Abstract:

This paper studies Yetter-Drinfeld modules over weak Hopf π coalgebra, discusses its properties over weak Hopf π coalgebra and gives its equivalent condition. The paper introduces monoidal categories, center and weak center over monoidal categories, which are divided into left and right centers. Based on these, the relations between the center and the Yetter-Drinfeld modules categories are studied, and it is proved that the center and the Yetter-Drinfeld module categories are isomorphic. Weak Hopf π coalgebra and its structure are further studied. 

Key words: Yetter-Drinfeld modules; weak center; isomorphic