Compact semisimple 2-categories

Décoppet, Thibault

doi:10.1090/tran/9044

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.

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