Sheaf 📖 | CompData | 445 mathmath: Sheaf.cartesianMonoidalCategoryLift_val, GrothendieckTopology.overMapPullbackId_hom_app_val_app, GrothendieckTopology.W_sheafToPresheaf_map_iff_isIso, sheafBotEquivalence_functor, SheafOfModules.pushforward_assoc, Equivalence.sheafCongrPrecoherent_counitIso_hom_app_val_app, Functor.IsDenseSubsite.instIsIsoSheafAppCounitSheafAdjunctionCocontinuous, Sheaf.ΓHomEquiv_naturality_left_symm, isIso_sheafificationAdjunction_counit, Sheaf.isLocallySurjective_sheafToPresheaf_map_iff, Functor.sheafPushforwardContinuousIso_inv, GrothendieckTopology.MayerVietorisSquare.shortComplex_X₃, Equivalence.sheafCongr.counitIso_hom_app_val_app, GrothendieckTopology.preservesColimitsOfShape_yoneda_of_ofArrows_inj_mem, GrothendieckTopology.yonedaOpCompCoyoneda_hom_app_app_down, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, Equivalence.sheafCongrPreregular_counitIso_inv_app_val_app, Presheaf.coherentExtensiveEquivalence_functor_map_val, LightCondensed.ihomPoints_apply, Functor.IsDenseSubsite.instIsEquivalenceSheafSheafPushforwardContinuous, Equivalence.sheafCongr_functor, Functor.sheafPushforwardContinuousComp'_inv_app_val_app, sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_hom_app_app_val, Sheaf.instIsLocallySurjectiveAppArrowILocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, GrothendieckTopology.yonedaULiftEquiv_apply, GrothendieckTopology.yonedaEquiv_symm_app_apply, SheafOfModules.pushforwardNatIso_inv, GrothendieckTopology.W_eq_inverseImage_isomorphisms, Sheaf.toImage_ι_assoc, GrothendieckTopology.overMapPullback_comp_id, Functor.sheafPullbackConstruction.instPreservesFiniteLimitsSheafSheafPullback, typeEquiv_functor_obj_val_obj, GrothendieckTopology.overMapPullbackId_inv_app_val_app, sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_inv_app_app, CondensedMod.isDiscrete_tfae, instFullSheafSheafComposeOfFaithful, GrothendieckTopology.yoneda_map_val, CompHausLike.LocallyConstant.adjunction_counit, sheafificationNatIso_inv_app_val, GrothendieckTopology.instFaithfulSheafTypeUliftYoneda, GrothendieckTopology.MayerVietorisSquare.shortComplex_X₁, CondensedMod.LocallyConstant.instFullModuleCatSheafCompHausCoherentTopologyConstantSheaf, Condensed.discrete_map, instIsIsoFunctorOppositeValAppSheafCounitSheafificationAdjunction, sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_inv_app_app, GrothendieckTopology.Point.instPreservesFiniteLimitsSheafSheafFiberOfLocallySmallOfHasFiniteLimitsOfAB5OfSize, sheafificationNatIso_hom_app_val, constantCommuteCompose_hom_app_val, Sheaf.isLocallySurjective_comp, sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_app_app, Equivalence.instPreservesFiniteLimitsFunctorOppositeSheafTransportAndSheafify, SheafOfModules.instIsRightAdjointPushforwardCompSheafRingCatMapSheafPushforwardContinuous, Equivalence.sheafCongrPreregular_unitIso_hom_app_val_app, Sheaf.isLocallySurjective_iff_epi, Functor.IsDenseSubsite.sheafEquiv_functor, sheafCompose_map_val, Sheaf.comp_val, LightCondensed.discrete_map, AlgebraicGeometry.Scheme.LocalRepresentability.instIsLocallySurjectiveHomYonedaGluedToSheafOfIsLocallySurjectiveZariskiTopologyDescFunctorOppositeType, Sheaf.isPullback_square_op_map_yoneda_presheafToSheaf_yoneda_iff, SheafOfModules.toSheaf_obj_val, sheafToPresheaf_μ, sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_hom_app_app_val, Presheaf.isLocallyInjective_presheafToSheaf_map_iff, GrothendieckTopology.uliftYonedaEquiv_naturality, instEpiSheafTypeToImage, plusPlusSheaf_obj_val, Functor.sheafAdjunctionCocontinuous_counit_app_val, GrothendieckTopology.instFullSheafTypeYoneda, Equivalence.sheafCongrPreregular_inverse_obj_val_map, Sheaf.mem_essImage_of_isConstant, hasLimitsEssentiallySmallSite, GrothendieckTopology.MayerVietorisSquare.isPushout, sheafificationIso_inv_val, GrothendieckTopology.uliftYonedaEquiv_naturality', Sheaf.instHasColimitsOfShape, Functor.sheafPullbackConstruction.instIsRightAdjointSheafSheafPushforwardContinuousOfHasWeakSheafify, GrothendieckTopology.uliftYonedaEquiv_symm_map, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp_val_app, GrothendieckTopology.pseudofunctorOver_mapComp_inv_toNatTrans_app_val_app, Equivalence.sheafCongrPrecoherent_functor_obj_val_obj, Functor.sheafPushforwardContinuousNatTrans_app_val, CompHausLike.LocallyConstantModule.functor_map_val, CompHausLike.LocallyConstant.functor_map_val, Sheaf.instIsIsoAppCounitConstantSheafAdjOfFaithfulOfFullConstantSheafOfIsConstant, Presheaf.coherentExtensiveEquivalence_counitIso, Functor.sheafPushforwardContinuous_map_val_app, HasSheafify.isLeftExact, GrothendieckTopology.Point.Hom.sheafFiber_comp_assoc, topCatToSheafCompHausLike_map_val_app, GrothendieckTopology.yonedaULiftEquiv_naturality', GrothendieckTopology.preservesSheafification_iff_of_adjunctions, Functor.IsCoverDense.faithful_sheafPushforwardContinuous, instIsIsoFunctorOppositeSheafSheafComposeNatTrans, Sheaf.toImage_ι, instPreservesFiniteColimitsSheafExtensiveTopologyFunctorOppositeSheafToPresheafOfPreadditiveOfHasFiniteColimits, typeEquiv_inverse_obj, Sheaf.epi_of_isLocallySurjective', GrothendieckTopology.W_iff_isIso_map_of_adjunction, GrothendieckTopology.MayerVietorisSquare.shortComplex_shortExact, Equivalence.sheafCongrPreregular_functor_obj_val_obj, GrothendieckTopology.W_isInvertedBy_whiskeringRight_presheafToSheaf, Sheaf.ΓHomEquiv_naturality_left, SheafOfModules.pushforwardComp_inv_app_val_app, Sheaf.isConstant_iff_forget, Equivalence.sheafCongrPreregular_functor_map_val_app, Presheaf.coherentExtensiveEquivalence_inverse_map_val, instHasImagesSheafType, Sheaf.hasFilteredColimitsOfSize, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_val_obj, instPreservesFiniteLimitsFunctorOppositeSheafReflectorSheafToPresheaf, GrothendieckTopology.instFullSheafTypeUliftYoneda, SheafOfModules.pushforwardNatTrans_id, plusPlusSheaf_map_val, Functor.sheafPushforwardContinuousCompSheafToPresheafIso_inv_app_app, GrothendieckTopology.yonedaULiftEquiv_symm_naturality_left, equivYoneda'_inv_val, Equivalence.sheafCongrPreregular_inverse_map_val_app, Equivalence.sheafCongrPrecoherent_functor_obj_val_map, GrothendieckTopology.W_adj_unit_app, Sheaf.instHasFunctorialFactorizationLocallySurjectiveLocallyInjective, sheafToPresheaf_obj, sheafToPresheaf_map, Sheaf.isLocallySurjective_iff_epi', SheafOfModules.instAdditiveSheafAddCommGrpCatToSheaf, typeEquiv_unitIso_hom_app, CompHausLike.LocallyConstant.functor_obj_val, Equivalence.sheafCongrPreregular_functor_obj_val_map, LightCondMod.LocallyConstant.instFullModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf, Sheaf.cartesianMonoidalCategorySnd_val, GrothendieckTopology.yonedaULiftEquiv_symm_naturality_right, Sheaf.instMonoAppArrowPLocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, Equivalence.sheafCongrPrecoherent_inverse_map_val_app, fullyFaithfulSheafToPresheaf_preimage_val, SheafOfTypes.finitary_extensive, Sheaf.instIsGrothendieckAbelian, Sheaf.natTransΓRes_app, GrothendieckTopology.yonedaEquiv_naturality', GrothendieckTopology.uliftYonedaEquiv_uliftYoneda_map, SheafOfModules.Presentation.quasicoherentData_presentation, CompHausLike.LocallyConstantModule.functor_obj_val, SheafOfModules.toSheaf_map_val, instIsRightAdjointSheafΓ, GrothendieckTopology.instIsIsoFunctorOppositeSheafSheafComposeNatTransPlusPlusAdjunction, GrothendieckTopology.overMapPullback_assoc_assoc, Sheaf.isSheaf_of_isLimit, Sheaf.instHasFiniteColimits, sheafToPresheaf_δ, Sheaf.Hom.mono_iff_presheaf_mono, sheafBotEquivalence_inverse_map_val, typeEquiv_unitIso_inv_app, GrothendieckTopology.yonedaOpCompCoyoneda_inv_app_app, isRegularEpiCategory_sheaf, GrothendieckTopology.uliftYonedaCompSheafToPresheaf_inv_app_app, GrothendieckTopology.Point.Hom.sheafFiber_comp, PresheafOfModules.sheafification_map, toPresheafToSheafCompComposeAndSheafify_app, GrothendieckTopology.uliftYonedaCompSheafToPresheaf_hom_app_app, instPreservesFiniteLimitsFunctorOppositeSheafLeftAdjointSheafToPresheaf, SheafOfModules.pullback_comp_id, Equivalence.sheafCongrPrecoherent_inverse_obj_val_obj, GrothendieckTopology.map_yonedaEquiv', sheafBotEquivalence_unitIso, SheafOfModules.instPreservesFiniteLimitsFunctorOppositeAddCommGrpCatCompSheafToSheafSheafToPresheaf, typeEquiv_counitIso_inv_app_val_app, sheafBotEquivalence_inverse_obj_val, PresheafOfModules.toSheaf_map_sheafificationHomEquiv_symm, isSheaf_pointwiseColimit, topCatToSheafCompHausLike_obj, Equivalence.sheafCongr.inverse_obj_val_obj, Sheaf.adjunction_counit_app_val, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id_val_app, SheafOfTypes.adhesive, GrothendieckTopology.yonedaEquiv_comp, GrothendieckTopology.MayerVietorisSquare.instEpiSheafAddCommGrpCatGShortComplex, Sheaf.isSeparating, Sheaf.isGrothendieckAbelian_of_essentiallySmall, GrothendieckTopology.yonedaEquiv_symm_map, Functor.IsDenseSubsite.sheafEquiv_inverse, Sheaf.ΓObjEquivSections_naturality_symm, Sheaf.mono_of_isLocallyInjective, Sheaf.ΓRes_map_assoc, Functor.sheafPushforwardContinuous_obj_val_map, Sheaf.ab5ofSize, GrothendieckTopology.uliftYonedaEquiv_symm_app_apply, Sheaf.