Theorems · Definition · category theory

TopCat.Presheaf.stalkPushforward

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasColimits C] →
      {X Y : TopCat} →
        (f : X ⟶ Y) →
          (F : TopCat.Presheaf C X) →
            (x : ↑X) →
              ((TopCat.Presheaf.pushforward C f).obj F).stalk ((CategoryTheory.ConcreteCategory.hom f) x) ⟶ F.stalk x

For a presheaf F on a space X, a continuous map f : X ⟶ Y induces a morphisms between the stalk of f _ * F at f x and the stalk of F at x.

Defined in

Mathlib.Topology.Sheaves.Stalks

Cited by

12 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimits