Finitary birepresentations of finitary bicategories

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MacKaay, Marco, Mazorchuk, Volodymyr, Miemietz, Vanessa, Tubbenhauer, Daniel and Zhang, Xiaoting (2021) Finitary birepresentations of finitary bicategories. Forum Mathematicum, 33 (5). pp. 1261-1320.

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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.

Item Type:	Article
Uncontrolled Keywords:	finitary bicategory,bicomodule,coalgebra,double centralizer theorem,simple transitive birepresentation,strong h-reduction,mathematics(all),applied mathematics ,/dk/atira/pure/subjectarea/asjc/2600
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://arxiv.org/abs/2008.01658
Depositing User:	LivePure Connector
Date Deposited:	02 Jul 2021 01:09
Last Modified:	16 Dec 2024 01:35
URI:	https://ueaeprints.uea.ac.uk/id/eprint/80378
DOI:	10.1515/forum-2021-0021

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