Hopf modules in the braided monoidal category $_LM$

Abstract

Suppose that L is a quasitriangular weak Hopf algebra with a bijective antipode and H is a weak Hopf algebra in the braided nonoidal category _LM. We prove that the fundamental theorem for right H-Hopf modules in _LM. Our results in this paper generalize previous fundamental theorem for Hopf module on the Hopf algebras and weak Hopf algebras.