Hom-Hopf-modules And Yetter-Drinfeld Hom-modules On The Montidal Hom-Hopf Algebra

In quasi-Hopf algebra,the category of two sided two cosided Hopf module and the category of generalized Yetter-Drinfeld Hom module are important research objects,D.Bulacu et.al.discussed these module categories and revealed their equivalence.In this thesis,we shall discuss these module categories in momoidal Hom-Hopf algebra setting,the main contents are as follows:(1)we shall introduce the concept of two-sided Hom-Hopf module,and prove the equivalence between the category of two sided(H,A)-Hom-Hopf module and the category of A-module.(2)we shall introduce the concepts of two-sided two-cosided Hopf module and Yetter-Drinfeld Hom-module,and proves the equivalence between these module categories.