Documentation Verification Report

AffineScheme

📁 Source: Mathlib/AlgebraicGeometry/AffineScheme.lean

Statistics

MetricCount
DefinitionsAffineScheme, createsLimitsForgetToScheme, equivCommRingCat, forgetToScheme, mk, of, ofHom, Γ, IsAffine, IsAffineOpen, appBasicOpenIsoAwayMap, arrowStalkMapIso, basicOpenSectionsToAffine, fromSpec, instAlgebraCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecPresheafOpOpens, isoSpec, primeIdealOf, affineOpensEquiv, liftQuotient, toSpecΓ, affineBasicOpen, affineOpens, arrowStalkMapSpecIso, isoSpec, stalkIso, SpecMapRestrictBasicOpenIso, affineOpensRestrict, arrowIsoSpecΓOfIsAffine, arrowIsoΓSpecOfIsAffine, instCategoryAffineScheme, specTargetImage, specTargetImageFactorization, specTargetImageIdeal, specTargetImageRingHom
34
TheoremsSpec_essSurj, Spec_faithful, Spec_full, forgetToScheme_faithful, forgetToScheme_full, forgetToScheme_map, forgetToScheme_obj, forgetToScheme_preservesLimits, hasColimits, hasLimits, instIsEquivalenceOppositeCommRingCatOpRightOpΓ, instIsEquivalenceOppositeCommRingCatRightOpΓ, mk_obj, ΓIsEquiv, Γ_preservesLimits, affine, iff_of_isIso, of_isIso, SpecMap_appLE_fromSpec, SpecMap_appLE_fromSpec_assoc, Spec_basicOpen, Spec_map_appLE_fromSpec, Spec_map_appLE_fromSpec_assoc, algebraMap_Spec_obj, appLE_eq_away_map, app_basicOpen_eq_away_map, basicOpen, basicOpenSectionsToAffine_isIso, basicOpen_basicOpen_is_basicOpen, basicOpen_fromSpec_app, basicOpen_union_eq_self_iff, comap_primeIdealOf_appLE, exists_basicOpen_le, fromSpec_app_of_le, fromSpec_app_self, fromSpec_app_self_apply, fromSpec_image_basicOpen, fromSpec_image_zeroLocus, fromSpec_preimage_basicOpen, fromSpec_preimage_basicOpen', fromSpec_preimage_self, fromSpec_preimage_zeroLocus, fromSpec_primeIdealOf, fromSpec_toSpecΓ, fromSpec_toSpecΓ_assoc, fromSpec_top, iSup_basicOpen_eq_self_iff, ideal_ext_iff, ideal_le_iff, image_of_isOpenImmersion, instAwayCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecPresheafOpOpensBasicOpen, instIsAffineToSchemeBasicOpen, isCompact, isLocalization_basicOpen, isLocalization_of_eq_basicOpen, isLocalization_stalk, isLocalization_stalk', isOpenImmersion_fromSpec, isoSpec_hom, isoSpec_hom_appTop, isoSpec_hom_apply, isoSpec_hom_base_apply, isoSpec_inv, isoSpec_inv_appTop, isoSpec_inv_toSpecΓ, isoSpec_inv_toSpecΓ_assoc, isoSpec_inv_ι, isoSpec_inv_ι_assoc, map_fromSpec, map_fromSpec_assoc, mem_ideal_iff, opensRange_fromSpec, preimage_of_isIso, preimage_of_isOpenImmersion, primeIdealOf_eq_map_closedPoint, primeIdealOf_isMaximal_of_isClosed, range_fromSpec, self_le_basicOpen_union_iff, self_le_iSup_basicOpen_iff, stalkMap_injective, toSpecΓ_fromSpec, toSpecΓ_fromSpec_assoc, toSpecΓ_isoSpec_inv, toSpecΓ_isoSpec_inv_assoc, ΓSpecIso_hom_fromSpec_app, ι_basicOpen_preimage, affineOpensEquiv_apply_coe_coe, affineOpensEquiv_symm_apply_coe, isAffineOpen_iff_of_isOpenImmersion, liftQuotient_comp, liftQuotient_comp_assoc, toSpecΓ_SpecMap_appLE, toSpecΓ_SpecMap_appLE_assoc, toSpecΓ_SpecMap_map, toSpecΓ_SpecMap_map_assoc, toSpecΓ_SpecMap_presheaf_map, toSpecΓ_SpecMap_presheaf_map_assoc, toSpecΓ_SpecMap_presheaf_map_top, toSpecΓ_SpecMap_presheaf_map_top_assoc, toSpecΓ_appTop, toSpecΓ_appTop_assoc, toSpecΓ_naturality, toSpecΓ_naturality_assoc, toSpecΓ_preimage_basicOpen, toSpecΓ_preimage_zeroLocus, toSpecΓ_top, affineBasicOpen_coe, affineBasicOpen_le, compactSpace_of_isAffine, eq_zeroLocus_of_isClosed_of_isAffine, isAffine_affineBasisCover, isAffine_affineCover, isAffine_affineOpenCover, isBasis_affineOpens, isoSpec_Spec, isoSpec_Spec_hom, isoSpec_Spec_inv, isoSpec_hom, isoSpec_hom_naturality, isoSpec_hom_naturality_assoc, isoSpec_image_zeroLocus, isoSpec_inv_image_zeroLocus, isoSpec_inv_naturality, isoSpec_inv_naturality_assoc, isoSpec_inv_preimage_zeroLocus, isoSpec_inv_toSpecΓ, isoSpec_inv_toSpecΓ_assoc, localRingHom_comp_stalkIso, localRingHom_comp_stalkIso_apply, map_PrimeSpectrum_basicOpen_of_affine, toSpecΓ_image_zeroLocus, toSpecΓ_isoSpec_inv, toSpecΓ_isoSpec_inv_assoc, toSpecΓ_preimage_zeroLocus, zeroLocus_biInf, zeroLocus_biInf_of_nonempty, zeroLocus_iInf, zeroLocus_iInf_of_nonempty, zeroLocus_inf, algebraMap_stalkIso_inv, algebraMap_stalkIso_inv_assoc, germ_stalkMapIso_hom, germ_stalkMapIso_hom_assoc, affineOpensRestrict_apply_coe_coe, affineOpensRestrict_symm_apply_coe, eq_of_SpecMap_comp_eq_of_isAffineOpen, essImage_Spec, exists_basicOpen_le_affine_inter, exists_isAffineOpen_mem_and_subset, ext_of_isAffine, iSup_affineOpens_eq_top, iSup_basicOpen_of_span_eq_top, instIsAffineObjOppositeCommRingCatSchemeSpec, instIsAffineToSchemeValOpensMemSetAffineOpens, instIsAffineXSchemeCoverOfIsIsoIsOpenImmersionId, instIsAffineXSchemeFiniteSubcover, instIsIsoSchemeAppUnitOppositeCommRingCatAdjunctionOfIsAffine, isAffineOpen_opensRange, isAffineOpen_top, isAffine_Spec, isAffine_affineScheme, isBasis_affine_open, isBasis_basicOpen, isLocalization_away_of_isAffine, of_affine_open_cover, preservesColimit_Γ, preservesLimit_rightOp_Γ, specTargetImageFactorization_app_injective, specTargetImageFactorization_comp, specTargetImageFactorization_comp_assoc, specTargetImageRingHom_surjective, stalkMap_injective_of_isAffine, Γ_restrict_isLocalization
173
Total207

AlgebraicGeometry

Definitions

NameCategoryTheorems
AffineScheme 📖CompOp
14 mathmath: AffineScheme.Spec_faithful, AffineScheme.instIsEquivalenceOppositeCommRingCatOpRightOpΓ, AffineScheme.hasLimits, AffineScheme.instIsEquivalenceOppositeCommRingCatRightOpΓ, AffineScheme.forgetToScheme_preservesLimits, AffineScheme.hasColimits, AffineScheme.Γ_preservesLimits, AffineScheme.forgetToScheme_full, AffineScheme.forgetToScheme_faithful, AffineScheme.forgetToScheme_map, AffineScheme.Spec_essSurj, AffineScheme.forgetToScheme_obj, AffineScheme.Spec_full, AffineScheme.ΓIsEquiv
IsAffine 📖CompData
37 mathmath: instIsAffinePullbackSchemeOfIsAffineHom_1, instHasAffinePropertyIsAffineHomIsAffine, ExistsHomHomCompEqCompAux.h𝒰S, Scheme.exists_hom_isAffine_of_isLocalAtSource, IsAffine.of_isIso, isAffine_of_isEmpty, Scheme.exists_isAffine_of_isLimit, instIsAffineXSchemeAffineCover, instIsAffineOfSubsingletonCarrierCarrierCommRingCat, instIsAffineCoprodScheme, Scheme.isAffine_affineBasisCover, ExistsHomHomCompEqCompAux.h𝒰X, isAffine_of_isAffineHom, IsFinite.instHasAffinePropertyAndIsAffineFiniteCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTopHomAppTop, IsAffineOpen.instIsAffineToSchemeBasicOpen, instIsAffineFiberOfIsAffineHom, isAffine_affineScheme, instIsAffineObjOppositeCommRingCatSchemeSpec, IsClosedImmersion.hasAffineProperty, AffineSpace.instIsAffine, IsAffine.iff_of_isIso, instIsAffineTerminalScheme, instIsAffineOfFiniteOfDiscreteTopologyCarrierCarrierCommRingCat, instIsAffineXSchemeCoverOfIsIsoIsOpenImmersionId, affineAnd_apply, IsClosedImmersion.isAffine_surjective_of_isAffine, IsIntegralHom.hasAffineProperty, instHasAffinePropertyIsomorphismsSchemeAndIsAffineIsIsoCommRingCatAppTop, isAffine_of_isAffineOpen_basicOpen, instIsAffineToSchemeValOpensMemSetAffineOpens, isAffine_Spec, instIsAffinePullbackSchemeOfIsAffineHom, Scheme.isAffine_affineCover, Scheme.exists_hom_isAffine_of_isZariskiLocalAtSource, essImage_Spec, Scheme.Pullback.isAffine_of_isAffine_isAffine_isAffine, Scheme.isAffine_affineOpenCover
IsAffineOpen 📖MathDef
35 mathmath: isAffineOpen_top, exists_isAffineOpen_preimage_eq, IsAffineOpen.basicOpen, Scheme.exists_germ_injective, isAffineOpen_opensRange, Proj.isAffineOpen_basicOpen, isBasis_preimage_isAffineOpen, Scheme.AffineZariskiSite.restrictIsoSpec_hom_app, exists_isAffineOpen_mem_and_subset, Scheme.Hom.isAffineOpen_iff_of_isOpenImmersion, IsAffineOpen.image_of_isOpenImmersion, Scheme.AffineZariskiSite.directedCover_X, targetAffineLocally_affineAnd_iff, affinePreimage, isAffineHom_iff, Scheme.AffineZariskiSite.directedCover_f, IsAffineOpen.ι_basicOpen_preimage, Scheme.IsGermInjectiveAt.cond, IsAffineOpen.preimage_of_isIso, IsAffineOpen.preimage_of_isOpenImmersion, Scheme.AffineZariskiSite.cocone_ι_app, isAffineOpen_bot, IsAffineOpen.sup_of_disjoint, IsAffineHom.isAffine_preimage, Scheme.exists_le_and_germ_injective, Scheme.openCoverBasicOpenTop_f, Scheme.AffineZariskiSite.PreservesLocalization.colimitDesc_preimage, Scheme.IsQuasiAffine.isBasis_basicOpen, Scheme.AffineZariskiSite.basicOpen_coe, QuasiCompactCover.exists_isAffineOpen_of_isCompact, Scheme.AffineZariskiSite.restrictIsoSpec_inv_app, IsAffineOpen.of_subsingleton, IsAffineOpen.preimage, IsAffineOpen.Spec_basicOpen, exists_lift_of_germInjective
SpecMapRestrictBasicOpenIso 📖CompOp
affineOpensRestrict 📖CompOp
2 mathmath: affineOpensRestrict_apply_coe_coe, affineOpensRestrict_symm_apply_coe
arrowIsoSpecΓOfIsAffine 📖CompOp
arrowIsoΓSpecOfIsAffine 📖CompOp
instCategoryAffineScheme 📖CompOp
14 mathmath: AffineScheme.Spec_faithful, AffineScheme.instIsEquivalenceOppositeCommRingCatOpRightOpΓ, AffineScheme.hasLimits, AffineScheme.instIsEquivalenceOppositeCommRingCatRightOpΓ, AffineScheme.forgetToScheme_preservesLimits, AffineScheme.hasColimits, AffineScheme.Γ_preservesLimits, AffineScheme.forgetToScheme_full, AffineScheme.forgetToScheme_faithful, AffineScheme.forgetToScheme_map, AffineScheme.Spec_essSurj, AffineScheme.forgetToScheme_obj, AffineScheme.Spec_full, AffineScheme.ΓIsEquiv
specTargetImage 📖CompOp
4 mathmath: specTargetImageFactorization_comp_assoc, specTargetImageFactorization_comp, specTargetImageFactorization_app_injective, specTargetImageRingHom_surjective
specTargetImageFactorization 📖CompOp
3 mathmath: specTargetImageFactorization_comp_assoc, specTargetImageFactorization_comp, specTargetImageFactorization_app_injective
specTargetImageIdeal 📖CompOp
specTargetImageRingHom 📖CompOp
3 mathmath: specTargetImageFactorization_comp_assoc, specTargetImageFactorization_comp, specTargetImageRingHom_surjective

