Researches On Some Questions Of The Localization Of Quasi-Abelian Categories

Quasi-abelian category is not only the foundation of Abelian category, but also its natural generalization. The theories depending on the quasi-abelian categories, have more general theoretical significance. The Localization of categories is not only one of the basic research methods of algebraic K-theory, representation theory of algebras, category theory and other fields, but also one of the important tools for researching in algebras. This dissertation is devoted to considering the quasi-abelian categories and their localizations, discussing the functor categories and quotient categories of quasi-abelian categories.The dissertation is divided into two parts. The first one introduces the re-searching background and basic knowledge of quasi-abelian categories. The second one is shown into five chapters.In the first chapter, we consider the localization categories of quasi-abelian categories and show that the localization category of a quasi-abelian category is also a quasi-abelian category.In the second chapter, we discuss the properties of the functors between quasi-abelian categories and localization categories.In the third chapter, depending on the localizing classes of quasi-abelian cat-egories, we construct the localizing classes of functor categories. Furthermore, we consider the relationship between localization categories of functor categories and functor categories of localization categories.In the fourth chapter, we construct the quotient category of a quasi-abelian cat-egory depending on its ideal. With the localizing class of a quasi-abelian category and its ideal, we construct the localizing class of its quotient category. Further-more, we consider the relationship between localization categories of quasi-abelian categories and localization categories of quotient categories.The fifth chapter sums up the main results of this dissertation.