A categorified Dwyer-Kan correspondence

The classical Dold-Kan correspondence is known to admit a categorification in the form of an equivalence between the $\mathrm{\infty }$-categories of $2$-simplicial stable $\mathrm{\infty }$-categories and connective chain complexes of stable $\mathrm{\infty }$-categories. In this work, we extend these concepts to give a categorification of the classical Dwyer-Kan correspondence by showing that the $\mathrm{\infty }$-category of $2$-duplicial stable $\mathrm{\infty }$-categories is equivalent to the $\mathrm{\infty }$-category of conective chain complexes with right adjoints.