Theorems · Definition · ring theory

AddMonoidAlgebra.mapDomainOfBialgHom

{R : Type u_1} →
  {G : Type u_5} →
    {H : Type u_6} →
      [inst : CommRing R] →
        [IsDomain R] →
          [inst_2 : AddGroup G] → [inst_3 : AddGroup H] → (AddMonoidAlgebra R G →ₐc[R] AddMonoidAlgebra R H) → G →+ H

A bialgebra homomorphism R[G] → R[H] between group algebras over a domain R comes from a group hom G → H. See MonoidAlgebra.mapDomainBialgHom for the forward map.

Defined in

Mathlib.RingTheory.Bialgebra.MonoidAlgebra

Cited by

6 results in Mathlib

Foundations

Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomainAddGroupAddGroup