Quantum Physics, Topology, Formal Languages, Computation: A Categorical View as Homage to David Hilbert

The deep structural properties of a quantum information theoretic approach to formal languages and universal computation (the unifying tool being the Quantum Spin Network Automaton scheme of computation), as well as those of the topology problem of defining the presentation of the Mapping Class Group of a smooth, compact manifold are shown to be grounded in the common categorical features of the two problems.