On the classification of weakly integral modular categories
The aim of this paper is to 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. More precisely, the main result establishes that, if \(\mathcal C\) is a weakly integral modular category either of \(rank \leq 7\) or with Frobenius-Perron dimension \(4m\), where \(m\) is an odd square-free integer, then \(\mathcal C\) is equivalent to a (Deligne) product of the following: pointed categories, Ising categories and metaplectic categories.
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