Finitary birepresentations of finitary bicategories-Reference-Cited by-同舟云学术

Finitary birepresentations of finitary bicategories

Published:2021-08-07 Issue:5 Volume:33 Page:1261-1320
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Mackaay Marco¹,Mazorchuk Volodymyr²,Miemietz Vanessa³,Tubbenhauer Daniel⁴^ORCID,Zhang Xiaoting⁵

Affiliation:

1. Center for Mathematical Analysis, Geometry, and Dynamical Systems , Departamento de Matemática , Instituto Superior Técnico , 1049-001 Lisboa ; and Departamento de Matemática, FCT, Universidade do Algarve, Campus de Gambelas, 8005-139 Faro , Portugal

2. Department of Mathematics , Uppsala University , Box. 480, SE-75106 , Uppsala , Sweden

3. School of Mathematics , University of East Anglia , Norwich NR4 7TJ , United Kingdom

4. School of Mathematics and Statistics , The University of Sydney , F07 – Carslaw Building, Office Carslaw 827, NSW 2006 , Sydney , Australia

5. Beijing Advanced Innovation Center for Imaging Theory and Technology , Academy for Multidisciplinary Studies , Capital Normal University , Beijing 100048 , P. R. China

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/forum-2021-0021/pdf

Reference28 articles.

1. H. Bass, Algebraic 𝐾-Theory, W. A. Benjamin, New York, 1968.

2. J. Bénabou, Introduction to bicategories, Reports of the Midwest Category Seminar, Springer, Berlin (1967), 1–77.

3. A. Chan and V. Mazorchuk, Diagrams and discrete extensions for finitary 2-representations, Math. Proc. Cambridge Philos. Soc. 166 (2019), no. 2, 325–352.

4. A. Chan and V. Miemietz, Coidempotent subcoalgebras and short exact sequences of finitary 2-representations, Nagoya Math. J. (2020), 10.1017/nmj.2020.1.

5. B. Elias and G. Williamson, The Hodge theory of Soergel bimodules, Ann. of Math. (2) 180 (2014), no. 3, 1089–1136.

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