Langlands equivalence conjecture for the quiver Hecke and quantum affine representation categories

Let $R$ be the quiver Hecke algebra and let $\mathscr{C}_{\mathscr{Q}}$ be the representation category associated with $\mathscr{Q}$. Consider the functor

$$\mathcal{F}_{\mathscr{Q}}\colon \operatorname{Rep}(R)\to\mathscr{C}_{\mathscr{Q}}.$$

Langlands equivalence conjecture. The functor $\mathcal{F}_{\mathscr{Q}}\colon \operatorname{Rep}(R)\to\mathscr{C}_{\mathscr{Q}}$ is an equivalence of categories. This is proposed as a Langlands analogue of the cited conjecture for the corresponding quantum affine representation category; the source presents the categorical equivalence as conjectural.