2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66700We show that the non-trivially associated tensor category constructed from left coset representatives of a subgroup of a finite group is a modular category. Also we give a definition of the character of an object in a ribbon category which is the category of representations of a braided Hopf algebra in the category. The definition is shown to be adjoint invariant and multiplicative. A detailed example is given. Finally we show an equivalence of categories between the non-trivially associated double D and the category of representations of the double of the group D(X).Approx 43 pages, uses LaTeX picture environmentQuantum Algebra18D10text