6 problems

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

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…