In this talk I will explain how to extract an `anyon theory' (braided tensor category) from a gapped ground state of an infinite two-dimensional lattice spin system. Just as in the DHR formalism from AQFT, the anyon types correspond to certain superselection sectors of the observable algebra of the spin system. We apply this formalism to Kitaev's quantum double model for finite gauge group G, and find that the anyon types correspond precisely to the representations of the quantum double algebra of G. The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0