31 problems

Let $A$ range over the homotopy or deformation algebras mentioned in the paper, including the various $( - )_{\infty}$-algebras, and let $\operatorname{Mod}(A)$ denote the category…

Coherent associativity conjecture. The bifunctor $\otimes^K_0$ is coherently associative. This would strengthen the displayed associativity isomorphism to coherent associativity of…

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 $\mathfrak{U}^\imath$ be the 2-category categorifying the quasi-split iquantum group in the general setup, allowing symmetrizable Cartan matrices and general choices of the pol…

Let $G=SU(2)$, and let $\operatorname{Inn}G=G\xrightarrow{\operatorname{id}}G$ be the inner automorphism 2-group. The associated 4d BF-BB theory is a special case of 2-Chern-Simons…

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…

An appropriately nice PIE-limit 2-theory is a two-dimensional theory whose models and pseudo morphisms form the 2-category under consideration. Accessibility conjecture. The 2-cate…

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 $\mathcal{E}$ be an elementary topos with a natural numbers object, and let $\mathbf{Cat}(\mathcal{E})$ denote the 2-category of internal categories in $\mathcal{E}$. Existence…

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…

The A-model concerns the Fukaya-type 2-category of boundary conditions for a 3-dimensional A-model associated with a 3d $\mathcal N=4$ theory. Inspired by analogous theorems for Fu…

Faithfulness conjecture. This 2-functor extends to a faithful 2-functor

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

Nondegeneracy conjecture. The endomorphism superalgebra $[?]$ has a basis given by certain products of bubbles.

2-category conjecture. There is a 2-category structure upon $\mathrm{\mathsf{{ContDiffSut}}}$ such that $\mathrm{\mathsf{DiffSutTor}}_2^\perp$ is a 2-subcategory of this, and such…

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)…

Strict-slice characterization. The following two statements are equivalent:

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.

Ara's conjecture. A $2$-functor $F$ is a biequivalence if and only if $N_sF$ is a weak equivalence in the model structure for $2$-quasi-categories.

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…

The bEM conjecture. The category $\operatorname{bEM}(\mathcal K)$ is the Eilenberg–Moore category for bimonads, with the displayed embedding 2-functor.

Let ${\rm Bimnd}({\mathcal K})$ be the 2-category of bimonads in a 2-category ${\mathcal K}$, and let ${\rm bEM}({\mathcal K})$ be the 2-category whose 2-cells consist of pairs of…

Let $\gamma$ be the surjective homomorphism of locally unital ${\mathcal L}$-algebras … where ${\mathcal L}=\mathbb{Z}[q,q^{-1},\pi]/(\pi^2-1)$. Decategorification Conjecture. The…