IsSheaf 📖 | MathDef | 906 mathmath: CategoryTheory.Functor.IsDenseSubsite.mapPreimage_map_of_fac, CategoryTheory.Sheaf.cartesianMonoidalCategoryLift_val, CategoryTheory.GrothendieckTopology.W_sheafToPresheaf_map_iff_isIso, CategoryTheory.sheafBotEquivalence_functor, SheafOfModules.pushforward_assoc, CategoryTheory.Functor.IsDenseSubsite.instIsIsoSheafAppCounitSheafAdjunctionCocontinuous, CategoryTheory.Equivalence.preregular_isSheaf_iff, SheafOfModules.instAdditivePresheafOfModulesObjFunctorOppositeRingCatIsSheafForget, CategoryTheory.Sheaf.ΓHomEquiv_naturality_left_symm, CategoryTheory.isIso_sheafificationAdjunction_counit, CategoryTheory.Sheaf.isLocallySurjective_sheafToPresheaf_map_iff, CategoryTheory.Functor.sheafPushforwardContinuousIso_inv, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_X₃, CategoryTheory.GrothendieckTopology.preservesColimitsOfShape_yoneda_of_ofArrows_inj_mem, isSheaf_of_isSheaf_comp, isSheaf_of_isTerminal, TopCat.Sheaf.interUnionPullbackCone_snd, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_apply, AlgebraicGeometry.Scheme.Modules.instFaithfulPresheafOfModulesToPresheafOfModules, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app, CategoryTheory.GrothendieckTopology.Point.skyscraperSheafFunctor_obj_obj, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_hom_app_app_down, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_map₂, AlgebraicGeometry.StructureSheaf.globalSectionsIso_inv, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_id, LightCondensed.ihomPoints_apply, Condensed.instPreservesFiniteProductsOppositeStoneanObjFunctorIsSheafCoherentTopology, CategoryTheory.Functor.sheafAdjunctionCocontinuous_homEquiv_apply_hom, CategoryTheory.eval_app, CategoryTheory.Functor.IsDenseSubsite.instIsEquivalenceSheafSheafPushforwardContinuous, CategoryTheory.Equivalence.sheafCongr_functor, CategoryTheory.GrothendieckTopology.uliftYonedaIsoYoneda_inv_app_hom_app_down, CompHausLike.LocallyConstant.functor_obj_obj, coherentExtensiveEquivalence_inverse_map_hom, AlgebraicGeometry.StructureSheaf.comap_id, PresheafOfModules.instIsLocallySurjectiveToSheafify, CategoryTheory.Equivalence.sheafCongr.inverse_obj_obj_map, condensedSetToTopCat_obj_carrier, AlgebraicGeometry.StructureSheaf.const_mul_rev, LightCondensed.instPreservesFiniteProductsOppositeLightProfiniteObjFunctorIsSheafCoherentTopology, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_inv_app_hom_app, CategoryTheory.Equivalence.sheafCongr.unitIso_inv_app_hom_app, CategoryTheory.Sheaf.instIsLocallySurjectiveAppArrowILocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, Condensed.hom_ext_iff, CategoryTheory.ran_isSheaf_of_isCocontinuous, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_apply, AlgebraicGeometry.StructureSheaf.comap_comp, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_app_apply, SheafOfModules.pushforwardNatIso_inv, PresheafOfModules.Sheafify.add_smul, CategoryTheory.Functor.IsCoverDense.Types.sheafIso_inv_hom, CategoryTheory.GrothendieckTopology.W_eq_inverseImage_isomorphisms, AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf_map, CategoryTheory.Sheaf.toImage_ι_assoc, CategoryTheory.GrothendieckTopology.overMapPullback_comp_id, AlgebraicGeometry.StructureSheaf.const_self, LightCondensed.ihomPoints_symm_comp, CategoryTheory.Functor.sheafPullbackConstruction.instPreservesFiniteLimitsSheafSheafPullback, CondensedSet.topCatAdjunctionUnit_hom_app_apply, AlgebraicGeometry.Proj.pow_apply, AlgebraicGeometry.Spec_presheaf, CategoryTheory.Sheaf.isPullback_χ_truth, CategoryTheory.Functor.sheafPushforwardContinuous_map_hom_app, LightCondSet.continuous_coinducingCoprod, LightCondSet.epi_iff_locallySurjective_on_lightProfinite, CategoryTheory.Sheaf.classifier_χ, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap_apply, CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_inv_app_app, CategoryTheory.Equivalence.sheafCongr.functor_obj_obj_map, isSheaf_iff_isLimit_coverage, CondensedMod.isDiscrete_tfae, SheafOfModules.evaluationPreservesLimit, PresheafOfModules.homEquivOfIsLocallyBijective_symm_apply, CategoryTheory.instFullSheafSheafComposeOfFaithful, CategoryTheory.Equivalence.precoherent_isSheaf_iff_of_essentiallySmall, SheafOfModules.forgetToSheafModuleCat_map_hom, AlgebraicGeometry.Proj.mul_apply, AlgebraicGeometry.StructureSheaf.comap_id', CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff, CondensedSet.hom_naturality_apply, CompHausLike.LocallyConstant.adjunction_counit, CategoryTheory.typeEquiv_functor_map_hom_app, CategoryTheory.sheafificationNatIso_hom_app_hom, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_symm_assoc, CompHausLike.LocallyConstantModule.functor_obj_obj_map_hom_apply_apply, SheafOfModules.inl_freeSumIso_hom, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_carrier, CategoryTheory.GrothendieckTopology.instFaithfulSheafTypeUliftYoneda, CategoryTheory.Functor.op_comp_isSheaf_of_isSheaf, AlgebraicGeometry.StructureSheaf.const_add, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_X₁, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_sub_apply, CondensedMod.LocallyConstant.instFullModuleCatSheafCompHausCoherentTopologyConstantSheaf, Condensed.discrete_map, PresheafOfModules.toSheafify_app_apply', CategoryTheory.Functor.IsCoverDense.Types.sheafIso_hom_hom, CategoryTheory.GrothendieckTopology.overMapPullbackId_inv_app_hom_app, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_inv_app_app, CategoryTheory.GrothendieckTopology.Point.instPreservesFiniteLimitsSheafSheafFiberOfLocallySmallOfHasFiniteLimitsOfAB5OfSize, AlgebraicGeometry.structureSheafInType.mul_apply, CategoryTheory.constantCommuteCompose_hom_app_val, AlgebraicGeometry.StructureSheaf.exists_const, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_inv_toNatTrans_app_hom_app, TopCat.Sheaf.pushforward_map, isSheaf_of_iso_iff, CategoryTheory.Sheaf.isLocallySurjective_comp, CategoryTheory.Functor.IsCoverDense.isoOver_hom_app, AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.structurePresheafInCommRing_obj_carrier, SheafOfModules.inr_freeSumIso_hom, smoothSheaf.