Bimodule categories and monoidal 2-structure

<p>We define a notion of tensor product of bimodule categories and prove that with this product the 2-category of C -bimodule categories for fixed tensor C is a monoidal 2-category in the sense of Kapranov and Voevodsky ([KV91]). We then provide a monoidal-structure preserving 2-equivalence between the 2-category of C -bimodule categories and Z( C )-module categories (module categories over the center of C ). The (braided) tensor structure of C1&amp;timesb;D C2 for (braided) fusion categories over braided fusion D is introduced. For a finite group G we show that de-equivariantization is equivalent to the tensor product over Rep( G). The fusion rules for the Grothendeick ring of Rep(G)-module categories are derived and it is shown that the group of invertible Rep( G)-module categories is isomorphic to H2 (G, kx), extending results in [ENO09].</p>

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Dissertation

Year

2010

Author dc:creator

• Greenough, Justin

Contributors dc:contributor

• Dmitri Nikshych

• Mathematics
• Physics
• Theory

Repository record dc:identifier

https://scholars.unh.edu/dissertation/532

OAI identifier oai:identifier

oai:scholars.unh.edu:dissertation-1531