Theorems

NameKindAssumesProvesValidatesDepends On
affineOpensRestrict_apply_coe_coe 📖mathematicalScheme.Opens
Set
Set.instMembership
Scheme.affineOpens
Set.Elem
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
SheafedSpace.instTopologicalSpaceCarrierCarrier
DFunLike.coe
Equiv
Scheme.Opens.toScheme
EquivLike.toFunLike
Equiv.instEquivLike
affineOpensRestrict
CategoryTheory.Functor.obj
Preorder.smallCategory
Scheme.Hom.opensFunctor
Scheme.Opens.ι
Scheme.Opens.instIsOpenImmersionι
affineOpensRestrict_symm_apply_coe 📖mathematicalScheme.Opens
Scheme.Opens.toScheme
Set
Set.instMembership
Scheme.affineOpens
DFunLike.coe
Equiv
Set.Elem
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
SheafedSpace.instTopologicalSpaceCarrierCarrier
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
affineOpensRestrict
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.str
TopologicalSpace.Opens.map
PresheafedSpace.Hom.base
LocallyRingedSpace.Hom.toHom
Scheme.Hom.toLRSHom'
Scheme.Opens.ι
eq_of_SpecMap_comp_eq_of_isAffineOpen 📖CommRingCat.carrier
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
CommRingCat
CommRingCat.instCategory
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
RingHom.instFunLike
CommRingCat.instConcreteCategoryRingHomCarrier
CategoryTheory.Functor.obj
Scheme.Opens
Preorder.smallCategory
TopologicalSpace.Opens
TopCat.carrier
PresheafedSpace.carrier
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
TopCat.str
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
Spec
TopologicalSpace.Opens.map
PresheafedSpace.Hom.base
LocallyRingedSpace.Hom.toHom
Scheme.Hom.toLRSHom'
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
CategoryTheory.CategoryStruct.comp
Scheme
CategoryTheory.Category.toCategoryStruct
Scheme.instCategory
Spec.map
CategoryTheory.ConcreteCategory.mono_of_injective
Scheme.Opens.instIsOpenImmersionι
Scheme.Opens.range_ι
Eq.ge
IsOpenImmersion.lift_fac
CategoryTheory.cancel_mono
IsOpenImmersion.mono
IsOpenImmersion.of_isIso
CategoryTheory.Iso.isIso_hom
Equiv.injective
Spec.map_injective
Spec.map_comp
Spec.map_preimage
CategoryTheory.Category.assoc
essImage_Spec 📖mathematicalCategoryTheory.Functor.essImage
Opposite
CommRingCat
Scheme
CategoryTheory.Category.opposite
CommRingCat.instCategory
Scheme.instCategory
Scheme.Spec
IsAffine
CategoryTheory.Functor.essImage.unit_isIso
CategoryTheory.Adjunction.mem_essImage_of_unit_isIso
instIsIsoSchemeAppUnitOppositeCommRingCatAdjunctionOfIsAffine
exists_basicOpen_le_affine_inter 📖mathematicalTopCat.carrier
PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
Scheme.Opens
SetLike.instMembership
TopologicalSpace.Opens.instSetLike
SheafedSpace.instTopologicalSpaceCarrierCarrier
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
Scheme.basicOpenIsAffineOpen.exists_basicOpen_le
IsAffineOpen.basicOpen_basicOpen_is_basicOpen
RingedSpace.basicOpen_res
inf_eq_right
exists_isAffineOpen_mem_and_subset 📖mathematicalTopCat.carrier
PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
Scheme.Opens
SetLike.instMembership
TopologicalSpace.Opens.instSetLike
SheafedSpace.instTopologicalSpaceCarrierCarrier
IsAffineOpen
Set
Set.instHasSubset
TopologicalSpace.Opens.carrier
SetLike.coe
Scheme.exists_affine_mem_range_and_range_subset
isAffineOpen_opensRange
isAffine_Spec
ext_of_isAffine 📖Scheme.Hom.appTopCategoryTheory.cancel_mono
IsOpenImmersion.mono
IsOpenImmersion.of_isIso
IsAffine.affine
Scheme.toSpecΓ_naturality
iSup_affineOpens_eq_top 📖mathematicaliSup
Scheme.Opens
Set.Elem
Scheme.affineOpens
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
TopCat.carrier
PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
SheafedSpace.instTopologicalSpaceCarrierCarrier
Set
Set.instMembership
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
TopologicalSpace.Opens.ext
TopologicalSpace.Opens.coe_iSup
TopologicalSpace.IsTopologicalBasis.sUnion_eq
Set.image_eq_range
Scheme.isBasis_affineOpens
iSup_basicOpen_of_span_eq_top 📖mathematicalIdeal.span
CommRingCat.carrier
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
PresheafedSpace.presheaf
Opposite.op
Scheme.Opens
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
Top.top
Ideal
Submodule.instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
SheafedSpace.instTopologicalSpaceCarrierCarrier
Set
Set.instMembership
Scheme.basicOpen
le_antisymm
iSup₂_le_iff
Scheme.basicOpen_le
TopologicalSpace.IsTopologicalBasis.exists_subset_of_mem_open
Scheme.isBasis_affineOpens
TopologicalSpace.Opens.is_open'
SetLike.mem_of_subset
IsAffineOpen.iSup_basicOpen_eq_self_iff
Ideal.map_span
RingHom.instRingHomClass
Ideal.map_top
isOpen_iUnion
Set.iUnion_coe_set
Set.iUnion_congr_Prop
Set.iUnion_exists
Set.biUnion_and'
Set.iUnion_iUnion_eq_right
Scheme.basicOpen_res
HasSubset.Subset.trans
Set.instIsTransSubset
Set.inter_subset_right
Set.subset_iUnion₂
instIsAffineObjOppositeCommRingCatSchemeSpec 📖mathematicalIsAffine
CategoryTheory.Functor.obj
Opposite
CommRingCat
CategoryTheory.Category.opposite
CommRingCat.instCategory
Scheme
Scheme.instCategory
Scheme.Spec
isAffine_affineScheme
CategoryTheory.Functor.obj_mem_essImage
instIsAffineToSchemeValOpensMemSetAffineOpens 📖mathematicalIsAffine
Scheme.Opens.toScheme
Scheme.Opens
Set
Set.instMembership
Scheme.affineOpens
instIsAffineXSchemeCoverOfIsIsoIsOpenImmersionId 📖mathematicalIsAffine
CategoryTheory.PreZeroHypercover.X
Scheme
Scheme.instCategory
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover
Scheme.precoverage
IsOpenImmersion
Scheme.coverOfIsIso
CategoryTheory.MorphismProperty.IsMultiplicative.toContainsIdentities
isOpenImmersion_isMultiplicative
isOpenImmersion_respectsIso
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.IsIso.id
CategoryTheory.MorphismProperty.IsMultiplicative.toContainsIdentities
isOpenImmersion_isMultiplicative
isOpenImmersion_respectsIso
CategoryTheory.IsIso.id
instIsAffineXSchemeFiniteSubcover 📖mathematicalIsAffine
CategoryTheory.PreZeroHypercover.X
Scheme
Scheme.instCategory
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover
Scheme.precoverage
IsOpenImmersion
Scheme.OpenCover.finiteSubcoverScheme.instJointlySurjectivePrecoverage
instIsIsoSchemeAppUnitOppositeCommRingCatAdjunctionOfIsAffine 📖mathematicalCategoryTheory.IsIso
Scheme
Scheme.instCategory
CategoryTheory.Functor.obj
CategoryTheory.Functor.id
CategoryTheory.Functor.comp
Opposite
CommRingCat
CategoryTheory.Category.opposite
CommRingCat.instCategory
CategoryTheory.Functor.rightOp
Scheme.Γ
Scheme.Spec
CategoryTheory.NatTrans.app
CategoryTheory.Adjunction.unit
ΓSpec.adjunction
IsAffine.affine
isAffineOpen_opensRange 📖mathematicalIsAffineOpen
Scheme.Hom.opensRange
IsAffine.of_isIso
IsOpenImmersion.ofRestrict
Subtype.range_val
CategoryTheory.Iso.isIso_inv
isAffineOpen_top 📖mathematicalIsAffineOpen
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
IsOpenImmersion.of_isIso
CategoryTheory.IsIso.id
TopologicalSpace.Opens.ext
Set.range_id
isAffineOpen_opensRange
isAffine_Spec 📖mathematicalIsAffine
Spec
isAffine_affineScheme
CategoryTheory.Functor.obj_mem_essImage
isAffine_affineScheme 📖mathematicalIsAffine
CategoryTheory.ObjectProperty.FullSubcategory.obj
Scheme
Scheme.instCategory
CategoryTheory.Functor.essImage
Opposite
CommRingCat
CategoryTheory.Category.opposite
CommRingCat.instCategory
Scheme.Spec
CategoryTheory.Functor.essImage.unit_isIso
CategoryTheory.ObjectProperty.FullSubcategory.property
isBasis_affine_open 📖mathematicalTopologicalSpace.Opens.IsBasis
TopCat.carrier
PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
SheafedSpace.instTopologicalSpaceCarrierCarrier
Scheme.affineOpens
Scheme.isBasis_affineOpens
isBasis_basicOpen 📖mathematicalTopologicalSpace.Opens.IsBasis
TopCat.carrier
PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
SheafedSpace.instTopologicalSpaceCarrierCarrier
Set.range
TopologicalSpace.Opens
CommRingCat.carrier
CategoryTheory.Functor.obj
Opposite
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
PresheafedSpace.presheaf
Opposite.op
Scheme.Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
Scheme.basicOpen
IsOpen.preimage
Topology.IsInducing.continuous
Homeomorph.isInducing
TopologicalSpace.Opens.is_open'
Set.ext
TopologicalSpace.Opens.IsBasis.of_isInducing
PrimeSpectrum.isBasis_basic_opens
isLocalization_away_of_isAffine 📖mathematicalIsLocalization.Away
CommRingCat.carrier
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
PresheafedSpace.presheaf
Opposite.op
Scheme.Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
CommRing.toCommSemiring
CommRingCat.commRing
Scheme.basicOpen
Scheme.algebra_section_section_basicOpen
IsAffineOpen.isLocalization_basicOpen
isAffineOpen_top
of_affine_open_cover 📖iSup
Scheme.Opens
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
TopCat.carrier
PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
SheafedSpace.instTopologicalSpaceCarrierCarrier
Set
Set.instMembership
Scheme.affineOpens
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
Scheme.affineBasicOpen
TopologicalSpace.Opens.mem_iSup
Eq.ge
Set.mem_univ
exists_basicOpen_le_affine_inter
Subtype.prop
IsAffineOpen.self_le_iSup_basicOpen_iff
iSup_range'
Ideal.span_eq_top_iff_finite
preservesColimit_Γ 📖mathematicalIsAffine
Opposite.unop
Scheme
CategoryTheory.Functor.obj
Opposite
CategoryTheory.Category.opposite
Scheme.instCategory
CategoryTheory.Limits.PreservesColimit
CommRingCat
CommRingCat.instCategory
Scheme.Γ
CategoryTheory.Functor.leftOp_obj
CategoryTheory.Limits.preservesColimit_of_rightOp
preservesLimit_rightOp_Γ
preservesLimit_rightOp_Γ 📖mathematicalIsAffine
CategoryTheory.Functor.obj
Scheme
Scheme.instCategory
CategoryTheory.Limits.PreservesLimit
Opposite
CommRingCat
CategoryTheory.Category.opposite
CommRingCat.instCategory
CategoryTheory.Functor.rightOp
Scheme.Γ
IsAffine.affine
CategoryTheory.NatIso.isIso_of_isIso_app
CategoryTheory.Limits.preservesLimit_of_natIso
CategoryTheory.Limits.PreservesLimitsOfShape.preservesLimit
CategoryTheory.Functor.instPreservesLimitsOfShapeOfIsRightAdjoint
CategoryTheory.Functor.IsLeftAdjoint.op
CategoryTheory.Functor.isLeftAdjoint_of_isEquivalence
CategoryTheory.Functor.isEquivalence_refl
CategoryTheory.preservesLimit_comp_of_createsLimit
CategoryTheory.Limits.preservesLimit_of_iso_diagram
specTargetImageFactorization_app_injective 📖mathematicalCommRingCat.carrier
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
Spec
specTargetImage
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
PresheafedSpace.presheaf
Opposite.op
Scheme.Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
RingHom.instFunLike
CommRingCat.instConcreteCategoryRingHomCarrier
Scheme.Hom.appTop
specTargetImageFactorization
ΓSpec_adjunction_homEquiv_eq
RingHom.instRingHomClass
RingHom.instIsTwoSidedKer
RingHom.kerLift_injective
Function.Bijective.injective
CategoryTheory.ConcreteCategory.isIso_iff_bijective
CommRingCat.forgetReflectIsos
CategoryTheory.Iso.isIso_hom
specTargetImageFactorization_comp 📖mathematicalCategoryTheory.CategoryStruct.comp
Scheme
CategoryTheory.Category.toCategoryStruct
Scheme.instCategory
Spec
specTargetImage
specTargetImageFactorization
Spec.map
specTargetImageRingHom
Scheme.Hom.liftQuotient_comp
specTargetImageFactorization_comp_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
Scheme
CategoryTheory.Category.toCategoryStruct
Scheme.instCategory
Spec
specTargetImage
specTargetImageFactorization
Spec.map
specTargetImageRingHom
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
specTargetImageFactorization_comp
specTargetImageRingHom_surjective 📖mathematicalCommRingCat.carrier
specTargetImage
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
CommRingCat
CommRingCat.instCategory
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
RingHom.instFunLike
CommRingCat.instConcreteCategoryRingHomCarrier
specTargetImageRingHom
Ideal.Quotient.mk_surjective
stalkMap_injective_of_isAffine 📖mathematicalDFunLike.coe
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
PresheafedSpace.presheaf
Opposite.op
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
PresheafedSpace.Hom.base
LocallyRingedSpace.Hom.toHom
Scheme.Hom.toLRSHom'
CommRingCat.carrier
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
RingHom.instFunLike
CommRingCat.instConcreteCategoryRingHomCarrier
TopCat.Presheaf.Γgerm
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Scheme.Hom.stalkMapCommRingCat.Colimits.hasColimits_commRingCat
IsAffineOpen.stalkMap_injective
isAffineOpen_top
Γ_restrict_isLocalization 📖mathematicalIsLocalization.Away
CommRingCat.carrier
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
PresheafedSpace.presheaf
Opposite.op
Scheme.Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
CommRing.toCommSemiring
CommRingCat.commRing
Scheme.Opens.toScheme
Scheme.basicOpen
ΓRestrictAlgebra
IsAffineOpen.isLocalization_of_eq_basicOpen
isAffineOpen_top
TopologicalSpace.Opens.isOpenEmbedding_obj_top

