Q-system completion for C⁎ 2-categories

Abstract

A Q-system in a C⁎ 2-category is a unitary version of a separable Frobenius algebra object and can be viewed as a unitary version of a higher idempotent. We define a higher unitary idempotent completion for C⁎ 2-categories called Q-system completion and study its properties. We show that the C⁎ 2-category of right correspondences of unital C⁎-algebras is Q-system complete by constructing an inverse realization †-2-functor. We use this result to construct induced actions of group theoretical unitary fusion categories on continuous trace C⁎-algebras with connected spectra.