Unitary braided-enriched monoidal categories
Zachary Dell, Peter Huston, and David Penneys
TL;DR
This paper introduces a notion of unitarity for braided-enriched monoidal categories, extending existing theoretical frameworks and connecting them to physical systems in condensed matter physics.
Contribution
It defines unitarity for enriched categories and braided monoidal categories, and extends the 2-category equivalence to include the unitary setting.
Findings
Defined unitarity for enriched categories and braided monoidal categories
Extended the 2-equivalence to the unitary setting
Applied to topologically ordered systems in physics
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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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Intracranial Aneurysms: Treatment and Complications