ΓObjEquivHom_naturality_symm, instPreservesFiniteLimitsFunctorOppositeSheafPresheafToSheaf, Equivalence.sheafCongr.unitIso_hom_app_val_app, Sheaf.hasSeparator, instFaithfulSheafSheafCompose, SheafOfModules.conjugateEquiv_pullbackComp_inv, typeEquiv_functor_obj_val_map, Sheaf.Hom.mono_of_presheaf_mono, Sheaf.instHasExactColimitsOfShapeOfHasFiniteLimitsOfPreservesColimitsOfShapeFunctorOppositeSheafToPresheaf, Functor.IsCoverDense.Types.sheafIso_hom_val, sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_app_app, GrothendieckTopology.sheafToPresheaf_map_sheafComposeNatTrans_eq_sheafifyCompIso_inv, Sheaf.instHasFiniteLimits, GrothendieckTopology.uliftYonedaIsoYoneda_hom_app_val_app, Functor.sheafPushforwardContinuousComp_inv_app_val_app, instFinitaryExtensiveSheafOfHasPullbacksOfHasSheafify, CompHausLike.LocallyConstant.adjunction_left_triangle, Sheaf.isLocallyInjective_forget, PresheafOfModules.instReflectsIsomorphismsSheafOfModulesSheafAddCommGrpCatToSheaf, SheafOfModules.pullback_id_comp, Equivalence.sheafCongrPreregular_counitIso_hom_app_val_app, instReflectsIsomorphismsSheafSheafCompose, AlgebraicGeometry.Scheme.LocalRepresentability.yoneda_toGlued_yonedaGluedToSheaf_assoc, GrothendieckTopology.Point.instPreservesColimitsOfSizeSheafSheafFiberOfHasSheafifyOfWEqualsLocallyBijectiveOfReflectsIsomorphismsOfPreservesFilteredColimitsOfSizeForgetOfLocallySmall, Equivalence.sheafCongrPrecoherent_counitIso_inv_app_val_app, Functor.sheafPushforwardCocontinuousCompSheafToPresheafIso_inv, Sheaf.coneΓ_pt, Equivalence.sheafCongr.functor_map_val_app, Functor.sheafPushforwardContinuousComp_hom_app_val_app, instReflectsIsomorphismsSheafFunctorOppositeSheafToPresheaf, instPreservesColimitsOfShapeSheafExtensiveTopologyFunctorOppositeSheafToPresheafOfPreservesFiniteProductsColim, Functor.sheafPushforwardContinuous_obj_val_obj, Sheaf.isConstant_iff_isIso_counit_app', SheafOfTypes.balanced, preservesFiniteLimits_presheafToSheaf, typeEquiv_inverse_map, SheafOfModules.pushforward_map_val, plusPlusAdjunction_counit_app_val, GrothendieckTopology.overMapPullbackCongr_eq_eqToIso, Functor.sheafPushforwardCocontinuousCompSheafToPresheafIso_hom, SheafOfModules.pushforwardComp_hom_app_val_app, CondensedMod.LocallyConstant.instFaithfulSheafCompHausCoherentTopologyTypeConstantSheaf, GrothendieckTopology.preservesSheafification_iff_of_adjunctions_of_hasSheafCompose, Sheaf.adjunction_unit_app_val, SheafOfModules.instIsLeftAdjointOverOverRingCatPushforwardIdSheafOver, Functor.sheafPushforwardContinuousId_hom_app_val_app, Functor.sheafPushforwardContinuousId'_inv_app_val_app, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_hom_app_val_app_apply, Equivalence.sheafCongr_counitIso, AlgebraicGeometry.Scheme.LocalRepresentability.instIsIsoSheafZariskiTopologyTypeYonedaGluedToSheaf, Functor.toSheafify_pullbackSheafificationCompatibility, Sheaf.ΓHomEquiv_naturality_right_symm, Equivalence.sheafCongr.functor_obj_val_map, GrothendieckTopology.preservesLimitsOfSize_yoneda, Equivalence.sheafCongrPrecoherent_unitIso_inv_app_val_app, Sheaf.ΓObjEquivHom_naturality, Sheaf.ΓRes_map, SheafOfModules.pushforwardCongr_symm, GrothendieckTopology.map_uliftYonedaEquiv', AlgebraicGeometry.Scheme.LocalRepresentability.yoneda_toGlued_yonedaGluedToSheaf, Sheaf.cartesianMonoidalCategoryWhiskerRight_val, SheafOfModules.instFaithfulSheafAddCommGrpCatToSheaf, CondensedSet.isDiscrete_tfae, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map_val_app, Sheaf.instHasLimitsOfShape, Functor.IsCoverDense.iso_of_restrict_iso, GrothendieckTopology.overMapPullback_comp_id_assoc, GrothendieckTopology.MayerVietorisSquare.shortComplex_g, plusPlusSheaf_preservesZeroMorphisms, GrothendieckTopology.MayerVietorisSquare.isPushoutAddCommGrpFreeSheaf, Sheaf.instIsLocallyInjectiveAppArrowPLocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, GrothendieckTopology.yoneda_obj_val, Functor.IsCoverDense.Types.sheafIso_inv_val, Sheaf.isConstant_iff_mem_essImage, Sheaf.instPreservesFiniteLimitsFunctorOppositeSheafToPresheafOfHasFiniteLimits, GrothendieckTopology.yonedaEquiv_naturality, sheafificationAdjunction_unit_app, typeEquiv_counitIso_hom_app_val_app, Presheaf.coherentExtensiveEquivalence_unitIso, instFaithfulSheafFunctorOppositeSheafToPresheaf, AlgebraicGeometry.Scheme.LocalRepresentability.instIsLocallyInjectiveHomYonedaGluedToSheaf, instFaithfulSheafFunctorOppositeCompSheafComposeSheafToPresheaf, GrothendieckTopology.Point.Hom.sheafFiber_id, Sheaf.instHasExactLimitsOfShapeOfHasFiniteColimitsOfPreservesFiniteColimitsFunctorOppositeSheafToPresheaf, GrothendieckTopology.map_yonedaULiftEquiv', SheafOfModules.unitToPushforwardObjUnit_val_app_apply, SheafOfModules.pullback_assoc, GrothendieckTopology.uliftYonedaEquiv_apply, Functor.IsCoverDense.sheafIso_inv_val, GrothendieckTopology.uliftYonedaOpCompCoyoneda_hom_app_app_down, presheafToSheaf_additive, LightCondensed.ihomPoints_symm_apply, sheafificationIso_hom_val, LightCondensed.discrete_obj, Sheaf.Hom.epi_of_presheaf_epi, Sheaf.isLocallyInjective_sheafToPresheaf_map_iff, Sheaf.id_val, Functor.sheafPullbackConstruction.preservesFiniteLimits, GrothendieckTopology.uliftYonedaEquiv_symm_naturality_left, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_val_map, GrothendieckTopology.overMapPullbackComp_inv_app_val_app, Sheaf.isConstant_iff_of_equivalence, Sheaf.hasExactColimitsOfShape, presheafToSheafCompComposeAndSheafifyIso_inv_app, Sheaf.instHasFiniteCoproducts, Presheaf.coherentExtensiveEquivalence_functor_obj_val, yoneda'_obj_val, LightCondMod.LocallyConstant.instFaithfulModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf, GrothendieckTopology.instFaithfulSheafTypeYoneda, Sheaf.instIsLocallySurjectiveHomMapTypeSheafComposeForget, plusPlusAdjunction_unit_app, Equivalence.sheafCongrPrecoherent_inverse_obj_val_map, Equivalence.sheafCongrPrecoherent_unitIso_hom_app_val_app, Sheaf.mono_of_injective, GrothendieckTopology.instIsLocalizationFunctorOppositeSheafPresheafToSheafW, GrothendieckTopology.uliftYonedaOpCompCoyoneda_app_app, Functor.sheafPushforwardContinuousCompSheafToPresheafIso_hom_app_app, Sheaf.epi_of_isLocallySurjective, sheafToPresheaf_η, CompHausLike.LocallyConstant.instIsIsoFunctorTypeUnitSheafCoherentTopologyAdjunction, Equivalence.sheafCongrPreregular_inverse_obj_val_obj, CompHausLike.LocallyConstant.counit_app_val, Sheaf.instHasColimitsOfSize, SheafOfModules.pushforwardNatTrans_app_val_app, GrothendieckTopology.W_iff, GrothendieckTopology.W_eq_inverseImage_isomorphisms_of_adjunction, typeEquiv_functor_map_val_app, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_α, Functor.sheafPushforwardContinuousIso_hom, GrothendieckTopology.yonedaULiftEquiv_naturality, Equivalence.sheafCongr.inverse_obj_val_map, Sheaf.cartesianMonoidalCategoryFst_val, Sheaf.