On the Classification of Weakly Integral Modular Categories

Understand

We classify all modular categories of dimension $4m$, where $m$ is an odd square-free integer, and all ranks $6$ and $7$ weakly integral modular categories.

• This completes the classification of weakly integral modular categories through rank $7$.
• Our results imply that all integral modular categories of rank at most $7$ are pointed (that is, every simple object has dimension $1$).
• All strictly weakly integral (weakly integral but non-integral) modular categories of ranks $6$ and $7$ have dimension $4m$, with $m$ an odd square free integer, so their classification is an application of our main result.