Description
The talk is based on joint work with Victor Ostrik. I will describe a construction of braided finite tensor categories that generalizes the usual semisimplification construction applied to tilting modules over quantum groups. The categories we obtain are no longer semisimple, but (after an appropriate de-equivariantization procedure) modular. (At least) one of these categories gives a rather nice and small example of a category not Witt equivalent to a semisimple category, existence of which was not known before.