  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.