AlgebraicGeometry.AffineScheme

Definitions

NameCategoryTheorems
createsLimitsForgetToScheme 📖CompOp
equivCommRingCat 📖CompOp
forgetToScheme 📖CompOp
5 mathmath: forgetToScheme_preservesLimits, forgetToScheme_full, forgetToScheme_faithful, forgetToScheme_map, forgetToScheme_obj
mk 📖CompOp
of 📖CompOp
ofHom 📖CompOp
Γ 📖CompOp
4 mathmath: instIsEquivalenceOppositeCommRingCatOpRightOpΓ, instIsEquivalenceOppositeCommRingCatRightOpΓ, Γ_preservesLimits, ΓIsEquiv

Theorems

NameKindAssumesProvesValidatesDepends On
Spec_essSurj 📖mathematicalCategoryTheory.Functor.EssSurj
Opposite
CommRingCat
AlgebraicGeometry.AffineScheme
CategoryTheory.Category.opposite
CommRingCat.instCategory
AlgebraicGeometry.instCategoryAffineScheme
Spec
CategoryTheory.Functor.EssSurj.toEssImage
Spec_faithful 📖mathematicalCategoryTheory.Functor.Faithful
Opposite
CommRingCat
CategoryTheory.Category.opposite
CommRingCat.instCategory
AlgebraicGeometry.AffineScheme
AlgebraicGeometry.instCategoryAffineScheme
Spec
CategoryTheory.Functor.Faithful.toEssImage
AlgebraicGeometry.Spec.faithful
Spec_full 📖mathematicalCategoryTheory.Functor.Full
Opposite
CommRingCat
CategoryTheory.Category.opposite
CommRingCat.instCategory
AlgebraicGeometry.AffineScheme
AlgebraicGeometry.instCategoryAffineScheme
Spec
CategoryTheory.Functor.Full.toEssImage
AlgebraicGeometry.Spec.full
forgetToScheme_faithful 📖mathematicalCategoryTheory.Functor.Faithful
AlgebraicGeometry.AffineScheme
AlgebraicGeometry.instCategoryAffineScheme
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
forgetToScheme
CategoryTheory.ObjectProperty.faithful_ι
forgetToScheme_full 📖mathematicalCategoryTheory.Functor.Full
AlgebraicGeometry.AffineScheme
AlgebraicGeometry.instCategoryAffineScheme
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
forgetToScheme
CategoryTheory.ObjectProperty.full_ι
forgetToScheme_map 📖mathematicalCategoryTheory.Functor.map
AlgebraicGeometry.AffineScheme
AlgebraicGeometry.instCategoryAffineScheme
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
forgetToScheme
CategoryTheory.InducedCategory.Hom.hom
CategoryTheory.ObjectProperty.FullSubcategory
CategoryTheory.Functor.essImage
Opposite
CommRingCat
CategoryTheory.Category.opposite
CommRingCat.instCategory
AlgebraicGeometry.Scheme.Spec
CategoryTheory.ObjectProperty.FullSubcategory.obj
forgetToScheme_obj 📖mathematicalCategoryTheory.Functor.obj
AlgebraicGeometry.AffineScheme
AlgebraicGeometry.instCategoryAffineScheme
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
forgetToScheme
CategoryTheory.ObjectProperty.FullSubcategory.obj
CategoryTheory.Functor.essImage
Opposite
CommRingCat
CategoryTheory.Category.opposite
CommRingCat.instCategory
AlgebraicGeometry.Scheme.Spec
forgetToScheme_preservesLimits 📖mathematicalCategoryTheory.Limits.PreservesLimits
AlgebraicGeometry.AffineScheme
AlgebraicGeometry.instCategoryAffineScheme
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
forgetToScheme
CategoryTheory.Limits.preservesLimits_of_natIso
CategoryTheory.Limits.comp_preservesLimits
CategoryTheory.Functor.instPreservesLimitsOfSizeOfIsRightAdjoint
CategoryTheory.Functor.isRightAdjoint_of_isEquivalence
CategoryTheory.Equivalence.isEquivalence_functor
CategoryTheory.instIsRightAdjointOfMonadicRightAdjoint
hasColimits 📖mathematicalCategoryTheory.Limits.HasColimits
AlgebraicGeometry.AffineScheme
AlgebraicGeometry.instCategoryAffineScheme
CategoryTheory.Adjunction.has_colimits_of_equivalence
CategoryTheory.Equivalence.isEquivalence_inverse
CategoryTheory.Limits.hasColimits_op_of_hasLimits
CategoryTheory.Adjunction.has_limits_of_equivalence
ΓIsEquiv
CommRingCat.hasLimits
hasLimits 📖mathematicalCategoryTheory.Limits.HasLimits
AlgebraicGeometry.AffineScheme
AlgebraicGeometry.instCategoryAffineScheme
CategoryTheory.Adjunction.has_limits_of_equivalence
CategoryTheory.Equivalence.isEquivalence_inverse
CategoryTheory.Limits.hasLimits_op_of_hasColimits
CategoryTheory.Adjunction.has_colimits_of_equivalence
ΓIsEquiv
CommRingCat.Colimits.hasColimits_commRingCat
instIsEquivalenceOppositeCommRingCatOpRightOpΓ 📖mathematicalCategoryTheory.Functor.IsEquivalence
Opposite
AlgebraicGeometry.AffineScheme
CategoryTheory.Category.opposite
AlgebraicGeometry.instCategoryAffineScheme
CommRingCat
CommRingCat.instCategory
CategoryTheory.Functor.op
CategoryTheory.Functor.rightOp
Γ
CategoryTheory.Equivalence.isEquivalence_functor
instIsEquivalenceOppositeCommRingCatRightOpΓ 📖mathematicalCategoryTheory.Functor.IsEquivalence
AlgebraicGeometry.AffineScheme
AlgebraicGeometry.instCategoryAffineScheme
Opposite
CommRingCat
CategoryTheory.Category.opposite
CommRingCat.instCategory
CategoryTheory.Functor.rightOp
Γ
CategoryTheory.Equivalence.isEquivalence_functor
mk_obj 📖mathematicalCategoryTheory.ObjectProperty.FullSubcategory.obj
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CategoryTheory.Functor.essImage
Opposite
CommRingCat
CategoryTheory.Category.opposite
CommRingCat.instCategory
AlgebraicGeometry.Scheme.Spec
ΓIsEquiv 📖mathematicalCategoryTheory.Functor.IsEquivalence
Opposite
AlgebraicGeometry.AffineScheme
CategoryTheory.Category.opposite
AlgebraicGeometry.instCategoryAffineScheme
CommRingCat
CommRingCat.instCategory
Γ
CategoryTheory.Functor.isEquivalence_trans
instIsEquivalenceOppositeCommRingCatOpRightOpΓ
CategoryTheory.Equivalence.isEquivalence_functor
Γ_preservesLimits 📖mathematicalCategoryTheory.Limits.PreservesLimits
AlgebraicGeometry.AffineScheme
AlgebraicGeometry.instCategoryAffineScheme
Opposite
CommRingCat
CategoryTheory.Category.opposite
CommRingCat.instCategory
CategoryTheory.Functor.rightOp
Γ
CategoryTheory.Functor.instPreservesLimitsOfSizeOfIsRightAdjoint
CategoryTheory.Functor.IsLeftAdjoint.rightOp
CategoryTheory.Functor.isLeftAdjoint_of_isEquivalence
ΓIsEquiv

AlgebraicGeometry.IsAffine

Theorems

NameKindAssumesProvesValidatesDepends On
affine 📖mathematicalCategoryTheory.IsIso
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Spec
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
AlgebraicGeometry.Scheme.toSpecΓ
iff_of_isIso 📖mathematicalAlgebraicGeometry.IsAffineof_isIso
CategoryTheory.IsIso.inv_isIso
of_isIso 📖mathematicalAlgebraicGeometry.IsAffineAlgebraicGeometry.essImage_Spec
CategoryTheory.Functor.essImage.ofIso

AlgebraicGeometry.IsAffineOpen

Definitions

NameCategoryTheorems
appBasicOpenIsoAwayMap 📖CompOp
arrowStalkMapIso 📖CompOp
basicOpenSectionsToAffine 📖CompOp
1 mathmath: basicOpenSectionsToAffine_isIso
fromSpec 📖CompOp
33 mathmath: map_fromSpec_assoc, map_fromSpec, opensRange_fromSpec, basicOpen_fromSpec_app, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_ideal, fromSpec_preimage_zeroLocus, fromSpec_app_self, fromSpec_preimage_self, toSpecΓ_fromSpec_assoc, fromSpec_app_self_apply, fromSpec_preimage_basicOpen, AlgebraicGeometry.Scheme.Hom.ι_fromNormalization_assoc, range_fromSpec, AlgebraicGeometry.Scheme.AffineZariskiSite.cocone_ι_app, SpecMap_appLE_fromSpec_assoc, fromSpec_top, Spec_map_appLE_fromSpec, fromSpec_image_basicOpen, Spec_map_appLE_fromSpec_assoc, fromSpec_toSpecΓ_assoc, fromSpec_image_zeroLocus, isOpenImmersion_fromSpec, AlgebraicGeometry.Scheme.Hom.ι_fromNormalization, fromSpec_preimage_basicOpen', AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjι_ι, ΓSpecIso_hom_fromSpec_app, SpecMap_appLE_fromSpec, fromSpec_app_of_le, fromSpec_toSpecΓ, isoSpec_inv_ι, toSpecΓ_fromSpec, fromSpec_primeIdealOf, isoSpec_inv_ι_assoc
instAlgebraCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecPresheafOpOpens 📖CompOp
2 mathmath: algebraMap_Spec_obj, instAwayCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecPresheafOpOpensBasicOpen
isoSpec 📖CompOp
16 mathmath: isoSpec_inv_appTop, isoSpec_inv, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_hom_app, isoSpec_inv_toSpecΓ, toSpecΓ_isoSpec_inv, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι, isoSpec_hom_apply, isoSpec_inv_toSpecΓ_assoc, isoSpec_hom_base_apply, isLocalization_stalk', isoSpec_hom, toSpecΓ_isoSpec_inv_assoc, isoSpec_inv_ι, isoSpec_hom_appTop, isoSpec_inv_ι_assoc, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_inv_app
primeIdealOf 📖CompOp
8 mathmath: AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.quasiFiniteAt, primeIdealOf_isMaximal_of_isClosed, AlgebraicGeometry.formallySmooth_stalkMap_iff, comap_primeIdealOf_appLE, primeIdealOf_eq_map_closedPoint, isLocalization_stalk, fromSpec_primeIdealOf, primeIdealOf_genericPoint

