Mathlib Map

Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom

{X : AlgebraicGeometry.Scheme} →
  {I J : X.IdealSheafData} → I ≤ J → (U : ↑X.affineOpens) → J.glueDataObj U ⟶ I.glueDataObj U

Given I ≤ J, this is the map Spec(Γ(X, U)/J(U)) ⟶ Spec(Γ(X, U)/I(U)).

Defined in
Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme
Cited by
10 results in Mathlib
Foundations
Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.Scheme.IdealSheafData.inclusion · cited by 12IdealSheafData.inclusionAlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom_ι · cited by 3IdealSheafData.glueDataOb…AlgebraicGeometry.Scheme.IdealSheafData.subSchemeCover_map_inclusion · cited by 3IdealSheafData.subSchemeC…AlgebraicGeometry.Scheme.IdealSheafData.inclusion_subschemeι · cited by 3IdealSheafData.inclusion_…AlgebraicGeometry.Scheme.IdealSheafData.subSchemeCover_map_inclusion_assoc · cited by 2IdealSheafData.subSchemeC…AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom_comp · cited by 1IdealSheafData.glueDataOb…AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom_comp_assoc · cited by 1IdealSheafData.glueDataOb…AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom_id · cited by 1IdealSheafData.glueDataOb…AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom_ι_assoc · cited by 1IdealSheafData.glueDataOb…AlgebraicGeometry.Scheme.IdealSheafData.inclusion_comp · cited by 1IdealSheafData.inclusion_…AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom.congr_simp · cited by 0glueDataObjHom.congr_simpQuiver.Hom · cited by 32603Quiver.HomSet.Elem · cited by 7166Set.ElemAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.Scheme.Opens · cited by 1149Scheme.OpensAlgebraicGeometry.Spec.map · cited by 332Spec.mapCommRingCat.ofHom · cited by 259CommRingCat.ofHomAlgebraicGeometry.Scheme.affineOpens · cited by 220Scheme.affineOpensAlgebraicGeometry.Scheme.IdealSheafData · cited by 192Scheme.IdealSheafDataIdeal.Quotient.factor · cited by 33Quotient.factorAlgebraicGeometry.Scheme.IdealSheafData.glueDataObj · cited by 24IdealSheafData.glueDataObjIdealSheafData.glueDataObjHomCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by11

Results whose statement or proof uses this declaration.