Spin-net formalism for 3-dimensional topological quantum field theories

The graphical formalism of string nets, due to Levin, Wen and Kirillov, is an elegant way to describe the vector spaces assigned to oriented surfaces in the Turaev-Viro model. It takes as input a spherical fusion category. What happens if one starts with just a "bare" fusion category? I will describe a "spin net" formalism for this case, which applies to surfaces equipped with a spin structure. In this way one obtains representations of the spin mapping class groups of surfaces.