Braided module categories, 2-centers, and higher Morita equivalences for braided tensor categories

Dmitri Nikshych (U of New Hampshire)

Aug 10. 2022, 11:30 — 12:30

Module categories over a braided tensor category C form a tensor 2-category Mod(C).  Its 2-center is a braided tensor 2-category. We describe the objects of this 2-center as braided C-module categories. Any such a module category gives rise to a representation of a type B Artin braid group. We also introduce a higher Morita theory for braided tensor categories, where a Morita context for pair of braided tensor categories C, D consists of their embeddings into  a non-degenerate braided tensor category whose images centralize each other in the sense of Mueger.  We relate higher Morita equivalences between C, D with braided 2-equivalences between the 2-centers of Mod(C), Mod(D).

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Higher Structures and Field Theory (Thematic Programme)
Anton Alekseev (U Genève)
Stefan Fredenhagen (U Vienna)
Nicolai Reshetikhin (UC, Berkeley)
Thomas Strobl (U Lyon)
Chenchang Zhu (U Göttingen)