8 problems

Drinfeld-center classification conjecture. The map

Let $G$ be a group. For a multifusion category $\mathcal{C}$ with a $G$-action, write $\mathcal{C}^G$ for its equivariantization and $\mathbf{Mod}(\mathcal{C})$ for its delooping.…

Let $\mathcal{C}$ be a fusion 2-category and let $2\operatorname{Vec}$ be the 2-category of finite semisimple 1-categories. A fiber 2-functor is a tensor 2-functor…

A fusion 2-category is a finite semisimple tensor 2-category with simple tensor unit and duals for objects and 1-morphisms. An object of a symmetric monoidal 4-category is fully du…

Johnson–Freyd's conjecture. Every rigid algebra in a fusion 2-category over $\mathbb{C}$ is automatically separable.

Douglas–Reutter conjecture. Fusion 2-categories are fully dualizable objects, that is, 4-dualizable objects, in an appropriate symmetric monoidal 4-category.

A fusion 2-category is the type of higher category considered in the theory of fusion 2-categories. The conjecture concerns the collection of all such fusion 2-categories and the s…

Let $\mathfrak{C}$ be a fusion 2-category over an algebraically closed field of characteristic zero, and let $A$ be a rigid algebra in $\mathfrak{C}$. JFR's separability conjecture…