论文标题
常规类别简介
An introduction to regular categories
论文作者
论文摘要
本文简要介绍了常规类别的概念及其在分类代数中的使用。我们首先证明了一些基本属性，并考虑一些基本代数示例。然后，我们分析满足其他Mal'tSeV公理的类别的代数特性，然后分析较弱的Goursat公理。这些后一种情况可以看作是$ 2 $ - permutability的属性的分类对应物，在环球代数中的一致性$ 3 $ -Permutability。在过去的几年中，对Mal'Tsev和Goursat类别进行了深入研究：我们在这里提出了一些基本属性，这些属性对于读取更高级的文本很有用。
This paper provides a short introduction to the notion of regular category and its use in categorical algebra. We first prove some of its basic properties, and consider some fundamental algebraic examples. We then analyse the algebraic properties of the categories satisfying the additional Mal'tsev axiom, and then the weaker Goursat axiom. These latter contexts can be seen as the categorical counterparts of the properties of $2$-permutability and of $3$-permutability of congruences in universal algebra. Mal'tsev and Goursat categories have been intensively studied in the last years: we present here some of their basic properties, which are useful to read more advanced texts in categorical algebra.
