On one conjugate object in the symmetric tensor C*-category and the statistics of superselection sectors

In this work, a model of a symmetric tensor 𝐶*-category with conjugation is constructed for the dimension of the object 𝑑 = 3. It is proved that the constructed conjugate object of the category satisfies the conjugation equations. The classes of morphisms between objects of the modeled category are considered and studied, and the algebra of observables in the presence of such an conjugate object is introduced. As an application of the model, we consider the theory of quantum information transfer, where it is necessary to take into account the constraints associated with the superselection rules.