Theorems · Theorem · category theory

TopCat.Presheaf.germ_stalkPullbackInv_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 Y) (x : ↑X) (V : TopologicalSpace.Opens ↑X) (hV : x ∈ V) {Z : C}
  (h : F.stalk ((CategoryTheory.ConcreteCategory.hom f) x) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (((TopCat.Presheaf.pullback C f).obj F).germ V x hV)
      (CategoryTheory.CategoryStruct.comp (TopCat.Presheaf.stalkPullbackInv C f F x) h) =
    CategoryTheory.CategoryStruct.comp (TopCat.Presheaf.germToPullbackStalk C f F V x hV) h

Defined in

Mathlib.Topology.Sheaves.Stalks

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimits