论文标题
在富含Ord含有的类别
On lax protomodularity of Ord-enriched categories
论文作者
论文摘要
我们的主要重点涉及原化类别的原始性代数特性的LAX版本。我们激励人心的例子是预订的阿贝尔群体的类别；实际上，尽管阿贝尔群体构成了原始的类别，但Ordab却没有。 考虑到逗号对象在丰富的上下文中的作用，我们考虑了与逗号对象相对于逗号对象而不是回调的一些特征性属性。我们表明，在富含ORD的任何有限完整的类别中，逗号对象方便地替换逗号对象时，造型性和某些属性之间的等效性也可以保持，并建议将LAX lax Tromomodular称为此类ORD-ORD-END-EN-ENRICHEN-END-EN-END-END-END-END-END-END-END-END-ENPERICHED类别。最后，我们通过研究配备合适的ORD浓度的ORDAB的这种LAX型原始性，并表明ORDAB相对于前瘤物体的较弱概念实现了等效的Lax brotomodular属性；我们称此类类别lax preprotomodular。
Our main focus concerns a possible lax version of the algebraic property of protomodularity for Ord-enriched categories. Our motivating example is the category OrdAb of preordered abelian groups; indeed, while abelian groups form a protomodular category, OrdAb does not. Having in mind the role of comma objects in the enriched context, we consider some of the characteristic properties of protomodularity with respect to comma objects instead of pullbacks. We show that the equivalence between protomodularity and certain properties on pullbacks also holds when replacing conveniently pullbacks by comma objects in any finitely complete category enriched in Ord, and propose to call lax protomodular such Ord-enriched categories. We conclude by studying this sort of lax protomodularity for OrdAb, equipped with a suitable Ord-enrichment, and show that OrdAb fulfills the equivalent lax protomodular properties with respect to the weaker notion of precomma object; we call such categories lax preprotomodular.
