Abstract
The purpose of this paper is to introduce an equivalence relation on quasitriangular quasi-Turaev group coalgebras such that the categories of representations of two quasitriangular quasi-Turaev group coalgebras are tensor [Formula: see text]-equivalent. As an application, we construct a new Turaev braided group category by a gauge transformation and give a new solution of Yang–Baxter type equation.
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