| Name | Category | Theorems |
|---|
carrier 📖 | CompOp | 2024 mathmath: Presheaf.generateEquivalenceOpensLe_functor'_obj_obj, isInducing_pullback_to_prod, TopologicalSpace.OpenNhds.coe_id, AlgebraicGeometry.Scheme.toSpecΓ_apply, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen, AlgebraicGeometry.Γ_map_morphismRestrict, AlgebraicGeometry.Scheme.Hom.smoothLocus_eq_top_iff, Sequential.homeoOfIso_apply, AlgebraicGeometry.Scheme.Modules.pushforward_obj_presheaf_map, binaryCofan_isColimit_iff, DiscreteContAction.instDiscreteTopologyCarrierObjTopCatForget₂ContinuousMap, smoothSheafCommRing.ι_forgetStalk_inv, AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality_assoc, AlgebraicGeometry.Proj.awayMap_awayToSection_assoc, AlgebraicGeometry.QuasiCompact.isCompact_preimage_singleton, LightCondensed.free_internallyProjective_iff_tensor_condition, AlgebraicGeometry.Scheme.fromSpecStalk_closedPoint, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst_assoc, AlgebraicGeometry.Scheme.Hom.toPartialMap_hom, AlgebraicGeometry.irreducibleSpace_of_isIntegral, AlgebraicGeometry.Scheme.height_of_isClosed, AlgebraicGeometry.Scheme.map_PrimeSpectrum_basicOpen_of_affine, PrelocalPredicate.res, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_injective, TopologicalSpace.Opens.id_apply, AlgebraicGeometry.Scheme.isoOfEq_inv, AlgebraicGeometry.StructureSheaf.instIsScalarTowerCarrierStalkCommRingCatStructurePresheafInCommRingCatCarrierAbPresheafOpensCarrierTopModuleStructurePresheaf, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv_assoc, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_appTop, LightProfinite.proj_comp_transitionMap, TopologicalSpace.Opens.map_id_obj_unop, LightProfinite.Extend.functorOp_obj, AlgebraicGeometry.Scheme.zeroLocus_iInf, AlgebraicGeometry.Scheme.Modules.pushforwardId_inv_app_app, pullbackIsoProdSubtype_hom_fst, AlgebraicGeometry.IsAffineOpen.map_fromSpec_assoc, LightCondensed.lanPresheafIso_hom, AlgebraicGeometry.IsAffineOpen.isLocalization_of_eq_basicOpen, TopologicalSpace.Opens.inclusion'_hom_apply, SimplexCategory.instNonemptyCarrierObjTopCatToTop₀, AlgebraicGeometry.Scheme.Hom.opensRange_pullbackSnd, AlgebraicGeometry.LocallyRingedSpace.residueFieldMap_comp, isoOfHomeo_inv, AlgebraicGeometry.Scheme.AffineZariskiSite.instFaithfulOpensToOpensFunctor, presheafToType_map, Sheaf.interUnionPullbackCone_snd, LightCondensed.isoFinYonedaComponents_hom_apply, AlgebraicGeometry.instCompactSpaceCarrierCarrierCommRingCatEqualizerSchemeOfQuasiSeparatedSpace, TopologicalSpace.Opens.map_coe, AlgebraicGeometry.Scheme.Spec_map_stalkMap_fromSpecStalk, AlgebraicGeometry.Scheme.Hom.image_preimage_eq_opensRange_inter, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_apply, AlgebraicGeometry.Scheme.Cover.LocallyDirected.directed, ProfiniteGrp.coe_of, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.stalk_iso, ProfiniteGrp.instReflectsIsomorphismsProfiniteForget₂ContinuousMonoidHomCarrierToTopTotallyDisconnectedSpaceToProfiniteContinuousMap, AlgebraicGeometry.Scheme.Modules.instFaithfulPresheafOfModulesToPresheafOfModules, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app, AlgebraicGeometry.GeometricallyIrreducible.geometrically_irreducibleSpace, AlgebraicGeometry.Scheme.IsQuasiAffine.toIsImmersion, AlgebraicGeometry.StructureSheaf.globalSectionsIso_inv, AlgebraicGeometry.iSup_affineOpens_eq_top, AlgebraicGeometry.isAffineOpen_top, GlueData.preimage_image_eq_image, ContinuousMap.yonedaPresheaf'_obj, AlgebraicGeometry.RingedSpace.basicOpen_res, AlgebraicGeometry.Scheme.Hom.denseRange, AlgebraicGeometry.Scheme.isEmpty_pullback_iff, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv, GlueData.π_surjective, AlgebraicGeometry.Scheme.Hom.quasiFiniteLocus_comp, LightCondensed.ihomPoints_apply, AlgebraicGeometry.Scheme.app_eq, DeltaGenerated.topToDeltaGenerated_map_hom_hom_apply, AlgebraicGeometry.Scheme.Hom.closePoints_subset_preimage_closedPoints, AlgebraicGeometry.Scheme.support_nilradical, isOpenEmbedding_iff_comp_isIso, AlgebraicGeometry.opensCone_pt, CondensedSet.instUCompactlyGeneratedSpaceCarrierToTopCat, AlgebraicGeometry.Scheme.zeroLocus_empty_eq_univ, AlgebraicGeometry.coprodSpec_apply, AlgebraicGeometry.IsAffineOpen.isCompact, AlgebraicGeometry.morphismRestrict_base_coe, AlgebraicGeometry.Scheme.Hom.fiberHomeo_apply, AlgebraicGeometry.surjectiveOnStalks_iff, AlgebraicGeometry.StructureSheaf.comap_id, Profinite.Extend.cocone_pt, FundamentalGroupoidFunctor.piIso_hom, TopModuleCat.instPreservesLimitTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitOfModuleCatCompLinearMapForget, AlgebraicGeometry.instCompactSpaceCarrierCarrierCommRingCatPullbackSchemeOfQuasiCompact, Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_π_app, Stonean.instExtremallyDisconnectedCarrierToTop, condensedSetToTopCat_obj_carrier, AlgebraicGeometry.Scheme.Hom.instIsContinuousOpensOpensFunctorGrothendieckTopologyCarrierCarrierCommRingCat, CondensedMod.IsSolid.isIso_solidification_map, AlgebraicGeometry.IsAffineOpen.map_fromSpec, Presheaf.Pushforward.id_inv_app, AlgebraicGeometry.Scheme.affineBasisCover_is_basis, Profinite.forget_preservesLimits, AlgebraicGeometry.IsLocallyArtinian.isArtinianRing_presheaf_obj, AlgebraicGeometry.Scheme.Opens.toSpecΓ_naturality, CompactlyGenerated.homeoOfIso_apply, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top, AlgebraicGeometry.range_eq_range_of_surjective, skyscraperPresheaf_obj, AlgebraicGeometry.LocallyRingedSpace.notMem_prime_iff_unit_in_stalk, AlgebraicGeometry.Scheme.restrictFunctorΓ_inv_app, AlgebraicGeometry.Scheme.Cover.isOpenMap_fromGlued, coe_of_of, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_counit_app_app, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_specStalkEquiv, AlgebraicGeometry.instGeometricallyIrreducibleMorphismRestrict, AlgebraicGeometry.instIsDomainCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTopOfIsIntegral, instFullFintypeCatProfiniteToProfinite, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_x, GlueData.open_image_open, LightCondensed.forget_obj_val_map, Stonean.instProjective, AlgebraicGeometry.Scheme.Opens.mem_ι_image_iff, AlgebraicGeometry.Scheme.Hom.exists_isIso_morphismRestrict_toNormalization, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_symm_apply, AlgebraicGeometry.morphismRestrict_ι_assoc, Profinite.Extend.functorOp_map, AlgebraicGeometry.functionField_isFractionRing_of_isAffineOpen, AlgebraicGeometry.Scheme.IdealSheafData.ideal_sSup, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_point, AlgebraicGeometry.ValuativeCriterion.Existence.specializingMap, AlgebraicGeometry.Scheme.fromSpecStalk_toSpecΓ_assoc, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_fromSpec, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_hom_app_app, AlgebraicGeometry.AffineSpace.SpecIso_hom_appTop, AlgebraicGeometry.LocallyRingedSpace.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, AlgebraicGeometry.SheafedSpace.colimit_exists_rep, AlgebraicGeometry.Scheme.Modules.pushforward_obj_obj, ProfiniteGrp.limit_one_val, AlgebraicGeometry.Scheme.Hom.range_fiberι, AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf_map, TopologicalSpace.Opens.coe_inclusion', ProfiniteAddGrp.ofHom_hom, AlgebraicGeometry.Scheme.Hom.preimage_bot, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp, TopologicalSpace.OpenNhds.inclusionMapIso_hom, AlgebraicGeometry.Scheme.Cover.iUnion_range, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_naturality, AlgebraicGeometry.Scheme.mem_basicOpen', LightCondensed.ihomPoints_symm_comp, AlgebraicGeometry.instPrespectralSpaceCarrierCarrierCommRingCat, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_morphismRestrict_assoc, AlgebraicGeometry.Scheme.Hom.mem_opensRange, Profinite.instEnoughProjectives, AlgebraicGeometry.Scheme.zeroLocus_eq_univ_iff_subset_nilradical, AlgebraicGeometry.Scheme.Opens.topIso_inv, AlgebraicGeometry.Scheme.SpecToEquivOfField_eq_iff, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_preimage_basicOpen, Sequential.homeoOfIso_symm_apply, AlgebraicGeometry.Proj.pow_apply, alexDiscEquivPreord_inverse_obj_carrier, CompHausLike.coe_of, AlgebraicGeometry.isCompact_iff_exists, ProfiniteGrp.ProfiniteCompletion.lift_eta, Presheaf.SheafConditionEqualizerProducts.piOpens.hom_ext_iff, AlgebraicGeometry.Spec_presheaf, AlgebraicGeometry.Scheme.RationalMap.dense_domain, LightCondSet.continuous_coinducingCoprod, AlgebraicGeometry.HasRingHomProperty.stalkMap, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app_assoc, AlgebraicGeometry.Scheme.Hom.resLE_eq_morphismRestrict, ContinuousMap.Homotopy.apply_zero_path, LightCondSet.epi_iff_locallySurjective_on_lightProfinite, TopCommRingCat.instReflectsIsomorphismsTopCatForget₂SubtypeRingHomαContinuousCoeContinuousMapCarrier, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap_apply, sigmaIsoSigma_hom_ι, AlgebraicGeometry.Scheme.Hom.iUnion_support_ker_openCover_map_comp, uliftFunctorObjHomeo_symm_naturality_apply, AlgebraicGeometry.Scheme.inv_app, LightProfinite.instCountableClopensCarrierToTopAndTotallyDisconnectedSpaceSecondCountableTopology, LightCondensed.isoFinYoneda_inv_app, AlgebraicGeometry.Scheme.Hom.id_appTop, CondensedMod.isDiscrete_tfae, AlgebraicGeometry.Proj.basicOpenIsoAway_hom, smoothSheafCommRing.ι_evalHom_apply, uliftFunctorCompForgetIso_hom_app, AlgebraicGeometry.image_morphismRestrict_preimage, AlgebraicGeometry.Scheme.IdealSheafData.gc, AlgebraicGeometry.Scheme.emptyTo_base, CompHaus.toStonean_toTop, CompHausLike.coe_id, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_hom_apply_asIdeal, AlgebraicGeometry.Scheme.zeroLocus_mul, AlgebraicGeometry.Proj.mul_apply, AlgebraicGeometry.StructureSheaf.comap_id', TopologicalSpace.OpenNhds.comp_apply, AlgebraicGeometry.Scheme.OpenCover.finiteSubcover_f, LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition, AlgebraicGeometry.SpecMap_preimage_basicOpen, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_isModule, Profinite.Extend.cone_π_app, AlgebraicGeometry.Scheme.ideal_ker_le_ker_ΓSpecIso_inv_comp, AlgebraicGeometry.Scheme.stalkMap_congr_assoc, instFaithfulFintypeCatLightProfiniteToLightProfinite, ProfiniteAddGrp.ofHom_apply, smoothSheafCommRing.eval_germ, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_surjective, AlgebraicGeometry.instIsGermInjectiveAtCoeContinuousMapCarrierCarrierCommRingCatHomTopCatBaseOfIsOpenImmersion, LightCondensed.finYoneda_map, AlgebraicGeometry.Scheme.isoSpec_inv_toSpecΓ, AlgebraicGeometry.Scheme.Pullback.SpecTensorTo_SpecOfPoint, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.instIsIsoInvApp, ContinuousMap.Homotopy.evalAt_eq, AlgebraicGeometry.Scheme.hom_inv_apply, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app_apply, AlgebraicGeometry.Scheme.Hom.range_asFiberHom, SimplexCategory.instPathConnectedSpaceCarrierObjTopCatToTop, Sequential.isoEquivHomeo_apply, TopologicalSpace.Opens.comp_apply, AlgebraicGeometry.isIso_ΓSpec_adjunction_unit_app_basicOpen, AlgebraicGeometry.isNoetherian_iff_of_finite_affine_openCover, AlgebraicGeometry.Scheme.Hom.tendsto_cofinite_cofinite, AlgebraicGeometry.Scheme.ι_toIso_inv, Sequential.isoEquivHomeo_symm_apply, TopologicalSpace.OpenNhds.val_apply, AlgebraicGeometry.isPullback_opens_inf, AlgebraicGeometry.SmoothOfRelativeDimension.exists_isStandardSmoothOfRelativeDimension, AlgebraicGeometry.noetherianSpace_of_isAffine, AlgebraicGeometry.Scheme.Hom.preimageIso_hom_ι_assoc, isOpenEmbedding_iff, ProfiniteGrp.coe_id, AlgebraicGeometry.IsClosedImmersion.base_closed, AlgebraicGeometry.quasiCompact_iff, Profinite.effectiveEpi_tfae, TopologicalSpace.OpenNhds.inclusionMapIso_inv, AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine_apply, AlgebraicGeometry.structureSheafInType.mul_apply, range_prod_map, Stonean.instEffectivelyEnoughCompHausToCompHaus, TopModuleCat.instIsRightAdjointTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, skyscraperPresheafCocone_pt, AlgebraicGeometry.isEmpty_of_commSq_sigmaι_of_ne, AlgebraicGeometry.Scheme.Modules.Hom.zero_app, Sheaf.pushforward_map, AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine_symm_apply, AlgebraicGeometry.Scheme.congr_app, AlgebraicGeometry.Scheme.IdealSheafData.ideal_mul, AlgebraicGeometry.IsZariskiLocalAtTarget.restrict, AlgebraicGeometry.Scheme.Opens.stalkIso_inv, AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.structurePresheafInCommRing_obj_carrier, AlgebraicGeometry.Scheme.SpecΓIdentity_hom_app, AlgebraicGeometry.locallyQuasiFinite_iff, AlgebraicGeometry.Scheme.preimage_comp, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom_assoc, smoothSheaf.ι_evalHom_apply, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.toBase_preimage_eq_opensRange_ι, AlgebraicGeometry.Scheme.IdealSheafData.support_mul, TopModuleCat.coe_freeObj, Presheaf.SheafConditionEqualizerProducts.fork_π_app_walkingParallelPair_one, LightCondMod.isDiscrete_tfae, AlgebraicGeometry.sourceLocalClosure.iff_forall_exists, AlgebraicGeometry.IsFinite.instMorphismRestrict, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap, AlgebraicGeometry.Scheme.Pullback.Triplet.isPullback_SpecMap_tensor, AlgebraicGeometry.Scheme.forget_map, GlueData.isOpen_iff, AlgebraicGeometry.sigmaMk_mk, Presheaf.pushforwardToOfIso_app, AlgebraicGeometry.affineLocally_iff_forall_isAffineOpen, AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_base_snd, LocallyConstant.freeOfProfinite, Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_hom_app_hom, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_point_assoc, AlgebraicGeometry.Scheme.isoSpec_inv_preimage_zeroLocus, FinTopCat.coe_of, instFaithfulLightDiagramProfiniteLightDiagramToProfinite, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app_assoc, instPreservesEpimorphismsLightProfiniteLightCondSetLightProfiniteToLightCondSet, AlgebraicGeometry.PresheafedSpace.Γ_obj_op, LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace, TopologicalSpace.Opens.map_comp_obj_unop, AlgebraicGeometry.IsPreimmersion.isEmbedding, AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf', Profinite.NobelingProof.spanFunctorIsoIndexFunctor_hom_app_hom_hom_apply_coe, coequalizer_isOpen_iff, Sheaf.interUnionPullbackCone_fst, AlgebraicGeometry.functionField_isScalarTower, forget_preservesColimits, GlueData.ι_fromOpenSubsetsGlue_apply, ProfiniteGrp.ProfiniteCompletion.lift_eta_assoc, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app, InfiniteGalois.toAlgEquivAux_eq_proj_of_mem, GlueData.MkCore.V_id, AlgebraicGeometry.Scheme.Hom.SpecMap_residueFieldMap_fromSpecResidueField_assoc, LightCondensed.discrete_map, AlgebraicGeometry.Scheme.exists_germ_injective, AlgebraicGeometry.IsOpenImmersion.iff_isIso_stalkMap, AlgebraicGeometry.Scheme.Cover.instIsIsoCommRingCatStalkMapFromGlued, AlgebraicGeometry.StructureSheaf.instIsLocalizedModuleObjOppositeOpensCarrierTopValStructureSheafInTypeOpBasicOpenPowersToOpenₗ, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_eq, LightProfinite.proj_comp_transitionMapLE', AlgebraicGeometry.Scheme.Hom.preimage_top, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd_assoc, lightDiagramToProfinite_map, AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimage, AlgebraicGeometry.Scheme.Pullback.carrierEquiv_eq_iff, AlgebraicGeometry.Proj.one_apply, AlgebraicGeometry.Scheme.Hom.toImage_app_injective, AlgebraicGeometry.Scheme.isoSpec_hom, AlgebraicGeometry.instHasAffinePropertyQuasiSeparatedQuasiSeparatedSpaceCarrierCarrierCommRingCat, AlgebraicGeometry.Scheme.ι_toIso_inv_assoc, AlgebraicGeometry.Scheme.Hom.id_preimage, AlgebraicGeometry.Flat.instMorphismRestrict, AlgebraicGeometry.StructureSheaf.to_basicOpen_epi, AlgebraicGeometry.IsAffineOpen.opensRange_fromSpec, pullback_topology, AlgebraicGeometry.Scheme.IdealSheafData.ideal_le_ker_glueDataObjι, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_c_app, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_snd_coe, LightProfinite.Extend.cocone_ι_app, AlgebraicGeometry.instQuasiCompactMorphismRestrict, AlgebraicGeometry.Scheme.forget_obj, AlgebraicGeometry.Scheme.eqToHom_c_app, GlueData.ofOpenSubsets_toGlueData_t, AlgebraicGeometry.IsAffineOpen.self_le_iSup_basicOpen_iff, AlgebraicGeometry.Scheme.zeroLocus_biInf, AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_hom_π, AlgebraicGeometry.PresheafedSpace.componentwiseDiagram_map, AlgebraicGeometry.Proj.basicOpenToSpec_app_top, ProfiniteGrp.instFaithfulProfiniteForget₂ContinuousMonoidHomCarrierToTopTotallyDisconnectedSpaceToProfiniteContinuousMap, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_naturality, AlgebraicGeometry.Scheme.Hom.image_preimage_le, Condensed.lanPresheafExt_inv, AlgebraicGeometry.Scheme.AffineZariskiSite.generate_presieveOfSections, AlgebraicGeometry.Scheme.Hom.image_top_eq_opensRange, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app, ProfiniteAddGrp.instFaithfulProfiniteForget₂ContinuousAddMonoidHomCarrierToTopTotallyDisconnectedSpaceToProfiniteContinuousMap, AlgebraicGeometry.IsOpenImmersion.isOpen_range, AlgebraicGeometry.Scheme.affineOpenCover_idx, AlgebraicGeometry.Scheme.Hom.fromNormalization_preimage, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.stalk_iso, AlgebraicGeometry.Scheme.toSpecΓ_naturality_assoc, AlgebraicGeometry.LocallyRingedSpace.iso_inv_base_hom_base_apply, AlgebraicGeometry.Scheme.Pullback.Triplet.snd_SpecTensorTo_apply, AlgebraicGeometry.Scheme.Modules.pushforwardComp_inv_app_app, AlgebraicGeometry.SurjectiveOnStalks.iff_of_isAffine, AlgebraicGeometry.SpecMap_ΓSpecIso_hom, AlgebraicGeometry.Scheme.compactSpace_of_isAffine, AlgebraicGeometry.IsAffineOpen.isLocalization_basicOpen, pullbackFst_apply, AlgebraicGeometry.Scheme.zeroLocus_iUnion, sigmaCofan_ι_app, AlgebraicGeometry.IsReduced.component_reduced, instFaithfulFintypeCatProfiniteToProfinite, AlgebraicGeometry.SheafedSpace.comp_hom_c_app, Profinite.injective_of_light, CompHausLike.LocallyConstant.locallyConstantIsoContinuousMap_inv_apply, LightCondSet.topCatAdjunctionUnit_val_app_apply, ProfiniteAddGrp.instPreservesLimitsProfiniteForget₂ContinuousAddMonoidHomCarrierToTopTotallyDisconnectedSpaceToProfiniteContinuousMap, AlgebraicGeometry.IsIntegralHom.isIntegral_app, AlgebraicGeometry.Scheme.ker_ideal_of_isPullback_of_isOpenImmersion, colimit_topology, Profinite.epi_iff_surjective, AlgebraicGeometry.Scheme.presieve₀_mem_precoverage_iff, lightProfiniteToLightDiagram_map, Sheaf.id_app, TopologicalSpace.Opens.isOpenEmbedding_obj_top, AlgebraicGeometry.LocallyRingedSpace.Γ_obj_op, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_appTop_coord, Profinite.exists_locallyConstant_finite_aux, AlgebraicGeometry.Scheme.Hom.image_preimage_eq_opensRange_inf, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over_assoc, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ_ΓToStalk, AlgebraicGeometry.isIso_iff_isIso_stalkMap, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom, ContinuousMap.Homotopy.ulift_apply, AlgebraicGeometry.Scheme.Hom.image_iSup₂, isOpenEmbedding_iff_isIso_comp', AlgebraicGeometry.Scheme.isoSpec_hom_naturality, topCatOpToFrm_map, AlgebraicGeometry.Scheme.zeroLocus_singleton, AlgebraicGeometry.instIsEmptyCarrierCarrierCommRingCatEmptyCollectionScheme, AlgebraicGeometry.PresheafedSpace.comp_c_app, AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv_assoc, AlgebraicGeometry.LocallyRingedSpace.component_nontrivial, AlgebraicGeometry.Scheme.Pullback.residueFieldCongr_inv_residueFieldMap_ofPoint, AlgebraicGeometry.Scheme.IdealSheafData.ideal_map, AlgebraicGeometry.IsOpenImmersion.range_pullbackSnd, GlueData.rel_equiv, AlgebraicGeometry.Proj.sub_apply, AlgebraicGeometry.IsImmersion.instMorphismRestrict, Profinite.instTotallyDisconnectedSpaceCarrierToTop, Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_π_app, AlgebraicGeometry.Scheme.Hom.isDiscrete_preimage_singleton, AlgebraicGeometry.Scheme.Hom.comp_app, pullbackSnd_apply, ProfiniteGrp.toLimit_surjective, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι_ι_eq_support_inter, LightProfinite.isClosedMap, AlgebraicGeometry.instIsScalarTowerObjOppositeOpensCarrierTopValStructureSheafInType, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr, AlgebraicGeometry.isNoetherian_iff, TopologicalSpace.Opens.mapId_hom_app, AlgebraicGeometry.IsOpenImmersion.range_pullback_fst_of_right, ProfiniteAddGrp.hom_neg_apply, TopologicalSpace.Opens.mapComp_hom_app, AlgebraicGeometry.Scheme.toSpecΓ_naturality, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app_assoc, lightDiagramToLightProfinite_obj, AlgebraicGeometry.Scheme.Hom.quasiFiniteLocus_eq_top, smoothSheaf.ι_evalHom_assoc, AlgebraicGeometry.pointEquivClosedPoint_apply_coe, AlgebraicGeometry.IsNoetherian.toCompactSpace, Profinite.isIso_indexCone_lift, Stonean.instHasExplicitFiniteCoproductsExtremallyDisconnectedCarrier, AlgebraicGeometry.IsIntegral.nonempty, AlgebraicGeometry.Scheme.Hom.ι_toNormalization, AlgebraicGeometry.LocallyRingedSpace.Γ_Spec_left_triangle, Condensed.isoFinYonedaComponents_hom_apply, isIso_iff_isHomeomorph, AlgebraicGeometry.Scheme.IdealSheafData.ideal_pow, AlgebraicGeometry.RingedSpace.mem_top_basicOpen, ProfiniteGrp.hom_id, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, AlgebraicGeometry.IsNoetherian.noetherianSpace, ProfiniteAddGrp.hom_id, AlgebraicGeometry.Scheme.range_fromSpecStalk, prod_topology, AlgebraicGeometry.Scheme.homeoOfIso_symm, FundamentalGroupoidFunctor.prodToProdTop_obj, AlgebraicGeometry.instCompactSpaceCarrierCarrierCommRingCatPullbackSchemeOfQuasiCompact_1, AlgebraicGeometry.IsAffineOpen.ideal_le_iff, CondensedSet.topCatAdjunctionCounit_bijective, Presheaf.IsSheaf.isSheafUniqueGluing_types, AlgebraicGeometry.quasiCompact_affineProperty_iff_quasiSeparatedSpace, Profinite.Extend.functorOp_obj, AlgebraicGeometry.Scheme.Hom.congr_app, AlgebraicGeometry.Scheme.Hom.preimage_iSup, AlgebraicGeometry.Scheme.Hom.toPartialMap_domain, ProfiniteAddGrp.neg_hom_apply, AlgebraicGeometry.coprodMk_inl, AlgebraicGeometry.RingedSpace.zeroLocus_isClosed, AlgebraicGeometry.Scheme.Opens.toSpecΓ_naturality_assoc, CondensedSet.topCatAdjunctionCounit_hom_apply, AlgebraicGeometry.Scheme.Pullback.Triplet.hy, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_assoc, AlgebraicGeometry.IsAffineOpen.isoSpec_inv, forget_preservesLimitsOfSize, AlgebraicGeometry.Scheme.Hom.id_app, sigmaIsoSigma_inv_apply, Presheaf.comp_app, AlgebraicGeometry.Scheme.Γ_obj, CompHausLike.homeoOfIso_symm_apply, AlgebraicGeometry.isLocallyNoetherian_iff_of_affine_openCover, Condensed.finYoneda_map, AlgebraicGeometry.Scheme.IdealSheafData.instIsEmptyCarrierCarrierCommRingCatSubschemeTop, AlgebraicGeometry.Scheme.Pullback.carrierEquiv_symm_fst, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberι_assoc, AlgebraicGeometry.instIsClosedUnderIsomorphismsSchemeIrreducibleSpaceCarrierCarrierCommRingCat, LightProfinite.lightToProfinite_map_proj_eq, AlgebraicGeometry.Proj.mem_basicOpen, AlgebraicGeometry.IsLocallyArtinian.isArtinianRing_of_isAffine, AlgebraicGeometry.StructureSheaf.toPushforwardStalkAlgHom_apply, AlgebraicGeometry.Scheme.preimage_basicOpen_top, CompHausLike.isClosedMap, AlgebraicGeometry.PresheafedSpace.GlueData.pullback_base, AlgebraicGeometry.Scheme.ΓSpecIso_inv, AlgebraicGeometry.Scheme.Hom.app_appIso_inv_assoc, Presheaf.SheafConditionPairwiseIntersections.coneEquiv_counitIso, AlgebraicGeometry.IsAffineOpen.basicOpen_fromSpec_app, FintypeCat.toProfinite_map_hom_hom_apply, FundamentalGroupoidFunctor.prodIso_hom, pullbackIsoProdSubtype_inv_fst_assoc, AlgebraicGeometry.quasiCompact_over_affine_iff, AlgebraicGeometry.Scheme.Pullback.range_fst_comp, Presheaf.pushforward_map_app, AlgebraicGeometry.Scheme.Hom.coequifibered_normalizationDiagramMap, TopologicalSpace.OpenNhds.op_map_id_obj, AlgebraicGeometry.Scheme.isoSpec_hom_naturality_assoc, prodIsoProd_hom_snd_assoc, AlgebraicGeometry.Scheme.isoSpec_inv_image_zeroLocus, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι_ι, AlgebraicGeometry.Scheme.germToFunctionField_injective, ProfiniteGrp.denseRange_toLimit, Profinite.hasColimits, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app', ProfiniteAddGrp.limit_zero_val, AlgebraicGeometry.isIso_morphismRestrict_iff_isIso_app, AlgebraicGeometry.Proj.iSup_basicOpen_eq_top', ProfiniteGrp.comp_apply, AlgebraicGeometry.morphismRestrict_base, CompHausLike.isoEquivHomeo_symm_apply, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen_topIso_inv, continuousPrelocal_pred, AlgebraicGeometry.Scheme.zeroLocus_setMul, AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ, AlgebraicGeometry.Scheme.Opens.nonempty_iff, AlgebraicGeometry.Scheme.toSpecΓ_preimage_zeroLocus, LightProfinite.effectiveEpi_iff_surjective, Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_π_app, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.imageBasicOpen_image_open, AlgebraicGeometry.Scheme.Hom.preimage_image_eq, Stonean.effectiveEpiFamily_tfae, ProfiniteAddGrp.coe_of, AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_comp_iff_of_isOpenImmersion, SimplexCategory.instPathConnectedSpaceCarrierObjTopCatToTop₀, TopologicalSpace.Opens.inclusion'_top_functor, Presheaf.stalk_open_algebraMap, AlgebraicGeometry.isBasis_preimage_isAffineOpen, AlgebraicGeometry.Scheme.Cover.isOpenEmbedding_fromGlued, AlgebraicGeometry.Scheme.Hom.app_surjective, AlgebraicGeometry.coe_opensRestrict_symm_apply, GlueData.instIsIsoT, ProfiniteAddGrp.comp_apply, Presheaf.presheafEquivOfIso_inverse_obj_map, Presheaf.pushforwardEq_hom_app, AlgebraicGeometry.affineLocally_iff_affineOpens_le, AlgebraicGeometry.Scheme.fromSpecStalk_appTop, AlgebraicGeometry.RingedSpace.basicOpen_pow, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturality_assoc, AlgebraicGeometry.Scheme.OpenCover.isOpenCover_opensRange, AlgebraicGeometry.pullbackRestrictIsoRestrict_inv_fst, presheafToTop_obj, AlgebraicGeometry.Scheme.Hom.isCompact_preimage_singleton, AlgebraicGeometry.Scheme.Opens.toScheme_presheaf_obj, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_ideal, AlgebraicGeometry.PresheafedSpace.Γ_map_op, AlgebraicGeometry.Scheme.Pullback.Triplet.Spec_map_tensor_isPullback, FundamentalGroupoidFunctor.piToPiTop_map, LightProfinite.continuous_iff_convergent, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app_apply, AlgebraicGeometry.Scheme.id_appTop, AlgebraicGeometry.Scheme.Cover.covers, alexDiscEquivPreord_inverse_map, Profinite.instPreregular, LightCondensed.internallyProjective_iff_tensor_condition, AlgebraicGeometry.Scheme.Spec_map_presheaf_map_eqToHom, AlgebraicGeometry.Scheme.Opens.toSpecΓ_appTop_assoc, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_point_assoc, TopologicalSpace.Opens.map_functor_eq, TopCommRingCat.forgetToTopCatTopologicalRing, Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_inv_app_hom, AlgebraicGeometry.instIrreducibleSpaceCarrierCarrierCommRingCatSpecOfIsDomainCarrier, AlgebraicGeometry.Scheme.stalkMap_congr_point_assoc, AlgebraicGeometry.Scheme.GlueData.isOpen_iff, ofHom_hom, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_assoc, ContinuousMap.Homotopy.apply_one_path, AlgebraicGeometry.IsAffineOpen.primeIdealOf_isMaximal_of_isClosed, AlgebraicGeometry.Scheme.fromSpecStalk_toSpecΓ, AlgebraicGeometry.Scheme.ker_toSpecΓ, LightProfinite.instPreservesEpimorphismsProfiniteLightToProfinite, AlgebraicGeometry.Scheme.IdealSheafData.ideal_bot, LightProfinite.instHasExplicitFiniteCoproductsAndTotallyDisconnectedSpaceCarrierSecondCountableTopology, LightProfinite.instCountableDiscreteQuotient, AlgebraicGeometry.Scheme.ker_of_isAffine, ProfiniteGrp.ofHom_hom, AlgebraicGeometry.IsAffineOpen.algebraMap_Spec_obj, AlgebraicGeometry.isBasis_basicOpen, TopologicalSpace.Opens.map_id_obj, AlgebraicGeometry.Scheme.Hom.mem_preimage, Condensed.instPreservesLimitsOfShapeOppositeProfiniteDiscreteCarrierToTopTotallyDisconnectedSpaceOfFinite, AlgebraicGeometry.Scheme.Spec_map_stalkMap_fromSpecStalk_assoc, AlgebraicGeometry.isInitial_iff_isEmpty, AlgebraicGeometry.LocallyRingedSpace.isLocalHomStalkMap, AlgebraicGeometry.IsImmersion.isLocallyClosed_range, AlgebraicGeometry.Scheme.Γevaluation_naturality_apply, AlgebraicGeometry.Scheme.basicOpen_le, AlgebraicGeometry.locallyOfFiniteType_iff, CompHausLike.finiteCoproduct.isOpenEmbedding_ι, AlgebraicGeometry.SheafedSpace.comp_c_app, AlgebraicGeometry.Flat.flat_and_surjective_iff_faithfullyFlat_of_isAffine, Presheaf.SheafConditionEqualizerProducts.w, CompHausLike.Sigma.isOpenEmbedding_ι, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top_assoc, AlgebraicGeometry.liftCoborder_app, AlgebraicGeometry.LocallyRingedSpace.coe_toΓSpecSheafedSpace_hom_base_hom_apply_asIdeal, ProfiniteGrp.topologicalGroup, AlgebraicGeometry.Scheme.Opens.toSpecΓ_preimage_basicOpen, Presheaf.isSheaf_iff_isSheaf_comp, range_pullback_map, AlgebraicGeometry.isIntegral_appTop_of_universallyClosed, AlgebraicGeometry.Scheme.Cover.exists_lift_trans_eq, AlgebraicGeometry.SheafedSpace.id_hom_c_app, AlgebraicGeometry.Scheme.zeroLocus_def, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_continuous, AlgebraicGeometry.Spec_map_localization_isIso, AlgebraicGeometry.StructureSheaf.isLocalizedModule_toPushforwardStalkAlgHom_aux, AlgebraicGeometry.Scheme.stalkClosedPointTo_fromSpecStalk, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_assoc, AlgebraicGeometry.ΓSpec.adjunction_counit_app, AlgebraicGeometry.StructureSheaf.algebraMap_self_map, prodIsoProd_inv_snd_assoc, instPreservesFiniteLimitsLightProfiniteLightCondSetLightProfiniteToLightCondSet, AlgebraicGeometry.Scheme.Hom.preimage_smoothLocus_eq, AlgebraicGeometry.tilde.isoTop_hom, AlgebraicGeometry.Scheme.coe_homeoOfIso_symm, LightProfinite.hasSheafify, AlgebraicGeometry.IsArtinianScheme.finite, AlgebraicGeometry.ProjectiveSpectrum.Proj.isLocalization_atPrime, AlgebraicGeometry.instIrreducibleSpaceCarrierCarrierCommRingCatPullbackSchemeOfGeometricallyIrreducibleOfUniversallyOpen, AlgebraicGeometry.Scheme.stalkMap_hom_inv_assoc, ProfiniteGrp.hom_comp, ModuleCat.Tilde.toOpen_res, AlgebraicGeometry.IsLocallyArtinian.iff_isLocallyNoetherian_and_discreteTopology, prodIsoProd_inv_fst_assoc, AlgebraicGeometry.Scheme.IdealSheafData.mem_supportSet_iff, AlgebraicGeometry.Scheme.IdealSheafData.range_subschemeι, AlgebraicGeometry.Scheme.Opens.toSpecΓ_appTop, AlgebraicGeometry.Scheme.IdealSheafData.mem_support_iff, AlgebraicGeometry.PresheafedSpace.GlueData.ι_image_preimage_eq, AlgebraicGeometry.Scheme.IdealSheafData.le_support_iff_le_vanishingIdeal, InfiniteGalois.mulEquivToLimit_symm_continuous, AlgebraicGeometry.PresheafedSpace.stalkMap.congr, AlgebraicGeometry.Scheme.Hom.isClosedMap, AlgebraicGeometry.Scheme.Hom.isLocallyClosed_range, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec_assoc, AlgebraicGeometry.opensDiagram_map, uliftFunctorObjHomeo_naturality_apply, smoothSheafCommRing.ι_evalHom, AlgebraicGeometry.Γ_restrict_isLocalization, homeoOfIso_apply, LightCondMod.LocallyConstant.instFullModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_presheafMap, AlgebraicGeometry.Scheme.Opens.toScheme_carrier, Stonean.epi_iff_surjective, AlgebraicGeometry.IsClosedImmersion.iff_isPreimmersion, AlgebraicGeometry.Scheme.Hom.app_eq, AlgebraicGeometry.morphismRestrict_ι, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_hom_app_app, AlgebraicGeometry.Scheme.Hom.preimageIso_inv_ι, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec, AlgebraicGeometry.Scheme.Hom.apply_mem_image_iff, AlgebraicGeometry.Scheme.Hom.asFiberHom_apply, LightProfinite.instWEqualsLocallyBijectiveCoherentTopology, ProfiniteAddGrp.instIsTopologicalAddGroupCarrierToTopTotallyDisconnectedSpacePtProfiniteLimitConeCompForget₂ContinuousAddMonoidHomToProfiniteContinuousMap, ProfiniteGrp.inv_hom_apply, SimplexCategory.instNonemptyCarrierObjTopCatToTop, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_inv_app_app, AlgebraicGeometry.