Theorems · Theorem · category theory

TopCat.Presheaf.germ_res_assoc

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

Defined in

Mathlib.Topology.Sheaves.Stalks

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimits