From an interesting conversation with @zanzi inspired by @johncarlosbaez's talk on higher categories last week:
Computer representation of free commutative monoids (aka bags, finite multisets) is hard because you can't get unique normal forms. Why not represent it as a 1-object monoidal category, or a 1-object 1-morphism 2-category? Because those have an interchange law, and computer representation of interchange laws is also hard... in fact the difficulty of representing commutativity and interchange now look to me like the same difficulty
