6 problems

Let $\cX$ be a truncated category, let $\Spant(\cX)$ denote its span $2$-category, let $\tA$ be a $2$-category, and let $\operatorname{\mbf{Fun}}^{\psa}(\cX^\op,\tA)$ denote the…

Carmeli–Schlank–Yanovski's conjecture. The functor $L_{T(n)}^{\tsadi}$ is an equivalence for $n>0$.

Height Finiteness Conjecture. For every $\mathcal{C}\in\Pr_{\mathrm{st}}^{\mathrm{\infty\text{-}semiadditive}}$, the full subcategory $\mathcal{C}_{\infty}$ is trivial.

Equivalence conjecture. For every $n\geq0$, the functor $L$ is an equivalence.

Bootstrap Conjecture. Every stable $p$-local presentable $1$-semiadditive $\infty$-category is in fact $\infty$-semiadditive.

A presentable stable $\infty$-category is an $\infty$-category that is presentable and stable, and $1$-semiadditive and $\infty$-semiadditive refer to the corresponding higher semi…