  In this paper, we examine Kitaev's lattice model for an arbitrary complex,
semisimple Hopf algebra. We prove that this model gives the same topological
invariants as Turaev-Viro theory. Using the description of Turaev-Viro theory
as an extended TQFT, we prove that the excited states of the Kitaev model
correspond to Turaev-Viro theory on a surface with boundary.
