Martins-Ferreira, NelsonMontoli, AndreaSobral, Manuela2025-05-282025-05-282017-09-01Martins-Ferreira, N., Montoli, A., & Sobral, M. (2017). On some categorical-algebraic conditions in S-protomodular categories. Logical Methods in Computer Science, 13. 10.23638/lmcs-13(3:18)20171860-5974http://hdl.handle.net/10400.8/13024In 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 &amp;quot;absolute&amp;quot; protomodular context and to obtain a hierarchy among S-protomodular categories.</jats:p>engS-protomodular categoriesmonoidsmonoids with operationsJ´onsson-Tarski varietiesalgebraic cartesian closednessalgebraic coherencejournal article10.23638/lmcs-13(3:18)2017