comp_unop2, CategoryTheory.Functor.sheafPushforwardContinuous_obj_val_map, AlgebraicGeometry.SheafedSpace.Γ_map, CategoryTheory.Pseudofunctor.presheafHom_map, SimplicialObject.Splitting.IndexSet.fac_pull, CommAlgCat.snd_unop_hom, CategoryTheory.Limits.pullbackIsoOpPushout_inv_fst, CategoryTheory.Functor.op_commShiftIso_inv_app_assoc, CategoryTheory.CostructuredArrow.toStructuredArrow'_map, CategoryTheory.unop_add, CategoryTheory.Limits.pullbackIsoOpPushout_inv_snd, CategoryTheory.typeEquiv_functor_obj_val_map, CategoryTheory.IsPushout.unop, AlgebraicGeometry.Scheme.Hom.appLE_map_assoc, CategoryTheory.MorphismProperty.LeftFraction.unop_s, CategoryTheory.Under.opEquivOpOver_functor_obj, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHomLeft_unop, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_map, CategoryTheory.unop_mono_of_epi, CategoryTheory.uliftYoneda_obj_map_down, HomotopicalAlgebra.weakEquivalences_unop_iff, CategoryTheory.SimplicialObject.Truncated.trunc_obj_map, CategoryTheory.Functor.leftOpRightOpEquiv_unitIso_hom_app, HomologicalComplex.unopSymm_d, AlgebraicGeometry.Scheme.Γ_map, CategoryTheory.cones_obj_map_app, CategoryTheory.NatTrans.removeRightOp_app, TopCat.Presheaf.germ_res_apply', CategoryTheory.Square.opFunctor_map_τ₁, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀'_assoc, Bicategory.Opposite.unopFunctor_obj, CategoryTheory.unopHom_apply, HomotopicalAlgebra.instFibrationUnopOfCofibrationOpposite, CategoryTheory.Limits.isLimitOfCoconeRightOpOfCone_lift, CategoryTheory.Limits.PullbackCone.unop_ι_app, CategoryTheory.Square.unop_f₁₃, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality_assoc, CategoryTheory.Limits.FormalCoproduct.evalOp_map_app, CategoryTheory.GrothendieckTopology.diagram_map, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_counitIso, CategoryTheory.Functor.op_commShiftIso_inv_app, CategoryTheory.isIso_unop, RingCat.moduleCatRestrictScalarsPseudofunctor_map, CategoryTheory.Over.opEquivOpUnder_counitIso, CategoryTheory.Iso.unop2_hom, CategoryTheory.CategoryOfElements.fromCostructuredArrow_map_coe, CategoryTheory.Square.opFunctor_map_τ₂, CategoryTheory.RetractArrow.unop_r_right, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_inv_app, CategoryTheory.Functor.unop_map, CategoryTheory.Limits.isLimitConeOfCoconeRightOp_lift, CategoryTheory.Functor.RepresentableBy.homEquiv_unop_comp, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_map_left_right, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHom_unop, CategoryTheory.Functor.opInv_map, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality_assoc, TopCat.subpresheafToTypes_map_coe, CategoryTheory.Limits.coneLeftOpOfCocone_π_app, CategoryTheory.unop_epi_iff, CategoryTheory.Limits.FormalCoproduct.cech_map, AlgebraicGeometry.Scheme.Hom.naturality_assoc, unop_inj_iff, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop, CategoryTheory.Iso.unop_inv, TopCat.Presheaf.pushforward_obj_map, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_unitIso, CategoryTheory.Limits.opProdIsoCoprod_hom_fst, CategoryTheory.Limits.isLimitOfCoconeOfConeUnop_lift, CategoryTheory.Limits.walkingCospanOpEquiv_functor_map, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop_assoc, CategoryTheory.Limits.pushoutIsoOpPullback_inr_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality, CategoryTheory.Equivalence.sheafCongr.functor_obj_val_map, AlgebraicGeometry.LocallyRingedSpace.Γ_map, CategoryTheory.CommSq.unop, CategoryTheory.kernelUnopUnop_hom, CommAlgCat.toUnit_unop_hom, unop_inj, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv', CategoryTheory.nerve_map, AlgebraicGeometry.AffineSpace.functor_map_app, AlgebraicGeometry.LocallyRingedSpace.restrict_presheaf_map, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inl, CategoryTheory.ShortComplex.Homotopy.unop_h₁, CategoryTheory.Comma.unopFunctor_map, CategoryTheory.simplicialCosimplicialEquiv_functor_map_app, CategoryTheory.Functor.leftOpRightOpEquiv_counitIso_hom_app_app, CategoryTheory.Limits.walkingSpanOpEquiv_functor_map, CategoryTheory.Limits.unop_zero, CategoryTheory.Square.unop_f₂₄, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