Documentation Verification Report

OpenImmersion

📁 Source: Mathlib/AlgebraicGeometry/OpenImmersion.lean

Statistics

MetricCount
DefinitionsIsOpenImmersion, forgetCreatesPullbackOfLeft, forgetCreatesPullbackOfRight, isoOfRangeEq, isoRestrict, opensEquiv, ΓIso, ΓIsoTop, scheme, toScheme, toSchemeHom, appIso, opensFunctor, opensRange, ofRestrict, restrict, stalkMapIsoOfIsPullback, «term_''ᵁ_»
18
Theoremsapp_eq_appIso_inv_app_of_comp_eq, app_eq_invApp_app_of_comp_eq_aux, app_ΓIso_hom, app_ΓIso_hom_apply, app_ΓIso_hom_assoc, comp, comp_lift, comp_lift_assoc, hasLimit_cospan_forget_of_left, hasLimit_cospan_forget_of_left', hasLimit_cospan_forget_of_right, hasLimit_cospan_forget_of_right', hasPullback_of_left, hasPullback_of_right, iff_isIso_stalkMap, iff_stalk_iso, image_preimage_eq_preimage_image_of_isPullback, instFstScheme, instHasOfPostcompPropertyScheme, instIsIsoCommRingCatStalkMap, instIsOpenImmersionMapSchemeLocallyRingedSpaceForgetToLocallyRingedSpace, instLift, instPreservesLimitSchemeLocallyRingedSpaceWalkingCospanCospanForgetToLocallyRingedSpace, instPreservesLimitSchemeLocallyRingedSpaceWalkingCospanCospanForgetToLocallyRingedSpace_1, instPreservesLimitSchemeTopCatWalkingCospanCospanForgetToTop, instPreservesLimitSchemeTopCatWalkingCospanCospanForgetToTop_1, instPreservesLimitSchemeWalkingCospanCospanForget, instPreservesLimitSchemeWalkingCospanCospanForget_1, instSndScheme, instπWalkingCospanSchemeCospanOne, isIso, isOpen_range, isPullback, isPullback_lift_id, isoOfRangeEq_hom_fac, isoOfRangeEq_hom_fac_assoc, isoOfRangeEq_inv_fac, isoOfRangeEq_inv_fac_assoc, le_monomorphisms, lift_app, lift_fac, lift_fac_assoc, lift_uniq, map_ΓIso_hom, map_ΓIso_inv, map_ΓIso_inv_apply, map_ΓIso_inv_assoc, mono, ofRestrict, of_comp, of_isIso, of_isIso_stalkMap, of_isLocalization, of_stalk_iso, opensEquiv_apply_coe, opensEquiv_symm_apply, opensRange_pullback_fst_of_right, opensRange_pullback_snd_of_left, range_pullbackFst, range_pullbackSnd, range_pullback_fst_of_right, range_pullback_snd_of_left, range_pullback_to_base_of_left, range_pullback_to_base_of_right, to_iso, ΓIso_inv, scheme_eq_of_locallyRingedSpace_eq, scheme_toScheme, toSchemeHom_isOpenImmersion, toSchemeHom_toPshHom, toScheme_toLocallyRingedSpace, appIso_hom, appIso_hom', appIso_inv_app, appIso_inv_appLE, appIso_inv_appLE_assoc, appIso_inv_app_apply, appIso_inv_app_assoc, appIso_inv_app_presheafMap, appIso_inv_naturality, appIso_inv_naturality_assoc, appLE_appIso_inv, appLE_appIso_inv_apply, appLE_appIso_inv_assoc, app_appIso_inv, app_appIso_inv_assoc, app_invApp', app_invApp'_assoc, apply_mem_image_iff, coe_image, coe_opensRange, comp_appIso, comp_image, id_appIso, id_image, image_iSup, image_iSup₂, image_injective, image_le_image_iff, image_le_image_of_le, image_le_opensRange, image_mono, image_preimage_eq_opensRange_inf, image_preimage_eq_opensRange_inter, image_preimage_le, image_top_eq_opensRange, instIsContinuousOpensOpensFunctorGrothendieckTopologyCarrierCarrierCommRingCat, instIsIsoCommRingCatAppObjOpensOpensFunctor, inv_image, isIso_app, isOpenEmbedding, map_mem_image_iff, mem_opensRange, opensFunctor_map_homOfLE, opensRange_comp, opensRange_comp_of_isIso, opensRange_of_isIso, opensRange_pullbackFst, opensRange_pullbackSnd, preimage_image_eq, preimage_opensRange, basic_open_isOpenImmersion, exists_affine_mem_range_and_range_subset, image_basicOpen, image_zeroLocus, instIsOpenImmersionMapOfHomAwayAlgebraMap, isOpenImmersion_SpecMap_localizationAway, ofRestrict_app, ofRestrict_appIso, ofRestrict_appLE, ofRestrict_toLRSHom_base, ofRestrict_toLRSHom_c_app, restrict_carrier, restrict_presheaf_map, restrict_presheaf_obj, restrict_toPresheafedSpace, isIso_iff_isIso_stalkMap, isIso_iff_isOpenImmersion, isIso_iff_isOpenImmersion_and_epi_base, isIso_iff_stalk_iso, isIso_of_isOpenImmersion_of_opensRange_eq_top, isOpenImmersion_isMultiplicative, isOpenImmersion_isStableUnderComposition, isOpenImmersion_respectsIso, isOpenImmersion_stableUnderBaseChange
145
Total163

