Classification of fusion categories generated by a self-dual simple object of FP-dimension 2

In this paper, we consider fusion categories generated by a self-dual simple object of FP-dimension 2. We use the classification results of indecomposable generalized Cartan matrices to determine possible types of these fusion categories. It turns out that there are only five types for such categories. Moreover, the fusion rules of all types of these fusion categories are explicitly described according to their valued graphs. This gives a classification of these fusion categories up to Grothendieck equivalence.