Documentation Verification Report

Basic

šŸ“ Source: Mathlib/AlgebraicGeometry/Morphisms/Basic.lean

Statistics

MetricCount
DefinitionsAffineTargetMorphismProperty, IsLocal, IsStableUnderBaseChange, of, toProperty, HasAffineProperty, IsLocalAtSource, IsLocalAtTarget, IsZariskiLocalAtSource, IsZariskiLocalAtTarget, targetAffineLocally
11
Theoremsof_basicOpenCover, respectsIso, to_basicOpen, mk, arrow_mk_iso_iff, cancel_left_of_respectsIso, cancel_right_of_respectsIso, ext, ext_iff, instIsLocalOfOfIsZariskiLocalAtTarget, respectsIso_mk, respectsIso_of, toProperty_apply, copy, eq_targetAffineLocally, eq_targetAffineLocally', iff, iff_of_iSup_eq_top, iff_of_isAffine, iff_of_openCover, instIsZariskiLocalAtTarget, instRespectsIsoScheme, instTargetAffineLocallyOfIsLocal, isLocal_affineProperty, isStableUnderBaseChange, isZariskiLocalAtSource, of_iSup_eq_top, of_isLocalAtTarget, of_isPullback, of_isZariskiLocalAtTarget, of_openCover, restrict, comp, iff_exists_resLE, iff_of_iSup_eq_top, iff_of_openCover, isLocalAtTarget, mk', of_iSup_eq_top, of_isOpenImmersion, of_openCover, resLE, respectsLeft_isOpenImmersion, sigmaDesc, iff_of_iSup_eq_top, iff_of_openCover, mk', of_iSup_eq_top, of_isPullback, of_openCover, of_range_subset_iSup, restrict, comp, iff_exists_resLE, iff_of_iSup_eq_top, iff_of_openCover, isZariskiLocalAtTarget, mk', of_iSup_eq_top, of_isOpenImmersion, of_openCover, resLE, respectsLeft_isOpenImmersion, sigmaDesc, coprodMap, iff_of_iSup_eq_top, iff_of_openCover, mk', of_forall_exists_morphismRestrict, of_forall_source_exists_preimage, of_iSup_eq_top, of_isPullback, of_openCover, of_range_subset_iSup, restrict, hasOfPostcompProperty_isOpenImmersion_of_morphismRestrict, instHasOfPostcompPropertySchemeIsOpenImmersionOfIsStableUnderBaseChange, instRespectsIsoSchemeTargetAffineLocallyOfToProperty, of_targetAffineLocally_of_isPullback
79
Total90

AlgebraicGeometry

Definitions

NameCategoryTheorems
AffineTargetMorphismProperty šŸ“–CompOp—
HasAffineProperty šŸ“–CompData
16 mathmath: instHasAffinePropertyIsAffineHomIsAffine, HasAffineProperty.instTargetAffineLocallyOfIsLocal, instHasAffinePropertyQuasiSeparatedQuasiSeparatedSpaceCarrierCarrierCommRingCat, HasAffineProperty.copy, HasRingHomProperty.HasAffineProperty, IsFinite.instHasAffinePropertyAndIsAffineFiniteCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTopHomAppTop, IsClosedImmersion.hasAffineProperty, HasAffineProperty.affineAnd_iff, HasAffineProperty.iff, IsIntegralHom.hasAffineProperty, instHasAffinePropertyIsomorphismsSchemeAndIsAffineIsIsoCommRingCatAppTop, HasAffineProperty.of_isZariskiLocalAtTarget, HasAffineProperty.of_isLocalAtTarget, IsSeparated.hasAffineProperty, instHasAffinePropertyQuasiCompactCompactSpaceCarrierCarrierCommRingCat, instHasAffinePropertyDiagonalSchemeDiagonal
IsLocalAtSource šŸ“–MathDef—
IsLocalAtTarget šŸ“–MathDef—
IsZariskiLocalAtSource šŸ“–MathDef
20 mathmath: instIsZariskiLocalAtSourceDiagonalSchemeOfHasOfPostcompPropertyOfRespectsRightIsOpenImmersion, HasRingHomProperty.instIsZariskiLocalAtSource, IsZariskiLocalAtSource.mk', instIsZariskiLocalAtSourceTopologicallyGeneralizingMap, topologically_isLocalAtSource, IsLocalIso.instIsZariskiLocalAtSource, IsLocalIso.eq_iInf, sourceLocalClosure.instIsZariskiLocalAtSourceIsOpenImmersionOfRespectsIsoOfRespectsLeftScheme, stalkwise_isZariskiLocalAtSource_of_respectsIso, SurjectiveOnStalks.instIsZariskiLocalAtSource, topologically_isZariskiLocalAtSource', topologically_isZariskiLocalAtSource, topologically_isLocalAtSource', UniversallyOpen.instIsZariskiLocalAtSource, IsLocalAtSource.mk', HasAffineProperty.isZariskiLocalAtSource, universally_isZariskiLocalAtSource, universally_isLocalAtSource, stalkwise_isLocalAtSource_of_respectsIso, instIsZariskiLocalAtSourceTopologicallyIsOpenMap
IsZariskiLocalAtTarget šŸ“–MathDef
39 mathmath: isClosedEmbedding_isZariskiLocalAtTarget, instIsZariskiLocalAtTargetGeometricallyOfIsClosedUnderIsomorphismsScheme, topologically_isZariskiLocalAtTarget', topologically_isZariskiLocalAtTarget, stalkwiseIsLocalAtTarget_of_respectsIso, instIsZariskiLocalAtTargetMonomorphismsScheme, HasAffineProperty.instIsZariskiLocalAtTarget, IsLocalAtSource.isLocalAtTarget, surjective_isZariskiLocalAtTarget, isOpenMap_isZariskiLocalAtTarget, isOpenEmbedding_isZariskiLocalAtTarget, injective_isZariskiLocalAtTarget, specializingMap_isZariskiLocalAtTarget, universallyInjective_isZariskiLocalAtTarget, IsImmersion.instIsZariskiLocalAtTarget, isClosedMap_isZariskiLocalAtTarget, universallyClosed_isZariskiLocalAtTarget, universally_isLocalAtTarget, SurjectiveOnStalks.instIsZariskiLocalAtTarget, stalkwiseIsZariskiLocalAtTarget_of_respectsIso, instIsZariskiLocalAtTargetStalkwiseBijectiveCoeRingHom, topologically_isLocalAtTarget, IsDominant.isZariskiLocalAtTarget, HasRingHomProperty.instIsZariskiLocalAtTarget, HasAffineProperty.iff, IsProper.instIsZariskiLocalAtTarget, IsClosedImmersion.isZariskiLocalAtTarget, IsZariskiLocalAtTarget.mk', universally_isZariskiLocalAtTarget, isOpenImmersion_isZariskiLocalAtTarget, UniversallyOpen.instIsZariskiLocalAtTarget, IsZariskiLocalAtSource.isZariskiLocalAtTarget, instIsZariskiLocalAtTargetTopologicallyGeneralizingMap, IsSeparated.instIsZariskiLocalAtTarget, instIsZariskiLocalAtTargetDiagonalScheme, IsPreimmersion.instIsZariskiLocalAtTarget, IsLocalAtTarget.mk', isEmbedding_isZariskiLocalAtTarget, topologically_isLocalAtTarget'
targetAffineLocally šŸ“–CompOp
9 mathmath: HasAffineProperty.instTargetAffineLocallyOfIsLocal, HasAffineProperty.eq_targetAffineLocally', targetAffineLocally_affineAnd_iff, targetAffineLocally_affineAnd_eq_affineLocally, instRespectsIsoSchemeTargetAffineLocallyOfToProperty, targetAffineLocally_affineAnd_iff', targetAffineLocally_affineAnd_le, targetAffineLocally_affineAnd_iff_affineLocally, HasAffineProperty.eq_targetAffineLocally

