A PARTIALLY DEFINED BRAIDING ON A NON-BRAIDED CATEGORY
In this paper, the braiding for a braided tensor category is extended to a partially defined braiding on a non-braided tensor category is constructed by considering a choice of left cosets representatives M for the action of a subgroup G of a finite group X on X. The objects of are the right representations of G that graded by M. The group action and the grading in the definition of were combined by considering a single object A spanned by a basis for and The double construction gives rise to a braided category the category of the representations of an algebra D which combines the actions and the gradings in the definition of
non-trivially associated tensor categories, braided tensor categories, algebras in tensor categories, Hopf algebras in braided tensor categories.