Structure of braided tensor categories

A certain equivalence relation (Witt equivalence) allows one to organize braided tensor categories into a manageable set of classes. For example under this equivalence symmetric tensor categories form just two classes (Tannakian and super-Tannakian). In the fusion braided case the equivalence classes form a group (a generalization of the Witt group). The structure of this group is related to a conjecture of Moore and Seiberg about chiral algebras of rational conformal field theories.