Theorems · Definition · category theory

TopCat.Presheaf.germToPullbackStalk

(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) →
            (U : TopologicalSpace.Opens ↑X) →
              (x : ↑X) →
                x ∈ U →
                  (((TopCat.Presheaf.pullback C f).obj F).obj (Opposite.op U) ⟶
                    F.stalk ((CategoryTheory.ConcreteCategory.hom f) x))

The morphism (f⁻¹ℱ)(U) ⟶ ℱ_{f(x)} for some U ∋ x.

Defined in

Mathlib.Topology.Sheaves.Stalks

Cited by

9 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimits