small rank fusion categories

Many properties of fusion categories, for example unitarity, can be deduced from the \(F\)-symbols that encode the associators. In  [1], we used a all premodular categories of rank \(⩽5\) to check a conjectural form of the topological entanglement entropy of Walker-Wang modes, while in (missing reference), we initially checked our results using similar data.

In this on-going projects, we are compiling such data. For all multiplicity-free, unitary fusion categories of rank ⩽6, the data can be found here: .

When the categories admit braidings, all braidings are included (up to equivalence).