Theorems · Theorem · category theory

TopCat.Presheaf.map_restrict

∀ {X : TopCat} {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {FC : C → C → Type u_1} {CC : C → Type u_2}
  [inst_1 : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)] [inst_2 : CategoryTheory.ConcreteCategory C FC]
  {F G : TopCat.Presheaf C X} (e : F ⟶ G) {U V : TopologicalSpace.Opens ↑X} (h : U ≤ V)
  (x : CategoryTheory.ToType (F.obj (Opposite.op V))),
  (CategoryTheory.ConcreteCategory.hom (e.app (Opposite.op U))) (TopCat.Presheaf.restrictOpen x U h) =
    TopCat.Presheaf.restrictOpen ((CategoryTheory.ConcreteCategory.hom (e.app (Opposite.op V))) x) U h

Defined in

Mathlib.Topology.Sheaves.Presheaf

Cited by

1 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategory