Relation between categories of representations of the super-Yangian of a special linear Lie superalgebra and quantum loop superalgebra

Using the approach developed by Toledano Laredo and Gautam, we introduce analogues of the category $\mathfrak{O}$ for representations of the Yangian $Y_\hbar(A(m,n))$ of a special linear Lie superalgebra and the quantum loop superalgebra $U_q(LA(m,n))$. We investigate the relation between them and conjecture that these categories are equivalent.