论文标题
确切类别的交叉点，总和和Jordan-Hölder属性
Intersections, sums, and the Jordan-Hölder property for exact categories
论文作者
论文摘要
我们研究了相交的概念和子对象的总和如何携带到确切的类别。我们从Hassoun和Roy的意义上承认可接受的交叉点，从而获得了准阿布尔类别的新特征。阿贝尔类别也有许多替代特征，因为那些还接受可接受的总和，并且就可以接受的形态的特性而言。然后，我们定义了每个确切类别承认的交叉点和总和的广义概念。使用这些新概念，我们定义和研究确切类别的类别的类别，这些类别满足了Jordan-Hölder属性的确切类别，即钻石确切类别和Artin-Wedderburn确切类别。通过明确描述$ \ Mathcal {a} = \ mbox {rep} \，λ$的所有精确结构，对于Nakayama Algebra $λ$，我们表征了所有Artin-Wedderburn在$ \ Mathcal {a} $上的所有artin-Wedderburn精确结构，并证明了这些精确的结构，这些结构与Jordan-ander the Jordan-Houlder proppertures。
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 Hassoun and Roy. 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 $\mathcal{A}= \mbox{rep}\, Λ$ 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.
