Finitary birepresentations of finitary bicategories

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.

Significant revision of the original version

References in corpus (3)

• Cell 2-representations of finitary 2-categories
• Simple transitive 2-representations via (co)algebra 1-morphisms
• Diagrams and discrete extensions for finitary 2-representations

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