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arXiv · 2008.01658

Finitary birepresentations of finitary bicategories

Marco Mackaay·Volodymyr Mazorchuk·Vanessa Miemietz·Daniel Tubbenhauer·Xiaoting Zhang
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Abstract

In this paper, we discuss the generalization of finitary $2$-representation theory of finitary $2$-categories to finitary birepresentation theory of finitary bicategories. In previous papers on the subject, the classification of simple transitive $2$-representations of a given $2$-category was reduced to that for certain subquotients. These reduction results were all formulated as bijections between equivalence classes of $2$-representations. In this paper, we generalize them to biequivalences between certain $2$-categories of birepresentations. Furthermore, we prove an analog of the double centralizer theorem in finitary birepresentation theory.

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Marco Mackaay, Volodymyr Mazorchuk, Vanessa Miemietz, Daniel Tubbenhauer, Xiaoting Zhang. 2020-08-04. Finitary birepresentations of finitary bicategories. https://doi.org/10.1515/forum-2021-0021

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