9 problems

Let $D^b_{\operatorname{GL}_n}(\operatorname{GL}_n)$ be the bounded equivariant derived category of the algebraic group $\operatorname{GL}_n$, equipped with its canonical braided m…

Let a braided monoidal 2-category be a 2-categorical structure equipped with a braided monoidal product. Baez–Dolan conjecture. Braided monoidal 2-categories are 4-categories with…

It was shown that a 2-shifted Poisson structure $\pi$ on a semi-free commutative differential graded algebra $A$ induces an infinitesimal 2-braiding $t^\pi$ on the homotopy 2-categ…

Let $(\mathcal{E},\otimes)$ be a $\mathcal{G}$-monoidal dg category with t-structure, for $\mathcal{G}$ as in the source. This induces an $\mathbb{E}_1$-factorisation cosheaf of ca…

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…

Let $V$ be a vertex operator algebra, and let $\mathcal{C}_1(V)$ denote the category of $C_1$-cofinite $V$-modules. Braided-structure conjecture. For any VOA $V$, the category…

Let the word problem for 3-cells of Gray categories be the problem of deciding whether two such cells are equal, and likewise let the word problem for cells of braided monoidal cat…

The all-degree extension conjecture. This homomorphism extends to all degrees.

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…