On two approaches to 3-dimensional TQFTs

Let C be a spherical fusion category. We prove that the Turaev-Viro-Barrett-Westbury state sum invariant of 3-manifolds derived from C is equal to the Reshetikhin-Turaev surgery invariant of 3-manifolds derived from Z©, where Z© is the Drinfeld-Joyal-Street center of C.