Simple transitive 2-representations via (co)-algebra 1-morphisms

Marco MacKaay, Volodymyr Mazorchuk, Vanessa Miemietz, Daniel Tubbenhauer

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17 Citations (Scopus)


For any fiat 2-category C, we show how its simple transitive 2-representations can be constructed using coalgebra 1-morphisms in the injective abelianization of C. Dually, we show that these can also be constructed using algebra 1-morphisms in the projective abelianization of C. We also extend Morita–Takeuchi theory to our setup and work out several examples, including that of Soergel bimodules for dihedral groups, explicitly.
Original languageEnglish
Pages (from-to)1-33
Number of pages33
JournalIndiana University Mathematics Journal
Issue number1
Publication statusPublished - 1 Jan 2019

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