6 papers · 1 filter
Aspects of the Category SKB of Skew Braces
Dominique Bourn, Alberto Facchini, Mara Pompili
We examine the pointed protomodular category SKB of left skew braces. We study the notion of commutator of ideals in a left skew brace. Notice that in the literature, "product" of…
Normalizers in the non-pointed context: a weak case of extremal decomposition
Dominique Bourn
The aim of this work is to point out a strong structural phenomenon hidden behind the existence of normalizers through the investigation of this property in the non-pointed context…
On the cocartesian image of preorders and equivalence relations in regular categories
Dominique Bourn
In a regular category , the direct image along a regular epimorphism of a preorder is not a preorder in general. In , its best preorder approximation is then it…
On Congruence Modular Varieties and Gumm Categories
Dominique Bourn
In (B-Gran, 2004), was given a categorical formulation of the Shifting Lemma which is a characterization of the Congruence Modular Varieties among all the variety of Universal Alge…
On the naturalness of Mal'tsev categories
Dominique Bourn, Marino Gran, Pierre-Alain Jacqmin
Mal'tsev categories turned out to be a central concept in categorical algebra. On one hand, the simplicity and the beauty of the notion is revealed through a lot of characterizatio…
The 3x3 lemma in the -Maltsev and -protomodular settings. Applications to monoids and quandles
Dominique Bourn, Andrea Montoli
We investigate what is remaining of the 3x3 lemma and of the denormalized 3x3 lemma, respectively valid in a pointed protomodular and in a Maltsev category, in the context of parti…