Theorems

NameKindAssumesProvesValidatesDepends On
hasOfPostcompProperty_isOpenImmersion_of_morphismRestrict šŸ“–mathematicalScheme.Opens.toScheme
CategoryTheory.Functor.obj
Scheme.Opens
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.carrier
PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
TopCat.str
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
PresheafedSpace.Hom.base
LocallyRingedSpace.Hom.toHom
Scheme.Hom.toLRSHom'
morphismRestrict
CategoryTheory.MorphismProperty.HasOfPostcompProperty
Scheme
Scheme.instCategory
IsOpenImmersion
—Scheme.Hom.preimage_opensRange
Scheme.Opens.instIsOpenImmersionι
Scheme.Opens.range_ι
CategoryTheory.cancel_mono
IsOpenImmersion.mono
CategoryTheory.Category.assoc
IsOpenImmersion.isoOfRangeEq_hom_fac
morphismRestrict_ι
Scheme.isoOfEq_inv_ι_assoc
Scheme.toIso_inv_ι_assoc
CategoryTheory.MorphismProperty.cancel_left_of_respectsIso
CategoryTheory.Iso.isIso_inv
CategoryTheory.MorphismProperty.cancel_right_of_respectsIso
CategoryTheory.Iso.isIso_hom
instHasOfPostcompPropertySchemeIsOpenImmersionOfIsStableUnderBaseChange šŸ“–mathematical—CategoryTheory.MorphismProperty.HasOfPostcompProperty
Scheme
Scheme.instCategory
IsOpenImmersion
—CategoryTheory.MorphismProperty.HasOfPostcompProperty.of_le
CategoryTheory.MorphismProperty.IsStableUnderBaseChange.hasOfPostcompProperty_monomorphisms
IsOpenImmersion.mono
instRespectsIsoSchemeTargetAffineLocallyOfToProperty šŸ“–mathematical—CategoryTheory.MorphismProperty.RespectsIso
Scheme
Scheme.instCategory
targetAffineLocally
—instIsAffineToSchemeValOpensMemSetAffineOpens
morphismRestrict_comp
AffineTargetMorphismProperty.cancel_left_of_respectsIso
instIsIsoSchemeMorphismRestrict
CategoryTheory.Iso.isIso_hom
IsAffineOpen.preimage_of_isIso
AffineTargetMorphismProperty.cancel_right_of_respectsIso
of_targetAffineLocally_of_isPullback šŸ“–ā€”CategoryTheory.IsPullback
Scheme
Scheme.instCategory
targetAffineLocally
——Scheme.Pullback.instHasPullback
AffineTargetMorphismProperty.cancel_left_of_respectsIso
AffineTargetMorphismProperty.IsLocal.respectsIso
CategoryTheory.Iso.isIso_inv
CategoryTheory.IsPullback.isoPullback_inv_snd
instIsAffineToSchemeValOpensMemSetAffineOpens
isAffineOpen_opensRange
IsOpenImmersion.hasPullback_of_right
IsAffine.of_isIso
CategoryTheory.Arrow.isIso_right
AffineTargetMorphismProperty.arrow_mk_iso_iff

AlgebraicGeometry.AffineTargetMorphismProperty

Definitions

NameCategoryTheorems
IsLocal šŸ“–CompData
6 mathmath: AlgebraicGeometry.affineAnd_isLocal, AlgebraicGeometry.affineAnd_isLocal_of_propertyIsLocal, AlgebraicGeometry.sourceAffineLocally_isLocal, AlgebraicGeometry.HasAffineProperty.diagonal_affineProperty_isLocal, AlgebraicGeometry.HasAffineProperty.isLocal_affineProperty, instIsLocalOfOfIsZariskiLocalAtTarget
IsStableUnderBaseChange šŸ“–MathDef
2 mathmath: IsStableUnderBaseChange.mk, AlgebraicGeometry.affineAnd_isStableUnderBaseChange
of šŸ“–CompOp
5 mathmath: AlgebraicGeometry.HasAffineProperty.iff, respectsIso_of, instIsLocalOfOfIsZariskiLocalAtTarget, AlgebraicGeometry.HasAffineProperty.of_isZariskiLocalAtTarget, AlgebraicGeometry.HasAffineProperty.of_isLocalAtTarget
toProperty šŸ“–CompOp
7 mathmath: IsLocal.respectsIso, AlgebraicGeometry.affineAnd_respectsIso, respectsIso_mk, toProperty_apply, AlgebraicGeometry.sourceAffineLocally_respectsIso, respectsIso_of, diagonal_respectsIso

Theorems

NameKindAssumesProvesValidatesDepends On
arrow_mk_iso_iff šŸ“–mathematical—AlgebraicGeometry.IsAffine.of_isIso
CategoryTheory.CommaMorphism.right
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Functor.id
CategoryTheory.Iso.inv
CategoryTheory.Arrow
CategoryTheory.instCategoryArrow
CategoryTheory.Arrow.isIso_right
CategoryTheory.Iso.isIso_inv
—AlgebraicGeometry.IsAffine.of_isIso
CategoryTheory.Arrow.isIso_right
CategoryTheory.Iso.isIso_inv
toProperty_apply
CategoryTheory.MorphismProperty.arrow_mk_iso_iff
cancel_left_of_respectsIso šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
—toProperty_apply
CategoryTheory.MorphismProperty.cancel_left_of_respectsIso
cancel_right_of_respectsIso šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
—toProperty_apply
CategoryTheory.MorphismProperty.cancel_right_of_respectsIso
ext šŸ“–ā€”ā€”ā€”ā€”ā€”
ext_iff šŸ“–ā€”ā€”ā€”ā€”ext
instIsLocalOfOfIsZariskiLocalAtTarget šŸ“–mathematical—IsLocal
of
—respectsIso_of
CategoryTheory.MorphismProperty.IsLocalAtTarget.toRespects
AlgebraicGeometry.Scheme.instHasPullbacksPrecoverageOfHasPullbacks
AlgebraicGeometry.Scheme.instHasPullbacksIsOpenImmersion
AlgebraicGeometry.IsZariskiLocalAtTarget.restrict
AlgebraicGeometry.IsZariskiLocalAtTarget.of_iSup_eq_top
AlgebraicGeometry.IsAffineOpen.iSup_basicOpen_eq_self_iff
AlgebraicGeometry.isAffineOpen_top
respectsIso_mk šŸ“–mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Iso.hom
AlgebraicGeometry.IsAffine.of_isIso
CategoryTheory.Iso.inv
CategoryTheory.Iso.isIso_inv
CategoryTheory.MorphismProperty.RespectsIso
toProperty
—AlgebraicGeometry.IsAffine.of_isIso
CategoryTheory.Iso.isIso_inv
respectsIso_of šŸ“–mathematical—CategoryTheory.MorphismProperty.RespectsIso
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
toProperty
of
—CategoryTheory.MorphismProperty.RespectsIso.precomp
CategoryTheory.Iso.isIso_hom
CategoryTheory.MorphismProperty.RespectsIso.postcomp
toProperty_apply šŸ“–mathematical—toProperty——

AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal

Theorems

NameKindAssumesProvesValidatesDepends On
of_basicOpenCover šŸ“–ā€”Ideal.span
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
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
SetLike.coe
Finset
Finset.instSetLike
Ideal
Submodule.instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
AlgebraicGeometry.Scheme.Opens.toScheme
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.Scheme.basicOpen
SetLike.instMembership
AlgebraicGeometry.morphismRestrict
AlgebraicGeometry.IsAffineOpen.instIsAffineToSchemeBasicOpen
———
respectsIso šŸ“–mathematical—CategoryTheory.MorphismProperty.RespectsIso
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.AffineTargetMorphismProperty.toProperty
——
to_basicOpen šŸ“–mathematical—AlgebraicGeometry.Scheme.Opens.toScheme
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.basicOpen
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
AlgebraicGeometry.morphismRestrict
AlgebraicGeometry.IsAffineOpen.instIsAffineToSchemeBasicOpen
——

AlgebraicGeometry.AffineTargetMorphismProperty.IsStableUnderBaseChange

Theorems

NameKindAssumesProvesValidatesDepends On
mk šŸ“–mathematicalCategoryTheory.Limits.pullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.Pullback.instHasPullback
CategoryTheory.Limits.pullback.fst
AlgebraicGeometry.AffineTargetMorphismProperty.IsStableUnderBaseChange—AlgebraicGeometry.Scheme.Pullback.instHasPullback
AlgebraicGeometry.AffineTargetMorphismProperty.cancel_left_of_respectsIso
CategoryTheory.Iso.isIso_inv
CategoryTheory.IsPullback.isoPullback_inv_fst

