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We study the mathematical foundations of physics. We reconstruct textbook quantum theory from a single symmetric monoidal functor GNS : Phys⟶∗Mod, based on the Gelfand-Naimark-Segal construction and the notion of representability. We derive the probabilistic interpretation of quantum mechanics, including the Born rule, the Schrödinger and Heisenberg pictures, the relation between symmetries and group representations, and a theory of quantum Markov processes, including wave function collapse.arXiv:1709.09096v2 fatcat:3zlwsidjevednbdavqbpaxmbwa