(R : Type u₀) →
  [inst : CommSemiring R] →
    {A : Type u₁} →
      [inst_1 : Ring A] →
        [inst_2 : Algebra R A] →
          {B : Type u₂} → [inst_3 : Ring B] → [inst_4 : Algebra R B] → MoritaEquivalence R A B → MoritaEquivalence R B A