Theorems

NameKindAssumesProvesValidatesDepends On
SpecMap_appLE_fromSpec 📖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'
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Spec
Opposite
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Spec.map
AlgebraicGeometry.Scheme.Hom.appLE
fromSpec
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
CategoryTheory.Category.assoc
AlgebraicGeometry.Scheme.homOfLE_ι
AlgebraicGeometry.morphismRestrict_ι
AlgebraicGeometry.Scheme.isoSpec_inv_naturality_assoc
AlgebraicGeometry.Spec.map_comp_assoc
AlgebraicGeometry.Scheme.Hom.comp_appTop
AlgebraicGeometry.image_morphismRestrict_preimage
AlgebraicGeometry.morphismRestrict_appTop
AlgebraicGeometry.Scheme.ι_image_homOfLE_le_ι_image
AlgebraicGeometry.Scheme.homOfLE_appTop
le_rfl
AlgebraicGeometry.Scheme.Hom.app_eq_appLE
LE.le.trans
AlgebraicGeometry.Scheme.Hom.appLE_map
AlgebraicGeometry.Scheme.Hom.map_appLE
SpecMap_appLE_fromSpec_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
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Spec
Opposite
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Spec.map
AlgebraicGeometry.Scheme.Hom.appLE
fromSpec
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
SpecMap_appLE_fromSpec
Spec_basicOpen 📖mathematicalAlgebraicGeometry.IsAffineOpen
AlgebraicGeometry.Spec
PrimeSpectrum.basicOpen
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
basicOpen
AlgebraicGeometry.isAffineOpen_top
AlgebraicGeometry.isAffine_Spec
AlgebraicGeometry.basicOpen_eq_of_affine
Spec_map_appLE_fromSpec 📖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'
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Spec
Opposite
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Spec.map
AlgebraicGeometry.Scheme.Hom.appLE
fromSpec
SpecMap_appLE_fromSpec
Spec_map_appLE_fromSpec_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
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Spec
Opposite
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Spec.map
AlgebraicGeometry.Scheme.Hom.appLE
fromSpec
SpecMap_appLE_fromSpec_assoc
algebraMap_Spec_obj 📖mathematicalalgebraMap
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
AlgebraicGeometry.Spec
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
CommRing.toCommSemiring
CommRingCat.commRing
CommSemiring.toSemiring
instAlgebraCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecPresheafOpOpens
CommRingCat.Hom.hom
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
CategoryTheory.Iso.inv
AlgebraicGeometry.Scheme.ΓSpecIso
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.homOfLE
le_top
appLE_eq_away_map 📖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.Hom.appLE
AlgebraicGeometry.Scheme.basicOpen
DFunLike.coe
Opposite
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
CommRingCat.ofHom
IsLocalization.Away.map
AlgebraicGeometry.Scheme.algebra_section_section_basicOpen
CommRingCat.Hom.hom
isLocalization_basicOpen
CommRingCat.hom_ext
isLocalization_basicOpen
IsLocalization.ringHom_ext
IsLocalization.Away.map.eq_1
CommRingCat.hom_ofHom
IsLocalization.map_comp
AlgebraicGeometry.Scheme.basicOpen_le
RingHom.algebraMap_toAlgebra
CommRingCat.hom_comp
LE.le.trans
AlgebraicGeometry.Scheme.Hom.appLE_map
AlgebraicGeometry.Scheme.Hom.map_appLE
app_basicOpen_eq_away_map 📖mathematicalAlgebraicGeometry.Scheme.Hom.app
AlgebraicGeometry.Scheme.basicOpen
CategoryTheory.CategoryStruct.comp
CommRingCat
CategoryTheory.Category.toCategoryStruct
CommRingCat.instCategory
CommRingCat.of
CommRingCat.carrier
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
CommRingCat.commRing
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
CommRingCat.instConcreteCategoryRingHomCarrier
CommRingCat.ofHom
IsLocalization.Away.map
AlgebraicGeometry.Scheme.algebra_section_section_basicOpen
CommRingCat.Hom.hom
isLocalization_basicOpen
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.eqToHom
CommRingCat.hom_ext
isLocalization_basicOpen
IsLocalization.ringHom_ext
IsLocalization.Away.map.eq_1
CommRingCat.hom_comp
RingHom.comp_assoc
CommRingCat.hom_ofHom
IsLocalization.map_comp
AlgebraicGeometry.Scheme.basicOpen_le
RingHom.algebraMap_toAlgebra
CategoryTheory.Functor.map_comp
LE.le.trans
le_of_eq
Opposite.op_injective
CategoryTheory.NatTrans.naturality
CategoryTheory.eqToHom_op
basicOpen 📖mathematicalAlgebraicGeometry.IsAffineOpen
AlgebraicGeometry.Scheme.basicOpen
isOpenImmersion_fromSpec
fromSpec_image_basicOpen
AlgebraicGeometry.Scheme.Hom.isAffineOpen_iff_of_isOpenImmersion
AlgebraicGeometry.Scheme.isOpenImmersion_SpecMap_localizationAway
TopologicalSpace.Opens.ext
PrimeSpectrum.localization_away_comap_range
Localization.isLocalization
AlgebraicGeometry.isAffineOpen_opensRange
AlgebraicGeometry.isAffine_Spec
basicOpenSectionsToAffine_isIso 📖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.Scheme.basicOpen
AlgebraicGeometry.Spec
PrimeSpectrum.basicOpen
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
basicOpenSectionsToAffine
CategoryTheory.IsIso.comp_isIso'
AlgebraicGeometry.Scheme.Hom.isIso_app
isOpenImmersion_fromSpec
AlgebraicGeometry.Scheme.basicOpen_le
opensRange_fromSpec
CategoryTheory.Functor.map_isIso
CategoryTheory.isIso_op
CategoryTheory.instIsIsoEqToHom
basicOpen_basicOpen_is_basicOpen 📖mathematicalAlgebraicGeometry.Scheme.basicOpenisLocalization_basicOpen
IsLocalization.surj''
Algebra.smul_def
AlgebraicGeometry.Scheme.basicOpen_mul
AlgebraicGeometry.Scheme.basicOpen_le
RingHom.algebraMap_toAlgebra
AlgebraicGeometry.Scheme.basicOpen_res
inf_eq_left
LE.le.trans_eq
inf_le_left
AlgebraicGeometry.Scheme.basicOpen_of_isUnit
Submonoid.leftInv_le_isUnit
Subtype.prop
basicOpen_fromSpec_app 📖mathematicalAlgebraicGeometry.Scheme.basicOpen
AlgebraicGeometry.Spec
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'
fromSpec
DFunLike.coe
CommRingCat.carrier
CategoryTheory.ConcreteCategory.hom
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
RingHom.instFunLike
CommRingCat.instConcreteCategoryRingHomCarrier
AlgebraicGeometry.Scheme.Hom.app
PrimeSpectrum.basicOpen
fromSpec_preimage_basicOpen
AlgebraicGeometry.Scheme.preimage_basicOpen
basicOpen_union_eq_self_iff 📖mathematicaliSup
AlgebraicGeometry.Scheme.Opens
Set.Elem
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
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
AlgebraicGeometry.Scheme.basicOpen
Set
Set.instMembership
Ideal.span
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
Top.top
Ideal
Submodule.instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
iSup_basicOpen_eq_self_iff
comap_primeIdealOf_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
AlgebraicGeometry.Scheme.Hom.toLRSHom'
SetLike.instMembership
TopologicalSpace.Opens.instSetLike
PrimeSpectrum.comap
CommRingCat.carrier
Opposite
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
CommRing.toCommSemiring
CommRingCat.commRing
CommRingCat.Hom.hom
AlgebraicGeometry.Scheme.Hom.appLE
primeIdealOf
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_appLE
AlgebraicGeometry.Scheme.Hom.comp_apply
AlgebraicGeometry.Scheme.Hom.coe_resLE_apply
exists_basicOpen_le 📖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
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.Scheme.basicOpen
TopologicalSpace.IsTopologicalBasis.exists_subset_of_mem_open
AlgebraicGeometry.isBasis_basicOpen
TopologicalSpace.Opens.isOpen
AlgebraicGeometry.Scheme.Opens.mem_basicOpen_toScheme
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
AlgebraicGeometry.Scheme.image_basicOpen
AlgebraicGeometry.Scheme.Opens.ι_appIso
LE.le.trans
AlgebraicGeometry.Scheme.Hom.image_mono
AlgebraicGeometry.Scheme.Hom.image_preimage_le
CategoryTheory.eqToHom_op
AlgebraicGeometry.Scheme.basicOpen_res_eq
CategoryTheory.instIsIsoEqToHom
fromSpec_app_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
AlgebraicGeometry.Scheme.Hom.app
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
fromSpec
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.homOfLE
Top.top
OrderTop.toTop
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
CategoryTheory.Iso.inv
AlgebraicGeometry.Scheme.ΓSpecIso
le_top
eq_top_iff
le_top
fromSpec.eq_1
AlgebraicGeometry.Scheme.Hom.comp_app
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
Set.image_preimage_subset
AlgebraicGeometry.Scheme.Opens.ι_app
AlgebraicGeometry.Scheme.Hom.app_eq
AlgebraicGeometry.Scheme.Hom.appTop.eq_1
isoSpec_inv_appTop
CategoryTheory.Category.assoc
CategoryTheory.Functor.map_comp_assoc
fromSpec_app_self 📖mathematicalAlgebraicGeometry.Scheme.Hom.app
AlgebraicGeometry.Spec
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
fromSpec
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.Iso.inv
AlgebraicGeometry.Scheme.ΓSpecIso
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.eqToHom
fromSpec_preimage_self
fromSpec_preimage_self
ΓSpecIso_hom_fromSpec_app
CategoryTheory.Iso.inv_hom_id_assoc
fromSpec_app_self_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.Spec
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
fromSpec
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
RingHom.instFunLike
CategoryTheory.ConcreteCategory.hom
CommRingCat.instConcreteCategoryRingHomCarrier
AlgebraicGeometry.Scheme.Hom.app
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
CategoryTheory.Functor.map
CategoryTheory.eqToHom
CategoryTheory.CategoryStruct.opposite
CategoryTheory.Category.toCategoryStruct
fromSpec_preimage_self
CategoryTheory.Iso.inv
AlgebraicGeometry.Scheme.ΓSpecIso
fromSpec_preimage_self
CategoryTheory.comp_apply
Mathlib.Tactic.Elementwise.hom_elementwise
fromSpec_app_self
CategoryTheory.eqToHom_op
fromSpec_image_basicOpen 📖mathematicalCategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.Spec
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.SheafedSpace.instTopologicalSpaceCarrierCarrier
AlgebraicGeometry.Scheme.Hom.opensFunctor
fromSpec
isOpenImmersion_fromSpec
PrimeSpectrum.basicOpen
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
AlgebraicGeometry.Scheme.basicOpen
isOpenImmersion_fromSpec
fromSpec_preimage_basicOpen
TopologicalSpace.Opens.ext
Set.image_preimage_eq_inter_range
Set.inter_eq_left
range_fromSpec
AlgebraicGeometry.Scheme.basicOpen_le
fromSpec_image_zeroLocus 📖mathematicalSet.image
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
fromSpec
PrimeSpectrum.zeroLocus
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
Set
Set.instInter
AlgebraicGeometry.Scheme.zeroLocus
SetLike.coe
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
fromSpec_preimage_zeroLocus
Set.image_preimage_eq_inter_range
range_fromSpec
fromSpec_preimage_basicOpen 📖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
AlgebraicGeometry.Spec
Opposite
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
fromSpec
AlgebraicGeometry.Scheme.basicOpen
PrimeSpectrum.basicOpen
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
fromSpec_preimage_basicOpen'
AlgebraicGeometry.basicOpen_eq_of_affine
fromSpec_preimage_basicOpen' 📖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
AlgebraicGeometry.Spec
Opposite
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
fromSpec
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
DFunLike.coe
CommRingCat.carrier
CategoryTheory.ConcreteCategory.hom
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
RingHom.instFunLike
CommRingCat.instConcreteCategoryRingHomCarrier
CategoryTheory.Iso.inv
AlgebraicGeometry.Scheme.ΓSpecIso
AlgebraicGeometry.Scheme.preimage_basicOpen
fromSpec_preimage_self
fromSpec_app_self
AlgebraicGeometry.Scheme.basicOpen_res_eq
CategoryTheory.isIso_op
CategoryTheory.instIsIsoEqToHom
fromSpec_preimage_self 📖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
AlgebraicGeometry.Spec
Opposite
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
fromSpec
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
isOpenImmersion_fromSpec
opensRange_fromSpec
AlgebraicGeometry.Scheme.Hom.preimage_opensRange
fromSpec_preimage_zeroLocus 📖mathematicalSet.preimage
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
fromSpec
AlgebraicGeometry.Scheme.zeroLocus
PrimeSpectrum.zeroLocus
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
Set.ext
isOpenImmersion_fromSpec
fromSpec_image_basicOpen
fromSpec_primeIdealOf 📖mathematicalDFunLike.coe
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
fromSpec
primeIdealOf
SetLike.instMembership
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
AlgebraicGeometry.Scheme.Hom.comp_apply
CategoryTheory.Iso.hom_inv_id_assoc
fromSpec_toSpecΓ 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Spec
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
fromSpec
AlgebraicGeometry.Scheme.toSpecΓ
AlgebraicGeometry.Spec.map
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.homOfLE
le_top
le_top
fromSpec.eq_1
CategoryTheory.Category.assoc
AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top
isoSpec_inv_toSpecΓ_assoc
fromSpec_toSpecΓ_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Spec
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
fromSpec
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
AlgebraicGeometry.Scheme.toSpecΓ
AlgebraicGeometry.Spec.map
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.homOfLE
le_top
le_top
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
fromSpec_toSpecΓ
fromSpec_top 📖mathematicalfromSpec
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.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
AlgebraicGeometry.isAffineOpen_top
CategoryTheory.Iso.inv
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.isoSpec
AlgebraicGeometry.isAffineOpen_top
fromSpec.eq_1
CategoryTheory.Iso.inv_comp_eq
AlgebraicGeometry.Scheme.Opens.toSpecΓ_top
CategoryTheory.Category.assoc
AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv
CategoryTheory.Category.comp_id
iSup_basicOpen_eq_self_iff 📖mathematicaliSup
AlgebraicGeometry.Scheme.Opens
Set.Elem
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
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
AlgebraicGeometry.Scheme.basicOpen
Set
Set.instMembership
Ideal.span
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
Top.top
Ideal
Submodule.instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
TopologicalSpace.Opens.ext
Set.Subset.antisymm
TopologicalSpace.Opens.coe_iSup
AlgebraicGeometry.Scheme.basicOpen_le
Set.inter_self
range_fromSpec
Set.image_preimage_eq_inter_range
isOpen_iUnion
TopologicalSpace.Opens.is_open'
TopologicalSpace.Opens.iSup_def
Set.preimage_iUnion
fromSpec_preimage_basicOpen
fromSpec_preimage_self
PrimeSpectrum.basicOpen_eq_zeroLocus_compl
Set.compl_iInter
Set.compl_univ_iff
PrimeSpectrum.zeroLocus_iUnion
PrimeSpectrum.zeroLocus_empty_iff_eq_top
PrimeSpectrum.zeroLocus_span
Set.iUnion_singleton_eq_range
Subtype.range_val_subtype
ideal_ext_iff 📖mathematicalIdeal.map
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
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
RingHom.instFunLike
CommRingCat.Hom.hom
TopCat.Presheaf.germ
CommRingCat.Colimits.hasColimits_commRingCat
ideal_le_iff
ideal_le_iff 📖mathematicalIdeal
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
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
Preorder.toLE
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
Ideal.map
RingHom
RingHom.instFunLike
CommRingCat.Hom.hom
TopCat.Presheaf.germ
CommRingCat.Colimits.hasColimits_commRingCat
Ideal.map_mono
mem_ideal_iff
Ideal.mem_map_of_mem
image_of_isOpenImmersion 📖mathematicalAlgebraicGeometry.IsAffineOpen
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
AlgebraicGeometry.Scheme.Hom.isAffineOpen_iff_of_isOpenImmersion
instAwayCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecPresheafOpOpensBasicOpen 📖mathematicalIsLocalization.Away
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.Spec
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
PrimeSpectrum.basicOpen
instAlgebraCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecPresheafOpOpens
AlgebraicGeometry.StructureSheaf.IsLocalization.to_basicOpen
instIsAffineToSchemeBasicOpen 📖mathematicalAlgebraicGeometry.IsAffine
AlgebraicGeometry.Scheme.Opens.toScheme
AlgebraicGeometry.Scheme.basicOpen
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.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
