∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (T : CategoryTheory.Functor C D) {X Y : D} (f : X ⟶ Y),
  (CategoryTheory.CostructuredArrow.functor T).map f = (CategoryTheory.CostructuredArrow.map f).toCatHom