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.Comment: 31 pages, introduction expanded, minor errors correcte