Theorems · Definition · algebraic geometry

AlgebraicGeometry.LocallyRingedSpace.Hom.stalkMap

{X Y : AlgebraicGeometry.LocallyRingedSpace} →
  (f : X ⟶ Y) →
    (x : ↑X.toTopCat) → Y.presheaf.stalk ((CategoryTheory.ConcreteCategory.hom f.base) x) ⟶ X.presheaf.stalk x

A morphism of locally ringed spaces f : X ⟶ Y induces a local ring homomorphism from Y.stalk (f x) to X.stalk x for any x : X.

Defined in

Mathlib.Geometry.RingedSpace.LocallyRingedSpace

Cited by

34 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound