10 problems

Let $\lModl$ be the 2-category of loosely discrete opfibrations and $\TwModl$ the 2-category of twisted bimodules, with the 2-functor $\twsection{-}: \lModl \to \TwModl$ given by t…

Let $m$ and $n$ denote objects indexing Rouquier complexes, and let $m\boxtimes n\rightarrow n\boxtimes m$ be the corresponding Rouquier complexes. Let $\tau_{m,n}$ be the naturali…

Pseudoadjunction conjecture. There is a pseudoadjunction between the locally discrete 2-category of bicategorical graphs and the 2-category of bicategories, pseudofunctors and icon…

Let $(X\supset\mathbb L)$ and $(X^\vee\supset\mathbb L^\vee)$ be dual pairs of sectorial conical symplectic resolutions. Let $2\mathcal O_{\mathsf A}$ and $2\mathcal O_{\mathsf B}$…

Let $(X\supset\mathbb L)$ be a sectorial conical symplectic resolution, and let $\mathbb L$ denote its distinguished Lagrangian. Write $2\mathcal O_{\mathsf A}$ and…

Let $M$ be a holomorphic symplectic manifold with complex structure $I$ and holomorphic symplectic form $\Omega_I$. For $I$-holomorphic Lagrangian submanifolds $L_1,L_2\subset M$,…

Lax- and pseudo-slice characterization. The pair $(L,\lambda)$ is a $2$-limit of the $2$-functor $F$ precisely when it is a $2$-terminal object in the lax-slice (or pseudo-slice)…

The cofinality conjecture. Precomposition with $F$ preserves marked $(\infty,2)$-colimits if and only if, for every object $d\in\mathbfcal{D}$: (1) there are $c\in\mathbfcal{C}$ an…

Existence conjecture. There is a theory of marked $(\infty,2)$-colimits in every $(\infty,2)$-category, with input and output as above.

Let $\Gamma$ be the fixed data defining the unitary $*$-2-category $\operatorname{TLJ}(\Gamma)$. A MW-type bipartite balanced $\Gamma$-fair graph is a bipartite balanced $\Gamma$-f…