Theorems · Theorem · category theory

TopCat.Presheaf.stalkFunctor_map_germ_apply

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasColimits C] {X : TopCat}
  {FC : C → C → Type u_1} {CC : C → Type u_2} [inst_2 : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)]
  [inst_3 : CategoryTheory.ConcreteCategory C FC] {F G : TopCat.Presheaf C X} (U : TopologicalSpace.Opens ↑X) (x : ↑X)
  (hx : x ∈ U) (f : F ⟶ G) (s : CC (F.obj (Opposite.op U))),
  (CategoryTheory.ConcreteCategory.hom ((TopCat.Presheaf.stalkFunctor C x).map f))
      ((CategoryTheory.ConcreteCategory.hom (F.germ U x hx)) s) =
    (CategoryTheory.ConcreteCategory.hom (G.germ U x hx))
      ((CategoryTheory.ConcreteCategory.hom (f.app (Opposite.op U))) s)

Defined in

Mathlib.Topology.Sheaves.Stalks

Cited by

7 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimitsFunLikeCategoryTheory.ConcreteCategory