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?

For example:

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

For example:

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