论文标题
矩阵分类学和Bourn本地化
Matrix taxonomy and Bourn localization
论文作者
论文摘要
在最近的一篇论文中，已经提出了一种算法，用于确定由矩阵表示的特定类型的类别理论属性之间的含义 - 所谓的“矩阵属性”。在本文中，我们将此算法扩展到包括涉及类别尖锐性的矩阵属性，例如类别的属性是UNITAR，例如UNITAL，非常重要或减法。此外，该扩展算法也可以用于确定给定的矩阵属性是否是另一个的Bourn定位，从而导致Mal'TSEV，多数和算术类别的新特征。使用我们的算法的计算机实现，我们可以显示由固定尺寸的矩阵给出的所有此类属性，根据其BOURN本地化分组以及它们之间的含义。
In a recent paper, an algorithm has been presented for determining implications between a particular kind of category theoretic property represented by matrices -- the so called `matrix properties'. In this paper we extend this algorithm to include matrix properties involving pointedness of a category, such as the properties of a category to be unital, strongly unital or subtractive, for example. Moreover, this extended algorithm can also be used to determine whether a given matrix property is the Bourn localization of another, thus leading to new characterizations of Mal'tsev, majority and arithmetical categories. Using a computer implementation of our algorithm, we can display all such properties given by matrices of fixed dimensions, grouped according to their Bourn localizations, as well as the implications between them.
