Theorems · Theorem · category theory

TopCat.Presheaf.stalkFunctor_map_germ_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasColimits C] {X : TopCat}
  {F G : TopCat.Presheaf C X} (U : TopologicalSpace.Opens ↑X) (x : ↑X) (hx : x ∈ U) (f : F ⟶ G) {Z : C}
  (h : (TopCat.Presheaf.stalkFunctor C x).obj G ⟶ Z),
  CategoryTheory.CategoryStruct.comp (F.germ U x hx)
      (CategoryTheory.CategoryStruct.comp ((TopCat.Presheaf.stalkFunctor C x).map f) h) =
    CategoryTheory.CategoryStruct.comp (f.app (Opposite.op U)) (CategoryTheory.CategoryStruct.comp (G.germ U x hx) h)

Defined in

Mathlib.Topology.Sheaves.Stalks

Cited by

3 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimits