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