AlgebraicGeometry.HasAffineProperty

Theorems

NameKindAssumesProvesValidatesDepends On
copy šŸ“–mathematical—AlgebraicGeometry.HasAffineProperty—isLocal_affineProperty
eq_targetAffineLocally
eq_targetAffineLocally šŸ“–mathematical—AlgebraicGeometry.targetAffineLocally—eq_targetAffineLocally'
eq_targetAffineLocally' šŸ“–mathematical—AlgebraicGeometry.targetAffineLocally——
iff šŸ“–mathematical—AlgebraicGeometry.HasAffineProperty
AlgebraicGeometry.IsZariskiLocalAtTarget
AlgebraicGeometry.AffineTargetMorphismProperty.of
—instIsZariskiLocalAtTarget
AlgebraicGeometry.AffineTargetMorphismProperty.ext
iff_of_isAffine
of_isZariskiLocalAtTarget
iff_of_iSup_eq_top šŸ“–mathematicaliSup
AlgebraicGeometry.Scheme.Opens
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
Set
Set.instMembership
AlgebraicGeometry.Scheme.affineOpens
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
AlgebraicGeometry.Scheme.Opens.toScheme
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.str
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.morphismRestrict
AlgebraicGeometry.instIsAffineToSchemeValOpensMemSetAffineOpens
—AlgebraicGeometry.instIsAffineToSchemeValOpensMemSetAffineOpens
restrict
of_iSup_eq_top
iff_of_isAffine šŸ“–ā€”ā€”ā€”ā€”CategoryTheory.MorphismProperty.IsMultiplicative.toContainsIdentities
AlgebraicGeometry.isOpenImmersion_isMultiplicative
AlgebraicGeometry.isOpenImmersion_respectsIso
CategoryTheory.IsIso.id
AlgebraicGeometry.Scheme.instIsStableUnderBaseChangePrecoverageOfIsJointlySurjectivePreservingOfIsStableUnderBaseChange
AlgebraicGeometry.Scheme.instIsJointlySurjectivePreservingIsOpenImmersion
AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange
AlgebraicGeometry.Scheme.Pullback.instHasPullback
iff_of_openCover
CategoryTheory.Category.comp_id
CategoryTheory.Limits.pullback.condition
AlgebraicGeometry.AffineTargetMorphismProperty.cancel_left_of_respectsIso
AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal.respectsIso
isLocal_affineProperty
CategoryTheory.Limits.pullback_fst_iso_of_right_iso
iff_of_openCover šŸ“–mathematicalAlgebraicGeometry.IsAffine
CategoryTheory.PreZeroHypercover.X
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover
AlgebraicGeometry.Scheme.precoverage
AlgebraicGeometry.IsOpenImmersion
CategoryTheory.Precoverage.ZeroHypercover.pullback₁
AlgebraicGeometry.Scheme.instIsStableUnderBaseChangePrecoverageOfIsJointlySurjectivePreservingOfIsStableUnderBaseChange
AlgebraicGeometry.Scheme.instIsJointlySurjectivePreservingIsOpenImmersion
AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange
AlgebraicGeometry.Scheme.Pullback.instHasPullback
CategoryTheory.PreZeroHypercover.f
AlgebraicGeometry.Scheme.Cover.pullbackHom
—AlgebraicGeometry.Scheme.instIsStableUnderBaseChangePrecoverageOfIsJointlySurjectivePreservingOfIsStableUnderBaseChange
AlgebraicGeometry.Scheme.instIsJointlySurjectivePreservingIsOpenImmersion
AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange
AlgebraicGeometry.Scheme.Pullback.instHasPullback
AlgebraicGeometry.Scheme.instIsOpenImmersionF
AlgebraicGeometry.isAffineOpen_opensRange
AlgebraicGeometry.instIsAffineToSchemeValOpensMemSetAffineOpens
iff_of_iSup_eq_top
AlgebraicGeometry.Scheme.OpenCover.iSup_opensRange
AlgebraicGeometry.AffineTargetMorphismProperty.arrow_mk_iso_iff
AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal.respectsIso
isLocal_affineProperty
AlgebraicGeometry.IsOpenImmersion.hasPullback_of_right
instIsZariskiLocalAtTarget šŸ“–mathematical—AlgebraicGeometry.IsZariskiLocalAtTarget—AlgebraicGeometry.IsZariskiLocalAtTarget.mk'
instRespectsIsoScheme
eq_targetAffineLocally
AlgebraicGeometry.instIsAffineToSchemeValOpensMemSetAffineOpens
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
AlgebraicGeometry.IsAffine.of_isIso
CategoryTheory.Arrow.isIso_right
CategoryTheory.Iso.isIso_inv
AlgebraicGeometry.AffineTargetMorphismProperty.arrow_mk_iso_iff
AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal.respectsIso
isLocal_affineProperty
AlgebraicGeometry.IsOpenImmersion.ofRestrict
AlgebraicGeometry.IsAffineOpen.image_of_isOpenImmersion
of_openCover
AlgebraicGeometry.Scheme.isAffine_affineOpenCover
AlgebraicGeometry.Scheme.instIsStableUnderBaseChangePrecoverageOfIsJointlySurjectivePreservingOfIsStableUnderBaseChange
AlgebraicGeometry.Scheme.instIsJointlySurjectivePreservingIsOpenImmersion
AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange
AlgebraicGeometry.Scheme.Pullback.instHasPullback
AlgebraicGeometry.IsOpenImmersion.hasPullback_of_right
AlgebraicGeometry.Scheme.instIsOpenImmersionF
CategoryTheory.MorphismProperty.arrow_mk_iso_iff
AlgebraicGeometry.Scheme.Opens.opensRange_ι
AlgebraicGeometry.AffineTargetMorphismProperty.cancel_left_of_respectsIso
AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_pullbackHom
of_isPullback
CategoryTheory.IsPullback.of_hasPullback
instRespectsIsoScheme šŸ“–mathematical—CategoryTheory.MorphismProperty.RespectsIso
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
—eq_targetAffineLocally
AlgebraicGeometry.instRespectsIsoSchemeTargetAffineLocallyOfToProperty
AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal.respectsIso
isLocal_affineProperty
instTargetAffineLocallyOfIsLocal šŸ“–mathematical—AlgebraicGeometry.HasAffineProperty
AlgebraicGeometry.targetAffineLocally
——
isLocal_affineProperty šŸ“–mathematical—AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal——
isStableUnderBaseChange šŸ“–mathematicalAlgebraicGeometry.AffineTargetMorphismProperty.IsStableUnderBaseChangeCategoryTheory.MorphismProperty.IsStableUnderBaseChange
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
—CategoryTheory.MorphismProperty.IsStableUnderBaseChange.mk'
CategoryTheory.MorphismProperty.IsLocalAtTarget.toRespects
AlgebraicGeometry.Scheme.instHasPullbacksPrecoverageOfHasPullbacks
AlgebraicGeometry.Scheme.instHasPullbacksIsOpenImmersion
instIsZariskiLocalAtTarget
AlgebraicGeometry.Scheme.instIsStableUnderBaseChangePrecoverageOfIsJointlySurjectivePreservingOfIsStableUnderBaseChange
AlgebraicGeometry.Scheme.instIsJointlySurjectivePreservingIsOpenImmersion
AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange
AlgebraicGeometry.Scheme.Pullback.instHasPullback
CategoryTheory.Precoverage.ZeroHypercover.instHasPullbackFOfHasPullbacksPresieveā‚€_1
CategoryTheory.Precoverage.ZeroHypercover.instHasPullbacksPresieveā‚€OfHasPullbacks
CategoryTheory.MorphismProperty.iff_of_zeroHypercover_target
