论文标题
有限完成类别的矩阵分类学
The matrix taxonomy of finitely complete categories
论文作者
论文摘要
本文涉及基于“矩阵属性”的有限完整类别的分类学 - 这些是可以由整数矩阵表示的特定类型的精确性属性。特别是，本文的主要结果给出了一种算法，用于确定此类属性的结合是否意味着另一种此类属性。该算法的计算机实现使人们可以凝视“矩阵类”的POSET的复杂结构，即由矩阵属性确定的有限完整类别的所有集合的poset。在此POSET的要素中，有Mal'tSev类别的集合，多数类别，（有限完整）算术类别，以及根据文献中发现的特殊类型的Mal'tSev条件定义的各种品种的有限完整的扩展。
This paper is concerned with the taxonomy of finitely complete categories, based on 'matrix properties' - these are a particular type of exactness properties that can be represented by integer matrices. In particular, the main result of the paper gives an algorithm for deciding whether a conjunction of such properties implies another such property. Computer implementation of this algorithm allows one to peer into the complex structure of the poset of `matrix classes', i.e., the poset of all collections of finitely complete categories determined by matrix properties. Among elements of this poset are the collections of Mal'tsev categories, majority categories, (finitely complete) arithmetical categories, as well as finitely complete extensions of various classes of varieties defined by a special type of Mal'tsev conditions found in the literature.
