Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk_assoc

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) {x : ↥X} {Z : AlgebraicGeometry.Scheme} (h : Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Spec.map (AlgebraicGeometry.Scheme.Hom.stalkMap f x))
      (CategoryTheory.CategoryStruct.comp (Y.fromSpecStalk (f x)) h) =
    CategoryTheory.CategoryStruct.comp (X.fromSpecStalk x) (CategoryTheory.CategoryStruct.comp f h)

Defined in

Mathlib.AlgebraicGeometry.Stalk

Cited by

2 results in Mathlib

Foundations

Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound