Seminario del grupo de teoría de Lie

Gregor Schaumann – Lunes 10 de Agosto 14:00hs

Bridging the left and right exact realms of 2-representations

Abstract: Tensor categories can be seen as a categorification of rings and it is natural to study the 2-categories of their representations, where the tensor categories act on linear categories. Basic constructions as balanced tensor products, tensor-hom adjunction, et cetera,  have their «2-analogues».  However, there are novel features such as the distinction between left and right exact functors or the occurrence of pivotal structures.

In this talk we discuss aspects of the 2-representations of finite tensor categories using the language of ends and coends which allows to relate the realms of left and right exact functors. This bridge allows to study Nakajama functors, Serre functors, to relate these to Frobenius algebras in the presence of pivotal structures and to apply the  algebraic theory to topological quantum field theory. This is joint work with Christoph Schweigert and Jürgen Fuchs.