ΓSpecIso_obj_hom, ProfiniteAddGrp.id_apply, TopologicalSpace.Opens.map_comp_map, AlgebraicGeometry.Proj.basicOpen_mul, AlgebraicGeometry.genericPoint_eq_of_isOpenImmersion, AlgebraicGeometry.Scheme.homeoOfIso_apply, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_naturality_assoc, AlgebraicGeometry.Spec.germ_stalkMapIso_hom_assoc, AlgebraicGeometry.Scheme.IdealSheafData.le_ofIdeals_iff, AlgebraicGeometry.Scheme.Hom.preimage_basicOpen_top, InfiniteGalois.isOpen_mulEquivToLimit_image_fixingSubgroup, sigmaIsoSigma_hom_ι_assoc, LightCondensed.isColimitLocallyConstantPresheafDiagram_desc_apply, AlgebraicGeometry.StructureSheaf.IsLocalization.to_basicOpen, AlgebraicGeometry.Scheme.Modules.restrict_map, Sheaf.objSupIsoProdEqLocus_hom_fst, nonempty_isLimit_iff_eq_induced, AlgebraicGeometry.Scheme.PartialMap.restrict_id, AlgebraicGeometry.isIso_stalkMap_coprodSpec, AlgebraicGeometry.AffineSpace.spec_le_iff, AlgebraicGeometry.Scheme.IsLocallyDirected.homOfLE_tAux, AlgebraicGeometry.LocallyRingedSpace.residue_comp_residueFieldMap_eq_stalkMap_comp_residue, FundamentalGroupoidFunctor.projLeft_map, AlgebraicGeometry.HasRingHomProperty.iff_appLE, Stonean.instPreregular, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap_assoc, AlgebraicGeometry.instQuasiSoberCarrierCarrierCommRingCat, AlgebraicGeometry.Scheme.Opens.exists_toScheme, AlgebraicGeometry.IsAffineOpen.self_le_basicOpen_union_iff, AlgebraicGeometry.exists_appTop_π_eq_of_isAffine_of_isLimit, Condensed.instPreservesFiniteProductsOppositeProfiniteVal, AlgebraicGeometry.Scheme.instIsIsoCommRingCatResidueFieldMapOfIsOpenImmersion, ProfiniteGrp.cone_pt, TopologicalSpace.Opens.mapMapIso_functor, AlgebraicGeometry.Scheme.instIsOverMapResidueFieldMapOverInferInstanceOverClass, piFan_pt, AlgebraicGeometry.Scheme.OpenCover.iSup_opensRange, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.image_preimage_is_empty, AlgebraicGeometry.HasAffineProperty.restrict, ContinuousMap.yonedaPresheaf_map, instPreservesLimitsOfShapeLightProfiniteLightCondSetLightProfiniteToLightCondSetOfCountableCategory, Sequential.isoOfHomeo_inv, AlgebraicGeometry.instT0SpaceCarrierCarrierCommRingCat, isoOfHomeo_hom, AlgebraicGeometry.RingedSpace.mem_zeroLocus_iff, id_app, AlgebraicGeometry.Scheme.Γevaluation_naturality_assoc, AlgebraicGeometry.opensDiagramι_app, AlgebraicGeometry.Scheme.Pullback.carrierEquiv_symm_snd, TopologicalSpace.Opens.mapIso_inv_app, AlgebraicGeometry.Scheme.IdealSheafData.coe_support_ofIdealTop, hasLimit_iff_small_sections, AlgebraicGeometry.Scheme.IdealSheafData.support_antitone, AlgebraicGeometry.Scheme.component_nontrivial, AlgebraicGeometry.isCompl_range_inl_inr, Presheaf.presheafEquivOfIso_unitIso_hom_app_app, LightCondensed.isoFinYonedaComponents_inv_comp, AlgebraicGeometry.Scheme.zeroLocus_iInf_of_nonempty, AlgebraicGeometry.Scheme.AffineZariskiSite.generate_presieveOfSections_mem_grothendieckTopology, AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app, AlgebraicGeometry.Scheme.basicOpen_pow, AlgebraicGeometry.Scheme.Opens.toSpecΓ_top, AlgebraicGeometry.IsLocallyNoetherian.quasiSeparatedSpace, AlgebraicGeometry.Scheme.Hom.ker_apply, ProfiniteAddGrp.coe_id, FundamentalGroupoidFunctor.instIsIsoFanGrpdObjTopCatFundamentalGroupoidFunctorPiTopToPiCone, piIsoPi_inv_π_apply, AlgebraicGeometry.Scheme.IdealSheafData.ideal_comap_of_isOpenImmersion, hom_id, AlgebraicGeometry.Scheme.Pullback.range_map, AlgebraicGeometry.ProjIsoSpecTopComponent.fromSpec_toSpec, AlgebraicGeometry.SurjectiveOnStalks.isEmbedding_pullback, AlexDisc.forgetToTop_faithful, AlgebraicGeometry.AffineSpace.SpecIso_inv_appTop_coord, AlgebraicGeometry.germ_stalkClosedPointIso_hom_assoc, AlgebraicGeometry.Scheme.Hom.isSpectralMap, AlgebraicGeometry.Scheme.IdealSheafData.support_eq_top_iff, AlgebraicGeometry.mem_range_iff_of_surjective, LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition', CompHausLike.LocallyConstant.functorToPresheaves_map_app, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_hom_app, TopologicalSpace.OpenNhds.id_apply, CondensedSet.topCatAdjunctionUnit_val_app_apply, AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality, AlgebraicGeometry.instIsIsoSchemeMorphismRestrict, Profinite.instEpiAppDiscreteQuotientCarrierToTopTotallyDisconnectedSpaceπAsLimitCone, GlueData.f_open, Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_pt, instFaithfulLightProfiniteLightCondSetLightProfiniteToLightCondSet, Presheaf.SheafConditionEqualizerProducts.piInters.hom_ext_iff, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_invApp, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_apply, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_naturality_assoc, AlgebraicGeometry.Scheme.Hom.appIso_inv_app, AlgebraicGeometry.Scheme.Hom.liftCoborder_preimage, InfiniteGalois.proj_adjoin_singleton_val, Presheaf.stalk_mono_of_mono, AlgebraicGeometry.Scheme.stalkMap_congr_hom_assoc, TopologicalSpace.Opens.op_map_id_obj, AlgebraicGeometry.Scheme.Hom.opensRange_pullbackFst, AlgebraicGeometry.Scheme.IdealSheafData.mem_supportSet_iff_mem_support, AlgebraicGeometry.Scheme.zeroLocus_radical, Sheaf.interUnionPullbackConeLift_right, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_inv_app_app, Profinite.instHasExplicitFiniteCoproductsTotallyDisconnectedSpaceCarrier, LightProfinite.Extend.functor_map, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_ι_assoc, AlgebraicGeometry.affineOpensRestrict_apply_coe_coe, AlgebraicGeometry.compactSpace_iff_quasiCompact, LightCondensed.instPreservesLimitsOfShapeOppositeLightProfiniteDiscreteCarrier, CondensedSet.instUCompactlyGeneratedSpaceCarrierObjTopCatCondensedSetToTopCat, AlgebraicGeometry.Scheme.AffineZariskiSite.presieveOfSections_surjective, CompHausLike.instT2SpaceCarrierObjTopCatCompHausLikeToTop, TopologicalSpace.Opens.mapMapIso_unitIso, AlgebraicGeometry.RingedSpace.basicOpen_le, TopologicalSpace.OpenNhds.map_id_obj_unop, AlgebraicGeometry.StructureSheaf.const_one, AlgebraicGeometry.Scheme.Opens.ι_appIso, ProfiniteGrp.limit_mul_val, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_toSpecΓ, AlgebraicGeometry.StructureSheaf.globalSectionsIso_hom, AlgebraicGeometry.disjoint_opensRange_sigmaι, AlgebraicGeometry.instLocallyQuasiFiniteMorphismRestrict, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app', AlgebraicGeometry.IsAffineOpen.toSpecΓ_isoSpec_inv, AlgebraicGeometry.Scheme.Hom.appIso_inv_naturality, isOpenEmbedding_iff_comp_isIso', CompactlyGenerated.isoOfHomeo_hom, ProfiniteGrp.ProfiniteCompletion.denseRange, LightCondensed.forget_map_val_app, AlgebraicGeometry.Scheme.basicOpen_add_le, AlgebraicGeometry.Scheme.Hom.comp_app_assoc, AlgebraicGeometry.Scheme.comp_app, isOpenEmbedding_f_zeroHypercover, TopologicalSpace.Opens.isOpenEmbedding, AlgebraicGeometry.Scheme.Hom.finite_app, Presheaf.stalk_hom_ext_iff, LightCondensed.isoLocallyConstantOfIsColimit_inv, AlgebraicGeometry.Scheme.AffineZariskiSite.coequifibered_iff_forall_isLocalizationAway, AlgebraicGeometry.instGeometricallyReducedMorphismRestrict, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_zeroLocus, GlueData.range_fromOpenSubsetsGlue, coe_id, Profinite.instReflectsEffectiveEpisCompHausProfiniteToCompHaus, AlgebraicGeometry.Scheme.GlueData.ι_eq_iff, AlgebraicGeometry.ΓSpec.left_triangle, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app_assoc, AlgebraicGeometry.FormallyUnramified.instIsSeparableCarrierResidueFieldCoeContinuousMapCarrierCarrierCommRingCatHomTopCatBaseOfLocallyOfFiniteType, AlgebraicGeometry.Scheme.Hom.ideal_ker_le, AlgebraicGeometry.AffineSpace.comp_homOfVector, FintypeCat.toLightProfinite_map_hom_hom_apply, AlgebraicGeometry.smooth_iff, CompactlyGenerated.isoOfHomeo_inv, uliftFunctorCompForgetIso_inv_app, AlgebraicGeometry.Scheme.Hom.appIso_hom', Presheaf.SheafConditionPairwiseIntersections.coneEquiv_inverse, AlgebraicGeometry.Scheme.zeroLocus_inf, AlgebraicGeometry.AffineSpace.isOpenMap_over, AlgebraicGeometry.surjective_iff, AlgebraicGeometry.Scheme.IdealSheafData.ofIdeals_mono, AlgebraicGeometry.Scheme.instIsOpenImmersionToSpecΓOfIsQuasiAffine, Sequential.isoOfHomeo_hom, Condensed.instIsRightKanExtensionFintypeCatCondensedModProfiniteProfiniteSolidProfiniteSolidCounit, instTotallyDisconnectedSpaceCarrierToTopTrueObjProfiniteCompHausProfiniteToCompHaus, ContinuousMap.yonedaPresheaf_obj, AlgebraicGeometry.Scheme.isoSpec_inv_naturality_assoc, Presheaf.pushforward_obj_obj, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self, AlgebraicGeometry.IsOpenImmersion.opensEquiv_apply_coe, AlgebraicGeometry.isClosedImmersion_iff_isAffineHom, AlgebraicGeometry.PresheafedSpace.restrictTopIso_hom, AlgebraicGeometry.isLocalIso_iff, AlgebraicGeometry.AffineSpace.hom_ext_iff, AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk_assoc, AlgebraicGeometry.ΓSpec.unop_locallyRingedSpaceAdjunction_counit_app', Stonean.forget.preservesLimits, AlgebraicGeometry.Scheme.Hom.preimage_basicOpen, AlgebraicGeometry.Scheme.singleton_mem_precoverage_iff, AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app, AlgebraicGeometry.IsLocallyArtinian.discreteTopology, AlgebraicGeometry.Scheme.Hom.isOpenMap, AlgebraicGeometry.Scheme.PartialMap.equiv_iff_of_isSeparated, LightProfinite.injective, AlgebraicGeometry.Scheme.isoSpec_Spec_hom, CompHausLike.instHasPropCarrierToTop, LightCondensed.isLocallySurjective_iff_locallySurjective_on_lightProfinite, AlgebraicGeometry.Scheme.basicOpen_res_eq, Profinite.projective_ultrafilter, AlgebraicGeometry.StructureSheaf.isLocalizedModule_toPushforwardStalkAlgHom, AlgebraicGeometry.Scheme.Pullback.Triplet.hx, AlgebraicGeometry.Scheme.Hom.isAffineOpen_iff_of_isOpenImmersion, CompHaus.toProfinite_obj', GlueData.MkCore.t_inv, AlgebraicGeometry.isOpenImmersion_iff_stalk, AlgebraicGeometry.Scheme.image_basicOpen, AlgebraicGeometry.tilde.isIso_toOpen_top, AlgebraicGeometry.Scheme.instQuasiSeparatedSpaceCarrierCarrierCommRingCatOfIsSeparated, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app, AlgebraicGeometry.LocallyRingedSpace.Hom.prop, Presheaf.SubmonoidPresheaf.map, AlgebraicGeometry.SurjectiveOnStalks.surj_on_stalks, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp, AlgebraicGeometry.HasRingHomProperty.appTop, AlgebraicGeometry.LocallyRingedSpace.basicOpen_zero, AlgebraicGeometry.isIntegral_iff_irreducibleSpace_and_isReduced, isClosed_iff_of_isColimit, AlgebraicGeometry.IsAffineOpen.image_of_isOpenImmersion, CompHausLike.LocallyConstant.locallyConstantIsoContinuousMap_hom, Condensed.isoLocallyConstantOfIsColimit_inv, AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot, AlgebraicGeometry.SurjectiveOnStalks.stalkMap_surjective, pullbackIsoProdSubtype_inv_snd_apply, AlgebraicGeometry.IsIntegral.component_integral, AlgebraicGeometry.morphismRestrict_comp, LightCondSet.instSequentialSpaceCarrierObjTopCatLightCondSetToTopCat, AlgebraicGeometry.PresheafedSpace.stalkMap.isIso, TopologicalSpace.Opens.coe_id, AlgebraicGeometry.IsProper.instMorphismRestrict, presheafToTypes_map, Profinite.instPreservesEffectiveEpisCompHausProfiniteToCompHaus, AlgebraicGeometry.Scheme.isPullback_toSpecΓ_toSpecΓ, AlgebraicGeometry.Scheme.Hom.genericPoint_mem_smoothLocus_of_perfectField, AlgebraicGeometry.Scheme.instSubsingletonCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensBot, AlgebraicGeometry.IsArtinianScheme.toCompactSpace, GlueData.fromOpenSubsetsGlue_isOpenEmbedding, AlgebraicGeometry.Scheme.ΓSpecIso_naturality, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv, lightDiagramToProfinite_obj, AlgebraicGeometry.Scheme.IdealSheafData.support_comap, AlgebraicGeometry.Scheme.restrictFunctorΓ_hom_app, TopologicalSpace.Opens.set_range_inclusion', AlgebraicGeometry.Scheme.stalkMap_congr_hom, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_hom_app_app, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_sup, AlgebraicGeometry.Scheme.Pullback.range_snd_comp, ProfiniteAddGrp.limit_add_val, Stonean.instHasPropExtremallyDisconnectedCarrier, Sheaf.comp_app, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_inv_app_app, smoothSheafCommRing.ι_forgetStalk_inv_apply, Condensed.lanPresheafNatIso_hom_app, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_jointly_surjective, AlgebraicGeometry.SheafedSpace.Γ_map, AlgebraicGeometry.Scheme.Modules.pushforwardComp_hom_app_app, Presheaf.IsSheaf.isSheafPreservesLimitPairwiseIntersections, AlgebraicGeometry.germ_stalkClosedPointIso_hom, Presheaf.isLocallySurjective_iff, AlgebraicGeometry.range_eq_univ, AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv, AlgebraicGeometry.IsFinite.instHasAffinePropertyAndIsAffineFiniteCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTopHomAppTop, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_fst, AlgebraicGeometry.Scheme.Hom.comp_apply, AlgebraicGeometry.IsAffineOpen.instIsAffineToSchemeBasicOpen, AlgebraicGeometry.Scheme.Modules.mapPresheaf_app, AlgebraicGeometry.Scheme.Hom.isOpenEmbedding, LightProfinite.surjective_transitionMapLE, pullbackIsoProdSubtype_inv_fst, AlgebraicGeometry.opensDiagram_obj, AlgebraicGeometry.PresheafedSpace.GlueData.f_invApp_f_app_assoc, AlgebraicGeometry.Scheme.Hom.preservesLocalization_normalizationDiagramMap, AlgebraicGeometry.Proj.basicOpen_mono, Profinite.Extend.functor_obj, AlgebraicGeometry.Scheme.residueFieldCongr_trans, StructureGroupoid.LocalInvariantProp.section_spec, AlgebraicGeometry.Spec.map_apply, TopologicalSpace.Opens.mapMapIso_inverse, AlgebraicGeometry.pointOfClosedPoint_apply, AlgebraicGeometry.Spec.sheafedSpaceMap_hom_c_app, AlgebraicGeometry.PresheafedSpace.GlueData.ι_isOpenEmbedding, Presheaf.Pushforward.comp_inv_app, AlgebraicGeometry.Scheme.toIso_inv_ι_assoc, Presheaf.covering_presieve_eq_self, AlgebraicGeometry.morphismRestrict_app', AlgebraicGeometry.SheafedSpace.restrictTopIso_inv, AlgebraicGeometry.Scheme.Hom.isEmbedding, AlgebraicGeometry.sigmaι_eq_iff, AlgebraicGeometry.opensCone_π_app, AlgebraicGeometry.Scheme.toSpecΓ_appTop, AlgebraicGeometry.Scheme.Hom.appIso_inv_naturality_assoc, AlgebraicGeometry.IsOpenImmersion.opensEquiv_symm_apply, AlgebraicGeometry.Scheme.IdealSheafData.support_eq_bot_iff, AlgebraicGeometry.GeometricallyIrreducible.irreducibleSpace_of_subsingleton, smoothSheaf.obj_eq, CompHausLike.mono_iff_injective, subsheafToTypes_val, AlgebraicGeometry.Scheme.stalkMap_comp, TopologicalSpace.Opens.mapId_inv_app, AlgebraicGeometry.PresheafedSpace.comp_c_app_assoc, TopModuleCat.freeMap_map, LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology, AlgebraicGeometry.isCompactOpen_iff_eq_finset_affine_union, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_hom_c_app, AlgebraicGeometry.IsAffineOpen.iSup_basicOpen_eq_self_iff, AlgebraicGeometry.Scheme.Hom.comp_appIso, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_map, AlgebraicGeometry.instJacobsonSpaceCarrierCarrierCommRingCatSpecOfOfIsJacobsonRing, AlgebraicGeometry.Scheme.basicOpen_one, AlgebraicGeometry.IsOpenImmersion.range_pullback_to_base_of_left, coinduced_of_isColimit, LightCondensed.free_internallyProjective_iff_tensor_condition', AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp, ProfiniteGrp.profiniteCompletion_map, AlgebraicGeometry.Scheme.Modules.Hom.id_app, AlgebraicGeometry.Scheme.IdealSheafData.map_vanishingIdeal, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_assoc, AlgebraicGeometry.targetAffineLocally_affineAnd_iff, AlgebraicGeometry.StructureSheaf.algebraMap_obj_top_bijective, TopologicalSpace.Opens.inclusion'_map_eq_top, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_assoc, Sheaf.pushforward_obj_val, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.coequalizer_π_stalk_isLocalHom, LightProfinite.instHasCountableLimits, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_self, LightProfinite.forget_reflectsIsomorphisms, CompHausLike.forget_reflectsIsomorphisms, AlgebraicGeometry.Scheme.Hom.ker_eq_top_iff_isEmpty, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq, AlgebraicGeometry.isClosed_singleton_iff_locallyOfFiniteType, AlgebraicGeometry.Scheme.Cover.ulift_I₀, prodIsoProd_hom_snd, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.instIsIsoCommRingCatInvApp, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_apply, AlgebraicGeometry.Scheme.Modules.Hom.isIso_iff_isIso_app, Condensed.isoFinYonedaComponents_inv_comp, AlgebraicGeometry.Scheme.Hom.residueFieldMap_congr, AlgebraicGeometry.Spec_zeroLocus_eq_zeroLocus, pullbackIsoProdSubtype_hom_snd, stoneCechObj_toTop_carrier, AlgebraicGeometry.Scheme.Opens.ι_appTop, AlgebraicGeometry.Scheme.Modules.Hom.comp_app, AlgebraicGeometry.Scheme.Hom.map_mem_image_iff, Condensed.instFinalOppositeDiscreteQuotientCarrierToTopTotallyDisconnectedSpaceCostructuredArrowFintypeCatProfiniteOpToProfiniteOpPtAsLimitConeFunctorOp, AlgebraicGeometry.Scheme.IdealSheafData.support_iSup, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd, Presheaf.presieveOfCovering.indexOfHom_spec, AlgebraicGeometry.Scheme.map_basicOpen, AlgebraicGeometry.IsOpenImmersion.affineOpensEquiv_apply_coe_coe, CondensedSet.continuous_coinducingCoprod, TopologicalSpace.Opens.adjunction_counit_map_functor, AlgebraicGeometry.coprodSpec_coprodMk, Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_inv_app_hom, AlgebraicGeometry.Scheme.IdealSheafData.opensRange_subschemeCover_map, AlgebraicGeometry.Proj.zero_apply, LightProfinite.instHasExplicitPullbacksAndTotallyDisconnectedSpaceCarrierSecondCountableTopology, AlgebraicGeometry.isRetrocompact_basicOpen, AlgebraicGeometry.Scheme.Hom.preimageIso_hom_ι, AlgebraicGeometry.affinePreimage, AlgebraicGeometry.Scheme.Hom.injective, AlgebraicGeometry.quasiSeparatedSpace_of_isAffine, AlgebraicGeometry.Scheme.isoSpec_inv_naturality, ProfiniteAddGrp.limit_ext_iff, AlgebraicGeometry.IsAffineOpen.toSpecΓ_fromSpec_assoc, AlgebraicGeometry.Spec_carrier, Sheaf.objSupIsoProdEqLocus_inv_snd, AlgebraicGeometry.isArtinianScheme_iff, Profinite.lift_lifts_assoc, pullbackIsoProdSubtype_inv_snd, AlgebraicGeometry.Scheme.Hom.id_appIso, AlgebraicGeometry.Scheme.empty_carrier_carrier, smoothSheafCommRing.ι_forgetStalk_inv_assoc, AlgebraicGeometry.IsArtinianScheme.iff_isNoetherian_and_discreteTopology, skyscraperPresheafCocone_ι_app, AlgebraicGeometry.Scheme.Hom.preimageIso_inv_ι_assoc, AlgebraicGeometry.Scheme.Hom.quasiFiniteLocus_eq_top_iff, AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.SectionSubring.one_mem', AlgebraicGeometry.instQuasiSeparatedToSpecΓOfQuasiSeparatedSpaceCarrierCarrierCommRingCat, AlgebraicGeometry.IsAffineOpen.basicOpenSectionsToAffine_isIso, AlgebraicGeometry.isAffineHom_iff, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberι, hasColimit_iff_small_colimitType, AlgebraicGeometry.PresheafedSpace.map_id_c_app, compatiblePreserving_opens_map, Presheaf.germ_exist, AlgebraicGeometry.exists_smooth_of_formallySmooth_stalk, AlgebraicGeometry.Scheme.comp_appTop_assoc, AlgebraicGeometry.QuasiCompact.compactSpace_of_compactSpace, Presheaf.SheafConditionEqualizerProducts.res_π, AlgebraicGeometry.Scheme.local_affine, AlgebraicGeometry.Proj.basicOpen_one, GlueData.fromOpenSubsetsGlue_injective, AlgebraicGeometry.PresheafedSpace.GlueData.f_invApp_f_app, prodIsoProd_inv_fst, AlgebraicGeometry.Scheme.IdealSheafData.ideal_top, AlgebraicGeometry.quasiSeparated_iff_quasiSeparatedSpace, TopologicalSpace.Opens.adjunction_counit_app_self, Presheaf.instIsLocalizationCarrierObjOppositeOpensCarrierCommRingCatObjLocalizationPresheaf, AlgebraicGeometry.LocallyOfFiniteType.stalkMap, TopologicalSpace.Opens.mem_map, AlgebraicGeometry.locallyQuasiFinite_iff_isDiscrete_preimage_singleton, instIsEquivalenceLightDiagramLightProfiniteLightDiagramToLightProfinite, AlgebraicGeometry.Scheme.IsLocallyDirected.ι_eq_ι_iff, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.coequalizer_π_app_isLocalHom, AlgebraicGeometry.Scheme.isoSpec_Spec, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_isIso, AlgebraicGeometry.instLocallyOfFiniteTypeMorphismRestrict, Presheaf.Pushforward.id_hom_app, AlgebraicGeometry.IsIntegralHom.instMorphismRestrict, Presheaf.pullback_obj_obj_ext_iff, LightCondSet.topCatAdjunctionCounit_bijective, CompactlyGenerated.homeoOfIso_symm_apply, Opens.coverDense_iff_isBasis, AlgebraicGeometry.isCompact_and_isOpen_iff_finite_and_eq_biUnion_affineOpens, AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_base_fst, AlgebraicGeometry.compactSpace_iff_exists, AlgebraicGeometry.instIrreducibleSpaceCarrierCarrierCommRingCatFiberOfGeometricallyIrreducible, AlgebraicGeometry.Scheme.Hom.preimage_sup, AlgebraicGeometry.IsClosedImmersion.hasAffineProperty, AlgebraicGeometry.Scheme.preimage_opensRange_toSpecΓ, AlgebraicGeometry.instIsOpenImmersionMorphismRestrict, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv, AlgebraicGeometry.Scheme.stalkMap_congr_point, topCatOpToFrm_obj_coe, AlgebraicGeometry.ProjectiveSpectrum.Proj.mk_mem_toSpec_base_apply, range_pullback_to_prod, AlgebraicGeometry.Scheme.eq_zeroLocus_of_isClosed_of_isAffine, LightProfinite.Extend.functorOp_map, Sheaf.interUnionPullbackConeLift_left, AlgebraicGeometry.Scheme.Opens.ι_preimage_self, GlueData.ι_isOpenEmbedding, AlgebraicGeometry.Scheme.stalkMap_hom_inv, subpresheafToTypes_map_coe, AlgebraicGeometry.Scheme.residueFieldCongr_refl, AlgebraicGeometry.Scheme.toSpecΓ_image_zeroLocus, AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c, AlgebraicGeometry.instQuasiSeparatedMorphismRestrict, AlgebraicGeometry.Scheme.Hom.image_iSup, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality, Alexandrov.lowerCone_π_app, AlgebraicGeometry.isImmersion_iff, AlgebraicGeometry.quasiSeparatedSpace_iff_forall_affineOpens, LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology, topToLocale_map, TopologicalSpace.Opens.map_comp_eq, CompHausLike.is_compact, AlgebraicGeometry.instNonemptyCarrierCarrierCommRingCatSpecOfNontrivialCarrier, pullback_fst_image_snd_preimage, AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv_assoc, TopModuleCat.instPreservesLimitsOfShapeTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitsOfShapeOfModuleCatForgetLinearMap, AlgebraicGeometry.SheafedSpace.Γ_obj_op, ProfiniteGrp.hom_inv_apply, AlgebraicGeometry.Scheme.Hom.comp_preimage, instEssentiallySmallLightProfinite, AlgebraicGeometry.Scheme.Modules.instIsIsoAbApp, AlgebraicGeometry.Scheme.Hom.naturality_assoc, AlgebraicGeometry.Scheme.IdealSheafData.opensRange_glueDataObjMap, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self_apply, AlgebraicGeometry.Scheme.stalkMap_hom_inv_apply, Presheaf.pushforward_map_app', continuous_iff_of_isColimit, AlgebraicGeometry.Scheme.Hom.iInf_ker_openCover_map_comp_apply, skyscraperPresheaf_eq_pushforward, AlgebraicGeometry.Scheme.Hom.isOpen_quasiFiniteAt, of.hasGroupoid, CondensedSet.topCatAdjunctionUnit_val_app, LightCondensed.hom_ext_iff, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_carrier, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_hom_app_val_app_apply, FundamentalGroupoid.map_eq, Presheaf.pushforward_obj_map, AlgebraicGeometry.Scheme.inv_appTop, AlgebraicGeometry.isLocalization_away_of_isAffine, AlgebraicGeometry.IsAffineOpen.ι_basicOpen_preimage, TopologicalSpace.Opens.map_iSup, Presheaf.presheafEquivOfIso_unitIso_inv_app_app, ProfiniteGrp.cone_π_app, AlgebraicGeometry.LocallyRingedSpace.isLocalHomStalkMap', AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv, instIsLeftAdjointForgetContinuousMapCarrier, pullbackIsoProdSubtype_inv_fst_apply, AlgebraicGeometry.structureSheafInType.add_apply, AlgebraicGeometry.morphismRestrict_appTop, AlgebraicGeometry.Scheme.Hom.exists_mem_and_isIso_morphismRestrict_toNormalization, AlgebraicGeometry.Scheme.IdealSheafData.ofIdealTop_ideal, LightCondensed.underlying_obj, CompHausLike.const_comp, AlgebraicGeometry.GeometricallyIrreducible.eq_geometrically, AlgebraicGeometry.Proj.basicOpen_eq_iSup_proj, AlgebraicGeometry.SheafedSpace.comp_hom_c_app', piIsoPi_hom_apply, AlgebraicGeometry.Scheme.Hom.preimage_opensRange, AlgebraicGeometry.ΓSpecIso_hom_stalkClosedPointIso_inv, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_apply, Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_π_app, AlgebraicGeometry.Proj.isBasis_basicOpen, AlgebraicGeometry.Scheme.descResidueField_stalkClosedPointTo_fromSpecResidueField, AlgebraicGeometry.Proj.ext_iff, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen, AlgebraicGeometry.LocallyRingedSpace.Γ_map, AlgebraicGeometry.isCompactOpen_iff_eq_basicOpen_union, Presheaf.presheafEquivOfIso_functor_obj_obj, AlexDisc.Iso.mk_inv, AlgebraicGeometry.PresheafedSpace.componentwiseDiagram_obj, CompHausLike.finiteCoproduct.ι_injective, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv, smoothSheaf.eval_germ, LightCondSet.hom_naturality_apply, AlgebraicGeometry.geometricallyIrreducible_iff, AlgebraicGeometry.isDominant_iff, AlgebraicGeometry.Flat.generalizingMap, AlgebraicGeometry.Scheme.Hom.fiberι_asFiber, AlgebraicGeometry.AffineSpace.isIntegralHom_over_iff_isEmpty, GlueData.MkCore.t_id, AlgebraicGeometry.HasAffineProperty.affineAnd_iff, AlgebraicGeometry.Scheme.default_asIdeal, AlgebraicGeometry.IsOpenImmersion.app_eq_appIso_inv_app_of_comp_eq, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.c_iso, AlgebraicGeometry.Scheme.IdealSheafData.ker_subschemeι_app, AlgebraicGeometry.IsOpenImmersion.ΓIso_inv, AlgebraicGeometry.Scheme.Modules.Hom.sub_app, Stonean.instHasExplicitPullbacksOfInclusionsExtremallyDisconnectedCarrier, AlgebraicGeometry.IsOpenImmersion.range_pullback_snd_of_left, AlgebraicGeometry.IsOpenImmersion.instIsIsoCommRingCatStalkMap, AlgebraicGeometry.isPreimmersion_iff, AlgebraicGeometry.Scheme.AffineCover.covers, AlgebraicGeometry.Proj.add_apply, AlgebraicGeometry.PresheafedSpace.Γ_obj, Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_map_hom, AlgebraicGeometry.Scheme.Hom.ι_toNormalization_assoc, AlgebraicGeometry.Scheme.Hom.Spec_map_residueFieldMap_fromSpecResidueField_assoc, AlgebraicGeometry.Scheme.isLocalHom_stalkClosedPointTo', AlgebraicGeometry.IsFinite.finite_preimage_singleton, AlgebraicGeometry.PresheafedSpace.toRestrictTop_c, AlgebraicGeometry.IsLocalAtTarget.restrict, CompactlyGenerated.is_compactly_generated, CondensedSet.isDiscrete_tfae, AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.mk_mem_carrier, LightProfinite.instTotallyDisconnectedSpaceCarrierToTopTruePtCompHausLimitConeCompLightProfiniteToCompHaus, AlgebraicGeometry.Scheme.Hom.fromNormalization_app_assoc, Profinite.exists_locallyConstant, AlgebraicGeometry.Scheme.isoSpec_inv_toSpecΓ_assoc, Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_pt, AlgebraicGeometry.ProjectiveSpectrum.Proj.isIso_toSpec, ContinuousMap.piComparison_fac, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app_apply, AlgebraicGeometry.Scheme.IdealSheafData.ideal_iInf, AlgebraicGeometry.stalkMap_toStalk_apply, AlgebraicGeometry.IsAffineOpen.primeIdealOf_eq_map_closedPoint, AlgebraicGeometry.Scheme.Hom.isoImage_inv_ι, Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_hom_app_hom, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι, AlgebraicGeometry.Scheme.Hom.isoImage_inv_ι_assoc, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc, AlgebraicGeometry.Scheme.Hom.instIsIsoCommRingCatAppObjOpensOpensFunctor, AlgebraicGeometry.Scheme.ker_morphismRestrict_ideal, AlgebraicGeometry.Scheme.Modules.pushforwardId_hom_app_app, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_ι, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst, Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_hom_hom, GlueData.preimage_range, AlgebraicGeometry.Scheme.toOpen_eq, alexDiscEquivPreord_unitIso, AlgebraicGeometry.IsOpenImmersion.range_pullback_to_base_of_right, isOpenEmbedding_iff_isIso_comp, AlgebraicGeometry.Scheme.Modules.restrict_obj, CompHaus.effectiveEpi_tfae, Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_pt, LightProfinite.instPreservesLimitsOfShapeOppositeNatForgetContinuousMapCarrierToTopAndTotallyDisconnectedSpaceSecondCountableTopology, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_assoc, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturality, TopologicalSpace.Opens.functor_map_eq_inf, Profinite.lift_lifts, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_unit_app_app, AlgebraicGeometry.isCompl_opensRange_inl_inr, AlgebraicGeometry.Scheme.Hom.isIntegral_app, AlgebraicGeometry.Scheme.Hom.app_eq_appLE, AlgebraicGeometry.Scheme.Pullback.Triplet.fst_SpecTensorTo_apply, AlgebraicGeometry.ΓSpecIso_inv_ΓSpec_adjunction_homEquiv, AlgebraicGeometry.RingedSpace.zeroLocus_empty_eq_univ, Presheaf.SubmonoidPresheaf.toLocalizationPresheaf_app, AlgebraicGeometry.StructureSheaf.res_apply, LightCondensed.equalizerCondition, CategoryTheory.Functor.mapPresheaf_map_c, AlgebraicGeometry.Scheme.Modules.Hom.add_app, instDiscreteTopologyCarrierObjDiscrete, AlgebraicGeometry.Scheme.IdealSheafData.isClosed_supportSet, AlexDisc.coe_forgetToTop, InfiniteGalois.toAlgEquivAux_eq_liftNormal, TopologicalSpace.OpenNhds.isOpenEmbedding, LightCondMod.hom_naturality_apply, TopModuleCat.forget₂_TopCat_obj, AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv, AlgebraicGeometry.isBasis_affine_open, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓUnitOpensCarrierCarrierCommRingCatRingCatSheaf, AlgebraicGeometry.IsClosedImmersion.isClosedEmbedding, AlgebraicGeometry.RingedSpace.basicOpen_mul, AlgebraicGeometry.Scheme.Hom.inv_appTop, CompHausLike.homeoOfIso_apply, topToPreord_map, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp_assoc, AlgebraicGeometry.IsLocallyArtinian.discreteTopology_of_isAffine, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.stalk_iso, AlgebraicGeometry.isIntegralHom_iff, GlueData.ofOpenSubsets_toGlueData_V, AlgebraicGeometry.RingedSpace.basicOpen_res_eq, LightCondensed.ihomPoints_symm_apply, AlgebraicGeometry.Spec_zeroLocus, AlgebraicGeometry.Scheme.basicOpen_mul, LightCondensed.discrete_obj, AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality, GlueData.image_inter, AlgebraicGeometry.Scheme.IdealSheafData.coe_support_eq_eq_iInter_zeroLocus, AlgebraicGeometry.Scheme.AffineZariskiSite.instIsDenseSubsiteOpensCarrierCarrierCommRingCatGrothendieckTopologyGrothendieckTopologyToOpensFunctor, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app, isEmbedding_pullback_to_prod, GlueData.ofOpenSubsets_toGlueData_f, AlgebraicGeometry.Scheme.PartialMap.mem_domain_ofFromSpecStalk, AlgebraicGeometry.Scheme.zeroLocus_biInf_of_nonempty, Condensed.StoneanProfinite.instPreservesEffectiveEpisStoneanProfiniteToProfinite, AlgebraicGeometry.Flat.stalkMap, ProfiniteGrp.toLimit_injective, AlgebraicGeometry.Scheme.Pullback.range_snd, Presheaf.isSheaf_on_punit_iff_isTerminal, AlgebraicGeometry.Scheme.Hom.stalkMap_comp, AlgebraicGeometry.Scheme.SpecΓIdentity_inv_app, AlexDisc.forgetToTop_full, Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_map_hom, pullbackIsoProdSubtype_hom_apply, AlgebraicGeometry.instJacobsonSpaceCarrierCarrierCommRingCatFiberOfLocallyOfFiniteType, Presheaf.isSheaf_iff_isSheaf_comp', AlgebraicGeometry.Scheme.Cover.exists_eq, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom, AlgebraicGeometry.Scheme.ofArrows_mem_precoverage_iff, lightProfiniteToLightDiagram_obj, Condensed.StoneanProfinite.instEffectivelyEnoughStoneanProfiniteToProfinite, AlgebraicGeometry.StructureSheaf.instIsLocalizedModuleCarrierStalkAbPresheafOpensCarrierTopModuleStructurePresheafPrimeComplAsIdealToStalkₗ, AlgebraicGeometry.Scheme.IsLocallyDirected.ι_jointly_surjective, AlgebraicGeometry.basicOpen_eq_of_affine', CompactlyGenerated.isoEquivHomeo_symm_apply, ProfiniteAddGrp.coe_comp, AlgebraicGeometry.IsPreimmersion.base_embedding, AlgebraicGeometry.Scheme.Hom.coe_image, AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom_appTop, AlgebraicGeometry.Scheme.Hom.coe_preimage, ofHom_apply, AlgebraicGeometry.Scheme.Opens.toScheme_presheaf_map, coneOfConeForget_π_app, LightDiagram.id_hom_hom_hom_apply, AlgebraicGeometry.instIsDominantToSpecΓOfCompactSpaceCarrierCarrierCommRingCat, LightCondMod.LocallyConstant.instFaithfulModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf, LightCondensed.lanPresheafNatIso_hom_app, smoothSheafCommRing.ι_forgetStalk_hom_apply, Sheaf.objSupIsoProdEqLocus_hom_snd, ProfiniteGrp.ofHom_apply, AlgebraicGeometry.Scheme.isoSpec_Spec_inv, AlgebraicGeometry.Scheme.IdealSheafData.supportSet_subset_zeroLocus, AlgebraicGeometry.Scheme.Hom.isClosedEmbedding, AlgebraicGeometry.Proj.awayι_preimage_basicOpen, AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiber, AlgebraicGeometry.isClosed_singleton_iff_isClosedImmersion, AlgebraicGeometry.IsFinite.finite_app, FundamentalGroupoidFunctor.piToPiTop_obj_as, lightCondSetToTopCat_obj_carrier, CompHaus.presentation.epi_π, AlgebraicGeometry.instSubsingletonCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensOfIsEmpty, AlgebraicGeometry.exists_eq_pow_mul_of_isAffineOpen, AlgebraicGeometry.Scheme.Opens.forall_toScheme, smoothSheafCommRing.ι_forgetStalk_hom_assoc, AlgebraicGeometry.Scheme.topIso_hom, AlgebraicGeometry.Proj.awayMap_awayToSection, AlgebraicGeometry.Scheme.Hom.finite_preimage_singleton, AlgebraicGeometry.finite_appTop_of_universallyClosed, AlgebraicGeometry.Scheme.AffineZariskiSite.toOpens_mono, Presheaf.presieveOfCovering.mem_grothendieckTopology, induced_of_isLimit, AlgebraicGeometry.IsLocallyNoetherian.component_noetherian, AlgebraicGeometry.Scheme.inv_hom_apply, AlgebraicGeometry.IsIntegralHom.integral_app, AlgebraicGeometry.isIso_SpecMap_stakMap_localization, AlgebraicGeometry.Scheme.residue_residueFieldMap_assoc, LightProfinite.Extend.cocone_pt, LightCondMod.epi_iff_locallySurjective_on_lightProfinite, Presheaf.SheafConditionEqualizerProducts.fork_pt, Profinite.instHasExplicitPullbacksTotallyDisconnectedSpaceCarrier, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app_assoc, AlgebraicGeometry.Scheme.IdealSheafData.support_map, ProfiniteGrp.instCompactSpaceSubtypeForallCarrierToTopTotallyDisconnectedSpaceToProfiniteObjMemSubgroupLimitConePtAux, Presheaf.SheafConditionEqualizerProducts.w_apply, AlgebraicGeometry.FormallyUnramified.stalkMap, AlgebraicGeometry.specTargetImageFactorization_app_injective, LightCondensed.ihom_map_val_app, AlgebraicGeometry.Scheme.IsGermInjectiveAt.cond, Presheaf.presheafEquivOfIso_counitIso_inv_app_app, AlgebraicGeometry.Scheme.IdealSheafData.zeroLocus_inter_subset_supportSet, AlgebraicGeometry.PresheafedSpace.stalkMap.congr_hom, AlgebraicGeometry.IsAffineOpen.preimage_of_isIso, AlgebraicGeometry.instIrreducibleSpaceCarrierCarrierCommRingCatPullbackSchemeOfGeometricallyIrreducibleOfUniversallyOpen_1, AlgebraicGeometry.PresheafedSpace.