Theorems · Definition · ring theory

AddMonoidAlgebra.domCongrBialgEquiv

(R : Type u_1) →
  (A : Type u_3) →
    {M : Type u_8} →
      {N : Type u_9} →
        [inst : CommSemiring R] →
          [inst_1 : Semiring A] →
            [inst_2 : Bialgebra R A] →
              [inst_3 : AddMonoid M] →
                [inst_4 : AddMonoid N] → M ≃+ N → AddMonoidAlgebra A M ≃ₐc[R] AddMonoidAlgebra A N

Isomorphic monoids have isomorphic monoid algebras.

Defined in

Mathlib.RingTheory.Bialgebra.MonoidAlgebra

Cited by

2 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringBialgebraAddMonoidAddMonoid