3 problems

Let $\mathfrak C$ be a monoidal $\mathbb K$-linear 2-category, subject to suitable assumptions. Write $\mathfrak C^\times$ for its subgroupoid of invertible objects, and let…

Splitting conjecture. In general, this sequence splits, so that

Fusion category classification conjecture. Cases (a)–(c) are each realized by a unique fusion category, and each such category has the following properties: it has $4$ invertible o…