Tensor categories and 2-rings

Nicola Gambino, University of Leeds. Part of the algebra seminar series.

Tensor categories and 2-rings are two possible “categorification" of the familiar notion of a ring. In recent years, there have been significant efforts to develop a counterpart of ordinary ring theory for tensor categories and 2-rings. I will give an overview of this research area, emphasizing similarities and differences. One interesting issue concerns the analogue of tensor product of rings: in the setting of tensor categories is the tensor product introduced by Deligne in his 1994 paper “Catégories tannakiennes”. Recent work of Ignacio Lopez Franco (https://arxiv.org/abs/1212.1545) shows that the Deligne tensor product is actually related from the tensor product of 2-rings.

After each talk at 4:15pm there will be tea/coffee in the Common Room at level 9 in Maths building. The current seminar organiser is Eleonore Faber. 

Nicola Gambino, University of Leeds