46 problems

Higher BV quantization conjecture. There is a natural equivalence

Let $(\bDelta^n)$ denote the oriented simplex, let $\tau_{n-1}(\bDelta^n)$ denote its $(n-1)$-truncation, and let $(\Delta^n)^t$ be the stratified simplicial space obtained from th…

Let $R\colon \Cat^L_\infty\hookrightarrow \Cat_\infty$ be the embedding of the category of presentable $\infty$-categories and colimit-preserving functors into the category of…

Cartesianity conjecture. If $C$ is an infinity-category, then

Let $\mathcal{S}$ be an abstract wrapped Floer setup, let $\mathcal{F}^{\text{pre}}_{\mathcal{S}}$ be its pre-wrapped Fukaya $A_\infty$-category, let $\widetilde{C}$ be the set of…

Let $X$ be a $\Gamma$-scheme, let $\mathbb T_X^\Gamma$ denote its $\Gamma$-tangent $\infty$-category, and let $\mathbb L_X^\Gamma$ denote its cotangent complex. Tangent–cotangent e…

Let $(S,n,{\bf a})$ be a parametrized surface and let $R(S,n,{\bf a};k)$ be the dga generated by diagrams of $k$ strands between the corresponding collections of arcs. Let $\mu_m$…

Let $M$ be an ungroup-like abelian monoid, let $X$ be a topological space, and define $\mathrm{SP}(X,M)$ to be the free strictly commutative topological monoid generated by $X$-man…

Let $\mathcal{C}$ be an $(\infty,n)$-category, and let $\mathrm{O}_{n-1}$ and $\Theta_n$ be the indexing shapes used to define the iterated constructions…

Let $\mathbf{CompCat}_{\Sigma, \Pi_\text{ext}, \text{Id}}$ be the category of models of intensional Martin–Löf type theory with dependent sums, extensional dependent products, and…

Let $\mathfrak{K}_{n}$ and $\mathfrak{M}_{n}$ be the model categories of marked Kan complexes and marked complicial sets, respectively, and let $(i_{\Delta},-_{\Delta})$ be the adj…

Let $n\text{-}\operatorname{Cat}$ denote the category of $n$-categories, let $\operatorname{Surj}_{\omega}$ denote the class of $\omega$-surjective morphisms, and let…

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 $\mathcal{N}(\bar{X},F_{0})$ be the Fukaya-type category and let $\widehat{\mathcal{W}}_{F}$ be its categorical formal completion. Suppose that…

Let $\mathcal{O}$ be an operad in an ambient $\infty$-category $\mathcal{C}$, and let $B\mathcal{O}$ denote its bar construction, a cooperad. Write…

Let $R$ be a ring and consider the corresponding $c6$-module functors, ${\square\square\square}B$-pair functors, and vector bundle functors over ${\square\square\square}FF$ functor…

Let $\mathcal{S}\mathrm{trat}$ denote a homotopy theory of topological stratified spaces, and let $\iCat$ denote the homotopy theory of $\infty$-categories. The exit path construct…

Let $\FIVAnly$ be the $\infty$-category of analytic $\FI$-objects, and let $\FIVTors$ be the full sub-$\infty$-category of torsion $\FI$-objects. For full subcategories…

Let $C$ be an $\infty$-category, and let $W\subseteq (\operatorname{Cat}\!\slice C)^{\Delta^1}$ be a set of maps satisfying three conditions: it is stable under 2-out-of-3 and retra…

Let $G$ be a smooth algebraic group and let $X$ be a left $G$-variety over $\operatorname{Spec} K$. Let $\mathsf{Ner}(\operatorname{\mathbf{SfResl}}_G(X)^{\operatorname{op}})$ be t…

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…

The infinity-categorical structure conjecture. The simplicial sets $\mathrm{HOM}_{\mathsf{\Omega B As\text{-}Alg}}(A,B)_\bullet$ are $\infty$-categories.

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 $R(*)$ be the terminal object of $\mathrm{RepOrbSpc}$, and let $\mathrm{Rep}\{\mathbf B G\}$ be the full subcategory spanned by the classifying orbispaces of finite groups. Poi…