Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.residue_residueFieldMap_assoc

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (x : ↥X) {Z : CommRingCat} (h : X.residueField x ⟶ Z),
  CategoryTheory.CategoryStruct.comp (Y.residue (f x))
      (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.residueFieldMap f x) h) =
    CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.stalkMap f x)
      (CategoryTheory.CategoryStruct.comp (X.residue x) h)

Defined in: Mathlib.AlgebraicGeometry.ResidueField
Cited by: 1 results in Mathlib
Foundations: Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

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

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Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.descResidueField_stalkClosedPointTo_compproof · cited by 1