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.
Unitary braided-enriched monoidal categories
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abstract
Braided-enriched monoidal categories were introduced in work of Morrison-Penneys, where they were characterized using braided central functors. Recent work of Kong-Yuan-Zhang-Zheng and Dell extended this characterization to an equivalence of 2-categories. Since their introduction, braided-enriched fusion categories have been used to describe certain phenomena in topologically ordered systems in theoretical condensed matter physics. While these systems are unitary, there was previously no general notion of unitarity for enriched categories in the literature. We supply the notion of unitarity for enriched categories and braided enriched monoidal categories and extend the above 2-equivalence to the unitary setting.
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2026 1verdicts
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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.