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arXiv · 2212.00363

Braided crossed category over crossed group-cograded weak Hopf quasigroups

Huili Liu·Lingli Zhu·Tao Yang
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Abstract

In this paper, we generalizing the main result in Liu[10] to weak Hopf coquasigroups case. We first define and study group-cograded weak Hopf quasigroups, which generalize both group-cograded Hopf quasigroups and weak Hopf group-coalgebras. Then we introduce the notion of p-Yetter-Drinfeld weak quasimodule over group-cograded weak Hopf quasigroups H. If the antipode of H is bijective, we show that the category YDWQ(H) of Yetter-Drinfeld weak quasimodules over H is a crossed category, and the subcategory YD(H) of Yetter-Drinfeld modules is a braided crossed category.

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Huili Liu, Lingli Zhu, Tao Yang. 2022-12-01. Braided crossed category over crossed group-cograded weak Hopf quasigroups. https://arxiv.org/abs/2212.00363

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