basicOpen
AlgebraicGeometry.isAffineOpen_top
isCompact 📖mathematicalIsCompact
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
SetLike.coe
AlgebraicGeometry.Scheme.Opens
TopologicalSpace.Opens.instSetLike
Set.image_univ
range_fromSpec
IsCompact.image
CompactSpace.isCompact_univ
PrimeSpectrum.compactSpace
AlgebraicGeometry.Scheme.Hom.continuous
isLocalization_basicOpen 📖mathematicalIsLocalization.Away
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
CommRing.toCommSemiring
CommRingCat.commRing
AlgebraicGeometry.Scheme.basicOpen
AlgebraicGeometry.Scheme.algebra_section_section_basicOpen
basicOpenSectionsToAffine_isIso
IsLocalization.isLocalization_iff_of_ringEquiv
Algebra.algebra_ext
AlgebraicGeometry.Scheme.basicOpen_le
le_top
AlgebraicGeometry.Scheme.Hom.naturality_assoc
fromSpec_preimage_self
fromSpec_app_self
AlgebraicGeometry.StructureSheaf.IsLocalization.to_basicOpen
isLocalization_of_eq_basicOpen 📖mathematicalAlgebraicGeometry.Scheme.basicOpenIsLocalization.Away
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
CommRing.toCommSemiring
CommRingCat.commRing
RingHom.toAlgebra
CommRingCat.Hom.hom
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
isLocalization_basicOpen
isLocalization_stalk 📖mathematicalIsLocalization.AtPrime
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
CommRing.toCommSemiring
CommRingCat.commRing
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
SetLike.instMembership
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
TopCat.Presheaf.algebra_section_stalk
PrimeSpectrum.asIdeal
primeIdealOf
PrimeSpectrum.isPrime
CommRingCat.Colimits.hasColimits_commRingCat
PrimeSpectrum.isPrime
fromSpec_primeIdealOf
isLocalization_stalk'
isLocalization_stalk' 📖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
DFunLike.coe
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
fromSpec
IsLocalization.AtPrime
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
TopCat.Presheaf.algebra_section_stalk
AlgebraicGeometry.Scheme.Opens.toScheme
TopCat.Hom.hom'
AlgebraicGeometry.Scheme.Hom.toLRSHom
CategoryTheory.Iso.inv
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
isoSpec
PrimeSpectrum.asIdeal
PrimeSpectrum.isPrime
PrimeSpectrum.isPrime
CommRingCat.Colimits.hasColimits_commRingCat
AlgebraicGeometry.IsOpenImmersion.instIsIsoCommRingCatStalkMap
isOpenImmersion_fromSpec
IsLocalization.isLocalization_iff_of_ringEquiv
fromSpec_preimage_self
AlgebraicGeometry.Scheme.Hom.germ_stalkMap
fromSpec_app_self
CategoryTheory.eqToHom_op
CategoryTheory.Category.assoc
TopCat.Presheaf.germ_res'
AlgebraicGeometry.StructureSheaf.IsLocalization.to_stalk
isOpenImmersion_fromSpec 📖mathematicalAlgebraicGeometry.IsOpenImmersion
AlgebraicGeometry.Spec
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
fromSpec
AlgebraicGeometry.IsOpenImmersion.comp
AlgebraicGeometry.IsOpenImmersion.of_isIso
CategoryTheory.Iso.isIso_inv
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
isoSpec_hom 📖mathematicalCategoryTheory.Iso.hom
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.Opens.toScheme
AlgebraicGeometry.Spec
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
isoSpec
AlgebraicGeometry.Scheme.Opens.toSpecΓ
isoSpec_hom_appTop 📖mathematicalAlgebraicGeometry.Scheme.Hom.appTop
AlgebraicGeometry.Scheme.Opens.toScheme
AlgebraicGeometry.Spec
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
CategoryTheory.Iso.hom
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
isoSpec
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
AlgebraicGeometry.Scheme.ΓSpecIso
CategoryTheory.Iso.inv
AlgebraicGeometry.Scheme.Opens.topIso
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
CategoryTheory.eqToHom_op
AlgebraicGeometry.Scheme.toSpecΓ_appTop
AlgebraicGeometry.Scheme.ΓSpecIso_naturality
isoSpec_hom_apply 📖mathematicalDFunLike.coe
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.Scheme.Opens.toScheme
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.Iso.hom
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
isoSpec
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
SetLike.instMembership
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
AlgebraicGeometry.Spec.map
TopCat.Presheaf.germ
IsLocalRing.closedPoint
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
AlgebraicGeometry.LocallyRingedSpace.instIsLocalRingCarrierStalkCommRingCatPresheaf
CommRingCat.Colimits.hasColimits_commRingCat
AlgebraicGeometry.LocallyRingedSpace.instIsLocalRingCarrierStalkCommRingCatPresheaf
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
AlgebraicGeometry.Scheme.Hom.comp_apply
AlgebraicGeometry.Spec.map_comp
CategoryTheory.Iso.eq_comp_inv
AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom
TopCat.Presheaf.germ_res_assoc
IsLocalRing.comap_closedPoint
isLocalHom_of_isIso
CategoryTheory.Iso.isIso_inv
isoSpec_hom_base_apply 📖mathematicalDFunLike.coe
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.Scheme.Opens.toScheme
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.Iso.hom
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
isoSpec
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
SetLike.instMembership
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
AlgebraicGeometry.Spec.map
TopCat.Presheaf.germ
IsLocalRing.closedPoint
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
AlgebraicGeometry.LocallyRingedSpace.instIsLocalRingCarrierStalkCommRingCatPresheaf
isoSpec_hom_apply
isoSpec_inv 📖mathematicalCategoryTheory.Iso.inv
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.Opens.toScheme
AlgebraicGeometry.Spec
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
isoSpec
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
AlgebraicGeometry.Spec.map
CategoryTheory.Functor.map
TopCat
TopCat.instCategory
TopologicalSpace.Opens.toTopCat
IsOpenMap.functor
TopologicalSpace.Opens.inclusion'
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
AlgebraicGeometry.Scheme.Hom.opensFunctor
AlgebraicGeometry.Scheme.Opens.ι
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
CategoryTheory.eqToHom
AlgebraicGeometry.Scheme.isoSpec
isoSpec_inv_appTop 📖mathematicalAlgebraicGeometry.Scheme.Hom.appTop
AlgebraicGeometry.Spec
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.Scheme.Opens.toScheme
CategoryTheory.Iso.inv
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
isoSpec
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
CategoryTheory.Iso.hom
AlgebraicGeometry.Scheme.Opens.topIso
AlgebraicGeometry.Scheme.ΓSpecIso
CategoryTheory.cancel_mono
CategoryTheory.mono_of_strongMono
CategoryTheory.instStrongMonoOfIsRegularMono
CategoryTheory.instIsRegularMonoOfIsSplitMono
CategoryTheory.IsSplitMono.of_iso
AlgebraicGeometry.Scheme.Hom.instIsIsoCommRingCatApp
CategoryTheory.Iso.isIso_hom
AlgebraicGeometry.Scheme.Hom.comp_appTop
isoSpec_hom_appTop
CategoryTheory.Iso.hom_inv_id
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
CategoryTheory.eqToHom_op
AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality
CategoryTheory.Category.assoc
AlgebraicGeometry.Scheme.ΓSpecIso_naturality_assoc
CategoryTheory.eqToHom_map_comp
CategoryTheory.Functor.map_id
CategoryTheory.Iso.inv_hom_id_assoc
isoSpec_inv_toSpecΓ 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Spec
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.Scheme.Opens.toScheme
CategoryTheory.Iso.inv
isoSpec
AlgebraicGeometry.Scheme.Opens.toSpecΓ
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.inv_hom_id
isoSpec_inv_toSpecΓ_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Spec
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.Scheme.Opens.toScheme
CategoryTheory.Iso.inv
isoSpec
AlgebraicGeometry.Scheme.Opens.toSpecΓ
CategoryTheory.Category.assoc
CategoryTheory.Category.id_comp
Mathlib.Tactic.Reassoc.eq_whisker'
isoSpec_inv_toSpecΓ
isoSpec_inv_ι 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Spec
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.Scheme.Opens.toScheme
CategoryTheory.Iso.inv
isoSpec
AlgebraicGeometry.Scheme.Opens.ι
fromSpec
isoSpec_inv_ι_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Spec
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.Scheme.Opens.toScheme
CategoryTheory.Iso.inv
isoSpec
AlgebraicGeometry.Scheme.Opens.ι
fromSpec
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
isoSpec_inv_ι
map_fromSpec 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Spec
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.Spec.map
CategoryTheory.Functor.map
fromSpec
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
AlgebraicGeometry.Scheme.ι_image_homOfLE_le_ι_image
fromSpec.eq_1
AlgebraicGeometry.Scheme.homOfLE_ι
isoSpec_inv
CategoryTheory.Category.assoc
AlgebraicGeometry.Scheme.isoSpec_inv_naturality_assoc
AlgebraicGeometry.Spec.map_comp_assoc
AlgebraicGeometry.Scheme.homOfLE_appTop
CategoryTheory.Functor.map_comp
map_fromSpec_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Spec
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.Spec.map
CategoryTheory.Functor.map
fromSpec
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
map_fromSpec
mem_ideal_iff 📖mathematicalCommRingCat.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
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
Ideal.map
RingHom
RingHom.instFunLike
CommRingCat.Hom.hom
TopCat.Presheaf.germ
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
CommRingCat.instConcreteCategoryRingHomCarrier
CommRingCat.Colimits.hasColimits_commRingCat
Ideal.mem_map_of_mem
isLocalization_stalk'
Submodule.mem_of_localization_maximal
Ideal.IsMaximal.isPrime
instIsLocalizedModuleLinearMapOfIsLocalization
Ideal.IsMaximal.isPrime'
IsScalarTower.right
Ideal.localized₀_eq_restrictScalars_map
opensRange_fromSpec 📖mathematicalAlgebraicGeometry.Scheme.Hom.opensRange
AlgebraicGeometry.Spec
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
fromSpec
isOpenImmersion_fromSpec
TopologicalSpace.Opens.ext
isOpenImmersion_fromSpec
range_fromSpec
preimage_of_isIso 📖mathematicalAlgebraicGeometry.IsAffineOpen
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
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.IsAffine.of_isIso
AlgebraicGeometry.instIsIsoSchemeMorphismRestrict
preimage_of_isOpenImmersion 📖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
AlgebraicGeometry.IsAffineOpen
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.Scheme.Hom.isAffineOpen_iff_of_isOpenImmersion
AlgebraicGeometry.Scheme.Hom.image_preimage_eq_opensRange_inf
inf_eq_right
primeIdealOf_eq_map_closedPoint 📖mathematicalprimeIdealOf
DFunLike.coe
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.Spec
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
AlgebraicGeometry.PresheafedSpace.presheaf
TopCat.carrier
AlgebraicGeometry.Scheme.Opens
SetLike.instMembership
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
Opposite.op
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.Spec.map
TopCat.Presheaf.germ
IsLocalRing.closedPoint
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
AlgebraicGeometry.LocallyRingedSpace.instIsLocalRingCarrierStalkCommRingCatPresheaf
isoSpec_hom_apply
primeIdealOf_isMaximal_of_isClosed 📖mathematicalIdeal.IsMaximal
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
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
PrimeSpectrum.asIdeal
primeIdealOf
Set.preimage_image_eq
Subtype.val_injective
IsClosed.preimage
Topology.IsOpenEmbedding.continuous
TopologicalSpace.Opens.isOpenEmbedding'
PrimeSpectrum.isClosed_singleton_iff_isMaximal
primeIdealOf.eq_1
Set.image_singleton
Topology.IsClosedEmbedding.isClosed_iff_image_isClosed
IsHomeomorph.isClosedEmbedding
TopCat.isIso_iff_isHomeomorph
AlgebraicGeometry.Scheme.Hom.isIso_base
CategoryTheory.Iso.isIso_hom
range_fromSpec 📖mathematicalSet.range
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
fromSpec
SetLike.coe
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
Set.range_comp
Set.range_eq_univ
TopCat.coe_comp
TopCat.epi_iff_surjective
CategoryTheory.epi_comp
CategoryTheory.epi_of_effectiveEpi
CategoryTheory.instEffectiveEpiOfIsIso
AlgebraicGeometry.Scheme.Hom.isIso_base
AlgebraicGeometry.instIsIsoSchemeMapOfCommRingCat
CategoryTheory.Functor.map_isIso
CategoryTheory.isIso_op
CategoryTheory.instIsIsoEqToHom
CategoryTheory.Iso.isIso_inv
Set.image_univ
Subtype.range_coe
self_le_basicOpen_union_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
iSup
Set.Elem
CommRingCat.carrier
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.Scheme.basicOpen
Set
Set.instMembership
Ideal.span
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
Top.top
Ideal
Submodule.instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
self_le_iSup_basicOpen_iff
self_le_iSup_basicOpen_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
iSup
Set.Elem
CommRingCat.carrier
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.Scheme.basicOpen
Set
Set.instMembership
Ideal.span
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
Top.top
Ideal
Submodule.instTop
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
iSup_basicOpen_eq_self_iff
comm
IsEquiv.toSymm
eq_isEquiv
le_antisymm
AlgebraicGeometry.Scheme.basicOpen_le
le_of_eq
stalkMap_injective 📖mathematicalTopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
TopologicalSpace.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
SetLike.instMembership
TopologicalSpace.Opens.instSetLike
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.Functor.obj
Opposite
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
CommRingCat.carrier
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
RingHom.instFunLike
CommRingCat.instConcreteCategoryRingHomCarrier
TopCat.Presheaf.germ
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
AlgebraicGeometry.Scheme.Hom.stalkMapCommRingCat.Colimits.hasColimits_commRingCat
IsLocalization.injective_of_map_algebraMap_zero
PrimeSpectrum.isPrime
isLocalization_stalk
toSpecΓ_fromSpec 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.Opens.toScheme
AlgebraicGeometry.Spec
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.Scheme.Opens.toSpecΓ
fromSpec
AlgebraicGeometry.Scheme.Opens.ι
toSpecΓ_isoSpec_inv_assoc
toSpecΓ_fromSpec_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.Opens.toScheme
AlgebraicGeometry.Spec
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.Scheme.Opens.toSpecΓ
fromSpec
AlgebraicGeometry.Scheme.Opens.ι
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
toSpecΓ_fromSpec
toSpecΓ_isoSpec_inv 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.Opens.toScheme
AlgebraicGeometry.Spec
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.Scheme.Opens.toSpecΓ
CategoryTheory.Iso.inv
isoSpec
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.hom_inv_id
toSpecΓ_isoSpec_inv_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
AlgebraicGeometry.Scheme.Opens.toScheme
AlgebraicGeometry.Spec
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.Scheme.Opens.toSpecΓ
CategoryTheory.Iso.inv
isoSpec
CategoryTheory.Category.assoc
CategoryTheory.Category.id_comp
Mathlib.Tactic.Reassoc.eq_whisker'
toSpecΓ_isoSpec_inv
ΓSpecIso_hom_fromSpec_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
AlgebraicGeometry.Spec
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
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
fromSpec
CategoryTheory.Iso.hom
AlgebraicGeometry.Scheme.ΓSpecIso
AlgebraicGeometry.Scheme.Hom.app
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.eqToHom
fromSpec_preimage_self
fromSpec_preimage_self
le_top
fromSpec_app_of_le
CategoryTheory.Functor.map_id
CategoryTheory.Category.id_comp
CategoryTheory.Iso.hom_inv_id_assoc
ι_basicOpen_preimage 📖mathematicalAlgebraicGeometry.IsAffineOpen
AlgebraicGeometry.Scheme.Opens.toScheme
AlgebraicGeometry.Scheme.basicOpen
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.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens.instPartialOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
AlgebraicGeometry.Scheme.Opens.ι
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
AlgebraicGeometry.Scheme.Hom.isAffineOpen_iff_of_isOpenImmersion
AlgebraicGeometry.Scheme.Hom.image_preimage_eq_opensRange_inf
AlgebraicGeometry.Scheme.Opens.opensRange_ι
inf_comm
le_top
AlgebraicGeometry.Scheme.basicOpen_res
basicOpen

