∀ {R : Type u_1} {S : Type u_2} {A : Type u_3} {B : Type u_4} {C : Type u_5} {D : Type u_6} [inst : CommSemiring R]
  [inst_1 : CommSemiring S] [inst_2 : Semiring A] [inst_3 : Semiring B] [inst_4 : Bialgebra S A]
  [inst_5 : Bialgebra R B] [inst_6 : Algebra R A] [inst_7 : Algebra R S] [inst_8 : IsScalarTower R S A]
  [inst_9 : Semiring C] [inst_10 : Semiring D] [inst_11 : Bialgebra S C] [inst_12 : Bialgebra R D]
  [inst_13 : Algebra R C] [inst_14 : IsScalarTower R S C] (f : A →ₐc[S] C) (g : B →ₐc[R] D),
  ↑(Bialgebra.TensorProduct.map f g) = Coalgebra.TensorProduct.map ↑f ↑g