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A linear Gr-category is a category of finite-dimensional vector spaces gradedby a finite group together with natural tensor product. We classify the braidedmonoidal structures of a class of linear Gr-categories via explicitcomputations of the 3-cocycles and quasi-bicharacters of finite abelian groupswhich are direct product of two cyclic groups.

The braided monoidal structures on a class of linear Gr-categories