Γ_map, AlgebraicGeometry.instIsClosedImmersionMorphismRestrict, AlgebraicGeometry.Scheme.Hom.preimage_inf, FundamentalGroupoidFunctor.piIso_inv, Profinite.instEffectivelyEnoughCompHausProfiniteToCompHaus, TopologicalSpace.Opens.op_map_comp_obj, AlgebraicGeometry.SheafedSpace.id_c_app, AlgebraicGeometry.isPullback_morphismRestrict, prodIsoProd_hom_apply, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal', AlgebraicGeometry.Scheme.residue_residueFieldCongr, CompHausLike.toCompHausLike_map, AlgebraicGeometry.StructureSheaf.toOpenₗ_top_bijective, AlgebraicGeometry.StructureSheaf.comap_id_eq_map, AlgebraicGeometry.Scheme.Hom.appIso_hom, Condensed.isColimitLocallyConstantPresheafDiagram_desc_apply, AlgebraicGeometry.Scheme.OpenCover.finiteSubcover_X, AlgebraicGeometry.quasiSeparatedSpace_of_quasiSeparated, AlgebraicGeometry.Scheme.Pullback.range_fst, comp_app, AlgebraicGeometry.IsOpenImmersion.iff_stalk_iso, AlexDisc.Iso.mk_hom, AlgebraicGeometry.Scheme.Cover.fromGlued_isOpenEmbedding, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_apply, LightCondSet.LocallyConstant.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopologySubtypeToTop, InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj, AlgebraicGeometry.Scheme.residue_residueFieldMap, AlgebraicGeometry.Scheme.IdealSheafData.ideal_sup, AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom, AlgebraicGeometry.tilde.toOpen_res, Alexandrov.projSup_obj, AlgebraicGeometry.tilde.toOpen_res_assoc, AlgebraicGeometry.PresheafedSpace.stalkMap.comp, AlgebraicGeometry.Scheme.Hom.ι_fromNormalization_assoc, pullbackIsoProdSubtype_inv_snd_assoc, AlgebraicGeometry.Scheme.emptyTo_c_app, presheafToType_obj, epi_iff_surjective, AlgebraicGeometry.Scheme.stalkMap_inv_hom_apply, AlgebraicGeometry.instCompactSpaceCarrierCarrierCommRingCatFiberOfQuasiCompact, AlgebraicGeometry.Scheme.IsQuasiAffine.toCompactSpace, CompHaus.instCompactSpaceCarrierToTopTrue, AlgebraicGeometry.IsLocalIso.exists_isOpenImmersion, AlgebraicGeometry.Scheme.Opens.mem_basicOpen_toScheme, AlgebraicGeometry.affineAnd_apply, AlgebraicGeometry.Scheme.SpecMap_residue_apply, AlgebraicGeometry.tilde.isUnit_algebraMap_end_basicOpen, Condensed.instPreservesFiniteProductsOppositeStoneanVal, prodIsoProd_hom_fst, FundamentalGroupoidFunctor.prodIso_inv, Condensed.StoneanProfinite.instReflectsEffectiveEpisStoneanProfiniteToProfinite, CompactlyGenerated.isoEquivHomeo_apply, Profinite.Extend.cocone_ι_app, AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE_locally, AlgebraicGeometry.Scheme.Hom.image_le_opensRange, AlgebraicGeometry.noetherianSpace_of_isAffineOpen, AlgebraicGeometry.Scheme.Pullback.range_diagonal_subset_diagonalCoverDiagonalRange, AlgebraicGeometry.targetAffineLocally_affineAnd_iff', AlgebraicGeometry.AffineSpace.reindex_appTop_coord, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv_assoc, Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_inv_hom, AlgebraicGeometry.smoothOfRelativeDimension_iff, topToPreord_obj_coe, AlgebraicGeometry.quasiCompact_iff_forall_isAffineOpen, instIsRightAdjointForgetContinuousMapCarrier, AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE, AlgebraicGeometry.Scheme.Hom.mem_smoothLocus, AlgebraicGeometry.instSmoothMorphismRestrict, GlueData.fromOpenSubsetsGlue_isOpenMap, LightCondSet.instSequentialSpaceCarrierToTopCat, AlgebraicGeometry.Scheme.IdealSheafData.ideal_mono, AlgebraicGeometry.RingedSpace.isUnit_res_basicOpen, AlgebraicGeometry.Scheme.empty_presheaf, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_apply, AlgebraicGeometry.Scheme.Opens.ι_app_self, TopologicalSpace.Opens.mapComp_inv_app, AlgebraicGeometry.ΓSpec.toSpecΓ_of, AlgebraicGeometry.Scheme.zeroLocus_span, Presheaf.IsSheaf.isSheafPairwiseIntersections, AlgebraicGeometry.Scheme.IdealSheafData.ideal_iSup, AlgebraicGeometry.Scheme.Hom.naturality, AlgebraicGeometry.quasiSeparatedSpace_iff_quasiSeparated, AlgebraicGeometry.Scheme.Hom.image_injective, Presheaf.isGluing_iff_pairwise, Alexandrov.lowerCone_pt, AlgebraicGeometry.exists_isFinite_morphismRestrict_of_finite_preimage_singleton, AlgebraicGeometry.IsAffine.affine, AlgebraicGeometry.IsAffineOpen.instAwayCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecPresheafOpOpensBasicOpen, AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal.to_basicOpen, AlgebraicGeometry.Scheme.Pullback.Triplet.Spec_ofPointTensor_SpecTensorTo, AlgebraicGeometry.SheafedSpace.Γ_obj, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_top, AlgebraicGeometry.Proj.basicOpen_zero, FundamentalGroupoidFunctor.projRight_map, AlgebraicGeometry.formallyUnramified_iff, adj₂_counit, TopologicalSpace.Opens.map_comp_obj, AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf_map', Stonean.instReflectsEffectiveEpisCompHausToCompHaus, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_s, AlgebraicGeometry.Scheme.mem_basicOpen_top, AlgebraicGeometry.QuasiCompactCover.isCompactOpenCovered_of_isAffineOpen, Condensed.isoFinYoneda_hom_app, AlgebraicGeometry.Scheme.Opens.range_ι, AlgebraicGeometry.IsAffineOpen.range_fromSpec, AlgebraicGeometry.IsOpenImmersion.image_preimage_eq_preimage_image_of_isPullback, AlgebraicGeometry.isClosedImmersion_iff, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen', prodIsoProd_inv_snd, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_assoc, TopModuleCat.instPreservesLimitsTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, Profinite.Extend.cone_pt, AlgebraicGeometry.Spec_closedPoint, AlgebraicGeometry.Scheme.Hom.range_subset_ker_support, instFullLightProfiniteLightCondSetLightProfiniteToLightCondSet, Profinite.NobelingProof.spanFunctorIsoIndexFunctor_inv_app, lightDiagramToLightProfinite_map, AlgebraicGeometry.LocallyRingedSpace.preimage_basicOpen, AlgebraicGeometry.ProjectiveSpectrum.Proj.stalkMap_toSpec, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_toSpecΓ_assoc, hom_inv_id_apply, piIsoPi_inv_π, nonempty_isColimit_iff_eq_coinduced, AlgebraicGeometry.AffineSpace.homOverEquiv_apply, AlgebraicGeometry.Scheme.Hom.finite_preimage, AlgebraicGeometry.Scheme.Opens.ι_apply, LightProfinite.surjective_transitionMap, AlgebraicGeometry.Scheme.Modules.instFullPresheafOfModulesToPresheafOfModules, CompHaus.epi_iff_surjective, AlgebraicGeometry.Scheme.Hom.dense_smoothLocus_of_perfectField, AlgebraicGeometry.quasiCompact_iff_compactSpace, mono_iff_injective, AlgebraicGeometry.pullbackRestrictIsoRestrict_inv_fst_assoc, AlgebraicGeometry.Scheme.basicOpen_res, AlgebraicGeometry.Scheme.iso_inv_base_hom_base_apply, AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp, AlgebraicGeometry.Scheme.Hom.continuous, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberToSpecResidueField, TopologicalSpace.Opens.mapIso_hom_app, Sheaf.objSupIsoProdEqLocus_inv_fst, smoothSheaf.ι_evalHom, homeoOfIso_symm_apply, AlgebraicGeometry.Smooth.exists_isStandardSmooth, ProfiniteGrp.coe_comp, AlgebraicGeometry.Scheme.Pullback.Triplet.exists_preimage, AlgebraicGeometry.Scheme.comp_appTop, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv_apply, smoothSheafCommRing.ι_evalHom_assoc, AlgebraicGeometry.Surjective.surj, AlgebraicGeometry.Scheme.IdealSheafData.radical_ideal, AlgebraicGeometry.isCompact_iff_finite_and_eq_biUnion_affineOpens, Presheaf.Pushforward.comp_hom_app, AlgebraicGeometry.IsClosedImmersion.isAffine_surjective_of_isAffine, AlgebraicGeometry.Scheme.AffineZariskiSite.mem_grothendieckTopology, AlgebraicGeometry.Scheme.stalkMap_inv_hom, AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp_assoc, ContinuousMap.yonedaPresheaf'_map, AlgebraicGeometry.StructureSheaf.toOpenₗ_eq_const, Profinite.projective_of_extrDisc, LightCondensed.lanPresheafExt_inv, LightProfinite.epi_iff_surjective, AlgebraicGeometry.Scheme.comp_base_apply, Condensed.lanPresheafExt_hom, AlgebraicGeometry.isGermInjectiveAt_iff_of_isOpenImmersion, AlgebraicGeometry.IsAffineOpen.isLocalization_stalk, instFullLightDiagramProfiniteLightDiagramToProfinite, AlgebraicGeometry.PresheafedSpace.GlueData.ι_jointly_surjective, smoothSheaf.contMDiff_section, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_comp, AlgebraicGeometry.isField_of_universallyClosed, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_base_apply, Profinite.injective_of_finite, AlgebraicGeometry.Scheme.IdealSheafData.ideal_inf, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_eq_zero_iff_notMem_basicOpen, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq_comap, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv_assoc, Stonean.instProjectiveCompHausCompHaus, smoothSheafCommRing.ι_forgetStalk_hom, AlgebraicGeometry.IsDominant.denseRange, InfiniteGalois.mk_toAlgEquivAux, AlgebraicGeometry.instGeometricallyIntegralMorphismRestrict, AlgebraicGeometry.mem_basicOpen_den, AlgebraicGeometry.Flat.iff_flat_stalkMap, AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app_surjective, AlgebraicGeometry.Scheme.preimage_zeroLocus, AlgebraicGeometry.PresheafedSpace.congr_app, AlgebraicGeometry.isIso_iff_stalk_iso, AlgebraicGeometry.Scheme.instIsOverMapStalkMapOverInferInstanceOverClass, AlgebraicGeometry.Scheme.AffineZariskiSite.cocone_ι_app, Presheaf.presheafEquivOfIso_counitIso_hom_app_app, AlgebraicGeometry.Scheme.Hom.smoothLocus_eq_top, instCompactSpaceCarrierDiskBoundary, GlueData.ι_jointly_surjective, AlgebraicGeometry.Scheme.IdealSheafData.coe_support_inter, CompHausLike.isoOfHomeo_inv_hom_hom_apply, AlgebraicGeometry.compactSpace_of_universallyClosed, AlgebraicGeometry.IsAffineOpen.fromSpec_top, AlgebraicGeometry.Scheme.Hom.support_ker, AlgebraicGeometry.SpecToEquivOfLocalRing_symm_apply, AlgebraicGeometry.Scheme.Hom.homeomorph_apply, AlgebraicGeometry.Scheme.Hom.stalkMap_congr, AlgebraicGeometry.Scheme.IdealSheafData.support_top, AlgebraicGeometry.Scheme.map_basicOpen_map, prodIsoProd_hom_fst_assoc, AlgebraicGeometry.affineOpensRestrict_symm_apply_coe, CompHaus.Gleason, AlgebraicGeometry.PresheafedSpace.id_c_app, AlgebraicGeometry.Scheme.Hom.comp_appTop, AlgebraicGeometry.instNoetherianSpaceCarrierCarrierCommRingCatSpecOfIsNoetherianRingCarrier, AlgebraicGeometry.IsOpenImmersion.opensRange_pullback_snd_of_left, LightCondMod.LocallyConstant.instFullSheafLightProfiniteCoherentTopologyTypeConstantSheaf, AlgebraicGeometry.IsIntegralHom.hasAffineProperty, AlgebraicGeometry.instJacobsonSpaceCarrierCarrierCommRingCatSpecOfIsJacobsonRingCarrier, CompHausLike.hom_ofHom, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec, AlexDisc.is_alexandrovDiscrete, AlgebraicGeometry.Scheme.basicOpen_zero, InfiniteGalois.proj_of_le, AlgebraicGeometry.Scheme.Hom.surjective, AlgebraicGeometry.Scheme.residue_residueFieldCongr_assoc, AlgebraicGeometry.Scheme.IdealSheafData.ideal_ofIdeals_le, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.sigma_ι_isOpenEmbedding, Stonean.instProjectiveProfiniteObjToProfinite, AlgebraicGeometry.Scheme.IsLocallyDirected.exists_of_pullback_V_V, AlgebraicGeometry.Scheme.SpecMap_presheaf_map_eqToHom, AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.SectionSubring.zero_mem', AlgebraicGeometry.IsAffineOpen.fromSpec_image_basicOpen, AlgebraicGeometry.instHasAffinePropertyIsomorphismsSchemeAndIsAffineIsIsoCommRingCatAppTop, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_morphismRestrict, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.imageBasicOpen_image_preimage, TopologicalSpace.Opens.infLELeft_apply, isOpen_iff_of_isColimit_cofork, AlgebraicGeometry.IsAffineOpen.basicOpen_union_eq_self_iff, LightCondSet.isDiscrete_tfae, AlgebraicGeometry.isFinite_iff, Presheaf.presheafEquivOfIso_inverse_obj_obj, LightCondSet.topCatAdjunctionUnit_val_app, AlgebraicGeometry.etale_iff, LightDiagram.comp_hom_hom_hom_apply, AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_inv_ι_app, TopModuleCat.instReflectsIsomorphismsTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, Profinite.presentation.epi_π, LightCondensed.instFinalNatCostructuredArrowOppositeFintypeCatLightProfiniteOpToLightProfiniteOpPtAsLimitConeFunctorOp, instIsContinuousOpensCarrierMapGrothendieckTopology, isQuotientMap_of_isColimit_cofork, AlgebraicGeometry.isAffineOpen_bot, AlgebraicGeometry.Scheme.IsLocallyDirected.V_self, AlgebraicGeometry.Scheme.Opens.ι_image_le, LightProfinite.instPreregular, forget_preservesColimitsOfSize, LightCondMod.LocallyConstant.instHasSheafifyLightProfiniteCoherentTopologyModuleCat, AlgebraicGeometry.StructureSheaf.comap_basicOpen, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_assoc, AlgebraicGeometry.IsOpenImmersion.opensRange_pullback_fst_of_right, AlgebraicGeometry.Scheme.mem_basicOpen'', AlgebraicGeometry.Scheme.AffineZariskiSite.cocone_pt, ProfiniteGrp.toLimitFun_continuous, Action.isContinuous_def, AlgebraicGeometry.isEmpty_pullback_sigmaι_of_ne, AlgebraicGeometry.Scheme.stalkMap_inv_hom_assoc, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.preimage_toBase_eq_range_ι, isOpen_iff_of_isColimit, AlgebraicGeometry.tilde.toOpen_map_app_assoc, AlgebraicGeometry.locallyQuasiFinite_iff_finite_preimage_singleton, AlgebraicGeometry.Spec.topObj_forget, adj₂_unit, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_ne_zero_iff_mem_basicOpen, AlgebraicGeometry.basicOpen_eq_of_affine, AlgebraicGeometry.LocallyRingedSpace.Γ_map_op, TopologicalSpace.OpenNhds.map_id_obj, ProfiniteGrp.diagram_map, forget_preservesLimits, AlgebraicGeometry.Scheme.ΓSpecIso_naturality_assoc, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ_assoc, AlgebraicGeometry.Scheme.Hom.comp_image, AlgebraicGeometry.IsOpenImmersion.range_pullbackFst, AlgebraicGeometry.IsAffineOpen.fromSpec_image_zeroLocus, AlgebraicGeometry.PresheafedSpace.toRestrictTop_base, AlgebraicGeometry.LocallyRingedSpace.isUnit_res_toΓSpecMapBasicOpen, AlgebraicGeometry.Scheme.affineBasisCover_map_range, LightCondensed.id_val, InfiniteGalois.algEquivToLimit_continuous, AlgebraicGeometry.ΓSpec_adjunction_homEquiv_eq, AlgebraicGeometry.Flat.isQuotientMap_of_surjective, AlgebraicGeometry.Scheme.Opens.ι_app, AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.isClopen_singleton_asFiber, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_inv_app_app, AlgebraicGeometry.Scheme.IdealSheafData.supportSet_inter, AlgebraicGeometry.instIsPreimmersionAsFiberHom, AlgebraicGeometry.locallyOfFinitePresentation_iff, AlgebraicGeometry.Scheme.Hom.isoImage_hom_ι, AlgebraicGeometry.IsAffineOpen.isOpenImmersion_fromSpec, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_hom_assoc, AlgebraicGeometry.spread_out_unique_of_isGermInjective', AlgebraicGeometry.quasiCompact_iff_spectral, AlgebraicGeometry.Scheme.iso_hom_base_inv_base_apply, prodIsoProd_inv_fst_apply, LightProfinite.Extend.functor_obj, LightCondensed.isoFinYoneda_hom_app, AlgebraicGeometry.instUniversallyClosedMorphismRestrict, AlgebraicGeometry.Scheme.toIso_inv_ι, AlgebraicGeometry.SheafedSpace.congr_hom_app, AlgebraicGeometry.quasiCompact_iff_isSpectralMap, AlgebraicGeometry.Scheme.Hom.instIsIsoCommRingCatApp, AlgebraicGeometry.Scheme.residueFieldCongr_trans_hom, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_preimage_basicOpen, sigmaCofan_pt, effectiveEpi_iff_isQuotientMap, AlgebraicGeometry.Scheme.Hom.inv_image, colimit_isOpen_iff, ProfiniteGrp.id_apply, adj₁_unit, TopologicalSpace.Opens.map_top, AlgebraicGeometry.IsPreimmersion.instMorphismRestrict, AlgebraicGeometry.PresheafedSpace.GlueData.ιInvApp_π, Profinite.Nobeling.isClosedEmbedding, Presheaf.presheafEquivOfIso_functor_map_app, LightProfinite.proj_surjective, AlgebraicGeometry.Scheme.Hom.opensRange_comp, AlgebraicGeometry.Scheme.Hom.ι_fromNormalization, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_zeroLocus_eq, AlgebraicGeometry.exists_finite_imageι_comp_morphismRestrict_of_finite_image_preimage, AlgebraicGeometry.genericPoint_eq_bot_of_affine, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_hom_app, AlgebraicGeometry.IsAffineOpen.isCompactOpenCovered, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.base_open, AlgebraicGeometry.instIsQuasicoherentOpensCarrierCarrierCommRingCatSpecTilde, adj₁_counit, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_hom, AlgebraicGeometry.LocallyRingedSpace.evaluation_ne_zero_iff_mem_basicOpen, alexDiscEquivPreord_counitIso, TopologicalSpace.Opens.apply_def, AlgebraicGeometry.Scheme.IdealSheafData.coe_support_vanishingIdeal, AlgebraicGeometry.Scheme.Γevaluation_naturality, LightProfinite.proj_comp_transitionMapLE, LightProfinite.instEpiAppOppositeNatπAsLimitCone, CompHausLike.isoEquivHomeo_apply, AlgebraicGeometry.IsSeparated.instMorphismRestrict, AlgebraicGeometry.Scheme.PartialMap.dense_domain, GlueData.ι_eq_iff_rel, AlgebraicGeometry.basicOpen_eq_bot_iff, AlgebraicGeometry.Scheme.IdealSheafData.ker_glueDataObjι_appTop, AlgebraicGeometry.Spec.germ_stalkMapIso_hom, TopologicalSpace.Opens.mapMapIso_counitIso, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_apply, AlgebraicGeometry.HasRingHomProperty.stalkMap_of_respectsIso, AlgebraicGeometry.Scheme.restrictFunctor_obj_left, LightCondMod.LocallyConstant.instFaithfulSheafLightProfiniteCoherentTopologyTypeConstantSheaf, AlgebraicGeometry.LocallyOfFiniteType.jacobsonSpace, ProfiniteGrp.isIso_toLimit, AlgebraicGeometry.Spec.fromSpecStalk_eq, AlgebraicGeometry.quasiCompact_iff_forall_affine, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over, AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf, Presheaf.stalkSpecializes_refl, AlgebraicGeometry.instLocallyOfFinitePresentationMorphismRestrict, AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_π, LightCondensed.instHasColimitsOfShapeCostructuredArrowOppositeFintypeCatLightProfiniteOpToLightProfiniteType, AlgebraicGeometry.Scheme.IdealSheafData.ideal_biInf, AlgebraicGeometry.Scheme.isLocalHom_stalkClosedPointTo, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality, AlgebraicGeometry.Proj.iSup_basicOpen_eq_top, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen', AlgebraicGeometry.Scheme.basicOpen_restrict, CompHausLike.is_hausdorff, AlgebraicGeometry.structurePresheafInCommRingCat_obj_carrier, AlgebraicGeometry.Scheme.IdealSheafData.support_bot, AlgebraicGeometry.Scheme.Hom.opensRange_of_isIso, instSecondCountableTopologyCarrierToTopTotallyDisconnectedSpacePtOppositeNatProfiniteCone, AlgebraicGeometry.IsAffineOpen.app_basicOpen_eq_away_map, AlgebraicGeometry.LocallyRingedSpace.toΓSpecMapBasicOpen_eq, InfiniteGalois.limitToAlgEquiv_symm_apply, coe_of, LightCondensed.internallyProjective_iff_tensor_condition', AlgebraicGeometry.StructureSheaf.instAwayObjOppositeOpensCarrierTopValStructureSheafInTypeOpBasicOpen, AlgebraicGeometry.Scheme.preimage_basicOpen, AlgebraicGeometry.Scheme.Opens.instIsIsoCommRingCatAppLEιTopToScheme, LightProfinite.hasSheafify_type, AlgebraicGeometry.IsAffineHom.isAffine_preimage, LightCondensed.comp_val, Presheaf.toPushforwardOfIso_app, AlgebraicGeometry.IsAffineOpen.ΓSpecIso_hom_fromSpec_app, AlgebraicGeometry.SpecToEquivOfLocalRing_eq_iff, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_inv_app_val_app_hom_hom, AlgebraicGeometry.Scheme.restrictFunctor_map_left, CompHausLike.instCompactSpaceCarrierObjTopCatCompHausLikeToTop, AlgebraicGeometry.Scheme.Hom.SpecMap_residueFieldMap_fromSpecResidueField, coe_comp, AlgebraicGeometry.Scheme.affineOpenCover_X, AlgebraicGeometry.Scheme.comp_app_assoc, Presheaf.generateEquivalenceOpensLe_functor'_map, AlgebraicGeometry.IsAffineOpen.isQuasiSeparated, AlexDisc.coe_of, CompHausLike.isoOfHomeo_hom_hom_hom_apply, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_y, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp_assoc, AlgebraicGeometry.instQuasiCompactToSpecΓOfCompactSpaceCarrierCarrierCommRingCat, SkyscraperPresheafFunctor.map'_app, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_assoc, AlgebraicGeometry.morphismRestrict_app, AlgebraicGeometry.AffineSpace.comp_homOfVector_assoc, AlgebraicGeometry.Scheme.PartialMap.le_domain_toRationalMap, AlgebraicGeometry.LocallyRingedSpace.toStalk_stalkMap_toΓSpec, AlgebraicGeometry.Scheme.Modules.instIsRightAdjointPresheafOfModulesToPresheafOfModules, AlgebraicGeometry.Scheme.Opens.ι_image_top, AlgebraicGeometry.Scheme.Hom.toImage_app, AlgebraicGeometry.Scheme.range_fromSpecResidueField, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_hom_app_app, Sheaf.eq_of_locally_eq_iff, AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk, LightCondensed.underlying_map, exists_mem_zeroHypercover_range, AlgebraicGeometry.Scheme.zeroLocus_isClosed, AlgebraicGeometry.Scheme.AffineZariskiSite.instIsLocallyFullOpensToOpensFunctorGrothendieckTopologyCarrierCarrierCommRingCat, AlgebraicGeometry.IsAffineOpen.isoSpec_hom, AlgebraicGeometry.Scheme.Modules.Hom.app_smul, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec, AlgebraicGeometry.Scheme.Γ_obj_op, sigmaIsoSigma_hom_ι_apply, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_invApp, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_apply, Presheaf.IsSheaf.isSheafOpensLeCover, AlgebraicGeometry.Scheme.Hom.mem_quasiFiniteLocus, LightCondMod.isDiscrete_iff_isDiscrete_forget, coverPreserving_opens_map, Presheaf.IsSheaf.isSheafUniqueGluing, AlgebraicGeometry.quasiCompactCover_iff, AlgebraicGeometry.Scheme.image_zeroLocus, AlgebraicGeometry.Scheme.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, AlgebraicGeometry.HasRingHomProperty.iff_of_source_openCover, AlgebraicGeometry.Scheme.Hom.isoImage_hom_ι_assoc, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCBasicOpens_app, AlgebraicGeometry.LocallyRingedSpace.evaluation_eq_zero_iff_notMem_basicOpen, AlgebraicGeometry.Proj.res_apply, AlgebraicGeometry.Scheme.isBasis_affineOpens, Presheaf.app_injective_iff_stalkFunctor_map_injective, AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.preimage_basicOpen, AlgebraicGeometry.Scheme.Hom.fiberToSpecResidueField_apply, AlgebraicGeometry.Scheme.Opens.topIso_hom, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv_assoc, DeltaGenerated.deltaGenerated, AlgebraicGeometry.Scheme.IdealSheafData.support_sup, AlgebraicGeometry.StructureSheaf.toOpen_res, AlgebraicGeometry.structurePresheafInModuleCat_obj_carrier, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec_assoc, AlgebraicGeometry.Scheme.IsLocallyDirected.homOfLE_tAux_assoc, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_SpecTensorTo, AlgebraicGeometry.SheafedSpace.congr_app, AlgebraicGeometry.Scheme.OpenCover.restrict_X, AlgebraicGeometry.Scheme.zeroLocus_univ, instIsEquivalenceLightProfiniteLightDiagramLightProfiniteToLightDiagram, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_spec, FundamentalGroupoidFunctor.prodToProdTop_map, Presheaf.SheafConditionPairwiseIntersections.coneEquiv_functor, AlgebraicGeometry.Scheme.JointlySurjective.exists_eq, AlgebraicGeometry.Scheme.Hom.image_le_image_iff, LightCondSet.toTopCatMap_hom_apply, AlgebraicGeometry.Scheme.Hom.comp_appTop_assoc, CompHaus.effectiveEpiFamily_tfae, AlgebraicGeometry.AffineSpace.map_appTop_coord, AlgebraicGeometry.Scheme.toSpecΓ_preimage_basicOpen, LightCondensed.lanPresheafExt_hom, AlgebraicGeometry.LocallyRingedSpace.isLocalHom_stalkMap_congr, ext_iff, AlgebraicGeometry.Scheme.residueFieldCongr_trans_hom_assoc, Presheaf.isIso_iff_stalkFunctor_map_iso, AlgebraicGeometry.Scheme.Hom.app_appIso_inv, limit_topology, AlgebraicGeometry.isIso_fromTildeΓ_iff, Sequential.is_sequential, Sheaf.interUnionPullbackCone_pt, AlgebraicGeometry.Scheme.residueFieldCongr_inv, Presheaf.SheafConditionPairwiseIntersections.coneEquiv_unitIso, Profinite.exists_locallyConstant_finite_nonempty, AlgebraicGeometry.Scheme.coe_homeoOfIso, AlgebraicGeometry.PresheafedSpace.restrictTopIso_inv, Presheaf.stalkPushforward.comp, Alexandrov.isSheaf_principalsKanExtension, AlgebraicGeometry.Scheme.Hom.normalizationObjIso_hom_val, AlgebraicGeometry.Scheme.openCoverBasicOpenTop_f, AlgebraicGeometry.pointEquivClosedPoint_symm_apply_coe, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_hom_c_app, Profinite.hasLimits, Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_pt, AlgebraicGeometry.Scheme.Hom.appLE_eq_app, AlgebraicGeometry.Scheme.RationalMap.mem_domain, AlgebraicGeometry.Scheme.IdealSheafData.support_sSup, AlgebraicGeometry.instHasAffinePropertyQuasiCompactCompactSpaceCarrierCarrierCommRingCat, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app_assoc, AlgebraicGeometry.StructureSheaf.const_apply, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec.image_basicOpen_eq_basicOpen, AlgebraicGeometry.IsOpenImmersion.app_eq_invApp_app_of_comp_eq_aux, AlgebraicGeometry.isField_of_isIntegral_of_subsingleton, AlgebraicGeometry.spec_punit_isEmpty, AlgebraicGeometry.isClosedMap_iff_specializingMap, pullback_snd_range, AlgebraicGeometry.PresheafedSpace.map_comp_c_app, Presheaf.coveringOfPresieve_apply, AlgebraicGeometry.Scheme.image_preimage_eq_of_isPullback, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app, AlgebraicGeometry.Scheme.Hom.instIsLocalHomCarrierStalkCommRingCatPresheafCoeContinuousMapCarrierCarrierHomTopCatBaseRingHomHomStalkMap, ProfiniteGrp.instPreservesLimitsProfiniteForget₂ContinuousMonoidHomCarrierToTopTotallyDisconnectedSpaceToProfiniteContinuousMap, subpresheafToTypes_obj, Presheaf.submonoidPresheafOfStalk_obj, Condensed.isoFinYoneda_inv_app, AlgebraicGeometry.LocallyRingedSpace.stalkMap_comp, AlgebraicGeometry.Scheme.GlueData.ι_jointly_surjective, AlgebraicGeometry.SheafedSpace.isColimit_exists_rep, FundamentalGroupoidFunctor.proj_map, AlgebraicGeometry.StructureSheaf.algebraMap_pushforward_stalk, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_iSup, AlexDisc.forgetToTop_of, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_invApp, AlgebraicGeometry.Scheme.IdealSheafData.strictMono_ideal, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv_apply, AlgebraicGeometry.Scheme.codisjoint_zeroLocus, DeltaGenerated.topToDeltaGenerated_obj_toTop_carrier, of_carrier, TopologicalSpace.OpenNhds.inclusionMapIso_inv_app, AlgebraicGeometry.Scheme.PartialMap.restrict_id_hom, AlgebraicGeometry.Scheme.stalkClosedPointTo_comp, ProfiniteGrp.limit_ext_iff, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_apply, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ, AlgebraicGeometry.map_injective_of_isIntegral, CompHaus.instExtremallyDisconnectedCarrierToTopTrueOfProjective, AlgebraicGeometry.AffineSpace.homOfVector_appTop_coord, AlgebraicGeometry.Scheme.Spec_map_residue_apply, AlgebraicGeometry.sourceAffineLocally_morphismRestrict, Profinite.exists_locallyConstant_fin_two, AlgebraicGeometry.Scheme.IsQuasiAffine.isBasis_basicOpen, AlgebraicGeometry.initial_isEmpty, AlgebraicGeometry.Proj.stalkIso'_symm_mk, GlueData.ι_injective, AlgebraicGeometry.Scheme.residueFieldMap_comp, AlgebraicGeometry.structureSheafInType.smul_apply, AlgebraicGeometry.Etale.instMorphismRestrict, ProfiniteAddGrp.hom_comp, AlgebraicGeometry.Scheme.isoSpec_image_zeroLocus, Profinite.effectiveEpiFamily_tfae, AlgebraicGeometry.Scheme.Hom.fiberι_fiberHomeo_symm, AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_eq_id, AlgebraicGeometry.Scheme.IdealSheafData.ideal_map_of_isAffineHom, AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalk, AlgebraicGeometry.isCompact_and_isOpen_iff_finite_and_eq_biUnion_basicOpen, hom_comp, LightProfinite.proj_comp_transitionMap', AlgebraicGeometry.LocallyRingedSpace.isLocalHomValStalkMap, AlgebraicGeometry.IsAffineOpen.toSpecΓ_isoSpec_inv_assoc, AlgebraicGeometry.PresheafedSpace.restrict_top_presheaf, piFan_π_app, coconeOfCoconeForget_ι_app, AlgebraicGeometry.Scheme.Modules.pushforward_map_app, AlgebraicGeometry.Scheme.mem_toGrothendieck_smallPretopology, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_point, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom, AlgebraicGeometry.coe_opensRestrict_apply_coe, AlgebraicGeometry.Scheme.AffineZariskiSite.presieveOfSections_eq_ofArrows, ProfiniteGrp.instIsTopologicalGroupCarrierToTopTotallyDisconnectedSpacePtProfiniteLimitConeCompForget₂ContinuousMonoidHomToProfiniteContinuousMap, AlgebraicGeometry.Spec.toTop_obj_carrier, AlgebraicGeometry.Scheme.Hom.inv_app, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app', AlgebraicGeometry.Scheme.restrictFunctor_obj_hom, AlgebraicGeometry.finite_irreducibleComponents_of_isNoetherian, AlgebraicGeometry.Scheme.Hom.app_injective, CategoryTheory.Functor.mapPresheaf_obj_presheaf, Profinite.Extend.functor_map, Presheaf.mono_iff_stalk_mono, Stonean.instPreservesEffectiveEpisCompHausToCompHaus, AlgebraicGeometry.Scheme.Modules.inv_app, Condensed.locallyConstantIsoFinYoneda_hom_app, AlgebraicGeometry.Scheme.Hom.Spec_map_residueFieldMap_fromSpecResidueField, Presheaf.ext_iff, AlgebraicGeometry.Scheme.Opens.toSpecΓ_preimage_zeroLocus, AlgebraicGeometry.Scheme.Cover.fromGlued_open_map, inv_hom_id_apply, ProfiniteAddGrp.instCompactSpaceSubtypeForallCarrierToTopTotallyDisconnectedSpaceToProfiniteObjMemAddSubgroupLimitConePtAux, alexDiscEquivPreord_functor, AlgebraicGeometry.coprodMk_inr, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_bijective, AlgebraicGeometry.LocallyRingedSpace.comp_c_app, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_isAddCommGroup, AlgebraicGeometry.Scheme.Hom.isProperMap, Presheaf.presheafEquivOfIso_functor_obj_map, AlgebraicGeometry.Scheme.isoOfEq_hom, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_basicOpen_eq, instFullFintypeCatLightProfiniteToLightProfinite, AlgebraicGeometry.Scheme.le_iff_specializes, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberToSpecResidueField_assoc, AlgebraicGeometry.quasiSeparatedSpace_iff_quasiCompact_prod_lift, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_sSup, AlgebraicGeometry.Scheme.AffineZariskiSite.mem_grothendieckTopology_iff_sectionsOfPresieve, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_ι, Condensed.equalizerCondition_profinite, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_appTop, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal_basicOpen, AlgebraicGeometry.Scheme.AffineZariskiSite.toOpensFunctor_obj, pullback_fst_range, Presheaf.presheafEquivOfIso_inverse_map_app, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓFreeOpensCarrierCarrierCommRingCat, AlgebraicGeometry.RingedSpace.zeroLocus_singleton, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_hom, TopologicalSpace.OpenNhds.inclusionMapIso_hom_app, Profinite.instHasPropTotallyDisconnectedSpaceCarrier, TopologicalSpace.Opens.mapIso_refl, CompHausLike.LocallyConstant.functorToPresheaves_obj_map, AlgebraicGeometry.Scheme.Hom.isOpen_smoothLocus, FundamentalGroupoidFunctor.coneDiscreteComp_obj_mapCone, AlgebraicGeometry.Scheme.mem_zeroLocus_iff, AlgebraicGeometry.Scheme.Hom.fromNormalization_app, AlgebraicGeometry.Scheme.Opens.ι_base_apply, AlgebraicGeometry.Scheme.Hom.eqToHom_app, presheafToTypes_obj, instRepresentablyFlatOpensCarrierMap, AlgebraicGeometry.instIsAffineHomιBasicOpen, Profinite.isIso_asLimitCone_lift, AlgebraicGeometry.Scheme.id_app, GlueData.preimage_image_eq_image', Alexandrov.projSup_map, AlgebraicGeometry.flat_iff, Presheaf.SheafConditionEqualizerProducts.res_π_apply, AlgebraicGeometry.Scheme.zeroLocus_map_of_eq, AlgebraicGeometry.IsAffineOpen.toSpecΓ_fromSpec, AlgebraicGeometry.Scheme.residueFieldCongr_symm, Condensed.lanPresheafIso_hom, AlgebraicGeometry.IsAffineOpen.fromSpec_primeIdealOf, pullback_snd_image_fst_preimage, Stonean.effectiveEpi_tfae, TopologicalSpace.Opens.val_apply, AlgebraicGeometry.LocallyRingedSpace.iso_hom_base_inv_base_apply, CompHausLike.coe_comp, AlgebraicGeometry.Scheme.homOfLE_rfl, CompHausLike.finiteCoproduct.ι_jointly_surjective, AlgebraicGeometry.Scheme.fromSpecResidueField_apply, AlgebraicGeometry.Scheme.AffineZariskiSite.instIsCoverDenseOpensToOpensFunctorGrothendieckTopologyCarrierCarrierCommRingCat, ProfiniteAddGrp.topologicalAddGroup, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_ι_assoc, ContinuousMap.Homotopy.hcast_def, AlgebraicGeometry.HasRingHomProperty.iff_of_isAffine, TopModuleCat.hom_forget₂_TopCat_map, AlgebraicGeometry.Scheme.Hom.coe_opensRange, AlgebraicGeometry.quasiSeparatedSpace_iff_affine, AlgebraicGeometry.Scheme.IdealSheafData.le_def, AlgebraicGeometry.SheafedSpace.restrictTopIso_hom, AlgebraicGeometry.Scheme.stalkMap_congr, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_inv_app, AlgebraicGeometry.ΓSpec.toSpecΓ_unop, AlgebraicGeometry.isClosedImmersion_diagonal_restrict_diagonalCoverDiagonalRange, LightCondensed.instPreservesFiniteProductsOppositeLightProfiniteVal, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_bot, AlgebraicGeometry.SheafedSpace.Γ_map_op, Profinite.exists_hom, AlgebraicGeometry.tilde.instIsLocalizedModuleCarrierCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecModuleCatPresheafModulesSheafModulesSpecToSheafOpBasicOpenPowersHomToOpen, AlgebraicGeometry.SheafedSpace.GlueData.ι_jointly_surjective, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.instIsIsoInvApp, AlgebraicGeometry.quasiSeparated_over_affine_iff, AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_apply, AlgebraicGeometry.PresheafedSpace.stalkMap.congr_point, LightCondensed.instIsMonoidalFunctorOppositeLightProfiniteModuleCatWCoherentTopology, skyscraperPresheaf_map, AlgebraicGeometry.Scheme.IdealSheafData.supportSet_eq_iInter_zeroLocus, StalkSkyscraperPresheafAdjunctionAuxs.toSkyscraperPresheaf_app, AlgebraicGeometry.Scheme.Modules.map_smul, AlgebraicGeometry.RingedSpace.mem_basicOpen', piIsoPi_inv_π_assoc, AlgebraicGeometry.IsOpenImmersion.affineOpensEquiv_symm_apply_coe, AlgebraicGeometry.Scheme.affineBasicOpen_le, AlgebraicGeometry.SheafedSpace.comp_c_app', prodIsoProd_inv_snd_apply, AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalk_assoc, AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ_assoc, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_apply, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_iff, AlgebraicGeometry.IsAffineOpen.preimage, ContinuousMap.Homotopy.eq_diag_path, CompHausLike.LocallyConstant.functorToPresheaves_obj_obj, AlgebraicGeometry.LocallyRingedSpace.Γ_obj, AlgebraicGeometry.Spec.sheafedSpaceObj_presheaf, AlgebraicGeometry.Spec.map_app, AlgebraicGeometry.Scheme.Spec_fromSpecStalk, ProfiniteGrp.diagram_obj, AlgebraicGeometry.Scheme.Cover.fromGlued_injective, AlgebraicGeometry.IsAffineOpen.ideal_ext_iff, topToCompHaus_obj, AlgebraicGeometry.Spec.map_base_apply, AlgebraicGeometry.morphismRestrict_id, AlgebraicGeometry.Scheme.Hom.stalkMap_surjective, AlgebraicGeometry.tilde.toOpen_map_app, CompHausLike.finiteCoproduct.ι_desc_apply, instCompactSpaceCarrierDisk, TopologicalSpace.Opens.map_id_eq, AlgebraicGeometry.IsAffineOpen.primeIdealOf_genericPoint, ProfiniteGrp.instReflectsIsomorphismsForgetContinuousMonoidHomCarrierToTopTotallyDisconnectedSpaceToProfinite, AlgebraicGeometry.Scheme.Hom.id_image, AlgebraicGeometry.IsAffineOpen.mem_ideal_iff, AlgebraicGeometry.Scheme.toSpecΓ_base, AlgebraicGeometry.Smooth.iff_forall_exists_isStandardSmooth, CompHaus.instT2SpaceCarrierToTopTrue
