I don't know if I quite get what this question is asking. Is it to map the components of the List Algebra to a Monoid and vice-versa?
a) List(X) = 1 + A.X
\\( 1 \mapsto e \\)
\\( . \mapsto * \\)
or in Haskell
> alg2monoid :: Algebra a -> Monoid a
> alg2monoid Nil = mempty
> alg2monoid (Cons a x) = a <> x