ΓHomEquiv_naturality_right, Sheaf.instIsLeftAdjointComposeAndSheafify, Sheaf.isSeparator, GrothendieckTopology.map_uliftYonedaEquiv, GrothendieckTopology.uliftYonedaIsoYoneda_inv_app_val_app_down, GrothendieckTopology.MayerVietorisSquare.shortComplex_f, Sheaf.isLocallyBijective_iff_isIso, instIsConstantObjSheafSheafCompose, instIsIsoFunctorOppositeSheafToPresheafToSheafCompComposeAndSheafify, sheafToPresheaf_ε, GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app, sheafificationAdjunction_counit_app_val, preservesLimitsOfShape_presheafToSheaf, GrothendieckTopology.yonedaULiftEquiv_comp, AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_comp, GrothendieckTopology.MayerVietorisSquare.instMonoSheafAddCommGrpCatFShortComplex, GrothendieckTopology.overMapPullbackComp_hom_app_val_app, hasColimitsEssentiallySmallSite, CondensedMod.LocallyConstant.instFullSheafCompHausCoherentTopologyTypeConstantSheaf, SheafOfModules.pushforward_comp_id, Equivalence.sheafCongr_inverse, GrothendieckTopology.overMapPullback_id_comp_assoc, LightCondMod.LocallyConstant.instFullSheafLightProfiniteCoherentTopologyTypeConstantSheaf, constantSheafAdj_counit_w, sheafCompose_id, CompHausLike.LocallyConstant.unit_app, Sheaf.comp_val_assoc, GrothendieckTopology.pseudofunctorOver_mapComp_hom_toNatTrans_app_val_app, yoneda'_comp, SheafOfModules.forgetToSheafModuleCat_map_val, GrothendieckTopology.yonedaULiftEquiv_symm_app_apply, PresheafOfModules.instReflectsIsomorphismsSheafOfModulesFunctorOppositeAddCommGrpCatCompSheafToSheafSheafToPresheaf, Sheaf.sheafifyCocone_ι_app_val_assoc, SheafOfModules.conjugateEquiv_pullbackId_hom, Sheaf.Hom.add_app, Sheaf.hasLimitsOfSize, Equivalence.sheafCongr.inverse_map_val_app, GrothendieckTopology.yonedaULiftEquiv_symm_map, equivYoneda'_hom_val, GrothendieckTopology.overMapPullbackCongr_hom_app_val_app, sheafToPresheaf_isRightAdjoint, instFullSheafFunctorOppositeCompSheafComposeSheafToPresheafOfFaithful, Functor.sheafPushforwardContinuousId_inv_app_val_app, GrothendieckTopology.uliftYonedaEquiv_symm_naturality_right, SheafOfModules.instPreservesFiniteLimitsSheafAddCommGrpCatToSheaf, GrothendieckTopology.W_eq_isLocal_range_sheafToPresheaf_obj, GrothendieckTopology.instIsIsoSheafAppFunctorOppositeSheafComposeNatTransPlusPlusAdjunction, GrothendieckTopology.yonedaEquiv_symm_naturality_left, GrothendieckTopology.MayerVietorisSquare.shortComplex_X₂, Sheaf.instIsRightAdjointSheafComposeOfHasWeakSheafify, SheafOfModules.pushforwardNatTrans_app_val_app_apply, LightCondMod.LocallyConstant.instFaithfulSheafLightProfiniteCoherentTopologyTypeConstantSheaf, PresheafOfModules.instReflectsFiniteLimitsSheafOfModulesSheafAddCommGrpCatToSheaf, instIsRegularEpiCategorySheafTypeOfHasSheafify, SheafOfModules.pushforward_id_comp, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_inv_app_val_app_hom_hom, sheafBotEquivalence_counitIso, GrothendieckTopology.W_eq_W_range_sheafToPresheaf_obj, Equivalence.sheafCongrPrecoherent_functor_map_val_app, sheafification_reflective, Functor.SmallCategories.instPreservesFiniteLimitsSheafSheafPullbackOfRepresentablyFlat, sheafHomSectionsEquiv_symm_apply_coe_apply, GrothendieckTopology.Point.sheafFiberCompIso_hom_app, Equivalence.sheafCongr.functor_obj_val_obj, Equivalence.sheafCongrPreregular_unitIso_inv_app_val_app, Equivalence.sheafCongr.unitIso_inv_app_val_app, GrothendieckTopology.map_yonedaEquiv, Sheaf.isLocallySurjective_iff_isIso, GrothendieckTopology.overMapPullback_assoc, Sheaf.