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