Explicit HRS-tilting

Abstract

For an abelian category A equipped with a torsion pair, we give an explicit description for the tilted abelian category B introduced in [HaReSm], and also for the categories Ch(B) and \mathcal{D}(B). We also describe the DG structure on Ch(B). As a consequence, we find new proofs of certain results of [ibid.]. The main ingredient is the category of decorated complexes.