> @Matthew -- re:
>
> while `Maybe a` is not necessarily a monoid, `Maybe [a]` *is*
>
> This seems to be a special case of a more general result, namely that if `Moo` is a monoid, then we can define a canonical monoid structure on `Maybe Moo`.
>
> The unit is `Nothing`, and we define `(Just x) <> (Just y)` to be `Just (x <> y)`.

You are absolutely right!

Haskell's defines the instance `Semigroup a => Semigroup (Maybe a)` in the [Prelude](https://hackage.haskell.org/package/base-4.11.1.0/docs/src/GHC.Base.html#line-406), following your specification:



instance Semigroup a => Semigroup (Maybe a) where

    Nothing <> b       = b

    a       <> Nothing = a

    Just a  <> Just b  = Just (a <> b)


And the *unit* for this monoid is defined in [Data.Monoid](https://hackage.haskell.org/package/base-4.11.1.0/docs/src/GHC.Base.html#line-422), again exactly as you suggest:



instance Semigroup a => Monoid (Maybe a) where

    mempty = Nothing