Left triangulated categories arising from contravariantly finite subcategories

摘要

Let modA be the category of finitely generated right A-modules over an artin algebra ⋀, and F be an additive subfunctor of. LetP(F)denote the full sucategory of A with objects theF-projective modules. If the functorFhas enoughF- projectives, then we show that the stable categorymodp(F)⋀has a left triangulated structure. In case, the above statement implies that the stable categorymodp⋀ has a left triangulated structure. Dual statements for the case of F-injective modules are also true