ι_evalHom_apply, CategoryTheory.Sheaf.adjunction_unit_app_hom, Condensed.instPreservesFiniteProductsOppositeProfiniteObjFunctorIsSheafCoherentTopology, CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_app_app, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap, CategoryTheory.Equivalence.sheafCongrPrecoherent_functor_obj_obj_obj, CategoryTheory.Equivalence.instPreservesFiniteLimitsFunctorOppositeSheafTransportAndSheafify, CategoryTheory.Equivalence.sheafCongrPreregular_functor_obj_obj_obj, isSheaf_iff_preservesFiniteProducts, SheafOfModules.instIsRightAdjointPushforwardCompSheafRingCatMapSheafPushforwardContinuous, AlgebraicGeometry.Scheme.LocalRepresentability.isRepresentable, CategoryTheory.Sheaf.isLocallySurjective_iff_epi, AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf', TopCat.Sheaf.interUnionPullbackCone_fst, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app, CategoryTheory.Functor.sheafPushforwardContinuousNatTrans_app_hom, SheafOfModules.evaluationPreservesLimitsOfShape, LightCondensed.discrete_map, AlgebraicGeometry.Scheme.LocalRepresentability.instIsLocallySurjectiveHomYonedaGluedToSheafOfIsLocallySurjectiveZariskiTopologyDescFunctorOppositeType, CategoryTheory.Sheaf.cartesianMonoidalCategoryLift_hom, CategoryTheory.Sheaf.isPullback_square_op_map_yoneda_presheafToSheaf_yoneda_iff, CategoryTheory.sheafToPresheaf_μ, isSheaf_iff_preservesFiniteProducts_and_equalizerCondition, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_π_assoc, AlgebraicGeometry.Proj.one_apply, Condensed.epi_iff_surjective_on_stonean, isLocallyInjective_presheafToSheaf_map_iff, CategoryTheory.Functor.sheafPushforwardContinuousId'_hom_app_hom_app, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality, AlgebraicGeometry.StructureSheaf.to_basicOpen_epi, CategoryTheory.instEpiSheafTypeToImage, CategoryTheory.Functor.sheafAdjunctionCocontinuous_counit_app_val, isSheaf_coherent_of_hasPullbacks_of_comp, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.biprodAddEquiv_symm_biprodIsoProd_hom_toBiprod_apply, CategoryTheory.GrothendieckTopology.instFullSheafTypeYoneda, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjObjIso.inv_π, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_map, CategoryTheory.Sheaf.mem_essImage_of_isConstant, CategoryTheory.GrothendieckTopology.overMapPullbackComp_hom_app_hom_app, CategoryTheory.hasLimitsEssentiallySmallSite, CategoryTheory.GrothendieckTopology.overMapPullbackId_hom_app_hom_app, CategoryTheory.Functor.IsCoverDense.Types.appHom_valid_glue, PresheafOfModules.toPresheaf_map_toSheafify, CategoryTheory.Equivalence.sheafCongr.functor_obj_obj_obj, CategoryTheory.Adjunction.sheafPushforwardContinuous_unit_app_hom_app, TopCat.Sheaf.id_app, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_hom_app_hom_app, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.isPushout, AlgebraicGeometry.StructureSheaf.comap_const, Condensed.id_hom, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality', PresheafOfModules.Sheafify.map_smul_eq, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.sheafCondition_of_sheaf, CategoryTheory.Sheaf.instHasColimitsOfShape, AlgebraicGeometry.Proj.sub_apply, CategoryTheory.Functor.sheafPullbackConstruction.instIsRightAdjointSheafSheafPushforwardContinuousOfHasWeakSheafify, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_comp_assoc, CategoryTheory.Functor.IsCoverDense.Types.pushforwardFamily_def, Condensed.isSheafStonean, PresheafOfModules.instFullSheafOfModulesCompObjFunctorOppositeRingCatIsSheafForgetRestrictScalars, CategoryTheory.Functor.OneHypercoverDenseData.essSurj, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_map, smoothSheaf.ι_evalHom_assoc, CategoryTheory.Functor.IsCoverDense.sheafHom_eq, AlgebraicGeometry.StructureSheaf.comap_apply, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj_mapPreimage_condition, CategoryTheory.Sheaf.instIsIsoAppCounitConstantSheafAdjOfFaithfulOfFullConstantSheafOfIsConstant, AlgebraicGeometry.isSheaf_propQCTopology_iff, SheafOfModules.evaluationPreservesLimitsOfSize, CategoryTheory.Functor.sheafAdjunctionCocontinuous_unit_app_hom, CategoryTheory.Functor.IsCoverDense.sheafIso_hom_hom, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_symm, CategoryTheory.Sheaf.terminal_obj, CategoryTheory.Sheaf.imageι_hom, CategoryTheory.HasSheafify.isLeftExact, isSheaf_yoneda', LightCondensed.comp_hom, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_obj_obj, CategoryTheory.GrothendieckTopology.Point.Hom.sheafFiber_comp_assoc, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality', AlgebraicGeometry.StructureSheaf.toPushforwardStalkAlgHom_apply, CategoryTheory.GrothendieckTopology.preservesSheafification_iff_of_adjunctions, AlgebraicGeometry.Scheme.ΓSpecIso_inv, CategoryTheory.Functor.IsCoverDense.faithful_sheafPushforwardContinuous, CategoryTheory.Sheaf.tensorProd_isSheaf, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_restriction_assoc, SheafOfModules.isSheaf, CategoryTheory.instIsIsoFunctorOppositeSheafSheafComposeNatTrans, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjObjIso.inv_π_assoc, CategoryTheory.Sheaf.toImage_ι, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app', CategoryTheory.sheafBotEquivalence_inverse_map_hom, CategoryTheory.instPreservesFiniteColimitsSheafExtensiveTopologyFunctorOppositeSheafToPresheafOfPreadditiveOfHasFiniteColimits, LightCondensed.ofSheafLightProfinite_obj, isSheaf_coherent_iff_regular_and_extensive, CategoryTheory.ObjectProperty.IsConservativeFamilyOfPoints.jointlyReflectMonomorphisms, CategoryTheory.Functor.IsCoverDense.sheafHom_restrict_eq, CategoryTheory.typeEquiv_inverse_obj, CategoryTheory.GrothendieckTopology.Point.isSheaf_skyscraperPresheaf, coherentExtensiveEquivalence_unitIso_hom_app_hom_app, CategoryTheory.Sheaf.epi_of_isLocallySurjective', CategoryTheory.GrothendieckTopology.W_iff_isIso_map_of_adjunction, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_shortExact, CategoryTheory.GrothendieckTopology.W_isInvertedBy_whiskeringRight_presheafToSheaf, CategoryTheory.Sheaf.