AlgebraicGeometry.IsOpenImmersion

Definitions

NameCategoryTheorems
affineOpensEquiv 📖CompOp
2 mathmath: affineOpensEquiv_apply_coe_coe, affineOpensEquiv_symm_apply_coe

Theorems

NameKindAssumesProvesValidatesDepends On
affineOpensEquiv_apply_coe_coe 📖mathematicalAlgebraicGeometry.Scheme.Opens
Set
Set.instMembership
AlgebraicGeometry.Scheme.affineOpens
Set.Elem
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
RelIso
RelIso.instFunLike
affineOpensEquiv
CategoryTheory.Functor.obj
Preorder.smallCategory
AlgebraicGeometry.Scheme.Hom.opensFunctor
affineOpensEquiv_symm_apply_coe 📖mathematicalAlgebraicGeometry.Scheme.Opens
Set
Set.instMembership
AlgebraicGeometry.Scheme.affineOpens
DFunLike.coe
RelIso
Set.Elem
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
RelIso.instFunLike
RelIso.symm
affineOpensEquiv
CategoryTheory.Functor.obj
Preorder.smallCategory
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'

AlgebraicGeometry.Scheme

Definitions

NameCategoryTheorems
affineBasicOpen 📖CompOp
5 mathmath: IdealSheafData.opensRange_glueDataObjMap, IdealSheafData.isOpenImmersion_glueDataObjMap, affineBasicOpen_coe, IdealSheafData.map_ideal_basicOpen, affineBasicOpen_le
affineOpens 📖CompOp
88 mathmath: AlgebraicGeometry.iSup_affineOpens_eq_top, IdealSheafData.glueDataObjHom_ι_assoc, AlgebraicGeometry.IsLocallyArtinian.isArtinianRing_presheaf_obj, IdealSheafData.ideal_sSup, ideal_ker_le_ker_ΓSpecIso_inv_comp, IdealSheafData.equivOfIsAffine_apply, IdealSheafData.glueDataObjHom_ι, IdealSheafData.ideal_mul, Hom.toNormalization_app_preimage, Hom.toImage_app_injective, IdealSheafData.ideal_le_ker_glueDataObjι, Hom.fromNormalization_preimage, ker_ideal_of_isPullback_of_isOpenImmersion, IdealSheafData.ideal_map, IdealSheafData.range_glueDataObjι_ι_eq_support_inter, Hom.ι_toNormalization, IdealSheafData.ideal_pow, directedAffineCover_f, IdealSheafData.range_glueDataObjι_ι, AlgebraicGeometry.affineLocally_iff_affineOpens_le, IdealSheafData.vanishingIdeal_ideal, IdealSheafData.ideal_bot, IdealSheafData.subschemeCover_map_subschemeι, IdealSheafData.mem_supportSet_iff, IdealSheafData.mem_support_iff, directedAffineCover_I₀, IdealSheafData.le_ofIdeals_iff, AlgebraicGeometry.HasRingHomProperty.iff_appLE, AlgebraicGeometry.HasAffineProperty.restrict, Hom.ker_apply, IdealSheafData.ideal_comap_of_isOpenImmersion, AlgebraicGeometry.affineOpensRestrict_apply_coe_coe, Hom.ideal_ker_le, IdealSheafData.ofIdeals_mono, IdealSheafData.subschemeι_app, directedAffineCover_X, AlgebraicGeometry.isCompactOpen_iff_eq_finset_affine_union, AlgebraicGeometry.IsOpenImmersion.affineOpensEquiv_apply_coe_coe, IdealSheafData.opensRange_subschemeCover_map, IdealSheafData.ideal_top, AlgebraicGeometry.isCompact_and_isOpen_iff_finite_and_eq_biUnion_affineOpens, AlgebraicGeometry.quasiSeparatedSpace_iff_forall_affineOpens, IdealSheafData.opensRange_glueDataObjMap, Hom.iInf_ker_openCover_map_comp_apply, IdealSheafData.ofIdealTop_ideal, IdealSheafData.ker_subschemeι_app, Hom.ι_toNormalization_assoc, IdealSheafData.ideal_iInf, IdealSheafData.range_glueDataObjι, ker_morphismRestrict_ideal, affineBasicOpen_coe, IdealSheafData.instIsPreimmersionGlueDataObjι, AlgebraicGeometry.isBasis_affine_open, IdealSheafData.coe_support_eq_eq_iInter_zeroLocus, IdealSheafData.supportSet_subset_zeroLocus, AlgebraicGeometry.IsLocallyNoetherian.component_noetherian, IdealSheafData.zeroLocus_inter_subset_supportSet, IdealSheafData.map_ideal', IdealSheafData.ideal_sup, Hom.ι_fromNormalization_assoc, AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE_locally, AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE, IdealSheafData.ideal_mono, IdealSheafData.ideal_iSup, IdealSheafData.radical_ideal, AlgebraicGeometry.isCompact_iff_finite_and_eq_biUnion_affineOpens, IdealSheafData.ideal_inf, IdealSheafData.subschemeι_app_surjective, IdealSheafData.coe_support_inter, AlgebraicGeometry.affineOpensRestrict_symm_apply_coe, IdealSheafData.ideal_ofIdeals_le, IdealSheafData.supportSet_inter, AlgebraicGeometry.instIsAffineToSchemeValOpensMemSetAffineOpens, Hom.ι_fromNormalization, IdealSheafData.ker_glueDataObjι_appTop, IdealSheafData.ideal_biInf, IdealSheafData.glueDataObjι_ι, Hom.toImage_app, isBasis_affineOpens, IdealSheafData.strictMono_ideal, AlgebraicGeometry.sourceAffineLocally_morphismRestrict, IdealSheafData.ideal_map_of_isAffineHom, IdealSheafData.map_ideal_basicOpen, AlgebraicGeometry.quasiSeparatedSpace_iff_affine, IdealSheafData.le_def, IdealSheafData.supportSet_eq_iInter_zeroLocus, AlgebraicGeometry.IsOpenImmersion.affineOpensEquiv_symm_apply_coe, affineBasicOpen_le
arrowStalkMapSpecIso 📖CompOp
isoSpec 📖CompOp
21 mathmath: map_PrimeSpectrum_basicOpen_of_affine, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv, isoSpec_inv_toSpecΓ, isoSpec_inv_preimage_zeroLocus, isoSpec_hom, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over_assoc, isoSpec_hom_naturality, toSpecΓ_isoSpec_inv_assoc, AlgebraicGeometry.IsAffineOpen.isoSpec_inv, isoSpec_hom_naturality_assoc, isoSpec_inv_image_zeroLocus, isoSpec_inv_naturality_assoc, isoSpec_Spec_hom, toSpecΓ_isoSpec_inv, isoSpec_inv_naturality, isoSpec_Spec, isoSpec_inv_toSpecΓ_assoc, isoSpec_Spec_inv, AlgebraicGeometry.IsAffineOpen.fromSpec_top, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over, isoSpec_image_zeroLocus

