On some categorical-algebraic conditions in S-protomodular categories

• Autor(a) principal: Martins-Ferreira, Nelson
• Data de Publicação: 2017
• Outros Autores: Montoli, Andrea, Sobral, Manuela
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10316/43919; https://doi.org/10.23638/LMCS-13(3:18)2017
• topic: Mathematics - Category Theory

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 Joónsson-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.