Martins-Ferreira, Nelson and Montoli, Andrea and Sobral, Manuela - On some categorical-algebraic conditions in S-protomodular categories

lmcs:3893 - Logical Methods in Computer Science, September 1, 2017, Volume 13, Issue 3
On some categorical-algebraic conditions in S-protomodular categories

Authors: Martins-Ferreira, Nelson and Montoli, Andrea and Sobral, Manuela

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.


Source : oai:arXiv.org:1611.09148
DOI : 10.23638/LMCS-13(3:18)2017
Volume: Volume 13, Issue 3
Published on: September 1, 2017
Submitted on: September 1, 2017
Keywords: Mathematics - Category Theory,18G50, 02C05, 08C05, 18D35


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