A categorified Dold-Kan correspondence

Abstract

In this work, we establish a categorification of the classical Dold-Kan correspondence in the form of an equivalence between suitably defined $\infty$-categories of simplicial stable $\infty$-categories and connective chain complexes of stable $\infty$-categories. The result may be regarded as a contribution to the foundations of an emerging subject that could be termed categorified homological algebra.