Theorems · Definition · category theory

TopCat.Presheaf.stalkPullbackInv

(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 Y) →
            (x : ↑X) →
              ((TopCat.Presheaf.pullback C f).obj F).stalk x ⟶ F.stalk ((CategoryTheory.ConcreteCategory.hom f) x)

The morphism (f⁻¹ℱ)ₓ ⟶ ℱ_{f(x)}.

Defined in

Mathlib.Topology.Sheaves.Stalks

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimits