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Abstract In our previous article (http://arxiv.org/abs/1607.06041), we established an equivalence between pointed pivotal module tensor categories and anchored planar algebras. This article introduces the notion of unitarity for both module tensor categories and anchored planar algebras, and establishes the unitary analog of the above equivalence. Our constructions use Baez’s 2-Hilbert spaces (i.e., semisimple$$\textrm{C}^*$$ -categories equipped with unitary traces), the unitary Yoneda embedding, and the notion of unitary adjunction for dagger functors between 2-Hilbert spaces.
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Unitary braided-enriched monoidal categories
Braided-enriched monoidal categories were introduced in the work of Morrison–Penneys, where they were characterized using braided central functors. The 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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- PAR ID:
- 10628221
- Publisher / Repository:
- European Mathematical Society
- Date Published:
- Journal Name:
- Quantum Topology
- Volume:
- 15
- Issue:
- 3
- ISSN:
- 1663-487X
- Page Range / eLocation ID:
- 567 to 632
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.4171/QT/226
