The Properties And Application Of The Intersection And Union Of Subobjects In Abel Category

In this paper, we discuss the properties for the intersection and union of two subobjects and three subobjects and get some exact sequences about the intersections and unions and coproducts of subobjects. Abel group category is an Abel category. In this category, the intersection of some subobjects is the intersection of these subgroups and the union of some subobjects is the subgroup generated by the union of these subgroups. The exact sequences we get in Abel category induce some isomorphism relations of Abel groups.