Mutation In Triangulated Categories

The notions of mutation pair and torsion pair in triangulated categories are introduced by Iyama-Yoshino. In this thesis, we are mainly focused on the properties of mutation pair in triangulated categories. This master degree thesis consists of three chapters.In the first chapter, we recall some basic conceptions, properties and backgrounds needed in the paper and listed the main contents of this thesis.In the second chapter, we firstly recall the notion of functionally finite subcategory, and characterize its related properties; secondly we recall the definition of torsion pair and researched its basic properties; finally we recall the notion of mutation pair, and equivalent describes the basic properties of mutation pair in triangulated categories, and studied the conditions of sub-category X, y needed to structure D-mutation pair in triangulated categories C.In the third chapter, we firstly recall the concepts and properties of n-rigid subcategories, n-cluster tilting subcategories, then give some basic conclusions needed in the paper. Basis on these properties and conclusions we studied the correspondence of mutations in triangulated categories and triangulated quotient categories.