(R : Type u_1) →
  (A : Type u_4) →
    {M : Type u_7} →
      {N : Type u_8} →
        [inst : CommSemiring R] →
          [inst_1 : Semiring A] →
            [inst_2 : Algebra R A] →
              [inst_3 : Monoid M] → [inst_4 : Monoid N] → (M →* N) → MonoidAlgebra A M →ₐ[R] MonoidAlgebra A N