A categorified Dold-Kan correspondence

TL;DR

This paper develops a categorified version of the Dold-Kan correspondence, establishing an equivalence between certain $ abla$-categories of simplicial stable $ abla$-categories and connective chain complexes of stable $ abla$-categories, advancing categorified homological algebra.

Contribution

It introduces a new equivalence in higher category theory that generalizes the classical Dold-Kan correspondence to the setting of stable $ abla$-categories.

Findings

Establishes an equivalence between $ abla$-categories of simplicial stable $ abla$-categories and connective chain complexes.

Contributes to the foundations of categorified homological algebra.

Advances the understanding of higher categorical structures in homological algebra.

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.