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

MacKaay, Marco, Mazorchuk, Volodymyr, Miemietz, Vanessa and Tubbenhauer, Daniel (2019) Simple transitive 2-representations via (co)-algebra 1-morphisms. Indiana University Mathematics Journal, 68 (1). pp. 1-33. ISSN 1943-5258

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Abstract

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.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics (former - to 2024) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Related URLs:	http://www.scopus.com/inward/record.url?... https://www.iumj.indiana.edu/IUMJ/FULLTE... https://arxiv.org/abs/1612.06325
Depositing User:	Pure Connector
Date Deposited:	06 Dec 2017 06:06
Last Modified:	16 Oct 2025 18:31
URI:	https://ueaeprints.uea.ac.uk/id/eprint/65677
DOI:	10.1512/iumj.2019.68.7554

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