中文摘要：

在T-余代数上定义了反-Yetter-Drinfeld模,给出其相容条等价条件.证明了一个左-左α-反-Yetter-Drinfeld模M和左-左β-反-Yetter-Drinfeld模N的张量积M×N是左-左αβ-反-Yetter-Drinfeld模,以及^βM是左-左βαβ^-1-反-Yetter-Drinfeld模.最后证明了同构定理及Hom（M,N）也是反-Yetter-Drinfeld模.

英文摘要：

This paper defined the anti-Yetter-Drinfeld module over T-coalgebras,and discussed the equivalence of compatibility condition.The results prove that M×N are left-left αβ-anti-Yetter-Drinfeld module where M and N are left-left α,β anti-Yetter-Drinfeld module,respectively,and ^βM is left-left βαβ^-1-anti-Yetter-Drinfeld module,demonstrate an isomorphism theory and that Hom（M,N） is anti-Yetter-Drinfeld module as well.