Strict n-categories and augmented directed complexes model homotopy types

Abstract

In this paper we show that both the homotopy category of strict n-categories, 1⩽n⩽∞, and the homotopy category of Steiner's augmented directed complexes are equivalent to the category of homotopy types. In order to do so, we first prove a general result, based on a strategy of Fritsch and Latch, giving sufficient conditions for a nerve functor with values in simplicial sets to induce an equivalence at the level of homotopy categories. We then apply this result to strict n-categories and augmented directed complexes, where the assumption of our theorem was first established by Ara and Maltsiniotis and of which we give an independent proof.