map_val_app, CategoryTheory.Iso.unop_hom_inv_id_app_assoc, CommAlgCat.one_op_of_unop_hom, CategoryTheory.yonedaPairing_map, AlgebraicGeometry.Spec.toSheafedSpace_map, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply, CategoryTheory.Limits.BinaryCofan.unop_mk, CategoryTheory.unop_inv, CategoryTheory.unop_comp_assoc, CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv', CategoryTheory.Limits.Cofork.unop_π_app_zero, CategoryTheory.ShiftedHom.opEquiv'_zero_add_symm, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_hom_app_unop_assoc, CategoryTheory.Functor.shift_map_op, CategoryTheory.Pretriangulated.shiftFunctor_op_map, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_inv_comp_π, CategoryTheory.Limits.opProdIsoCoprod_hom_fst_assoc, CategoryTheory.Limits.isLimitConeLeftOpOfCocone_lift, CategoryTheory.cokernelUnopUnop_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_inv_app_eq, Bicategory.Opposite.unop2_comp, CategoryTheory.simplicialCosimplicialEquiv_unitIso_inv_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_val_map, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_obj, CommMonCat.coyoneda_map_app, CategoryTheory.unop_inv_braiding, CategoryTheory.unop_id_op, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_fst_assoc, CategoryTheory.Limits.opProdIsoCoprod_inv_inr, AlgebraicGeometry.Spec.coe_toTop_map_hom_apply_asIdeal, AlgebraicGeometry.Scheme.Opens.toScheme_presheaf_map, CategoryTheory.ShortComplex.LeftHomologyMapData.unop_φH, CategoryTheory.Limits.pushoutIsoOpPullback_inl_hom_assoc, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionRight_unop, CategoryTheory.Functor.CorepresentableBy.uniqueUpToIso_hom, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHomRight, CategoryTheory.imageUnopOp_hom_comp_image_ι, CategoryTheory.Limits.limitUnopIsoUnopColimit_hom_comp_ι_assoc, CategoryTheory.Limits.isColimitCoconeOfConeRightOp_desc, CategoryTheory.Equivalence.sheafCongrPrecoherent_inverse_obj_val_map, CategoryTheory.CommSq.LiftStruct.unop_l, CategoryTheory.Groupoid.invEquivalence_counitIso, CategoryTheory.HasLiftingProperty.iff_unop, CategoryTheory.Square.opFunctor_map_τ₃, CategoryTheory.Limits.coconeLeftOpOfCone_ι_app, CategoryTheory.MorphismProperty.RightFraction.unop_f, CategoryTheory.Limits.ι_comp_colimitUnopIsoOpLimit_hom_assoc, CategoryTheory.LocalizerMorphism.RightResolution.unop_w, RingCat.moduleCatRestrictScalarsPseudofunctor_mapComp, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHomLeft, AlgebraicGeometry.PresheafedSpace.Γ_map, CategoryTheory.Iso.unop_hom, CategoryTheory.MonoidalClosed.internalHom_map, CategoryTheory.Limits.opProdIsoCoprod_hom_snd, CategoryTheory.Functor.closedSieves_map_coe, SimplicialObject.Splitting.IndexSet.epiComp_snd_coe, CategoryTheory.Limits.PullbackCone.unop_pt, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHom, CategoryTheory.ShortComplex.unop_g, CategoryTheory.cokernelOpUnop_hom, CategoryTheory.Equivalence.rightOp_unitIso_inv_app, CategoryTheory.Limits.widePushoutShapeUnop_map, CategoryTheory.kernel.ι_op, CategoryTheory.unopUnop_map, HomotopicalAlgebra.fibration_unop_iff, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app_assoc, TopCat.Presheaf.germ_res'_assoc, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHomLeft, TopCat.toSheafCompHausLike_val_map, CategoryTheory.Functor.map_shift_unop_assoc, AlgebraicGeometry.Scheme.Hom.naturality, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_assoc, CategoryTheory.Equivalence.sheafCongr.inverse_obj_val_map, Bicategory.Opposite.bicategory_homCategory_id_unop2, CategoryTheory.Arrow.cechNerve_map, CategoryTheory.LocalizerMorphism.RightResolution.unopFunctor_map_f, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.Limits.opProdIsoCoprod_inv_inr_assoc, Bicategory.Opposite.unop2_id, CategoryTheory.Limits.FormalCoproduct.evalOp_obj_map, CategoryTheory.Limits.Cofork.op_unop_π, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τl, HomotopicalAlgebra.instCofibrationUnopOfFibrationOpposite, AddCommGrpCat.coyoneda_map_app, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inr, ContinuousMap.yonedaPresheaf'_map, CategoryTheory.prodOpEquiv_functor_map, Bicategory.Opposite.bicategory_homCategory_comp_unop2, CategoryTheory.IsPullback.unop, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHom, CategoryTheory.ShiftedHom.opEquiv_symm_apply, CategoryTheory.prodOpEquiv_counitIso_hom_app, CategoryTheory.Limits.coconeEquivalenceOpConeOp_counitIso, CategoryTheory.simplicialToCosimplicialAugmented_map_right, CategoryTheory.Sieve.functor_map_coe, CategoryTheory.Limits.opProdIsoCoprod_inv_inl_assoc, CategoryTheory.CosimplicialObject.Augmented.leftOp_hom_app, CategoryTheory.Functor.leftOp_map, CategoryTheory.Equivalence.leftOp_counitIso_hom_app, PresheafOfModules.pushforward_obj_map_apply', CategoryTheory.unop_hom_rightUnitor, CategoryTheory.Limits.pushoutIsoOpPullback_inv_snd, HomotopicalAlgebra.cofibration_unop_iff, CategoryTheory.Limits.pullbackIsoOpPushout_inv_snd_assoc, CategoryTheory.Iso.unop_inv_hom_id_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_hom_toNatTrans_app_val_app, SSet.op_map, CategoryTheory.HasLiftingProperty.transfiniteComposition.sqFunctor_map, CategoryTheory.unop_hom_braiding, CategoryTheory.RetractArrow.unop_i_left, CategoryTheory.cosimplicialToSimplicialAugmented_map, AlgebraicGeometry.Spec.toPresheafedSpace_map, commBialgCatEquivComonCommAlgCat_inverse_map_unop_hom, CategoryTheory.unop_zsmul, CategoryTheory.Under.opEquivOpOver_counitIso, CategoryTheory.Functor.opHom_map_app, CategoryTheory.ShortComplex.unopMap_τ₃, AlgebraicGeometry.Spec.toLocallyRingedSpace_map, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_map, CategoryTheory.Limits.PushoutCocone.unop_pt, Bicategory.Opposite.bicategory_associator_inv_unop2, CategoryTheory.RetractArrow.unop_i_right, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_hom_comp_ι_assoc, CompHausLike.LocallyConstant.incl_comap, CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction_actionHom, AlgebraicGeometry.Scheme.Spec_map, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_inv_app_unop_assoc, CategoryTheory.cosimplicialSimplicialEquiv_inverse_map, CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionHomLeft, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₁, AlgebraicGeometry.Scheme.Hom.map_appLE, CategoryTheory.Iso.unop_inv_hom_id_app_assoc, CategoryTheory.Limits.π_comp_colimitUnopIsoOpLimit_inv_assoc, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app, CategoryTheory.ShortComplex.RightHomologyData.unop_π, CategoryTheory.Functor.op_commShiftIso_hom_app, CategoryTheory.Groupoid.invEquivalence_unitIso, CategoryTheory.Limits.coconeEquivalenceOpConeOp_inverse_map_hom, CategoryTheory.Over.opEquivOpUnder_functor_map, CategoryTheory.ShortComplex.Homotopy.unop_h₀, CategoryTheory.Limits.isColimitOfConeOfCoconeUnop_desc, CategoryTheory.cokernelUnopOp_inv, CategoryTheory.Limits.Fork.op_unop_ι, HomologicalComplex.unop_d, CategoryTheory.Limits.ι_comp_colimitLeftOpIsoUnopLimit_hom_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv_assoc, CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor_obj_obj_map_app, CategoryTheory.Limits.pullbackIsoOpPushout_hom_inl_assoc, CategoryTheory.kernelOpOp_hom, AlgebraicGeometry.Scheme.Modules.pseudofunctor_map_r, CategoryTheory.Subobject.functor_map, CategoryTheory.SimplicialObject.augmentedCechNerve_obj_left_map, CategoryTheory.Functor.leftOpRightOpEquiv_functor_map_app, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app_assoc, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_inv_comp_π_assoc, CategoryTheory.unop_hom_associator, CategoryTheory.Limits.Cofork.unop_ι, CategoryTheory.Under.opEquivOpOver_functor_map, CategoryTheory.yonedaEquiv_symm_map, AlgebraicGeometry.Scheme.Hom.appLE_map, CategoryTheory.Limits.pullbackIsoUnopPushout_inv_snd_assoc, AlgebraicGeometry.Proj.res_apply, CategoryTheory.CostructuredArrow.projectQuotient_factors, CategoryTheory.Limits.