Abstract: We defined and discussed the category of generalized Hom-comodules of a monoidal Hom-Hopf algebra. We used the Tannaka dual method to describe the rigid and balanced structures. Furthermore, we gave equivalent conditions of the ribbon category, and introduced the definition of the coribbon forms.

Key words: monoidal Hom-Hopf algebras, corepresentations, ribbon structure, coribbon forms