29 research outputs found
Explicit HRS-Tilting
For an abelian category equipped with a torsion pair, we give an explicit
description for the abelian category introduced by Happel-Reiten-Smalo, and
also for the category of chain complexes and the derived category
of . We also describe the DG structure on . 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
Lectures on derived and triangulated categories
These notes are meant to provide a rapid introduction to triangulated
categories. We start with the definition of an additive category and end with a
glimps of tilting theory. Some exercises are included.Comment: Lecture notes. To appear in the proceedings volume of the
"International Workshop on Noncommutative Geometry", IPM, Tehran 200