ΓHomEquiv_naturality_left, CategoryTheory.Sheaf.classifier_truth, CategoryTheory.Sheaf.classifier_Ω₀, SheafOfModules.pushforwardComp_inv_app_val_app, CategoryTheory.Sheaf.instHasSubobjectClassifierTypeOfEssentiallySmall, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp_hom_app, isSheaf_coherent_of_projective_comp, CategoryTheory.Functor.IsCoverDense.sheafIso_inv_hom, CategoryTheory.Sheaf.isConstant_iff_forget, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjObjIso.hom_map_assoc, CategoryTheory.Functor.OneHypercoverDenseData.isEquivalence, isSheaf_iff_extensiveSheaf_of_projective, CategoryTheory.instHasImagesSheafType, CategoryTheory.Sheaf.hasFilteredColimitsOfSize, CategoryTheory.plusPlusSheaf_map_hom, TopCat.Sheaf.extend_hom_app, CategoryTheory.presheaf_mono_of_mono, CategoryTheory.instPreservesFiniteLimitsFunctorOppositeSheafReflectorSheafToPresheaf, CategoryTheory.GrothendieckTopology.instFullSheafTypeUliftYoneda, PresheafOfModules.toSheaf_map_sheafificationAdjunction_counit_app, SheafOfModules.pushforwardNatTrans_id, topCatToSheafCompHausLike_map_hom_app, SheafOfModules.restrictScalars_obj_val, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_hom_app_hom_app, instPreservesFiniteCoproductsSheafTypeUliftYonedaOfPreservesFiniteProductsOppositeObjFunctorIsSheaf, SheafOfModules.instSmallElemForallObjCompModuleCatCarrierOppositeRingCatObjFunctorIsSheafPresheafOfModulesForgetEvaluationForgetLinearMapIdCarrierSections, CategoryTheory.Functor.sheafPushforwardContinuousCompSheafToPresheafIso_inv_app_app, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_left, AlgebraicGeometry.StructureSheaf.isLocalizedModule_toPushforwardStalkAlgHom_aux, coherentExtensiveEquivalence_functor_obj_obj, CategoryTheory.GrothendieckTopology.W_adj_unit_app, CategoryTheory.Sheaf.cartesianMonoidalCategorySnd_hom, CategoryTheory.Sheaf.instHasFunctorialFactorizationLocallySurjectiveLocallyInjective, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj_condition_assoc, AlgebraicGeometry.StructureSheaf.algebraMap_self_map, isSheaf_comp_of_isSheaf, CategoryTheory.Sheaf.isLocallySurjective_iff_epi', SheafOfModules.instAdditiveSheafAddCommGrpCatToSheaf, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjObjIso_inv_naturality, CondensedMod.epi_iff_surjective_on_stonean, CategoryTheory.typeEquiv_unitIso_hom_app, instPreservesFiniteProductsOppositeObjFunctorIsSheafCoherentTopology, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_inv_app_hom_app, CategoryTheory.regularTopology.isSheaf_of_projective, AlgebraicGeometry.Spec.map_appLE, IsSheaf.of_le, LightCondMod.LocallyConstant.instFullModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf, CategoryTheory.Sheaf.cartesianMonoidalCategorySnd_val, CategoryTheory.Sheaf.χ_hom, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_inv_app_hom_app_hom_hom, CategoryTheory.Sheaf.classifier_Ω, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_right, CategoryTheory.Sheaf.instMonoAppArrowPLocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, CompHausLike.LocallyConstant.counit_app_hom_app, CategoryTheory.Functor.sheafAdjunctionCocontinuous_counit_app_hom, CategoryTheory.instMonoFunctorOppositeHomFullSubcategoryIsSheafOfHasWeakSheafifyOfSheaf, CondensedSet.epi_iff_surjective_on_stonean, coherentExtensiveEquivalence_inverse_obj_obj, CategoryTheory.Equivalence.sheafCongrPrecoherent_counitIso_hom_app_hom_app, PresheafOfModules.instReflectsIsomorphismsSheafOfModulesSheafAddCommGrpCatToSheaf_1, AlgebraicGeometry.StructureSheaf.IsLocalization.to_basicOpen, CategoryTheory.SheafOfTypes.finitary_extensive, CategoryTheory.Sheaf.instIsGrothendieckAbelian, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_assoc, TopCat.Sheaf.objSupIsoProdEqLocus_hom_fst, CategoryTheory.Sheaf.toImage_hom, CategoryTheory.GrothendieckTopology.Point.skyscraperSheafAdjunction_homEquiv_symm_apply, CategoryTheory.Sheaf.natTransΓRes_app, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjObjIso.hom_mapPreimage, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality', CategoryTheory.Sheaf.image_obj, CategoryTheory.equivYoneda'_hom_hom, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_uliftYoneda_map, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap_assoc, CategoryTheory.Presieve.FamilyOfElements.Compatible.functorPushforward, CategoryTheory.Functor.IsCoverDense.presheafIso_hom_app, SheafOfModules.Presentation.quasicoherentData_presentation, TopCat.Presheaf.app_surjective_of_injective_of_locally_surjective, AlgebraicGeometry.StructureSheaf.const_mul_cancel, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.isSheaf, CategoryTheory.Functor.IsDenseSubsite.sheafifyHomEquivOfIsEquivalence_naturality_left, CategoryTheory.typeEquiv_counitIso_hom_app_hom_app, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.mk₀_f_comp_biprodAddEquiv_symm_biprodIsoProd_hom, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_comp_map, isSheaf_iff_of_isGeneratedByOneHypercovers, isSheaf_iff_isSheaf', SheafOfModules.pushforwardCongr_hom_app_val_app, CategoryTheory.GrothendieckTopology.instIsIsoFunctorOppositeSheafSheafComposeNatTransPlusPlusAdjunction, CategoryTheory.GrothendieckTopology.overMapPullback_assoc_assoc, CategoryTheory.Sheaf.isSheaf_of_isLimit, CategoryTheory.Equivalence.sheafCongr.unitIso_hom_app_hom_app, CategoryTheory.Sheaf.cartesianMonoidalCategoryWhiskerLeft_hom, AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, CategoryTheory.Functor.sheafPushforwardContinuousId_hom_app_hom_app, CategoryTheory.Sheaf.instHasFiniteColimits, CategoryTheory.sheafToPresheaf_δ, CategoryTheory.Sheaf.Hom.mono_iff_presheaf_mono, TopCat.Sheaf.existsUnique_gluing, CategoryTheory.typeEquiv_unitIso_inv_app, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_inv_app_app, CategoryTheory.isRegularEpiCategory_sheaf, CategoryTheory.GrothendieckTopology.uliftYonedaCompSheafToPresheaf_inv_app_app, CategoryTheory.GrothendieckTopology.Point.Hom.sheafFiber_comp, PresheafOfModules.sheafification_map, CategoryTheory.toPresheafToSheafCompComposeAndSheafify_app, TopCat.Presheaf.stalk_mono_of_mono, TopCat.Presheaf.app_surjective_of_stalkFunctor_map_bijective, TopCat.Sheaf.interUnionPullbackConeLift_right, CategoryTheory.GrothendieckTopology.uliftYonedaCompSheafToPresheaf_hom_app_app, CompHausLike.LocallyConstant.functor_map_hom, CategoryTheory.instPreservesFiniteLimitsFunctorOppositeSheafLeftAdjointSheafToPresheaf, SheafOfModules.pullback_comp_id, CategoryTheory.GrothendieckTopology.map_yonedaEquiv', CategoryTheory.sheafBotEquivalence_unitIso, AlgebraicGeometry.StructureSheaf.const_one, AlgebraicGeometry.StructureSheaf.globalSectionsIso_hom, SheafOfModules.instPreservesFiniteLimitsFunctorOppositeAddCommGrpCatCompSheafToSheafSheafToPresheaf, CategoryTheory.Functor.IsDenseSubsite.sheafifyHomEquivOfIsEquivalence_naturality_right, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_zero_apply, Condensed.comp_val, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app_assoc, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_add_apply, isSheaf_coherent_of_projective_of_comp, CondensedMod.hom_naturality_apply, PresheafOfModules.toSheaf_map_sheafificationHomEquiv_symm, TopCat.toSheafCompHausLike_obj_obj, AlgebraicGeometry.StructureSheaf.smul_const, CategoryTheory.GrothendieckTopology.Point.skyscraperSheafFunctor_map_hom, CategoryTheory.isSheaf_pointwiseColimit, AlgebraicGeometry.