Q-system completion is a 3-functor

Abstract

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 † 3-functor on the † 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.

Unitary anchored planar algebras

“…In this section, we shall often use the graphical calculus for Cat, denoting linear categories by two-dimensional regions, functors by strands, and natural transformations by junctures. As in [CP22], we may identify a category A with the category of C-linear functors Vect → A. Given a functor F : A → B and objects a ∈ A and b ∈ B, this allows us to give a graphical representation e.g.…”