Some Researches On One-sided Exact Categories

Bazzoni S. and Crivei S. have studied the homological properties of one-sided exact categories, and many perfect results have been obtained. This disserta-tion is devoted to investigating the one-sided exact categories and their localiza-tion,homological properties,and the expansion problems with trivial extensions, func-tor categories, quotient categories.The dissertation is divided into two parts. The first one introduces the re-searching background and developments of one-sided exact categories. There are four chapters in the second one.In the first chapter, depending on the method of the localization of categories,we prove that the localization categories of one-sided exact categories are also one-sided exact categories in some conditions. Then we show two kinds of morphisms category on the right exact category.In the second chapter, we first prove the complete3x31emma similar to exact categories’, and introduce the admissible morphism on right exact categories,show the Five lemma and Half Snake lemma. At last, starting from the injective objects of right exact categories, we obtain the Comparison theorem and Horseshoe lemma.In the third chapter,we mainly consider the expansion problems of right exact categories with trivial extensions, functor categories,and quotient categories, prove that the trivial extensions, functor categories,and quotient categories of right exact categories are also right exact categories.In the fourth chapter, we sum up the main results of this dissertation.