Theorems · Theorem · category theory

CategoryTheory.yonedaEquiv_naturality

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} {F : CategoryTheory.Functor Cᵒᵖ (Type v₁)}
  (f : CategoryTheory.yoneda.obj X ⟶ F) (g : Y ⟶ X),
  (CategoryTheory.ConcreteCategory.hom (F.map g.op)) (CategoryTheory.yonedaEquiv f) =
    CategoryTheory.yonedaEquiv (CategoryTheory.CategoryStruct.comp (CategoryTheory.yoneda.map g) f)

See also yonedaEquiv_naturality' for a more general version.

Defined in

Mathlib.CategoryTheory.Yoneda

Cited by

6 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category