4 problems

Frobenius–Perron growth conjecture. For every $X\in\mathcal{C}$,

Solvability conjecture. Every fusion category $\mathcal{C}$ whose Frobenius–Perron dimension $\operatorname{FPdim}(\mathcal{C})$ is odd is solvable.

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.