ΓObjEquivSections_naturality, Presheaf.coherentExtensiveEquivalence_inverse_obj_val, constantSheafAdj_counit_app, sheafSectionsNatIsoEvaluation_hom_app, SheafOfModules.instIsRightAdjointPushforwardIdSheafRingCat, GrothendieckTopology.overMapPullback_id_comp, Functor.sheafAdjunctionCocontinuous_homEquiv_apply_val, GrothendieckTopology.yonedaULiftEquiv_yonedaULift_map, GrothendieckTopology.uliftYoneda_obj_val_obj, Functor.sheafPushforwardContinuousId'_hom_app_val_app, Functor.IsCoverDense.sheafIso_hom_val, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, instAdhesiveSheafOfHasPullbacksOfHasPushoutsOfHasSheafify, GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_val_app, instFullSheafFunctorOppositeSheafToPresheaf, Sheaf.isConstant_iff_isIso_counit_app, SheafOfModules.forgetToSheafModuleCat_obj_val, yoneda'_map_val, instIsLeftAdjointFunctorOppositeSheafPresheafToSheaf, GrothendieckTopology.uliftYoneda_obj_val_map_down, Sheaf.cartesianMonoidalCategoryWhiskerLeft_val, Sheaf.ΓRes_naturality, SheafOfModules.pushforwardNatIso_hom, Equivalence.sheafCongr_unitIso, GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_val_app, Sheaf.sheafifyCocone_ι_app_val, Functor.pushforwardContinuousSheafificationCompatibility_hom_app_val, Functor.IsDenseSubsite.full_sheafPushforwardContinuous, Functor.sheafPushforwardContinuousComp'_hom_app_val_app, GrothendieckTopology.map_yonedaULiftEquiv, GrothendieckTopology.overMapPullbackCongr_inv_app_val_app, Equivalence.sheafCongr.counitIso_inv_app_val_app, sheafSectionsNatIsoEvaluation_inv_app, Sheaf.IsConstant.mem_essImage, Functor.sheafAdjunctionCocontinuous_unit_app_val, SheafOfModules.pushforward_obj_val, AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_toGlued, GrothendieckTopology.Point.sheafFiberCompIso_inv_app, GrothendieckTopology.uliftYoneda_map_val_app_down, sheafCompose_obj_val, Sheaf.instHasFiniteProducts, GrothendieckTopology.yonedaEquiv_yoneda_map, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv, Condensed.discrete_obj, GrothendieckTopology.uliftYonedaEquiv_comp, sheafComposeNatTrans_fac, GrothendieckTopology.yonedaEquiv_apply, GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app_val_app, GrothendieckTopology.yonedaEquiv_symm_naturality_right, CompHausLike.LocallyConstant.adjunction_unit, Functor.IsDenseSubsite.faithful_sheafPushforwardContinuous, Presheaf.isLocallySurjective_presheafToSheaf_map_iff, SheafOfModules.pushforwardNatTrans_comp, Sheaf.instEpiAppArrowILocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, PresheafOfModules.instPreservesFiniteLimitsSheafAddCommGrpCatCompSheafOfModulesSheafificationToSheaf, instMonoSheafTypeImageι, Functor.IsCoverDense.full_sheafPushforwardContinuous, GrothendieckTopology.MayerVietorisSquare.shortComplex_exact, sheafCompose_comp
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