∀ {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 : D} {Y : C} {S : CategoryTheory.Functor C D} (f : S.obj Y ⟶ T),
  CategoryTheory.CostructuredArrow.mk
      (CategoryTheory.CategoryStruct.comp (S.map (CategoryTheory.CategoryStruct.id Y))
        (CategoryTheory.CostructuredArrow.mk f).hom) =
    CategoryTheory.CostructuredArrow.mk f