  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.