AlgebraicGeometry

Definitions

NameCategoryTheorems
IsOpenImmersion 📖CompOp
202 mathmath: descendsAlong_isOpenImmersion_surjective_inf_flat_inf_quasicompact', Scheme.AffineOpenCover.openCover_f, Scheme.Cover.gluedCoverT'_snd_snd_assoc, instIsLocallyArtinianXScheme, Scheme.affineBasisCover_is_basis, Scheme.Pullback.openCoverOfLeftRight_f, IsOpenImmersion.instLift, isOpenImmersion_isStableUnderComposition, Scheme.Cover.glued_cover_cocycle_fst, sigmaOpenCover_X, Scheme.Hom.iUnion_support_ker_openCover_map_comp, Scheme.Pullback.openCoverOfBase_I₀, Algebra.FormallyUnramified.isOpenImmersion_SpecMap_lmul, Scheme.OpenCover.finiteSubcover_f, Scheme.Pullback.openCoverOfBase_f, Scheme.Pullback.openCoverOfRight_I₀, Scheme.basic_open_isOpenImmersion, ExistsHomHomCompEqCompAux.exists_eq, Scheme.openCoverOfIsOpenCover_I₀, instIsOpenImmersionLeftSchemeDiscretePUnitMapWalkingSpanOverTopMorphismPropertySpan, ExistsHomHomCompEqCompAux.h𝒰S, Scheme.Cover.glued_cover_cocycle, Scheme.affineOpenCover_I₀, Scheme.Cover.gluedCover_t, sourceLocalClosure.iff_forall_exists, Scheme.Cover.gluedCover_U, IsOpenImmersion.iff_isIso_stalkMap, Scheme.isOpenImmersion_SpecMap_localizationAway, Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_pullbackHom, Scheme.exists_affine_mem_range_and_range_subset, Scheme.instIsOpenImmersionMapOfHomAwayAlgebraMap, Scheme.affineOpenCover_idx, Scheme.Hom.fromNormalization_preimage, HasRingHomProperty.respects_isOpenImmersion, Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap, Scheme.Pullback.left_affine_comp_pullback_hasPullback, IsLocalAtSource.iff_of_openCover, Scheme.Hom.ι_toNormalization, Scheme.Cover.ColimitGluingData.transitionCocone_pt, Scheme.GlueData.openCover_f, instIsAffineXSchemeAffineCover, Scheme.Cover.ColimitGluingData.transitionMap_id, Scheme.directedAffineCover_f, Scheme.pullback_map_isOpenImmersion, Scheme.Cover.gluedCover_V, IsOpenImmersion.instπWalkingCospanSchemeCospanOne, Scheme.Cover.ι_fromGlued_assoc, Scheme.GlueData.f_open, Scheme.OpenCover.isOpenCover_opensRange, Scheme.openCoverOfIsOpenCover_f, Scheme.Cover.gluedCoverT'_fst_fst, IsOpenImmersion.comp, QuasiCompactCover.exists_hom, Scheme.IdealSheafData.subschemeCover_map_subschemeι, Scheme.Cover.gluedCoverT'_snd_fst, Scheme.isAffine_affineBasisCover, Scheme.directedAffineCover_I₀, Scheme.Cover.RelativeGluingData.equifibered, IsOpenImmersion.of_stalk_iso, Scheme.AffineOpenCover.instIsOpenImmersionF, ExistsHomHomCompEqCompAux.h𝒰X, isOpenImmersion_stableUnderBaseChange, sourceLocalClosure.instIsZariskiLocalAtSourceIsOpenImmersionOfRespectsIsoOfRespectsLeftScheme, hasOfPostcompProperty_isOpenImmersion_of_morphismRestrict, Scheme.OpenCover.restrict_f, Scheme.OpenCover.iSup_opensRange, Scheme.GlueData.ι_isOpenImmersion, FormallyUnramified.isOpenImmersion_diagonal, instIsOpenImmersionCompSchemeιQuasiFiniteLocusToNormalization, Scheme.Pullback.openCoverOfRight_f, Scheme.Hom.iInf_ker_openCover_map_comp, isOpenImmersion_SpecMap_iff_of_surjective, instIsOpenImmersionInrScheme, instIsOpenImmersionToNormalizationOfLocallyQuasiFiniteOfLocallyOfFiniteType, Scheme.Cover.gluedCover_J, Scheme.Cover.ColimitGluingData.transitionCocone_ι_app, isIso_iff_isOpenImmersion_and_surjective, Scheme.Opens.instIsOpenImmersionι, isIso_iff_isOpenImmersion, isOpenImmersion_isMultiplicative, Scheme.Cover.glued_cover_cocycle_snd, Scheme.openCoverOfIsOpenCover_X, Scheme.instIsOpenImmersionToSpecΓOfIsQuasiAffine, Scheme.affineOpenCoverOfSpanRangeEqTop_X_carrier, IsImmersion.isImmersion_iff_exists, IsLocalAtSource.respectsLeft_isOpenImmersion, isLocalIso_iff, Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_pullbackHom_assoc, QuasiCompactCover.inst, isOpenImmersion_iff_stalk, Scheme.GlueData.openCover_X, Scheme.directedAffineCover_X, isOpenImmersion_of_isEmpty, instIsOpenImmersionMapScheme, isOpenImmersion_respectsIso, Scheme.AffineZariskiSite.directedCover_X, IsOpenImmersion.of_isIso, Scheme.OpenCover.instIsOpenImmersionTrans, Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap_assoc, IsOpenImmersion.instHasOfPostcompPropertyScheme, Scheme.IdealSheafData.opensRange_subschemeCover_map, isIso_iff_isOpenImmersion_and_epi_base, instRespectsSchemeLocallyQuasiFiniteIsOpenImmersion, Scheme.Pullback.openCoverOfRight_X, Scheme.Cover.gluedCoverT'_snd_fst_assoc, IsZariskiLocalAtSource.respectsLeft_isOpenImmersion, Scheme.AffineZariskiSite.directedCover_f, isOpenImmersion_eq_inf, instIsOpenImmersionMorphismRestrict, IsZariskiLocalAtSource.iff_of_openCover, Scheme.Hom.iInf_ker_openCover_map_comp_apply, instIsOpenImmersionInlScheme, Scheme.Pullback.openCoverOfBase_X, Scheme.Pullback.openCoverOfBase'_f, instIsOpenImmersionMapWalkingSpanSchemeSpan, Scheme.Cover.gluedCover_f, Scheme.Hom.ι_toNormalization_assoc, IsOpenImmersion.of_flat_of_mono, instIsOpenImmersionMapOfHomForallEvalRingHom, IsLocalAtTarget.iff_of_openCover, Scheme.IdealSheafData.isOpenImmersion_glueDataObjMap, Scheme.directedAffineCover_trans, instIsOpenImmersionSigmaSpec, Scheme.AffineZariskiSite.opensRange_relativeGluingData_map, Scheme.Cover.ColimitGluingData.prop_trans, Scheme.Cover.gluedCoverT'_fst_snd_assoc, instIsOpenImmersionAppOverSchemeOpensDiagramι, Scheme.Cover.ColimitGluingData.trans_app_left, instIsOpenImmersionHomOfLE, Scheme.affineBasisCover_obj, Scheme.Cover.ColimitGluingData.transitionMap_comp, sigmaOpenCover_I₀, isomorphisms_eq_isOpenImmersion_inf_surjective, Scheme.IdealSheafData.subSchemeCover_map_inclusion_assoc, instIsAffineXSchemeCoverOfIsIsoIsOpenImmersionId, Scheme.OpenCover.finiteSubcover_X, IsOpenImmersion.iff_stalk_iso, Scheme.Hom.ι_fromNormalization_assoc, IsLocalIso.exists_isOpenImmersion, Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_map, IsOpenImmersion.of_isIso_stalkMap, Scheme.IdealSheafData.subSchemeCover_map_inclusion, Scheme.Pullback.openCoverOfLeftRight_I₀, Scheme.affineOpenCoverOfSpanRangeEqTop_idx, Scheme.instHasPullbacksIsOpenImmersion, Scheme.Cover.gluedCoverT'_snd_snd, IsOpenImmersion.of_comp, IsZariskiLocalAtTarget.iff_of_openCover, Scheme.affineOpenCoverOfSpanRangeEqTop_f, instIsLocallyNoetherianXScheme, sigmaOpenCover_f, Scheme.instIsLocalAtTargetIsomorphismsZariskiPrecoverage, Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_map_assoc, isLocallyArtinian_iff_openCover, Scheme.AffineOpenCover.openCover_I₀, Scheme.OpenCover.restrict_I₀, Scheme.Pullback.openCoverOfLeft_I₀, IsImmersion.instIsOpenImmersionToImageOfQuasiCompact, Scheme.instIsOpenImmersionF, Scheme.affineOpenCover_f, Scheme.Cover.gluedCoverT'_fst_snd, Scheme.AffineZariskiSite.PreservesLocalization.opensRange_map, isOpenImmersion_isZariskiLocalAtTarget, instHasOfPostcompPropertySchemeIsOpenImmersionOfIsStableUnderBaseChange, Scheme.affineBasisCover_map_range, IsAffineOpen.isOpenImmersion_fromSpec, Scheme.Hom.instIsLocallyDirectedI₀DirectedCoverCompFunctorNormalizationGlueDataForget, instRespectsSchemeSmoothIsOpenImmersion, IsOpenImmersion.le_monomorphisms, Scheme.Hom.ι_fromNormalization, IsOpenImmersion.of_isLocalization, Scheme.GlueData.openCover_I₀, Proj.instIsOpenImmersionAwayι, isLocallyNoetherian_iff_openCover, Scheme.affineOpenCover_X, IsOpenImmersion.ofRestrict, IsLocalIso.eq_sourceLocalClosure_isOpenImmersion, Scheme.Cover.instIsOpenImmersionFromGlued, Scheme.Cover.ColimitGluingData.functor_map, IsImmersion.isImmersion_iff_exists_of_quasiCompact, Scheme.Pullback.openCoverOfLeft_f, Scheme.OpenCover.restrict_X, Scheme.openCoverBasicOpenTop_f, Scheme.Cover.gluedCoverT'_fst_fst_assoc, Scheme.OpenCover.instIsOpenImmersionMapI₀FunctorOfLocallyDirected, Scheme.affineOpenCoverOfSpanRangeEqTop_I₀, Scheme.AffineZariskiSite.PreservesLocalization.colimitDesc_preimage, Scheme.Cover.ColimitGluingData.functor_obj, Scheme.Pullback.openCoverOfLeftRight_X, Scheme.isAffine_affineCover, Scheme.AffineZariskiSite.directedCover_I₀, IsOpenImmersion.instSndScheme, Scheme.AffineOpenCover.openCover_X, IsOpenImmersion.instFstScheme, Scheme.AffineZariskiSite.PreservesLocalization.isOpenImmersion, PresheafedSpace.IsOpenImmersion.toSchemeHom_isOpenImmersion, Scheme.Pullback.openCoverOfLeft_X, Scheme.Cover.RelativeGluingData.instIsOpenImmersionMapI₀Functor, Scheme.Pullback.diagonalCover_map, Scheme.Cover.ι_fromGlued, Scheme.instIsJointlySurjectivePreservingIsOpenImmersion, Scheme.isAffine_affineOpenCover
«term_''ᵁ_» 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
isIso_iff_isIso_stalkMap 📖mathematicalCategoryTheory.IsIso
Scheme
Scheme.instCategory
TopCat
TopCat.instCategory
PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
PresheafedSpace.Hom.base
LocallyRingedSpace.Hom.toHom
Scheme.Hom.toLRSHom'
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
PresheafedSpace.presheaf
DFunLike.coe
TopCat.carrier
CategoryTheory.ConcreteCategory.hom
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
Scheme.Hom.stalkMap
CommRingCat.Colimits.hasColimits_commRingCat
isIso_iff_isOpenImmersion_and_epi_base
IsOpenImmersion.iff_isIso_stalkMap
Topology.IsEmbedding.injective
Topology.IsOpenEmbedding.toIsEmbedding
TopCat.epi_iff_surjective
Topology.IsOpenEmbedding.continuous
Topology.IsOpenEmbedding.isOpenMap
CategoryTheory.Iso.isIso_hom
CategoryTheory.epi_of_effectiveEpi
CategoryTheory.instEffectiveEpiOfIsIso
Homeomorph.isOpenEmbedding
isIso_iff_isOpenImmersion 📖mathematicalCategoryTheory.IsIso
Scheme
Scheme.instCategory
IsOpenImmersion
CategoryTheory.Epi
TopCat
TopCat.instCategory
PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
PresheafedSpace.Hom.base
LocallyRingedSpace.Hom.toHom
Scheme.Hom.toLRSHom'
isIso_iff_isOpenImmersion_and_epi_base
isIso_iff_isOpenImmersion_and_epi_base 📖mathematicalCategoryTheory.IsIso
Scheme
Scheme.instCategory
IsOpenImmersion
CategoryTheory.Epi
TopCat
TopCat.instCategory
PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
PresheafedSpace.Hom.base
LocallyRingedSpace.Hom.toHom
Scheme.Hom.toLRSHom'
IsOpenImmersion.of_isIso
CategoryTheory.epi_of_effectiveEpi
CategoryTheory.instEffectiveEpiOfIsIso
Scheme.Hom.isIso_base
IsOpenImmersion.isIso
isIso_iff_stalk_iso 📖mathematicalCategoryTheory.IsIso
Scheme
Scheme.instCategory
TopCat
TopCat.instCategory
PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
PresheafedSpace.Hom.base
LocallyRingedSpace.Hom.toHom
Scheme.Hom.toLRSHom'
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
PresheafedSpace.presheaf
DFunLike.coe
TopCat.carrier
CategoryTheory.ConcreteCategory.hom
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
Scheme.Hom.stalkMap
isIso_iff_isIso_stalkMap
isIso_of_isOpenImmersion_of_opensRange_eq_top 📖mathematicalScheme.Hom.opensRange
Top.top
Scheme.Opens
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
TopCat.carrier
PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
CategoryTheory.IsIso
Scheme
Scheme.instCategory
isIso_iff_isOpenImmersion_and_epi_base
TopCat.epi_iff_surjective
Set.range_eq_univ
TopologicalSpace.Opens.ext_iff
isOpenImmersion_isMultiplicative 📖mathematicalCategoryTheory.MorphismProperty.IsMultiplicative
Scheme
Scheme.instCategory
IsOpenImmersion
IsOpenImmersion.of_isIso
CategoryTheory.IsIso.id
isOpenImmersion_isStableUnderComposition
isOpenImmersion_isStableUnderComposition 📖mathematicalCategoryTheory.MorphismProperty.IsStableUnderComposition
Scheme
Scheme.instCategory
IsOpenImmersion
LocallyRingedSpace.IsOpenImmersion.comp
isOpenImmersion_respectsIso 📖mathematicalCategoryTheory.MorphismProperty.RespectsIso
Scheme
Scheme.instCategory
IsOpenImmersion
CategoryTheory.MorphismProperty.respectsIso_of_isStableUnderComposition
isOpenImmersion_isStableUnderComposition
IsOpenImmersion.of_isIso
isOpenImmersion_stableUnderBaseChange 📖mathematicalCategoryTheory.MorphismProperty.IsStableUnderBaseChange
Scheme
Scheme.instCategory
IsOpenImmersion
CategoryTheory.MorphismProperty.IsStableUnderBaseChange.mk'
isOpenImmersion_respectsIso
IsOpenImmersion.instFstScheme

