Q-system completion is a 3-functor

Quan Chen and David Penneys

Q-systems are unitary versions of Frobenius algebra objects which appeared in the theory of subfactors. In recent joint work with R. Hernández Palomares and C. Jones, the authors defined a notion of Q-system completion for C*/W* 2-categories, which is a unitary version of a higher idempotent completion in the spirit of Douglas-Reutter and Gaiotto-Johnson-Freyd. In this article, we prove that Q-system completion is a dagger 3-functor on the dagger 3-category of C*/W* 2-categories. We also prove that Q-system completion satisfies a universal property analogous to the universal property satisfied by idempotent completion for 1-categories.

Keywords: Q-systems, higher idempotent completion, C*/W* 2-categories, 3-functors

2020 MSC: 46M15, 18N10, 18N20, 18M30

Theory and Applications of Categories, Vol. 38, 2022, No. 4, pp 101-134.

Published 2022-01-11.


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