Theorems · Theorem · category theory

TopCat.Presheaf.stalkSpecializes_stalkFunctor_map

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasColimits C] {X : TopCat}
  {F G : TopCat.Presheaf C X} (f : F ⟶ G) {x y : ↑X} (h : x ⤳ y),
  CategoryTheory.CategoryStruct.comp (F.stalkSpecializes h) ((TopCat.Presheaf.stalkFunctor C x).map f) =
    CategoryTheory.CategoryStruct.comp ((TopCat.Presheaf.stalkFunctor C y).map f) (G.stalkSpecializes h)

Defined in

Mathlib.Topology.Sheaves.Stalks

Cited by

2 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimits