论文标题
扭转理论和预订组的覆盖物
Torsion theories and coverings of preordered groups
论文作者
论文摘要
在本文中，我们探讨了预分组类别中的非亚伯扭转理论：无扭转子类别的对象是部分有序的组，而扭转子类别的对象是组（总顺序）。从预分组组到此无扭转子类别的反射器具有稳定的单元，我们证明它诱导了单调轻度分解系统。我们描述了相对于与该反射器自然相关的Galois结构的覆盖物，并解释了如何将这些覆盖物分类为Galois groupoid的内部作用。最后，我们证明，在预定组的类别中，还有一个预处理理论，其扭转子类别可以用一类内部组识别。后者正是Clementino，Martins-Ferreira和Montoli最近发现的预分组类别类别中的原始物体的子类别。
In this article we explore a non-abelian torsion theory in the category of preordered groups: the objects of its torsion-free subcategory are the partially ordered groups, whereas the objects of the torsion subcategory are groups (with the total order). The reflector from the category of preordered groups to this torsion-free subcategory has stable units, and we prove that it induces a monotone-light factorization system. We describe the coverings relative to the Galois structure naturally associated with this reflector, and explain how these coverings can be classified as internal actions of a Galois groupoid. Finally, we prove that in the category of preordered groups there is also a pretorsion theory, whose torsion subcategory can be identified with a category of internal groups. This latter is precisely the subcategory of protomodular objects in the category of preordered groups, as recently discovered by Clementino, Martins-Ferreira, and Montoli.
