#### Vol. 306, No. 2, 2020

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$2$-categories of symmetric bimodules and their $2$-representations

### Volodymyr Mazorchuk, Vanessa Miemietz and Xiaoting Zhang

Vol. 306 (2020), No. 2, 645–678
##### Abstract

In this article we analyze the structure of $2$-categories of symmetric projective bimodules over a finite dimensional algebra with respect to the action of a finite abelian group. We determine under which condition the resulting $2$-category is fiat (in the sense of Mazorchuk and Miemietz (2011)) and classify simple transitive $2$-representations of this $2$-category (under some mild technical assumption). We also study several classes of examples in detail.

##### Keywords
finite abelian group, symmetric bimodule, 2-category, simple transitive 2-representation
Primary: 18D05