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discrete 📖 | CompOp | 5 mathmath: CompHausLike.LocallyConstant.locallyConstantIsoContinuousMap_inv_apply, CompHausLike.LocallyConstant.locallyConstantIsoContinuousMap_hom, instDiscreteTopologyCarrierObjDiscrete, adj₁_unit, adj₁_counit
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homeoOfIso 📖 | CompOp | 4 mathmath: of_isoOfHomeo, homeoOfIso_apply, of_homeoOfIso, homeoOfIso_symm_apply
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inhabited 📖 | CompOp | — |
instCategory 📖 | CompOp | 861 mathmath: isInducing_pullback_to_prod, AlgebraicGeometry.Scheme.toSpecΓ_apply, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen, binaryCofan_isColimit_iff, DiscreteContAction.instDiscreteTopologyCarrierObjTopCatForget₂ContinuousMap, AlgebraicGeometry.QuasiCompact.isCompact_preimage_singleton, AlgebraicGeometry.Scheme.fromSpecStalk_closedPoint, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_injective, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv_assoc, TopologicalSpace.Opens.map_id_obj_unop, pullbackIsoProdSubtype_hom_fst, TopologicalSpace.Opens.inclusion'_hom_apply, SimplexCategory.instNonemptyCarrierObjTopCatToTop₀, AlgebraicGeometry.LocallyRingedSpace.residueFieldMap_comp, CompHausLike.instPreservesFiniteCoproductsTopCatCompHausLikeToTopOfHasExplicitFiniteCoproducts, isoOfHomeo_inv, TopologicalSpace.Opens.map_coe, AlgebraicGeometry.Scheme.Spec_map_stalkMap_fromSpecStalk, AlgebraicGeometry.Scheme.Cover.LocallyDirected.directed, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.stalk_iso, AlgebraicGeometry.QuasiCompact.isCompact_preimage, GlueData.preimage_image_eq_image, ContinuousMap.yonedaPresheaf'_obj, AlgebraicGeometry.Scheme.Hom.denseRange, AlgebraicGeometry.Scheme.isEmpty_pullback_iff, GlueData.π_surjective, DeltaGenerated.topToDeltaGenerated_map_hom_hom_apply, AlgebraicGeometry.Scheme.Hom.closePoints_subset_preimage_closedPoints, isOpenEmbedding_iff_comp_isIso, instMonoBallInclusion, AlgebraicGeometry.coprodSpec_apply, AlgebraicGeometry.morphismRestrict_base_coe, AlgebraicGeometry.Scheme.Hom.fiberHomeo_apply, AlgebraicGeometry.surjectiveOnStalks_iff, FundamentalGroupoidFunctor.piIso_hom, TopModuleCat.instPreservesLimitTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitOfModuleCatCompLinearMapForget, condensedSetToTopCat_obj_carrier, Presheaf.Pushforward.id_inv_app, AlgebraicGeometry.Scheme.affineBasisCover_is_basis, AlgebraicGeometry.range_eq_range_of_surjective, AlgebraicGeometry.Scheme.restrictFunctorΓ_inv_app, AlgebraicGeometry.Scheme.Cover.isOpenMap_fromGlued, coe_of_of, Presheaf.stalkSpecializes_stalkPushforward, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_specStalkEquiv, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_x, GlueData.open_image_open, DeltaGenerated.instFaithfulTopCatTopToDeltaGenerated, AlgebraicTopology.singularChainComplexFunctor_exactAt_of_totallyDisconnectedSpace, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_point, AlgebraicGeometry.ValuativeCriterion.Existence.specializingMap, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_fromSpec, CompHausLike.instPreservesPullbacksOfInclusionsTopCatCompHausLikeToTopOfHasExplicitPullbacksOfInclusions, AlgebraicGeometry.SheafedSpace.colimit_exists_rep, AlgebraicGeometry.Scheme.Hom.range_fiberι, TopologicalSpace.Opens.coe_inclusion', AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp, TopologicalSpace.OpenNhds.inclusionMapIso_hom, AlgebraicGeometry.Scheme.Cover.iUnion_range, AlgebraicGeometry.Scheme.Hom.mem_opensRange, AlgebraicGeometry.Scheme.Opens.topIso_inv, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_preimage_basicOpen, AlgebraicGeometry.isCompact_iff_exists, AlgebraicGeometry.PresheafedSpace.isoOfComponents_inv, GlueData.ι_fromOpenSubsetsGlue, AlgebraicGeometry.HasRingHomProperty.stalkMap, ContinuousMap.Homotopy.apply_zero_path, TopCommRingCat.instReflectsIsomorphismsTopCatForget₂SubtypeRingHomαContinuousCoeContinuousMapCarrier, sigmaIsoSigma_hom_ι, uliftFunctorObjHomeo_symm_naturality_apply, uliftFunctorCompForgetIso_hom_app, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_hom_apply_asIdeal, AlgebraicGeometry.Scheme.OpenCover.finiteSubcover_f, AlgebraicGeometry.Scheme.stalkSpecializes_stalkMap, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_inv_app, CondensedSet.instEpiTopCatAppCounitTopCatAdjunction, LightCondSet.instFaithfulTopCatTopCatToLightCondSet, AlgebraicGeometry.Scheme.stalkMap_congr_assoc, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_surjective, AlgebraicGeometry.instIsGermInjectiveAtCoeContinuousMapCarrierCarrierCommRingCatHomTopCatBaseOfIsOpenImmersion, AlgebraicGeometry.Scheme.Pullback.SpecTensorTo_SpecOfPoint, TopModuleCat.free_map, ContinuousMap.Homotopy.evalAt_eq, AlgebraicGeometry.Scheme.hom_inv_apply, AlgebraicGeometry.Scheme.Hom.range_asFiberHom, SimplexCategory.instPathConnectedSpaceCarrierObjTopCatToTop, TopologicalSpace.Opens.map_obj, AlgebraicGeometry.Scheme.Hom.tendsto_cofinite_cofinite, AlgebraicGeometry.Scheme.Hom.stalkSpecializes_stalkMap, AlgebraicGeometry.Scheme.Hom.coe_resLE_base, AlgebraicGeometry.IsAffineOpen.fromSpecStalk_closedPoint, Presheaf.Pushforward.comp_eq, isOpenEmbedding_iff, GlueData.ofOpenSubsets_toGlueData_U, AlgebraicGeometry.IsClosedImmersion.base_closed, instIsLeftKanExtensionSimplexCategoryTopCatSSetToTopInvFunctorToTopSimplex, AlgebraicGeometry.quasiCompact_iff, TopologicalSpace.OpenNhds.inclusionMapIso_inv, range_prod_map, TopModuleCat.instIsRightAdjointTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, Sequential.sequentialToTop_obj, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom_assoc, AlgebraicGeometry.Scheme.Pullback.Triplet.isPullback_SpecMap_tensor, AlgebraicGeometry.Scheme.forget_map, GlueData.isOpen_iff, AlgebraicGeometry.sigmaMk_mk, Presheaf.pushforwardToOfIso_app, AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_base_snd, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_point_assoc, AlgebraicGeometry.Scheme.isoSpec_inv_preimage_zeroLocus, toSheafCompHausLike_val_obj, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app_assoc, TopologicalSpace.Opens.map_comp_obj_unop, AlgebraicGeometry.IsPreimmersion.isEmbedding, Profinite.NobelingProof.spanFunctorIsoIndexFunctor_hom_app_hom_hom_apply_coe, coequalizer_isOpen_iff, forget_preservesColimits, GlueData.ι_fromOpenSubsetsGlue_apply, AlgebraicGeometry.Scheme.Hom.SpecMap_residueFieldMap_fromSpecResidueField_assoc, AlgebraicGeometry.Scheme.forgetToTop_map, AlgebraicGeometry.IsOpenImmersion.iff_isIso_stalkMap, AlgebraicGeometry.Scheme.Cover.instIsIsoCommRingCatStalkMapFromGlued, ContinuousMap.Homotopy.heq_path_of_eq_image, AlgebraicGeometry.Scheme.Pullback.carrierEquiv_eq_iff, pullback_topology, instFaithfulUliftFunctor, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_c_app, Presheaf.germ_stalkPullbackInv_assoc, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_snd_coe, GlueData.ofOpenSubsets_toGlueData_t, AlgebraicGeometry.Scheme.exists_affine_mem_range_and_range_subset, ContinuousMap.Homotopy.eq_path_of_eq_image, AlgebraicGeometry.Scheme.forgetToTop_obj, AlgebraicGeometry.IsOpenImmersion.isOpen_range, AlgebraicGeometry.Scheme.affineOpenCover_idx, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.stalk_iso, AlgebraicGeometry.LocallyRingedSpace.iso_inv_base_hom_base_apply, AlgebraicGeometry.Scheme.Pullback.Triplet.snd_SpecTensorTo_apply, topCat_hasColimitsOfShape, pullbackFst_apply, sigmaCofan_ι_app, AlgebraicGeometry.PresheafedSpace.stalkMap.stalkSpecializes_stalkMap, CompHausLike.LocallyConstant.locallyConstantIsoContinuousMap_inv_apply, LightCondSet.topCatAdjunctionUnit_val_app_apply, colimit_topology, AlgebraicGeometry.Scheme.presieve₀_mem_precoverage_iff, lightProfiniteToLightDiagram_map, AlgebraicGeometry.Scheme.comp_base, TopologicalSpace.Opens.isOpenEmbedding_obj_top, Profinite.exists_locallyConstant_finite_aux, AlgebraicGeometry.PresheafedSpace.isoOfComponents_hom, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ_ΓToStalk, AlgebraicGeometry.isIso_iff_isIso_stalkMap, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom, isOpenEmbedding_iff_isIso_comp', topCatOpToFrm_map, instPreservesLimitsOfSizeUliftFunctor, AlgebraicGeometry.Scheme.Pullback.residueFieldCongr_inv_residueFieldMap_ofPoint, instRespectsIsoIsOpenEmbedding, topCat_hasLimitsOfSize, AlgebraicGeometry.IsOpenImmersion.range_pullbackSnd, GlueData.rel_equiv, AlgebraicGeometry.Scheme.Hom.isDiscrete_preimage_singleton, pullbackSnd_apply, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι_ι_eq_support_inter, AlgebraicGeometry.Scheme.hom_base_inv_base, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr, CompactlyGenerated.compactlyGeneratedToTop_obj, TopologicalSpace.Opens.mapId_hom_app, AlgebraicGeometry.IsOpenImmersion.range_pullback_fst_of_right, TopologicalSpace.Opens.mapComp_hom_app, AlgebraicGeometry.Scheme.Hom.coe_resLE_apply, AlgebraicGeometry.pointEquivClosedPoint_apply_coe, isIso_iff_isHomeomorph, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv, AlgebraicGeometry.Scheme.range_fromSpecStalk, prod_topology, FundamentalGroupoidFunctor.prodToProdTop_obj, AlgebraicGeometry.Scheme.comp_coeBase_assoc, CondensedSet.topCatAdjunctionCounit_bijective, AlgebraicGeometry.coprodMk_inl, ofHom_comp, TopologicalSpace.Opens.map_id_obj', AlgebraicGeometry.Scheme.Pullback.Triplet.hy, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_assoc, AlgebraicGeometry.IsAffineOpen.isoSpec_inv, forget_preservesLimitsOfSize, sigmaIsoSigma_inv_apply, CompHausLike.homeoOfIso_symm_apply, AlgebraicGeometry.Scheme.Pullback.carrierEquiv_symm_fst, topCatToSheafCompHausLike_map_val_app, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberι_assoc, CompHausLike.instFullTopCatCompHausLikeToTop, AlgebraicGeometry.PresheafedSpace.GlueData.pullback_base, AlgebraicGeometry.Scheme.Hom.app_appIso_inv_assoc, FintypeCat.toProfinite_map_hom_hom_apply, FundamentalGroupoidFunctor.prodIso_hom, pullbackIsoProdSubtype_inv_fst_assoc, AlgebraicGeometry.Scheme.Pullback.range_fst_comp, TopologicalSpace.OpenNhds.op_map_id_obj, SimplexCategory.toTop_obj, prodIsoProd_hom_snd_assoc, AlgebraicGeometry.Scheme.isoSpec_inv_image_zeroLocus, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι_ι, AlgebraicGeometry.instPreservesColimitsOfShapeSchemeTopCatDiscreteForgetToTopOfSmall, AlgebraicGeometry.Scheme.Hom.isIso_base, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_hom_app, AlgebraicGeometry.Spec.topMap_id, AlgebraicGeometry.Scheme.hom_base_inv_base_assoc, AlgebraicGeometry.morphismRestrict_base, AlgebraicGeometry.Scheme.toSpecΓ_preimage_zeroLocus, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.imageBasicOpen_image_open, SimplexCategory.toTop_map, topCat_hasColimits, AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_comp_iff_of_isOpenImmersion, SimplexCategory.instPathConnectedSpaceCarrierObjTopCatToTop₀, TopologicalSpace.Opens.inclusion'_top_functor, AlgebraicGeometry.Scheme.Cover.isOpenEmbedding_fromGlued, AlgebraicGeometry.coe_opensRestrict_symm_apply, GlueData.instIsIsoT, Presheaf.presheafEquivOfIso_inverse_obj_map, presheafToTop_obj, AlgebraicGeometry.Scheme.Hom.isCompact_preimage_singleton, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_ideal, instSmallPrecoverage, AlgebraicGeometry.Scheme.Pullback.Triplet.Spec_map_tensor_isPullback, FundamentalGroupoidFunctor.piToPiTop_map, AlgebraicGeometry.Scheme.Cover.covers, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_point_assoc, TopologicalSpace.Opens.map_functor_eq, TopCommRingCat.forgetToTopCatTopologicalRing, AlgebraicGeometry.Scheme.stalkMap_congr_point_assoc, AlgebraicGeometry.Scheme.GlueData.isOpen_iff, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_assoc, ContinuousMap.Homotopy.apply_one_path, AlgebraicGeometry.QuasiCompactCover.isCompactOpenCovered_of_isCompact, TopologicalSpace.Opens.map_id_obj, AlgebraicGeometry.SheafedSpace.comp_base, SimplexCategory.toTop₀_map, AlgebraicGeometry.Scheme.Hom.mem_preimage, AlgebraicGeometry.Scheme.Spec_map_stalkMap_fromSpecStalk_assoc, AlgebraicGeometry.Scheme.Hom.isConstructible_preimage, AlgebraicGeometry.LocallyRingedSpace.isLocalHomStalkMap, AlgebraicGeometry.IsImmersion.isLocallyClosed_range, AlgebraicGeometry.PresheafedSpace.colimitCocone_ι_app_base, AlgebraicGeometry.Scheme.Γevaluation_naturality_apply, AlgebraicGeometry.ExistsHomHomCompEqCompAux.exists_index, AlgebraicGeometry.Scheme.Cover.exists_lift_trans_eq, AlgebraicGeometry.Spec_map_localization_isIso, AlgebraicGeometry.Scheme.stalkClosedPointTo_fromSpecStalk, AlgebraicGeometry.Scheme.GlueData.instPreservesColimitTopCatWalkingMultispanProdJMultispanDiagramForgetToTop, prodIsoProd_inv_snd_assoc, AlgebraicGeometry.Scheme.coe_homeoOfIso_symm, AlgebraicGeometry.ProjectiveSpectrum.Proj.isLocalization_atPrime, AlgebraicGeometry.Scheme.stalkMap_hom_inv_assoc, prodIsoProd_inv_fst_assoc, AlgebraicGeometry.Scheme.id.base, AlgebraicGeometry.Scheme.IdealSheafData.range_subschemeι, AlgebraicGeometry.PresheafedSpace.GlueData.ι_image_preimage_eq, AlgebraicGeometry.PresheafedSpace.stalkMap.congr, AlgebraicGeometry.Scheme.Hom.isClosedMap, AlgebraicGeometry.Scheme.Hom.isLocallyClosed_range, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec_assoc, uliftFunctorObjHomeo_naturality_apply, homeoOfIso_apply, AlgebraicGeometry.morphismRestrict_appLE, AlgebraicGeometry.IsClosedImmersion.iff_isPreimmersion, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec, CompHausLike.instFaithfulTopCatCompHausLikeToTop, AlgebraicGeometry.Scheme.Hom.apply_mem_image_iff, AlgebraicGeometry.Scheme.Hom.asFiberHom_apply, Presheaf.germToPullbackStalk_stalkPullbackHom, SimplexCategory.instNonemptyCarrierObjTopCatToTop, AlgebraicGeometry.PresheafedSpace.instPreservesColimitsOfShapeTopCatForget, TopologicalSpace.Opens.map_comp_map, AlgebraicGeometry.genericPoint_eq_of_isOpenImmersion, AlgebraicGeometry.Scheme.homeoOfIso_apply, sigmaIsoSigma_hom_ι_assoc, CompactlyGenerated.compactlyGeneratedToTop_map, LightCondensed.isColimitLocallyConstantPresheafDiagram_desc_apply, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv_assoc, AlgebraicGeometry.formallySmooth_stalkMap_iff, nonempty_isLimit_iff_eq_induced, AlgebraicGeometry.isIso_stalkMap_coprodSpec, SimplexCategory.toTop₀_obj, AlgebraicGeometry.PresheafedSpace.forget_obj, topCat_hasLimits, AlgebraicGeometry.LocallyRingedSpace.residue_comp_residueFieldMap_eq_stalkMap_comp_residue, FundamentalGroupoidFunctor.projLeft_map, TopologicalSpace.Opens.map_comp_obj', AlgebraicGeometry.Scheme.instIsIsoCommRingCatResidueFieldMapOfIsOpenImmersion, TopologicalSpace.Opens.mapMapIso_functor, AlgebraicGeometry.Scheme.instIsOverMapResidueFieldMapOverInferInstanceOverClass, piFan_pt, topToLocale_obj, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.image_preimage_is_empty, AlgebraicGeometry.IsOpenImmersion.instPreservesLimitSchemeTopCatWalkingCospanCospanForgetToTop_1, ContinuousMap.yonedaPresheaf_map, Sequential.isoOfHomeo_inv, Sequential.instFaithfulTopCatSequentialToTop, isoOfHomeo_hom, id_app, AlgebraicGeometry.Scheme.Γevaluation_naturality_assoc, AlgebraicGeometry.Scheme.Pullback.carrierEquiv_symm_snd, hasLimit_iff_small_sections, AlgebraicGeometry.isCompl_range_inl_inr, Presheaf.presheafEquivOfIso_unitIso_hom_app_app, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app, AlgebraicGeometry.LocallyRingedSpace.comp_base, FundamentalGroupoidFunctor.instIsIsoFanGrpdObjTopCatFundamentalGroupoidFunctorPiTopToPiCone, piIsoPi_inv_π_apply, topCat_hasLimitsOfShape, hom_id, AlgebraicGeometry.Scheme.Pullback.range_map, AlgebraicGeometry.ProjIsoSpecTopComponent.fromSpec_toSpec, AlgebraicGeometry.SurjectiveOnStalks.isEmbedding_pullback, AlexDisc.forgetToTop_faithful, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.sheafedSpace_forgetPreserves_of_right, AlgebraicGeometry.Scheme.Hom.isSpectralMap, AlgebraicGeometry.mem_range_iff_of_surjective, Condensed.isColimitLocallyConstantPresheaf_desc_apply, CompHausLike.LocallyConstant.functorToPresheaves_map_app, CondensedSet.topCatAdjunctionUnit_val_app_apply, AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality, GlueData.f_open, AlgebraicGeometry.Scheme.Hom.isLocallyConstructible_image, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_apply, AlgebraicGeometry.Scheme.stalkMap_congr_hom_assoc, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom, TopologicalSpace.Opens.op_map_id_obj, AlgebraicGeometry.Scheme.stalkSpecializes_stalkMap_apply, CondensedSet.instUCompactlyGeneratedSpaceCarrierObjTopCatCondensedSetToTopCat, CompHausLike.instT2SpaceCarrierObjTopCatCompHausLikeToTop, TopologicalSpace.Opens.mapMapIso_unitIso, TopologicalSpace.OpenNhds.map_id_obj_unop, Sequential.sequentialToTop_map, AlgebraicGeometry.Scheme.comp_base_assoc, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app', AlgebraicGeometry.SheafedSpace.id_hom_base, isOpenEmbedding_iff_comp_isIso', DeltaGenerated.deltaGeneratedToTop_map, isOpenEmbedding_f_zeroHypercover, TopologicalSpace.Opens.isOpenEmbedding, AlgebraicGeometry.isIso_iff_isOpenImmersion, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_zeroLocus, GlueData.range_fromOpenSubsetsGlue, coe_id, AlgebraicGeometry.Scheme.GlueData.ι_eq_iff, AlgebraicGeometry.FormallyUnramified.instIsSeparableCarrierResidueFieldCoeContinuousMapCarrierCarrierCommRingCatHomTopCatBaseOfLocallyOfFiniteType, FintypeCat.toLightProfinite_map_hom_hom_apply, uliftFunctorCompForgetIso_inv_app, AlgebraicGeometry.PresheafedSpace.forget_map, LightCondSet.instEpiTopCatAppCounitTopCatAdjunction, AlgebraicGeometry.AffineSpace.isOpenMap_over, AlgebraicGeometry.surjective_iff, Sequential.isoOfHomeo_hom, ContinuousMap.yonedaPresheaf_obj, AlgebraicGeometry.PresheafedSpace.restrictTopIso_hom, AlgebraicGeometry.PresheafedSpace.sheafIsoOfIso_inv, AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk_assoc, AlgebraicGeometry.Scheme.singleton_mem_precoverage_iff, topCatToSheafCompHausLike_obj, AlgebraicGeometry.Scheme.Hom.isOpenMap, AlgebraicGeometry.Scheme.Pullback.Triplet.hx, GlueData.MkCore.t_inv, AlgebraicGeometry.isOpenImmersion_iff_stalk, AlgebraicGeometry.LocallyRingedSpace.Hom.prop, AlgebraicGeometry.SurjectiveOnStalks.surj_on_stalks, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp, TopModuleCat.instIsLeftAdjointTopCatFree, isClosed_iff_of_isColimit, CompHausLike.LocallyConstant.locallyConstantIsoContinuousMap_hom, AlgebraicGeometry.SurjectiveOnStalks.stalkMap_surjective, pullbackIsoProdSubtype_inv_snd_apply, LightCondSet.instSequentialSpaceCarrierObjTopCatLightCondSetToTopCat, AlgebraicGeometry.PresheafedSpace.stalkMap.isIso, GlueData.fromOpenSubsetsGlue_isOpenEmbedding, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv, AlgebraicGeometry.Scheme.IdealSheafData.support_comap, AlgebraicGeometry.Scheme.restrictFunctorΓ_hom_app, TopologicalSpace.Opens.set_range_inclusion', AlgebraicGeometry.Scheme.stalkMap_congr_hom, AlgebraicGeometry.Scheme.Pullback.range_snd_comp, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_jointly_surjective, AlgebraicGeometry.Scheme.iso_inv_base_hom_base, AlgebraicGeometry.range_eq_univ, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.sheafedSpace_forgetPreserves_of_left, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_fst, AlgebraicGeometry.Scheme.Hom.comp_apply, AlgebraicGeometry.Scheme.Hom.isOpenEmbedding, pullbackIsoProdSubtype_inv_fst, AlgebraicGeometry.Spec.map_apply, TopologicalSpace.Opens.mapMapIso_inverse, AlgebraicGeometry.pointOfClosedPoint_apply, AlgebraicGeometry.PresheafedSpace.GlueData.ι_isOpenEmbedding, Presheaf.Pushforward.comp_inv_app, AlgebraicGeometry.SheafedSpace.restrictTopIso_inv, AlgebraicGeometry.Scheme.Hom.isEmbedding, AlgebraicGeometry.sigmaι_eq_iff, AlgebraicGeometry.Scheme.stalkMap_comp, TopologicalSpace.Opens.mapId_inv_app, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_hom_c_app, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_map, AlgebraicGeometry.IsOpenImmersion.range_pullback_to_base_of_left, coinduced_of_isColimit, AlgebraicGeometry.PresheafedSpace.base_isIso_of_iso, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp, AlgebraicGeometry.Scheme.IdealSheafData.map_vanishingIdeal, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_assoc, TopologicalSpace.Opens.inclusion'_map_eq_top, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.coequalizer_π_stalk_isLocalHom, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.forgetToTop_preservesPullback_of_left, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq, prodIsoProd_hom_snd, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_apply, AlgebraicGeometry.Scheme.Hom.residueFieldMap_congr, pullbackIsoProdSubtype_hom_snd, AlgebraicGeometry.Scheme.Hom.map_mem_image_iff, TopologicalSpace.Opens.adjunction_counit_map_functor, AlgebraicGeometry.coprodSpec_coprodMk, AlgebraicGeometry.Scheme.Hom.injective, AlgebraicGeometry.isIso_iff_isOpenImmersion_and_epi_base, pullbackIsoProdSubtype_inv_snd, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberι, hasColimit_iff_small_colimitType, AlgebraicGeometry.PresheafedSpace.map_id_c_app, AlgebraicGeometry.Scheme.local_affine, GlueData.fromOpenSubsetsGlue_injective, prodIsoProd_inv_fst, TopologicalSpace.Opens.adjunction_counit_app_self, AlgebraicGeometry.LocallyOfFiniteType.stalkMap, AlgebraicGeometry.locallyQuasiFinite_iff_isDiscrete_preimage_singleton, AlgebraicGeometry.Scheme.IsLocallyDirected.ι_eq_ι_iff, CompHausOpToFrame.faithful, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_isIso, Presheaf.Pushforward.id_hom_app, LightCondSet.topCatAdjunctionCounit_bijective, AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_base_fst, AlgebraicGeometry.compactSpace_iff_exists, Presheaf.id_pushforward, Presheaf.Pushforward.id_eq, AlgebraicGeometry.Scheme.iso_hom_base_inv_base, AlgebraicGeometry.Scheme.stalkMap_congr_point, topCatOpToFrm_obj_coe, AlgebraicGeometry.ProjectiveSpectrum.Proj.mk_mem_toSpec_base_apply, range_pullback_to_prod, AlgebraicGeometry.IsAffineOpen.comap_primeIdealOf_appLE, GlueData.ι_isOpenEmbedding, AlgebraicGeometry.Scheme.stalkMap_hom_inv, AlgebraicGeometry.Scheme.toSpecΓ_image_zeroLocus, AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality, AlgebraicGeometry.isImmersion_iff, topToLocale_map, TopologicalSpace.Opens.map_comp_eq, pullback_fst_image_snd_preimage, CompHausLike.instPreservesLimitTopCatWalkingCospanCospanCompHausLikeToTop, TopModuleCat.instPreservesLimitsOfShapeTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitsOfShapeOfModuleCatForgetLinearMap, AlgebraicGeometry.PresheafedSpace.colimit_presheaf, AlgebraicGeometry.Scheme.stalkMap_hom_inv_apply, continuous_iff_of_isColimit, CondensedSet.topCatAdjunctionUnit_val_app, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_hom_app_val_app_apply, FundamentalGroupoid.map_eq, Presheaf.presheafEquivOfIso_unitIso_inv_app_app, instPreservesColimitsOfSizeUliftFunctor, AlgebraicGeometry.Scheme.Hom.stalkSpecializes_stalkMap_apply, AlgebraicGeometry.LocallyRingedSpace.isLocalHomStalkMap', AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv, instIsLeftAdjointForgetContinuousMapCarrier, pullbackIsoProdSubtype_inv_fst_apply, AlgebraicGeometry.Scheme.Hom.exists_mem_and_isIso_morphismRestrict_toNormalization, GlueData.ofOpenSubsets_toGlueData_J, AlgebraicGeometry.PresheafedSpace.id_base, piIsoPi_hom_apply, Presheaf.stalkPushforward.id, AlgebraicGeometry.Scheme.descResidueField_stalkClosedPointTo_fromSpecResidueField, Presheaf.presheafEquivOfIso_functor_obj_obj, CategoryTheory.finitaryExtensive_TopCat, AlgebraicGeometry.isDominant_iff, AlgebraicGeometry.Flat.generalizingMap, AlgebraicGeometry.Scheme.Hom.fiberι_asFiber, GlueData.MkCore.t_id, AlgebraicGeometry.Scheme.Hom.id_base, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.c_iso, AlgebraicGeometry.IsOpenImmersion.range_pullback_snd_of_left, AlgebraicGeometry.IsOpenImmersion.instIsIsoCommRingCatStalkMap, AlgebraicGeometry.isPreimmersion_iff, AlgebraicGeometry.Scheme.AffineCover.covers, AlgebraicGeometry.SheafedSpace.comp_hom_base, AlgebraicGeometry.PresheafedSpace.forget_preservesColimits, AlgebraicGeometry.Scheme.Hom.Spec_map_residueFieldMap_fromSpecResidueField_assoc, AlgebraicGeometry.Scheme.isLocalHom_stalkClosedPointTo', AlgebraicGeometry.IsFinite.finite_preimage_singleton, AlgebraicGeometry.PresheafedSpace.toRestrictTop_c, Presheaf.germ_stalkPullbackInv, Profinite.exists_locallyConstant, AlgebraicGeometry.ProjectiveSpectrum.Proj.isIso_toSpec, ContinuousMap.piComparison_fac, AlgebraicGeometry.LocallyRingedSpace.forgetToTop_map, AlgebraicGeometry.IsAffineOpen.primeIdealOf_eq_map_closedPoint, AlgebraicGeometry.PresheafedSpace.comp_base, AlgebraicGeometry.Scheme.GlueData.ι_isoCarrier_inv, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc, DeltaGenerated.instFullTopCatDeltaGeneratedToTop, GlueData.preimage_range, alexDiscEquivPreord_unitIso, AlgebraicGeometry.IsOpenImmersion.range_pullback_to_base_of_right, isOpenEmbedding_iff_isIso_comp, TopologicalSpace.Opens.functor_map_eq_inf, AlgebraicGeometry.Scheme.Pullback.Triplet.fst_SpecTensorTo_apply, GlueData.ι_mono, instDiscreteTopologyCarrierObjDiscrete, AlexDisc.coe_forgetToTop, TopologicalSpace.OpenNhds.isOpenEmbedding, TopModuleCat.forget₂_TopCat_obj, FundamentalGroupoidFunctor.preservesProduct, AlgebraicGeometry.IsClosedImmersion.isClosedEmbedding, CompHausLike.homeoOfIso_apply, topToPreord_map, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp_assoc, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.stalk_iso, GlueData.ofOpenSubsets_toGlueData_V, GlueData.image_inter, AlgebraicGeometry.Spec.topMap_comp, isEmbedding_pullback_to_prod, GlueData.ofOpenSubsets_toGlueData_f, AlgebraicGeometry.Flat.stalkMap, AlgebraicGeometry.Scheme.Pullback.range_snd, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom_assoc, AlgebraicGeometry.Scheme.Hom.stalkMap_comp, AlexDisc.forgetToTop_full, pullbackIsoProdSubtype_hom_apply, AlgebraicGeometry.Scheme.Cover.exists_eq, AlgebraicGeometry.Scheme.ofArrows_mem_precoverage_iff, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullback_cone_of_left_condition, AlgebraicGeometry.Scheme.IsLocallyDirected.ι_jointly_surjective, AlgebraicGeometry.IsPreimmersion.base_embedding, AlgebraicGeometry.Scheme.Hom.coe_image, AlgebraicGeometry.Scheme.Hom.coe_preimage, ofHom_apply, AlgebraicGeometry.LocallyRingedSpace.stalkSpecializes_stalkMap_apply, AlgebraicGeometry.Spec.coe_toTop_map_hom_apply_asIdeal, coneOfConeForget_π_app, LightDiagram.id_hom_hom_hom_apply, AlgebraicGeometry.Scheme.Hom.isClosedEmbedding, AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiber, FundamentalGroupoidFunctor.piToPiTop_obj_as, lightCondSetToTopCat_obj_carrier, AlgebraicGeometry.Scheme.Hom.finite_preimage_singleton, induced_of_isLimit, AlgebraicGeometry.Scheme.inv_hom_apply, CompHausLike.compHausLikeToTop_map, AlgebraicGeometry.isIso_SpecMap_stakMap_localization, AlgebraicGeometry.Scheme.residue_residueFieldMap_assoc, AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit_map, AlgebraicGeometry.Scheme.IdealSheafData.support_map, AlgebraicGeometry.FormallyUnramified.stalkMap, Presheaf.presheafEquivOfIso_counitIso_inv_app_app, Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk, AlgebraicGeometry.PresheafedSpace.stalkMap.congr_hom, AlgebraicGeometry.SheafedSpace.id_hom_c, FundamentalGroupoidFunctor.piIso_inv, TopologicalSpace.Opens.op_map_comp_obj, prodIsoProd_hom_apply, CompHausLike.toCompHausLike_map, Condensed.isColimitLocallyConstantPresheafDiagram_desc_apply, AlgebraicGeometry.Scheme.OpenCover.finiteSubcover_X, AlgebraicGeometry.Scheme.Pullback.range_fst, AlgebraicGeometry.IsOpenImmersion.instPreservesLimitSchemeTopCatWalkingCospanCospanForgetToTop, comp_app, AlgebraicGeometry.IsOpenImmersion.iff_stalk_iso, AlgebraicGeometry.Scheme.Cover.fromGlued_isOpenEmbedding, AlgebraicGeometry.Scheme.residue_residueFieldMap, AlgebraicGeometry.PresheafedSpace.stalkMap.comp, AlgebraicGeometry.LocallyRingedSpace.iso_inv_base_hom_base, pullbackIsoProdSubtype_inv_snd_assoc, epi_iff_surjective, AlgebraicGeometry.Scheme.stalkMap_inv_hom_apply, AlgebraicGeometry.Scheme.Opens.mem_basicOpen_toScheme, AlgebraicGeometry.Scheme.Hom.comp_base_assoc, AlgebraicGeometry.Scheme.SpecMap_residue_apply, prodIsoProd_hom_fst, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.forget_preservesLimitsOfRight, FundamentalGroupoidFunctor.prodIso_inv, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.forget_preservesLimitsOfLeft, AlgebraicGeometry.Scheme.Pullback.range_diagonal_subset_diagonalCoverDiagonalRange, topToPreord_obj_coe, instIsRightAdjointForgetContinuousMapCarrier, AlgebraicGeometry.Scheme.Hom.mem_smoothLocus, GlueData.fromOpenSubsetsGlue_isOpenMap, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_apply, TopModuleCat.free_obj, AlgebraicGeometry.Scheme.Opens.ι_app_self, TopologicalSpace.Opens.mapComp_inv_app, toSheafCompHausLike_val_map, AlgebraicGeometry.PresheafedSpace.comp_base_assoc, AlgebraicGeometry.Scheme.Pullback.Triplet.Spec_ofPointTensor_SpecTensorTo, FundamentalGroupoidFunctor.projRight_map, adj₂_counit, TopologicalSpace.Opens.map_comp_obj, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_s, AlgebraicGeometry.QuasiCompactCover.isCompactOpenCovered_of_isAffineOpen, AlgebraicGeometry.Scheme.Opens.range_ι, AlgebraicGeometry.IsAffineOpen.range_fromSpec, AlgebraicGeometry.isClosedImmersion_iff, prodIsoProd_inv_snd, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_assoc, TopModuleCat.instPreservesLimitsTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, AlgebraicGeometry.Spec_closedPoint, AlgebraicGeometry.Scheme.Hom.range_subset_ker_support, topCat_hasColimitsOfSize, AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit_obj, lightDiagramToLightProfinite_map, AlgebraicGeometry.ProjectiveSpectrum.Proj.stalkMap_toSpec, hom_inv_id_apply, piIsoPi_inv_π, nonempty_isColimit_iff_eq_coinduced, AlgebraicGeometry.Scheme.Hom.finite_preimage, AlgebraicGeometry.Scheme.Opens.