5 problems

Let $\mathcal{C}$ be a Gray monoid. A braided and symmetric pseudomonoid additivity conjecture. Every braiding on $\mathcal{C}$ induces an equivalence … of 2-categories, and every…

Let $\mathcal{B}$ be a monoidal bicategory. For each monoid object in $\mathcal{B}$, consider lax monoidal $1$-cells and monoidal $2$-cells. Iterated lax monoid conjecture. It shou…

Symmetric lax monoidal Kleisli biadjunction conjecture. The Kleisli biadjunction becomes a symmetric lax monoidal biadjunction. Equivalently, it is sufficient to show that the left…

The oriented two-dimensional bordism bicategory $\mathbb{B}ord_{2}^{or}$ is the source for oriented two-dimensional topological field theories, and a fully dualizable object is an…

Coherence conjecture. Every diagram of 2-cells in the free braided Gray monoid generated by a multigraph commutes, without restricting the source and target 1-cells to be positive.