6 problems

Let $k$ be a perfect field, and let $\mathcal{A}$ be a finite braided tensor category over $k$. The symmetric center of $\mathcal{A}$ is finite semisimple precisely when…

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.

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…

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…

Let $A$ be a finite algebra, and let $|A|$ denote its cardinality. An alter ego of $A$ is a structure whose compatible partial operations determine a duality for $A$; the arity bou…

Split centralizer conjecture. Under these global assumptions, $\mathbf{a}$ is dualizable if and only if $\mathbf{a}$ has a parallelogram term operation and satisfies the split cent…