Strict n-categories and augmented directed complexes model homotopy types

In this paper we show that both the homotopy category of strict n-categories, 1 <= n <= infinity, 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. (C) 2018 Elsevier Inc. All rights reserved.