Center for Mathematics, University of Coimbra

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The Nine Lemma and the push forward construction for special Schreier extensions of monoids with operations

Publication . Martins-Ferreira, Nelson; Montoli, Andrea; Sobral, Manuela

We show that the Nine Lemma holds for special Schreier extensions of monoids with operations. This fact is used to obtain a push forward construction for special Schreier extensions with abelian kernel. This construction permits to give a functorial description of the Baer sum of such extensions.

2018-08-10Journal article

Open access

On the categorical behaviour of preordered groups

Publication . Clementino, Maria Manuel; Martins-Ferreira, Nelson; Montoli, Andrea

We study the categorical properties of preordered groups. We first give a description of limits and colimits in this category, and study some classical exactness properties. Then we point out a strong analogy between the algebraic behaviour of preordered groups and monoids, and we apply two different recent approaches to relative categorical algebra to obtain some homological properties of preordered groups.

2019Journal article

Open access

On some categorical-algebraic conditions in S-protomodular categories

Publication . Martins-Ferreira, Nelson; Montoli, Andrea; 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 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.

2017-09-01Journal article

Open access