标题： 关系微积分的丰富方面和$2$-可交换性 显示英文标题

标题： Enriched aspects of calculus of relations and $2$-permutability

摘要： 本工作的目的是进一步发展正则Ord-范畴C的(内部)关系微积分。为了捕捉正则Ord-范畴的丰富特性并获得良好的微积分，我们所处理的关系正是C中的理想。然后，我们关注1维代数2可交换(也称为Mal'tsev)性质的丰富版本及其通过普通关系上的性质表达的著名等价特征。我们引入Ord-Mal'tsev范畴的概念，并表明这些可以通过上述提到的适应于理想的丰富版本的性质来表征。任何1维Mal'tsev范畴的Ord-丰富必定是一个Ord-Mal'tsev范畴。我们还给出了一些不是Mal'tsev范畴但却是Ord-Mal'tsev范畴的范畴的例子。 显示英文摘要

摘要： The aim of this work is to further develop the calculus of (internal) relations for a regular Ord-category C. To capture the enriched features of a regular Ord-category and obtain a good calculus, the relations we work with are precisely the ideals in C. We then focus on an enriched version of the 1-dimensional algebraic 2-permutable (also called Mal'tsev) property and its well-known equivalent characterisations expressed through properties on ordinary relations. We introduce the notion of Ord-Mal'tsev category and show that these may be characterised through enriched versions of the above mentioned properties adapted to ideals. Any Ord-enrichment of a 1-dimensional Mal'tsev category is necessarily an Ord-Mal'tsev category. We also give some examples of categories which are not Mal'tsev categories, but are Ord-Mal'tsev categories.