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Q-system completion is a 3-functor

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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.

http://www.tac.mta.ca/tac/volumes/38/4/38-04.pdf

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