Some Researches And Applications On The (Semi-)Perfect Properties Of Pushout Categories

In this thesis, by using the techniques of pushout categories and (semi-)perfect categories, we study the projective covers of pushout categories, the relationship-s between the (semi-)perfect properties of Abel categories and the (semi-)perfect properties of its pushout categories, as well as the (semi-)perfect properties of the pushout categories of complex categories.At the beginning of this thesis, we first introduce the background of this paper, which includes the history and the trend of Abel categories, pullback and pushout, (semi-)perfect categories as well as pushout categories. Moreover, the framework of this dissertation will be presented.The first chapter is devoted to the concept and some lemmas of pushout cat-egories, then we gives the existence conditions of projective cover in pushout cat-egories and proves the (semi-)perfect properties of pushout category as well as an application on rings.In the second chapter, we discuss the pushout categories of complex categories and the (semi-)perfect properties of complex categories. Furthermore, we get that the pushout categories of complex categories keep the (semi-)perfect properties.