In particular, the paper discusses the category of finite sets and relations, in which the two element set acts as a system of observables, capable of modelling much of the behaviour of a qubit, just as in M theory. It will be interesting to extend this observation to a richer arithmetic setting. These days, similarities between sets and Hilbert spaces always invoke the notion of a field with one element, over which a set is just a vector space. And the natural groups to study in association with this field are the braid groups, especially at roots of unity.
Oh wait. Gee, that's what we're using to unify particle mass triplets and mixing matrices. But Dr Mottle tells us that this is completely idiotic and cannot possibly work, so maybe we should just go outside and make snowmen.