ι_apply, mono_iff_injective, AlgebraicGeometry.Scheme.iso_inv_base_hom_base_apply, AlgebraicGeometry.Scheme.Hom.continuous, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberToSpecResidueField, homeoOfIso_symm_apply, AlgebraicGeometry.Scheme.Pullback.Triplet.exists_preimage, AlgebraicGeometry.Scheme.Hom.isConstructible_image, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv_apply, AlgebraicGeometry.Surjective.surj, Presheaf.Pushforward.comp_hom_app, AlgebraicGeometry.Scheme.stalkMap_inv_hom, ContinuousMap.yonedaPresheaf'_map, AlgebraicGeometry.Scheme.comp_base_apply, coconeOfCoconeForget_pt, AlgebraicGeometry.isGermInjectiveAt_iff_of_isOpenImmersion, GlueData.MkCore.t_inter, AlgebraicGeometry.PresheafedSpace.GlueData.ι_jointly_surjective, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_base_apply, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq_comap, DeltaGenerated.instFaithfulTopCatDeltaGeneratedToTop, AlgebraicGeometry.IsDominant.denseRange, AlgebraicGeometry.Scheme.homOfLE_base, AlgebraicGeometry.Flat.iff_flat_stalkMap, AlgebraicGeometry.Scheme.preimage_zeroLocus, AlgebraicGeometry.isIso_iff_stalk_iso, AlgebraicGeometry.Scheme.instIsOverMapStalkMapOverInferInstanceOverClass, Presheaf.presheafEquivOfIso_counitIso_hom_app_app, GlueData.ι_jointly_surjective, CompHausLike.isoOfHomeo_inv_hom_hom_apply, AlgebraicGeometry.Scheme.Hom.support_ker, LightCondensed.isColimitLocallyConstantPresheaf_desc_apply, AlgebraicGeometry.Scheme.Hom.homeomorph_apply, AlgebraicGeometry.Scheme.Hom.stalkMap_congr, prodIsoProd_hom_fst_assoc, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec, AlgebraicGeometry.LocallyRingedSpace.stalkSpecializes_stalkMap, AlgebraicGeometry.Scheme.Hom.surjective, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.sigma_ι_isOpenEmbedding, AlgebraicGeometry.Scheme.IsLocallyDirected.exists_of_pullback_V_V, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.imageBasicOpen_image_preimage, isOpen_iff_of_isColimit_cofork, AlgebraicGeometry.SheafedSpace.id_c, Presheaf.presheafEquivOfIso_inverse_obj_obj, LightCondSet.topCatAdjunctionUnit_val_app, LightDiagram.comp_hom_hom_hom_apply, TopModuleCat.instReflectsIsomorphismsTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, isQuotientMap_of_isColimit_cofork, condensedSetToTopCat_map, AlgebraicGeometry.SheafedSpace.instPreservesColimitsOfShapeTopCatForgetOfSmallOfHasLimitsOfShapeOpposite, instFullUliftFunctor, forget_preservesColimitsOfSize, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_assoc, AlgebraicGeometry.LocallyRingedSpace.forgetToTop_obj, instMonoDiskBoundaryInclusion, Action.isContinuous_def, AlgebraicGeometry.SheafedSpace.instPreservesColimitsTopCatForgetOfHasLimits, AlgebraicGeometry.Scheme.stalkMap_inv_hom_assoc, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.preimage_toBase_eq_range_ι, isOpen_iff_of_isColimit, AlgebraicGeometry.locallyQuasiFinite_iff_finite_preimage_singleton, AlgebraicGeometry.Spec.topObj_forget, adj₂_unit, TopologicalSpace.OpenNhds.map_id_obj, forget_preservesLimits, AlgebraicGeometry.Scheme.Opens.ι_appLE, AlgebraicGeometry.IsOpenImmersion.range_pullbackFst, AlgebraicGeometry.IsAffineOpen.fromSpec_image_zeroLocus, AlgebraicGeometry.Scheme.Cover.instEpiTopCatBaseCommRingCatFromGlued, AlgebraicGeometry.PresheafedSpace.toRestrictTop_base, AlgebraicGeometry.Scheme.affineBasisCover_map_range, instIsStableUnderBaseChangeIsOpenEmbedding, AlgebraicGeometry.Flat.isQuotientMap_of_surjective, AlgebraicGeometry.Scheme.Opens.ι_app, AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.isClopen_singleton_asFiber, AlgebraicGeometry.instIsPreimmersionAsFiberHom, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_hom_assoc, AlgebraicGeometry.SheafedSpace.id_base, CompHausLike.LocallyConstant.incl_comap, AlgebraicGeometry.PresheafedSpace.colimit_carrier, AlgebraicGeometry.quasiCompact_iff_spectral, AlgebraicGeometry.Scheme.iso_hom_base_inv_base_apply, prodIsoProd_inv_fst_apply, AlgebraicGeometry.quasiCompact_iff_isSpectralMap, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_preimage_basicOpen, sigmaCofan_pt, effectiveEpi_iff_isQuotientMap, colimit_isOpen_iff, AlgebraicGeometry.isomorphisms_eq_stalkwise, adj₁_unit, ContinuousMap.comp_yonedaPresheaf', Presheaf.presheafEquivOfIso_functor_map_app, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_zeroLocus_eq, AlgebraicGeometry.Scheme.Hom.comp_base, AlgebraicGeometry.IsAffineOpen.isCompactOpenCovered, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.base_open, adj₁_counit, alexDiscEquivPreord_counitIso, subcanonical_grothendieckTopology, AlgebraicGeometry.Scheme.Γevaluation_naturality, GlueData.ι_eq_iff_rel, TopologicalSpace.Opens.mapMapIso_counitIso, AlgebraicGeometry.HasRingHomProperty.stalkMap_of_respectsIso, AlgebraicGeometry.ExistsHomHomCompEqCompAux.range_g_subset, TopologicalSpace.Opens.toTopCat_map, AlgebraicGeometry.Scheme.isLocalHom_stalkClosedPointTo, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality, Presheaf.germToPullbackStalk_stalkPullbackHom_assoc, Presheaf.toPushforwardOfIso_app, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_inv_app_val_app_hom_hom, CompHausLike.instCompactSpaceCarrierObjTopCatCompHausLikeToTop, AlgebraicGeometry.Scheme.Hom.SpecMap_residueFieldMap_fromSpecResidueField, coe_comp, AlgebraicGeometry.Scheme.affineOpenCover_X, CompHausLike.isoOfHomeo_hom_hom_hom_apply, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_y, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp_assoc, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_assoc, AlgebraicGeometry.LocallyRingedSpace.toStalk_stalkMap_toΓSpec, AlgebraicGeometry.Scheme.range_fromSpecResidueField, AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk, exists_mem_zeroHypercover_range, sigmaIsoSigma_hom_ι_apply, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_apply, AlgebraicGeometry.quasiCompactCover_iff, lightCondSetToTopCat_map, AlgebraicGeometry.Scheme.image_zeroLocus, AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.preimage_basicOpen, AlgebraicGeometry.Scheme.Hom.fiberToSpecResidueField_apply, AlgebraicGeometry.Scheme.inv_base_hom_base_assoc, AlgebraicGeometry.Scheme.Opens.topIso_hom, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv_assoc, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_SpecTensorTo, FundamentalGroupoidFunctor.prodToProdTop_map, AlgebraicGeometry.Scheme.JointlySurjective.exists_eq, AlgebraicGeometry.SheafedSpace.instEpiTopCatBaseHomPresheafedSpaceπ, AlgebraicGeometry.LocallyRingedSpace.isLocalHom_stalkMap_congr, ext_iff, AlgebraicGeometry.Scheme.Hom.app_appIso_inv, limit_topology, Profinite.exists_locallyConstant_finite_nonempty, AlgebraicGeometry.Scheme.coe_homeoOfIso, AlgebraicGeometry.PresheafedSpace.restrictTopIso_inv, Presheaf.stalkPushforward.comp, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec.image_basicOpen_eq_basicOpen, AlgebraicGeometry.isClosedMap_iff_specializingMap, pullback_snd_range, AlgebraicGeometry.PresheafedSpace.map_comp_c_app, AlgebraicGeometry.Scheme.image_preimage_eq_of_isPullback, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app, AlgebraicGeometry.Scheme.Hom.instIsLocalHomCarrierStalkCommRingCatPresheafCoeContinuousMapCarrierCarrierHomTopCatBaseRingHomHomStalkMap, CompactlyGenerated.instFullTopCatCompactlyGeneratedToTop, AlgebraicGeometry.LocallyRingedSpace.stalkMap_comp, AlgebraicGeometry.Scheme.GlueData.ι_jointly_surjective, AlgebraicGeometry.SheafedSpace.isColimit_exists_rep, FundamentalGroupoidFunctor.proj_map, AlexDisc.forgetToTop_of, GlueData.MkCore.cocycle, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv_apply, AlgebraicGeometry.Scheme.Opens.eq_presheaf_map_eqToHom, DeltaGenerated.topToDeltaGenerated_obj_toTop_carrier, TopologicalSpace.OpenNhds.inclusionMapIso_inv_app, AlgebraicGeometry.Scheme.stalkClosedPointTo_comp, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_apply, AlgebraicGeometry.Scheme.Spec_map_residue_apply, Profinite.exists_locallyConstant_fin_two, GlueData.ι_injective, AlgebraicGeometry.Scheme.residueFieldMap_comp, AlgebraicGeometry.Scheme.isoSpec_image_zeroLocus, AlgebraicGeometry.Scheme.Hom.fiberι_fiberHomeo_symm, AlgebraicGeometry.Scheme.comp_coeBase, AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalk, Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk_assoc, AlgebraicGeometry.LocallyRingedSpace.iso_hom_base_inv_base, hom_comp, AlgebraicGeometry.LocallyRingedSpace.isLocalHomValStalkMap, DeltaGenerated.deltaGeneratedToTop_obj, AlgebraicGeometry.PresheafedSpace.restrict_top_presheaf, piFan_π_app, coconeOfCoconeForget_ι_app, AlgebraicGeometry.Scheme.mem_toGrothendieck_smallPretopology, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_point, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom, AlgebraicGeometry.Spec.toTop_obj_carrier, AlgebraicGeometry.Scheme.Hom.Spec_map_residueFieldMap_fromSpecResidueField, AlgebraicGeometry.Scheme.Opens.toSpecΓ_preimage_zeroLocus, AlgebraicGeometry.Scheme.Cover.fromGlued_open_map, inv_hom_id_apply, alexDiscEquivPreord_functor, AlgebraicGeometry.coprodMk_inr, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_bijective, AlgebraicGeometry.Scheme.Hom.isProperMap, Presheaf.presheafEquivOfIso_functor_obj_map, AlgebraicTopology.isZero_singularHomologyFunctor_of_totallyDisconnectedSpace, AlgebraicGeometry.QuasiCompactCover.exists_isAffineOpen_of_isCompact, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberToSpecResidueField_assoc, pullback_fst_range, Presheaf.presheafEquivOfIso_inverse_map_app, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_hom, ofHom_id, TopologicalSpace.OpenNhds.inclusionMapIso_hom_app, CondensedSet.instFaithfulTopCatTopCatToCondensedSet, CompHausLike.LocallyConstant.functorToPresheaves_obj_map, AlgebraicGeometry.PresheafedSpace.colimitCocone_ι_app_c, AlgebraicGeometry.Scheme.Hom.isOpen_smoothLocus, FundamentalGroupoidFunctor.coneDiscreteComp_obj_mapCone, AlgebraicGeometry.Scheme.Opens.ι_base_apply, AlgebraicGeometry.Scheme.Hom.isDiscrete_preimage, coneOfConeForget_pt, GlueData.preimage_image_eq_image', AlgebraicGeometry.Scheme.homOfLE_apply, AlgebraicGeometry.IsAffineOpen.fromSpec_primeIdealOf, pullback_snd_image_fst_preimage, AlgebraicGeometry.LocallyRingedSpace.iso_hom_base_inv_base_apply, AlgebraicGeometry.Scheme.fromSpecResidueField_apply, Sequential.instFullTopCatSequentialToTop, TopModuleCat.hom_forget₂_TopCat_map, instIsMultiplicativeIsOpenEmbedding, AlgebraicGeometry.Scheme.Hom.coe_opensRange, AlgebraicGeometry.SheafedSpace.restrictTopIso_hom, AlgebraicGeometry.Scheme.stalkMap_congr, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom, AlgebraicGeometry.Scheme.inv_base_hom_base, AlgebraicGeometry.SheafedSpace.GlueData.ι_jointly_surjective, AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_apply, AlgebraicGeometry.PresheafedSpace.stalkMap.congr_point, piIsoPi_inv_π_assoc, prodIsoProd_inv_snd_apply, AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalk_assoc, CompactlyGenerated.instFaithfulTopCatCompactlyGeneratedToTop, ContinuousMap.Homotopy.eq_diag_path, CompHausToLocale.faithful, ContinuousMap.instPreservesFiniteProductsOppositeTopCatYonedaPresheaf', AlgebraicGeometry.Scheme.Cover.fromGlued_injective, topToCompHaus_obj, AlgebraicGeometry.Spec.map_base_apply, AlgebraicGeometry.Scheme.Hom.stalkMap_surjective, TopologicalSpace.Opens.map_id_eq, AlgebraicGeometry.Scheme.toSpecΓ_base
|
instCoeSortType 📖 | CompOp | — |
instConcreteCategoryContinuousMapCarrier 📖 | CompOp | 551 mathmath: isInducing_pullback_to_prod, AlgebraicGeometry.Scheme.toSpecΓ_apply, binaryCofan_isColimit_iff, DiscreteContAction.instDiscreteTopologyCarrierObjTopCatForget₂ContinuousMap, AlgebraicGeometry.QuasiCompact.isCompact_preimage_singleton, AlgebraicGeometry.Scheme.fromSpecStalk_closedPoint, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_injective, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv_assoc, pullbackIsoProdSubtype_hom_fst, AlgebraicGeometry.LocallyRingedSpace.residueFieldMap_comp, TopologicalSpace.Opens.map_coe, AlgebraicGeometry.Scheme.Spec_map_stalkMap_fromSpecStalk, AlgebraicGeometry.Scheme.Cover.LocallyDirected.directed, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.stalk_iso, AlgebraicGeometry.QuasiCompact.isCompact_preimage, GlueData.preimage_image_eq_image, AlgebraicGeometry.Scheme.Hom.denseRange, AlgebraicGeometry.Scheme.isEmpty_pullback_iff, GlueData.π_surjective, DeltaGenerated.topToDeltaGenerated_map_hom_hom_apply, AlgebraicGeometry.Scheme.Hom.closePoints_subset_preimage_closedPoints, isOpenEmbedding_iff_comp_isIso, AlgebraicGeometry.coprodSpec_apply, AlgebraicGeometry.morphismRestrict_base_coe, AlgebraicGeometry.Scheme.Hom.fiberHomeo_apply, AlgebraicGeometry.surjectiveOnStalks_iff, TopModuleCat.instPreservesLimitTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitOfModuleCatCompLinearMapForget, AlgebraicGeometry.Scheme.affineBasisCover_is_basis, AlgebraicGeometry.range_eq_range_of_surjective, AlgebraicGeometry.Scheme.Cover.isOpenMap_fromGlued, coe_of_of, Presheaf.stalkSpecializes_stalkPushforward, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_specStalkEquiv, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_x, GlueData.open_image_open, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_point, AlgebraicGeometry.ValuativeCriterion.Existence.specializingMap, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_fromSpec, AlgebraicGeometry.SheafedSpace.colimit_exists_rep, AlgebraicGeometry.Scheme.Hom.range_fiberι, TopologicalSpace.Opens.coe_inclusion', AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp, TopologicalSpace.OpenNhds.inclusionMapIso_hom, AlgebraicGeometry.Scheme.Cover.iUnion_range, AlgebraicGeometry.Scheme.Hom.mem_opensRange, AlgebraicGeometry.isCompact_iff_exists, AlgebraicGeometry.HasRingHomProperty.stalkMap, TopCommRingCat.instReflectsIsomorphismsTopCatForget₂SubtypeRingHomαContinuousCoeContinuousMapCarrier, uliftFunctorObjHomeo_symm_naturality_apply, uliftFunctorCompForgetIso_hom_app, AlgebraicGeometry.Scheme.OpenCover.finiteSubcover_f, AlgebraicGeometry.Scheme.stalkSpecializes_stalkMap, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_inv_app, AlgebraicGeometry.Scheme.stalkMap_congr_assoc, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_surjective, AlgebraicGeometry.instIsGermInjectiveAtCoeContinuousMapCarrierCarrierCommRingCatHomTopCatBaseOfIsOpenImmersion, AlgebraicGeometry.Scheme.Pullback.SpecTensorTo_SpecOfPoint, AlgebraicGeometry.Scheme.hom_inv_apply, AlgebraicGeometry.Scheme.Hom.range_asFiberHom, TopologicalSpace.Opens.map_obj, AlgebraicGeometry.Scheme.Hom.tendsto_cofinite_cofinite, AlgebraicGeometry.Scheme.Hom.stalkSpecializes_stalkMap, AlgebraicGeometry.Scheme.Hom.coe_resLE_base, AlgebraicGeometry.IsAffineOpen.fromSpecStalk_closedPoint, isOpenEmbedding_iff, AlgebraicGeometry.IsClosedImmersion.base_closed, AlgebraicGeometry.quasiCompact_iff, TopologicalSpace.OpenNhds.inclusionMapIso_inv, range_prod_map, TopModuleCat.instIsRightAdjointTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom_assoc, AlgebraicGeometry.Scheme.Pullback.Triplet.isPullback_SpecMap_tensor, AlgebraicGeometry.Scheme.forget_map, GlueData.isOpen_iff, AlgebraicGeometry.sigmaMk_mk, AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_base_snd, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_point_assoc, AlgebraicGeometry.Scheme.isoSpec_inv_preimage_zeroLocus, AlgebraicGeometry.IsPreimmersion.isEmbedding, coequalizer_isOpen_iff, forget_preservesColimits, GlueData.ι_fromOpenSubsetsGlue_apply, AlgebraicGeometry.Scheme.Hom.SpecMap_residueFieldMap_fromSpecResidueField_assoc, AlgebraicGeometry.IsOpenImmersion.iff_isIso_stalkMap, AlgebraicGeometry.Scheme.Cover.instIsIsoCommRingCatStalkMapFromGlued, AlgebraicGeometry.Scheme.Pullback.carrierEquiv_eq_iff, pullback_topology, Presheaf.germ_stalkPullbackInv_assoc, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_snd_coe, AlgebraicGeometry.Scheme.exists_affine_mem_range_and_range_subset, AlgebraicGeometry.IsOpenImmersion.isOpen_range, AlgebraicGeometry.Scheme.affineOpenCover_idx, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.stalk_iso, AlgebraicGeometry.LocallyRingedSpace.iso_inv_base_hom_base_apply, AlgebraicGeometry.Scheme.Pullback.Triplet.snd_SpecTensorTo_apply, pullbackFst_apply, AlgebraicGeometry.PresheafedSpace.stalkMap.stalkSpecializes_stalkMap, colimit_topology, AlgebraicGeometry.Scheme.presieve₀_mem_precoverage_iff, TopologicalSpace.Opens.isOpenEmbedding_obj_top, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ_ΓToStalk, AlgebraicGeometry.isIso_iff_isIso_stalkMap, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom, isOpenEmbedding_iff_isIso_comp', AlgebraicGeometry.Scheme.Pullback.residueFieldCongr_inv_residueFieldMap_ofPoint, AlgebraicGeometry.IsOpenImmersion.range_pullbackSnd, AlgebraicGeometry.Scheme.Hom.isDiscrete_preimage_singleton, pullbackSnd_apply, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι_ι_eq_support_inter, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr, AlgebraicGeometry.IsOpenImmersion.range_pullback_fst_of_right, AlgebraicGeometry.Scheme.Hom.coe_resLE_apply, AlgebraicGeometry.pointEquivClosedPoint_apply_coe, isIso_iff_isHomeomorph, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv, AlgebraicGeometry.Scheme.range_fromSpecStalk, prod_topology, CondensedSet.topCatAdjunctionCounit_bijective, AlgebraicGeometry.coprodMk_inl, AlgebraicGeometry.Scheme.Pullback.Triplet.hy, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_assoc, forget_preservesLimitsOfSize, sigmaIsoSigma_inv_apply, CompHausLike.homeoOfIso_symm_apply, AlgebraicGeometry.Scheme.Pullback.carrierEquiv_symm_fst, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberι_assoc, AlgebraicGeometry.PresheafedSpace.GlueData.pullback_base, AlgebraicGeometry.Scheme.Hom.app_appIso_inv_assoc, pullbackIsoProdSubtype_inv_fst_assoc, AlgebraicGeometry.Scheme.Pullback.range_fst_comp, TopologicalSpace.OpenNhds.op_map_id_obj, AlgebraicGeometry.Scheme.isoSpec_inv_image_zeroLocus, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι_ι, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_hom_app, AlgebraicGeometry.morphismRestrict_base, AlgebraicGeometry.Scheme.toSpecΓ_preimage_zeroLocus, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.imageBasicOpen_image_open, AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_comp_iff_of_isOpenImmersion, TopologicalSpace.Opens.inclusion'_top_functor, AlgebraicGeometry.Scheme.Cover.isOpenEmbedding_fromGlued, AlgebraicGeometry.coe_opensRestrict_symm_apply, AlgebraicGeometry.Scheme.Hom.isCompact_preimage_singleton, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_ideal, AlgebraicGeometry.Scheme.Pullback.Triplet.Spec_map_tensor_isPullback, AlgebraicGeometry.Scheme.Cover.covers, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_point_assoc, TopologicalSpace.Opens.map_functor_eq, TopCommRingCat.forgetToTopCatTopologicalRing, AlgebraicGeometry.Scheme.stalkMap_congr_point_assoc, AlgebraicGeometry.Scheme.GlueData.isOpen_iff, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_assoc, AlgebraicGeometry.QuasiCompactCover.isCompactOpenCovered_of_isCompact, AlgebraicGeometry.Scheme.Hom.mem_preimage, AlgebraicGeometry.Scheme.Spec_map_stalkMap_fromSpecStalk_assoc, AlgebraicGeometry.Scheme.Hom.isConstructible_preimage, AlgebraicGeometry.LocallyRingedSpace.isLocalHomStalkMap, AlgebraicGeometry.IsImmersion.isLocallyClosed_range, AlgebraicGeometry.Scheme.Γevaluation_naturality_apply, AlgebraicGeometry.ExistsHomHomCompEqCompAux.exists_index, range_pullback_map, AlgebraicGeometry.Scheme.Cover.exists_lift_trans_eq, AlgebraicGeometry.Spec_map_localization_isIso, AlgebraicGeometry.Scheme.stalkClosedPointTo_fromSpecStalk, AlgebraicGeometry.Scheme.coe_homeoOfIso_symm, AlgebraicGeometry.ProjectiveSpectrum.Proj.isLocalization_atPrime, AlgebraicGeometry.Scheme.stalkMap_hom_inv_assoc, AlgebraicGeometry.Scheme.IdealSheafData.range_subschemeι, AlgebraicGeometry.PresheafedSpace.GlueData.ι_image_preimage_eq, AlgebraicGeometry.PresheafedSpace.stalkMap.congr, AlgebraicGeometry.Scheme.Hom.isClosedMap, AlgebraicGeometry.Scheme.Hom.isLocallyClosed_range, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec_assoc, uliftFunctorObjHomeo_naturality_apply, homeoOfIso_apply, AlgebraicGeometry.morphismRestrict_appLE, AlgebraicGeometry.IsClosedImmersion.iff_isPreimmersion, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec, AlgebraicGeometry.Scheme.Hom.apply_mem_image_iff, AlgebraicGeometry.Scheme.Hom.asFiberHom_apply, Presheaf.germToPullbackStalk_stalkPullbackHom, AlgebraicGeometry.genericPoint_eq_of_isOpenImmersion, AlgebraicGeometry.Scheme.homeoOfIso_apply, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv_assoc, AlgebraicGeometry.formallySmooth_stalkMap_iff, nonempty_isLimit_iff_eq_induced, AlgebraicGeometry.isIso_stalkMap_coprodSpec, AlgebraicGeometry.LocallyRingedSpace.residue_comp_residueFieldMap_eq_stalkMap_comp_residue, AlgebraicGeometry.Scheme.instIsIsoCommRingCatResidueFieldMapOfIsOpenImmersion, AlgebraicGeometry.Scheme.instIsOverMapResidueFieldMapOverInferInstanceOverClass, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.image_preimage_is_empty, id_app, AlgebraicGeometry.Scheme.Γevaluation_naturality_assoc, AlgebraicGeometry.Scheme.Pullback.carrierEquiv_symm_snd, hasLimit_iff_small_sections, AlgebraicGeometry.isCompl_range_inl_inr, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app, piIsoPi_inv_π_apply, AlgebraicGeometry.Scheme.Pullback.range_map, AlgebraicGeometry.ProjIsoSpecTopComponent.fromSpec_toSpec, AlgebraicGeometry.SurjectiveOnStalks.isEmbedding_pullback, AlexDisc.forgetToTop_faithful, AlgebraicGeometry.Scheme.Hom.isSpectralMap, AlgebraicGeometry.mem_range_iff_of_surjective, GlueData.f_open, AlgebraicGeometry.Scheme.Hom.isLocallyConstructible_image, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_apply, AlgebraicGeometry.Scheme.stalkMap_congr_hom_assoc, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom, AlgebraicGeometry.Scheme.stalkSpecializes_stalkMap_apply, TopologicalSpace.OpenNhds.map_id_obj_unop, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app', isOpenEmbedding_iff_comp_isIso', isOpenEmbedding_f_zeroHypercover, TopologicalSpace.Opens.isOpenEmbedding, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_zeroLocus, GlueData.range_fromOpenSubsetsGlue, coe_id, AlgebraicGeometry.Scheme.GlueData.ι_eq_iff, AlgebraicGeometry.FormallyUnramified.instIsSeparableCarrierResidueFieldCoeContinuousMapCarrierCarrierCommRingCatHomTopCatBaseOfLocallyOfFiniteType, uliftFunctorCompForgetIso_inv_app, AlgebraicGeometry.AffineSpace.isOpenMap_over, AlgebraicGeometry.surjective_iff, AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk_assoc, AlgebraicGeometry.Scheme.singleton_mem_precoverage_iff, AlgebraicGeometry.Scheme.Hom.isOpenMap, AlgebraicGeometry.Scheme.Pullback.Triplet.hx, GlueData.MkCore.t_inv, AlgebraicGeometry.isOpenImmersion_iff_stalk, AlgebraicGeometry.LocallyRingedSpace.Hom.prop, AlgebraicGeometry.SurjectiveOnStalks.surj_on_stalks, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp, isClosed_iff_of_isColimit, AlgebraicGeometry.SurjectiveOnStalks.stalkMap_surjective, pullbackIsoProdSubtype_inv_snd_apply, AlgebraicGeometry.PresheafedSpace.stalkMap.isIso, GlueData.fromOpenSubsetsGlue_isOpenEmbedding, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv, AlgebraicGeometry.Scheme.IdealSheafData.support_comap, TopologicalSpace.Opens.set_range_inclusion', AlgebraicGeometry.Scheme.stalkMap_congr_hom, AlgebraicGeometry.Scheme.Pullback.range_snd_comp, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_jointly_surjective, AlgebraicGeometry.range_eq_univ, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_fst, AlgebraicGeometry.Scheme.Hom.comp_apply, AlgebraicGeometry.Scheme.Hom.isOpenEmbedding, pullbackIsoProdSubtype_inv_fst, AlgebraicGeometry.Spec.map_apply, AlgebraicGeometry.pointOfClosedPoint_apply, AlgebraicGeometry.PresheafedSpace.GlueData.ι_isOpenEmbedding, AlgebraicGeometry.Scheme.Hom.isEmbedding, AlgebraicGeometry.sigmaι_eq_iff, AlgebraicGeometry.Scheme.stalkMap_comp, AlgebraicGeometry.IsOpenImmersion.range_pullback_to_base_of_left, coinduced_of_isColimit, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp, AlgebraicGeometry.Scheme.IdealSheafData.map_vanishingIdeal, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_assoc, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.coequalizer_π_stalk_isLocalHom, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_apply, AlgebraicGeometry.Scheme.Hom.residueFieldMap_congr, pullbackIsoProdSubtype_hom_snd, AlgebraicGeometry.Scheme.Hom.map_mem_image_iff, TopologicalSpace.Opens.adjunction_counit_map_functor, AlgebraicGeometry.coprodSpec_coprodMk, AlgebraicGeometry.Scheme.Hom.injective, pullbackIsoProdSubtype_inv_snd, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberι, hasColimit_iff_small_colimitType, GlueData.fromOpenSubsetsGlue_injective, TopologicalSpace.Opens.adjunction_counit_app_self, AlgebraicGeometry.LocallyOfFiniteType.stalkMap, AlgebraicGeometry.locallyQuasiFinite_iff_isDiscrete_preimage_singleton, AlgebraicGeometry.Scheme.IsLocallyDirected.ι_eq_ι_iff, LightCondSet.topCatAdjunctionCounit_bijective, AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_base_fst, AlgebraicGeometry.compactSpace_iff_exists, AlgebraicGeometry.Scheme.stalkMap_congr_point, AlgebraicGeometry.ProjectiveSpectrum.Proj.mk_mem_toSpec_base_apply, range_pullback_to_prod, AlgebraicGeometry.IsAffineOpen.comap_primeIdealOf_appLE, GlueData.ι_isOpenEmbedding, AlgebraicGeometry.Scheme.stalkMap_hom_inv, AlgebraicGeometry.Scheme.toSpecΓ_image_zeroLocus, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality, AlgebraicGeometry.isImmersion_iff, pullback_fst_image_snd_preimage, TopModuleCat.instPreservesLimitsOfShapeTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitsOfShapeOfModuleCatForgetLinearMap, AlgebraicGeometry.Scheme.stalkMap_hom_inv_apply, continuous_iff_of_isColimit, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_hom_app_val_app_apply, AlgebraicGeometry.Scheme.Hom.stalkSpecializes_stalkMap_apply, AlgebraicGeometry.LocallyRingedSpace.isLocalHomStalkMap', AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv, instIsLeftAdjointForgetContinuousMapCarrier, pullbackIsoProdSubtype_inv_fst_apply, AlgebraicGeometry.Scheme.Hom.exists_mem_and_isIso_morphismRestrict_toNormalization, piIsoPi_hom_apply, AlgebraicGeometry.Scheme.descResidueField_stalkClosedPointTo_fromSpecResidueField, AlgebraicGeometry.isDominant_iff, AlgebraicGeometry.Flat.generalizingMap, AlgebraicGeometry.Scheme.Hom.fiberι_asFiber, GlueData.MkCore.t_id, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.c_iso, AlgebraicGeometry.IsOpenImmersion.range_pullback_snd_of_left, AlgebraicGeometry.IsOpenImmersion.instIsIsoCommRingCatStalkMap, AlgebraicGeometry.isPreimmersion_iff, AlgebraicGeometry.Scheme.AffineCover.covers, AlgebraicGeometry.Scheme.Hom.Spec_map_residueFieldMap_fromSpecResidueField_assoc, AlgebraicGeometry.Scheme.isLocalHom_stalkClosedPointTo', AlgebraicGeometry.IsFinite.finite_preimage_singleton, Presheaf.germ_stalkPullbackInv, AlgebraicGeometry.IsAffineOpen.primeIdealOf_eq_map_closedPoint, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc, GlueData.preimage_range, alexDiscEquivPreord_unitIso, AlgebraicGeometry.IsOpenImmersion.range_pullback_to_base_of_right, isOpenEmbedding_iff_isIso_comp, TopologicalSpace.Opens.functor_map_eq_inf, AlgebraicGeometry.Scheme.Pullback.Triplet.fst_SpecTensorTo_apply, AlexDisc.coe_forgetToTop, TopologicalSpace.OpenNhds.isOpenEmbedding, TopModuleCat.forget₂_TopCat_obj, AlgebraicGeometry.IsClosedImmersion.isClosedEmbedding, CompHausLike.homeoOfIso_apply, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp_assoc, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.stalk_iso, GlueData.image_inter, isEmbedding_pullback_to_prod, AlgebraicGeometry.Flat.stalkMap, AlgebraicGeometry.Scheme.Pullback.range_snd, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom_assoc, AlgebraicGeometry.Scheme.Hom.stalkMap_comp, AlexDisc.forgetToTop_full, pullbackIsoProdSubtype_hom_apply, AlgebraicGeometry.Scheme.Cover.exists_eq, AlgebraicGeometry.Scheme.ofArrows_mem_precoverage_iff, AlgebraicGeometry.Scheme.IsLocallyDirected.ι_jointly_surjective, AlgebraicGeometry.IsPreimmersion.base_embedding, AlgebraicGeometry.Scheme.Hom.coe_image, AlgebraicGeometry.Scheme.Hom.coe_preimage, ofHom_apply, AlgebraicGeometry.LocallyRingedSpace.stalkSpecializes_stalkMap_apply, coneOfConeForget_π_app, AlgebraicGeometry.Scheme.Hom.isClosedEmbedding, AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiber, AlgebraicGeometry.Scheme.Hom.finite_preimage_singleton, induced_of_isLimit, AlgebraicGeometry.Scheme.inv_hom_apply, AlgebraicGeometry.isIso_SpecMap_stakMap_localization, AlgebraicGeometry.Scheme.residue_residueFieldMap_assoc, AlgebraicGeometry.Scheme.IdealSheafData.support_map, AlgebraicGeometry.FormallyUnramified.stalkMap, Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk, AlgebraicGeometry.PresheafedSpace.stalkMap.congr_hom, prodIsoProd_hom_apply, AlgebraicGeometry.Scheme.OpenCover.finiteSubcover_X, AlgebraicGeometry.Scheme.Pullback.range_fst, comp_app, AlgebraicGeometry.IsOpenImmersion.iff_stalk_iso, AlgebraicGeometry.Scheme.Cover.fromGlued_isOpenEmbedding, AlgebraicGeometry.Scheme.residue_residueFieldMap, AlgebraicGeometry.PresheafedSpace.stalkMap.comp, pullbackIsoProdSubtype_inv_snd_assoc, epi_iff_surjective, AlgebraicGeometry.Scheme.stalkMap_inv_hom_apply, AlgebraicGeometry.Scheme.SpecMap_residue_apply, AlgebraicGeometry.Scheme.Pullback.range_diagonal_subset_diagonalCoverDiagonalRange, instIsRightAdjointForgetContinuousMapCarrier, AlgebraicGeometry.Scheme.Hom.mem_smoothLocus, GlueData.fromOpenSubsetsGlue_isOpenMap, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_apply, AlgebraicGeometry.Scheme.Pullback.Triplet.Spec_ofPointTensor_SpecTensorTo, adj₂_counit, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_s, AlgebraicGeometry.QuasiCompactCover.isCompactOpenCovered_of_isAffineOpen, AlgebraicGeometry.Scheme.Opens.range_ι, AlgebraicGeometry.IsAffineOpen.range_fromSpec, AlgebraicGeometry.isClosedImmersion_iff, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_assoc, TopModuleCat.instPreservesLimitsTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, AlgebraicGeometry.Spec_closedPoint, AlgebraicGeometry.Scheme.Hom.range_subset_ker_support, AlgebraicGeometry.ProjectiveSpectrum.Proj.stalkMap_toSpec, hom_inv_id_apply, nonempty_isColimit_iff_eq_coinduced, AlgebraicGeometry.Scheme.Hom.finite_preimage, AlgebraicGeometry.Scheme.Opens.ι_apply, mono_iff_injective, AlgebraicGeometry.Scheme.iso_inv_base_hom_base_apply, AlgebraicGeometry.Scheme.Hom.continuous, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberToSpecResidueField, homeoOfIso_symm_apply, AlgebraicGeometry.Scheme.Pullback.Triplet.exists_preimage, AlgebraicGeometry.Scheme.Hom.isConstructible_image, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv_apply, AlgebraicGeometry.Surjective.surj, AlgebraicGeometry.Scheme.stalkMap_inv_hom, ContinuousMap.yonedaPresheaf'_map, AlgebraicGeometry.Scheme.comp_base_apply, AlgebraicGeometry.isGermInjectiveAt_iff_of_isOpenImmersion, GlueData.MkCore.t_inter, AlgebraicGeometry.PresheafedSpace.GlueData.ι_jointly_surjective, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_base_apply, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq_comap, AlgebraicGeometry.IsDominant.denseRange, AlgebraicGeometry.Flat.iff_flat_stalkMap, AlgebraicGeometry.Scheme.preimage_zeroLocus, AlgebraicGeometry.isIso_iff_stalk_iso, AlgebraicGeometry.Scheme.instIsOverMapStalkMapOverInferInstanceOverClass, GlueData.ι_jointly_surjective, AlgebraicGeometry.Scheme.Hom.support_ker, AlgebraicGeometry.Scheme.Hom.homeomorph_apply, AlgebraicGeometry.Scheme.Hom.stalkMap_congr, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec, AlgebraicGeometry.LocallyRingedSpace.stalkSpecializes_stalkMap, AlgebraicGeometry.Scheme.Hom.surjective, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.sigma_ι_isOpenEmbedding, AlgebraicGeometry.Scheme.IsLocallyDirected.exists_of_pullback_V_V, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.imageBasicOpen_image_preimage, isOpen_iff_of_isColimit_cofork, TopModuleCat.instReflectsIsomorphismsTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, isQuotientMap_of_isColimit_cofork, forget_preservesColimitsOfSize, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_assoc, Action.isContinuous_def, AlgebraicGeometry.Scheme.stalkMap_inv_hom_assoc, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.preimage_toBase_eq_range_ι, isOpen_iff_of_isColimit, AlgebraicGeometry.locallyQuasiFinite_iff_finite_preimage_singleton, AlgebraicGeometry.Spec.topObj_forget, adj₂_unit, TopologicalSpace.OpenNhds.map_id_obj, forget_preservesLimits, AlgebraicGeometry.Scheme.Opens.