Abelian Groups in omega-categories

Abstract

We study abelian group objects in $\omega$-categories and discuss the well-known Dold-Kan correspondence from the perspective of $\omega$-categories as a model for strict $\infty$-categories. The first part of the paper is intended to compile results from the existing literature and to fill some gaps therein. We go on to consider a parameterized Dold-Kan correspondence, i.e. a Dold-Kan correspondence for presheaves of $\omega$-categories. The main result is to describe the descent or sheaf condition in terms of a glueing condition that is familiar for 1 and 2-stacks.