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.

Original languageEnglish
Pages (from-to)1261-1320
Number of pages60
JournalForum Mathematicum
Volume33
Issue number5
Early online date7 Aug 2021
DOIs
Publication statusPublished - 2021

Keywords

  • Finitary bicategory
  • bicomodule
  • coalgebra
  • double centralizer theorem
  • simple transitive birepresentation
  • strong H-reduction

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