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Q-system completion is a 3-functor
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Q-systems are unitary versions of Frobenius algebra objects which appeared in the theory of subfactors. In recent joint work with R. Hern\'andez 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.
Forward citations
Cited by 2 Pith papers
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On the Higher Categorical Structure of Topological Defects in Quantum Field Theories
Categories of topological defects with arbitrary tangential structures are proposed to be structured higher dagger categories, proven for stable structures admitting direct sums under the stratified cobordism hypothesis.
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Orthonormal bases for higher Hilbert spaces
For finite-dimensional 3-Hilbert spaces, orthonormal bases exist uniquely up to contractible choice, and the Yoneda embedding into the presheaf 3-Hilbert space is an isometric equivalence.
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