Theorems · Theorem · category theory

TopCat.Presheaf.stalkPushforward_germ_assoc

∀ (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) (U : TopologicalSpace.Opens ↑Y) (x : ↑X)
  (hx : (CategoryTheory.ConcreteCategory.hom f) x ∈ U) {Z : C} (h : F.stalk x ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (((TopCat.Presheaf.pushforward C f).obj F).germ U ((CategoryTheory.ConcreteCategory.hom f) x) hx)
      (CategoryTheory.CategoryStruct.comp (TopCat.Presheaf.stalkPushforward C f F x) h) =
    CategoryTheory.CategoryStruct.comp (F.germ ((TopologicalSpace.Opens.map f).obj U) x hx) h

Defined in

Mathlib.Topology.Sheaves.Stalks

Cited by

1 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimits