18 problems

Drinfeld-center classification conjecture. The map

Let ${\mathcal C}_\zeta^{{\underline c}_f}$ be the monoidal category associated with a finite two-sided cell ${\underline c}_f\subset W_f(\zeta)$, and let…

Let $\mathfrak g$ be a semisimple Lie algebra with weight and root lattices $P$ and $Q$, respectively. For $q\in\mathbb{C}$, let $U_q(\mathfrak g)\mathbf{-mod}$ be the category of…

Crystal Temperley–Lieb center conjecture. The canonical functor $G$ is a monoidal equivalence. This conjecture asserts that the only objects in the Drinfeld center are those induce…

Let $\mathcal C$ be a near-group category of type $\mathbb Z/4\mathbb Ztimes \mathbb Z/4\mathbb Z+16$, provided that such a category exists, and let $Z(\mathcal C)$ denote its Drin…

Let $G$ be a group and let $\mathcal{C}_G$ be a $G$-graded fusion category. Assume the extension class $\omega_2$ is trivial, and let ${}^{\mathrm{sVect}}\mathcal{C}_G$ denote the…

Drinfeld-center reconstruction conjecture. This prescription enables one to reconstruct the Drinfeld center

Let $\mathcal{C}$ be a fusion category, and let an associative zesting of $\mathcal{C}$ induce a zesting on its center $\mathcal{Z}(\mathcal{C})$. Induced zesting conjecture. The i…

Let $\mathcal{C}_{3,9,3}$ be a quadratic category with the fusion rules specified below, let $\mathcal{C}_{4,8,4}$ be a fusion category with invertibles…

Let $\mathcal{C}$ be the $\operatorname{SL}_2(\mathbb{C})^*$-graded category described in the paper, let $\mathcal{D}$ be the doubled category constructed from $\mathcal{C}$, and l…

Universal property conjecture. The category $\mathrm{Hom}(\mathbb{I}\mathrm{d},\mathbb{I}\mathrm{d})$ is universal among categories equipped with this collection of functors and na…

Inverse-limit conjecture. The category $\mathrm{Hom}(\mathbb{I}\mathrm{d},\mathbb{I}\mathrm{d})$ is the inverse limit of the Drinfeld centers…

Let $\mathrm{MF}^0_{\mathrm{Dr}}$ be the degree-zero Drinfeld matrix-factorization category, let $\mathrm{MF}$ be the corresponding matrix-factorization category, and let…

Let $D(\operatorname{Fib})$ denote the double of the Fibonacci category, and let $D(\operatorname{Haag}_k)$ denote the sequence defined later in the source. Haagerup sequence conje…

Let $V$ be a unitary topological modular functor (UTMF), and let $\mathcal{B}$ be its associated unitary modular category. Let $\mathcal{C}$ be a unitary fusion category. UTMF real…

Let $N\subset M$ be a finite-depth subfactor, let $P$ be its associated subfactor planar algebra, and let the $N$-$N$-bimodule category generated by $_N L^2(M)_M$ be the category w…

Let $\Lambda$ be a $\mathbb{C}$-linear category. Let $\Lambda^{\mathcal R}$ and $\Lambda^{\mathcal A}$ be, respectively, the rectangular and annular versions of the corresponding l…

Categorified Deligne conjecture. The Drinfeld center $Z(\mathcal C)$ is an $\mathcal E_2$-category.