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.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/HS2015