论文标题
关于$ v $ -groups的分类行为
On the categorical behaviour of $V$-groups
论文作者
论文摘要
我们考虑在$ v $ - 类别上兼容的组结构，其中$ v $是一个量子，我们研究了此类群体的拓扑和代数属性。此类结构的示例是预排序组，度量和超级群，概率（Ultra）度量组。特别是，我们表明，当$ v $是一个框架时，对称$ v $ -groups满足非常强大的分类代数属性，这是组类别的典型特征。特别是，对称$ v $ - 群体形成了一个原始类别。
We consider compatible group structures on a $V$-category, where $V$ is a quantale, and we study the topological and algebraic properties of such groups. Examples of such structures are preordered groups, metric and ultrametric groups, probabilistic (ultra)metric groups. In particular, we show that, when $V$ is a frame, symmetric $V$-groups satisfy very strong categorical-algebraic properties, typical of the category of groups. In particular, symmetric $V$-groups form a protomodular category.
