Closed Subbifunctors of the Extension Functor

✍ Scribed by Aslak Bakke Buan

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 163 KB
• Volume: 244
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2001.8858

✦ Synopsis

DEDICATED TO IDUN REITEN ON THE OCCASION OF HER 60TH BIRTHDAY 1 Ž . Given a subbifunctor F of Ext , , one can ask if one can generalize the construction of the derived category to obtain a relative derived category, where one localizes with respect to F-acyclic sequences. We show that this is possible if and only if F is closed. We also show that for artin algebras the closed subbifunctors correspond to Serre subcategories of a category of finitely presented functors that vanish on projectives, and we use this to find new examples of closed subbifunctors. Using relatively derived categories, we give a relative version of Happel's result on derived equivalences induced by tilting, and we show in an example how this can be used to find ordinary derived equivalences.