AlgebraicGeometry.IsOpenImmersion

Definitions

NameCategoryTheorems
forgetCreatesPullbackOfLeft 📖CompOp
forgetCreatesPullbackOfRight 📖CompOp
isoOfRangeEq 📖CompOp
4 mathmath: isoOfRangeEq_inv_fac_assoc, isoOfRangeEq_hom_fac, isoOfRangeEq_hom_fac_assoc, isoOfRangeEq_inv_fac
isoRestrict 📖CompOp
opensEquiv 📖CompOp
2 mathmath: opensEquiv_apply_coe, opensEquiv_symm_apply
ΓIso 📖CompOp
7 mathmath: map_ΓIso_inv_assoc, ΓIso_inv, app_ΓIso_hom_assoc, map_ΓIso_inv, app_ΓIso_hom, app_ΓIso_hom_apply, map_ΓIso_hom
ΓIsoTop 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
app_eq_appIso_inv_app_of_comp_eq 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.Hom.app
CommRingCat
CommRingCat.instCategory
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
AlgebraicGeometry.Scheme.Hom.opensFunctor
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.Iso.inv
AlgebraicGeometry.Scheme.Hom.appIso
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.eqToHom
app_eq_invApp_app_of_comp_eq_aux
app_eq_invApp_app_of_comp_eq_aux
AlgebraicGeometry.Scheme.Hom.comp_app
CategoryTheory.Category.assoc
AlgebraicGeometry.Scheme.Hom.preimage_image_eq
AlgebraicGeometry.Scheme.Hom.appIso_inv_app_assoc
AlgebraicGeometry.Scheme.Hom.naturality_assoc
CategoryTheory.Functor.map_comp
CategoryTheory.op_comp
Quiver.Hom.unop_op
CategoryTheory.eqToHom_map
CategoryTheory.eqToHom_trans
CategoryTheory.eqToHom_op
CategoryTheory.eqToHom_refl
CategoryTheory.Functor.map_id
CategoryTheory.Category.comp_id
app_eq_invApp_app_of_comp_eq_aux 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
AlgebraicGeometry.Scheme.Hom.opensFunctor
AlgebraicGeometry.Scheme.Hom.preimage_image_eq
app_ΓIso_hom 📖mathematicalCategoryTheory.CategoryStruct.comp
CommRingCat
CategoryTheory.Category.toCategoryStruct
CommRingCat.instCategory
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.Scheme.Hom.opensRange
AlgebraicGeometry.Scheme.Hom.app
CategoryTheory.Iso.hom
ΓIso
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
SemilatticeInf.toPartialOrder
CategoryTheory.homOfLE
inf_le_right
inf_le_right
map_ΓIso_inv
CategoryTheory.Category.assoc
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id
app_ΓIso_hom_apply 📖mathematicalDFunLike.coe
RingHom
CommRingCat.carrier
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.Scheme.Hom.opensRange
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
RingHom.instFunLike
CategoryTheory.ConcreteCategory.hom
CommRingCat.instConcreteCategoryRingHomCarrier
CategoryTheory.Iso.hom
ΓIso
AlgebraicGeometry.Scheme.Hom.app
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
SemilatticeInf.toPartialOrder
CategoryTheory.homOfLE
inf_le_right
inf_le_right
CategoryTheory.comp_apply
Mathlib.Tactic.Elementwise.hom_elementwise
app_ΓIso_hom
app_ΓIso_hom_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CommRingCat
CategoryTheory.Category.toCategoryStruct
CommRingCat.instCategory
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.Scheme.Hom.app
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.Scheme.Hom.opensRange
CategoryTheory.Iso.hom
ΓIso
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
SemilatticeInf.toPartialOrder
CategoryTheory.homOfLE
inf_le_right
inf_le_right
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
app_ΓIso_hom
comp 📖mathematicalAlgebraicGeometry.IsOpenImmersion
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.comp
comp_lift 📖mathematicalSet
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
Set.instHasSubset
Set.range
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
lift
HasSubset.Subset.trans
Set.instIsTransSubset
HasSubset.Subset.trans
Set.instIsTransSubset
CategoryTheory.cancel_mono
mono
CategoryTheory.Category.assoc
lift_fac
comp_lift_assoc 📖mathematicalSet
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
Set.instHasSubset
Set.range
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
lift
HasSubset.Subset.trans
Set.instIsTransSubset
HasSubset.Subset.trans
Set.instIsTransSubset
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
comp_lift
hasLimit_cospan_forget_of_left 📖mathematicalCategoryTheory.Limits.HasLimit
CategoryTheory.Limits.WalkingCospan
CategoryTheory.Limits.WidePullbackShape.category
CategoryTheory.Limits.WalkingPair
AlgebraicGeometry.LocallyRingedSpace
AlgebraicGeometry.LocallyRingedSpace.instCategory
CategoryTheory.Functor.comp
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Limits.cospan
AlgebraicGeometry.Scheme.forgetToLocallyRingedSpace
CategoryTheory.Limits.hasLimit_iff_of_iso
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.hasPullback_of_left
instIsOpenImmersionMapSchemeLocallyRingedSpaceForgetToLocallyRingedSpace
hasLimit_cospan_forget_of_left' 📖mathematicalCategoryTheory.Limits.HasLimit
CategoryTheory.Limits.WalkingCospan
CategoryTheory.Limits.WidePullbackShape.category
CategoryTheory.Limits.WalkingPair
AlgebraicGeometry.LocallyRingedSpace
AlgebraicGeometry.LocallyRingedSpace.instCategory
CategoryTheory.Limits.cospan
CategoryTheory.Functor.obj
CategoryTheory.Functor.comp
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.forgetToLocallyRingedSpace
CategoryTheory.Limits.WalkingCospan.left
CategoryTheory.Limits.WalkingCospan.right
CategoryTheory.Limits.WalkingCospan.one
CategoryTheory.Functor.map
CategoryTheory.Limits.WalkingCospan.Hom.inl
CategoryTheory.Limits.WalkingCospan.Hom.inr
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.hasPullback_of_left
instIsOpenImmersionMapSchemeLocallyRingedSpaceForgetToLocallyRingedSpace
hasLimit_cospan_forget_of_right 📖mathematicalCategoryTheory.Limits.HasLimit
CategoryTheory.Limits.WalkingCospan
CategoryTheory.Limits.WidePullbackShape.category
CategoryTheory.Limits.WalkingPair
AlgebraicGeometry.LocallyRingedSpace
AlgebraicGeometry.LocallyRingedSpace.instCategory
CategoryTheory.Functor.comp
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Limits.cospan
AlgebraicGeometry.Scheme.forgetToLocallyRingedSpace
CategoryTheory.Limits.hasLimit_iff_of_iso
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.hasPullback_of_right
instIsOpenImmersionMapSchemeLocallyRingedSpaceForgetToLocallyRingedSpace
hasLimit_cospan_forget_of_right' 📖mathematicalCategoryTheory.Limits.HasLimit
CategoryTheory.Limits.WalkingCospan
CategoryTheory.Limits.WidePullbackShape.category
CategoryTheory.Limits.WalkingPair
AlgebraicGeometry.LocallyRingedSpace
AlgebraicGeometry.LocallyRingedSpace.instCategory
CategoryTheory.Limits.cospan
CategoryTheory.Functor.obj
CategoryTheory.Functor.comp
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.forgetToLocallyRingedSpace
CategoryTheory.Limits.WalkingCospan.left
CategoryTheory.Limits.WalkingCospan.right
CategoryTheory.Limits.WalkingCospan.one
CategoryTheory.Functor.map
CategoryTheory.Limits.WalkingCospan.Hom.inl
CategoryTheory.Limits.WalkingCospan.Hom.inr
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.hasPullback_of_right
instIsOpenImmersionMapSchemeLocallyRingedSpaceForgetToLocallyRingedSpace
hasPullback_of_left 📖mathematicalCategoryTheory.Limits.HasPullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.hasLimit_of_created
hasLimit_cospan_forget_of_left
hasPullback_of_right 📖mathematicalCategoryTheory.Limits.HasPullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.hasLimit_of_created
hasLimit_cospan_forget_of_right
iff_isIso_stalkMap 📖mathematicalAlgebraicGeometry.IsOpenImmersion
Topology.IsOpenEmbedding
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.IsIso
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
AlgebraicGeometry.PresheafedSpace.presheaf
AlgebraicGeometry.Scheme.Hom.stalkMap
CommRingCat.Colimits.hasColimits_commRingCat
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.base_open
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.stalk_iso
AlgebraicGeometry.instIsOpenImmersionCommRingCatOfIsOpenImmersion
of_isIso_stalkMap
iff_stalk_iso 📖mathematicalAlgebraicGeometry.IsOpenImmersion
Topology.IsOpenEmbedding
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.IsIso
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
AlgebraicGeometry.PresheafedSpace.presheaf
AlgebraicGeometry.Scheme.Hom.stalkMap
iff_isIso_stalkMap
image_preimage_eq_preimage_image_of_isPullback 📖mathematicalCategoryTheory.IsPullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
AlgebraicGeometry.Scheme.Hom.opensFunctor
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
TopologicalSpace.Opens
TopCat.str
TopologicalSpace.Opens.ext
Set.ext
CategoryTheory.CommSq.w
CategoryTheory.IsPullback.toCommSq
hasPullback_of_left
Eq.ge
range_pullbackSnd
CategoryTheory.IsPullback.isoPullback_inv_snd
instFstScheme 📖mathematicalAlgebraicGeometry.IsOpenImmersion
CategoryTheory.Limits.pullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
hasPullback_of_right
CategoryTheory.Limits.pullback.fst
hasPullback_of_right
CategoryTheory.Limits.hasPullback_symmetry
CategoryTheory.Limits.pullbackSymmetry_hom_comp_snd
comp
of_isIso
CategoryTheory.Iso.isIso_hom
instSndScheme
instHasOfPostcompPropertyScheme 📖mathematicalCategoryTheory.MorphismProperty.HasOfPostcompProperty
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.IsOpenImmersion
of_comp
instIsIsoCommRingCatStalkMap 📖mathematicalCategoryTheory.IsIso
CommRingCat
CommRingCat.instCategory
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.PresheafedSpace.presheaf
DFunLike.coe
TopCat.carrier
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.Scheme.Hom.stalkMap
CommRingCat.Colimits.hasColimits_commRingCat
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.stalk_iso
instIsOpenImmersionMapSchemeLocallyRingedSpaceForgetToLocallyRingedSpace 📖mathematicalAlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion
CategoryTheory.Functor.obj
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.LocallyRingedSpace
AlgebraicGeometry.LocallyRingedSpace.instCategory
AlgebraicGeometry.Scheme.forgetToLocallyRingedSpace
CategoryTheory.Functor.map
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.base_open
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.c_iso
instLift 📖mathematicalSet
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
Set.instHasSubset
Set.range
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.IsOpenImmersion
lift
of_comp
lift_fac
instPreservesLimitSchemeLocallyRingedSpaceWalkingCospanCospanForgetToLocallyRingedSpace 📖mathematicalCategoryTheory.Limits.PreservesLimit
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.LocallyRingedSpace
AlgebraicGeometry.LocallyRingedSpace.instCategory
CategoryTheory.Limits.WalkingCospan
CategoryTheory.Limits.WidePullbackShape.category
CategoryTheory.Limits.WalkingPair
CategoryTheory.Limits.cospan
AlgebraicGeometry.Scheme.forgetToLocallyRingedSpace
CategoryTheory.preservesLimit_of_createsLimit_and_hasLimit
hasLimit_cospan_forget_of_left
instPreservesLimitSchemeLocallyRingedSpaceWalkingCospanCospanForgetToLocallyRingedSpace_1 📖mathematicalCategoryTheory.Limits.PreservesLimit
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.LocallyRingedSpace
AlgebraicGeometry.LocallyRingedSpace.instCategory
CategoryTheory.Limits.WalkingCospan
CategoryTheory.Limits.WidePullbackShape.category
CategoryTheory.Limits.WalkingPair
CategoryTheory.Limits.cospan
AlgebraicGeometry.Scheme.forgetToLocallyRingedSpace
CategoryTheory.Limits.preservesPullback_symmetry
instPreservesLimitSchemeLocallyRingedSpaceWalkingCospanCospanForgetToLocallyRingedSpace
instPreservesLimitSchemeTopCatWalkingCospanCospanForgetToTop 📖mathematicalCategoryTheory.Limits.PreservesLimit
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
TopCat
TopCat.instCategory
CategoryTheory.Limits.WalkingCospan
CategoryTheory.Limits.WidePullbackShape.category
CategoryTheory.Limits.WalkingPair
CategoryTheory.Limits.cospan
AlgebraicGeometry.Scheme.forgetToTop
CategoryTheory.Limits.comp_preservesLimit
instPreservesLimitSchemeLocallyRingedSpaceWalkingCospanCospanForgetToLocallyRingedSpace
CategoryTheory.Limits.preservesLimit_of_iso_diagram
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.forgetToTop_preservesPullback_of_left
instPreservesLimitSchemeTopCatWalkingCospanCospanForgetToTop_1 📖mathematicalCategoryTheory.Limits.PreservesLimit
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
TopCat
TopCat.instCategory
CategoryTheory.Limits.WalkingCospan
CategoryTheory.Limits.WidePullbackShape.category
CategoryTheory.Limits.WalkingPair
CategoryTheory.Limits.cospan
AlgebraicGeometry.Scheme.forgetToTop
CategoryTheory.Limits.preservesPullback_symmetry
instPreservesLimitSchemeTopCatWalkingCospanCospanForgetToTop
instPreservesLimitSchemeWalkingCospanCospanForget 📖mathematicalCategoryTheory.Limits.PreservesLimit
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.types
CategoryTheory.Limits.WalkingCospan
CategoryTheory.Limits.WidePullbackShape.category
CategoryTheory.Limits.WalkingPair
CategoryTheory.Limits.cospan
AlgebraicGeometry.Scheme.forget
CategoryTheory.Limits.comp_preservesLimit
instPreservesLimitSchemeTopCatWalkingCospanCospanForgetToTop
CategoryTheory.Limits.PreservesLimitsOfShape.preservesLimit
CategoryTheory.Limits.PreservesFiniteLimits.preservesFiniteLimits
CategoryTheory.Limits.PreservesLimits.preservesFiniteLimits
TopCat.forget_preservesLimits
instPreservesLimitSchemeWalkingCospanCospanForget_1 📖mathematicalCategoryTheory.Limits.PreservesLimit
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.types
CategoryTheory.Limits.WalkingCospan
CategoryTheory.Limits.WidePullbackShape.category
CategoryTheory.Limits.WalkingPair
CategoryTheory.Limits.cospan
AlgebraicGeometry.Scheme.forget
CategoryTheory.Limits.comp_preservesLimit
instPreservesLimitSchemeTopCatWalkingCospanCospanForgetToTop_1
CategoryTheory.Limits.PreservesLimitsOfShape.preservesLimit
CategoryTheory.Limits.PreservesFiniteLimits.preservesFiniteLimits
CategoryTheory.Limits.PreservesLimits.preservesFiniteLimits
TopCat.forget_preservesLimits
instSndScheme 📖mathematicalAlgebraicGeometry.IsOpenImmersion
CategoryTheory.Limits.pullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
hasPullback_of_left
CategoryTheory.Limits.pullback.snd
hasPullback_of_left
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.hasPullback_of_left
instIsOpenImmersionMapSchemeLocallyRingedSpaceForgetToLocallyRingedSpace
instPreservesLimitSchemeLocallyRingedSpaceWalkingCospanCospanForgetToLocallyRingedSpace
CategoryTheory.Limits.PreservesPullback.iso_hom_snd
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.comp
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.of_isIso
CategoryTheory.Iso.isIso_hom
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.pullback_snd_of_left
instπWalkingCospanSchemeCospanOne 📖mathematicalAlgebraicGeometry.IsOpenImmersion
CategoryTheory.Limits.limit
CategoryTheory.Limits.WalkingCospan
CategoryTheory.Limits.WidePullbackShape.category
CategoryTheory.Limits.WalkingPair
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Limits.cospan
hasPullback_of_right
CategoryTheory.Functor.obj
CategoryTheory.Limits.WalkingCospan.one
CategoryTheory.Limits.limit.π
hasPullback_of_right
CategoryTheory.Limits.limit.w
comp
instFstScheme
isIso 📖mathematicalCategoryTheory.IsIso
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.isIso_of_reflects_iso
