Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom_comp

∀ {X : AlgebraicGeometry.Scheme} {I J K : X.IdealSheafData} (hIJ : I ≤ J) (hJK : J ≤ K) (U : ↑X.affineOpens),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom hJK U)
      (AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom hIJ U) =
    AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom ⋯ U

Defined in: Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme
Cited by: 1 results in Mathlib
Foundations: Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites14

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

Quiver.Homstatement · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
Set.Elemstatement and proof · cited by 7,166
CategoryTheory.Category.assocproof · cited by 6,433
LE.le.transstatement and proof · cited by 3,151
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
AlgebraicGeometry.Scheme.Opensstatement · cited by 1,149
CategoryTheory.cancel_monoproof · cited by 435
AlgebraicGeometry.Scheme.affineOpensstatement and proof · cited by 220
AlgebraicGeometry.Scheme.IdealSheafDatastatement and proof · cited by 192
AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjstatement · cited by 24
AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjιproof · cited by 20

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjHom_comp_assocproof · cited by 1