Auslander–Reiten Triangles and a Theorem of Zimmermann.

A classical theorem of Zimmermann describes the relation between almost split sequences in the category of finitely presented modules and those in the category of all modules over some fixed ring. An analogue of Auslander–Reiten triangles in triangulated categories is proved in this paper. This is used to explain the relation between different existence results for Auslander–Reiten triangles, which are based either on Brown's representability theorem, or on the existence of Serre functors. 2000 Mathematics Subject Classification 18E30, 16G70 (primary), 14F05, 55U35 (secondary). [ABSTRACT FROM PUBLISHER]