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arXiv · 2411.18453

Nondegenerate module categories

Chelsea Walton·Harshit Yadav
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Abstract

Due to the work of Shimizu (2019), various nondegeneracy conditions for braided finite tensor categories are equivalent. This theory is partially extended to braided module categories here. We introduce when a braided module category is "nondegenerate" and "factorizable", and establish that these properties are equivalent. The proof involves a new monadicity result for module categories. Lastly, we examine the Hopf case, using Kolb's (2020) notion of a quasitriangular comodule algebra to introduce "factorizable" comodule algebras. We then show that the representation category of a quasitriangular comodule algebra is nondegenerate in our sense precisely when the comodule algebra is factorizable. Several examples are provided.

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Chelsea Walton, Harshit Yadav. 2024-11-27. Nondegenerate module categories. https://arxiv.org/abs/2411.18453

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