A braided module category is nondegenerate exactly when it is factorizable; in the Hopf case, the representation category B-FdMod is nondegenerate exactly when the quasitriangular comodule algebra B is factorizable.
Shimizu, Recent developments of the categorical Verlinde formula , Proceedings of the Meeting for Study of Number Theory, Hopf Algebras and Related Topics, 20 19, pp
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Nondegenerate module categories
A braided module category is nondegenerate exactly when it is factorizable; in the Hopf case, the representation category B-FdMod is nondegenerate exactly when the quasitriangular comodule algebra B is factorizable.