Some Propositions On Extriangulated Categories

This thesis mainly studies the construction of functorially finite subcategory of exact category and extriangulated category,and the construction of partial extriangulated category.The general framework of this thesis is as follows:In chapter 1,we mainly introduce the background of functorially finite subcategory,partial extriangulated category and some main results of this thesis.In chapter 2,we mainly introduce some basic theorems and main definitions.In chapter 3,we have the following conclusions:LetC be an exact category,and let X and Y be two subcategories of C.Assume that X*Y is a covariantly finite subcategory in C.If HomC(X,Y)=0,then Y is a covariantly finite subcategory in C.In chapter 4,we replace exact category with an extriangulated category,which still denote by C.Let(C,E,s)be an extriangulated category,and let X and Y be two subcategories of C.Assume that X*Y is a strongly covariantly finite subcategory in C.If HomC(X,Y)=0,then Y is a strongly covariantly finite subcategory in C.In chapter 5,we have the following conclusion:Let C be an extriangulated category and X(?)A be two additive subcategories of C.If A is special X-monic closed,then C is a partial extriangulated category.In chapter 6,we mainly study the necessary and sufficient conditions for X to be a rigid subcategory on extriangulated category.