Compact semisimple 2-categories
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- by Thibault D. Décoppet;
- Trans. Amer. Math. Soc. 376 (2023), 8309-8336
- DOI: https://doi.org/10.1090/tran/9044
- Published electronically: September 29, 2023
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Abstract:
Working over an arbitrary field, we define compact semisimple 2-categories, and show that every compact semisimple 2-category is equivalent to the 2-category of separable module 1-categories over a finite semisimple tensor 1-category. Then, we prove that, over an algebraically closed field or a real closed field, compact semisimple 2-categories are finite. Finally, we explain how a number of key results in the theory of finite semisimple 2-categories over an algebraically closed field of characteristic zero can be generalized to compact semisimple 2-categories.References
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Bibliographic Information
- Thibault D. Décoppet
- Affiliation: Mathematical Institute, University of Oxford, Oxford, OX2 6GG, United Kingdom
- Address at time of publication: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02139
- ORCID: 0000-0003-0443-4204
- Email: decoppet@math.harvard.edu
- Received by editor(s): December 13, 2021
- Received by editor(s) in revised form: June 26, 2022
- Published electronically: September 29, 2023
- © Copyright 2023 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 376 (2023), 8309-8336
- MSC (2020): Primary 18M20, 18N25; Secondary 16T05, 18M05, 18N10
- DOI: https://doi.org/10.1090/tran/9044
- MathSciNet review: 4669298