Yetter–Drinfeld Modules for Group-Cograded Hopf Quasigroups

Abstract

Let H be a crossed group-cograded Hopf quasigroup. We first introduce the notion of p-Yetter–Drinfeld quasimodule over H. If the antipode of H is bijective, we show that the category YDQ(H) of Yetter–Drinfeld quasimodules over H is a crossed category, and the subcategory YD(H) of Yetter–Drinfeld modules is a braided crossed category.