Not being especially mathematically inclined, every once and a while I get a little panicked when I notice that, e.g. Data.Map mappend is a plain left-biased union, and doesn't actually mappend the values of the map. Then I remember that monoids are associative, not commutative, and it's totally allowed to do that. Even if you mappend the values, the result is only as commutative as the monoid instance for the values. But clearly you can make that choice. For instance, Maybe's Monoid wants to mappend the elements. This is always a little disconcerting to me because the MonadPlus instance for Maybe doesn't do that. So there's a range of possible Monoid instances for each type, and maybe they were chosen by historical happenstance rather than some kind of "principle monoid" (is there such a thing?). Is there a name for the thing that's like a monoid, but the operator is commutative too? That would narrow down the implementation choices, e.g. Data.Map would have to combine the values. So it seems like if your operation is commutative, you can put it in "c-monoid" and not rely so much on the happenstance of the instances, since they are more constrained. And of course you are then free to reorder things, which is a nice bit of flexibility. So is there a typeclass for that? This article is about the mathematical concept. For the alien creatures in the Doctor Who adventure, see The Ark (Doctor Who). I guess I never saw that episode... but it sounds like they're closer to warm fuzzies than the slimy sleeping bag monster I imagined.