Left triangulated categories arising from contravariantly finite subcategories

Abstract

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