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.

arXiv comment48 pages, many tikz figures, comments welcome!

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• Quantum graphs, subfactors and tensor categories I
• Inclusions of Operator Algebras from Tensor Categories: beyond irreducibility
• Separable algebras in multitensor C${}^{\ast }$-categories are unitarizable
• On a Connes Fusion Approach to Finite Index Extensions of Conformal Nets
• A categorical Connes' $\chi (M)$
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• Entanglement-invertible channels
• Discrete Inclusions of C*-algebras
• The stable uniqueness theorem for unitary tensor category equivariant KK-theory