Theorems

NameKindAssumesProvesValidatesDepends On
affineBasicOpen_coe 📖mathematicalOpens
Set
Set.instMembership
affineOpens
affineBasicOpen
basicOpen
affineBasicOpen_le 📖mathematicalSet.Elem
Opens
affineOpens
Preorder.toLE
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
Set
Set.instMembership
affineBasicOpen
basicOpen_le
compactSpace_of_isAffine 📖mathematicalCompactSpace
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
AlgebraicGeometry.IsAffineOpen.isCompact
AlgebraicGeometry.isAffineOpen_top
eq_zeroLocus_of_isClosed_of_isAffine 📖mathematicalIsClosed
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
zeroLocus
Top.top
Opens
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
SetLike.coe
Ideal
CommRingCat.carrier
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Homeomorph.isClosedMap
CategoryTheory.Iso.isIso_hom
PrimeSpectrum.isClosed_iff_zeroLocus_ideal
Set.preimage_image_eq
Function.Bijective.injective
CategoryTheory.ConcreteCategory.bijective_of_isIso
Hom.isIso_base
zeroLocus_isClosed
isAffine_affineBasisCover 📖mathematicalAlgebraicGeometry.IsAffine
CategoryTheory.PreZeroHypercover.X
AlgebraicGeometry.Scheme
instCategory
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover
precoverage
AlgebraicGeometry.IsOpenImmersion
affineBasisCover
AlgebraicGeometry.isAffine_Spec
local_affine
isAffine_affineCover 📖mathematicalAlgebraicGeometry.IsAffine
CategoryTheory.PreZeroHypercover.X
AlgebraicGeometry.Scheme
instCategory
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover
precoverage
AlgebraicGeometry.IsOpenImmersion
affineCover
AlgebraicGeometry.isAffine_Spec
local_affine
isAffine_affineOpenCover 📖mathematicalAlgebraicGeometry.IsAffine
CategoryTheory.PreZeroHypercover.X
AlgebraicGeometry.Scheme
instCategory
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover
precoverage
AlgebraicGeometry.IsOpenImmersion
AffineOpenCover.openCover
AlgebraicGeometry.isAffine_Spec
isBasis_affineOpens 📖mathematicalTopologicalSpace.Opens.IsBasis
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
affineOpens
TopologicalSpace.Opens.isBasis_iff_nbhd
TopologicalSpace.IsTopologicalBasis.exists_subset_of_mem_open
affineBasisCover_is_basis
TopologicalSpace.Opens.isOpen
TopologicalSpace.IsTopologicalBasis.isOpen
AlgebraicGeometry.isAffineOpen_opensRange
isAffine_affineBasisCover
instIsOpenImmersionF
isoSpec_Spec 📖mathematicalisoSpec
AlgebraicGeometry.Spec
AlgebraicGeometry.isAffine_Spec
CategoryTheory.Functor.mapIso
Opposite
CommRingCat
CategoryTheory.Category.opposite
CommRingCat.instCategory
AlgebraicGeometry.Scheme
instCategory
Spec
Opposite.op
CategoryTheory.Functor.obj
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
TopCat.str
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
CategoryTheory.Iso.op
ΓSpecIso
CategoryTheory.Iso.ext
AlgebraicGeometry.isAffine_Spec
AlgebraicGeometry.SpecMap_ΓSpecIso_hom
isoSpec_Spec_hom 📖mathematicalCategoryTheory.Iso.hom
AlgebraicGeometry.Scheme
instCategory
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
isoSpec
AlgebraicGeometry.isAffine_Spec
AlgebraicGeometry.Spec.map
ΓSpecIso
AlgebraicGeometry.SpecMap_ΓSpecIso_hom
isoSpec_Spec_inv 📖mathematicalCategoryTheory.Iso.inv
AlgebraicGeometry.Scheme
instCategory
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
isoSpec
AlgebraicGeometry.isAffine_Spec
AlgebraicGeometry.Spec.map
ΓSpecIso
AlgebraicGeometry.isAffine_Spec
isoSpec_Spec
isoSpec_hom 📖mathematicalCategoryTheory.Iso.hom
AlgebraicGeometry.Scheme
instCategory
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
isoSpec
toSpecΓ
isoSpec_hom_naturality 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
instCategory
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
CategoryTheory.Iso.hom
isoSpec
AlgebraicGeometry.Spec.map
Hom.appTop
toSpecΓ_naturality
isoSpec_hom_naturality_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
instCategory
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
CategoryTheory.Iso.hom
isoSpec
AlgebraicGeometry.Spec.map
Hom.appTop
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
isoSpec_hom_naturality
isoSpec_image_zeroLocus 📖mathematicalSet.image
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
Hom.toLRSHom'
CategoryTheory.Iso.hom
AlgebraicGeometry.Scheme
instCategory
isoSpec
zeroLocus
PrimeSpectrum.zeroLocus
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
toSpecΓ_preimage_zeroLocus
Set.image_congr
Set.image_preimage_eq
Function.Bijective.surjective
CategoryTheory.ConcreteCategory.bijective_of_isIso
Hom.isIso_base
AlgebraicGeometry.IsAffine.affine
isoSpec_inv_image_zeroLocus 📖mathematicalSet.image
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
Hom.toLRSHom'
CategoryTheory.Iso.inv
AlgebraicGeometry.Scheme
instCategory
isoSpec
PrimeSpectrum.zeroLocus
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
zeroLocus
isoSpec_inv_preimage_zeroLocus
Set.image_preimage_eq
Function.Bijective.surjective
CategoryTheory.ConcreteCategory.bijective_of_isIso
Hom.isIso_base
CategoryTheory.Iso.isIso_inv
isoSpec_inv_naturality 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
instCategory
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
AlgebraicGeometry.Spec.map
Hom.appTop
CategoryTheory.Iso.inv
isoSpec
CategoryTheory.Iso.eq_inv_comp
AlgebraicGeometry.IsAffine.affine
isoSpec.eq_1
CategoryTheory.asIso_hom
toSpecΓ_naturality_assoc
CategoryTheory.asIso_inv
CategoryTheory.IsIso.hom_inv_id
CategoryTheory.Category.comp_id
isoSpec_inv_naturality_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
instCategory
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
AlgebraicGeometry.Spec.map
Hom.appTop
CategoryTheory.Iso.inv
isoSpec
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
isoSpec_inv_naturality
isoSpec_inv_preimage_zeroLocus 📖mathematicalSet.preimage
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
Hom.toLRSHom'
CategoryTheory.Iso.inv
AlgebraicGeometry.Scheme
instCategory
isoSpec
zeroLocus
PrimeSpectrum.zeroLocus
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
toSpecΓ_preimage_zeroLocus
Set.preimage_comp
TopCat.coe_comp
Hom.comp_base
isoSpec_inv_toSpecΓ
isoSpec_inv_toSpecΓ 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
instCategory
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
CategoryTheory.Iso.inv
isoSpec
toSpecΓ
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.inv_hom_id
isoSpec_inv_toSpecΓ_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
instCategory
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
CategoryTheory.Iso.inv
isoSpec
toSpecΓ
CategoryTheory.Category.assoc
CategoryTheory.Category.id_comp
Mathlib.Tactic.Reassoc.eq_whisker'
isoSpec_inv_toSpecΓ
localRingHom_comp_stalkIso 📖mathematicalCategoryTheory.CategoryStruct.comp
CommRingCat
CategoryTheory.Category.toCategoryStruct
CommRingCat.instCategory
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.Spec
AlgebraicGeometry.PresheafedSpace.presheaf
PrimeSpectrum.comap
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
CommRingCat.Hom.hom
CommRingCat.of
Localization.AtPrime
PrimeSpectrum.asIdeal
PrimeSpectrum.isPrime
OreLocalization.instCommRing
Ideal.primeCompl
CommSemiring.toSemiring
OreLocalization.oreSetComm
CommSemiring.toCommMonoid
CategoryTheory.Iso.hom
AlgebraicGeometry.Spec.stalkIso
CommRingCat.ofHom
Localization.localRingHom
Ideal
CategoryTheory.Iso.inv
Hom.stalkMap
AlgebraicGeometry.Spec.map
AlgebraicGeometry.localRingHom_comp_stalkIso
localRingHom_comp_stalkIso_apply 📖mathematicalDFunLike.coe
RingHom
Localization.AtPrime
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
PrimeSpectrum.asIdeal
PrimeSpectrum.isPrime
TopCat.Presheaf.stalk
CommRingCat
CommRingCat.instCategory
CommRingCat.Colimits.hasColimits_commRingCat
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.Spec
AlgebraicGeometry.PresheafedSpace.presheaf
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
OreLocalization.instCommRing
Ideal.primeCompl
OreLocalization.oreSetComm
CommSemiring.toCommMonoid
RingHom.instFunLike
CategoryTheory.ConcreteCategory.hom
CommRingCat.instConcreteCategoryRingHomCarrier
CommRingCat.of
CategoryTheory.Iso.inv
AlgebraicGeometry.Spec.stalkIso
Ideal.comap
CommRingCat.Hom.hom
RingHom.instRingHomClass
PrimeSpectrum.comap
Localization.localRingHom
Ideal
CategoryTheory.Iso.hom
Hom.stalkMap
AlgebraicGeometry.Spec.map
CommRingCat.Colimits.hasColimits_commRingCat
PrimeSpectrum.isPrime
RingHom.instRingHomClass
CategoryTheory.comp_apply
Mathlib.Tactic.Elementwise.hom_elementwise
localRingHom_comp_stalkIso
map_PrimeSpectrum_basicOpen_of_affine 📖mathematicalCategoryTheory.Functor.obj
Opens
AlgebraicGeometry.Spec
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
Hom.toLRSHom'
CategoryTheory.Iso.hom
AlgebraicGeometry.Scheme
instCategory
isoSpec
PrimeSpectrum.basicOpen
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
basicOpen
toSpecΓ_preimage_basicOpen
toSpecΓ_image_zeroLocus 📖mathematicalSet.image
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
Hom.toLRSHom'
toSpecΓ
zeroLocus
PrimeSpectrum.zeroLocus
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
isoSpec_image_zeroLocus
toSpecΓ_isoSpec_inv 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
instCategory
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
toSpecΓ
CategoryTheory.Iso.inv
isoSpec
CategoryTheory.CategoryStruct.id
CategoryTheory.Iso.hom_inv_id
toSpecΓ_isoSpec_inv_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
instCategory
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
toSpecΓ
CategoryTheory.Iso.inv
isoSpec
CategoryTheory.Category.assoc
CategoryTheory.Category.id_comp
Mathlib.Tactic.Reassoc.eq_whisker'
toSpecΓ_isoSpec_inv
toSpecΓ_preimage_zeroLocus 📖mathematicalSet.preimage
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
Hom.toLRSHom'
toSpecΓ
PrimeSpectrum.zeroLocus
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
zeroLocus
AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_zeroLocus_eq
zeroLocus_biInf 📖mathematicalzeroLocus
SetLike.coe
Ideal
CommRingCat.carrier
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
iInf
Submodule.instInfSet
Set
Set.instMembership
Set.instUnion
Set.iUnion
Compl.compl
Set.instCompl
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
Set.Finite.induction_on
iInf_congr_Prop
iInf_neg
iInf_top
zeroLocus_univ
Set.iUnion_congr_Prop
Set.iUnion_of_empty
instIsEmptyFalse
Set.iUnion_empty
Set.empty_union
Set.iUnion_iUnion_eq_or_left
Set.union_assoc
Submodule.coe_iInf
Set.iInter_iInter_eq_or_left
zeroLocus_biInf_of_nonempty 📖mathematicalSet.NonemptyzeroLocus
SetLike.coe
Ideal
CommRingCat.carrier
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
iInf
Submodule.instInfSet
Set
Set.instMembership
Set.iUnion
zeroLocus_biInf
Set.union_eq_left
Set.mem_iUnion₂_of_mem
codisjoint_iff_compl_le_left
codisjoint_zeroLocus
zeroLocus_iInf 📖mathematicalzeroLocus
SetLike.coe
Ideal
CommRingCat.carrier
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
iInf
Submodule.instInfSet
Set
Set.instUnion
Set.iUnion
Compl.compl
Set.instCompl
TopologicalSpace.Opens.instSetLike
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
Submodule.coe_iInf
iInf_congr_Prop
iInf_pos
Set.iUnion_congr_Prop
Set.iUnion_true
zeroLocus_biInf
Set.finite_univ
zeroLocus_iInf_of_nonempty 📖mathematicalzeroLocus
SetLike.coe
Ideal
CommRingCat.carrier
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
iInf
Submodule.instInfSet
Set.iUnion
Submodule.coe_iInf
iInf_congr_Prop
iInf_pos
Set.iUnion_congr_Prop
Set.iUnion_true
zeroLocus_biInf_of_nonempty
Set.finite_univ
zeroLocus_inf 📖mathematicalzeroLocus
SetLike.coe
Ideal
CommRingCat.carrier
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Opens
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Submodule.instMin
Set
Set.instUnion
Opens.toSpecΓ_preimage_zeroLocus
PrimeSpectrum.zeroLocus_inf
Set.ext
codisjoint_iff_compl_le_left
codisjoint_zeroLocus

AlgebraicGeometry.Scheme.Hom

Definitions

NameCategoryTheorems
liftQuotient 📖CompOp
2 mathmath: liftQuotient_comp, liftQuotient_comp_assoc

Theorems

NameKindAssumesProvesValidatesDepends On
isAffineOpen_iff_of_isOpenImmersion 📖mathematicalAlgebraicGeometry.IsAffineOpen
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
AlgebraicGeometry.IsAffine.iff_of_isIso
AlgebraicGeometry.IsOpenImmersion.comp
AlgebraicGeometry.Scheme.Opens.instIsOpenImmersionι
Set.range_comp
AlgebraicGeometry.Scheme.Opens.range_ι
Set.image_congr
CategoryTheory.Iso.isIso_inv
liftQuotient_comp 📖mathematicalIdeal
CommRingCat.carrier
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
RingHom.ker
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
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
Top.top
OrderTop.toTop
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
RingHom
RingHom.instFunLike
RingHom.instRingHomClass
CommRingCat.Hom.hom
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Spec
CategoryTheory.Iso.inv
AlgebraicGeometry.Scheme.ΓSpecIso
appTop
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CommRingCat.of
HasQuotient.Quotient
Ideal.instHasQuotient_1
Ideal.Quotient.commRing
liftQuotient
AlgebraicGeometry.Spec.map
CommRingCat.ofHom
CommRing.toRing
Ideal.instIsTwoSided_1
RingHom.instRingHomClass
Ideal.instIsTwoSided_1
liftQuotient.eq_1
CategoryTheory.Category.assoc
AlgebraicGeometry.Spec.map_comp
CommRingCat.ofHom_comp
CategoryTheory.Iso.inv_hom_id
AlgebraicGeometry.Spec.map_id
CategoryTheory.Category.comp_id
liftQuotient_comp_assoc 📖mathematicalIdeal
CommRingCat.carrier
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
RingHom.ker
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
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
Top.top
OrderTop.toTop
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
RingHom
RingHom.instFunLike
RingHom.instRingHomClass
CommRingCat.Hom.hom
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Spec
CategoryTheory.Iso.inv
AlgebraicGeometry.Scheme.ΓSpecIso
appTop
AlgebraicGeometry.Scheme
AlgebraicGeometry.Scheme.instCategory
CommRingCat.of
HasQuotient.Quotient
Ideal.instHasQuotient_1
Ideal.Quotient.commRing
liftQuotient
AlgebraicGeometry.Spec.map
CommRingCat.ofHom
CommRing.toRing
Ideal.instIsTwoSided_1
RingHom.instRingHomClass
Ideal.instIsTwoSided_1
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
liftQuotient_comp

AlgebraicGeometry.Scheme.Opens

Definitions

NameCategoryTheorems
toSpecΓ 📖CompOp
27 mathmath: toSpecΓ_naturality, toSpecΓ_SpecMap_presheaf_map_top, AlgebraicGeometry.Scheme.ideal_ker_le_ker_ΓSpecIso_inv_comp, toSpecΓ_SpecMap_map, AlgebraicGeometry.Scheme.Hom.ι_toNormalization, toSpecΓ_naturality_assoc, toSpecΓ_SpecMap_presheaf_map_assoc, toSpecΓ_appTop_assoc, toSpecΓ_SpecMap_presheaf_map_top_assoc, toSpecΓ_preimage_basicOpen, toSpecΓ_appTop, toSpecΓ_SpecMap_map_assoc, toSpecΓ_top, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_toSpecΓ, AlgebraicGeometry.IsAffineOpen.toSpecΓ_isoSpec_inv, toSpecΓ_SpecMap_presheaf_map, toSpecΓ_SpecMap_appLE_assoc, AlgebraicGeometry.IsAffineOpen.toSpecΓ_fromSpec_assoc, AlgebraicGeometry.Scheme.Hom.ι_toNormalization_assoc, fromSpecStalkOfMem_toSpecΓ, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_toSpecΓ_assoc, fromSpecStalkOfMem_toSpecΓ_assoc, AlgebraicGeometry.IsAffineOpen.isoSpec_hom, toSpecΓ_SpecMap_appLE, AlgebraicGeometry.IsAffineOpen.toSpecΓ_isoSpec_inv_assoc, toSpecΓ_preimage_zeroLocus, AlgebraicGeometry.IsAffineOpen.toSpecΓ_fromSpec