ΓSpec.unop_locallyRingedSpaceAdjunction_counit_app', CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_presheafObjObjIso_hom, TopCat.Presheaf.app_bijective_of_stalkFunctor_map_bijective, topCatToSheafCompHausLike_obj, Condensed.epi_iff_locallySurjective_on_compHaus, CategoryTheory.Functor.op_comp_isSheaf_of_types, CategoryTheory.Sheaf.adjunction_counit_app_val, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_hom_app, CategoryTheory.SheafOfTypes.adhesive, SheafOfModules.id_val, LightCondensed.isLocallySurjective_iff_locallySurjective_on_lightProfinite, CategoryTheory.GrothendieckTopology.yonedaEquiv_comp, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.instEpiSheafAddCommGrpCatGShortComplex, AlgebraicGeometry.StructureSheaf.isLocalizedModule_toPushforwardStalkAlgHom, PresheafOfModules.instIsIsoFunctorSheafOfModulesCounitSheafificationAdjunction, CategoryTheory.Equivalence.sheafCongr.inverse_obj_obj_obj, CategoryTheory.Equivalence.sheafCongrPreregular_inverse_obj_obj_obj, LightCondensed.forget_map_hom_app, CategoryTheory.Sheaf.isSeparating, CategoryTheory.Sheaf.isGrothendieckAbelian_of_essentiallySmall, CategoryTheory.Functor.IsCoverDense.Types.appHom_restrict, CategoryTheory.Sheaf.cond, CategoryTheory.ObjectProperty.IsConservativeFamilyOfPoints.jointlyReflectIsomorphisms_type, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_map, CategoryTheory.Functor.IsDenseSubsite.sheafEquiv_inverse, TopCat.Sheaf.existsUnique_gluing', CategoryTheory.Sheaf.ΓObjEquivSections_naturality_symm, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjObjIso.hom_mapPreimage_assoc, CategoryTheory.Sheaf.mono_of_isLocallyInjective, CategoryTheory.Sheaf.isLocallyInjective_iff_injective, Topology.IsUpperSet.isSheaf_of_isRightKanExtension, CategoryTheory.Sheaf.classifier_χ₀, AlgebraicGeometry.StructureSheaf.const_zero, CategoryTheory.Functor.sheafPushforwardContinuous_obj_obj_obj, CategoryTheory.regularTopology.equalizerCondition_iff_isSheaf, CategoryTheory.Sheaf.ΓRes_map_assoc, CategoryTheory.Functor.IsCoverDense.Types.pushforwardFamily_compatible, TopCat.Sheaf.comp_app, CategoryTheory.Sheaf.ab5ofSize, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_app_apply, CategoryTheory.Sheaf.ΓObjEquivHom_naturality_symm, TopCat.Sheaf.IsFlasque.epi_of_shortExact, LightCondensed.forget_obj_obj_map, SheafOfModules.toSheaf_obj_obj, SheafOfModules.pushforwardCongr_inv_app_val_app, CategoryTheory.instPreservesFiniteLimitsFunctorOppositeSheafPresheafToSheaf, CategoryTheory.Functor.IsCoverDense.Types.appIso_inv, PresheafOfModules.Sheafify.smul_add, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_presheafObjObjIso_hom_assoc, CategoryTheory.Sheaf.hasSeparator, CategoryTheory.instFaithfulSheafSheafCompose, CategoryTheory.GrothendieckTopology.Point.instIsMonoidalFunctorOppositeHomPresheafToSheafCompSheafFiberIso, SheafOfModules.conjugateEquiv_pullbackComp_inv, AlgebraicGeometry.Spec.sheafedSpaceMap_hom_c_app, IsSheaf.hom, CategoryTheory.Equivalence.sheafCongrPreregular_inverse_map_hom_app, CategoryTheory.Sheaf.Hom.mono_of_presheaf_mono, CategoryTheory.Sheaf.instHasExactColimitsOfShapeOfHasFiniteLimitsOfPreservesColimitsOfShapeFunctorOppositeSheafToPresheaf, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_app_app, SheafOfModules.inl_freeSumIso_hom_assoc, CategoryTheory.GrothendieckTopology.sheafToPresheaf_map_sheafComposeNatTrans_eq_sheafifyCompIso_inv, CategoryTheory.plusPlusSheaf_obj_obj, isSheaf_iff_isLimit, CategoryTheory.sheafComposeNatTrans_app_uniq, coherentExtensiveEquivalence_functor_map_hom, CategoryTheory.Sheaf.instHasFiniteLimits, SheafOfModules.pushforwardPushforwardAdj_unit_app_val_app, CategoryTheory.Equivalence.sheafCongrPreregular_inverse_obj_obj_map, CategoryTheory.instFinitaryExtensiveSheafOfHasPullbacksOfHasSheafify, CompHausLike.LocallyConstant.adjunction_left_triangle, AlgebraicGeometry.StructureSheaf.algebraMap_obj_top_bijective, CategoryTheory.extensiveTopology.isLocallySurjective_iff, TopCat.Sheaf.pushforward_obj_val, isSheaf_iff_multiequalizer, SheafOfModules.fullyFaithfulForget_preimage_val, CategoryTheory.Sheaf.isLocallyInjective_forget, PresheafOfModules.instReflectsIsomorphismsSheafOfModulesSheafAddCommGrpCatToSheaf, SheafOfModules.pullback_id_comp, TopCat.Sheaf.sections_exact_of_left_exact, CategoryTheory.Sheaf.truth_hom, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_assoc, SheafOfModules.restrictScalars_map_val, PresheafOfModules.isSheaf_of_isLimit, CategoryTheory.instReflectsIsomorphismsSheafSheafCompose, CategoryTheory.sheafificationNatIso_inv_app_hom, AlgebraicGeometry.Scheme.LocalRepresentability.yoneda_toGlued_yonedaGluedToSheaf_assoc, CategoryTheory.Functor.sheafPushforwardCocontinuousCompSheafToPresheafIso_inv, CategoryTheory.Sheaf.coneΓ_pt, AlgebraicGeometry.isSheaf_fpqcTopology_continuousMapPresheafAb, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_nsmul_apply, CategoryTheory.instPreservesColimitsOfShapeSheafExtensiveTopologyFunctorOppositeSheafToPresheafOfPreservesFiniteProductsColim, CondensedSet.continuous_coinducingCoprod, AlgebraicGeometry.Proj.zero_apply, CategoryTheory.Functor.IsCoverDense.Types.presheafIso_inv_app, CategoryTheory.GrothendieckTopology.overMapPullbackComp_inv_app_hom_app, CategoryTheory.GrothendieckTopology.uliftYoneda_obj_obj_map_down, CategoryTheory.Sheaf.isConstant_iff_isIso_counit_app', CategoryTheory.SheafOfTypes.balanced, TopCat.Sheaf.objSupIsoProdEqLocus_inv_snd, AlgebraicGeometry.StructureSheaf.const_algebraMap, CategoryTheory.preservesFiniteLimits_presheafToSheaf, CategoryTheory.GrothendieckTopology.sheafify_isSheaf, CategoryTheory.typeEquiv_counitIso_inv_app_hom_app, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_neg_apply, SheafOfModules.inr_freeSumIso_hom_assoc, CategoryTheory.typeEquiv_inverse_map, isSheaf_iff_multifork, SheafOfModules.pushforward_map_val, CategoryTheory.sheafToPresheafCompYonedaCompWhiskeringLeftSheafToPresheaf_hom_app_app_hom, CategoryTheory.GrothendieckTopology.Point.instIsLeftAdjointSheafSheafFiber, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_eq_eqToIso, CategoryTheory.Functor.sheafPushforwardCocontinuousCompSheafToPresheafIso_hom, CategoryTheory.Sheaf.cartesianMonoidalCategoryFst_hom, SheafOfModules.pushforwardComp_hom_app_val_app, CondensedMod.LocallyConstant.instFaithfulSheafCompHausCoherentTopologyTypeConstantSheaf, AlgebraicGeometry.Scheme.LocalRepresentability.glueData_V, SheafOfModules.unit_val, CategoryTheory.GrothendieckTopology.preservesSheafification_iff_of_adjunctions_of_hasSheafCompose, LightCondSet.topCatAdjunctionUnit_hom_app_apply, SheafOfModules.Presentation.map_relations_I, CategoryTheory.Equivalence.sheafCongrPreregular_functor_map_hom_app, CategoryTheory.Sheaf.adjunction_unit_app_val, TopCat.Presheaf.app_injective_of_stalkFunctor_map_injective, SheafOfModules.instIsLeftAdjointOverOverRingCatPushforwardIdSheafOver, TopCat.Sheaf.interUnionPullbackConeLift_left, CategoryTheory.GrothendieckTopology.uliftYoneda_obj_obj_obj, instPreservesColimitSheafTypeYonedaOfPreservesLimitOppositeOpObjFunctorIsSheaf, isSheaf_iff_preservesFiniteProducts_of_projective, instPreservesColimitsOfShapeSheafTypeYonedaOfPreservesLimitsOfShapeOppositeObjFunctorIsSheaf, CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_inv_app_hom_app, SheafOfModules.Presentation.mapRelations_mapGenerators, LightCondensed.hom_ext_iff, CategoryTheory.sheafificationIso_inv_hom, AlgebraicGeometry.Scheme.GlueData.sheafValGluedMk_val, CategoryTheory.Equivalence.sheafCongr_counitIso, PresheafOfModules.instFaithfulSheafOfModulesCompObjFunctorOppositeRingCatIsSheafForgetRestrictScalars, CategoryTheory.GrothendieckTopology.uliftYonedaIsoYoneda_hom_app_hom_app, SheafOfModules.relationsOfIsCokernelFree_I, AlgebraicGeometry.Scheme.LocalRepresentability.instIsIsoSheafZariskiTopologyTypeYonedaGluedToSheaf, AlgebraicGeometry.Scheme.LocalRepresentability.glueData_f, AlgebraicGeometry.structureSheafInType.add_apply, CategoryTheory.Functor.sheafPushforwardContinuous_obj_obj_map, LightCondensed.underlying_obj, AlgebraicGeometry.Scheme.LocalRepresentability.glueData_t', CategoryTheory.Functor.toSheafify_pullbackSheafificationCompatibility, CategoryTheory.Sheaf.Ω_obj, CategoryTheory.Sheaf.ΓHomEquiv_naturality_right_symm, CategoryTheory.Functor.IsCoverDense.Types.naturality_apply, CategoryTheory.GrothendieckTopology.preservesLimitsOfSize_yoneda, CategoryTheory.Sheaf.coneΓ_π_app, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj_condition, TopCat.subsheafToTypes_obj, CategoryTheory.Sheaf.ΓObjEquivHom_naturality, CategoryTheory.Sheaf.ΓRes_map, SheafOfModules.pushforwardCongr_symm, CategoryTheory.GrothendieckTopology.Point.sheafFiberComapIso_hom_app, LightCondSet.hom_naturality_apply, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv', SheafOfModules.add_val, AlgebraicGeometry.Scheme.LocalRepresentability.yoneda_toGlued_yonedaGluedToSheaf, CategoryTheory.isSheaf_iff_isSheaf_of_type, CategoryTheory.Sheaf.cartesianMonoidalCategoryWhiskerRight_val, AlgebraicGeometry.Proj.add_apply, PresheafOfModules.sheafifyMap_val, SheafOfModules.instFaithfulSheafAddCommGrpCatToSheaf, CategoryTheory.ObjectProperty.IsConservativeFamilyOfPoints.jointlyFaithful, CondensedSet.isDiscrete_tfae, CategoryTheory.Equivalence.precoherent_isSheaf_iff, isSheaf_bot, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isModule_smul_apply, AlgebraicGeometry.stalkMap_toStalk_apply, PresheafOfModules.comp_toPresheaf_map_sheafifyHomEquiv'_symm_hom, CategoryTheory.Equivalence.sheafCongr.counitIso_inv_app_hom_app, CategoryTheory.sheafBotEquivalence_inverse_obj_obj, CategoryTheory.Pseudofunctor.IsPrestack.isSheaf, TopCat.Sheaf.IsFlasque.structured_arrows_elements_sheaf_chains_bounded, CategoryTheory.Sheaf.instHasLimitsOfShape, CategoryTheory.Functor.IsCoverDense.iso_of_restrict_iso, CategoryTheory.GrothendieckTopology.overMapPullback_comp_id_assoc, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_g, CategoryTheory.plusPlusSheaf_preservesZeroMorphisms, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.isPushoutAddCommGrpFreeSheaf, CategoryTheory.coherentTopology.epi_π_app_zero_of_epi, CategoryTheory.Sheaf.instIsLocallyInjectiveAppArrowPLocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, CategoryTheory.Functor.IsCoverDense.presheafIso_inv, CategoryTheory.Sheaf.isConstant_iff_mem_essImage, CategoryTheory.Sheaf.instPreservesFiniteLimitsFunctorOppositeSheafToPresheafOfHasFiniteLimits, CategoryTheory.sheafCompose_map_hom, AlgebraicGeometry.StructureSheaf.comapₗ_const, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality, CategoryTheory.sheafificationAdjunction_unit_app, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_comp_map_assoc, CategoryTheory.sheafificationIso_hom_hom, AlgebraicGeometry.StructureSheaf.algebraMap_germ_assoc, AlgebraicGeometry.StructureSheaf.res_apply, LightCondensed.equalizerCondition, AlgebraicGeometry.Scheme.LocalRepresentability.instIsLocallyInjectiveHomYonedaGluedToSheaf, CategoryTheory.instFaithfulSheafFunctorOppositeCompSheafComposeSheafToPresheaf, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_zsmul_apply, CategoryTheory.GrothendieckTopology.Point.Hom.sheafFiber_id, CategoryTheory.instIsIsoFunctorOppositeHomFullSubcategoryIsSheafAppSheafCounitSheafificationAdjunction, CategoryTheory.Sheaf.instHasExactLimitsOfShapeOfHasFiniteColimitsOfPreservesFiniteColimitsFunctorOppositeSheafToPresheaf, LightCondMod.hom_naturality_apply, CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv', SheafOfModules.unitToPushforwardObjUnit_val_app_apply, SheafOfModules.pullback_assoc, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_apply, CategoryTheory.CompatiblePreserving.apply_map, instPreservesColimitSheafTypeYonedaOfPreservesLimitOppositeOpObjFunctorIsSheaf_1, SheafOfModules.forget_map, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_hom_app_hom_app_apply, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_hom_app_app_down, isSheaf_functorEnrichedHom, CategoryTheory.presheafToSheaf_additive, LightCondensed.ihomPoints_symm_apply, LightCondensed.discrete_obj, SheafOfModules.forgetPreservesLimitsOfSize, isSheaf_iff_isSheaf_comp, CategoryTheory.Sheaf.Hom.epi_of_presheaf_epi, CategoryTheory.Sheaf.isLocallyInjective_sheafToPresheaf_map_iff, SheafOfModules.instFaithfulPresheafOfModulesObjFunctorOppositeRingCatIsSheafForget, CategoryTheory.Functor.IsCoverDense.sheafCoyonedaHom_app, CategoryTheory.Functor.sheafPullbackConstruction.preservesFiniteLimits, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_left, instPreservesColimitSheafTypeUliftYonedaOfPreservesLimitOppositeOpObjFunctorIsSheaf, AlgebraicGeometry.StructureSheaf.algebraMap_germ, CategoryTheory.Sheaf.isConstant_iff_of_equivalence