# What categorical mathematical structure(s) best describe the space of “localized events” in “relational quantum mechanics”?

In a recent (and to me, very beautiful) paper, entitled "Relational EPR",


Smerlak and Rovelli present a way of thinking about EPR which relies upon Rovelli's previously published work on relational quantum mechanics (see http://arxiv.org/abs/quant-ph/9609002 ). In relational quantum mechanics, there is no non-locality, but the definition of when an event occurs is weakened from Einstein's strict definition and instead is localized to each observer-measurement apparatus, including subsequent observers. There are (informal) coherence assumptions to ensure the consistency of reports from different subsequent observers (all possible friends of Wigner).

All of this seems very similar to various results in modern categorical mathematics. Is there a standard mathematical structure which well describes the structure of the space of localized measurements which Rovelli has envisioned? I know of Isham's work on topos theory and quantum mechanics, but I think he is aiming at something a little different.

PS I first asked this on mathunderflow, but was advised to repost here.

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## 1 Answer

I wouldn't say it is a standard structure (yet), but Samson Abramsky has recently given a relational/categorical account of a lot of properties like non-locality and no-signaling. Relations between these notions, including no-go theorems, that are surprisingly involved in other formulations, are quite simply derived, indicating that this could be a good way to state things. See arxiv:1007.2754.

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