CategoryTheory.Limits.hasPullback_symmetry
CategoryTheory.Limits.hasPullbackHorizPaste
CategoryTheory.Category.comp_id
CategoryTheory.Category.id_comp
CategoryTheory.Limits.pullback.condition
CategoryTheory.Limits.pullback.map_isIso
CategoryTheory.IsIso.id
CategoryTheory.Category.assoc
CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_fst
CategoryTheory.Limits.limit.lift_Ļ€
CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_fst
CategoryTheory.Limits.pullbackSymmetry_hom_comp_fst
CategoryTheory.MorphismProperty.cancel_left_of_respectsIso
CategoryTheory.Iso.isIso_hom
AlgebraicGeometry.Scheme.isAffine_affineCover
CategoryTheory.Limits.pullbackSymmetry_hom_comp_snd
AlgebraicGeometry.AffineTargetMorphismProperty.cancel_left_of_respectsIso
AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal.respectsIso
isLocal_affineProperty
of_isPullback
AlgebraicGeometry.Scheme.instIsOpenImmersionF
CategoryTheory.IsPullback.of_hasPullback
isZariskiLocalAtSource šŸ“–mathematicalCategoryTheory.PreZeroHypercover.X
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover
AlgebraicGeometry.Scheme.precoverage
AlgebraicGeometry.IsOpenImmersion
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.PreZeroHypercover.f
AlgebraicGeometry.IsZariskiLocalAtSource—CategoryTheory.MorphismProperty.IsLocalAtSource.mk_of_iff
CategoryTheory.MorphismProperty.IsLocalAtTarget.toRespects
AlgebraicGeometry.Scheme.instHasPullbacksPrecoverageOfHasPullbacks
AlgebraicGeometry.Scheme.instHasPullbacksIsOpenImmersion
instIsZariskiLocalAtTarget
AlgebraicGeometry.IsZariskiLocalAtTarget.iff_of_iSup_eq_top
AlgebraicGeometry.iSup_affineOpens_eq_top
AlgebraicGeometry.instIsAffineToSchemeValOpensMemSetAffineOpens
AlgebraicGeometry.morphismRestrict_comp
of_iSup_eq_top šŸ“–ā€”iSup
AlgebraicGeometry.Scheme.Opens
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
Set
Set.instMembership
AlgebraicGeometry.Scheme.affineOpens
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
AlgebraicGeometry.Scheme.Opens.toScheme
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.str
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.morphismRestrict
AlgebraicGeometry.instIsAffineToSchemeValOpensMemSetAffineOpens
——AlgebraicGeometry.instIsAffineToSchemeValOpensMemSetAffineOpens
eq_targetAffineLocally
AlgebraicGeometry.of_affine_open_cover
AlgebraicGeometry.IsAffineOpen.instIsAffineToSchemeBasicOpen
AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal.to_basicOpen
isLocal_affineProperty
Topology.IsOpenEmbedding.isOpenMap
TopologicalSpace.Opens.isOpenEmbedding
TopologicalSpace.Opens.isOpenEmbedding_obj_top
AlgebraicGeometry.IsAffine.of_isIso
CategoryTheory.Arrow.isIso_right
CategoryTheory.Iso.isIso_inv
AlgebraicGeometry.AffineTargetMorphismProperty.arrow_mk_iso_iff
AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal.respectsIso
AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal.of_basicOpenCover
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
CategoryTheory.eqToHom_op
Finset.coe_image
RingHom.instRingHomClass
Ideal.map_top
Finset.mem_image
of_isLocalAtTarget šŸ“–mathematical—AlgebraicGeometry.HasAffineProperty
AlgebraicGeometry.AffineTargetMorphismProperty.of
—of_isZariskiLocalAtTarget
of_isPullback šŸ“–ā€”CategoryTheory.IsPullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
——AlgebraicGeometry.of_targetAffineLocally_of_isPullback
isLocal_affineProperty
eq_targetAffineLocally
of_isZariskiLocalAtTarget šŸ“–mathematical—AlgebraicGeometry.HasAffineProperty
AlgebraicGeometry.AffineTargetMorphismProperty.of
—AlgebraicGeometry.AffineTargetMorphismProperty.instIsLocalOfOfIsZariskiLocalAtTarget
CategoryTheory.MorphismProperty.ext
AlgebraicGeometry.instIsAffineToSchemeValOpensMemSetAffineOpens
AlgebraicGeometry.IsZariskiLocalAtTarget.restrict
CategoryTheory.MorphismProperty.of_zeroHypercover_target
AlgebraicGeometry.Scheme.instHasPullbacksPrecoverageOfHasPullbacks
AlgebraicGeometry.Scheme.instHasPullbacksIsOpenImmersion
CategoryTheory.Precoverage.instSmallOfSmall
AlgebraicGeometry.Scheme.instSmallPrecoverage
AlgebraicGeometry.of_targetAffineLocally_of_isPullback
CategoryTheory.Precoverage.ZeroHypercover.instHasPullbackFOfHasPullbacksPresieveā‚€_1
CategoryTheory.Precoverage.ZeroHypercover.instHasPullbacksPresieveā‚€OfHasPullbacks
AlgebraicGeometry.Scheme.isAffine_affineCover
AlgebraicGeometry.Scheme.instIsOpenImmersionF
CategoryTheory.IsPullback.of_hasPullback
of_openCover šŸ“–ā€”AlgebraicGeometry.IsAffine
CategoryTheory.PreZeroHypercover.X
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover
AlgebraicGeometry.Scheme.precoverage
AlgebraicGeometry.IsOpenImmersion
CategoryTheory.Precoverage.ZeroHypercover.pullback₁
AlgebraicGeometry.Scheme.instIsStableUnderBaseChangePrecoverageOfIsJointlySurjectivePreservingOfIsStableUnderBaseChange
AlgebraicGeometry.Scheme.instIsJointlySurjectivePreservingIsOpenImmersion
AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange
AlgebraicGeometry.Scheme.Pullback.instHasPullback
CategoryTheory.PreZeroHypercover.f
AlgebraicGeometry.Scheme.Cover.pullbackHom
——AlgebraicGeometry.Scheme.instIsStableUnderBaseChangePrecoverageOfIsJointlySurjectivePreservingOfIsStableUnderBaseChange
AlgebraicGeometry.Scheme.instIsJointlySurjectivePreservingIsOpenImmersion
AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange
AlgebraicGeometry.Scheme.Pullback.instHasPullback
of_iSup_eq_top
AlgebraicGeometry.Scheme.instIsOpenImmersionF
AlgebraicGeometry.isAffineOpen_opensRange
AlgebraicGeometry.Scheme.OpenCover.iSup_opensRange
AlgebraicGeometry.instIsAffineToSchemeValOpensMemSetAffineOpens
AlgebraicGeometry.IsOpenImmersion.hasPullback_of_right
AlgebraicGeometry.IsAffine.of_isIso
CategoryTheory.Arrow.isIso_right
CategoryTheory.Iso.isIso_inv
AlgebraicGeometry.AffineTargetMorphismProperty.arrow_mk_iso_iff
AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal.respectsIso
isLocal_affineProperty
restrict šŸ“–mathematical—AlgebraicGeometry.Scheme.Opens.toScheme
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'
Set
Set.instMembership
AlgebraicGeometry.Scheme.affineOpens
AlgebraicGeometry.morphismRestrict
AlgebraicGeometry.instIsAffineToSchemeValOpensMemSetAffineOpens
—of_isPullback
AlgebraicGeometry.instIsAffineToSchemeValOpensMemSetAffineOpens
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
CategoryTheory.IsPullback.flip
AlgebraicGeometry.isPullback_morphismRestrict

AlgebraicGeometry.IsLocalAtSource

Theorems

NameKindAssumesProvesValidatesDepends On
comp šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
—AlgebraicGeometry.IsZariskiLocalAtSource.comp
iff_exists_resLE šŸ“–mathematical—AlgebraicGeometry.Scheme.Opens.toScheme
AlgebraicGeometry.Scheme.Hom.resLE
—AlgebraicGeometry.IsZariskiLocalAtSource.iff_exists_resLE
iff_of_iSup_eq_top šŸ“–mathematicaliSup
AlgebraicGeometry.Scheme.Opens
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
AlgebraicGeometry.Scheme.Opens.toScheme
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.Opens.ι
—AlgebraicGeometry.IsZariskiLocalAtSource.iff_of_iSup_eq_top
iff_of_openCover šŸ“–mathematical—CategoryTheory.PreZeroHypercover.X
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover
AlgebraicGeometry.Scheme.precoverage
AlgebraicGeometry.IsOpenImmersion
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.PreZeroHypercover.f
—AlgebraicGeometry.IsZariskiLocalAtSource.iff_of_openCover
isLocalAtTarget šŸ“–mathematical—AlgebraicGeometry.IsZariskiLocalAtTarget—AlgebraicGeometry.IsZariskiLocalAtSource.isZariskiLocalAtTarget
mk' šŸ“–mathematicalAlgebraicGeometry.Scheme.Opens.toScheme
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.Opens.ι
AlgebraicGeometry.IsZariskiLocalAtSource—AlgebraicGeometry.IsZariskiLocalAtSource.mk'
of_iSup_eq_top šŸ“–ā€”iSup
AlgebraicGeometry.Scheme.Opens
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
AlgebraicGeometry.Scheme.Opens.toScheme
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.Opens.ι
——AlgebraicGeometry.IsZariskiLocalAtSource.of_iSup_eq_top
of_isOpenImmersion šŸ“–ā€”ā€”ā€”ā€”AlgebraicGeometry.IsZariskiLocalAtSource.of_isOpenImmersion
of_openCover šŸ“–ā€”CategoryTheory.PreZeroHypercover.X
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover
AlgebraicGeometry.Scheme.precoverage
AlgebraicGeometry.IsOpenImmersion
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.PreZeroHypercover.f
——AlgebraicGeometry.IsZariskiLocalAtSource.of_openCover
resLE šŸ“–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
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.Scheme.Opens.toScheme
AlgebraicGeometry.Scheme.Hom.resLE
—AlgebraicGeometry.IsZariskiLocalAtSource.resLE
respectsLeft_isOpenImmersion šŸ“–mathematical—CategoryTheory.MorphismProperty.RespectsLeft
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.IsOpenImmersion
—AlgebraicGeometry.IsZariskiLocalAtSource.respectsLeft_isOpenImmersion
sigmaDesc šŸ“–mathematical—CategoryTheory.Limits.sigmaObj
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.IsLocallyDirected.instHasColimit
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
AlgebraicGeometry.IsOpenImmersion.of_isIso
CategoryTheory.Functor.obj
CategoryTheory.Functor.map
CategoryTheory.Functor.map_isIso
CategoryTheory.Discrete.instIsIso
CategoryTheory.instIsLocallyDirectedDiscrete
CategoryTheory.Functor.comp
CategoryTheory.types
AlgebraicGeometry.Scheme.forget
CategoryTheory.Discrete.instSubsingletonDiscreteHom
CategoryTheory.instSmallDiscrete
CategoryTheory.Limits.Sigma.desc
—AlgebraicGeometry.IsZariskiLocalAtSource.sigmaDesc