Theorems

NameKindAssumesProvesValidatesDepends On
toSpecΓ_SpecMap_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
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
toScheme
AlgebraicGeometry.Spec
Opposite
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
toSpecΓ
AlgebraicGeometry.Spec.map
AlgebraicGeometry.Scheme.Hom.appLE
AlgebraicGeometry.Scheme.Hom.resLE
AlgebraicGeometry.Spec.map_comp
toSpecΓ_SpecMap_presheaf_map_assoc
toSpecΓ_naturality
CategoryTheory.Category.assoc
toSpecΓ_SpecMap_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
AlgebraicGeometry.Scheme.Hom.toLRSHom'
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
toScheme
AlgebraicGeometry.Spec
Opposite
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
toSpecΓ
AlgebraicGeometry.Spec.map
AlgebraicGeometry.Scheme.Hom.appLE
AlgebraicGeometry.Scheme.Hom.resLE
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
toSpecΓ_SpecMap_appLE
toSpecΓ_SpecMap_map 📖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.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
toScheme
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
toSpecΓ
AlgebraicGeometry.Spec.map
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.homOfLE
AlgebraicGeometry.Scheme.homOfLE
toSpecΓ_SpecMap_presheaf_map
toSpecΓ_SpecMap_map_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.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
toScheme
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
toSpecΓ
AlgebraicGeometry.Spec.map
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.homOfLE
AlgebraicGeometry.Scheme.homOfLE
toSpecΓ_SpecMap_presheaf_map_assoc
toSpecΓ_SpecMap_presheaf_map 📖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.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
toScheme
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
toSpecΓ
AlgebraicGeometry.Spec.map
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.homOfLE
AlgebraicGeometry.Scheme.homOfLE
instIsOpenImmersionι
LE.le.trans
le_of_eq
Opposite.op_injective
AlgebraicGeometry.Scheme.ι_image_homOfLE_le_ι_image
CategoryTheory.eqToHom_op
CategoryTheory.Category.assoc
CategoryTheory.Functor.map_comp
AlgebraicGeometry.Scheme.toSpecΓ_naturality_assoc
AlgebraicGeometry.Scheme.homOfLE_app
toSpecΓ_SpecMap_presheaf_map_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.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
toScheme
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
toSpecΓ
AlgebraicGeometry.Spec.map
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.homOfLE
AlgebraicGeometry.Scheme.homOfLE
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
toSpecΓ_SpecMap_presheaf_map
toSpecΓ_SpecMap_presheaf_map_top 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
toScheme
AlgebraicGeometry.Spec
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
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
TopologicalSpace.Opens.instCompleteLattice
toSpecΓ
AlgebraicGeometry.Spec.map
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.homOfLE
le_top
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
ι
AlgebraicGeometry.Scheme.toSpecΓ
le_top
instIsOpenImmersionι
LE.le.trans
le_of_eq
Opposite.op_injective
Set.image_preimage_subset
CategoryTheory.eqToHom_op
CategoryTheory.Category.assoc
CategoryTheory.Functor.map_comp
AlgebraicGeometry.Scheme.toSpecΓ_naturality
toSpecΓ_SpecMap_presheaf_map_top_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
toScheme
AlgebraicGeometry.Spec
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
toSpecΓ
Top.top
OrderTop.toTop
Preorder.toLE
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.Spec.map
CategoryTheory.Functor.map
Quiver.Hom.op
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.homOfLE
le_top
ι
AlgebraicGeometry.Scheme.toSpecΓ
le_top
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
toSpecΓ_SpecMap_presheaf_map_top
toSpecΓ_appTop 📖mathematicalAlgebraicGeometry.Scheme.Hom.appTop
toScheme
AlgebraicGeometry.Spec
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
toSpecΓ
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
CategoryTheory.Iso.hom
AlgebraicGeometry.Scheme.ΓSpecIso
CategoryTheory.Iso.inv
topIso
instIsOpenImmersionι
CategoryTheory.eqToHom_op
AlgebraicGeometry.Scheme.toSpecΓ_appTop
AlgebraicGeometry.Scheme.ΓSpecIso_naturality
toSpecΓ_appTop_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
AlgebraicGeometry.Spec
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
toScheme
AlgebraicGeometry.Scheme.Hom.appTop
toSpecΓ
CategoryTheory.Iso.hom
AlgebraicGeometry.Scheme.ΓSpecIso
CategoryTheory.Iso.inv
topIso
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
toSpecΓ_appTop
toSpecΓ_naturality 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
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.Spec
Opposite
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
toSpecΓ
AlgebraicGeometry.Spec.map
AlgebraicGeometry.Scheme.Hom.app
AlgebraicGeometry.morphismRestrict
instIsOpenImmersionι
LE.le.trans
le_rfl
HasSubset.Subset.trans
Set.instIsTransSubset
Set.image_mono
Eq.le
AlgebraicGeometry.image_morphismRestrict_preimage
CategoryTheory.eqToHom_op
AlgebraicGeometry.Scheme.Hom.app_eq_appLE
CategoryTheory.Category.assoc
AlgebraicGeometry.Scheme.Hom.appLE_map
AlgebraicGeometry.Scheme.toSpecΓ_naturality_assoc
AlgebraicGeometry.morphismRestrict_appLE
AlgebraicGeometry.Scheme.Hom.map_appLE
toSpecΓ_naturality_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
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.Spec
Opposite
CategoryTheory.Category.opposite
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
toSpecΓ
AlgebraicGeometry.Spec.map
AlgebraicGeometry.Scheme.Hom.app
AlgebraicGeometry.morphismRestrict
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
toSpecΓ_naturality
toSpecΓ_preimage_basicOpen 📖mathematicalCategoryTheory.Functor.obj
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.Spec
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
toScheme
TopologicalSpace.Opens.map
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
toSpecΓ
PrimeSpectrum.basicOpen
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
ι
AlgebraicGeometry.Scheme.basicOpen
instIsOpenImmersionι
Set.image_preimage_subset
AlgebraicGeometry.Scheme.toSpecΓ_preimage_basicOpen
AlgebraicGeometry.Scheme.preimage_basicOpen
ι_preimage_self
AlgebraicGeometry.Scheme.basicOpen_res_eq
CategoryTheory.isIso_op
CategoryTheory.instIsIsoEqToHom
CategoryTheory.ConcreteCategory.comp_apply
CategoryTheory.eqToHom_op
CategoryTheory.eqToHom_unop
toSpecΓ_preimage_zeroLocus 📖mathematicalSet.preimage
TopCat.carrier
AlgebraicGeometry.PresheafedSpace.carrier
CommRingCat
CommRingCat.instCategory
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
toScheme
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
AlgebraicGeometry.Scheme.Opens
DFunLike.coe
CategoryTheory.ConcreteCategory.hom
TopCat
TopCat.instCategory
ContinuousMap
ContinuousMap.instFunLike
TopCat.instConcreteCategoryContinuousMapCarrier
AlgebraicGeometry.PresheafedSpace.Hom.base
AlgebraicGeometry.LocallyRingedSpace.Hom.toHom
AlgebraicGeometry.Scheme.Hom.toLRSHom'
toSpecΓ
PrimeSpectrum.zeroLocus
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
Set.Elem
TopologicalSpace.Opens.carrier
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
Set
Set.instMembership
AlgebraicGeometry.Scheme.zeroLocus
Set.ext
iff_not_comm
toSpecΓ_preimage_basicOpen
Set.mem_iInter₂
toSpecΓ_top 📖mathematicaltoSpecΓ
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.Scheme.toLocallyRingedSpace
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
CategoryTheory.CategoryStruct.comp
AlgebraicGeometry.Scheme
CategoryTheory.Category.toCategoryStruct
AlgebraicGeometry.Scheme.instCategory
toScheme
AlgebraicGeometry.Spec
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
ι
AlgebraicGeometry.Scheme.toSpecΓ
instIsOpenImmersionι
Set.image_preimage_subset
CategoryTheory.eqToHom_op
AlgebraicGeometry.Scheme.toSpecΓ_naturality

AlgebraicGeometry.Spec

Definitions

NameCategoryTheorems
stalkIso 📖CompOp
8 mathmath: germ_stalkMapIso_hom_assoc, AlgebraicGeometry.Scheme.Spec.residue_residueFieldIso_hom_assoc, algebraMap_stalkIso_inv, algebraMap_stalkIso_inv_assoc, germ_stalkMapIso_hom, AlgebraicGeometry.Scheme.localRingHom_comp_stalkIso, AlgebraicGeometry.Scheme.Spec.residue_residueFieldIso_hom, AlgebraicGeometry.Scheme.localRingHom_comp_stalkIso_apply

Theorems

NameKindAssumesProvesValidatesDepends On
algebraMap_stalkIso_inv 📖mathematicalCategoryTheory.CategoryStruct.comp
CommRingCat
CategoryTheory.Category.toCategoryStruct
CommRingCat.instCategory
CommRingCat.of
CommRingCat.carrier
CommRingCat.commRing
Localization.AtPrime
CommRing.toCommSemiring
PrimeSpectrum.asIdeal
PrimeSpectrum.isPrime
OreLocalization.instCommRing
Ideal.primeCompl
CommSemiring.toSemiring
OreLocalization.oreSetComm
CommSemiring.toCommMonoid
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.Spec
AlgebraicGeometry.PresheafedSpace.presheaf
CommRingCat.ofHom
algebraMap
OreLocalization.instAlgebra
Algebra.id
CategoryTheory.Iso.inv
stalkIso
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
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
AlgebraicGeometry.Scheme.ΓSpecIso
TopCat.Presheaf.germ
CommRingCat.hom_ext
CommRingCat.Colimits.hasColimits_commRingCat
PrimeSpectrum.isPrime
RingHom.ext
AlgEquiv.commutes
AlgebraicGeometry.StructureSheaf.IsLocalization.to_stalk
algebraMap_stalkIso_inv_assoc 📖mathematicalCategoryTheory.CategoryStruct.comp
CommRingCat
CategoryTheory.Category.toCategoryStruct
CommRingCat.instCategory
CommRingCat.of
CommRingCat.carrier
CommRingCat.commRing
Localization.AtPrime
CommRing.toCommSemiring
PrimeSpectrum.asIdeal
PrimeSpectrum.isPrime
OreLocalization.instCommRing
Ideal.primeCompl
CommSemiring.toSemiring
OreLocalization.oreSetComm
CommSemiring.toCommMonoid
CommRingCat.ofHom
algebraMap
OreLocalization.instAlgebra
Algebra.id
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
AlgebraicGeometry.PresheafedSpace.carrier
AlgebraicGeometry.SheafedSpace.toPresheafedSpace
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace
AlgebraicGeometry.Scheme.toLocallyRingedSpace
AlgebraicGeometry.Spec
AlgebraicGeometry.PresheafedSpace.presheaf
CategoryTheory.Iso.inv
stalkIso
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
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
AlgebraicGeometry.Scheme.ΓSpecIso
TopCat.Presheaf.germ
CommRingCat.Colimits.hasColimits_commRingCat
PrimeSpectrum.isPrime
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
algebraMap_stalkIso_inv
germ_stalkMapIso_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
AlgebraicGeometry.Spec
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
CommRingCat.of
Localization.AtPrime
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
PrimeSpectrum.asIdeal
PrimeSpectrum.isPrime
OreLocalization.instCommRing
Ideal.primeCompl
CommSemiring.toSemiring
OreLocalization.oreSetComm
CommSemiring.toCommMonoid
TopCat.Presheaf.germ
CategoryTheory.Iso.hom
stalkIso
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
AlgebraicGeometry.Scheme.ΓSpecIso
CommRingCat.ofHom
algebraMap
OreLocalization.instAlgebra
Algebra.id
PrimeSpectrum.isPrime
CommRingCat.Colimits.hasColimits_commRingCat
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id
germ_stalkMapIso_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
AlgebraicGeometry.Spec
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
AlgebraicGeometry.PresheafedSpace.presheaf
Opposite.op
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
TopCat.Presheaf.stalk
CommRingCat.Colimits.hasColimits_commRingCat
TopCat.Presheaf.germ
CommRingCat.of
Localization.AtPrime
CommRingCat.carrier
CommRing.toCommSemiring
CommRingCat.commRing
PrimeSpectrum.asIdeal
PrimeSpectrum.isPrime
OreLocalization.instCommRing
Ideal.primeCompl
CommSemiring.toSemiring
OreLocalization.oreSetComm
CommSemiring.toCommMonoid
CategoryTheory.Iso.hom
stalkIso
AlgebraicGeometry.Scheme.Opens
AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier
AlgebraicGeometry.Scheme.ΓSpecIso
CommRingCat.ofHom
algebraMap
OreLocalization.instAlgebra
Algebra.id
PrimeSpectrum.isPrime
CommRingCat.Colimits.hasColimits_commRingCat
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
germ_stalkMapIso_hom

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