Left triangulated categories arising from contravariantly finite subcategories

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