Theorems · Theorem · category theory

TopCat.Presheaf.germ_stalkSpecializes_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasColimits C] {X : TopCat}
  (F : TopCat.Presheaf C X) {U : TopologicalSpace.Opens ↑X} {y : ↑X} (hy : y ∈ U) {x : ↑X} (h : x ⤳ y) {Z : C}
  (h_1 : F.stalk x ⟶ Z),
  CategoryTheory.CategoryStruct.comp (F.germ U y hy) (CategoryTheory.CategoryStruct.comp (F.stalkSpecializes h) h_1) =
    CategoryTheory.CategoryStruct.comp (F.germ U x ⋯) h_1

Defined in

Mathlib.Topology.Sheaves.Stalks

Cited by

6 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimits