∀ (R S : CommRingCat) [inst : Algebra ↑R ↑S] {X Y : CategoryTheory.Under R} (f : X ⟶ Y),
  ((R.tensorProd S).map f).right =
    CommRingCat.ofHom ↑(Algebra.TensorProduct.map (AlgHom.id ↑S ↑S) (CommRingCat.toAlgHom f))