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

Braided crossed category over crossed group-cograded weak Hopf quasigroups