, CategoryTheory.Sheaf.hasExactColimitsOfShape, instPreservesLimitsOfShapeSheafTypeUliftYoneda, CategoryTheory.presheafToSheafCompComposeAndSheafifyIso_inv_app, CategoryTheory.Sheaf.instHasFiniteCoproducts, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_restriction, LightCondMod.LocallyConstant.instFaithfulModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf, CategoryTheory.GrothendieckTopology.instFaithfulSheafTypeYoneda, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_comp, TopCat.Sheaf.objSupIsoProdEqLocus_hom_snd, CategoryTheory.Sheaf.instIsLocallySurjectiveHomMapTypeSheafComposeForget, CategoryTheory.Functor.IsDenseSubsite.sheafifyHomEquivOfIsEquivalence_naturality_right_assoc, AlgebraicGeometry.StructureSheaf.const_mul_cancel', CategoryTheory.Functor.IsCoverDense.homOver_app, TopCat.Sheaf.objSupIsoProdEqLocus_inv_eq_iff, AlgebraicGeometry.instIsScalarTowerObjOppositeOpensCarrierTopObjFunctorTypeIsSheafGrothendieckTopologyStructureSheafInType, CategoryTheory.Sheaf.cohomologyFunctor_obj, lightCondSetToTopCat_obj_carrier, CategoryTheory.Sheaf.mono_of_injective, CategoryTheory.GrothendieckTopology.instIsLocalizationFunctorOppositeSheafPresheafToSheafW, SheafOfModules.Finite.forgetPreservesFiniteLimits, AlgebraicGeometry.Proj.sheafedSpaceMap_hom_c_app_hom_apply_coe, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, CategoryTheory.Sheaf.instIsClosedUnderLimitsOfShapeFunctorOppositeIsSheaf, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_app_app, SheafOfModules.forget_obj, CategoryTheory.Functor.IsCoverDense.Types.presheafIso_hom_app, CategoryTheory.Equivalence.sheafCongrPrecoherent_functor_obj_obj_map, CategoryTheory.Equivalence.sheafCongrPrecoherent_inverse_obj_obj_obj, CategoryTheory.Functor.sheafPushforwardContinuousCompSheafToPresheafIso_hom_app_app, LightCondMod.epi_iff_locallySurjective_on_lightProfinite, CategoryTheory.GrothendieckTopology.HasSheafCompose.isSheaf, SheafOfModules.comp_val_assoc, CategoryTheory.Equivalence.sheafCongrPrecoherent_inverse_obj_obj_map, CategoryTheory.Sheaf.epi_of_isLocallySurjective, LightCondensed.ihom_map_val_app, CategoryTheory.sheafToPresheaf_η, TopCat.Presheaf.app_isIso_of_stalkFunctor_map_iso, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_inv_app_hom_app, CompHausLike.LocallyConstant.instIsIsoFunctorTypeUnitSheafCoherentTopologyAdjunction, CategoryTheory.Functor.IsDenseSubsite.mapPreimage_of_eq, AlgebraicGeometry.StructureSheaf.toOpenₗ_top_bijective, AlgebraicGeometry.StructureSheaf.comap_id_eq_map, SheafOfModules.toSheaf_map_hom, CategoryTheory.ObjectProperty.IsConservativeFamilyOfPoints.jointlyReflectIsomorphisms, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj_hom_ext_iff, CategoryTheory.Sheaf.instHasColimitsOfSize, SheafOfModules.pushforwardNatTrans_app_val_app, CategoryTheory.GrothendieckTopology.W_iff, PresheafOfModules.Sheafify.one_smul, CategoryTheory.GrothendieckTopology.W_eq_inverseImage_isomorphisms_of_adjunction, CondensedMod.epi_iff_locallySurjective_on_compHaus, CategoryTheory.Equivalence.sheafCongrPreregular_unitIso_inv_app_hom_app, CategoryTheory.sheafOver_obj, AlgebraicGeometry.ΓSpec.toSpecΓ_of, CategoryTheory.Functor.sheafPushforwardContinuousIso_hom, CategoryTheory.Functor.IsCoverDense.Types.presheafHom_app, AlgebraicGeometry.StructureSheaf.toOpen_germ, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality, CategoryTheory.Functor.sheafPushforwardContinuousComp_inv_app_hom_app, TopCat.toSheafCompHausLike_obj_map, CategoryTheory.Sheaf.cartesianMonoidalCategoryFst_val, CategoryTheory.Sheaf.ΓHomEquiv_naturality_right, CategoryTheory.Sheaf.instIsLeftAdjointComposeAndSheafify, CategoryTheory.Equivalence.sheafCongr.functor_map_hom_app, CategoryTheory.GrothendieckTopology.Point.instIsRightAdjointSheafSkyscraperSheafFunctor, AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf_map', CategoryTheory.Sheaf.isSeparator, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv, coherentExtensiveEquivalence_unitIso_inv_app_hom_app, TopCat.Sheaf.eq_app_of_locally_eq, CategoryTheory.Equivalence.sheafCongrPrecoherent_functor_map_hom_app, CategoryTheory.GrothendieckTopology.Plus.isSheaf_plus_plus, CategoryTheory.Equivalence.sheafCongrPrecoherent_inverse_map_hom_app, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_f, CategoryTheory.Sheaf.isLocallyBijective_iff_isIso, AlgebraicGeometry.Scheme.Modules.instFullPresheafOfModulesToPresheafOfModules, CategoryTheory.Functor.IsCoverDense.isoOver_inv_app, SheafOfModules.instReflectsIsomorphismsPresheafOfModulesObjFunctorOppositeRingCatIsSheafForget, AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp, TopCat.Sheaf.objSupIsoProdEqLocus_inv_fst, CategoryTheory.instIsConstantObjSheafSheafCompose, smoothSheaf.ι_evalHom, CategoryTheory.instIsIsoFunctorOppositeSheafToPresheafToSheafCompComposeAndSheafify, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjObjIso.inv_restriction, AlgebraicGeometry.StructureSheaf.instAwayObjOppositeOpensCarrierTopObjFunctorTypeIsSheafGrothendieckTopologyStructureSheafInTypeOpBasicOpen, CategoryTheory.sheafToPresheaf_ε, AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp_assoc, AlgebraicGeometry.StructureSheaf.toOpenₗ_eq_const, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app, CategoryTheory.sheafificationAdjunction_counit_app_val, CategoryTheory.preservesLimitsOfShape_presheafToSheaf, AlgebraicGeometry.StructureSheaf.res_const, CategoryTheory.Functor.op_comp_isSheaf, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_comp, CategoryTheory.GrothendieckTopology.Point.skyscraperSheafAdjunction_homEquiv_apply_val, AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_comp, SheafOfModules.pushforwardPushforwardEquivalence_unit_app_val_app, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.instMonoSheafAddCommGrpCatFShortComplex, CategoryTheory.hasColimitsEssentiallySmallSite, CategoryTheory.GrothendieckTopology.Plus.isSheaf_of_sep, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_germ, CondensedMod.LocallyConstant.instFullSheafCompHausCoherentTopologyTypeConstantSheaf, SheafOfModules.pushforward_comp_id, CategoryTheory.Equivalence.sheafCongr_inverse, SheafOfModules.relationsOfIsCokernelFree_s, CategoryTheory.Pseudofunctor.sheafHom_obj, CategoryTheory.GrothendieckTopology.overMapPullback_id_comp_assoc, SheafOfModules.forgetToSheafModuleCat_obj_obj, LightCondMod.LocallyConstant.instFullSheafLightProfiniteCoherentTopologyTypeConstantSheaf, