Injective Objects In N-abelian Categories And N-cluster-tilting Subcategories

n-abelian and n-exact categories are analogs of abelian and exact cat-egories from the point of view of higher homological algebra,were introduced by Jasso[15]in 2014.In this thesis,we are mainly focused on injective objects in n-abelian categories and n-cluster-tilting subcategories.This master's degree thesis consists of three chapters.In first chapter,we mainly introduce some basic definitions and remarks about addictive category concerned in the master's thesis,and backgrounds needed in the sequel.In second chapter,firstly,we present notions of'n-pullback diagram,n-pullout diagram and n-exact diagram.Then,we give the applications of n-pullback diagram,n-pullout diagram and n-exact diagram in the n-abelian categories and n-exact categories.Also we generalize two classical pullout lemma in the document[27]to n-abelian categories and n-exact categories.In third chapter,we give an introduction of injective object in n-abelian categories.Which is based on Jasso's document[15],and is a dual depict and supplementary instruction of projective object in n-abelian categories.Based on conclusions about'n-cluster-tilting subcategories refered to Jasso's docu-ment[15],further,we supplement content of n-cluster-tilti,ng subcategories and get the relationship between exact sequence and n-pullback diagram of the category of coherent C-modules and n-cluster-tilting subcategories.