Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations

Marco MacKaay, Volodymyr Mazorchuk, Vanessa Miemietz, Xiaoting Zhang

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The main result of this paper establishes a bijection between the set of equivalence classes of simple transitive 2-representations with a fixed apex of a fiat 2-category and the set of equivalence classes of faithful simple transitive 2-representations of the fiat 2-subquotient of associated with a diagonal-cell in. As an application, we classify simple transitive 2-representations of various categories of Soergel bimodules, in particular, completing the classification in types and.

Original languageEnglish
Pages (from-to)1793-1829
Number of pages37
JournalJournal of the Institute of Mathematics of Jussieu
Issue number6
Early online date4 Dec 2018
Publication statusPublished - Nov 2020


  • 2-category
  • coalgebra 1-morphism
  • cotensor product
  • simple transitive 2-representation

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