Simplicial Structure on Complexes
  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. 
Djalal Mirmohades
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