Theorems · Theorem · category theory

CategoryTheory.Functor.RepresentableBy.homEquiv_comp

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

Defined in

Mathlib.CategoryTheory.Yoneda

Cited by

7 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.Category