  For an abelian category $A$ equipped with a torsion pair, we give an explicit
description for the abelian category $B$ introduced by Happel-Reiten-Smalo, and
also for the category of chain complexes $Ch(B)$ and the derived category
$D(B)$ of $B$. We also describe the DG structure on $Ch(B)$. As a consequence,
we find new proofs of certain results of Happel-Reiten-Smalo. The main
ingredient is the category of {\em decorated} complexes.
