2 problems

2-Tillmann conjecture. An object of the symmetric monoidal $3$-category $\mathbf{2Kar}$ is $1$-dualizable if and only if it is a finite semisimple $2$-category.

Let $\mathcal{V}$ be a symmetric monoidal $(\infty,1)$-category compatible with $\mathsf{simp}^{n,\operatorname{op}}$-colimits. Let $\mathfrak{alg}_{n}(\mathcal{V})$ denote the und…