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MODULES OVER TRIANGULATED CATEGORIES AND LOCALIZATION

George Ciprian Modoi

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Abstract

Abstract. For a compactly generated triangulated category we gives a new proof for the fact that the category of modules over its subcategory consisting of all compact objects it is not only the colocalization, but also the localization of the category of finitely presented modules over the full triangulated category. We do not only prove the existence of a right adjoint for the restriction functor, but we give it explicitly. A problem arising in the study of (compactly generated) triangulated cate-gories is to find some abelian categories closely related to a given triangulated one. A

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Abstract. For a compactly generated triangulated category we gives a new proof for the fact that the category of modules over its subcategory consisting of all compact objects it is not only the colocalization, but also the localization of the category of finitely presented modules over the full triangulated category. We do not only prove the existence of a right adjoint for the restriction functor, but we give it explicitly. A problem arising in the study of (compactly generated) triangulated cate-gories is to find some abelian categories closely related to a given triangulated one. A

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Available abstract

Abstract. For a compactly generated triangulated category we gives a new proof for the fact that the category of modules over its subcategory consisting of all compact objects it is not only the colocalization, but also the localization of the category of finitely presented modules over the full triangulated category. We do not only prove the existence of a right adjoint for the restriction functor, but we give it explicitly. A problem arising in the study of (compactly generated) triangulated cate-gories is to find some abelian categories closely related to a given triangulated one. A

Key concepts: Triangulated category, Mathematics, Subcategory, Functor, Abelian category, Derived category, Concrete category, Functor category

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