mapDomainBialgHom — Mathlib

English

Similarly for MonoidAlgebra, the bialgebra structure is inherited from A; the counit and comultiplication are defined componentwise.

Русский

Аналогично для MonoidAlgebra; биалгебраическая структура наследуется от A; counit и comul задаются по компонентам.

LaTeX

$$MonoidAlgebra.instBialgebra R A M$$

Lean4

/-- If `f : M → N` is a monoid hom, then `AddMonoidAlgebra.mapDomain f` is a bialgebra hom between
their monoid algebras. -/
@[simps]
noncomputable def mapDomainBialgHom (f : M →+ N) : R[M] →ₐc[R] R[N]
    where
  __ := mapDomainAlgHom R R f
  map_smul' m x := by simp
  counit_comp := by ext; simp
  map_comp_comul := by ext; simp

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