8 problems

Let $n\mathsf{Pr}$ be the $1$-category of presentable $n$-categories, defined as the filtered colimit … where $n\mathsf{Pr}^{\kappa}$ is the category of $\kappa$-compactly generate…

Internal-left-adjoint compact-generation conjecture. If the coevaluation morphism is an internal left adjoint, then $C$ is compactly generated. The paper states that no counterexam…

Let $\mathcal P$ be a “doubly-presentably” symmetric monoidal $(\infty,2)$-category. The $(\infty,1)$-category $\mathcal P^{\mathrm{dbl}}$ of dualizable objects and $\mathcal P$-in…

Let $\mathcal{C}$ be a presentable $\infty$-category and let $\mathcal{C}_0\subseteq\mathcal{C}$ be a full subcategory. Suppose that $\mathcal{C}_0$ is closed under small limits an…

Small-limit conjecture. The category $n\operatorname{Pr}^L$ has all small limits for all $n\geq 0$.

Let $\mathcal{V}$ be a presentable, closed monoidal $\infty$-category. Write $\operatorname{Cat}^{\mathcal{V}}$ for the $\infty$-category of $\mathcal{V}$-enriched categories and…

Let $G$ be a finite group, let $\text{Burn}_G^{(\infty,2)}$ be the genuine equivariant Burnside $(\infty,2)$-category, and let $\text{Pr}^{\text{L}}$ be the $\infty$-category of pr…

Let $\mathcal{X} \to \Delta^{\operatorname{op}}$ be an admissible double $\infty$-category and let $\mathcal{V}$ be a presentably monoidal $\infty$-category. Corollary 3.?? equips…