5 papers
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…