ι_appLE, AlgebraicGeometry.IsOpenImmersion.range_pullbackFst, AlgebraicGeometry.IsAffineOpen.fromSpec_image_zeroLocus, AlgebraicGeometry.Scheme.affineBasisCover_map_range, AlgebraicGeometry.Flat.isQuotientMap_of_surjective, AlgebraicGeometry.Scheme.Opens.ι_app, AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.isClopen_singleton_asFiber, AlgebraicGeometry.instIsPreimmersionAsFiberHom, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_hom_assoc, AlgebraicGeometry.quasiCompact_iff_spectral, AlgebraicGeometry.Scheme.iso_hom_base_inv_base_apply, prodIsoProd_inv_fst_apply, AlgebraicGeometry.quasiCompact_iff_isSpectralMap, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_preimage_basicOpen, effectiveEpi_iff_isQuotientMap, colimit_isOpen_iff, adj₁_unit, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_zeroLocus_eq, AlgebraicGeometry.IsAffineOpen.isCompactOpenCovered, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.base_open, adj₁_counit, alexDiscEquivPreord_counitIso, AlgebraicGeometry.Scheme.Γevaluation_naturality, GlueData.ι_eq_iff_rel, AlgebraicGeometry.HasRingHomProperty.stalkMap_of_respectsIso, AlgebraicGeometry.ExistsHomHomCompEqCompAux.range_g_subset, TopologicalSpace.Opens.toTopCat_map, AlgebraicGeometry.Scheme.isLocalHom_stalkClosedPointTo, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality, Presheaf.germToPullbackStalk_stalkPullbackHom_assoc, AlgebraicGeometry.Scheme.Hom.SpecMap_residueFieldMap_fromSpecResidueField, coe_comp, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_y, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp_assoc, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_assoc, AlgebraicGeometry.LocallyRingedSpace.toStalk_stalkMap_toΓSpec, AlgebraicGeometry.Scheme.range_fromSpecResidueField, AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk, exists_mem_zeroHypercover_range, sigmaIsoSigma_hom_ι_apply, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_apply, AlgebraicGeometry.quasiCompactCover_iff, AlgebraicGeometry.Scheme.image_zeroLocus, AlgebraicGeometry.Scheme.Hom.fiberToSpecResidueField_apply, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv_assoc, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_SpecTensorTo, AlgebraicGeometry.Scheme.JointlySurjective.exists_eq, AlgebraicGeometry.LocallyRingedSpace.isLocalHom_stalkMap_congr, ext_iff, AlgebraicGeometry.Scheme.Hom.app_appIso_inv, limit_topology, AlgebraicGeometry.Scheme.coe_homeoOfIso, Presheaf.stalkPushforward.comp, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec.image_basicOpen_eq_basicOpen, AlgebraicGeometry.isClosedMap_iff_specializingMap, pullback_snd_range, AlgebraicGeometry.Scheme.image_preimage_eq_of_isPullback, AlgebraicGeometry.Scheme.Hom.instIsLocalHomCarrierStalkCommRingCatPresheafCoeContinuousMapCarrierCarrierHomTopCatBaseRingHomHomStalkMap, AlgebraicGeometry.LocallyRingedSpace.stalkMap_comp, AlgebraicGeometry.Scheme.GlueData.ι_jointly_surjective, AlgebraicGeometry.SheafedSpace.isColimit_exists_rep, AlexDisc.forgetToTop_of, GlueData.MkCore.cocycle, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv_apply, TopologicalSpace.OpenNhds.inclusionMapIso_inv_app, AlgebraicGeometry.Scheme.stalkClosedPointTo_comp, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_apply, AlgebraicGeometry.Scheme.Spec_map_residue_apply, GlueData.ι_injective, AlgebraicGeometry.Scheme.residueFieldMap_comp, AlgebraicGeometry.Scheme.isoSpec_image_zeroLocus, AlgebraicGeometry.Scheme.Hom.fiberι_fiberHomeo_symm, AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalk, Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk_assoc, AlgebraicGeometry.LocallyRingedSpace.isLocalHomValStalkMap, coconeOfCoconeForget_ι_app, AlgebraicGeometry.Scheme.mem_toGrothendieck_smallPretopology, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_point, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom, AlgebraicGeometry.Scheme.Hom.Spec_map_residueFieldMap_fromSpecResidueField, AlgebraicGeometry.Scheme.Opens.toSpecΓ_preimage_zeroLocus, AlgebraicGeometry.Scheme.Cover.fromGlued_open_map, inv_hom_id_apply, alexDiscEquivPreord_functor, AlgebraicGeometry.coprodMk_inr, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_bijective, AlgebraicGeometry.Scheme.Hom.isProperMap, AlgebraicGeometry.QuasiCompactCover.exists_isAffineOpen_of_isCompact, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberToSpecResidueField_assoc, pullback_fst_range, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_hom, TopologicalSpace.OpenNhds.inclusionMapIso_hom_app, AlgebraicGeometry.Scheme.Hom.isOpen_smoothLocus, AlgebraicGeometry.Scheme.Opens.ι_base_apply, AlgebraicGeometry.Scheme.Hom.isDiscrete_preimage, GlueData.preimage_image_eq_image', AlgebraicGeometry.Scheme.homOfLE_apply, AlgebraicGeometry.IsAffineOpen.fromSpec_primeIdealOf, pullback_snd_image_fst_preimage, AlgebraicGeometry.LocallyRingedSpace.iso_hom_base_inv_base_apply, AlgebraicGeometry.Scheme.fromSpecResidueField_apply, TopModuleCat.hom_forget₂_TopCat_map, AlgebraicGeometry.Scheme.Hom.coe_opensRange, AlgebraicGeometry.Scheme.stalkMap_congr, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom, AlgebraicGeometry.SheafedSpace.GlueData.ι_jointly_surjective, AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_apply, AlgebraicGeometry.PresheafedSpace.stalkMap.congr_point, prodIsoProd_inv_snd_apply, AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalk_assoc, AlgebraicGeometry.Scheme.Cover.fromGlued_injective, AlgebraicGeometry.Spec.map_base_apply, AlgebraicGeometry.Scheme.Hom.stalkMap_surjective, AlgebraicGeometry.Scheme.toSpecΓ_base
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isoOfHomeo 📖 | CompOp | 4 mathmath: isoOfHomeo_inv, of_isoOfHomeo, isoOfHomeo_hom, of_homeoOfIso
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ofHom 📖 | CompOp | 28 mathmath: isoOfHomeo_inv, coe_of_of, ContinuousMap.Homotopy.apply_zero_path, hom_ofHom, AlgebraicGeometry.Scheme.emptyTo_base, ContinuousMap.Homotopy.evalAt_eq, ContinuousMap.Homotopy.heq_path_of_eq_image, GlueData.ofOpenSubsets_toGlueData_t, ContinuousMap.Homotopy.eq_path_of_eq_image, ofHom_comp, SimplexCategory.toTop_map, ofHom_hom, ContinuousMap.Homotopy.apply_one_path, SimplexCategory.toTop₀_map, Sequential.isoOfHomeo_inv, isoOfHomeo_hom, Sequential.isoOfHomeo_hom, skyscraperPresheaf_eq_pushforward, FundamentalGroupoid.map_eq, ofHom_apply, coneOfConeForget_π_app, AlgebraicGeometry.Scheme.emptyTo_c_app, AlgebraicGeometry.Spec.map_base, adj₂_unit, adj₁_counit, coconeOfCoconeForget_ι_app, ofHom_id, ContinuousMap.Homotopy.eq_diag_path
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str 📖 | CompOp | 1847 mathmath: Presheaf.generateEquivalenceOpensLe_functor'_obj_obj, isInducing_pullback_to_prod, TopologicalSpace.OpenNhds.coe_id, AlgebraicGeometry.Scheme.toSpecΓ_apply, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen, AlgebraicGeometry.Γ_map_morphismRestrict, Sequential.homeoOfIso_apply, AlgebraicGeometry.Scheme.Modules.pushforward_obj_presheaf_map, binaryCofan_isColimit_iff, DiscreteContAction.instDiscreteTopologyCarrierObjTopCatForget₂ContinuousMap, smoothSheafCommRing.ι_forgetStalk_inv, AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality_assoc, AlgebraicGeometry.Proj.awayMap_awayToSection_assoc, AlgebraicGeometry.QuasiCompact.isCompact_preimage_singleton, LightCondensed.free_internallyProjective_iff_tensor_condition, AlgebraicGeometry.Scheme.fromSpecStalk_closedPoint, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst_assoc, AlgebraicGeometry.Scheme.map_PrimeSpectrum_basicOpen_of_affine, PrelocalPredicate.res, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_injective, TopologicalSpace.Opens.id_apply, AlgebraicGeometry.StructureSheaf.instIsScalarTowerCarrierStalkCommRingCatStructurePresheafInCommRingCatCarrierAbPresheafOpensCarrierTopModuleStructurePresheaf, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv_assoc, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_appTop, LightProfinite.proj_comp_transitionMap, TopologicalSpace.Opens.map_id_obj_unop, LightProfinite.Extend.functorOp_obj, AlgebraicGeometry.Scheme.zeroLocus_iInf, AlgebraicGeometry.Scheme.Modules.pushforwardId_inv_app_app, pullbackIsoProdSubtype_hom_fst, AlgebraicGeometry.IsAffineOpen.map_fromSpec_assoc, LightCondensed.lanPresheafIso_hom, AlgebraicGeometry.IsAffineOpen.isLocalization_of_eq_basicOpen, TopologicalSpace.Opens.inclusion'_hom_apply, AlgebraicGeometry.Scheme.Hom.opensRange_pullbackSnd, AlgebraicGeometry.LocallyRingedSpace.residueFieldMap_comp, isoOfHomeo_inv, presheafToType_map, Sheaf.interUnionPullbackCone_snd, LightCondensed.isoFinYonedaComponents_hom_apply, TopologicalSpace.Opens.map_coe, AlgebraicGeometry.Scheme.Spec_map_stalkMap_fromSpecStalk, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_apply, AlgebraicGeometry.Scheme.Cover.LocallyDirected.directed, ProfiniteGrp.coe_of, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.stalk_iso, ProfiniteGrp.instReflectsIsomorphismsProfiniteForget₂ContinuousMonoidHomCarrierToTopTotallyDisconnectedSpaceToProfiniteContinuousMap, AlgebraicGeometry.Scheme.Modules.instFaithfulPresheafOfModulesToPresheafOfModules, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app, AlgebraicGeometry.Scheme.IsQuasiAffine.toIsImmersion, AlgebraicGeometry.StructureSheaf.globalSectionsIso_inv, AlgebraicGeometry.QuasiCompact.isCompact_preimage, GlueData.preimage_image_eq_image, ContinuousMap.yonedaPresheaf'_obj, AlgebraicGeometry.RingedSpace.basicOpen_res, AlgebraicGeometry.Scheme.Hom.app_invApp'_assoc, AlgebraicGeometry.Scheme.Hom.denseRange, AlgebraicGeometry.Scheme.isEmpty_pullback_iff, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv, GlueData.π_surjective, AlgebraicGeometry.Scheme.Hom.quasiFiniteLocus_comp, LightCondensed.ihomPoints_apply, AlgebraicGeometry.Scheme.app_eq, DeltaGenerated.topToDeltaGenerated_map_hom_hom_apply, AlgebraicGeometry.Scheme.Hom.closePoints_subset_preimage_closedPoints, isOpenEmbedding_iff_comp_isIso, AlgebraicGeometry.Scheme.zeroLocus_empty_eq_univ, AlgebraicGeometry.coprodSpec_apply, AlgebraicGeometry.morphismRestrict_base_coe, AlgebraicGeometry.Scheme.Hom.fiberHomeo_apply, AlgebraicGeometry.surjectiveOnStalks_iff, AlgebraicGeometry.StructureSheaf.comap_id, Profinite.Extend.cocone_pt, FundamentalGroupoidFunctor.piIso_hom, TopModuleCat.instPreservesLimitTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitOfModuleCatCompLinearMapForget, Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_π_app, Stonean.instExtremallyDisconnectedCarrierToTop, CondensedMod.IsSolid.isIso_solidification_map, AlgebraicGeometry.IsAffineOpen.map_fromSpec, Presheaf.Pushforward.id_inv_app, AlgebraicGeometry.Scheme.affineBasisCover_is_basis, Profinite.forget_preservesLimits, AlgebraicGeometry.IsLocallyArtinian.isArtinianRing_presheaf_obj, AlgebraicGeometry.Scheme.Opens.toSpecΓ_naturality, CompactlyGenerated.homeoOfIso_apply, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top, AlgebraicGeometry.range_eq_range_of_surjective, skyscraperPresheaf_obj, AlgebraicGeometry.LocallyRingedSpace.notMem_prime_iff_unit_in_stalk, AlgebraicGeometry.Scheme.restrictFunctorΓ_inv_app, AlgebraicGeometry.Scheme.Cover.isOpenMap_fromGlued, coe_of_of, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_counit_app_app, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_specStalkEquiv, AlgebraicGeometry.instGeometricallyIrreducibleMorphismRestrict, AlgebraicGeometry.instIsDomainCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTopOfIsIntegral, instFullFintypeCatProfiniteToProfinite, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_x, GlueData.open_image_open, LightCondensed.forget_obj_val_map, Stonean.instProjective, AlgebraicGeometry.Scheme.Hom.exists_isIso_morphismRestrict_toNormalization, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_symm_apply, AlgebraicGeometry.morphismRestrict_ι_assoc, Profinite.Extend.functorOp_map, AlgebraicGeometry.functionField_isFractionRing_of_isAffineOpen, AlgebraicGeometry.Scheme.IdealSheafData.ideal_sSup, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_point, AlgebraicGeometry.ValuativeCriterion.Existence.specializingMap, AlgebraicGeometry.Scheme.fromSpecStalk_toSpecΓ_assoc, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_fromSpec, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_hom_app_app, AlgebraicGeometry.AffineSpace.SpecIso_hom_appTop, AlgebraicGeometry.LocallyRingedSpace.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, AlgebraicGeometry.exists_isAffineOpen_preimage_eq, AlgebraicGeometry.SheafedSpace.colimit_exists_rep, AlgebraicGeometry.Scheme.Modules.pushforward_obj_obj, ProfiniteGrp.limit_one_val, AlgebraicGeometry.Scheme.Hom.range_fiberι, AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf_map, TopologicalSpace.Opens.coe_inclusion', ProfiniteAddGrp.ofHom_hom, AlgebraicGeometry.Scheme.Hom.preimage_bot, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp, TopologicalSpace.OpenNhds.inclusionMapIso_hom, AlgebraicGeometry.Scheme.Cover.iUnion_range, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_naturality, AlgebraicGeometry.Scheme.mem_basicOpen', LightCondensed.ihomPoints_symm_comp, AlgebraicGeometry.Scheme.Hom.mem_opensRange, Profinite.instEnoughProjectives, AlgebraicGeometry.Scheme.zeroLocus_eq_univ_iff_subset_nilradical, AlgebraicGeometry.Scheme.Opens.topIso_inv, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_preimage_basicOpen, Sequential.homeoOfIso_symm_apply, AlgebraicGeometry.Proj.pow_apply, AlgebraicGeometry.isCompact_iff_exists, ProfiniteGrp.ProfiniteCompletion.lift_eta, Presheaf.SheafConditionEqualizerProducts.piOpens.hom_ext_iff, AlgebraicGeometry.Spec_presheaf, LightCondSet.continuous_coinducingCoprod, AlgebraicGeometry.HasRingHomProperty.stalkMap, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app_assoc, ContinuousMap.Homotopy.apply_zero_path, LightCondSet.epi_iff_locallySurjective_on_lightProfinite, TopCommRingCat.instReflectsIsomorphismsTopCatForget₂SubtypeRingHomαContinuousCoeContinuousMapCarrier, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap_apply, sigmaIsoSigma_hom_ι, uliftFunctorObjHomeo_symm_naturality_apply, AlgebraicGeometry.Scheme.inv_app, LightProfinite.instCountableClopensCarrierToTopAndTotallyDisconnectedSpaceSecondCountableTopology, LightCondensed.isoFinYoneda_inv_app, AlgebraicGeometry.Scheme.Hom.id_appTop, CondensedMod.isDiscrete_tfae, AlgebraicGeometry.Proj.basicOpenIsoAway_hom, smoothSheafCommRing.ι_evalHom_apply, uliftFunctorCompForgetIso_hom_app, AlgebraicGeometry.image_morphismRestrict_preimage, AlgebraicGeometry.Scheme.emptyTo_base, CompHaus.toStonean_toTop, CompHausLike.coe_id, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_hom_apply_asIdeal, AlgebraicGeometry.Scheme.zeroLocus_mul, AlgebraicGeometry.Proj.mul_apply, AlgebraicGeometry.StructureSheaf.comap_id', TopologicalSpace.OpenNhds.comp_apply, AlgebraicGeometry.Scheme.OpenCover.finiteSubcover_f, AlgebraicGeometry.Scheme.stalkSpecializes_stalkMap, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_inv_app, LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition, AlgebraicGeometry.SpecMap_preimage_basicOpen, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_isModule, Profinite.Extend.cone_π_app, AlgebraicGeometry.Scheme.ideal_ker_le_ker_ΓSpecIso_inv_comp, AlgebraicGeometry.Scheme.stalkMap_congr_assoc, instFaithfulFintypeCatLightProfiniteToLightProfinite, ProfiniteAddGrp.ofHom_apply, smoothSheafCommRing.eval_germ, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_surjective, AlgebraicGeometry.instIsGermInjectiveAtCoeContinuousMapCarrierCarrierCommRingCatHomTopCatBaseOfIsOpenImmersion, LightCondensed.finYoneda_map, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_map, AlgebraicGeometry.Scheme.isoSpec_inv_toSpecΓ, AlgebraicGeometry.Scheme.Pullback.SpecTensorTo_SpecOfPoint, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.instIsIsoInvApp, ContinuousMap.Homotopy.evalAt_eq, AlgebraicGeometry.Scheme.hom_inv_apply, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app_apply, AlgebraicGeometry.Scheme.Hom.range_asFiberHom, SimplexCategory.instPathConnectedSpaceCarrierObjTopCatToTop, Sequential.isoEquivHomeo_apply, TopologicalSpace.Opens.comp_apply, AlgebraicGeometry.isIso_ΓSpec_adjunction_unit_app_basicOpen, AlgebraicGeometry.isNoetherian_iff_of_finite_affine_openCover, AlgebraicGeometry.Scheme.Hom.tendsto_cofinite_cofinite, Sequential.isoEquivHomeo_symm_apply, AlgebraicGeometry.Scheme.Hom.preimage_le_preimage_of_le, AlgebraicGeometry.Scheme.Hom.stalkSpecializes_stalkMap, AlgebraicGeometry.IsAffineOpen.fromSpecStalk_closedPoint, TopologicalSpace.OpenNhds.val_apply, AlgebraicGeometry.SmoothOfRelativeDimension.exists_isStandardSmoothOfRelativeDimension, AlgebraicGeometry.Scheme.Hom.preimageIso_hom_ι_assoc, AlgebraicGeometry.Scheme.IdealSheafData.ideal_le_comap_ideal, isOpenEmbedding_iff, ProfiniteGrp.coe_id, AlgebraicGeometry.IsClosedImmersion.base_closed, AlgebraicGeometry.quasiCompact_iff, Profinite.effectiveEpi_tfae, TopologicalSpace.OpenNhds.inclusionMapIso_inv, AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine_apply, AlgebraicGeometry.structureSheafInType.mul_apply, range_prod_map, Stonean.instEffectivelyEnoughCompHausToCompHaus, TopModuleCat.instIsRightAdjointTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, skyscraperPresheafCocone_pt, AlgebraicGeometry.Scheme.Modules.Hom.zero_app, Sheaf.pushforward_map, AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine_symm_apply, AlgebraicGeometry.Scheme.congr_app, AlgebraicGeometry.Scheme.IdealSheafData.ideal_mul, AlgebraicGeometry.IsZariskiLocalAtTarget.restrict, AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.structurePresheafInCommRing_obj_carrier, AlgebraicGeometry.Scheme.SpecΓIdentity_hom_app, AlgebraicGeometry.locallyQuasiFinite_iff, AlgebraicGeometry.Scheme.preimage_comp, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom_assoc, smoothSheaf.ι_evalHom_apply, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.toBase_preimage_eq_opensRange_ι, Presheaf.SheafConditionEqualizerProducts.fork_π_app_walkingParallelPair_one, LightCondMod.isDiscrete_tfae, AlgebraicGeometry.IsFinite.instMorphismRestrict, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap, AlgebraicGeometry.Scheme.Pullback.Triplet.isPullback_SpecMap_tensor, AlgebraicGeometry.Scheme.forget_map, GlueData.isOpen_iff, AlgebraicGeometry.sigmaMk_mk, Presheaf.pushforwardToOfIso_app, AlgebraicGeometry.affineLocally_iff_forall_isAffineOpen, AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_base_snd, LocallyConstant.freeOfProfinite, Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_hom_app_hom, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_point_assoc, AlgebraicGeometry.Scheme.isoSpec_inv_preimage_zeroLocus, instFaithfulLightDiagramProfiniteLightDiagramToProfinite, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app_assoc, instPreservesEpimorphismsLightProfiniteLightCondSetLightProfiniteToLightCondSet, AlgebraicGeometry.PresheafedSpace.Γ_obj_op, LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace, TopologicalSpace.Opens.map_comp_obj_unop, AlgebraicGeometry.IsPreimmersion.isEmbedding, AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf', Profinite.NobelingProof.spanFunctorIsoIndexFunctor_hom_app_hom_hom_apply_coe, coequalizer_isOpen_iff, Sheaf.interUnionPullbackCone_fst, AlgebraicGeometry.functionField_isScalarTower, forget_preservesColimits, GlueData.ι_fromOpenSubsetsGlue_apply, ProfiniteGrp.ProfiniteCompletion.lift_eta_assoc, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app, InfiniteGalois.toAlgEquivAux_eq_proj_of_mem, GlueData.MkCore.V_id, AlgebraicGeometry.Scheme.Hom.SpecMap_residueFieldMap_fromSpecResidueField_assoc, LightCondensed.discrete_map, AlgebraicGeometry.Scheme.exists_germ_injective, AlgebraicGeometry.IsOpenImmersion.iff_isIso_stalkMap, AlgebraicGeometry.Scheme.Cover.instIsIsoCommRingCatStalkMapFromGlued, AlgebraicGeometry.StructureSheaf.instIsLocalizedModuleObjOppositeOpensCarrierTopValStructureSheafInTypeOpBasicOpenPowersToOpenₗ, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_eq, LightProfinite.proj_comp_transitionMapLE', AlgebraicGeometry.Scheme.Hom.preimage_top, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd_assoc, lightDiagramToProfinite_map, AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimage, AlgebraicGeometry.Scheme.Pullback.carrierEquiv_eq_iff, AlgebraicGeometry.Proj.one_apply, AlgebraicGeometry.Scheme.Hom.toImage_app_injective, AlgebraicGeometry.Scheme.isoSpec_hom, AlgebraicGeometry.Scheme.Hom.id_preimage, AlgebraicGeometry.Flat.instMorphismRestrict, AlgebraicGeometry.StructureSheaf.to_basicOpen_epi, AlgebraicGeometry.IsAffineOpen.opensRange_fromSpec, pullback_topology, AlgebraicGeometry.Scheme.IdealSheafData.ideal_le_ker_glueDataObjι, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_c_app, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_snd_coe, LightProfinite.Extend.cocone_ι_app, AlgebraicGeometry.instQuasiCompactMorphismRestrict, AlgebraicGeometry.Scheme.eqToHom_c_app, GlueData.ofOpenSubsets_toGlueData_t, AlgebraicGeometry.IsAffineOpen.self_le_iSup_basicOpen_iff, AlgebraicGeometry.Scheme.zeroLocus_biInf, AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_hom_π, AlgebraicGeometry.PresheafedSpace.componentwiseDiagram_map, AlgebraicGeometry.Scheme.exists_affine_mem_range_and_range_subset, AlgebraicGeometry.Proj.basicOpenToSpec_app_top, ProfiniteGrp.instFaithfulProfiniteForget₂ContinuousMonoidHomCarrierToTopTotallyDisconnectedSpaceToProfiniteContinuousMap, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_naturality, Condensed.lanPresheafExt_inv, AlgebraicGeometry.Scheme.AffineZariskiSite.generate_presieveOfSections, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app, ProfiniteAddGrp.instFaithfulProfiniteForget₂ContinuousAddMonoidHomCarrierToTopTotallyDisconnectedSpaceToProfiniteContinuousMap, AlgebraicGeometry.IsOpenImmersion.isOpen_range, AlgebraicGeometry.Scheme.affineOpenCover_idx, AlgebraicGeometry.Scheme.Opens.isoOfLE_hom_ι_assoc, AlgebraicGeometry.Scheme.Hom.fromNormalization_preimage, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.stalk_iso, AlgebraicGeometry.Scheme.toSpecΓ_naturality_assoc, AlgebraicGeometry.LocallyRingedSpace.iso_inv_base_hom_base_apply, AlgebraicGeometry.Scheme.Pullback.Triplet.snd_SpecTensorTo_apply, AlgebraicGeometry.Scheme.Modules.pushforwardComp_inv_app_app, AlgebraicGeometry.SurjectiveOnStalks.iff_of_isAffine, AlgebraicGeometry.SpecMap_ΓSpecIso_hom, AlgebraicGeometry.IsAffineOpen.isLocalization_basicOpen, pullbackFst_apply, alexDiscEquivPreord_inverse_obj_str, AlgebraicGeometry.Scheme.zeroLocus_iUnion, sigmaCofan_ι_app, AlgebraicGeometry.IsReduced.component_reduced, AlgebraicGeometry.PresheafedSpace.stalkMap.stalkSpecializes_stalkMap, instFaithfulFintypeCatProfiniteToProfinite, AlgebraicGeometry.SheafedSpace.comp_hom_c_app, Profinite.injective_of_light, CompHausLike.LocallyConstant.locallyConstantIsoContinuousMap_inv_apply, LightCondSet.topCatAdjunctionUnit_val_app_apply, ProfiniteAddGrp.instPreservesLimitsProfiniteForget₂ContinuousAddMonoidHomCarrierToTopTotallyDisconnectedSpaceToProfiniteContinuousMap, AlgebraicGeometry.IsIntegralHom.isIntegral_app, AlgebraicGeometry.Scheme.ker_ideal_of_isPullback_of_isOpenImmersion, colimit_topology, Profinite.epi_iff_surjective, AlgebraicGeometry.Scheme.presieve₀_mem_precoverage_iff, lightProfiniteToLightDiagram_map, Sheaf.id_app, TopologicalSpace.Opens.isOpenEmbedding_obj_top, AlgebraicGeometry.LocallyRingedSpace.Γ_obj_op, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_appTop_coord, Profinite.exists_locallyConstant_finite_aux, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over_assoc, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ_ΓToStalk, AlgebraicGeometry.isIso_iff_isIso_stalkMap, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom, ContinuousMap.Homotopy.ulift_apply, isOpenEmbedding_iff_isIso_comp', AlgebraicGeometry.Scheme.isoSpec_hom_naturality, topCatOpToFrm_map, AlgebraicGeometry.Scheme.zeroLocus_singleton, AlgebraicGeometry.PresheafedSpace.comp_c_app, AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv_assoc, AlgebraicGeometry.LocallyRingedSpace.component_nontrivial, AlgebraicGeometry.Scheme.Pullback.residueFieldCongr_inv_residueFieldMap_ofPoint, AlgebraicGeometry.Scheme.IdealSheafData.ideal_map, AlgebraicGeometry.IsOpenImmersion.range_pullbackSnd, AlgebraicGeometry.Proj.sub_apply, AlgebraicGeometry.isLocallyArtinian_iff_of_isOpenCover, AlgebraicGeometry.IsImmersion.instMorphismRestrict, Profinite.instTotallyDisconnectedSpaceCarrierToTop, Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_π_app, AlgebraicGeometry.Scheme.Hom.isDiscrete_preimage_singleton, AlgebraicGeometry.Scheme.Hom.comp_app, pullbackSnd_apply, ProfiniteGrp.toLimit_surjective, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι_ι_eq_support_inter, LightProfinite.isClosedMap, AlgebraicGeometry.instIsScalarTowerObjOppositeOpensCarrierTopValStructureSheafInType, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr, TopologicalSpace.Opens.mapId_hom_app, AlgebraicGeometry.IsOpenImmersion.range_pullback_fst_of_right, ProfiniteAddGrp.hom_neg_apply, TopologicalSpace.Opens.mapComp_hom_app, AlgebraicGeometry.Scheme.toSpecΓ_naturality, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app_assoc, lightDiagramToLightProfinite_obj, smoothSheaf.ι_evalHom_assoc, AlgebraicGeometry.pointEquivClosedPoint_apply_coe, Profinite.isIso_indexCone_lift, Stonean.instHasExplicitFiniteCoproductsExtremallyDisconnectedCarrier, AlgebraicGeometry.Scheme.Hom.ι_toNormalization, AlgebraicGeometry.LocallyRingedSpace.Γ_Spec_left_triangle, Condensed.isoFinYonedaComponents_hom_apply, isIso_iff_isHomeomorph, AlgebraicGeometry.Scheme.IdealSheafData.ideal_pow, AlgebraicGeometry.RingedSpace.mem_top_basicOpen, ProfiniteGrp.hom_id, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv, ProfiniteAddGrp.hom_id, AlgebraicGeometry.Scheme.range_fromSpecStalk, prod_topology, FundamentalGroupoidFunctor.prodToProdTop_obj, AlgebraicGeometry.IsAffineOpen.ideal_le_iff, CondensedSet.topCatAdjunctionCounit_bijective, Presheaf.IsSheaf.isSheafUniqueGluing_types, Profinite.Extend.functorOp_obj, AlgebraicGeometry.Scheme.Hom.congr_app, AlgebraicGeometry.Scheme.Hom.preimage_iSup, ProfiniteAddGrp.neg_hom_apply, AlgebraicGeometry.coprodMk_inl, AlgebraicGeometry.Scheme.Opens.toSpecΓ_naturality_assoc, CondensedSet.topCatAdjunctionCounit_hom_apply, AlgebraicGeometry.Scheme.Pullback.Triplet.hy, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_assoc, AlgebraicGeometry.IsAffineOpen.isoSpec_inv, forget_preservesLimitsOfSize, AlgebraicGeometry.Scheme.Hom.id_app, sigmaIsoSigma_inv_apply, Presheaf.comp_app, AlgebraicGeometry.Scheme.Γ_obj, CompHausLike.homeoOfIso_symm_apply, AlgebraicGeometry.isLocallyNoetherian_iff_of_affine_openCover, Condensed.finYoneda_map, AlgebraicGeometry.Scheme.Pullback.carrierEquiv_symm_fst, AlgebraicGeometry.Scheme.IdealSheafData.mem_support_iff_of_mem, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberι_assoc, LightProfinite.lightToProfinite_map_proj_eq, AlgebraicGeometry.IsLocallyArtinian.isArtinianRing_of_isAffine, AlgebraicGeometry.StructureSheaf.toPushforwardStalkAlgHom_apply, AlgebraicGeometry.Scheme.preimage_basicOpen_top, CompHausLike.isClosedMap, AlgebraicGeometry.PresheafedSpace.GlueData.pullback_base, AlgebraicGeometry.Scheme.ΓSpecIso_inv, AlgebraicGeometry.Scheme.Hom.app_appIso_inv_assoc, Presheaf.SheafConditionPairwiseIntersections.coneEquiv_counitIso, AlgebraicGeometry.IsAffineOpen.basicOpen_fromSpec_app, FintypeCat.toProfinite_map_hom_hom_apply, FundamentalGroupoidFunctor.prodIso_hom, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_assoc, pullbackIsoProdSubtype_inv_fst_assoc, AlgebraicGeometry.Scheme.opensRange_homOfLE, AlgebraicGeometry.Scheme.Pullback.range_fst_comp, Presheaf.pushforward_map_app, TopologicalSpace.OpenNhds.op_map_id_obj, AlgebraicGeometry.Scheme.isoSpec_hom_naturality_assoc, prodIsoProd_hom_snd_assoc, AlgebraicGeometry.Scheme.isoSpec_inv_image_zeroLocus, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι_ι, AlgebraicGeometry.Scheme.germToFunctionField_injective, ProfiniteGrp.denseRange_toLimit, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_hom_app, Profinite.hasColimits, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app', ProfiniteAddGrp.limit_zero_val, AlgebraicGeometry.isIso_morphismRestrict_iff_isIso_app, ProfiniteGrp.comp_apply, AlgebraicGeometry.morphismRestrict_base, CompHausLike.isoEquivHomeo_symm_apply, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen_topIso_inv, continuousPrelocal_pred, AlgebraicGeometry.Scheme.zeroLocus_setMul, AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ, AlgebraicGeometry.Scheme.toSpecΓ_preimage_zeroLocus, LightProfinite.effectiveEpi_iff_surjective, Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_π_app, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.imageBasicOpen_image_open, AlgebraicGeometry.Scheme.Hom.preimage_image_eq, Stonean.effectiveEpiFamily_tfae, ProfiniteAddGrp.coe_of, AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_comp_iff_of_isOpenImmersion, SimplexCategory.instPathConnectedSpaceCarrierObjTopCatToTop₀, TopologicalSpace.Opens.inclusion'_top_functor, Presheaf.stalk_open_algebraMap, AlgebraicGeometry.Scheme.Cover.isOpenEmbedding_fromGlued, AlgebraicGeometry.Scheme.Hom.app_surjective, AlgebraicGeometry.coe_opensRestrict_symm_apply, GlueData.instIsIsoT, ProfiniteAddGrp.comp_apply, Presheaf.presheafEquivOfIso_inverse_obj_map, Presheaf.pushforwardEq_hom_app, AlgebraicGeometry.affineLocally_iff_affineOpens_le, AlgebraicGeometry.Scheme.fromSpecStalk_appTop, AlgebraicGeometry.RingedSpace.basicOpen_pow, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturality_assoc, AlgebraicGeometry.pullbackRestrictIsoRestrict_inv_fst, presheafToTop_obj, AlgebraicGeometry.Scheme.Hom.isCompact_preimage_singleton, AlgebraicGeometry.HasRingHomProperty.iff_of_iSup_eq_top, AlgebraicGeometry.Scheme.Opens.toScheme_presheaf_obj, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_ideal, AlgebraicGeometry.PresheafedSpace.Γ_map_op, AlgebraicGeometry.Scheme.Pullback.Triplet.Spec_map_tensor_isPullback, FundamentalGroupoidFunctor.piToPiTop_map, LightProfinite.continuous_iff_convergent, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app_apply, AlgebraicGeometry.Scheme.id_appTop, AlgebraicGeometry.Scheme.Cover.covers, alexDiscEquivPreord_inverse_map, Profinite.instPreregular, LightCondensed.internallyProjective_iff_tensor_condition, AlgebraicGeometry.Scheme.Spec_map_presheaf_map_eqToHom, AlgebraicGeometry.Scheme.Opens.toSpecΓ_appTop_assoc, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_point_assoc, TopologicalSpace.Opens.map_functor_eq, TopCommRingCat.forgetToTopCatTopologicalRing, Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_inv_app_hom, AlgebraicGeometry.Scheme.stalkMap_congr_point_assoc, AlgebraicGeometry.Scheme.GlueData.isOpen_iff, ofHom_hom, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_assoc, ContinuousMap.Homotopy.apply_one_path, AlgebraicGeometry.IsAffineOpen.primeIdealOf_isMaximal_of_isClosed, AlgebraicGeometry.QuasiCompactCover.isCompactOpenCovered_of_isCompact, AlgebraicGeometry.Scheme.fromSpecStalk_toSpecΓ, AlgebraicGeometry.Scheme.ker_toSpecΓ, LightProfinite.instPreservesEpimorphismsProfiniteLightToProfinite, AlgebraicGeometry.Scheme.IdealSheafData.ideal_bot, LightProfinite.instHasExplicitFiniteCoproductsAndTotallyDisconnectedSpaceCarrierSecondCountableTopology, LightProfinite.instCountableDiscreteQuotient, AlgebraicGeometry.Scheme.ker_of_isAffine, ProfiniteGrp.ofHom_hom, AlgebraicGeometry.IsAffineOpen.algebraMap_Spec_obj, AlgebraicGeometry.isBasis_basicOpen, TopologicalSpace.Opens.map_id_obj, AlgebraicGeometry.PresheafedSpace.stalkMap.stalkSpecializes_stalkMap_apply, AlgebraicGeometry.Scheme.Hom.mem_preimage, Condensed.instPreservesLimitsOfShapeOppositeProfiniteDiscreteCarrierToTopTotallyDisconnectedSpaceOfFinite, AlgebraicGeometry.Scheme.Spec_map_stalkMap_fromSpecStalk_assoc, AlgebraicGeometry.Scheme.Hom.isConstructible_preimage, AlgebraicGeometry.LocallyRingedSpace.isLocalHomStalkMap, AlgebraicGeometry.IsImmersion.isLocallyClosed_range, AlgebraicGeometry.Scheme.