Data.Functor.Compose: newtype Compose f g a = Compose { getCompose :: f (g a) } there's clear-cut, more traditional instances if `f` and `g` are Applicative: instance (Applicative f, Applicative g, Semigroup a) => Semigroup (Compose f g a) where (<>) = liftA2 (<>) instance (Applicative f, Applicative g, Monoid a) => Monoid (Compose f g a) where mempty = pure mempty There's an alternative with `QuantifiedConstraints`, but it's arguable that this is desirable: instance (forall x. Semigroup x => Semigroup (f x), forall x. Semigroup x => Semigroup (g x), Semigroup a) => Semigroup (Compose f g a) where Compose x <> Compose y = Compose (x <> y) Both to seem to fit the commonplace spirit of lifting monoids up through applicative contexts.