∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_3, u_1} C] {D : Type u_4}
  [inst_1 : CategoryTheory.Category.{u_2, u_4} D] (T : CategoryTheory.Functor C D) {X Y Z : Dᵒᵖ} (f : X ⟶ Y)
  (g : Y ⟶ Z),
  (CategoryTheory.StructuredArrow.map (CategoryTheory.CategoryStruct.comp f g).unop).toCatHom =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.StructuredArrow.map f.unop).toCatHom
      (CategoryTheory.StructuredArrow.map g.unop).toCatHom