We investigate how the concepts of intersection and sums of subobjects carry to exact categories. We obtain a new characterisation of quasi-abelian categories in terms of admitting admissible intersections in the sense of [23]. There are also many alternative characterisations of abelian categories as those that additionally admit admissible sums and in terms of properties of admissible morphisms. We then define a generalised notion of intersection and sum which every exact category admits. Using these new notions, we define and study classes of exact categories that satisfy the Jordan-Hölder property for exact categories, namely the Diamond exact categories and Artin-Wedderburn exact categories. By explicitly describing all exact structures on $\mathcal{A}=\text{rep}\mathrm{\Lambda }$ for a Nakayama algebra Λ we characterise all Artin-Wedderburn exact structures on $\mathcal{A}$ and show that these are precisely the exact structures with the Jordan-Hölder property.

我们研究了相交和子对象总和的概念如何精确地分类。根据[23]意义上的容许交点，我们获得了准阿贝尔类别的新特征。阿贝尔类别的替代特征还有很多，它们可以附加允许的总和，以及在允许的态射的性质方面。然后，我们定义了每个精确类别都认可的交集和之和的广义概念。使用这些新概念，我们定义并研究满足Jordan-Hölder属性的精确类别的精确类别，即Diamond精确类别和Artin-Wedderburn精确类别。通过明确描述上的所有确切结构$\mathcal{一个}=\text{代表}\mathrm{\Lambda }$ 对于中山代数Λ，我们刻画了所有Artin-Wedderburn精确结构 $\mathcal{一个}$ 并显示出这些正是乔丹·霍尔德（Jordan-Hölder）属性的确切结构。