4 problems

A fusion category is weakly integral if its Frobenius–Perron dimension is an integer, and it is weakly group-theoretical if it can be obtained from the trivial fusion category by a…

For $n\geq 1$, define … where $0_n=(0,0,\ldots,0)\in\mathbb{F}_2^n$ and $I_n\in SL_n(\mathbb{F}_2)$ is the identity matrix. Then $G_n\cong\mathbb{F}_2^{2n}\rtimes S_3$. Let…

Let ${\mathcal C}$ be a fusion category. Its Frobenius–Perron dimension is an integer if … A fusion category is weakly group-theoretical if it is categorically Morita equivalent to…

Weakly group-theoretical conjecture. Every fusion category of integer Frobenius–Perron dimension is weakly group-theoretical.