14 citations · 41 across the 12 of their papers we have counts for
14 papers
Kleisli categories, T-categories and internal categories
Dominique Bourn
We investigate the properties of the Kleisli category KlT of a monad (T,λ,μ) on a category E and in particular the existence of (some kind of) pullbacks. This culminates when the m…
On the concept of Algebraic Crystallography
Dominique Bourn
Category Theory provides us with a clear notion of what is an internal structure. This will allow us to focus our attention on a certain type of relationship between context and st…
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…
Algebraic logoi
D. Bourn, A. S. Cigoli, J. R. A. Gray +1
We introduce normal cores, as well as the more general action cores, in the context of a semi-abelian category, and further generalise those to split extension cores in the context…
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…
Central reflections and nilpotency in exact Mal'tsev categories
Clemens Berger, Dominique Bourn
We study nilpotency in the context of exact Mal'tsev categories taking central extensions as the primitive notion. This yields a nilpotency tower which is analysed from the perspec…
Partial Mal'tsevness and partial protomodularity
Dominique Bourn
We introduce the notion of Mal'tsev reflection which allows us to set up a partial notion of Mal'tsevness with respect to a class of split epimorphisms stable under pullback an…
Normalizers and split extensions
Dominique Bourn, James Richard Andrew Gray
We make explicit a larger structural phenomenon hidden behind the existence of normalizers in terms of existence of certain cartesian maps related to the kernel functor.
Aspects of algebraic exponentiation
Dominique Bourn, James R. A. Gray
We analyse some aspects of the notion of algebraic exponentiation introduced by the second author [16] and satisfied by the category of groups. We show how this notion provides a n…
The cohomological comparison arising from the associated abelian object
Dominique Bourn
We make explicit some conditions on a semi-abelian category D such that, for any abelian group A in D and any object Y in D, the cohomology group homomorphisms with coefficients in…