论文标题
整体类别的示例和非例子和可允许的交集属性
Examples and non-examples of integral categories and the admissible intersection property
论文作者
论文摘要
整体类别构成了亚伯前类别的子类，其系统的研究是由Rump于2001年启动的。在本文的第一部分中，我们确定几类拓扑和Bornological载体空间是否是不可或缺的。此外，我们确定整体类别类别不包含在准阿贝尔类别的类别中，并且存在既不是整数也不是准阿布尔语的半阿伯式类别。在文章的最后一部分中，我们表明，当且仅当它具有可允许的交叉点时，就br {ü} Stle，Hassoun和Tattar所考虑的意义上时，类别是准上的。这表明，具有该特性的丰富类别类别是在功能分析中自然出现的。
Integral categories form a sub-class of pre-abelian categories whose systematic study was initiated by Rump in 2001. In the first part of this article we determine whether several categories of topological and bornological vector spaces are integral. Moreover, we establish that the class of integral categories is not contained in the class of quasi-abelian categories, and that there exist semi-abelian categories that are neither integral nor quasi-abelian. In the last part of the article we show that a category is quasi-abelian if and only if it has admissible intersections, in the sense considered recently by Br{ü}stle, Hassoun and Tattar. This exhibits that a rich class of non-abelian categories having this property arises naturally in functional analysis.
