[skwosh]

I think using Haskell's type syntax is misleading in this context (and doesn't really imply the required associativity (much less commutativity if you wanted to consider Abelian monoids)).

The operation of a monoid maps from pairs of things to things. So in terms of types:

    <a,a> -> a

Or for some `twin` type constructor:

    twin a -> a

This is a bit more suggestive also in terms of F-algebras, where the operation has the following signature (f is a functor, or mappable container):

    f a -> a