Mutation Pairs And Quotient Categories Of N-Exangulated Categories

This thesis is mainly focused on mutation pairs and the construction of(n+2)-angulated quotient categories.The thesis is organised as follows.Firstly,we introduce the notion of D-mutation pairs of subcategories in an n-exangulated category.Let(C,E,s)be an n-exangulated category and D(?)Z be subcategories of C.If Z is extension-closed and(Z,Z)is a D-mutation pair,then we can construct the auto-equivalence functor<1>:Z/D →Z/D and the class Ωof(n+2)-<1>-sequences.As the main result,we prove that(Z/D,<1>,Ω)forms an(n+2)-angulated category.This result generalizes a theorem of Zhou and Zhu for extriangulated categories and a theorem of Jasso for Frobenius n-exact categories.Secondly,we introduce the notions of strongly covariantly finite subcategori-es,strongly contravariantly finite subcategories and strongly functorially finite subcategories in n-exangulated categories.Let(C,E,s)be an n-exangulated cate-gory and X be a subcategory of C.If X is strongly covariantly finite in C,then we prove that the quotient category C/X is a right(n+2)-angulated category.The re-sult generalizes the theorem of Beligiannis and Marmaridis for right triangulated categories.Finally,covariantly finiteness,contravariantly finiteness and functorially fini-teness are called homological finiteness.We study the homological finiteness of subcategories in a mutation pair.