Γevaluation_naturality_apply, AlgebraicGeometry.locallyOfFiniteType_iff, CompHausLike.finiteCoproduct.isOpenEmbedding_ι, AlgebraicGeometry.SheafedSpace.comp_c_app, AlgebraicGeometry.Flat.flat_and_surjective_iff_faithfullyFlat_of_isAffine, Presheaf.SheafConditionEqualizerProducts.w, CompHausLike.Sigma.isOpenEmbedding_ι, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top_assoc, AlgebraicGeometry.ExistsHomHomCompEqCompAux.exists_index, AlgebraicGeometry.liftCoborder_app, AlgebraicGeometry.LocallyRingedSpace.coe_toΓSpecSheafedSpace_hom_base_hom_apply_asIdeal, ProfiniteGrp.topologicalGroup, AlgebraicGeometry.Scheme.Opens.toSpecΓ_preimage_basicOpen, Presheaf.isSheaf_iff_isSheaf_comp, range_pullback_map, AlgebraicGeometry.isIntegral_appTop_of_universallyClosed, AlgebraicGeometry.Scheme.Cover.exists_lift_trans_eq, AlgebraicGeometry.SheafedSpace.id_hom_c_app, AlgebraicGeometry.Scheme.zeroLocus_def, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_continuous, AlgebraicGeometry.Spec_map_localization_isIso, AlgebraicGeometry.StructureSheaf.isLocalizedModule_toPushforwardStalkAlgHom_aux, AlgebraicGeometry.Scheme.stalkClosedPointTo_fromSpecStalk, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_assoc, AlgebraicGeometry.ΓSpec.adjunction_counit_app, AlgebraicGeometry.StructureSheaf.algebraMap_self_map, prodIsoProd_inv_snd_assoc, instPreservesFiniteLimitsLightProfiniteLightCondSetLightProfiniteToLightCondSet, AlgebraicGeometry.Scheme.Hom.preimage_smoothLocus_eq, AlgebraicGeometry.tilde.isoTop_hom, AlgebraicGeometry.Scheme.coe_homeoOfIso_symm, LightProfinite.hasSheafify, AlgebraicGeometry.ProjectiveSpectrum.Proj.isLocalization_atPrime, AlgebraicGeometry.Scheme.stalkMap_hom_inv_assoc, ProfiniteGrp.hom_comp, ModuleCat.Tilde.toOpen_res, prodIsoProd_inv_fst_assoc, AlgebraicGeometry.Scheme.IdealSheafData.mem_supportSet_iff, AlgebraicGeometry.Scheme.IdealSheafData.range_subschemeι, AlgebraicGeometry.Scheme.Opens.toSpecΓ_appTop, AlgebraicGeometry.Scheme.IdealSheafData.mem_support_iff, AlgebraicGeometry.PresheafedSpace.GlueData.ι_image_preimage_eq, InfiniteGalois.mulEquivToLimit_symm_continuous, AlgebraicGeometry.PresheafedSpace.stalkMap.congr, AlgebraicGeometry.Scheme.Hom.isClosedMap, AlgebraicGeometry.Scheme.Hom.isLocallyClosed_range, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec_assoc, uliftFunctorObjHomeo_naturality_apply, smoothSheafCommRing.ι_evalHom, AlgebraicGeometry.Γ_restrict_isLocalization, homeoOfIso_apply, LightCondMod.LocallyConstant.instFullModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_presheafMap, Stonean.epi_iff_surjective, AlgebraicGeometry.IsClosedImmersion.iff_isPreimmersion, AlgebraicGeometry.Scheme.Hom.app_eq, AlgebraicGeometry.RingedSpace.res_zero, AlgebraicGeometry.morphismRestrict_ι, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_hom_app_app, AlgebraicGeometry.Scheme.Hom.preimageIso_inv_ι, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec, AlgebraicGeometry.Scheme.Hom.apply_mem_image_iff, AlgebraicGeometry.Scheme.Hom.asFiberHom_apply, LightProfinite.instWEqualsLocallyBijectiveCoherentTopology, ProfiniteAddGrp.instIsTopologicalAddGroupCarrierToTopTotallyDisconnectedSpacePtProfiniteLimitConeCompForget₂ContinuousAddMonoidHomToProfiniteContinuousMap, ProfiniteGrp.inv_hom_apply, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_inv_app_app, AlgebraicGeometry.ΓSpecIso_obj_hom, ProfiniteAddGrp.id_apply, TopologicalSpace.Opens.map_comp_map, AlgebraicGeometry.genericPoint_eq_of_isOpenImmersion, AlgebraicGeometry.Scheme.homeoOfIso_apply, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_naturality_assoc, AlgebraicGeometry.Spec.germ_stalkMapIso_hom_assoc, AlgebraicGeometry.Scheme.IdealSheafData.le_ofIdeals_iff, AlgebraicGeometry.Scheme.Hom.preimage_basicOpen_top, InfiniteGalois.isOpen_mulEquivToLimit_image_fixingSubgroup, sigmaIsoSigma_hom_ι_assoc, LightCondensed.isColimitLocallyConstantPresheafDiagram_desc_apply, AlgebraicGeometry.StructureSheaf.IsLocalization.to_basicOpen, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv_assoc, AlgebraicGeometry.Scheme.Modules.restrict_map, Sheaf.objSupIsoProdEqLocus_hom_fst, nonempty_isLimit_iff_eq_induced, AlgebraicGeometry.isIso_stalkMap_coprodSpec, smoothSheafCommRing.evalHom_germ, AlgebraicGeometry.LocallyRingedSpace.residue_comp_residueFieldMap_eq_stalkMap_comp_residue, FundamentalGroupoidFunctor.projLeft_map, AlgebraicGeometry.HasRingHomProperty.iff_appLE, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_map_assoc, Stonean.instPreregular, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap_assoc, AlgebraicGeometry.Scheme.Opens.exists_toScheme, AlgebraicGeometry.IsAffineOpen.self_le_basicOpen_union_iff, AlgebraicGeometry.exists_appTop_π_eq_of_isAffine_of_isLimit, Condensed.instPreservesFiniteProductsOppositeProfiniteVal, AlgebraicGeometry.Scheme.instIsIsoCommRingCatResidueFieldMapOfIsOpenImmersion, ProfiniteGrp.cone_pt, TopologicalSpace.Opens.mapMapIso_functor, AlgebraicGeometry.Scheme.instIsOverMapResidueFieldMapOverInferInstanceOverClass, piFan_pt, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.image_preimage_is_empty, AlgebraicGeometry.HasAffineProperty.restrict, ContinuousMap.yonedaPresheaf_map, instPreservesLimitsOfShapeLightProfiniteLightCondSetLightProfiniteToLightCondSetOfCountableCategory, Sequential.isoOfHomeo_inv, isoOfHomeo_hom, id_app, AlgebraicGeometry.Scheme.Γevaluation_naturality_assoc, AlgebraicGeometry.Scheme.Pullback.carrierEquiv_symm_snd, TopologicalSpace.Opens.mapIso_inv_app, AlgebraicGeometry.Scheme.IdealSheafData.coe_support_ofIdealTop, hasLimit_iff_small_sections, AlgebraicGeometry.Scheme.component_nontrivial, AlgebraicGeometry.isCompl_range_inl_inr, Presheaf.presheafEquivOfIso_unitIso_hom_app_app, LightCondensed.isoFinYonedaComponents_inv_comp, AlgebraicGeometry.Scheme.zeroLocus_iInf_of_nonempty, AlgebraicGeometry.Scheme.AffineZariskiSite.generate_presieveOfSections_mem_grothendieckTopology, AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app, AlgebraicGeometry.Scheme.basicOpen_pow, AlgebraicGeometry.Scheme.Opens.toSpecΓ_top, AlgebraicGeometry.Scheme.Hom.ker_apply, ProfiniteAddGrp.coe_id, FundamentalGroupoidFunctor.instIsIsoFanGrpdObjTopCatFundamentalGroupoidFunctorPiTopToPiCone, piIsoPi_inv_π_apply, AlgebraicGeometry.Scheme.IdealSheafData.ideal_comap_of_isOpenImmersion, hom_id, AlgebraicGeometry.Scheme.Pullback.range_map, AlgebraicGeometry.ProjIsoSpecTopComponent.fromSpec_toSpec, AlgebraicGeometry.SurjectiveOnStalks.isEmbedding_pullback, AlexDisc.forgetToTop_faithful, AlgebraicGeometry.AffineSpace.SpecIso_inv_appTop_coord, AlgebraicGeometry.germ_stalkClosedPointIso_hom_assoc, AlgebraicGeometry.Scheme.Hom.isSpectralMap, AlgebraicGeometry.mem_range_iff_of_surjective, LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition', CompHausLike.LocallyConstant.functorToPresheaves_map_app, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_hom_app, TopologicalSpace.OpenNhds.id_apply, CondensedSet.topCatAdjunctionUnit_val_app_apply, AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality, AlgebraicGeometry.instIsIsoSchemeMorphismRestrict, Profinite.instEpiAppDiscreteQuotientCarrierToTopTotallyDisconnectedSpaceπAsLimitCone, GlueData.f_open, AlgebraicGeometry.Scheme.Hom.isLocallyConstructible_image, AlgebraicGeometry.Scheme.evaluation_eq_zero_iff_notMem_basicOpen, Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_pt, instFaithfulLightProfiniteLightCondSetLightProfiniteToLightCondSet, Presheaf.SheafConditionEqualizerProducts.piInters.hom_ext_iff, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_invApp, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_apply, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_naturality_assoc, AlgebraicGeometry.Scheme.Hom.appIso_inv_app, AlgebraicGeometry.Scheme.Hom.liftCoborder_preimage, InfiniteGalois.proj_adjoin_singleton_val, Presheaf.stalk_mono_of_mono, AlgebraicGeometry.Scheme.stalkMap_congr_hom_assoc, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom, TopologicalSpace.Opens.op_map_id_obj, AlgebraicGeometry.Scheme.Hom.opensRange_pullbackFst, AlgebraicGeometry.Scheme.stalkSpecializes_stalkMap_apply, AlgebraicGeometry.Scheme.zeroLocus_radical, Sheaf.interUnionPullbackConeLift_right, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_inv_app_app, Profinite.instHasExplicitFiniteCoproductsTotallyDisconnectedSpaceCarrier, LightProfinite.Extend.functor_map, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_ι_assoc, LightCondensed.instPreservesLimitsOfShapeOppositeLightProfiniteDiscreteCarrier, CondensedSet.instUCompactlyGeneratedSpaceCarrierObjTopCatCondensedSetToTopCat, AlgebraicGeometry.Scheme.AffineZariskiSite.presieveOfSections_surjective, CompHausLike.instT2SpaceCarrierObjTopCatCompHausLikeToTop, TopologicalSpace.Opens.mapMapIso_unitIso, TopologicalSpace.OpenNhds.map_id_obj_unop, AlgebraicGeometry.StructureSheaf.const_one, AlgebraicGeometry.Scheme.Opens.ι_appIso, ProfiniteGrp.limit_mul_val, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_toSpecΓ, AlgebraicGeometry.StructureSheaf.globalSectionsIso_hom, AlgebraicGeometry.instLocallyQuasiFiniteMorphismRestrict, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app', AlgebraicGeometry.IsAffineOpen.toSpecΓ_isoSpec_inv, AlgebraicGeometry.Scheme.Hom.appIso_inv_naturality, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal, isOpenEmbedding_iff_comp_isIso', AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map, CompactlyGenerated.isoOfHomeo_hom, ProfiniteGrp.ProfiniteCompletion.denseRange, LightCondensed.forget_map_val_app, AlgebraicGeometry.Scheme.basicOpen_add_le, AlgebraicGeometry.Scheme.Hom.comp_app_assoc, AlgebraicGeometry.Scheme.comp_app, isOpenEmbedding_f_zeroHypercover, TopologicalSpace.Opens.isOpenEmbedding, AlgebraicGeometry.Scheme.zeroLocus_map, AlgebraicGeometry.Scheme.Hom.finite_app, Presheaf.stalk_hom_ext_iff, LightCondensed.isoLocallyConstantOfIsColimit_inv, AlgebraicGeometry.instGeometricallyReducedMorphismRestrict, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_zeroLocus, AlgebraicGeometry.exists_preimage_eq, GlueData.range_fromOpenSubsetsGlue, coe_id, Profinite.instReflectsEffectiveEpisCompHausProfiniteToCompHaus, AlgebraicGeometry.Scheme.GlueData.ι_eq_iff, AlgebraicGeometry.ΓSpec.left_triangle, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app_assoc, AlgebraicGeometry.FormallyUnramified.instIsSeparableCarrierResidueFieldCoeContinuousMapCarrierCarrierCommRingCatHomTopCatBaseOfLocallyOfFiniteType, AlgebraicGeometry.Scheme.Hom.ideal_ker_le, AlgebraicGeometry.AffineSpace.comp_homOfVector, FintypeCat.toLightProfinite_map_hom_hom_apply, AlgebraicGeometry.smooth_iff, CompactlyGenerated.isoOfHomeo_inv, uliftFunctorCompForgetIso_inv_app, AlgebraicGeometry.Scheme.Hom.appIso_hom', Presheaf.SheafConditionPairwiseIntersections.coneEquiv_inverse, AlgebraicGeometry.Scheme.zeroLocus_inf, AlgebraicGeometry.AffineSpace.isOpenMap_over, AlgebraicGeometry.surjective_iff, AlgebraicGeometry.Scheme.IdealSheafData.ofIdeals_mono, AlgebraicGeometry.Scheme.instIsOpenImmersionToSpecΓOfIsQuasiAffine, Sequential.isoOfHomeo_hom, Condensed.instIsRightKanExtensionFintypeCatCondensedModProfiniteProfiniteSolidProfiniteSolidCounit, AlgebraicGeometry.Scheme.homOfLE_appTop, instTotallyDisconnectedSpaceCarrierToTopTrueObjProfiniteCompHausProfiniteToCompHaus, ContinuousMap.yonedaPresheaf_obj, AlgebraicGeometry.germ_injective_of_isIntegral, AlgebraicGeometry.Scheme.isoSpec_inv_naturality_assoc, Presheaf.pushforward_obj_obj, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self, AlgebraicGeometry.isClosedImmersion_iff_isAffineHom, AlgebraicGeometry.PresheafedSpace.restrictTopIso_hom, AlgebraicGeometry.AffineSpace.hom_ext_iff, AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk_assoc, AlgebraicGeometry.ΓSpec.unop_locallyRingedSpaceAdjunction_counit_app', Stonean.forget.preservesLimits, AlgebraicGeometry.Scheme.Hom.preimage_basicOpen, AlgebraicGeometry.Scheme.singleton_mem_precoverage_iff, AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app, AlgebraicGeometry.Scheme.Hom.isOpenMap, LightProfinite.injective, AlgebraicGeometry.Scheme.isoSpec_Spec_hom, CompHausLike.instHasPropCarrierToTop, LightCondensed.isLocallySurjective_iff_locallySurjective_on_lightProfinite, AlgebraicGeometry.Scheme.basicOpen_res_eq, Profinite.projective_ultrafilter, AlgebraicGeometry.StructureSheaf.isLocalizedModule_toPushforwardStalkAlgHom, AlgebraicGeometry.Scheme.Pullback.Triplet.hx, CompHaus.toProfinite_obj', AlgebraicGeometry.Scheme.Hom.app_invApp', GlueData.MkCore.t_inv, AlgebraicGeometry.isOpenImmersion_iff_stalk, AlgebraicGeometry.isNoetherian_iff_of_finite_iSup_eq_top, AlgebraicGeometry.Scheme.image_basicOpen, AlgebraicGeometry.tilde.isIso_toOpen_top, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app, AlgebraicGeometry.LocallyRingedSpace.Hom.prop, Presheaf.SubmonoidPresheaf.map, AlgebraicGeometry.SurjectiveOnStalks.surj_on_stalks, AlgebraicGeometry.Scheme.Hom.stalkSpecializes_stalkMap_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp_assoc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp, AlgebraicGeometry.HasRingHomProperty.appTop, AlgebraicGeometry.LocallyRingedSpace.basicOpen_zero, isClosed_iff_of_isColimit, CompHausLike.LocallyConstant.locallyConstantIsoContinuousMap_hom, Condensed.isoLocallyConstantOfIsColimit_inv, AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot, AlgebraicGeometry.SurjectiveOnStalks.stalkMap_surjective, pullbackIsoProdSubtype_inv_snd_apply, AlgebraicGeometry.IsIntegral.component_integral, AlgebraicGeometry.morphismRestrict_comp, LightCondSet.instSequentialSpaceCarrierObjTopCatLightCondSetToTopCat, AlgebraicGeometry.PresheafedSpace.stalkMap.isIso, TopologicalSpace.Opens.coe_id, AlgebraicGeometry.IsProper.instMorphismRestrict, presheafToTypes_map, Profinite.instPreservesEffectiveEpisCompHausProfiniteToCompHaus, AlgebraicGeometry.Scheme.isPullback_toSpecΓ_toSpecΓ, AlgebraicGeometry.IsZariskiLocalAtTarget.iff_of_iSup_eq_top, AlgebraicGeometry.Scheme.instSubsingletonCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensBot, GlueData.fromOpenSubsetsGlue_isOpenEmbedding, AlgebraicGeometry.Scheme.ΓSpecIso_naturality, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv, lightDiagramToProfinite_obj, AlgebraicGeometry.Scheme.IdealSheafData.support_comap, AlgebraicGeometry.Scheme.restrictFunctorΓ_hom_app, TopologicalSpace.Opens.set_range_inclusion', AlgebraicGeometry.Scheme.stalkMap_congr_hom, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_hom_app_app, AlgebraicGeometry.Scheme.Pullback.range_snd_comp, ProfiniteAddGrp.limit_add_val, Stonean.instHasPropExtremallyDisconnectedCarrier, Sheaf.comp_app, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_inv_app_app, smoothSheafCommRing.ι_forgetStalk_inv_apply, AlgebraicGeometry.Scheme.Opens.isoOfLE_hom_ι, Condensed.lanPresheafNatIso_hom_app, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_jointly_surjective, AlgebraicGeometry.SheafedSpace.Γ_map, AlgebraicGeometry.Scheme.Modules.pushforwardComp_hom_app_app, Presheaf.IsSheaf.isSheafPreservesLimitPairwiseIntersections, AlgebraicGeometry.germ_stalkClosedPointIso_hom, Presheaf.isLocallySurjective_iff, AlgebraicGeometry.range_eq_univ, AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv, AlgebraicGeometry.IsFinite.instHasAffinePropertyAndIsAffineFiniteCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTopHomAppTop, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_fst, AlgebraicGeometry.Scheme.Hom.comp_apply, AlgebraicGeometry.Scheme.Modules.mapPresheaf_app, AlgebraicGeometry.Scheme.Hom.isOpenEmbedding, LightProfinite.surjective_transitionMapLE, pullbackIsoProdSubtype_inv_fst, AlgebraicGeometry.PresheafedSpace.GlueData.f_invApp_f_app_assoc, Profinite.Extend.functor_obj, StructureGroupoid.LocalInvariantProp.section_spec, AlgebraicGeometry.Spec.map_apply, TopologicalSpace.Opens.mapMapIso_inverse, AlgebraicGeometry.pointOfClosedPoint_apply, AlgebraicGeometry.Spec.sheafedSpaceMap_hom_c_app, AlgebraicGeometry.PresheafedSpace.GlueData.ι_isOpenEmbedding, Presheaf.Pushforward.comp_inv_app, Presheaf.covering_presieve_eq_self, AlgebraicGeometry.morphismRestrict_app', AlgebraicGeometry.SheafedSpace.restrictTopIso_inv, AlgebraicGeometry.Scheme.Hom.isEmbedding, AlgebraicGeometry.sigmaι_eq_iff, AlgebraicGeometry.Scheme.toSpecΓ_appTop, AlgebraicGeometry.Scheme.Hom.appIso_inv_naturality_assoc, smoothSheaf.obj_eq, CompHausLike.mono_iff_injective, subsheafToTypes_val, AlgebraicGeometry.Scheme.stalkMap_comp, TopologicalSpace.Opens.mapId_inv_app, AlgebraicGeometry.PresheafedSpace.comp_c_app_assoc, TopModuleCat.freeMap_map, LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_hom_c_app, AlgebraicGeometry.IsAffineOpen.iSup_basicOpen_eq_self_iff, AlgebraicGeometry.Scheme.Hom.comp_appIso, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_map, AlgebraicGeometry.Scheme.basicOpen_one, AlgebraicGeometry.IsOpenImmersion.range_pullback_to_base_of_left, coinduced_of_isColimit, LightCondensed.free_internallyProjective_iff_tensor_condition', AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp, ProfiniteGrp.profiniteCompletion_map, AlgebraicGeometry.Scheme.Modules.Hom.id_app, AlgebraicGeometry.Scheme.IdealSheafData.map_vanishingIdeal, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_assoc, AlgebraicGeometry.targetAffineLocally_affineAnd_iff, AlgebraicGeometry.StructureSheaf.algebraMap_obj_top_bijective, TopologicalSpace.Opens.inclusion'_map_eq_top, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_assoc, Sheaf.pushforward_obj_val, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.coequalizer_π_stalk_isLocalHom, LightProfinite.instHasCountableLimits, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_self, LightProfinite.forget_reflectsIsomorphisms, CompHausLike.forget_reflectsIsomorphisms, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq, prodIsoProd_hom_snd, AlgebraicGeometry.Scheme.zeroLocus_eq_univ_iff_subset_nilradical_of_isCompact, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.instIsIsoCommRingCatInvApp, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_apply, AlgebraicGeometry.Scheme.Modules.Hom.isIso_iff_isIso_app, Condensed.isoFinYonedaComponents_inv_comp, AlgebraicGeometry.Scheme.Hom.residueFieldMap_congr, AlgebraicGeometry.Spec_zeroLocus_eq_zeroLocus, pullbackIsoProdSubtype_hom_snd, stoneCechObj_toTop_carrier, AlgebraicGeometry.Scheme.Opens.ι_appTop, AlgebraicGeometry.Scheme.Modules.Hom.comp_app, AlgebraicGeometry.Scheme.Hom.map_mem_image_iff, Condensed.instFinalOppositeDiscreteQuotientCarrierToTopTotallyDisconnectedSpaceCostructuredArrowFintypeCatProfiniteOpToProfiniteOpPtAsLimitConeFunctorOp, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd, Presheaf.presieveOfCovering.indexOfHom_spec, AlgebraicGeometry.Scheme.map_basicOpen, CondensedSet.continuous_coinducingCoprod, TopologicalSpace.Opens.adjunction_counit_map_functor, AlgebraicGeometry.coprodSpec_coprodMk, Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_inv_app_hom, AlgebraicGeometry.Scheme.IdealSheafData.opensRange_subschemeCover_map, AlgebraicGeometry.Proj.zero_apply, LightProfinite.instHasExplicitPullbacksAndTotallyDisconnectedSpaceCarrierSecondCountableTopology, AlgebraicGeometry.Scheme.Hom.preimageIso_hom_ι, AlgebraicGeometry.Scheme.Hom.injective, AlgebraicGeometry.Scheme.isoSpec_inv_naturality, ProfiniteAddGrp.limit_ext_iff, AlgebraicGeometry.IsAffineOpen.toSpecΓ_fromSpec_assoc, Sheaf.objSupIsoProdEqLocus_inv_snd, Profinite.lift_lifts_assoc, pullbackIsoProdSubtype_inv_snd, AlgebraicGeometry.Scheme.Hom.id_appIso, smoothSheafCommRing.ι_forgetStalk_inv_assoc, skyscraperPresheafCocone_ι_app, AlgebraicGeometry.Scheme.Hom.preimageIso_inv_ι_assoc, AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.SectionSubring.one_mem', AlgebraicGeometry.instQuasiSeparatedToSpecΓOfQuasiSeparatedSpaceCarrierCarrierCommRingCat, AlgebraicGeometry.IsAffineOpen.basicOpenSectionsToAffine_isIso, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberι, hasColimit_iff_small_colimitType, AlgebraicGeometry.PresheafedSpace.map_id_c_app, compatiblePreserving_opens_map, Presheaf.germ_exist, AlgebraicGeometry.exists_smooth_of_formallySmooth_stalk, AlgebraicGeometry.Scheme.comp_appTop_assoc, Presheaf.SheafConditionEqualizerProducts.res_π, AlgebraicGeometry.Scheme.local_affine, GlueData.fromOpenSubsetsGlue_injective, AlgebraicGeometry.PresheafedSpace.GlueData.f_invApp_f_app, prodIsoProd_inv_fst, AlgebraicGeometry.Scheme.IdealSheafData.ideal_top, TopologicalSpace.Opens.adjunction_counit_app_self, Presheaf.instIsLocalizationCarrierObjOppositeOpensCarrierCommRingCatObjLocalizationPresheaf, AlgebraicGeometry.LocallyOfFiniteType.stalkMap, TopologicalSpace.Opens.mem_map, AlgebraicGeometry.locallyQuasiFinite_iff_isDiscrete_preimage_singleton, instIsEquivalenceLightDiagramLightProfiniteLightDiagramToLightProfinite, AlgebraicGeometry.Scheme.IsLocallyDirected.ι_eq_ι_iff, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.coequalizer_π_app_isLocalHom, AlgebraicGeometry.Scheme.isoSpec_Spec, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_isIso, AlgebraicGeometry.instLocallyOfFiniteTypeMorphismRestrict, Presheaf.Pushforward.id_hom_app, AlgebraicGeometry.IsIntegralHom.instMorphismRestrict, Presheaf.pullback_obj_obj_ext_iff, LightCondSet.topCatAdjunctionCounit_bijective, CompactlyGenerated.homeoOfIso_symm_apply, AlgebraicGeometry.Scheme.IdealSheafData.isLocalization_away, Opens.coverDense_iff_isBasis, AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_base_fst, AlgebraicGeometry.compactSpace_iff_exists, AlgebraicGeometry.Scheme.Hom.preimage_sup, AlgebraicGeometry.IsClosedImmersion.hasAffineProperty, AlgebraicGeometry.Scheme.preimage_opensRange_toSpecΓ, AlgebraicGeometry.instIsOpenImmersionMorphismRestrict, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv, AlgebraicGeometry.Scheme.stalkMap_congr_point, topCatOpToFrm_obj_coe, AlgebraicGeometry.ProjectiveSpectrum.Proj.mk_mem_toSpec_base_apply, range_pullback_to_prod, AlgebraicGeometry.Scheme.eq_zeroLocus_of_isClosed_of_isAffine, LightProfinite.Extend.functorOp_map, Sheaf.interUnionPullbackConeLift_left, AlgebraicGeometry.Scheme.Opens.ι_preimage_self, GlueData.ι_isOpenEmbedding, AlgebraicGeometry.Scheme.stalkMap_hom_inv, subpresheafToTypes_map_coe, AlgebraicGeometry.Scheme.toSpecΓ_image_zeroLocus, AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c, AlgebraicGeometry.instQuasiSeparatedMorphismRestrict, AlgebraicGeometry.HasAffineProperty.iff_of_iSup_eq_top, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality, Alexandrov.lowerCone_π_app, AlgebraicGeometry.isImmersion_iff, LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology, topToLocale_map, TopologicalSpace.Opens.map_comp_eq, CompHausLike.is_compact, pullback_fst_image_snd_preimage, AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv_assoc, TopModuleCat.instPreservesLimitsOfShapeTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitsOfShapeOfModuleCatForgetLinearMap, AlgebraicGeometry.Scheme.homOfLE_app, AlgebraicGeometry.SheafedSpace.Γ_obj_op, ProfiniteGrp.hom_inv_apply, AlgebraicGeometry.Scheme.Hom.comp_preimage, instEssentiallySmallLightProfinite, AlgebraicGeometry.Scheme.Modules.instIsIsoAbApp, AlgebraicGeometry.Scheme.Hom.naturality_assoc, AlgebraicGeometry.Scheme.IdealSheafData.opensRange_glueDataObjMap, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self_apply, AlgebraicGeometry.Scheme.stalkMap_hom_inv_apply, Presheaf.pushforward_map_app', continuous_iff_of_isColimit, AlgebraicGeometry.Scheme.Hom.iInf_ker_openCover_map_comp_apply, skyscraperPresheaf_eq_pushforward, CondensedSet.topCatAdjunctionUnit_val_app, AlgebraicGeometry.eq_zero_of_basicOpen_eq_bot, LightCondensed.hom_ext_iff, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_carrier, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_hom_app_val_app_apply, FundamentalGroupoid.map_eq, Presheaf.pushforward_obj_map, AlgebraicGeometry.Scheme.inv_appTop, AlgebraicGeometry.isLocalization_away_of_isAffine, AlgebraicGeometry.Scheme.Hom.isIso_app, TopologicalSpace.Opens.map_iSup, Presheaf.presheafEquivOfIso_unitIso_inv_app_app, ProfiniteGrp.cone_π_app, AlgebraicGeometry.Scheme.Hom.stalkSpecializes_stalkMap_apply, AlgebraicGeometry.LocallyRingedSpace.isLocalHomStalkMap', AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv, instIsLeftAdjointForgetContinuousMapCarrier, pullbackIsoProdSubtype_inv_fst_apply, AlgebraicGeometry.structureSheafInType.add_apply, AlgebraicGeometry.morphismRestrict_appTop, AlgebraicGeometry.Scheme.Hom.exists_mem_and_isIso_morphismRestrict_toNormalization, AlgebraicGeometry.Scheme.IdealSheafData.ofIdealTop_ideal, LightCondensed.underlying_obj, CompHausLike.const_comp, AlgebraicGeometry.SheafedSpace.comp_hom_c_app', piIsoPi_hom_apply, AlgebraicGeometry.Scheme.Hom.preimage_opensRange, AlgebraicGeometry.ΓSpecIso_hom_stalkClosedPointIso_inv, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_apply, Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_π_app, AlgebraicGeometry.Scheme.descResidueField_stalkClosedPointTo_fromSpecResidueField, AlgebraicGeometry.Proj.ext_iff, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen, AlgebraicGeometry.LocallyRingedSpace.Γ_map, AlgebraicGeometry.isCompactOpen_iff_eq_basicOpen_union, Presheaf.presheafEquivOfIso_functor_obj_obj, AlexDisc.Iso.mk_inv, AlgebraicGeometry.PresheafedSpace.componentwiseDiagram_obj, CompHausLike.finiteCoproduct.ι_injective, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv, smoothSheaf.eval_germ, LightCondSet.hom_naturality_apply, AlgebraicGeometry.isDominant_iff, AlgebraicGeometry.Flat.generalizingMap, AlgebraicGeometry.Scheme.Hom.fiberι_asFiber, GlueData.MkCore.t_id, AlgebraicGeometry.HasAffineProperty.affineAnd_iff, AlgebraicGeometry.IsOpenImmersion.app_eq_appIso_inv_app_of_comp_eq, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.c_iso, AlgebraicGeometry.Scheme.IdealSheafData.ker_subschemeι_app, AlgebraicGeometry.IsOpenImmersion.ΓIso_inv, AlgebraicGeometry.Scheme.Modules.Hom.sub_app, Stonean.instHasExplicitPullbacksOfInclusionsExtremallyDisconnectedCarrier, AlgebraicGeometry.IsOpenImmersion.range_pullback_snd_of_left, AlgebraicGeometry.IsOpenImmersion.instIsIsoCommRingCatStalkMap, AlgebraicGeometry.isPreimmersion_iff, AlgebraicGeometry.Scheme.AffineCover.covers, AlgebraicGeometry.Proj.add_apply, AlgebraicGeometry.PresheafedSpace.Γ_obj, Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_map_hom, AlgebraicGeometry.Scheme.Opens.isoOfLE_inv_ι, AlgebraicGeometry.Scheme.Hom.ι_toNormalization_assoc, AlgebraicGeometry.Scheme.Hom.Spec_map_residueFieldMap_fromSpecResidueField_assoc, AlgebraicGeometry.Scheme.isLocalHom_stalkClosedPointTo', AlgebraicGeometry.IsFinite.finite_preimage_singleton, AlgebraicGeometry.PresheafedSpace.toRestrictTop_c, AlgebraicGeometry.IsLocalAtTarget.restrict, CompactlyGenerated.is_compactly_generated, CondensedSet.isDiscrete_tfae, AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.mk_mem_carrier, LightProfinite.instTotallyDisconnectedSpaceCarrierToTopTruePtCompHausLimitConeCompLightProfiniteToCompHaus, AlgebraicGeometry.Scheme.Hom.fromNormalization_app_assoc, Profinite.exists_locallyConstant, AlgebraicGeometry.Scheme.isoSpec_inv_toSpecΓ_assoc, Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_pt, AlgebraicGeometry.ProjectiveSpectrum.Proj.isIso_toSpec, ContinuousMap.piComparison_fac, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app_apply, AlgebraicGeometry.Scheme.IdealSheafData.ideal_iInf, AlgebraicGeometry.stalkMap_toStalk_apply, AlgebraicGeometry.IsAffineOpen.primeIdealOf_eq_map_closedPoint, Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_hom_app_hom, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc, AlgebraicGeometry.Scheme.Hom.instIsIsoCommRingCatAppObjOpensOpensFunctor, AlgebraicGeometry.Scheme.ker_morphismRestrict_ideal, AlgebraicGeometry.Scheme.Modules.pushforwardId_hom_app_app, AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_ι, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst, Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_hom_hom, GlueData.preimage_range, AlgebraicGeometry.Scheme.toOpen_eq, alexDiscEquivPreord_unitIso, AlgebraicGeometry.IsOpenImmersion.range_pullback_to_base_of_right, isOpenEmbedding_iff_isIso_comp, AlgebraicGeometry.Scheme.Modules.restrict_obj, CompHaus.effectiveEpi_tfae, Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_pt, LightProfinite.instPreservesLimitsOfShapeOppositeNatForgetContinuousMapCarrierToTopAndTotallyDisconnectedSpaceSecondCountableTopology, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_assoc, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturality, TopologicalSpace.Opens.functor_map_eq_inf, Profinite.lift_lifts, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_unit_app_app, AlgebraicGeometry.IsLocalAtTarget.iff_of_iSup_eq_top, AlgebraicGeometry.Scheme.Hom.isIntegral_app, AlgebraicGeometry.Scheme.Hom.app_eq_appLE, AlgebraicGeometry.Scheme.Pullback.Triplet.fst_SpecTensorTo_apply, AlgebraicGeometry.ΓSpecIso_inv_ΓSpec_adjunction_homEquiv, AlgebraicGeometry.RingedSpace.zeroLocus_empty_eq_univ, Presheaf.SubmonoidPresheaf.toLocalizationPresheaf_app, AlgebraicGeometry.StructureSheaf.res_apply, LightCondensed.equalizerCondition, CategoryTheory.Functor.mapPresheaf_map_c, AlgebraicGeometry.Scheme.Modules.Hom.add_app, instDiscreteTopologyCarrierObjDiscrete, AlexDisc.coe_forgetToTop, InfiniteGalois.toAlgEquivAux_eq_liftNormal, TopologicalSpace.OpenNhds.isOpenEmbedding, LightCondMod.hom_naturality_apply, TopModuleCat.forget₂_TopCat_obj, AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓUnitOpensCarrierCarrierCommRingCatRingCatSheaf, AlgebraicGeometry.IsClosedImmersion.isClosedEmbedding, AlgebraicGeometry.RingedSpace.basicOpen_mul, AlgebraicGeometry.Scheme.Hom.inv_appTop, CompHausLike.homeoOfIso_apply, topToPreord_map, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp_assoc, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.stalk_iso, AlgebraicGeometry.isIntegralHom_iff, GlueData.ofOpenSubsets_toGlueData_V, AlgebraicGeometry.RingedSpace.basicOpen_res_eq, LightCondensed.ihomPoints_symm_apply, AlgebraicGeometry.Spec_zeroLocus, AlgebraicGeometry.Scheme.basicOpen_mul, LightCondensed.discrete_obj, AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality, GlueData.image_inter, AlgebraicGeometry.Scheme.IdealSheafData.coe_support_eq_eq_iInter_zeroLocus, AlgebraicGeometry.exists_of_res_eq_of_qcqs_of_top, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app, isEmbedding_pullback_to_prod, GlueData.ofOpenSubsets_toGlueData_f, AlgebraicGeometry.Scheme.zeroLocus_biInf_of_nonempty, Condensed.StoneanProfinite.instPreservesEffectiveEpisStoneanProfiniteToProfinite, AlgebraicGeometry.Flat.stalkMap, ProfiniteGrp.toLimit_injective, AlgebraicGeometry.Scheme.Pullback.range_snd, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom_assoc, Presheaf.isSheaf_on_punit_iff_isTerminal, AlgebraicGeometry.Scheme.Hom.stalkMap_comp, AlgebraicGeometry.Scheme.SpecΓIdentity_inv_app, AlexDisc.forgetToTop_full, Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_map_hom, pullbackIsoProdSubtype_hom_apply, Presheaf.isSheaf_iff_isSheaf_comp', AlgebraicGeometry.Scheme.Cover.exists_eq, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom, AlgebraicGeometry.Scheme.ofArrows_mem_precoverage_iff, lightProfiniteToLightDiagram_obj, AlgebraicGeometry.isLocallyNoetherian_iff_of_iSup_eq_top, Condensed.StoneanProfinite.instEffectivelyEnoughStoneanProfiniteToProfinite, AlgebraicGeometry.StructureSheaf.instIsLocalizedModuleCarrierStalkAbPresheafOpensCarrierTopModuleStructurePresheafPrimeComplAsIdealToStalkₗ, AlgebraicGeometry.Scheme.IsLocallyDirected.ι_jointly_surjective, AlgebraicGeometry.basicOpen_eq_of_affine', CompactlyGenerated.isoEquivHomeo_symm_apply, ProfiniteAddGrp.coe_comp, AlgebraicGeometry.IsPreimmersion.base_embedding, AlgebraicGeometry.Scheme.Hom.coe_image, AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom_appTop, AlgebraicGeometry.Scheme.Hom.coe_preimage, AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem_toSpecΓ, ofHom_apply, AlgebraicGeometry.Scheme.Opens.toScheme_presheaf_map, coneOfConeForget_π_app, LightDiagram.id_hom_hom_hom_apply, AlgebraicGeometry.instIsDominantToSpecΓOfCompactSpaceCarrierCarrierCommRingCat, LightCondMod.LocallyConstant.instFaithfulModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf, LightCondensed.lanPresheafNatIso_hom_app, smoothSheafCommRing.ι_forgetStalk_hom_apply, Sheaf.objSupIsoProdEqLocus_hom_snd, ProfiniteGrp.ofHom_apply, AlgebraicGeometry.Scheme.isoSpec_Spec_inv, AlgebraicGeometry.Scheme.IdealSheafData.supportSet_subset_zeroLocus, AlgebraicGeometry.Scheme.Hom.isClosedEmbedding, AlgebraicGeometry.Proj.awayι_preimage_basicOpen, AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiber, AlgebraicGeometry.IsFinite.finite_app, FundamentalGroupoidFunctor.piToPiTop_obj_as, lightCondSetToTopCat_obj_carrier, CompHaus.presentation.epi_π, AlgebraicGeometry.instSubsingletonCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensOfIsEmpty, AlgebraicGeometry.exists_eq_pow_mul_of_isAffineOpen, AlgebraicGeometry.Scheme.Opens.forall_toScheme, smoothSheafCommRing.