On Quantization Functors of Lie Bialgebras

We show that the set of quantization functors of Lie bialgrebras has the structure of a torsor. Then we show that the Etingof–Kazhdan map is a morphism of torsors. We compute the infinitesimal of this map. As a corollary, we show that the quantization functors of finite-dimensional Lie bialgebras are independent of the choice of an associator.