ι_comp_colimitLeftOpIsoUnopLimit_hom, AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τr, CategoryTheory.ComposableArrows.opEquivalence_counitIso_hom_app_app, CategoryTheory.imageUnopOp_inv_comp_op_factorThruImage, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand', CategoryTheory.ShortComplex.Splitting.unop_s, CategoryTheory.Limits.limitLeftOpIsoUnopColimit_hom_comp_ι, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop_assoc, CategoryTheory.Equivalence.leftOp_functor_map, CategoryTheory.Functor.leibnizPullback_map_app, HomologicalComplex.unopFunctor_map_f, Bicategory.Opposite.homCategory_id_unop2, CategoryTheory.StructuredArrow.toCostructuredArrow'_map, CategoryTheory.Square.opFunctor_map_τ₄, CategoryTheory.RetractArrow.unop_r_left, CategoryTheory.CostructuredArrow.unop_left_comp_underlyingIso_hom_unop, CategoryTheory.ShortComplex.LeftHomologyData.unop_g', CategoryTheory.uliftYonedaEquiv_symm_map_assoc, CategoryTheory.StructuredArrow.toCostructuredArrow'_obj, commBialgCatEquivComonCommAlgCat_counitIso_hom_app, Bicategory.Opposite.op2_id_unbop, CategoryTheory.unop_inv_rightUnitor, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_val_app, CategoryTheory.unop_sub, CommGrpCat.coyoneda_map_app, commBialgCatEquivComonCommAlgCat_functor_map_unop_hom, CategoryTheory.Abelian.subobjectIsoSubobjectOp_symm_apply, CategoryTheory.unop_hom_leftUnitor, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence_functor, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_map, CategoryTheory.GrothendieckTopology.uliftYoneda_obj_val_map_down, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_eq, CategoryTheory.prodOpEquiv_counitIso_inv_app, CategoryTheory.Functor.rightOp_map_unop, CategoryTheory.Comon.MonOpOpToComonObj_comon_counit, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_val_app, CategoryTheory.cosimplicialSimplicialEquiv_functor_obj_map, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop, CategoryTheory.Limits.PushoutCocone.unop_snd, CategoryTheory.NatTrans.removeOp_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app, CategoryTheory.ShortComplex.opFunctor_map, HomologicalComplex.opInverse_map, CategoryTheory.Limits.limitUnopIsoUnopColimit_inv_comp_π, CategoryTheory.unop_whiskerLeft, CategoryTheory.eqToHom_unop, TopCat.Presheaf.presheafEquivOfIso_functor_obj_map, CategoryTheory.NatTrans.unop_app, CategoryTheory.unop_sum, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_hom_app_unop, CategoryTheory.Under.opEquivOpOver_inverse_map, CategoryTheory.Comon.monoidal_tensorObj_comon_counit, CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHomLeft, CompHausLike.LocallyConstant.functorToPresheaves_obj_map, CategoryTheory.op_comp_unop, CategoryTheory.CostructuredArrow.projectQuotient_mk, AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand'_assoc, unop_mk, Bicategory.Opposite.bicategory_rightUnitor_hom_unop2, CategoryTheory.CostructuredArrow.toStructuredArrow_map, CategoryTheory.MonoidalCategory.MonoidalRightAction.rightActionOfOppositeRightAction_actionHomLeft_unop, commBialgCatEquivComonCommAlgCat_counitIso_inv_app, CategoryTheory.Limits.Fork.unop_π, CategoryTheory.ShortComplex.RightHomologyMapData.unop_φH, CategoryTheory.cokernelOpOp_inv, CategoryTheory.Limits.PushoutCocone.unop_fst, CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor_obj_left_left_as, CategoryTheory.shrinkYonedaEquiv_symm_map, Bicategory.Opposite.bicategory_whiskerLeft_unop2, CategoryTheory.CommSq.HasLift.iff_unop, CategoryTheory.unop_id, AddCommGrpCat.coyonedaType_map_app, CategoryTheory.Over.opEquivOpUnder_functor_obj, Bicategory.Opposite.bicategory_rightUnitor_inv_unop2, CategoryTheory.Yoneda.obj_map_id, CategoryTheory.map_yonedaEquiv', CommMonCat.coyonedaType_map_app, CategoryTheory.CategoryOfElements.toCostructuredArrow_map, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality, CategoryTheory.Square.unop_f₃₄, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp_naturality_assoc, CategoryTheory.enrichedNatTransYoneda_map_app, Subobject.presheaf_map, CategoryTheory.Equivalence.symmEquivInverse_map_app, CategoryTheory.Comon.monoidal_tensorObj_comon_comul, CategoryTheory.Limits.ι_comp_colimitUnopIsoOpLimit_hom, CategoryTheory.Functor.op_map, CategoryTheory.preadditiveYonedaObj_map, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_assoc, CategoryTheory.Limits.compYonedaSectionsEquiv_symm_apply_coe, CategoryTheory.OverPresheafAux.counitForward_naturality₂
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