  While chain complexes are equipped with a differential $d$ satisfying $d^2 =
0$, their generalizations called $N$-complexes have a differential $d$
satisfying $d^N = 0$. In this paper we show that the lax nerve of the category
of chain complexes is pointwise adjoint equivalent to the d\'ecalage of the
simplicial category of $N$-complexes. This reveals additional simplicial
structure on the lax nerve of the category of chain complexes which provides a
categorfication of the triangulated homotopy category of chain complexes. We
study this phenomena in general and present evidence that the axioms of
triangulated categories have simplicial origin.
