Add to ORKGAbstract. We develop an Auslander-Reiten theory for triangulated categories which is based on Brown’s representability theorem. In a fundamental article [3], Auslander and Reiten introduced almost split sequences for the category of nitely generated modules over an artin algebra. These are short exact sequences which look almost like split exact sequences, but many authors prefer to call them Auslander-Reiten sequences. This concept is one of the most successful in modern algebra representation theory (cf. [4] for a good introduction). In fact, the existence theorem for almost split sequences has been generalized in various directions and became the starting point of what is now called Auslander-Reiten theory. Let us mention some of the mai...