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.to_iso
CategoryTheory.reflectsIsomorphisms_comp
CategoryTheory.reflectsIsomorphisms_of_full_and_faithful
AlgebraicGeometry.Scheme.instFullLocallyRingedSpaceForgetToLocallyRingedSpace
AlgebraicGeometry.Scheme.instFaithfulLocallyRingedSpaceForgetToLocallyRingedSpace
AlgebraicGeometry.LocallyRingedSpace.instReflectsIsomorphismsSheafedSpaceCommRingCatForgetToSheafedSpace
AlgebraicGeometry.SheafedSpace.forgetToPresheafedSpace_full
AlgebraicGeometry.SheafedSpace.forgetToPresheafedSpace_faithful
isOpen_range 📖mathematicalIsOpen
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
Set.range
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
Topology.IsOpenEmbedding.isOpen_range
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.base_open
isPullback 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.Scheme.Hom.opensRange
CategoryTheory.IsPullbackhasPullback_of_left
instSndScheme
range_pullbackSnd
CategoryTheory.cancel_mono
mono
CategoryTheory.Category.assoc
CategoryTheory.Limits.pullback.condition
isoOfRangeEq_inv_fac_assoc
CategoryTheory.IsPullback.paste_horiz
CategoryTheory.IsPullback.of_horiz_isIso
CategoryTheory.Iso.isIso_inv
CategoryTheory.IsIso.id
isoOfRangeEq_inv_fac
CategoryTheory.Category.comp_id
CategoryTheory.IsPullback.of_hasPullback
isPullback_lift_id 📖mathematicalSet
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
Set.instHasSubset
Set.range
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.IsPullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
lift
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Category.comp_id
lift_fac
CategoryTheory.IsPullback.paste_horiz
CategoryTheory.IsPullback.of_id_snd
CategoryTheory.IsKernelPair.id_of_mono
mono
isoOfRangeEq_hom_fac 📖mathematicalSet.range
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Iso.hom
isoOfRangeEq
lift_fac
le_of_eq
isoOfRangeEq_hom_fac_assoc 📖mathematicalSet.range
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Iso.hom
isoOfRangeEq
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
isoOfRangeEq_hom_fac
isoOfRangeEq_inv_fac 📖mathematicalSet.range
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Iso.inv
isoOfRangeEq
lift_fac
le_of_eq
isoOfRangeEq_inv_fac_assoc 📖mathematicalSet.range
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Iso.inv
isoOfRangeEq
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
isoOfRangeEq_inv_fac
le_monomorphisms 📖mathematicalCategoryTheory.MorphismProperty
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
Preorder.toLE
PartialOrder.toPreorder
OmegaCompletePartialOrder.toPartialOrder
CompleteLattice.instOmegaCompletePartialOrder
CompleteBooleanAlgebra.toCompleteLattice
CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra
AlgebraicGeometry.IsOpenImmersion
CategoryTheory.MorphismProperty.monomorphisms
CategoryTheory.MorphismProperty.monomorphisms.infer_property
mono
lift_app 📖mathematicalSet
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
Set.instHasSubset
Set.range
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.Scheme.Hom.app
lift
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
AlgebraicGeometry.Scheme.Hom.opensFunctor
TopologicalSpace.Opens.map
CategoryTheory.Iso.inv
AlgebraicGeometry.Scheme.Hom.appIso
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.eqToHom
app_eq_invApp_app_of_comp_eq_aux
Quiver.Hom
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
lift_fac
app_eq_appIso_inv_app_of_comp_eq
lift_fac
lift_fac 📖mathematicalSet
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
Set.instHasSubset
Set.range
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
lift
AlgebraicGeometry.Scheme.Hom.ext'
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.lift_fac
lift_fac_assoc 📖mathematicalSet
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
Set.instHasSubset
Set.range
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
lift
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
lift_fac
lift_uniq 📖mathematicalSet
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
Set.instHasSubset
Set.range
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
liftAlgebraicGeometry.Scheme.Hom.ext'
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.lift_uniq
map_ΓIso_hom 📖mathematicalCategoryTheory.CategoryStruct.comp
CommRingCat
CategoryTheory.Category.toCategoryStruct
CommRingCat.instCategory
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.Scheme.Hom.opensRange
AlgebraicGeometry.Scheme.Hom.app
CategoryTheory.Iso.hom
ΓIso
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
SemilatticeInf.toPartialOrder
CategoryTheory.homOfLE
inf_le_right
app_ΓIso_hom
map_ΓIso_inv 📖mathematicalCategoryTheory.CategoryStruct.comp
CommRingCat
CategoryTheory.Category.toCategoryStruct
CommRingCat.instCategory
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.Scheme.Hom.opensRange
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
SemilatticeInf.toPartialOrder
CategoryTheory.homOfLE
inf_le_right
CategoryTheory.Iso.inv
ΓIso
AlgebraicGeometry.Scheme.Hom.app
inf_le_right
LE.le.trans
ΓIso_inv
AlgebraicGeometry.Scheme.Hom.map_appLE
AlgebraicGeometry.Scheme.Hom.appLE_eq_app
map_ΓIso_inv_apply 📖mathematicalDFunLike.coe
RingHom
CommRingCat.carrier
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.Scheme.Hom.opensRange
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
RingHom.instFunLike
CategoryTheory.ConcreteCategory.hom
CommRingCat.instConcreteCategoryRingHomCarrier
AlgebraicGeometry.Scheme.Hom.appLE
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
SemilatticeInf.toPartialOrder
CategoryTheory.homOfLE
inf_le_right
AlgebraicGeometry.Scheme.Hom.app
inf_le_right
ΓIso_inv
CategoryTheory.comp_apply
Mathlib.Tactic.Elementwise.hom_elementwise
map_ΓIso_inv
map_ΓIso_inv_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CommRingCat
CategoryTheory.Category.toCategoryStruct
CommRingCat.instCategory
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.Scheme.Hom.opensRange
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
SemilatticeInf.toPartialOrder
CategoryTheory.homOfLE
inf_le_right
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.Iso.inv
ΓIso
AlgebraicGeometry.Scheme.Hom.app
inf_le_right
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
map_ΓIso_inv
mono 📖mathematicalCategoryTheory.Mono
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Functor.mono_of_mono_map
CategoryTheory.reflectsMonomorphisms_of_reflectsLimitsOfShape
CategoryTheory.Limits.ReflectsFiniteLimits.reflects
CategoryTheory.Limits.instReflectsFiniteLimitsOfReflectsLimits
CategoryTheory.Limits.fullyFaithful_reflectsLimits
AlgebraicGeometry.Scheme.instFullLocallyRingedSpaceForgetToLocallyRingedSpace
AlgebraicGeometry.Scheme.instFaithfulLocallyRingedSpaceForgetToLocallyRingedSpace
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.mono
ofRestrict 📖mathematicalTopology.IsOpenEmbedding
TopCat.carrier
TopCat.of
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopCat.str
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.IsOpenImmersion
AlgebraicGeometry.Scheme.restrict
AlgebraicGeometry.Scheme.ofRestrict
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.ofRestrict
of_comp 📖mathematicalAlgebraicGeometry.IsOpenImmersionof_isIso_stalkMap
Topology.IsOpenEmbedding.of_comp
AlgebraicGeometry.Scheme.Hom.isOpenEmbedding
CategoryTheory.IsIso.of_isIso_comp_left
CommRingCat.Colimits.hasColimits_commRingCat
instIsIsoCommRingCatStalkMap
AlgebraicGeometry.Scheme.Hom.stalkMap_comp
of_isIso 📖mathematicalAlgebraicGeometry.IsOpenImmersionAlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.of_isIso
AlgebraicGeometry.Scheme.Hom.isIso_toLRSHom
of_isIso_stalkMap 📖mathematicalTopology.IsOpenEmbedding
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.IsIso
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
AlgebraicGeometry.PresheafedSpace.presheaf
AlgebraicGeometry.Scheme.Hom.stalkMap
AlgebraicGeometry.IsOpenImmersionCommRingCat.Colimits.hasColimits_commRingCat
AlgebraicGeometry.SheafedSpace.IsOpenImmersion.of_stalk_iso
CommRingCat.hasLimits
CommRingCat.forgetReflectIsos
CommRingCat.forget_preservesLimits
CommRingCat.FilteredColimits.forget_preservesFilteredColimits
of_isLocalization 📖mathematicalAlgebraicGeometry.IsOpenImmersion
AlgebraicGeometry.Spec
CommRingCat.of
AlgebraicGeometry.Spec.map
CommRingCat.ofHom
algebraMap
CommRing.toCommSemiring
CommSemiring.toSemiring
AlgHomClass.toRingHomClass
AlgHom.algHomClass
Localization.isLocalization
AlgHom.comp_algebraMap
CommRingCat.ofHom_comp
AlgebraicGeometry.Spec.map_comp
CategoryTheory.Iso.isIso_inv
AlgEquivClass.toAlgHomClass
AlgEquiv.instAlgEquivClass
comp
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.of_isIso
AlgebraicGeometry.Scheme.Hom.isIso_toLRSHom
AlgebraicGeometry.instIsIsoSchemeMapOfCommRingCat
AlgebraicGeometry.Scheme.instIsOpenImmersionMapOfHomAwayAlgebraMap
of_stalk_iso 📖mathematicalTopology.IsOpenEmbedding
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.IsIso
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
AlgebraicGeometry.PresheafedSpace.presheaf
AlgebraicGeometry.Scheme.Hom.stalkMap
AlgebraicGeometry.IsOpenImmersionof_isIso_stalkMap
opensEquiv_apply_coe 📖mathematicalAlgebraicGeometry.Scheme.Opens
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
AlgebraicGeometry.Scheme.Hom.opensRange
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
opensEquiv
CategoryTheory.Functor.obj
Preorder.smallCategory
AlgebraicGeometry.Scheme.Hom.opensFunctor
opensEquiv_symm_apply 📖mathematicalDFunLike.coe
Equiv
AlgebraicGeometry.Scheme.Opens
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
AlgebraicGeometry.Scheme.Hom.opensRange
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
opensEquiv
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
opensRange_pullback_fst_of_right 📖mathematicalAlgebraicGeometry.Scheme.Hom.opensRange
CategoryTheory.Limits.pullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
hasPullback_of_right
CategoryTheory.Limits.pullback.fst
instFstScheme
CategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.Scheme.Hom.opensRange_pullbackFst
opensRange_pullback_snd_of_left 📖mathematicalAlgebraicGeometry.Scheme.Hom.opensRange
CategoryTheory.Limits.pullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
hasPullback_of_left
CategoryTheory.Limits.pullback.snd
instSndScheme
CategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.Scheme.Hom.opensRange_pullbackSnd
range_pullbackFst 📖mathematicalSet.range
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
CategoryTheory.Limits.pullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
hasPullback_of_right
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.Limits.pullback.fst
SetLike.coe
AlgebraicGeometry.Scheme.Opens
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.Scheme.Hom.opensRange
hasPullback_of_right
CategoryTheory.Limits.hasLimitOfHasLimitsOfShape
CategoryTheory.Limits.hasLimitsOfShape_widePullbackShape
Finite.of_fintype
CategoryTheory.Limits.hasFiniteWidePullbacks_of_hasFiniteLimits
CategoryTheory.Limits.hasFiniteLimits_of_hasLimits
TopCat.topCat_hasLimits
instPreservesLimitSchemeTopCatWalkingCospanCospanForgetToTop_1
CategoryTheory.Limits.PreservesPullback.iso_hom_fst
TopCat.coe_comp
Set.range_comp
Set.range_eq_univ
TopCat.epi_iff_surjective
CategoryTheory.epi_of_effectiveEpi
CategoryTheory.instEffectiveEpiOfIsIso
CategoryTheory.Iso.isIso_hom
Set.preimage_univ
TopCat.pullback_fst_image_snd_preimage
Set.image_univ
range_pullbackSnd 📖mathematicalSet.range
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
CategoryTheory.Limits.pullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
hasPullback_of_left
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.Limits.pullback.snd
SetLike.coe
AlgebraicGeometry.Scheme.Opens
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.Scheme.Hom.opensRange
hasPullback_of_left
CategoryTheory.Limits.hasLimitOfHasLimitsOfShape
CategoryTheory.Limits.hasLimitsOfShape_widePullbackShape
Finite.of_fintype
CategoryTheory.Limits.hasFiniteWidePullbacks_of_hasFiniteLimits
CategoryTheory.Limits.hasFiniteLimits_of_hasLimits
TopCat.topCat_hasLimits
instPreservesLimitSchemeTopCatWalkingCospanCospanForgetToTop
CategoryTheory.Limits.PreservesPullback.iso_hom_snd
TopCat.coe_comp
Set.range_comp
Set.range_eq_univ
TopCat.epi_iff_surjective
CategoryTheory.epi_of_effectiveEpi
CategoryTheory.instEffectiveEpiOfIsIso
CategoryTheory.Iso.isIso_hom
Set.preimage_univ
TopCat.pullback_snd_image_fst_preimage
Set.image_univ
range_pullback_fst_of_right 📖mathematicalSet.range
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
CategoryTheory.Limits.pullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
hasPullback_of_right
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.Limits.pullback.fst
SetLike.coe
AlgebraicGeometry.Scheme.Opens
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.Scheme.Hom.opensRange
range_pullbackFst
range_pullback_snd_of_left 📖mathematicalSet.range
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
CategoryTheory.Limits.pullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
hasPullback_of_left
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.Limits.pullback.snd
SetLike.coe
AlgebraicGeometry.Scheme.Opens
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.Scheme.Hom.opensRange
range_pullbackSnd
range_pullback_to_base_of_left 📖mathematicalSet.range
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
CategoryTheory.Limits.pullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
hasPullback_of_left
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.pullback.fst
Set
Set.instInter
hasPullback_of_left
CategoryTheory.Limits.pullback.condition
AlgebraicGeometry.Scheme.Hom.comp_base
TopCat.coe_comp
Set.range_comp
range_pullbackSnd
IsOpen.preimage
ContinuousMap.continuous
TopologicalSpace.Opens.is_open'
TopologicalSpace.Opens.map_obj
Set.image_preimage_eq_inter_range
TopologicalSpace.Opens.carrier_eq_coe
AlgebraicGeometry.Scheme.Hom.coe_opensRange
range_pullback_to_base_of_right 📖mathematicalSet.range
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
CategoryTheory.Limits.pullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
hasPullback_of_right
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Limits.pullback.fst
Set
Set.instInter
hasPullback_of_right
AlgebraicGeometry.Scheme.Hom.comp_base
TopCat.coe_comp
Set.range_comp
range_pullbackFst
IsOpen.preimage
ContinuousMap.continuous
TopologicalSpace.Opens.is_open'
TopologicalSpace.Opens.map_obj
Set.image_preimage_eq_inter_range
Set.inter_comm
TopologicalSpace.Opens.carrier_eq_coe
AlgebraicGeometry.Scheme.Hom.coe_opensRange
to_iso 📖mathematicalCategoryTheory.IsIso
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
isIso
ΓIso_inv 📖mathematicalCategoryTheory.Iso.inv
CommRingCat
CommRingCat.instCategory
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.Scheme.Hom.opensRange
ΓIso
AlgebraicGeometry.Scheme.Hom.appLE
LE.le.trans
Eq.ge
AlgebraicGeometry.Scheme.Hom.preimage_image_eq
CategoryTheory.eqToHom_op
AlgebraicGeometry.Scheme.Hom.appIso_hom'
AlgebraicGeometry.Scheme.Hom.map_appLE

AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion

Definitions

NameCategoryTheorems
scheme 📖CompOp

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion

Definitions

NameCategoryTheorems
toScheme 📖CompOp
4 mathmath: toScheme_toLocallyRingedSpace, scheme_toScheme, toSchemeHom_toPshHom, toSchemeHom_isOpenImmersion
toSchemeHom 📖CompOp
2 mathmath: toSchemeHom_toPshHom, toSchemeHom_isOpenImmersion

Theorems

NameKindAssumesProvesValidatesDepends On
scheme_eq_of_locallyRingedSpace_eq 📖AlgebraicGeometry.Scheme.toLocallyRingedSpaceTopologicalSpace.OpenNhds.isOpenEmbedding
scheme_toScheme 📖mathematicaltoScheme
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.PresheafedSpace.Hom.toPshHom
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.instIsOpenImmersionCommRingCatOfIsOpenImmersion
scheme_eq_of_locallyRingedSpace_eq
AlgebraicGeometry.instIsOpenImmersionCommRingCatOfIsOpenImmersion
locallyRingedSpace_toLocallyRingedSpace
toSchemeHom_isOpenImmersion 📖mathematicalAlgebraicGeometry.IsOpenImmersion
toScheme
toSchemeHom
toSchemeHom_toPshHom 📖mathematicalAlgebraicGeometry.PresheafedSpace.Hom.toPshHom
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
toScheme
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
toSchemeHom
toScheme_toLocallyRingedSpace 📖mathematicalAlgebraicGeometry.Scheme.toLocallyRingedSpace
toScheme
toLocallyRingedSpace

AlgebraicGeometry.Scheme

Definitions

NameCategoryTheorems
ofRestrict 📖CompOp
6 mathmath: ofRestrict_appIso, ofRestrict_toLRSHom_base, ofRestrict_toLRSHom_c_app, restrict_presheaf_map, AlgebraicGeometry.IsOpenImmersion.ofRestrict, ofRestrict_app
restrict 📖CompOp
9 mathmath: ofRestrict_appIso, restrict_toPresheafedSpace, ofRestrict_toLRSHom_base, restrict_presheaf_obj, ofRestrict_toLRSHom_c_app, restrict_presheaf_map, restrict_carrier, AlgebraicGeometry.IsOpenImmersion.ofRestrict, ofRestrict_app
stalkMapIsoOfIsPullback 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
basic_open_isOpenImmersion 📖mathematicalAlgebraicGeometry.IsOpenImmersion
AlgebraicGeometry.Spec
CommRingCat.of
Localization.Away
CommRingCat.carrier
CommRing.toCommMonoid
CommRingCat.commRing
OreLocalization.instCommRing
Submonoid.powers
CommMonoid.toMonoid
OreLocalization.oreSetComm
AlgebraicGeometry.Spec.map
CommRingCat.ofHom
algebraMap
CommRing.toCommSemiring
OreLocalization.instSemiring
Ring.toSemiring
CommRing.toRing
OreLocalization.instAlgebra
Algebra.id
isOpenImmersion_SpecMap_localizationAway
exists_affine_mem_range_and_range_subset 📖mathematicalTopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
Opens
SetLike.instMembership
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
AlgebraicGeometry.IsOpenImmersion
AlgebraicGeometry.Spec
Set
Set.instMembership
Set.range
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
Hom.toLRSHom'
Set.instHasSubset
SetLike.coe
TopologicalSpace.OpenNhds.isOpenEmbedding
local_affine
CategoryTheory.Iso.hom_inv_id
TopologicalSpace.IsTopologicalBasis.exists_subset_of_mem_open
PrimeSpectrum.isBasis_basic_opens
TopologicalSpace.Opens.is_open'
AlgebraicGeometry.IsOpenImmersion.comp
isOpenImmersion_SpecMap_localizationAway
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.comp
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.of_isIso
CategoryTheory.Iso.isIso_inv
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.ofRestrict
Hom.comp_base
TopCat.coe_comp
Set.range_comp
PrimeSpectrum.localization_away_comap_range
Localization.isLocalization
Set.image_subset_iff
image_basicOpen 📖mathematicalCategoryTheory.Functor.obj
Opens
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
Hom.opensFunctor
basicOpen
DFunLike.coe
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
CommRingCat.carrier
CategoryTheory.ConcreteCategory.hom
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
RingHom.instFunLike
CommRingCat.instConcreteCategoryRingHomCarrier
CategoryTheory.Iso.inv
Hom.appIso
preimage_basicOpen
inf_eq_right
LE.le.trans
basicOpen_le
Eq.ge
Hom.preimage_image_eq
basicOpen_res
Hom.appIso_inv_app_apply
Hom.image_preimage_eq_opensRange_inf
Set.Subset.trans
Set.image_subset_range
image_zeroLocus 📖mathematicalSet.image
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
Hom.toLRSHom'
zeroLocus
Set
Set.instInter
CategoryTheory.Functor.obj
Opens
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
Hom.opensFunctor
CommRingCat.carrier
Opposite
TopologicalSpace.Opens
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
RingHom.instFunLike
CommRingCat.Hom.hom
CategoryTheory.Iso.inv
Hom.appIso
Set.range
Set.ext
Set.image_congr
Function.Injective.mem_set_image
Topology.IsEmbedding.injective
Topology.IsOpenEmbedding.toIsEmbedding
Hom.isOpenEmbedding
Set.image_subset_range
instIsOpenImmersionMapOfHomAwayAlgebraMap 📖mathematicalAlgebraicGeometry.IsOpenImmersion
AlgebraicGeometry.Spec
CommRingCat.of
Localization.Away
CommRing.toCommMonoid
OreLocalization.instCommRing
Submonoid.powers
CommMonoid.toMonoid
OreLocalization.oreSetComm
AlgebraicGeometry.Spec.map
CommRingCat.ofHom
algebraMap
CommRing.toCommSemiring
OreLocalization.instSemiring
Ring.toSemiring
CommRing.toRing
OreLocalization.instAlgebra
Algebra.id
isOpenImmersion_SpecMap_localizationAway
isOpenImmersion_SpecMap_localizationAway 📖mathematicalAlgebraicGeometry.IsOpenImmersion
AlgebraicGeometry.Spec
CommRingCat.of
Localization.Away
CommRingCat.carrier
CommRing.toCommMonoid
CommRingCat.commRing
OreLocalization.instCommRing
Submonoid.powers
CommMonoid.toMonoid
OreLocalization.oreSetComm
AlgebraicGeometry.Spec.map
CommRingCat.ofHom
algebraMap
CommRing.toCommSemiring
OreLocalization.instSemiring
Ring.toSemiring
CommRing.toRing
OreLocalization.instAlgebra
Algebra.id
AlgebraicGeometry.SheafedSpace.IsOpenImmersion.of_stalk_iso
CommRingCat.hasLimits
CommRingCat.Colimits.hasColimits_commRingCat
CommRingCat.forgetReflectIsos
CommRingCat.forget_preservesLimits
CommRingCat.FilteredColimits.forget_preservesFilteredColimits
AlgebraicGeometry.isIso_SpecMap_stakMap_localization
PrimeSpectrum.localization_away_isOpenEmbedding
Localization.isLocalization
ofRestrict_app 📖mathematicalTopology.IsOpenEmbedding
TopCat.carrier
TopCat.of
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopCat.str
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
Hom.app
restrict
ofRestrict
CategoryTheory.Functor.map
Opposite
TopologicalSpace.Opens
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
CategoryTheory.Functor.obj
CategoryTheory.Functor.id
CategoryTheory.Functor.comp
TopologicalSpace.Opens.map
IsOpenMap.functor
Topology.IsOpenEmbedding.isOpenMap
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.NatTrans.app
CategoryTheory.Adjunction.counit
IsOpenMap.adjunction
ofRestrict_appIso 📖mathematicalTopology.IsOpenEmbedding
TopCat.carrier
TopCat.of
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopCat.str
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
Hom.appIso
restrict
ofRestrict
AlgebraicGeometry.IsOpenImmersion.ofRestrict
CategoryTheory.Iso.refl
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
Hom.opensFunctor
CategoryTheory.Iso.ext
AlgebraicGeometry.IsOpenImmersion.ofRestrict
Eq.ge
Hom.preimage_image_eq
Hom.appIso_hom'
ofRestrict_appLE
CategoryTheory.Functor.map_id
ofRestrict_appLE 📖mathematicalTopology.IsOpenEmbedding
TopCat.carrier
TopCat.of
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopCat.str
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
Opens
restrict
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
Hom.toLRSHom'
ofRestrict
Hom.appLE
CategoryTheory.Functor.map
Opposite
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Hom.opensFunctor
AlgebraicGeometry.IsOpenImmersion.ofRestrict
Opposite.unop
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.homOfLE
AlgebraicGeometry.IsOpenImmersion.ofRestrict
Topology.IsOpenEmbedding.isOpenMap
CategoryTheory.Functor.map_comp
ofRestrict_toLRSHom_base 📖mathematicalTopology.IsOpenEmbedding
TopCat.carrier
TopCat.of
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopCat.str
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.restrict
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
Hom.toLRSHom
restrict
ofRestrict
ofRestrict_toLRSHom_c_app 📖mathematicalTopology.IsOpenEmbedding
TopCat.carrier
TopCat.of
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopCat.str
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
CategoryTheory.NatTrans.app
Opposite
TopologicalSpace.Opens
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
CategoryTheory.Functor.obj
TopCat.Presheaf
AlgebraicGeometry.PresheafedSpace.restrict
TopCat.instCategoryPresheaf
TopCat.Presheaf.pushforward
AlgebraicGeometry.PresheafedSpace.Hom.c
AlgebraicGeometry.LocallyRingedSpace.restrict
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
Hom.toLRSHom
restrict
ofRestrict
CategoryTheory.Functor.map
Opposite.op
IsOpenMap.functor
TopologicalSpace.Opens.map
Opposite.unop
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.comp
CategoryTheory.Functor.id
CategoryTheory.Adjunction.counit
IsOpenMap.adjunction
restrict_carrier 📖mathematicalTopology.IsOpenEmbedding
TopCat.carrier
TopCat.of
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopCat.str
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
restrict
restrict_presheaf_map 📖mathematicalTopology.IsOpenEmbedding
TopCat.carrier
TopCat.of
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopCat.str
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
CategoryTheory.Functor.map
Opposite
TopologicalSpace.Opens
restrict
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
CategoryTheory.Functor.obj
Hom.opensFunctor
ofRestrict
AlgebraicGeometry.IsOpenImmersion.ofRestrict
Opposite.unop
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.homOfLE
restrict_presheaf_obj 📖mathematicalTopology.IsOpenEmbedding
TopCat.carrier
TopCat.of
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopCat.str
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
restrict
Opposite.op
IsOpenMap.functor
Opposite.unop
restrict_toPresheafedSpace 📖mathematicalTopology.IsOpenEmbedding
TopCat.carrier
TopCat.of
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopCat.str
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
restrict
AlgebraicGeometry.PresheafedSpace.restrict

AlgebraicGeometry.Scheme.Hom

Definitions

NameCategoryTheorems
appIso 📖CompOp
27 mathmath: AlgebraicGeometry.Scheme.ofRestrict_appIso, app_invApp'_assoc, AlgebraicGeometry.Scheme.ker_ideal_of_isPullback_of_isOpenImmersion, app_appIso_inv_assoc, appIso_inv_app_presheafMap, AlgebraicGeometry.Scheme.IdealSheafData.ideal_comap_of_isOpenImmersion, appIso_inv_app, AlgebraicGeometry.Scheme.Opens.ι_appIso, appIso_inv_naturality, appIso_hom', appLE_appIso_inv, app_invApp', AlgebraicGeometry.Scheme.image_basicOpen, appIso_inv_naturality_assoc, comp_appIso, appIso_inv_appLE_assoc, appIso_inv_app_assoc, id_appIso, appLE_appIso_inv_assoc, AlgebraicGeometry.IsOpenImmersion.app_eq_appIso_inv_app_of_comp_eq, appIso_hom, appLE_appIso_inv_apply, appIso_inv_app_apply, AlgebraicGeometry.Scheme.image_zeroLocus, app_appIso_inv, AlgebraicGeometry.IsOpenImmersion.lift_app, appIso_inv_appLE
opensFunctor 📖CompOp
111 mathmath: AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen, AlgebraicGeometry.Γ_map_morphismRestrict, image_preimage_eq_opensRange_inter, AlgebraicGeometry.Scheme.ofRestrict_appIso, app_invApp'_assoc, instIsContinuousOpensOpensFunctorGrothendieckTopologyCarrierCarrierCommRingCat, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_counit_app_app, AlgebraicGeometry.Scheme.Opens.mem_ι_image_iff, AlgebraicGeometry.Scheme.Opens.topIso_inv, opensFunctor_map_homOfLE, AlgebraicGeometry.image_morphismRestrict_preimage, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_inv_app, image_le_image_of_le, image_preimage_le, image_top_eq_opensRange, AlgebraicGeometry.Scheme.ker_ideal_of_isPullback_of_isOpenImmersion, image_preimage_eq_opensRange_inf, image_iSup₂, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv, AlgebraicGeometry.Scheme.ofRestrict_appLE, AlgebraicGeometry.IsAffineOpen.isoSpec_inv, app_appIso_inv_assoc, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_hom_app, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen_topIso_inv, AlgebraicGeometry.Scheme.ι_image_homOfLE_le_ι_image, preimage_image_eq, AlgebraicGeometry.Scheme.Opens.toScheme_presheaf_obj, AlgebraicGeometry.liftCoborder_app, AlgebraicGeometry.morphismRestrict_appLE, appIso_inv_app_presheafMap, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_hom_app_app, apply_mem_image_iff, AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_inv_app_app, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv_assoc, AlgebraicGeometry.Scheme.Modules.restrict_map, image_mono, AlgebraicGeometry.Scheme.IdealSheafData.ideal_comap_of_isOpenImmersion, appIso_inv_app, liftCoborder_preimage, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_inv_app_app, AlgebraicGeometry.affineOpensRestrict_apply_coe_coe, AlgebraicGeometry.Scheme.Opens.ι_appIso, appIso_inv_naturality, appIso_hom', AlgebraicGeometry.Scheme.homOfLE_appTop, AlgebraicGeometry.IsOpenImmersion.opensEquiv_apply_coe, appLE_appIso_inv, isAffineOpen_iff_of_isOpenImmersion, app_invApp', AlgebraicGeometry.Scheme.image_basicOpen, AlgebraicGeometry.IsAffineOpen.image_of_isOpenImmersion, AlgebraicGeometry.Scheme.Modules.restrictFunctorCongr_hom_app_app, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_inv_app_app, AlgebraicGeometry.morphismRestrict_app', appIso_inv_naturality_assoc, comp_appIso, appIso_inv_app_assoc, AlgebraicGeometry.Scheme.Opens.ι_appTop, map_mem_image_iff, AlgebraicGeometry.Scheme.map_basicOpen, AlgebraicGeometry.IsOpenImmersion.affineOpensEquiv_apply_coe_coe, id_appIso, appLE_appIso_inv_assoc, image_iSup, AlgebraicGeometry.Scheme.homOfLE_app, AlgebraicGeometry.Scheme.homOfLE_appLE, AlgebraicGeometry.morphismRestrict_appTop, AlgebraicGeometry.IsOpenImmersion.app_eq_appIso_inv_app_of_comp_eq, isoImage_inv_ι, isoImage_inv_ι_assoc, instIsIsoCommRingCatAppObjOpensOpensFunctor, AlgebraicGeometry.Scheme.ker_morphismRestrict_ideal, AlgebraicGeometry.Scheme.Modules.restrict_obj, AlgebraicGeometry.Scheme.Modules.restrictAdjunction_unit_app_app, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom_assoc, coe_image, AlgebraicGeometry.Scheme.Opens.toScheme_presheaf_map, resLE_preimage, le_preimage_resLE_iff, appIso_hom, image_le_opensRange, appLE_appIso_inv_apply, AlgebraicGeometry.Scheme.Opens.ι_app_self, image_injective, AlgebraicGeometry.Scheme.restrict_presheaf_map, AlgebraicGeometry.IsOpenImmersion.image_preimage_eq_preimage_image_of_isPullback, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen', AlgebraicGeometry.Scheme.map_basicOpen_map, AlgebraicGeometry.IsAffineOpen.fromSpec_image_basicOpen, AlgebraicGeometry.Scheme.Opens.ι_image_le, AlgebraicGeometry.Scheme.Opens.ι_appLE, comp_image, resLE_appLE, AlgebraicGeometry.Scheme.Opens.ι_app, isoImage_hom_ι, inv_image, opensRange_comp, appIso_inv_app_apply, AlgebraicGeometry.morphismRestrict_app, AlgebraicGeometry.Scheme.Opens.ι_image_top, AlgebraicGeometry.Scheme.Modules.restrictFunctorId_hom_app_app, AlgebraicGeometry.Scheme.image_zeroLocus, isoImage_hom_ι_assoc, AlgebraicGeometry.Scheme.Opens.topIso_hom, image_le_image_iff, app_appIso_inv, AlgebraicGeometry.IsOpenImmersion.app_eq_invApp_app_of_comp_eq_aux, le_resLE_preimage_iff, AlgebraicGeometry.IsOpenImmersion.lift_app, id_image
opensRange 📖CompOp
58 mathmath: opensRange_pullbackSnd, image_preimage_eq_opensRange_inter, mem_opensRange, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.toBase_preimage_eq_opensRange_ι, AlgebraicGeometry.IsAffineOpen.opensRange_fromSpec, image_top_eq_opensRange, fromNormalization_preimage, image_preimage_eq_opensRange_inf, AlgebraicGeometry.IsOpenImmersion.range_pullbackSnd, AlgebraicGeometry.isAffineOpen_opensRange, AlgebraicGeometry.IsOpenImmersion.range_pullback_fst_of_right, AlgebraicGeometry.Scheme.Opens.opensRange_ι, AlgebraicGeometry.Scheme.opensRange_homOfLE, AlgebraicGeometry.coe_opensRestrict_symm_apply, AlgebraicGeometry.Scheme.OpenCover.isOpenCover_opensRange, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_assoc, isoOpensRange_hom_ι_assoc, isoOpensRange_hom_ι, AlgebraicGeometry.Scheme.IsLocallyDirected.homOfLE_tAux, AlgebraicGeometry.Scheme.OpenCover.iSup_opensRange, opensRange_pullbackFst, AlgebraicGeometry.disjoint_opensRange_sigmaι, AlgebraicGeometry.IsOpenImmersion.opensEquiv_apply_coe, appLE_appIso_inv, AlgebraicGeometry.IsOpenImmersion.opensEquiv_symm_apply, AlgebraicGeometry.IsOpenImmersion.affineOpensEquiv_apply_coe_coe, AlgebraicGeometry.Scheme.IdealSheafData.opensRange_subschemeCover_map, AlgebraicGeometry.Scheme.preimage_opensRange_toSpecΓ, appLE_appIso_inv_assoc, AlgebraicGeometry.Proj.opensRange_awayι, AlgebraicGeometry.Scheme.IdealSheafData.opensRange_glueDataObjMap, preimage_opensRange, AlgebraicGeometry.IsOpenImmersion.ΓIso_inv, AlgebraicGeometry.IsOpenImmersion.range_pullback_snd_of_left, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_assoc, AlgebraicGeometry.isCompl_opensRange_inl_inr, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv, AlgebraicGeometry.Scheme.AffineZariskiSite.opensRange_relativeGluingData_map, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_apply, image_le_opensRange, appLE_appIso_inv_apply, isoOpensRange_inv_comp_assoc, AlgebraicGeometry.IsOpenImmersion.opensRange_pullback_snd_of_left, AlgebraicGeometry.Scheme.IsLocallyDirected.exists_of_pullback_V_V, AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.opensRange_map, AlgebraicGeometry.IsOpenImmersion.opensRange_pullback_fst_of_right, AlgebraicGeometry.IsOpenImmersion.range_pullbackFst, opensRange_comp_of_isIso, opensRange_comp, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_hom, opensRange_of_isIso, AlgebraicGeometry.Scheme.IsLocallyDirected.homOfLE_tAux_assoc, AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.colimitDesc_preimage, isoOpensRange_inv_comp, coe_opensRange, AlgebraicGeometry.IsOpenImmersion.affineOpensEquiv_symm_apply_coe, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_apply

