As an aside, it's worth noting that we bother giving `a -> a` a name other than `a -> a` here because there are other monoids for things of similar forms and th

As an aside, it's worth noting that we bother giving `a -> a` a name other than `a -> a` here because there are other monoids for things of similar forms and there's overlap. For instance, functions of the form `Monoid b => a -> b` can be combined by combining their output, and that gives us a different monoid with `const mempty` as the identity.