We define the notion of factorizable quasi-Hopf algebra by using a
categorical point of view. We show that the Drinfeld double D(H) of any
finite dimensional quasi-Hopf algebra H is factorizable, and we characterize
D(H) when H itself is factorizable. Finally, we prove that any finite
dimensional factorizable quasi-Hopf algebra is unimodular. In particular, we
obtain that the Drinfeld double D(H) is a unimodular quasi-Hopf algebra.Comment: 35 page