1994•Communications in AlgebraRequires access

Left triangulated categories arising from contravariantly finite subcategories

Apostolos Beligiannis, Nikolaos Marmaridis

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

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Key concepts: Mathematics, Functor, Triangulated category, Injective function, Derived category, Statement (logic), Pure mathematics, Dual (grammatical number)