17 problems

Let $(W,S)$ be a Coxeter system of finite rank, and let $\mathcal{J}$ be a two-sided cell of $W$. A two-sided cell is called connection-finite when the relevant connection sets are…

Let $W$ be a Coxeter group of finite rank, let $\mathcal{H}$ be a diagonal $H$-cell, and let $d$ be a Duflo involution in $\mathcal{H}$. Assume the Klein–Elias–Hogancamp conjecture…

Let $W$ be a Coxeter group of finite rank, let $\mathcal{H}$ be a two-sided cell with a diagonal $H$-cell, and let $d$ be a Duflo involution in that cell. Let…

Let $\TwoTDX$ be the bicategory of two-dimensional transducers, whose hom-categories are cocomplete and whose pre- and post-composition functors preserve colimits. It is fibred ove…

Relative equipment conjecture. Since functors are seldom both morphisms and comorphisms of sites, the third equipment axiom should be relaxed in order to study the structure of…

Preservation conjecture. The functor $\textrm{Lan}_{p}p\circ-$ sends left adjoint bicomodules to left adjoint bicomodules and preserves the ternary factorization system…

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 $\bbB$ be a bicategory. Recall that automata in the Kleisli category of the powerset monad model nondeterministic automata in $\operatorname{Set}$, and that the presheaf constr…

Let $T$ be a monad on $\operatorname{Set}$ and let $\mathcal{V}$ be a quantale. Write $T\mathcal{V}\operatorname{Prof}$ for the locally thin bicategory associated with…

Let $\bbB$ be a bicategory, and let $\cate{Mly}_\bbB$ denote the category of bicategorical Mealy machines defined in the paper. Let $\Omega\bbB$ denote the category of pseudofuncto…

Let $\sc\text{B}\hspace{1.0pt}_{n}^{\operatorname{str}}$ be the finitary bicategory under consideration, and let simple transitive $2$-representations of it be considered up to equ…

A black-boxing construction assigns to each open Markov process a linear relation between its boundary vector spaces, and the resulting symmetric monoidal double functor is … Here…

Existence conjecture. More generally, $\operatorname{SymPsMon}(\mathcal{C},\boxtimes)$ has bicategorical coinserters and coequifiers.

Soundness conjecture. Soundness is maintained if the cotensor is restricted to forming unions, via the morphisms $\blacktriangle_X$ and $\blacktriangledown_X$, and local minima, vi…

A braided monoidal bicategory is a bicategory equipped with monoidal structure and coherent braiding data; a b-bicategory is the bicategorical structure introduced in this paper, e…

Weak equivalence conjecture. The inclusion of simplicial sets $N(ubi\mathcal{C}tg)\longrightarrow i^*(w\mathcal{C}at^2)$ is a weak equivalence in the Joyal model structure on…

Let $t\in\Theta_2$ be an object, and let $h(t)\in\Theta_1$ denote its length. Let $\tau^-$ and $\tau^+$ be evaluations of $h(t)$, and let $E_2(t,\tau^-,\tau^+)$ be the correspondin…