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id_hom_app, CategoryTheory.constantSheafAdj_counit_w, CategoryTheory.sheafCompose_id, instPreservesFiniteCoproductsSheafTypeYonedaOfPreservesFiniteProductsOppositeObjFunctorIsSheaf, CompHausLike.LocallyConstant.unit_app, CategoryTheory.typeEquiv_functor_obj_obj_map, CategoryTheory.CompatiblePreserving.compatible, AlgebraicGeometry.Scheme.isZero_ellAdicSheaf_of_isEmpty, CategoryTheory.yoneda'_comp, CategoryTheory.GrothendieckTopology.overMapPullbackCongr_hom_app_hom_app, CategoryTheory.coherentTopology.isLocallySurjective_π_app_zero_of_isLocallySurjective_map, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_app_apply, LightCondSet.topCatAdjunctionUnit_hom_app, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjObjIso_inv_naturality_assoc, CategoryTheory.typeEquiv_functor_obj_obj_obj, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_hom_toNatTrans_app_hom_app, AlgebraicGeometry.StructureSheaf.comap_basicOpen, Condensed.underlying_obj, CategoryTheory.Sheaf.sheafifyCocone_ι_app_val_assoc, SheafOfModules.pushforwardPushforwardAdj_counit_app_val_app, SheafOfModules.conjugateEquiv_pullbackId_hom, CategoryTheory.Sheaf.Hom.add_app, CategoryTheory.Sheaf.hasLimitsOfSize, AlgebraicGeometry.tilde.toOpen_map_app_assoc, CategoryTheory.constantCommuteCompose_hom_app_hom, CategoryTheory.Equivalence.preregular_isSheaf_iff_of_essentiallySmall, CategoryTheory.Functor.IsDenseSubsite.map_eq_of_eq, CategoryTheory.Functor.op_comp_isSheaf_of_preservesOneHypercovers, CategoryTheory.Functor.IsCoverDense.sheaf_eq_amalgamation, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_π, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_map, CategoryTheory.Sheaf.adjunction_counit_app_hom, CategoryTheory.sheafToPresheaf_isRightAdjoint, LightCondensed.id_val, LightCondensed.ofSheafForgetLightProfinite_obj, CategoryTheory.sheafToPresheafCompCoyonedaCompWhiskeringLeftSheafToPresheaf_hom_app_app_hom, CategoryTheory.instFullSheafFunctorOppositeCompSheafComposeSheafToPresheafOfFaithful, PresheafOfModules.Sheafify.zero_smul, CategoryTheory.GrothendieckTopology.Point.sheafFiberComapIso_inv_app, CategoryTheory.Sheaf.hom_ext_iff, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_right, CategoryTheory.instPreservesFiniteProductsOppositeObjFunctorIsSheafExtensiveTopology, PresheafOfModules.sheafificationAdjunction_homEquiv_apply, Condensed.comp_hom, CategoryTheory.Functor.sheafPushforwardContinuousComp'_inv_app_hom_app, SheafOfModules.instPreservesFiniteLimitsSheafAddCommGrpCatToSheaf, CategoryTheory.GrothendieckTopology.W_eq_isLocal_range_sheafToPresheaf_obj, CategoryTheory.GrothendieckTopology.instIsIsoSheafAppFunctorOppositeSheafComposeNatTransPlusPlusAdjunction, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_left, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_X₂, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_hom_app, CategoryTheory.Functor.IsDenseSubsite.sheafifyHomEquivOfIsEquivalence_naturality_left_assoc, CategoryTheory.Functor.sheafPushforwardContinuousId'_inv_app_hom_app, AlgebraicGeometry.Scheme.LocalRepresentability.glueData_t, SheafOfModules.forgetPreservesLimitsOfShape, CategoryTheory.GrothendieckTopology.yoneda_map_hom, SheafOfModules.Presentation.IsFinite.finite_relations, CategoryTheory.Sheaf.instIsRightAdjointSheafComposeOfHasWeakSheafify, SheafOfModules.pushforwardNatTrans_app_val_app_apply, LightCondMod.LocallyConstant.instFaithfulSheafLightProfiniteCoherentTopologyTypeConstantSheaf, SheafOfModules.comp_val, PresheafOfModules.instReflectsFiniteLimitsSheafOfModulesSheafAddCommGrpCatToSheaf, AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf, CategoryTheory.Equivalence.sheafCongrPreregular_functor_obj_obj_map, CategoryTheory.instIsRegularEpiCategorySheafTypeOfHasSheafify, CategoryTheory.Functor.IsContinuous.op_comp_isSheaf_of_types, PresheafOfModules.toPresheaf_map_sheafificationAdjunction_unit_app, CondensedSet.toTopCatMap_hom_apply, AlgebraicGeometry.structurePresheafInCommRingCat_obj_carrier, CategoryTheory.sheafCompose_obj_obj, SheafOfModules.pushforward_id_comp, CategoryTheory.Functor.IsCoverDense.Types.appIso_hom, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_symm_assoc, LightCondensed.comp_val, LightCondensed.id_hom, CategoryTheory.sheafBotEquivalence_counitIso, CategoryTheory.Equivalence.sheafCongrPrecoherent_unitIso_hom_app_hom_app, AlgebraicGeometry.Scheme.instIsGrothendieckAbelianSheafProEtTopologyAb, PresheafOfModules.instIsLocallyInjectiveToSheafify, CategoryTheory.GrothendieckTopology.W_eq_W_range_sheafToPresheaf_obj, CategoryTheory.sheafification_reflective, CategoryTheory.Functor.SmallCategories.instPreservesFiniteLimitsSheafSheafPullbackOfRepresentablyFlat, AlgebraicGeometry.Scheme.Modules.instIsRightAdjointPresheafOfModulesToPresheafOfModules, CategoryTheory.sheafHomSectionsEquiv_symm_apply_coe_apply, TopCat.Sheaf.eq_of_locally_eq_iff, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjObjIso.hom_map, CategoryTheory.Functor.isEquivalence_of_isOneHypercoverDense, LightCondensed.underlying_map, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv_def, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec, CategoryTheory.GrothendieckTopology.Point.sheafFiberCompIso_hom_app, Condensed.underlying_map, CategoryTheory.Adjunction.sheafPushforwardContinuous_counit_app_hom_app, CategoryTheory.GrothendieckTopology.yoneda_obj_obj, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCBasicOpens_app, CategoryTheory.Functor.IsDenseSubsite.isIso_ranCounit_app_of_isDenseSubsite, AlgebraicGeometry.Proj.res_apply, TopCat.Presheaf.app_injective_iff_stalkFunctor_map_injective, AlgebraicGeometry.StructureSheaf.comapₗ_eq_localRingHom, SheafOfModules.pushforwardSections_coe, CategoryTheory.GrothendieckTopology.map_yonedaEquiv, PresheafOfModules.Sheafify.smul_zero, CategoryTheory.Sheaf.isLocallySurjective_iff_isIso, PresheafOfModules.Sheafify.map_smul, CategoryTheory.GrothendieckTopology.overMapPullback_assoc, AlgebraicGeometry.StructureSheaf.toOpen_res, isSheaf_coherent_of_hasPullbacks_comp, CategoryTheory.coherentTopology.isLocallySurjective_iff, AlgebraicGeometry.structurePresheafInModuleCat_obj_carrier, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec_assoc, CategoryTheory.Sheaf.