ι_forgetStalk_hom_assoc, AlgebraicGeometry.Proj.awayMap_awayToSection, AlgebraicGeometry.Scheme.Hom.finite_preimage_singleton, AlgebraicGeometry.finite_appTop_of_universallyClosed, Presheaf.presieveOfCovering.mem_grothendieckTopology, induced_of_isLimit, AlgebraicGeometry.IsLocallyNoetherian.component_noetherian, AlgebraicGeometry.Scheme.inv_hom_apply, AlgebraicGeometry.IsIntegralHom.integral_app, AlgebraicGeometry.isIso_SpecMap_stakMap_localization, AlgebraicGeometry.Scheme.residue_residueFieldMap_assoc, LightProfinite.Extend.cocone_pt, LightCondMod.epi_iff_locallySurjective_on_lightProfinite, Presheaf.SheafConditionEqualizerProducts.fork_pt, Profinite.instHasExplicitPullbacksTotallyDisconnectedSpaceCarrier, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app_assoc, AlgebraicGeometry.Scheme.IdealSheafData.support_map, ProfiniteGrp.instCompactSpaceSubtypeForallCarrierToTopTotallyDisconnectedSpaceToProfiniteObjMemSubgroupLimitConePtAux, Presheaf.SheafConditionEqualizerProducts.w_apply, AlgebraicGeometry.FormallyUnramified.stalkMap, AlgebraicGeometry.specTargetImageFactorization_app_injective, LightCondensed.ihom_map_val_app, AlgebraicGeometry.Scheme.IsGermInjectiveAt.cond, Presheaf.presheafEquivOfIso_counitIso_inv_app_app, AlgebraicGeometry.Scheme.IdealSheafData.zeroLocus_inter_subset_supportSet, AlgebraicGeometry.PresheafedSpace.stalkMap.congr_hom, AlgebraicGeometry.PresheafedSpace.Γ_map, AlgebraicGeometry.instIsClosedImmersionMorphismRestrict, AlgebraicGeometry.Scheme.Hom.preimage_inf, FundamentalGroupoidFunctor.piIso_inv, Profinite.instEffectivelyEnoughCompHausProfiniteToCompHaus, TopologicalSpace.Opens.op_map_comp_obj, AlgebraicGeometry.SheafedSpace.id_c_app, AlgebraicGeometry.isPullback_morphismRestrict, prodIsoProd_hom_apply, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal', AlgebraicGeometry.Scheme.residue_residueFieldCongr, CompHausLike.toCompHausLike_map, AlgebraicGeometry.StructureSheaf.toOpenₗ_top_bijective, AlgebraicGeometry.StructureSheaf.comap_id_eq_map, AlgebraicGeometry.Scheme.Hom.appIso_hom, Condensed.isColimitLocallyConstantPresheafDiagram_desc_apply, AlgebraicGeometry.Scheme.OpenCover.finiteSubcover_X, AlgebraicGeometry.Scheme.Pullback.range_fst, comp_app, AlgebraicGeometry.IsOpenImmersion.iff_stalk_iso, AlexDisc.Iso.mk_hom, AlgebraicGeometry.Scheme.Cover.fromGlued_isOpenEmbedding, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_apply, LightCondSet.LocallyConstant.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopologySubtypeToTop, InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj, AlgebraicGeometry.Scheme.residue_residueFieldMap, AlgebraicGeometry.Scheme.IdealSheafData.ideal_sup, AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom, AlgebraicGeometry.tilde.toOpen_res, Alexandrov.projSup_obj, AlgebraicGeometry.tilde.toOpen_res_assoc, AlgebraicGeometry.PresheafedSpace.stalkMap.comp, AlgebraicGeometry.Scheme.Hom.ι_fromNormalization_assoc, pullbackIsoProdSubtype_inv_snd_assoc, AlgebraicGeometry.Scheme.emptyTo_c_app, presheafToType_obj, epi_iff_surjective, AlgebraicGeometry.Scheme.stalkMap_inv_hom_apply, CompHaus.instCompactSpaceCarrierToTopTrue, AlgebraicGeometry.Scheme.Opens.mem_basicOpen_toScheme, AlgebraicGeometry.affineAnd_apply, AlgebraicGeometry.Scheme.SpecMap_residue_apply, AlgebraicGeometry.tilde.isUnit_algebraMap_end_basicOpen, Condensed.instPreservesFiniteProductsOppositeStoneanVal, prodIsoProd_hom_fst, FundamentalGroupoidFunctor.prodIso_inv, Condensed.StoneanProfinite.instReflectsEffectiveEpisStoneanProfiniteToProfinite, CompactlyGenerated.isoEquivHomeo_apply, Profinite.Extend.cocone_ι_app, AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE_locally, AlgebraicGeometry.Scheme.Pullback.range_diagonal_subset_diagonalCoverDiagonalRange, AlgebraicGeometry.targetAffineLocally_affineAnd_iff', AlgebraicGeometry.AffineSpace.reindex_appTop_coord, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv_assoc, Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_inv_hom, AlgebraicGeometry.smoothOfRelativeDimension_iff, instIsRightAdjointForgetContinuousMapCarrier, AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE, AlgebraicGeometry.Scheme.Hom.mem_smoothLocus, AlgebraicGeometry.instSmoothMorphismRestrict, GlueData.fromOpenSubsetsGlue_isOpenMap, AlgebraicGeometry.Scheme.IdealSheafData.ideal_mono, AlgebraicGeometry.RingedSpace.isUnit_res_basicOpen, AlgebraicGeometry.Scheme.empty_presheaf, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_apply, AlgebraicGeometry.Scheme.Opens.ι_app_self, TopologicalSpace.Opens.mapComp_inv_app, AlgebraicGeometry.ΓSpec.toSpecΓ_of, AlgebraicGeometry.Scheme.zeroLocus_span, Presheaf.IsSheaf.isSheafPairwiseIntersections, AlgebraicGeometry.Scheme.IdealSheafData.ideal_iSup, AlgebraicGeometry.Scheme.Hom.naturality, AlgebraicGeometry.exists_appTop_π_eq_of_isLimit, Presheaf.isGluing_iff_pairwise, Alexandrov.lowerCone_pt, AlgebraicGeometry.exists_isFinite_morphismRestrict_of_finite_preimage_singleton, AlgebraicGeometry.IsAffine.affine, AlgebraicGeometry.IsAffineOpen.instAwayCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecPresheafOpOpensBasicOpen, AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal.to_basicOpen, AlgebraicGeometry.Scheme.Pullback.Triplet.Spec_ofPointTensor_SpecTensorTo, AlgebraicGeometry.SheafedSpace.Γ_obj, FundamentalGroupoidFunctor.projRight_map, AlgebraicGeometry.formallyUnramified_iff, adj₂_counit, TopologicalSpace.Opens.map_comp_obj, AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf_map', Stonean.instReflectsEffectiveEpisCompHausToCompHaus, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_s, AlgebraicGeometry.Scheme.mem_basicOpen_top, AlgebraicGeometry.QuasiCompactCover.isCompactOpenCovered_of_isAffineOpen, Condensed.isoFinYoneda_hom_app, AlgebraicGeometry.Scheme.Opens.range_ι, AlgebraicGeometry.IsAffineOpen.range_fromSpec, AlgebraicGeometry.IsOpenImmersion.image_preimage_eq_preimage_image_of_isPullback, AlgebraicGeometry.isClosedImmersion_iff, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen', prodIsoProd_inv_snd, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_assoc, TopModuleCat.instPreservesLimitsTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, Profinite.Extend.cone_pt, AlgebraicGeometry.Spec_closedPoint, AlgebraicGeometry.Scheme.Hom.range_subset_ker_support, instFullLightProfiniteLightCondSetLightProfiniteToLightCondSet, Profinite.NobelingProof.spanFunctorIsoIndexFunctor_inv_app, lightDiagramToLightProfinite_map, AlgebraicGeometry.LocallyRingedSpace.preimage_basicOpen, AlgebraicGeometry.ProjectiveSpectrum.Proj.stalkMap_toSpec, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_toSpecΓ_assoc, hom_inv_id_apply, piIsoPi_inv_π, nonempty_isColimit_iff_eq_coinduced, AlgebraicGeometry.AffineSpace.homOverEquiv_apply, AlgebraicGeometry.Scheme.Hom.finite_preimage, AlgebraicGeometry.Scheme.Opens.ι_apply, LightProfinite.surjective_transitionMap, AlgebraicGeometry.Scheme.Modules.instFullPresheafOfModulesToPresheafOfModules, CompHaus.epi_iff_surjective, mono_iff_injective, AlgebraicGeometry.pullbackRestrictIsoRestrict_inv_fst_assoc, AlgebraicGeometry.Scheme.basicOpen_res, AlgebraicGeometry.Scheme.iso_inv_base_hom_base_apply, AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem_toSpecΓ_assoc, AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp, AlgebraicGeometry.Scheme.Hom.continuous, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberToSpecResidueField, TopologicalSpace.Opens.mapIso_hom_app, Sheaf.objSupIsoProdEqLocus_inv_fst, smoothSheaf.ι_evalHom, homeoOfIso_symm_apply, AlgebraicGeometry.Smooth.exists_isStandardSmooth, ProfiniteGrp.coe_comp, AlgebraicGeometry.Scheme.Pullback.Triplet.exists_preimage, AlgebraicGeometry.Scheme.comp_appTop, AlgebraicGeometry.Scheme.Hom.isConstructible_image, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv_apply, smoothSheafCommRing.ι_evalHom_assoc, AlgebraicGeometry.Surjective.surj, AlgebraicGeometry.Scheme.IdealSheafData.radical_ideal, Presheaf.Pushforward.comp_hom_app, AlgebraicGeometry.IsClosedImmersion.isAffine_surjective_of_isAffine, AlgebraicGeometry.Scheme.stalkMap_inv_hom, AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp_assoc, ContinuousMap.yonedaPresheaf'_map, AlgebraicGeometry.StructureSheaf.toOpenₗ_eq_const, Profinite.projective_of_extrDisc, LightCondensed.lanPresheafExt_inv, LightProfinite.epi_iff_surjective, AlgebraicGeometry.Scheme.comp_base_apply, AlgebraicGeometry.Scheme.fromSpecStalk_app, Condensed.lanPresheafExt_hom, AlgebraicGeometry.isGermInjectiveAt_iff_of_isOpenImmersion, AlgebraicGeometry.IsAffineOpen.isLocalization_stalk, instFullLightDiagramProfiniteLightDiagramToProfinite, AlgebraicGeometry.PresheafedSpace.GlueData.ι_jointly_surjective, smoothSheaf.contMDiff_section, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_comp, AlgebraicGeometry.isField_of_universallyClosed, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_base_apply, Profinite.injective_of_finite, AlgebraicGeometry.Scheme.IdealSheafData.ideal_inf, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_eq_zero_iff_notMem_basicOpen, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq_comap, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv_assoc, Stonean.instProjectiveCompHausCompHaus, smoothSheafCommRing.ι_forgetStalk_hom, AlgebraicGeometry.IsDominant.denseRange, InfiniteGalois.mk_toAlgEquivAux, AlgebraicGeometry.Scheme.homOfLE_base, AlgebraicGeometry.instGeometricallyIntegralMorphismRestrict, AlgebraicGeometry.Flat.iff_flat_stalkMap, AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app_surjective, AlgebraicGeometry.Scheme.preimage_zeroLocus, AlgebraicGeometry.PresheafedSpace.congr_app, AlgebraicGeometry.isIso_iff_stalk_iso, AlgebraicGeometry.Scheme.instIsOverMapStalkMapOverInferInstanceOverClass, AlgebraicGeometry.Scheme.AffineZariskiSite.cocone_ι_app, Presheaf.presheafEquivOfIso_counitIso_hom_app_app, instCompactSpaceCarrierDiskBoundary, GlueData.ι_jointly_surjective, AlgebraicGeometry.Scheme.IdealSheafData.coe_support_inter, CompHausLike.isoOfHomeo_inv_hom_hom_apply, AlgebraicGeometry.IsAffineOpen.fromSpec_top, AlgebraicGeometry.Scheme.Hom.support_ker, AlgebraicGeometry.Scheme.Hom.homeomorph_apply, AlgebraicGeometry.Scheme.Hom.stalkMap_congr, AlgebraicGeometry.Scheme.map_basicOpen_map, prodIsoProd_hom_fst_assoc, AlgebraicGeometry.affineOpensRestrict_symm_apply_coe, CompHaus.Gleason, AlgebraicGeometry.PresheafedSpace.id_c_app, AlgebraicGeometry.Scheme.Hom.comp_appTop, AlgebraicGeometry.IsOpenImmersion.opensRange_pullback_snd_of_left, LightCondMod.LocallyConstant.instFullSheafLightProfiniteCoherentTopologyTypeConstantSheaf, AlgebraicGeometry.IsIntegralHom.hasAffineProperty, AlgebraicGeometry.Scheme.Hom.preimage_mono, CompHausLike.hom_ofHom, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec, AlexDisc.is_alexandrovDiscrete, AlgebraicGeometry.Scheme.basicOpen_zero, InfiniteGalois.proj_of_le, AlgebraicGeometry.Scheme.Hom.surjective, AlgebraicGeometry.Scheme.residue_residueFieldCongr_assoc, AlgebraicGeometry.Scheme.IdealSheafData.ideal_ofIdeals_le, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.sigma_ι_isOpenEmbedding, Stonean.instProjectiveProfiniteObjToProfinite, AlgebraicGeometry.Scheme.IsLocallyDirected.exists_of_pullback_V_V, AlgebraicGeometry.Scheme.SpecMap_presheaf_map_eqToHom, AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.SectionSubring.zero_mem', AlgebraicGeometry.IsAffineOpen.fromSpec_image_basicOpen, AlgebraicGeometry.instHasAffinePropertyIsomorphismsSchemeAndIsAffineIsIsoCommRingCatAppTop, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.imageBasicOpen_image_preimage, TopologicalSpace.Opens.infLELeft_apply, isOpen_iff_of_isColimit_cofork, AlgebraicGeometry.IsAffineOpen.basicOpen_union_eq_self_iff, LightCondSet.isDiscrete_tfae, AlgebraicGeometry.isFinite_iff, Presheaf.presheafEquivOfIso_inverse_obj_obj, LightCondSet.topCatAdjunctionUnit_val_app, AlgebraicGeometry.etale_iff, LightDiagram.comp_hom_hom_hom_apply, AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_inv_ι_app, TopModuleCat.instReflectsIsomorphismsTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, Profinite.presentation.epi_π, LightCondensed.instFinalNatCostructuredArrowOppositeFintypeCatLightProfiniteOpToLightProfiniteOpPtAsLimitConeFunctorOp, instIsContinuousOpensCarrierMapGrothendieckTopology, isQuotientMap_of_isColimit_cofork, LightProfinite.instPreregular, forget_preservesColimitsOfSize, LightCondMod.LocallyConstant.instHasSheafifyLightProfiniteCoherentTopologyModuleCat, AlgebraicGeometry.StructureSheaf.comap_basicOpen, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_assoc, AlgebraicGeometry.IsOpenImmersion.opensRange_pullback_fst_of_right, AlgebraicGeometry.Scheme.mem_basicOpen'', AlgebraicGeometry.Scheme.AffineZariskiSite.cocone_pt, ProfiniteGrp.toLimitFun_continuous, Action.isContinuous_def, AlgebraicGeometry.Scheme.stalkMap_inv_hom_assoc, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.preimage_toBase_eq_range_ι, isOpen_iff_of_isColimit, AlgebraicGeometry.tilde.toOpen_map_app_assoc, AlgebraicGeometry.locallyQuasiFinite_iff_finite_preimage_singleton, AlgebraicGeometry.Spec.topObj_forget, adj₂_unit, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_ne_zero_iff_mem_basicOpen, AlgebraicGeometry.basicOpen_eq_of_affine, AlgebraicGeometry.LocallyRingedSpace.Γ_map_op, TopologicalSpace.OpenNhds.map_id_obj, ProfiniteGrp.diagram_map, forget_preservesLimits, AlgebraicGeometry.Scheme.ΓSpecIso_naturality_assoc, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ_assoc, AlgebraicGeometry.IsOpenImmersion.range_pullbackFst, AlgebraicGeometry.IsAffineOpen.fromSpec_image_zeroLocus, AlgebraicGeometry.Scheme.IdealSheafData.mem_supportSet_iff_of_mem, AlgebraicGeometry.PresheafedSpace.toRestrictTop_base, AlgebraicGeometry.LocallyRingedSpace.isUnit_res_toΓSpecMapBasicOpen, AlgebraicGeometry.Scheme.affineBasisCover_map_range, LightCondensed.id_val, InfiniteGalois.algEquivToLimit_continuous, AlgebraicGeometry.ΓSpec_adjunction_homEquiv_eq, AlgebraicGeometry.Flat.isQuotientMap_of_surjective, AlgebraicGeometry.Scheme.Opens.ι_app, AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.isClopen_singleton_asFiber, AlgebraicGeometry.Scheme.Modules.pushforwardCongr_inv_app_app, AlgebraicGeometry.Scheme.IdealSheafData.supportSet_inter, AlgebraicGeometry.instIsPreimmersionAsFiberHom, AlgebraicGeometry.locallyOfFinitePresentation_iff, AlgebraicGeometry.IsAffineOpen.isOpenImmersion_fromSpec, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_hom_assoc, AlgebraicGeometry.quasiCompact_iff_spectral, AlgebraicGeometry.Scheme.iso_hom_base_inv_base_apply, prodIsoProd_inv_fst_apply, LightProfinite.Extend.functor_obj, LightCondensed.isoFinYoneda_hom_app, AlgebraicGeometry.instUniversallyClosedMorphismRestrict, AlgebraicGeometry.SheafedSpace.congr_hom_app, AlgebraicGeometry.quasiCompact_iff_isSpectralMap, AlgebraicGeometry.Scheme.Hom.instIsIsoCommRingCatApp, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_preimage_basicOpen, sigmaCofan_pt, effectiveEpi_iff_isQuotientMap, AlgebraicGeometry.Scheme.Hom.inv_image, colimit_isOpen_iff, ProfiniteGrp.id_apply, adj₁_unit, TopologicalSpace.Opens.map_top, AlgebraicGeometry.IsPreimmersion.instMorphismRestrict, AlgebraicGeometry.PresheafedSpace.GlueData.ιInvApp_π, Profinite.Nobeling.isClosedEmbedding, Presheaf.presheafEquivOfIso_functor_map_app, LightProfinite.proj_surjective, AlgebraicGeometry.Scheme.Hom.ι_fromNormalization, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_zeroLocus_eq, AlgebraicGeometry.exists_finite_imageι_comp_morphismRestrict_of_finite_image_preimage, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_hom_app, AlgebraicGeometry.IsAffineOpen.isCompactOpenCovered, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.base_open, AlgebraicGeometry.instIsQuasicoherentOpensCarrierCarrierCommRingCatSpecTilde, adj₁_counit, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_hom, AlgebraicGeometry.LocallyRingedSpace.evaluation_ne_zero_iff_mem_basicOpen, alexDiscEquivPreord_counitIso, TopologicalSpace.Opens.apply_def, AlgebraicGeometry.Scheme.Γevaluation_naturality, LightProfinite.proj_comp_transitionMapLE, LightProfinite.instEpiAppOppositeNatπAsLimitCone, CompHausLike.isoEquivHomeo_apply, AlgebraicGeometry.IsSeparated.instMorphismRestrict, GlueData.ι_eq_iff_rel, AlgebraicGeometry.basicOpen_eq_bot_iff, AlgebraicGeometry.Scheme.IdealSheafData.ker_glueDataObjι_appTop, AlgebraicGeometry.Spec.germ_stalkMapIso_hom, TopologicalSpace.Opens.mapMapIso_counitIso, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_apply, AlgebraicGeometry.HasRingHomProperty.stalkMap_of_respectsIso, LightCondMod.LocallyConstant.instFaithfulSheafLightProfiniteCoherentTopologyTypeConstantSheaf, AlgebraicGeometry.ExistsHomHomCompEqCompAux.range_g_subset, ProfiniteGrp.isIso_toLimit, AlgebraicGeometry.Spec.fromSpecStalk_eq, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over, AlgebraicGeometry.Spec.locallyRingedSpaceObj_presheaf, Presheaf.stalkSpecializes_refl, AlgebraicGeometry.instLocallyOfFinitePresentationMorphismRestrict, AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_π, LightCondensed.instHasColimitsOfShapeCostructuredArrowOppositeFintypeCatLightProfiniteOpToLightProfiniteType, AlgebraicGeometry.Scheme.IdealSheafData.ideal_biInf, AlgebraicGeometry.Scheme.isLocalHom_stalkClosedPointTo, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen', CompHausLike.is_hausdorff, AlgebraicGeometry.structurePresheafInCommRingCat_obj_carrier, instSecondCountableTopologyCarrierToTopTotallyDisconnectedSpacePtOppositeNatProfiniteCone, AlgebraicGeometry.IsAffineOpen.app_basicOpen_eq_away_map, AlgebraicGeometry.LocallyRingedSpace.toΓSpecMapBasicOpen_eq, InfiniteGalois.limitToAlgEquiv_symm_apply, LightCondensed.internallyProjective_iff_tensor_condition', AlgebraicGeometry.StructureSheaf.instAwayObjOppositeOpensCarrierTopValStructureSheafInTypeOpBasicOpen, AlgebraicGeometry.Scheme.preimage_basicOpen, AlgebraicGeometry.Scheme.Opens.instIsIsoCommRingCatAppLEιTopToScheme, LightProfinite.hasSheafify_type, LightCondensed.comp_val, Presheaf.toPushforwardOfIso_app, AlgebraicGeometry.IsAffineOpen.ΓSpecIso_hom_fromSpec_app, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_inv_app_val_app_hom_hom, AlgebraicGeometry.Scheme.exists_le_and_germ_injective, CompHausLike.instCompactSpaceCarrierObjTopCatCompHausLikeToTop, AlgebraicGeometry.Scheme.Hom.SpecMap_residueFieldMap_fromSpecResidueField, coe_comp, AlgebraicGeometry.Scheme.affineOpenCover_X, AlgebraicGeometry.Scheme.comp_app_assoc, Presheaf.generateEquivalenceOpensLe_functor'_map, CompHausLike.isoOfHomeo_hom_hom_hom_apply, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_y, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp_assoc, AlgebraicGeometry.instQuasiCompactToSpecΓOfCompactSpaceCarrierCarrierCommRingCat, SkyscraperPresheafFunctor.map'_app, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_assoc, AlgebraicGeometry.morphismRestrict_app, AlgebraicGeometry.AffineSpace.comp_homOfVector_assoc, AlgebraicGeometry.LocallyRingedSpace.toStalk_stalkMap_toΓSpec, AlgebraicGeometry.Scheme.Modules.instIsRightAdjointPresheafOfModulesToPresheafOfModules, AlgebraicGeometry.Scheme.Hom.toImage_app, AlgebraicGeometry.Scheme.range_fromSpecResidueField, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_hom_app_app, Sheaf.eq_of_locally_eq_iff, AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk, LightCondensed.underlying_map, exists_mem_zeroHypercover_range, AlgebraicGeometry.IsAffineOpen.isoSpec_hom, AlgebraicGeometry.PresheafedSpace.stalkMap.stalkSpecializes_stalkMap_assoc, AlgebraicGeometry.Scheme.Modules.Hom.app_smul, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec, AlgebraicGeometry.Scheme.Γ_obj_op, sigmaIsoSigma_hom_ι_apply, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_invApp, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_apply, Presheaf.IsSheaf.isSheafOpensLeCover, LightCondMod.isDiscrete_iff_isDiscrete_forget, coverPreserving_opens_map, Presheaf.IsSheaf.isSheafUniqueGluing, AlgebraicGeometry.quasiCompactCover_iff, AlgebraicGeometry.Scheme.image_zeroLocus, AlgebraicGeometry.Scheme.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, AlgebraicGeometry.HasRingHomProperty.iff_of_source_openCover, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCBasicOpens_app, AlgebraicGeometry.LocallyRingedSpace.evaluation_eq_zero_iff_notMem_basicOpen, AlgebraicGeometry.Proj.res_apply, Presheaf.app_injective_iff_stalkFunctor_map_injective, AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.preimage_basicOpen, AlgebraicGeometry.Scheme.Hom.fiberToSpecResidueField_apply, AlgebraicGeometry.Scheme.Opens.topIso_hom, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv_assoc, DeltaGenerated.deltaGenerated, AlgebraicGeometry.StructureSheaf.toOpen_res, AlgebraicGeometry.structurePresheafInModuleCat_obj_carrier, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec_assoc, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_SpecTensorTo, AlgebraicGeometry.SheafedSpace.congr_app, AlgebraicGeometry.Scheme.OpenCover.restrict_X, AlgebraicGeometry.Scheme.zeroLocus_univ, instIsEquivalenceLightProfiniteLightDiagramLightProfiniteToLightDiagram, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_spec, FundamentalGroupoidFunctor.prodToProdTop_map, Presheaf.SheafConditionPairwiseIntersections.coneEquiv_functor, AlgebraicGeometry.Scheme.JointlySurjective.exists_eq, LightCondSet.toTopCatMap_hom_apply, AlgebraicGeometry.Scheme.Hom.comp_appTop_assoc, CompHaus.effectiveEpiFamily_tfae, AlgebraicGeometry.IsAffineOpen.fromSpec_app_of_le, AlgebraicGeometry.AffineSpace.map_appTop_coord, AlgebraicGeometry.Scheme.toSpecΓ_preimage_basicOpen, LightCondensed.lanPresheafExt_hom, AlgebraicGeometry.LocallyRingedSpace.isLocalHom_stalkMap_congr, ext_iff, Presheaf.isIso_iff_stalkFunctor_map_iso, AlgebraicGeometry.Scheme.Hom.app_appIso_inv, limit_topology, AlgebraicGeometry.isIso_fromTildeΓ_iff, Sequential.is_sequential, Sheaf.interUnionPullbackCone_pt, Presheaf.SheafConditionPairwiseIntersections.coneEquiv_unitIso, Profinite.exists_locallyConstant_finite_nonempty, AlgebraicGeometry.Scheme.coe_homeoOfIso, AlgebraicGeometry.PresheafedSpace.restrictTopIso_inv, Presheaf.stalkPushforward.comp, Alexandrov.isSheaf_principalsKanExtension, AlgebraicGeometry.Scheme.Hom.normalizationObjIso_hom_val, AlgebraicGeometry.Scheme.openCoverBasicOpenTop_f, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_hom_c_app, Profinite.hasLimits, Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_pt, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app_assoc, AlgebraicGeometry.StructureSheaf.const_apply, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec.image_basicOpen_eq_basicOpen, AlgebraicGeometry.IsOpenImmersion.app_eq_invApp_app_of_comp_eq_aux, AlgebraicGeometry.isField_of_isIntegral_of_subsingleton, AlgebraicGeometry.isClosedMap_iff_specializingMap, pullback_snd_range, AlgebraicGeometry.exists_of_res_eq_of_qcqs, AlgebraicGeometry.PresheafedSpace.map_comp_c_app, Presheaf.coveringOfPresieve_apply, AlgebraicGeometry.Scheme.image_preimage_eq_of_isPullback, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app, AlgebraicGeometry.Scheme.Hom.instIsLocalHomCarrierStalkCommRingCatPresheafCoeContinuousMapCarrierCarrierHomTopCatBaseRingHomHomStalkMap, ProfiniteGrp.instPreservesLimitsProfiniteForget₂ContinuousMonoidHomCarrierToTopTotallyDisconnectedSpaceToProfiniteContinuousMap, subpresheafToTypes_obj, Presheaf.submonoidPresheafOfStalk_obj, Condensed.isoFinYoneda_inv_app, AlgebraicGeometry.LocallyRingedSpace.stalkMap_comp, AlgebraicGeometry.Scheme.GlueData.ι_jointly_surjective, AlgebraicGeometry.SheafedSpace.isColimit_exists_rep, FundamentalGroupoidFunctor.proj_map, AlgebraicGeometry.StructureSheaf.algebraMap_pushforward_stalk, AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.colimitDesc_preimage, AlexDisc.forgetToTop_of, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_invApp, AlgebraicGeometry.isLocalization_basicOpen_of_qcqs, AlgebraicGeometry.Scheme.IdealSheafData.strictMono_ideal, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv_apply, AlgebraicGeometry.Scheme.Opens.eq_presheaf_map_eqToHom, of_carrier, TopologicalSpace.OpenNhds.inclusionMapIso_inv_app, AlgebraicGeometry.Scheme.stalkClosedPointTo_comp, ProfiniteGrp.limit_ext_iff, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_apply, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ, AlgebraicGeometry.map_injective_of_isIntegral, CompHaus.instExtremallyDisconnectedCarrierToTopTrueOfProjective, AlgebraicGeometry.exists_eq_pow_mul_of_isCompact_of_isQuasiSeparated, AlgebraicGeometry.AffineSpace.homOfVector_appTop_coord, AlgebraicGeometry.Scheme.Spec_map_residue_apply, AlgebraicGeometry.sourceAffineLocally_morphismRestrict, Profinite.exists_locallyConstant_fin_two, AlgebraicGeometry.Scheme.IsQuasiAffine.isBasis_basicOpen, AlgebraicGeometry.Proj.stalkIso'_symm_mk, GlueData.ι_injective, AlgebraicGeometry.Scheme.residueFieldMap_comp, AlgebraicGeometry.structureSheafInType.smul_apply, AlgebraicGeometry.Etale.instMorphismRestrict, ProfiniteAddGrp.hom_comp, AlgebraicGeometry.Scheme.isoSpec_image_zeroLocus, Profinite.effectiveEpiFamily_tfae, AlgebraicGeometry.Scheme.Hom.fiberι_fiberHomeo_symm, AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_eq_id, AlgebraicGeometry.Scheme.IdealSheafData.ideal_map_of_isAffineHom, AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalk, AlgebraicGeometry.isCompact_and_isOpen_iff_finite_and_eq_biUnion_basicOpen, hom_comp, LightProfinite.proj_comp_transitionMap', AlgebraicGeometry.LocallyRingedSpace.isLocalHomValStalkMap, AlgebraicGeometry.IsAffineOpen.toSpecΓ_isoSpec_inv_assoc, AlgebraicGeometry.PresheafedSpace.restrict_top_presheaf, piFan_π_app, coconeOfCoconeForget_ι_app, AlgebraicGeometry.Scheme.mem_toGrothendieck_smallPretopology, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_point, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom, AlgebraicGeometry.coe_opensRestrict_apply_coe, AlgebraicGeometry.Scheme.AffineZariskiSite.presieveOfSections_eq_ofArrows, ProfiniteGrp.instIsTopologicalGroupCarrierToTopTotallyDisconnectedSpacePtProfiniteLimitConeCompForget₂ContinuousMonoidHomToProfiniteContinuousMap, AlgebraicGeometry.Scheme.Hom.inv_app, AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app', AlgebraicGeometry.RingedSpace.mem_basicOpen, AlgebraicGeometry.Scheme.Hom.app_injective, CategoryTheory.Functor.mapPresheaf_obj_presheaf, Profinite.Extend.functor_map, Presheaf.mono_iff_stalk_mono, Stonean.instPreservesEffectiveEpisCompHausToCompHaus, AlgebraicGeometry.Scheme.Modules.inv_app, Condensed.locallyConstantIsoFinYoneda_hom_app, AlgebraicGeometry.Scheme.Hom.Spec_map_residueFieldMap_fromSpecResidueField, Presheaf.ext_iff, AlgebraicGeometry.Scheme.Opens.toSpecΓ_preimage_zeroLocus, AlgebraicGeometry.Scheme.Cover.fromGlued_open_map, inv_hom_id_apply, AlgebraicGeometry.Scheme.exists_isOpenCover_and_isAffine, ProfiniteAddGrp.instCompactSpaceSubtypeForallCarrierToTopTotallyDisconnectedSpaceToProfiniteObjMemAddSubgroupLimitConePtAux, alexDiscEquivPreord_functor, AlgebraicGeometry.coprodMk_inr, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_bijective, AlgebraicGeometry.LocallyRingedSpace.comp_c_app, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_isAddCommGroup, AlgebraicGeometry.Scheme.Hom.isProperMap, Presheaf.presheafEquivOfIso_functor_obj_map, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_basicOpen_eq, instFullFintypeCatLightProfiniteToLightProfinite, AlgebraicGeometry.QuasiCompactCover.exists_isAffineOpen_of_isCompact, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberToSpecResidueField_assoc, AlgebraicGeometry.Scheme.AffineZariskiSite.mem_grothendieckTopology_iff_sectionsOfPresieve, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_ι, Condensed.equalizerCondition_profinite, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_appTop, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal_basicOpen, pullback_fst_range, Presheaf.presheafEquivOfIso_inverse_map_app, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓFreeOpensCarrierCarrierCommRingCat, AlgebraicGeometry.RingedSpace.zeroLocus_singleton, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_hom, TopologicalSpace.OpenNhds.inclusionMapIso_hom_app, Profinite.instHasPropTotallyDisconnectedSpaceCarrier, TopologicalSpace.Opens.mapIso_refl, CompHausLike.LocallyConstant.functorToPresheaves_obj_map, AlgebraicGeometry.Scheme.Hom.isOpen_smoothLocus, FundamentalGroupoidFunctor.coneDiscreteComp_obj_mapCone, AlgebraicGeometry.Scheme.Hom.fromNormalization_app, AlgebraicGeometry.Scheme.stalkSpecializes_stalkMap_assoc, AlgebraicGeometry.Scheme.Opens.ι_base_apply, AlgebraicGeometry.Scheme.Hom.eqToHom_app, presheafToTypes_obj, instRepresentablyFlatOpensCarrierMap, AlgebraicGeometry.Scheme.Hom.isDiscrete_preimage, Profinite.isIso_asLimitCone_lift, AlgebraicGeometry.Scheme.id_app, GlueData.preimage_image_eq_image', Alexandrov.projSup_map, AlgebraicGeometry.flat_iff, Presheaf.SheafConditionEqualizerProducts.res_π_apply, AlgebraicGeometry.Scheme.homOfLE_apply, AlgebraicGeometry.Scheme.zeroLocus_map_of_eq, AlgebraicGeometry.IsAffineOpen.toSpecΓ_fromSpec, Condensed.lanPresheafIso_hom, AlgebraicGeometry.IsAffineOpen.fromSpec_primeIdealOf, pullback_snd_image_fst_preimage, Stonean.effectiveEpi_tfae, TopologicalSpace.Opens.val_apply, AlgebraicGeometry.LocallyRingedSpace.iso_hom_base_inv_base_apply, CompHausLike.coe_comp, CompHausLike.finiteCoproduct.ι_jointly_surjective, AlgebraicGeometry.Scheme.fromSpecResidueField_apply, ProfiniteAddGrp.topologicalAddGroup, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_ι_assoc, ContinuousMap.Homotopy.hcast_def, AlgebraicGeometry.HasRingHomProperty.iff_of_isAffine, TopModuleCat.hom_forget₂_TopCat_map, AlgebraicGeometry.Scheme.Hom.coe_opensRange, AlgebraicGeometry.Scheme.IdealSheafData.le_def, AlgebraicGeometry.SheafedSpace.restrictTopIso_hom, AlgebraicGeometry.Scheme.stalkMap_congr, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_inv_app, AlgebraicGeometry.ΓSpec.toSpecΓ_unop, AlgebraicGeometry.isClosedImmersion_diagonal_restrict_diagonalCoverDiagonalRange, LightCondensed.instPreservesFiniteProductsOppositeLightProfiniteVal, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom, AlgebraicGeometry.SheafedSpace.Γ_map_op, Profinite.exists_hom, AlgebraicGeometry.tilde.instIsLocalizedModuleCarrierCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecModuleCatPresheafModulesSheafModulesSpecToSheafOpBasicOpenPowersHomToOpen, AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot_of_isCompact, AlgebraicGeometry.SheafedSpace.GlueData.ι_jointly_surjective, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.instIsIsoInvApp, AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_apply, AlgebraicGeometry.PresheafedSpace.stalkMap.congr_point, LightCondensed.instIsMonoidalFunctorOppositeLightProfiniteModuleCatWCoherentTopology, skyscraperPresheaf_map, AlgebraicGeometry.Scheme.IdealSheafData.supportSet_eq_iInter_zeroLocus, StalkSkyscraperPresheafAdjunctionAuxs.toSkyscraperPresheaf_app, AlgebraicGeometry.Scheme.Modules.map_smul, AlgebraicGeometry.RingedSpace.mem_basicOpen', piIsoPi_inv_π_assoc, AlgebraicGeometry.Scheme.mem_basicOpen, AlgebraicGeometry.SheafedSpace.comp_c_app', prodIsoProd_inv_snd_apply, AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalk_assoc, AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ_assoc, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_apply, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_iff, ContinuousMap.Homotopy.eq_diag_path, CompHausLike.LocallyConstant.functorToPresheaves_obj_obj, AlgebraicGeometry.Scheme.Opens.isoOfLE_inv_ι_assoc, AlgebraicGeometry.LocallyRingedSpace.Γ_obj, AlgebraicGeometry.Spec.sheafedSpaceObj_presheaf, AlgebraicGeometry.Spec.map_app, AlgebraicGeometry.Scheme.Spec_fromSpecStalk, ProfiniteGrp.diagram_obj, AlgebraicGeometry.Scheme.Cover.fromGlued_injective, AlgebraicGeometry.IsAffineOpen.ideal_ext_iff, topToCompHaus_obj, AlgebraicGeometry.Spec.map_base_apply, AlgebraicGeometry.morphismRestrict_id, AlgebraicGeometry.Scheme.Hom.stalkMap_surjective, AlgebraicGeometry.tilde.toOpen_map_app, CompHausLike.finiteCoproduct.ι_desc_apply, instCompactSpaceCarrierDisk, TopologicalSpace.Opens.map_id_eq, AlgebraicGeometry.IsAffineOpen.primeIdealOf_genericPoint, ProfiniteGrp.instReflectsIsomorphismsForgetContinuousMonoidHomCarrierToTopTotallyDisconnectedSpaceToProfinite, AlgebraicGeometry.IsAffineOpen.mem_ideal_iff, AlgebraicGeometry.Scheme.toSpecΓ_base, AlgebraicGeometry.Smooth.iff_forall_exists_isStandardSmooth, CompHaus.instT2SpaceCarrierToTopTrue
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trivial 📖 | CompOp | 2 mathmath: adj₂_counit, adj₂_unit
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