∀ {C : Type u_3} [inst : CategoryTheory.Category.{u_2, u_3} C] {R : CategoryTheory.Functor Cᵒᵖ RingCat} (X : Cᵒᵖ),
  RingCat.Hom.hom (R.map (CategoryTheory.CategoryStruct.id X)) =
    { hom' := { toFun := id, map_one' := ⋯, map_mul' := ⋯, map_zero' := ⋯, map_add' := ⋯ } }.hom