ΓObjEquivSections_naturality, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_spec, LightCondSet.toTopCatMap_hom_apply, CondensedSet.epi_iff_locallySurjective_on_compHaus, AlgebraicGeometry.StructureSheaf.const_mul, CategoryTheory.Functor.sheafPushforwardContinuousComp'_hom_app_hom_app, CategoryTheory.constantSheafAdj_counit_app, PresheafOfModules.toSheafify_app_apply, TopCat.Presheaf.isIso_iff_stalkFunctor_map_iso, TopCat.Sheaf.interUnionPullbackCone_pt, CategoryTheory.GrothendieckTopology.uliftYoneda_map_hom_app_down, CategoryTheory.sheafSectionsNatIsoEvaluation_hom_app, isSheaf_iff_isSheaf_forget, SheafOfModules.instIsRightAdjointPushforwardIdSheafRingCat, CategoryTheory.GrothendieckTopology.overMapPullback_id_comp, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_hom_c_app, CategoryTheory.Functor.sheafAdjunctionCocontinuous_homEquiv_apply_val, SheafOfModules.instFullPresheafOfModulesObjFunctorOppositeRingCatIsSheafForget, CondensedSet.topCatAdjunctionUnit_hom_app, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_yonedaULift_map, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.isSheaf_iff, coherentExtensiveEquivalence_counitIso_inv_app_hom_app, TopCat.Sheaf.isLocallySurjective_iff_epi, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.restriction_map, AlgebraicGeometry.StructureSheaf.algebraMap_pushforward_stalk, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, CategoryTheory.instAdhesiveSheafOfHasPullbacksOfHasPushoutsOfHasSheafify, CategoryTheory.Sheaf.isConstant_iff_isIso_counit_app, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_obj_map, CategoryTheory.instIsLeftAdjointFunctorOppositeSheafPresheafToSheaf, CategoryTheory.Sheaf.cartesianMonoidalCategoryWhiskerLeft_val, CategoryTheory.Sheaf.ΓRes_naturality, coherentExtensiveEquivalence_counitIso_hom_app_hom_app, SheafOfModules.pushforwardNatIso_hom, AlgebraicGeometry.structureSheafInType.smul_apply, CategoryTheory.Functor.sheafPushforwardContinuousComp_hom_app_hom_app, CategoryTheory.Equivalence.sheafCongr_unitIso, CategoryTheory.GrothendieckTopology.Point.instPreservesFiniteColimitsSheafSheafFiber, CategoryTheory.GrothendieckTopology.OneHypercover.multiforkLift_map_assoc, Condensed.isSheafProfinite, CategoryTheory.Sheaf.sheafifyCocone_ι_app_val, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.restriction_eq_of_fac, CategoryTheory.Functor.pushforwardContinuousSheafificationCompatibility_hom_app_val, CategoryTheory.equivYoneda'_inv_hom, CategoryTheory.Sheaf.isSeparated, SheafOfModules.pushforwardPushforwardEquivalence_counit_app_val_app, CategoryTheory.Functor.IsDenseSubsite.full_sheafPushforwardContinuous, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right, Condensed.id_val, TopCat.Presheaf.mono_iff_stalk_mono, Condensed.instPreservesFiniteProductsOppositeCompHausObjFunctorIsSheafCoherentTopology, CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv, CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjObjIso.inv_restriction_assoc, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app_hom_app, isSheaf_sup, CategoryTheory.sheafSectionsNatIsoEvaluation_inv_app, CategoryTheory.Sheaf.IsConstant.mem_essImage, CategoryTheory.Functor.sheafPushforwardContinuousId_inv_app_hom_app, AlgebraicGeometry.isSheaf_fpqcTopology_continuousMapPresheaf, AlgebraicGeometry.StructureSheaf.algebraMap_germ_apply, CategoryTheory.Functor.sheafAdjunctionCocontinuous_unit_app_val, AlgebraicGeometry.isSheaf_zariskiTopology_continuousMapPresheaf, CategoryTheory.yoneda'_obj_obj, CompHausLike.LocallyConstantModule.functor_map_hom_app_hom_apply_apply, SheafOfModules.pushforward_obj_val, Condensed.equalizerCondition_profinite, AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_toGlued, PresheafOfModules.Sheafify.mul_smul, CategoryTheory.GrothendieckTopology.Point.skyscraperSheafAdjunction_homEquiv_apply_hom, CategoryTheory.GrothendieckTopology.Point.sheafFiberCompIso_inv_app, Condensed.equalizerCondition, instPreservesColimitsOfShapeSheafTypeUliftYonedaOfPreservesLimitsOfShapeOppositeObjFunctorIsSheaf, CategoryTheory.Sheaf.tensorUnit_isSheaf, instPreservesLimitsOfShapeSheafTypeYoneda, CategoryTheory.Sheaf.instHasFiniteProducts, PresheafOfModules.Sheafify.SMulCandidate.h, CategoryTheory.Functor.IsCoverDense.Types.pushforwardFamily_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_yoneda_map, CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map_hom_app, AlgebraicGeometry.StructureSheaf.instIsLocalizedModuleObjOppositeOpensCarrierTopObjFunctorTypeIsSheafGrothendieckTopologyStructureSheafInTypeOpBasicOpenPowersToOpenₗ, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv, Condensed.discrete_obj, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_comp, CategoryTheory.Functor.pushforwardContinuousSheafificationCompatibility_hom_app_hom, CategoryTheory.sheafComposeNatTrans_fac, CategoryTheory.ObjectProperty.IsConservativeFamilyOfPoints.jointlyReflectEpimorphisms, CategoryTheory.GrothendieckTopology.yonedaEquiv_apply, SheafOfModules.Finite.evaluationPreservesFiniteLimits, AlgebraicGeometry.ΓSpec.toSpecΓ_unop, CategoryTheory.Sheaf.instIsMonoidalFunctorOppositeIsSheaf, CategoryTheory.yoneda'_map_hom, CategoryTheory.Equivalence.sheafCongr.inverse_map_hom_app, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_right, CompHausLike.LocallyConstant.adjunction_unit, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_symm, CategoryTheory.Functor.IsDenseSubsite.faithful_sheafPushforwardContinuous, isLocallySurjective_presheafToSheaf_map_iff, SheafOfModules.pushforwardNatTrans_comp, CategoryTheory.Sheaf.instEpiAppArrowILocallySurjectiveLocallyInjectiveFunctorialLocallySurjectiveInjectiveFactorization, CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_hom_app, CategoryTheory.Sheaf.cartesianMonoidalCategoryWhiskerRight_hom, PresheafOfModules.instPreservesFiniteLimitsSheafAddCommGrpCatCompSheafOfModulesSheafificationToSheaf, CategoryTheory.instMonoSheafTypeImageι, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_iff, CategoryTheory.Sheaf.isTerminalTerminal_from_hom, CategoryTheory.Functor.IsCoverDense.full_sheafPushforwardContinuous, CategoryTheory.Functor.IsCoverDense.Types.naturality_assoc, AlgebraicGeometry.Spec.sheafedSpaceObj_presheaf, AlgebraicGeometry.Spec.map_app, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_exact, CategoryTheory.Equivalence.sheafCongr.counitIso_hom_app_hom_app, SheafOfModules.unitHomEquiv_apply_coe, isSheaf_iff_isLimit_pretopology, CategoryTheory.sheafCompose_comp, AlgebraicGeometry.tilde.toOpen_map_app, CategoryTheory.Functor.IsCoverDense.Types.naturality
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