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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.IdealSheafData.inclusion

{X : AlgebraicGeometry.Scheme} → {I J : X.IdealSheafData} → I ≤ J → (J.subscheme ⟶ I.subscheme)

The inclusion of ideal sheaf induces an inclusion of subschemes

Defined in
Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme
Cited by
12 results in Mathlib
Foundations
Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
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Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.IsClosedImmersion.lift · cited by 5IsClosedImmersion.liftAlgebraicGeometry.IsClosedImmersion.lift_fac · cited by 4IsClosedImmersion.lift_facAlgebraicGeometry.Scheme.IdealSheafData.subschemeFunctor · cited by 4IdealSheafData.subschemeF…AlgebraicGeometry.Scheme.IdealSheafData.inclusion_subschemeι · cited by 3IdealSheafData.inclusion_…AlgebraicGeometry.Scheme.IdealSheafData.subSchemeCover_map_inclusion · cited by 3IdealSheafData.subSchemeC…AlgebraicGeometry.Scheme.IdealSheafData.subSchemeCover_map_inclusion_assoc · cited by 2IdealSheafData.subSchemeC…AlgebraicGeometry.Scheme.IdealSheafData.le_map_iff_comap_le · cited by 2IdealSheafData.le_map_iff…AlgebraicGeometry.Scheme.IdealSheafData.inclusion_comp · cited by 1IdealSheafData.inclusion_…AlgebraicGeometry.Scheme.IdealSheafData.inclusion_id · cited by 1IdealSheafData.inclusion_…AlgebraicGeometry.Scheme.IdealSheafData.inclusion_subschemeι_assoc · cited by 1IdealSheafData.inclusion_…AlgebraicGeometry.IsClosedImmersion.overEquivIdealSheafData · cited by 1IsClosedImmersion.overEqu…AlgebraicGeometry.Scheme.IdealSheafData.inclusion_comp_assoc · cited by 0IdealSheafData.inclusion_…AlgebraicGeometry.Scheme.IdealSheafData.inclusion_id_assoc · cited by 0IdealSheafData.inclusion_…AlgebraicGeometry.Scheme.IdealSheafData.inclusion.congr_simp · cited by 0inclusion.congr_simpAlgebraicGeometry.Scheme.IdealSheafData.subschemeFunctor_map · cited by 0IdealSheafData.subschemeF…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.PreZeroHypercover.I₀ · cited by 763PreZeroHypercover.I₀CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover · cited by 469ZeroHypercover.toPreZeroH…AlgebraicGeometry.Scheme.IdealSheafData · cited by 192Scheme.IdealSheafDataAlgebraicGeometry.Scheme.IdealSheafData.subscheme · cited by 36IdealSheafData.subschemeAlgebraicGeometry.Scheme.AffineCover.f · cited by 24AffineCover.fAlgebraicGeometry.Scheme.AffineOpenCover.openCover · cited by 17AffineOpenCover.openCoverAlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom · cited by 10IdealSheafData.glueDataOb…AlgebraicGeometry.Scheme.IdealSheafData.subschemeCover · cited by 10IdealSheafData.subschemeC…AlgebraicGeometry.Scheme.Cover.glueMorphisms · cited by 10Cover.glueMorphismsIdealSheafData.inclusionCITED BYCITES

Cites12

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