Theorems

NameKindAssumesProvesValidatesDepends On
appIso_hom 📖mathematicalCategoryTheory.Iso.hom
CommRingCat
CommRingCat.instCategory
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
appIso
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
app
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.eqToHom
preimage_image_eq
AlgebraicGeometry.instIsOpenImmersionCommRingCatOfIsOpenImmersion
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.instIsIsoInvApp
preimage_image_eq
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_invApp
CategoryTheory.eqToHom_op
appIso_hom' 📖mathematicalCategoryTheory.Iso.hom
CommRingCat
CommRingCat.instCategory
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
appIso
appLE
Eq.ge
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
preimage_image_eq
appIso_hom
appIso_inv_app 📖mathematicalCategoryTheory.CategoryStruct.comp
CommRingCat
CategoryTheory.Category.toCategoryStruct
CommRingCat.instCategory
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
CategoryTheory.Iso.inv
appIso
app
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.eqToHom
preimage_image_eq
AlgebraicGeometry.instIsOpenImmersionCommRingCatOfIsOpenImmersion
preimage_image_eq
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app
CategoryTheory.eqToHom_op
appIso_inv_appLE 📖mathematicalAlgebraicGeometry.Scheme.Opens
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.str
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
opensFunctor
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Opposite
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
CategoryTheory.Iso.inv
appIso
appLE
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.homOfLE
preimage_image_eq
appIso_inv_app_assoc
CategoryTheory.eqToHom_op
CategoryTheory.Functor.map_comp
appIso_inv_appLE_assoc 📖mathematicalAlgebraicGeometry.Scheme.Opens
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.str
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
opensFunctor
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Opposite
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
CategoryTheory.Iso.inv
appIso
appLE
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.homOfLE
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
appIso_inv_appLE
appIso_inv_app_apply 📖mathematicalDFunLike.coe
RingHom
CommRingCat.carrier
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
RingHom.instFunLike
CategoryTheory.ConcreteCategory.hom
CommRingCat.instConcreteCategoryRingHomCarrier
app
CategoryTheory.Iso.inv
appIso
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.eqToHom
preimage_image_eq
preimage_image_eq
CategoryTheory.comp_apply
Mathlib.Tactic.Elementwise.hom_elementwise
appIso_inv_app
appIso_inv_app_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CommRingCat
CategoryTheory.Category.toCategoryStruct
CommRingCat.instCategory
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
CategoryTheory.Iso.inv
appIso
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
app
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.eqToHom
preimage_image_eq
preimage_image_eq
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
appIso_inv_app
appIso_inv_app_presheafMap 📖mathematicalCategoryTheory.CategoryStruct.comp
CommRingCat
CategoryTheory.Category.toCategoryStruct
CommRingCat.instCategory
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
CategoryTheory.Iso.inv
appIso
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
app
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.eqToHom
preimage_image_eq
CategoryTheory.CategoryStruct.id
preimage_image_eq
appIso_inv_app_assoc
CategoryTheory.Functor.map_comp
CategoryTheory.Functor.map_id
appIso_inv_naturality 📖mathematicalCategoryTheory.CategoryStruct.comp
CommRingCat
CategoryTheory.Category.toCategoryStruct
CommRingCat.instCategory
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
CategoryTheory.Functor.map
CategoryTheory.Iso.inv
appIso
CategoryTheory.Functor.op
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturality
AlgebraicGeometry.instIsOpenImmersionCommRingCatOfIsOpenImmersion
appIso_inv_naturality_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CommRingCat
CategoryTheory.Category.toCategoryStruct
CommRingCat.instCategory
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
CategoryTheory.Functor.map
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
CategoryTheory.Iso.inv
appIso
CategoryTheory.Functor.op
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
appIso_inv_naturality
appLE_appIso_inv 📖mathematicalAlgebraicGeometry.Scheme.Opens
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.str
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Opposite
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
opensFunctor
appLE
CategoryTheory.Iso.inv
appIso
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.homOfLE
LE.le.trans
image_mono
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
opensRange
inf_le_right
image_preimage_eq_opensRange_inf
LE.le.trans
image_mono
inf_le_right
image_preimage_eq_opensRange_inf
Set.image_preimage_subset
CategoryTheory.Category.assoc
appIso_inv_naturality
app_appIso_inv_assoc
CategoryTheory.Functor.map_comp
appLE_appIso_inv_apply 📖mathematicalAlgebraicGeometry.Scheme.Opens
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.str
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
DFunLike.coe
RingHom
CommRingCat.carrier
Opposite
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
opensFunctor
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
RingHom.instFunLike
CategoryTheory.ConcreteCategory.hom
CommRingCat.instConcreteCategoryRingHomCarrier
CategoryTheory.Iso.inv
appIso
appLE
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.homOfLE
LE.le.trans
image_mono
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
opensRange
inf_le_right
image_preimage_eq_opensRange_inf
LE.le.trans
image_mono
inf_le_right
image_preimage_eq_opensRange_inf
CategoryTheory.comp_apply
Mathlib.Tactic.Elementwise.hom_elementwise
appLE_appIso_inv
appLE_appIso_inv_assoc 📖mathematicalAlgebraicGeometry.Scheme.Opens
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.str
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Opposite
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
appLE
opensFunctor
CategoryTheory.Iso.inv
appIso
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.homOfLE
LE.le.trans
image_mono
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
opensRange
inf_le_right
image_preimage_eq_opensRange_inf
LE.le.trans
image_mono
inf_le_right
image_preimage_eq_opensRange_inf
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
appLE_appIso_inv
app_appIso_inv 📖mathematicalCategoryTheory.CategoryStruct.comp
CommRingCat
CategoryTheory.Category.toCategoryStruct
CommRingCat.instCategory
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
opensFunctor
app
CategoryTheory.Iso.inv
appIso
CategoryTheory.Functor.map
Quiver.Hom.op
Set
CategoryTheory.CategoryStruct.toQuiver
OmegaCompletePartialOrder.toPartialOrder
CompleteLattice.instOmegaCompletePartialOrder
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
Set.image
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
Set.preimage
TopologicalSpace.Opens.carrier
CategoryTheory.homOfLE
Set.image_preimage_subset
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp
AlgebraicGeometry.instIsOpenImmersionCommRingCatOfIsOpenImmersion
app_appIso_inv_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CommRingCat
CategoryTheory.Category.toCategoryStruct
CommRingCat.instCategory
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
app
opensFunctor
CategoryTheory.Iso.inv
appIso
CategoryTheory.Functor.map
Quiver.Hom.op
Set
CategoryTheory.CategoryStruct.toQuiver
OmegaCompletePartialOrder.toPartialOrder
CompleteLattice.instOmegaCompletePartialOrder
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
Set.image
DFunLike.coe
ContinuousMap
ContinuousMap.instFunLike
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
TopCat.instConcreteCategoryContinuousMapCarrier
Set.preimage
TopologicalSpace.Opens.carrier
CategoryTheory.homOfLE
Set.image_preimage_subset
Set.image_preimage_subset
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
app_appIso_inv
app_invApp' 📖mathematicalAlgebraicGeometry.Scheme.Opens
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensRange
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
opensFunctor
app
CategoryTheory.Iso.inv
appIso
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.eqToHom
TopologicalSpace.Opens.ext
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp
AlgebraicGeometry.instIsOpenImmersionCommRingCatOfIsOpenImmersion
app_invApp'_assoc 📖mathematicalAlgebraicGeometry.Scheme.Opens
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensRange
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
app
opensFunctor
CategoryTheory.Iso.inv
appIso
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.eqToHom
TopologicalSpace.Opens.ext
TopologicalSpace.Opens.ext
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
app_invApp'
apply_mem_image_iff 📖mathematicalTopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.Scheme.Opens
SetLike.instMembership
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
CategoryTheory.Functor.obj
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
opensFunctor
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
Function.Injective.mem_set_image
Topology.IsEmbedding.injective
Topology.IsOpenEmbedding.toIsEmbedding
isOpenEmbedding
coe_image 📖mathematicalSetLike.coe
AlgebraicGeometry.Scheme.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
CategoryTheory.Functor.obj
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
opensFunctor
Set.image
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
coe_opensRange 📖mathematicalSetLike.coe
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopologicalSpace.Opens.instSetLike
opensRange
Set.range
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
comp_appIso 📖mathematicalappIso
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.IsOpenImmersion.comp
CategoryTheory.Iso.trans
CommRingCat
CommRingCat.instCategory
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
CategoryTheory.Functor.mapIso
CategoryTheory.Iso.op
CategoryTheory.eqToIso
CategoryTheory.Iso.ext
AlgebraicGeometry.IsOpenImmersion.comp
LE.le.trans
preimage_image_eq
le_rfl
appIso_hom
app_eq_appLE
CategoryTheory.eqToHom_op
appLE_map
appLE_comp_appLE
map_appLE
comp_image 📖mathematicalCategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.IsOpenImmersion.comp
TopologicalSpace.Opens.ext
AlgebraicGeometry.IsOpenImmersion.comp
Set.image_comp
id_appIso 📖mathematicalappIso
CategoryTheory.CategoryStruct.id
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.of_isIso
AlgebraicGeometry.Scheme.toLocallyRingedSpace
toLRSHom
isIso_toLRSHom
CategoryTheory.IsIso.id
CategoryTheory.Functor.mapIso
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
CategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
CategoryTheory.Iso.op
CategoryTheory.eqToIso
CategoryTheory.Iso.ext
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.of_isIso
isIso_toLRSHom
CategoryTheory.IsIso.id
CommRingCat.hom_ext
RingHom.ext
preimage_image_eq
appIso_hom
CategoryTheory.eqToHom_op
CategoryTheory.Category.id_comp
id_image 📖mathematicalCategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
CategoryTheory.CategoryStruct.id
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.of_isIso
toLRSHom
isIso_toLRSHom
CategoryTheory.IsIso.id
TopologicalSpace.Opens.ext
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.of_isIso
isIso_toLRSHom
CategoryTheory.IsIso.id
Set.image_id
image_iSup 📖mathematicalCategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
TopologicalSpace.Opens.ext
Set.image_congr
TopologicalSpace.Opens.coe_iSup
Set.image_iUnion
isOpen_iUnion
TopologicalSpace.Opens.is_open'
image_iSup₂ 📖mathematicalCategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
TopologicalSpace.Opens.ext
isOpen_iUnion
TopologicalSpace.Opens.is_open'
TopologicalSpace.Opens.coe_iSup
Set.image_congr
Set.image_iUnion₂
image_injective 📖mathematicalAlgebraicGeometry.Scheme.Opens
CategoryTheory.Functor.obj
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
preimage_image_eq
image_le_image_iff 📖mathematicalAlgebraicGeometry.Scheme.Opens
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
CategoryTheory.Functor.obj
Preorder.smallCategory
opensFunctor
preimage_image_eq
preimage_mono
image_mono
image_le_image_of_le 📖mathematicalAlgebraicGeometry.Scheme.Opens
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
CategoryTheory.Functor.obj
Preorder.smallCategory
opensFunctor
image_mono
image_le_opensRange 📖mathematicalAlgebraicGeometry.Scheme.Opens
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
CategoryTheory.Functor.obj
Preorder.smallCategory
opensFunctor
opensRange
image_top_eq_opensRange
image_mono
le_top
image_mono 📖mathematicalAlgebraicGeometry.Scheme.Opens
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
CategoryTheory.Functor.obj
Preorder.smallCategory
opensFunctor
Set.image_mono
image_preimage_eq_opensRange_inf 📖mathematicalCategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
opensRange
TopologicalSpace.Opens.ext
Set.image_congr
Set.image_preimage_eq_range_inter
image_preimage_eq_opensRange_inter 📖mathematicalCategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
opensRange
image_preimage_eq_opensRange_inf
image_preimage_le 📖mathematicalAlgebraicGeometry.Scheme.Opens
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
CategoryTheory.Functor.obj
Preorder.smallCategory
opensFunctor
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
Eq.trans_le
image_preimage_eq_opensRange_inf
inf_le_right
image_top_eq_opensRange 📖mathematicalCategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
opensRange
TopologicalSpace.Opens.ext
Set.image_congr
Set.image_univ
instIsContinuousOpensOpensFunctorGrothendieckTopologyCarrierCarrierCommRingCat 📖mathematicalCategoryTheory.Functor.IsContinuous
AlgebraicGeometry.Scheme.Opens
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
Opens.grothendieckTopology
Topology.IsOpenEmbedding.functor_isContinuous
isOpenEmbedding
instIsIsoCommRingCatAppObjOpensOpensFunctor 📖mathematicalCategoryTheory.IsIso
CommRingCat
CommRingCat.instCategory
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
app
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.c_iso
AlgebraicGeometry.instIsOpenImmersionCommRingCatOfIsOpenImmersion
inv_image 📖mathematicalCategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
CategoryTheory.Iso.inv
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.of_isIso
toLRSHom
isIso_toLRSHom
CategoryTheory.Iso.isIso_inv
TopologicalSpace.Opens
TopCat.str
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
CategoryTheory.Iso.hom
TopologicalSpace.Opens.ext
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.of_isIso
isIso_toLRSHom
CategoryTheory.Iso.isIso_inv
Equiv.image_eq_preimage_symm
isIso_app 📖mathematicalAlgebraicGeometry.Scheme.Opens
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensRange
CategoryTheory.IsIso
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
app
TopologicalSpace.Opens.ext
Set.image_preimage_eq_of_subset
instIsIsoCommRingCatAppObjOpensOpensFunctor
isOpenEmbedding 📖mathematicalTopology.IsOpenEmbedding
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.base_open
map_mem_image_iff 📖mathematicalTopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.Scheme.Opens
SetLike.instMembership
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
CategoryTheory.Functor.obj
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
opensFunctor
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
apply_mem_image_iff
mem_opensRange 📖mathematicalTopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.Scheme.Opens
SetLike.instMembership
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensRange
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
TopCat.str
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
opensFunctor_map_homOfLE 📖mathematicalAlgebraicGeometry.Scheme.Opens
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
CategoryTheory.Functor.map
Preorder.smallCategory
opensFunctor
CategoryTheory.homOfLE
CategoryTheory.Functor.obj
image_mono
opensRange_comp 📖mathematicalopensRange
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.IsOpenImmersion.comp
CategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
TopologicalSpace.Opens.ext
AlgebraicGeometry.IsOpenImmersion.comp
Set.range_comp
opensRange_comp_of_isIso 📖mathematicalopensRange
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.IsOpenImmersion.comp
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.of_isIso
AlgebraicGeometry.Scheme.toLocallyRingedSpace
toLRSHom
isIso_toLRSHom
AlgebraicGeometry.IsOpenImmersion.comp
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.of_isIso
isIso_toLRSHom
opensRange_comp
opensRange_of_isIso
image_top_eq_opensRange
opensRange_of_isIso 📖mathematicalopensRange
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.of_isIso
AlgebraicGeometry.Scheme.toLocallyRingedSpace
toLRSHom
isIso_toLRSHom
Top.top
AlgebraicGeometry.Scheme.Opens
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
TopologicalSpace.Opens.ext
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.of_isIso
isIso_toLRSHom
Set.range_eq_univ
Homeomorph.surjective
opensRange_pullbackFst 📖mathematicalopensRange
CategoryTheory.Limits.pullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.IsOpenImmersion.hasPullback_of_right
CategoryTheory.Limits.pullback.fst
AlgebraicGeometry.IsOpenImmersion.instFstScheme
CategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
TopologicalSpace.Opens.ext
AlgebraicGeometry.IsOpenImmersion.hasPullback_of_right
AlgebraicGeometry.IsOpenImmersion.instFstScheme
AlgebraicGeometry.IsOpenImmersion.range_pullbackFst
opensRange_pullbackSnd 📖mathematicalopensRange
CategoryTheory.Limits.pullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.IsOpenImmersion.hasPullback_of_left
CategoryTheory.Limits.pullback.snd
AlgebraicGeometry.IsOpenImmersion.instSndScheme
CategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
TopologicalSpace.Opens.ext
AlgebraicGeometry.IsOpenImmersion.hasPullback_of_left
AlgebraicGeometry.IsOpenImmersion.instSndScheme
AlgebraicGeometry.IsOpenImmersion.range_pullbackSnd
preimage_image_eq 📖mathematicalCategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
opensFunctor
TopologicalSpace.Opens.ext
Set.image_congr
Set.preimage_image_eq
Topology.IsEmbedding.injective
Topology.IsOpenEmbedding.toIsEmbedding
isOpenEmbedding
preimage_opensRange 📖mathematicalCategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopCat.str
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
toLRSHom'
opensRange
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
Set.preimage_range
IsOpen.preimage
ContinuousMap.continuous

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