On the structure of the Witt group of braided fusion categories

We analyze the structure of the Witt group of braided fusion categories introduced in Davydov et al. (Journal fur die reine und angewandte Mathematik (Crelle's Journal), eprint arXiv: 1009.2117 [math.QA], 2010). We define a super version of the categorical Witt group, namely, the group of slightly degenerate braided fusion categories. We prove that is a direct sum of the classical part, an elementary Abelian 2-group, and a free Abelian group. Furthermore, we show that the kernel of the canonical homomorphism is generated by Ising categories and is isomorphic to . Finally, we give a complete description of ,tale algebras in tensor products of braided fusion categories.