Right N-cluster-tilting Subcategories In Abelian And Exact Categories

n-abelian categories and n-exact categories were introduced by Gustavo Jasso(see[20])in 2016,which are similar to abelian and exact categories from the point of view of higher homological algebra.In this thesis,we mainly study some basic properties of n-*abelian and n-exact categories,as well as the equivalent characterization of right(left)n-cluster-tilting subcategories of abelian and exact categories.This master's degree thesis consists of three chapters:Chapter 1,we recall some basic concepts and related properties of this thesis,as well as the signed symbols,and presents the historical background.Chapter 2,firstly,we introduce the definitions of n-abelian categories,n-kernels,n-cokernels,n-pushout diagrams and n-pullback diagrams.And then prove the equivalent characterization of n-pushout diagrams and n-pull-back diagrams,as well as the relationship between n-pushout diagrams and n-pushout diagrams.After that,on the basis of Jasso[20],we discussed some questions concerning n-cluster-tilting subcategories of abelian categories.Fi-nally,the right(left)n-cluster-tilting subcategories of abelian categories are defined,and the equivalent characterization is given and proved,immediately,we have the equivalent characterization of n-cluster-tilting subcategories of abelian categories.Chapter 3,first of all,let me introduce some of the concepts in n-exact category,and then we give a supplemental proof that the admissible monomor-phism of n-exact category with n-cokernel can be an admissible n-exact sequence.Finally,based on conclusions about the n-cluster-tilting subcate-gories of exact categories refer to Jasso's document[20],we gave the definition of the right(left)n-cluster-tilting subcategories of exact categories,at the same time,the equivalent characterization is given and proved,immediately,we have the equivalent characterization of n-cluster-tilting sub categories of exact categories.