一句话：为 S-原模范畴引入相对化附加条件，建立其类群行为的层级。
原模范畴中已有局部代数笛卡尔闭性、代数一致性等附加条件，用来刻画更接近群的结构行为。本文关注 S-原模范畴：其典型例子包括幺半群范畴、带运算的幺半群范畴以及 Jónsson-Tarski 簇。作者为这些条件引入相对版本，在 S-原模语境中重新表述并比较，说明它们与通常“绝对”原模语境下的对应关系，进而给出不同 S-原模范畴之间的层级。结果是在范畴论层面建立了 S-原模范畴的类群行为分类框架。
In the context of protomodular categories, several additional conditions have been considered in order to obtain a closer group-like behavior. Among them are locally algebraic cartesian closedness and algebraic coherence. The recent notion of S-protomodular category, whose main examples are the category of monoids and, more generally, categories of monoids with operations and Jo\'{o}nsson-Tarski varieties, raises a similar question: how to get a description of S-protomodular categories with a strong monoid-like behavior. In this paper we consider relative versions of the conditions mentioned above, in order to exhibit the parallelism with the "absolute" protomodular context and to obtain a hierarchy among S-protomodular categories.
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@article{Martins-Ferreira17,
title = {On some categorical-algebraic conditions in S-protomodular categories},
author = {Nelson Martins-Ferreira and Andrea Montoli and Manuela Sobral},
journal = {Logical Methods in Computer Science},
volume = {Volume 13, Issue 3},
year = {2017},
doi = {10.23638/lmcs-13(3:18)2017}
}