Stable Categories In N-exact Categories

n-abelian and n-exact categories were introduced by Jasso[19] in 2014,they are analogs of abelian and exact categories from the point of view of higher homological algebra.In this thesis,we are mainly focused on the stable catego-ry of a Frobenius n-exact category and the stable category of contravariantly finite subcategory of n-exact category. This master’s degree thesis consists of three chapters.In first chapter, we recall some basic definitions,backgrounds needed in the sequel and list the main results of this thesis.In second chapter, firstly, we present notions and properties of n-abelian categories and give a supplementary proof of the existence of n-pullback dia-gram.Then,we give notions and properties of n-exact categories,and promote a pullback diagram of an admissible monomorphism along an admissible epimor-phism receive an admissible monomorphism in exact categories generalization to n:in n-exactcategories,an n-pullback diagram of an admissible n-exact sequence along an admissible epimorphism produce an admissible n-exact sequence.In third chapter, we give an induced (n+2)-angle based on a stan-dard (n+2)-angle in Jasso[19] and prove the equivalence of these two defi-nitions,and base on an induced (n+2)-angle,we show that the stable cate-gory of a Frobenius n-exact category has a natural (n+2)-angulated struc-ture in a different and easier way. Then we introduce the category of coherent C-modules,denoted by mod C,and we conclude that for the stable category C of contravariantly finite subcategory of n-exact category,the category mod C is abelian.