AlgebraicGeometry.IsLocalAtTarget

Theorems

NameKindAssumesProvesValidatesDepends On
iff_of_iSup_eq_top šŸ“–mathematicaliSup
AlgebraicGeometry.Scheme.Opens
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
AlgebraicGeometry.Scheme.Opens.toScheme
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.str
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.morphismRestrict
—AlgebraicGeometry.IsZariskiLocalAtTarget.iff_of_iSup_eq_top
iff_of_openCover šŸ“–mathematical—CategoryTheory.PreZeroHypercover.X
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover
AlgebraicGeometry.Scheme.precoverage
AlgebraicGeometry.IsOpenImmersion
CategoryTheory.Precoverage.ZeroHypercover.pullback₁
AlgebraicGeometry.Scheme.instIsStableUnderBaseChangePrecoverageOfIsJointlySurjectivePreservingOfIsStableUnderBaseChange
AlgebraicGeometry.Scheme.instIsJointlySurjectivePreservingIsOpenImmersion
AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange
AlgebraicGeometry.Scheme.Pullback.instHasPullback
CategoryTheory.PreZeroHypercover.f
AlgebraicGeometry.Scheme.Cover.pullbackHom
—AlgebraicGeometry.IsZariskiLocalAtTarget.iff_of_openCover
mk' šŸ“–mathematicalAlgebraicGeometry.Scheme.Opens.toScheme
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.morphismRestrict
AlgebraicGeometry.IsZariskiLocalAtTarget—AlgebraicGeometry.IsZariskiLocalAtTarget.mk'
of_iSup_eq_top šŸ“–ā€”iSup
AlgebraicGeometry.Scheme.Opens
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
AlgebraicGeometry.Scheme.Opens.toScheme
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.str
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.morphismRestrict
——AlgebraicGeometry.IsZariskiLocalAtTarget.of_iSup_eq_top
of_isPullback šŸ“–ā€”CategoryTheory.IsPullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
——AlgebraicGeometry.IsZariskiLocalAtTarget.of_isPullback
of_openCover šŸ“–ā€”CategoryTheory.PreZeroHypercover.X
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover
AlgebraicGeometry.Scheme.precoverage
AlgebraicGeometry.IsOpenImmersion
CategoryTheory.Precoverage.ZeroHypercover.pullback₁
AlgebraicGeometry.Scheme.instIsStableUnderBaseChangePrecoverageOfIsJointlySurjectivePreservingOfIsStableUnderBaseChange
AlgebraicGeometry.Scheme.instIsJointlySurjectivePreservingIsOpenImmersion
AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange
AlgebraicGeometry.Scheme.Pullback.instHasPullback
CategoryTheory.PreZeroHypercover.f
AlgebraicGeometry.Scheme.Cover.pullbackHom
——AlgebraicGeometry.IsZariskiLocalAtTarget.of_openCover
of_range_subset_iSup šŸ“–ā€”Set
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'
SetLike.coe
AlgebraicGeometry.Scheme.Opens
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.Scheme.Opens.toScheme
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.morphismRestrict
——AlgebraicGeometry.IsZariskiLocalAtTarget.of_range_subset_iSup
restrict šŸ“–mathematical—AlgebraicGeometry.Scheme.Opens.toScheme
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.morphismRestrict
—AlgebraicGeometry.IsZariskiLocalAtTarget.restrict

AlgebraicGeometry.IsZariskiLocalAtSource

Theorems

NameKindAssumesProvesValidatesDepends On
comp šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
—CategoryTheory.MorphismProperty.iff_of_zeroHypercover_source
iff_exists_resLE šŸ“–mathematical—AlgebraicGeometry.Scheme.Opens.toScheme
AlgebraicGeometry.Scheme.Hom.resLE
—resLE
iff_of_iSup_eq_top
eq_top_iff
AlgebraicGeometry.Scheme.Hom.resLE_comp_ι
CategoryTheory.MorphismProperty.RespectsRight.postcomp
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
iff_of_iSup_eq_top šŸ“–mathematicaliSup
AlgebraicGeometry.Scheme.Opens
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
AlgebraicGeometry.Scheme.Opens.toScheme
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.Opens.ι
—comp
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
of_iSup_eq_top
iff_of_openCover šŸ“–mathematical—CategoryTheory.PreZeroHypercover.X
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover
AlgebraicGeometry.Scheme.precoverage
AlgebraicGeometry.IsOpenImmersion
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.PreZeroHypercover.f
—comp
AlgebraicGeometry.Scheme.instIsOpenImmersionF
of_openCover
isZariskiLocalAtTarget šŸ“–mathematical—AlgebraicGeometry.IsZariskiLocalAtTarget—AlgebraicGeometry.Scheme.instHasPullbacksPrecoverageOfHasPullbacks
AlgebraicGeometry.Scheme.instHasPullbacksIsOpenImmersion
CategoryTheory.MorphismProperty.IsLocalAtSource.toRespects
CategoryTheory.Precoverage.ZeroHypercover.instHasPullbackFOfHasPullbacksPresieveā‚€_1
CategoryTheory.Precoverage.ZeroHypercover.instHasPullbacksPresieveā‚€OfHasPullbacks
AlgebraicGeometry.Scheme.instIsOpenImmersionF
CategoryTheory.Limits.pullback.condition
comp
AlgebraicGeometry.IsOpenImmersion.instFstScheme
AlgebraicGeometry.Scheme.instIsStableUnderBaseChangePrecoverageOfIsJointlySurjectivePreservingOfIsStableUnderBaseChange
AlgebraicGeometry.Scheme.instIsJointlySurjectivePreservingIsOpenImmersion
AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange
AlgebraicGeometry.Scheme.Pullback.instHasPullback
CategoryTheory.MorphismProperty.iff_of_zeroHypercover_source
AlgebraicGeometry.Scheme.Cover.pullbackHom_map
CategoryTheory.MorphismProperty.comp_mem
CategoryTheory.MorphismProperty.IsMultiplicative.toIsStableUnderComposition
of_isOpenImmersion
CategoryTheory.MorphismProperty.IsMultiplicative.toContainsIdentities
mk' šŸ“–mathematicalAlgebraicGeometry.Scheme.Opens.toScheme
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.Opens.ι
AlgebraicGeometry.IsZariskiLocalAtSource—AlgebraicGeometry.Scheme.instIsOpenImmersionF
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
AlgebraicGeometry.Scheme.Opens.opensRange_ι
AlgebraicGeometry.IsOpenImmersion.isoOfRangeEq_hom_fac
CategoryTheory.Category.assoc
CategoryTheory.MorphismProperty.cancel_left_of_respectsIso
CategoryTheory.Iso.isIso_hom
AlgebraicGeometry.Scheme.OpenCover.iSup_opensRange
AlgebraicGeometry.IsOpenImmersion.isoOfRangeEq_inv_fac
CategoryTheory.Iso.isIso_inv
of_iSup_eq_top šŸ“–ā€”iSup
AlgebraicGeometry.Scheme.Opens
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
AlgebraicGeometry.Scheme.Opens.toScheme
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.Opens.ι
——TopologicalSpace.Opens.ext
Set.ext
isOpen_iUnion
TopologicalSpace.Opens.is_open'
Set.iUnion_coe_set
Set.iUnion_congr_Prop
Set.iUnion_exists
Set.iUnion_iUnion_eq'
TopologicalSpace.Opens.coe_iSup
CategoryTheory.MorphismProperty.iff_of_zeroHypercover_source
of_isOpenImmersion šŸ“–ā€”ā€”ā€”ā€”comp
CategoryTheory.MorphismProperty.id_mem
CategoryTheory.Category.comp_id
of_openCover šŸ“–ā€”CategoryTheory.PreZeroHypercover.X
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover
AlgebraicGeometry.Scheme.precoverage
AlgebraicGeometry.IsOpenImmersion
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.PreZeroHypercover.f
——of_iSup_eq_top
AlgebraicGeometry.Scheme.instIsOpenImmersionF
AlgebraicGeometry.Scheme.OpenCover.iSup_opensRange
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
AlgebraicGeometry.Scheme.Opens.opensRange_ι
AlgebraicGeometry.IsOpenImmersion.isoOfRangeEq_inv_fac
CategoryTheory.Category.assoc
CategoryTheory.MorphismProperty.cancel_left_of_respectsIso
CategoryTheory.MorphismProperty.IsLocalAtSource.toRespects
CategoryTheory.Iso.isIso_inv
resLE šŸ“–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
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.Scheme.Opens.toScheme
AlgebraicGeometry.Scheme.Hom.resLE
—comp
AlgebraicGeometry.IsZariskiLocalAtTarget.restrict
AlgebraicGeometry.instIsOpenImmersionHomOfLE
respectsLeft_isOpenImmersion šŸ“–mathematical—CategoryTheory.MorphismProperty.RespectsLeft
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.IsOpenImmersion
—comp
sigmaDesc šŸ“–mathematical—CategoryTheory.Limits.sigmaObj
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.IsLocallyDirected.instHasColimit
CategoryTheory.Discrete
CategoryTheory.discreteCategory
CategoryTheory.Discrete.functor
AlgebraicGeometry.IsOpenImmersion.of_isIso
CategoryTheory.Functor.obj
CategoryTheory.Functor.map
CategoryTheory.Functor.map_isIso
CategoryTheory.Discrete.instIsIso
CategoryTheory.instIsLocallyDirectedDiscrete
CategoryTheory.Functor.comp
CategoryTheory.types
AlgebraicGeometry.Scheme.forget
CategoryTheory.Discrete.instSubsingletonDiscreteHom
CategoryTheory.instSmallDiscrete
CategoryTheory.Limits.Sigma.desc
—AlgebraicGeometry.Scheme.IsLocallyDirected.instHasColimit
AlgebraicGeometry.IsOpenImmersion.of_isIso
CategoryTheory.Functor.map_isIso
CategoryTheory.Discrete.instIsIso
CategoryTheory.instIsLocallyDirectedDiscrete
CategoryTheory.Discrete.instSubsingletonDiscreteHom
CategoryTheory.instSmallDiscrete
iff_of_openCover
CategoryTheory.Limits.colimit.ι_desc

AlgebraicGeometry.IsZariskiLocalAtTarget

Theorems

NameKindAssumesProvesValidatesDepends On
coprodMap šŸ“–mathematical—CategoryTheory.Limits.coprod
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.IsLocallyDirected.instHasColimit
CategoryTheory.Discrete
CategoryTheory.Limits.WalkingPair
CategoryTheory.discreteCategory
CategoryTheory.Limits.pair
AlgebraicGeometry.IsOpenImmersion.of_isIso
CategoryTheory.Functor.obj
CategoryTheory.Functor.map
CategoryTheory.Functor.map_isIso
CategoryTheory.Discrete.instIsIso
CategoryTheory.instIsLocallyDirectedDiscrete
CategoryTheory.Functor.comp
CategoryTheory.types
AlgebraicGeometry.Scheme.forget
CategoryTheory.Discrete.instSubsingletonDiscreteHom
CategoryTheory.instSmallDiscrete
UnivLE.small
univLE_of_max
UnivLE.self
CategoryTheory.Limits.coprod.map
—of_openCover
AlgebraicGeometry.Scheme.IsLocallyDirected.instHasColimit
AlgebraicGeometry.IsOpenImmersion.of_isIso
CategoryTheory.Functor.map_isIso
CategoryTheory.Discrete.instIsIso
CategoryTheory.instIsLocallyDirectedDiscrete
CategoryTheory.Discrete.instSubsingletonDiscreteHom
CategoryTheory.instSmallDiscrete
UnivLE.small
univLE_of_max
UnivLE.self
AlgebraicGeometry.Scheme.instIsStableUnderBaseChangePrecoverageOfIsJointlySurjectivePreservingOfIsStableUnderBaseChange
AlgebraicGeometry.Scheme.instIsJointlySurjectivePreservingIsOpenImmersion
AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange
AlgebraicGeometry.Scheme.Pullback.instHasPullback
CategoryTheory.IsPullback.flip
AlgebraicGeometry.isPullback_inl_inl_coprodMap
CategoryTheory.MorphismProperty.cancel_left_of_respectsIso
CategoryTheory.MorphismProperty.IsLocalAtTarget.toRespects
AlgebraicGeometry.Scheme.instHasPullbacksPrecoverageOfHasPullbacks
AlgebraicGeometry.Scheme.instHasPullbacksIsOpenImmersion
CategoryTheory.Iso.isIso_hom
CategoryTheory.IsPullback.isoPullback_hom_snd
AlgebraicGeometry.isPullback_inr_inr_coprodMap
iff_of_iSup_eq_top šŸ“–mathematicaliSup
AlgebraicGeometry.Scheme.Opens
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
AlgebraicGeometry.Scheme.Opens.toScheme
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.str
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.morphismRestrict
—restrict
of_iSup_eq_top
iff_of_openCover šŸ“–mathematical—CategoryTheory.PreZeroHypercover.X
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover
AlgebraicGeometry.Scheme.precoverage
AlgebraicGeometry.IsOpenImmersion
CategoryTheory.Precoverage.ZeroHypercover.pullback₁
AlgebraicGeometry.Scheme.instIsStableUnderBaseChangePrecoverageOfIsJointlySurjectivePreservingOfIsStableUnderBaseChange
AlgebraicGeometry.Scheme.instIsJointlySurjectivePreservingIsOpenImmersion
AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange
AlgebraicGeometry.Scheme.Pullback.instHasPullback
CategoryTheory.PreZeroHypercover.f
AlgebraicGeometry.Scheme.Cover.pullbackHom
—AlgebraicGeometry.Scheme.instIsStableUnderBaseChangePrecoverageOfIsJointlySurjectivePreservingOfIsStableUnderBaseChange
AlgebraicGeometry.Scheme.instIsJointlySurjectivePreservingIsOpenImmersion
AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange
AlgebraicGeometry.Scheme.Pullback.instHasPullback
of_isPullback
AlgebraicGeometry.Scheme.instIsOpenImmersionF
CategoryTheory.IsPullback.of_hasPullback
of_openCover
mk' šŸ“–mathematicalAlgebraicGeometry.Scheme.Opens.toScheme
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.morphismRestrict
AlgebraicGeometry.IsZariskiLocalAtTarget—AlgebraicGeometry.Scheme.instHasPullbacksPrecoverageOfHasPullbacks
AlgebraicGeometry.Scheme.instHasPullbacksIsOpenImmersion
AlgebraicGeometry.Scheme.instIsOpenImmersionF
AlgebraicGeometry.IsOpenImmersion.hasPullback_of_right
CategoryTheory.MorphismProperty.arrow_mk_iso_iff
CategoryTheory.Precoverage.ZeroHypercover.instHasPullbackFOfHasPullbacksPresieveā‚€_1
CategoryTheory.Precoverage.ZeroHypercover.instHasPullbacksPresieveā‚€OfHasPullbacks
AlgebraicGeometry.Scheme.OpenCover.iSup_opensRange
of_forall_exists_morphismRestrict šŸ“–ā€”TopCat.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
AlgebraicGeometry.Scheme.Opens.toScheme
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.str
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.morphismRestrict
——of_iSup_eq_top
top_le_iff
of_forall_source_exists_preimage šŸ“–ā€”TopCat.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
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.Opens.toScheme
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.Opens.ι
——of_range_subset_iSup
TopologicalSpace.Opens.coe_iSup
CategoryTheory.MorphismProperty.of_postcomp
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
AlgebraicGeometry.morphismRestrict_ι
of_iSup_eq_top šŸ“–ā€”iSup
AlgebraicGeometry.Scheme.Opens
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
AlgebraicGeometry.Scheme.Opens.toScheme
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.str
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.morphismRestrict
——TopologicalSpace.Opens.ext
Set.ext
isOpen_iUnion
TopologicalSpace.Opens.is_open'
Set.iUnion_coe_set
Set.iUnion_congr_Prop
Set.iUnion_exists
Set.iUnion_iUnion_eq'
TopologicalSpace.Opens.coe_iSup
CategoryTheory.Precoverage.ZeroHypercover.instHasPullbackFOfHasPullbacksPresieveā‚€_1
CategoryTheory.Precoverage.ZeroHypercover.instHasPullbacksPresieveā‚€OfHasPullbacks
AlgebraicGeometry.Scheme.instHasPullbacksPrecoverageOfHasPullbacks
AlgebraicGeometry.Scheme.instHasPullbacksIsOpenImmersion
CategoryTheory.MorphismProperty.iff_of_zeroHypercover_target
AlgebraicGeometry.Scheme.instIsOpenImmersionF
AlgebraicGeometry.IsOpenImmersion.hasPullback_of_right
CategoryTheory.MorphismProperty.arrow_mk_iso_iff
CategoryTheory.MorphismProperty.IsLocalAtTarget.toRespects
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
AlgebraicGeometry.Scheme.Opens.opensRange_ι
of_isPullback šŸ“–ā€”CategoryTheory.IsPullback
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
——CategoryTheory.MorphismProperty.IsLocalAtTarget.of_isPullback
AlgebraicGeometry.Scheme.instHasPullbacksPrecoverageOfHasPullbacks
AlgebraicGeometry.Scheme.instHasPullbacksIsOpenImmersion
of_openCover šŸ“–ā€”CategoryTheory.PreZeroHypercover.X
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover
AlgebraicGeometry.Scheme.precoverage
AlgebraicGeometry.IsOpenImmersion
CategoryTheory.Precoverage.ZeroHypercover.pullback₁
AlgebraicGeometry.Scheme.instIsStableUnderBaseChangePrecoverageOfIsJointlySurjectivePreservingOfIsStableUnderBaseChange
AlgebraicGeometry.Scheme.instIsJointlySurjectivePreservingIsOpenImmersion
AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange
AlgebraicGeometry.Scheme.Pullback.instHasPullback
CategoryTheory.PreZeroHypercover.f
AlgebraicGeometry.Scheme.Cover.pullbackHom
——AlgebraicGeometry.Scheme.instIsStableUnderBaseChangePrecoverageOfIsJointlySurjectivePreservingOfIsStableUnderBaseChange
AlgebraicGeometry.Scheme.instIsJointlySurjectivePreservingIsOpenImmersion
AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange
AlgebraicGeometry.Scheme.Pullback.instHasPullback
of_iSup_eq_top
AlgebraicGeometry.Scheme.instIsOpenImmersionF
AlgebraicGeometry.Scheme.OpenCover.iSup_opensRange
AlgebraicGeometry.IsOpenImmersion.hasPullback_of_right
CategoryTheory.MorphismProperty.arrow_mk_iso_iff
CategoryTheory.MorphismProperty.IsLocalAtTarget.toRespects
AlgebraicGeometry.Scheme.instHasPullbacksPrecoverageOfHasPullbacks
AlgebraicGeometry.Scheme.instHasPullbacksIsOpenImmersion
of_range_subset_iSup šŸ“–ā€”Set
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'
SetLike.coe
AlgebraicGeometry.Scheme.Opens
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.Scheme.Opens.toScheme
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.morphismRestrict
——AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
AlgebraicGeometry.Scheme.Opens.range_ι
TopologicalSpace.Opens.coe_iSup
AlgebraicGeometry.IsOpenImmersion.lift_fac
CategoryTheory.MorphismProperty.RespectsRight.postcomp
iff_of_iSup_eq_top
AlgebraicGeometry.Scheme.Hom.image_injective
AlgebraicGeometry.Scheme.Hom.image_iSup
AlgebraicGeometry.Scheme.Hom.image_top_eq_opensRange
AlgebraicGeometry.Scheme.Opens.opensRange_ι
AlgebraicGeometry.Scheme.Hom.image_preimage_eq_opensRange_inf
inf_of_le_right
le_iSup
CategoryTheory.cancel_mono
AlgebraicGeometry.IsOpenImmersion.mono
CategoryTheory.Category.assoc
AlgebraicGeometry.morphismRestrict_ι
AlgebraicGeometry.Scheme.isoOfEq_hom_ι_assoc
AlgebraicGeometry.Scheme.Opens.isoOfLE_hom_ι
AlgebraicGeometry.morphismRestrict_ι_assoc
CategoryTheory.MorphismProperty.arrow_mk_iso_iff
CategoryTheory.MorphismProperty.IsLocalAtTarget.toRespects
AlgebraicGeometry.Scheme.instHasPullbacksPrecoverageOfHasPullbacks
AlgebraicGeometry.Scheme.instHasPullbacksIsOpenImmersion
restrict šŸ“–mathematical—AlgebraicGeometry.Scheme.Opens.toScheme
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.morphismRestrict
—of_isPullback
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
CategoryTheory.IsPullback.flip
AlgebraicGeometry.isPullback_morphismRestrict

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