Hopf 2-algebra conjecture for the categorified Hall algebra

Let $Q$ be a simply laced quiver, let $\mathcal{A}={\rm Rep}(Q)$ be the category of finite-dimensional representations over a finite field $\mathbb{F}_q$, and let $\mathcal{A}_0$ be the underlying groupoid of $\mathcal{A}$. The braided monoidal bicategory $\operatorname{Span}(\operatorname{Gpd}\downarrow\mathcal{A}_0)$ contains the groupoid $\mathcal{A}_0$ viewed over itself, together with the multiplication and comultiplication spans described in the chapter. Hopf 2-algebra conjecture. These data can be extended to a Hopf $2$-algebra in the braided monoidal bicategory

$$\operatorname{Span}(\operatorname{Gpd}\downarrow\mathcal{A}_0).$$

The conjecture would extend the categorified Hall-algebra structures so that degroupoidification produces the Hopf-algebra structure of the Hall algebra. The preceding theorem establishes the corresponding braided monoidal and Hall-algebra structures, but the Hopf $2$-algebra extension remains to be constructed.