A categorified Dold-Kan correspondence

Various recent developments, in particular in the context of topological Fukaya
categories, seem to be glimpses of an emerging theory of categorified homotopical and homological
algebra. The increasing number of meaningful examples and constructions make it desirable to develop
such a theory systematically. In this talk, we discuss a step towards this goal: a categorification
of the classical Dold--Kan correspondence.