  In this paper we show that both the homotopy category of strict
$n$-categories, $1\leqslant n \leqslant \infty$, 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 an abstract 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, for which the hypothesis of our theorem were
established by Ara and Maltsiniotis.
