7 problems

Naidu–Rowell's conjecture. The category $\mathbf{C}$ has property F precisely when $\operatorname{FPdim}(\mathbf{C})$ is an integer.

Let $\mathcal{C}$ be a braided fusion category and let $X$ be a simple object of $\mathcal{C}$. Denote by $\rho_X$ the braid-group representations on…

Braided 2-Morita conjecture. This definition of $E_2$-Morita equivalence extends to braided fusion categories without requiring non-degeneracy.

Let $\mathcal C$ be a braided fusion category over $\Bbb C$. For objects $X_1,\ldots,X_n,Y\in\mathcal C$, the space $\operatorname{Hom}(Y,X_1\otimes\cdots\otimes X_n)$ carries an a…

Let $s\mathcal{W}$ be the Witt group of completely anisotropic s-simple braided fusion categories of finite order, and let $s\mathcal{W}_2$ be its subgroup generated by their Witt…

Let $\mathcal{C}(so(2n+1),2n+1)$ denote the braided fusion category associated with $so(2n+1)$ at level $2n+1$, and let $S$ be the homomorphism sending a Witt class to its product…

Weak-integrality conjecture. A braided fusion category $\mathcal{C}$ has property $\mathbf{F}$ if and only if