Some Researches On Triangulated Categories And Recollements

Triangulated categories play an important role in many branches of algebra.In this thesis,we study some properties of triangulated categories and recollements of triangulated subcategories,and discuss some properties of torsion theories in Abel categories and localization of Abel semisimple categories.This thesis is divied six charpters.In chapter one,we introduce the background and development trend,and the main results of this thesis.In chapter two,we recall and describe notations and basic properties including triangulated categories,recollements and localization.In chapter three,we discuss some properties of homotopy cartesian in triangulat-ed categories and show some equivalent conditions of the octahedral axiom.In chapter four,we discuss the relationship between the torsion theories of A',A" and A in a given recollement of abel categories?A',A,A"?;and describe the rec-ollement of the hearts of stable t-structures from recollement of triangulated categories?C',C,C"?.In chapter five,we determine the recollement of thick subcategories from recolle-ment of triangulated categories?C',C,C"?,and discuss the triangulated subcategories of extension from the recollement of triangulated categories?C',C,C"?.In chapter six,we show that ???^-1 KB???(S^-1 K)B for Abel semisimple category K and a special saturated morphism set S.