Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.evaluation_naturality

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) {V : Y.Opens} (x : ↥X) (hx : f x ∈ V),
  CategoryTheory.CategoryStruct.comp (Y.evaluation V (f x) hx) (AlgebraicGeometry.Scheme.Hom.residueFieldMap f x) =
    CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.app f V)
      (X.evaluation ((TopologicalSpace.Opens.map f.base).obj V) x hx)

Defined in

Mathlib.AlgebraicGeometry.ResidueField

Cited by

1 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound