Braided crossed category over crossed group-cograded weak Hopf quasigroups
Rings and Algebras
2022-12-02 v1
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.
Keywords
Cite
@article{arxiv.2212.00363,
title = {Braided crossed category over crossed group-cograded weak Hopf quasigroups},
author = {Huili Liu and Lingli Zhu and Tao Yang},
journal= {arXiv preprint arXiv:2212.00363},
year = {2022}
}
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19pages