Theorems · Theorem · category theory

TopCat.Presheaf.stalkSpecializes_stalkPushforward

∀ {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) {x y : ↑X} (h : x ⤳ y),
  CategoryTheory.CategoryStruct.comp (((TopCat.Presheaf.pushforward C f).obj F).stalkSpecializes ⋯)
      (TopCat.Presheaf.stalkPushforward C f F x) =
    CategoryTheory.CategoryStruct.comp (TopCat.Presheaf.stalkPushforward C f F y) (F.stalkSpecializes h)

Defined in

Mathlib.Topology.Sheaves.Stalks

Cited by

2 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimits