Some Researches On Triangulated And Exact Categories

Triangulated categories and exact categories play important roles in the rep-resentation theory of algebras and categories theory. Triangulated categories and exact categories have been studied by many experts and authors, and many perfect results have been obtained. This thesis concentrates on the relationship between Triangulated categories and Abel categories, considers the relationship between the proper class of triangles, the preclass of triangles and exact subcategories of trian-gulated categories.At the beginning of the thesis, we introduce the researches related to the thesis, sum up the groundwork and give some descriptions of the main conclusions in the thesis. This thesis is divided into two chapters.Chapter one:We first consider the trianglar form of a triangulated category which is also an abelian category. Then we inverstigate the conditions for the local-ization category, which is determined by a Serre class on an abelian category, to be an abelian triangulated category.Chapter two:We introduce the notion of the preclass of triangles and obtain an exact subcategory of triangulated categories via the preclass of triangles.