Theorems · Theorem · category theory

TopCat.Presheaf.stalkSpecializes_stalkPushforward_apply

∀ {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) {F_1 : C → C → Type uF} {carrier : C → Type w}
  {instFunLike : (X Y : C) → FunLike (F_1 X Y) (carrier X) (carrier Y)} [inst_2 : CategoryTheory.ConcreteCategory C F_1]
  (x_1 : carrier (((TopCat.Presheaf.pushforward C f).obj F).stalk ((TopCat.Hom.hom f) y))),
  (CategoryTheory.ConcreteCategory.hom (TopCat.Presheaf.stalkPushforward C f F x))
      ((CategoryTheory.ConcreteCategory.hom (((TopCat.Presheaf.pushforward C f).obj F).stalkSpecializes ⋯)) x_1) =
    (CategoryTheory.ConcreteCategory.hom (F.stalkSpecializes h))
      ((CategoryTheory.ConcreteCategory.hom (TopCat.Presheaf.stalkPushforward C f F y)) x_1)

Defined in

Mathlib.Topology.Sheaves.Stalks

Cited by

0 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimitsCategoryTheory.ConcreteCategory