Some Researches On The Localization Of Categories And Loop Categories

The localization method is an important tool for research in algebra, especially in commutative algebra. Its related theory rearch occupies an important place in ring theory, algebraic geometry and algebra representation theory. The loop category also plays an important role in the research of K1 group. In this thesis, we research on the localization of category and loop category, systematically study the prevervability of localization category and properties of loop category and get many interesting results.The first chapter introduces the basic knowledge of fraction ring and localization of category.The second chapter discusses the relation between the localization of. categories and apply the results to rings.The third chapter researches on the relation between the localization of category and its center.The fourth chapter discusses the prevervability of four kinds of categories on the basic of studying the projective objects and the injective objects. Further, we give some applications on rings.The fifth chapter studies the relation between original category and loop cate-gory and prove a theory about K1 group. At last we use the Recollement of abelian categories to induce the Recollement of their loop categories.