Abstract
This paper studies Auslander-Reiten triangles in subcategories of triangulated categories. The main theorem shows that the Auslander-Reiten triangles in a subcategory are closely connected with the approximation properties of the subcategory. Namely, let X→Y→C→ be an object in the subcategory C of the triangulated category T, and let be an Auslander-Reiten triangle in T. Then under suitable assumptions, there is an Auslander-Reiten triangle A→B→C→ in C if and only if there is a minimal right-C-approximation of the form A→X. The theory is used to give a new proof of the existence of Auslander-Reiten sequences over finite dimensional algebras.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Journal of K-Theory |
| Vol/bind | 3 |
| Nummer | 3 |
| Sider (fra-til) | 583-601 |
| Antal sider | 19 |
| ISSN | 1865-2433 |
| DOI | |
| Status | Udgivet - jun. 2009 |
| Udgivet eksternt | Ja |