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.
Enriquez, Quasi-reflection algebras and cyclotomic associators , Selecta Math
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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.