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pro vyhledávání: '"Bourn, Dominique"'
Autor:
Bourn, Dominique
We investigate the properties of the Kleisli category KlT of a monad (T,{\lambda},{\mu}) on a category E and in particular the existence of (some kind of) pullbacks. This culminates when the monad is cartesian. In this case, we show that any T-catego
Externí odkaz:
http://arxiv.org/abs/2401.11781
Autor:
Bourn, Dominique
We investigate the split epimorphisms in the categories of digroups and left skew braces. We show that, unlike the category DiGp of digroups, the category SkB of left skew braces is strongly protomodular. From that, we describe the expected Baer sums
Externí odkaz:
http://arxiv.org/abs/2310.05568
Autor:
Bourn, Dominique
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 structure.
Comment: 18 pages
Comment: 18 pages
Externí odkaz:
http://arxiv.org/abs/2210.00748
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 ideals of skew braces is often considered. We show that Huq=Smith for
Externí odkaz:
http://arxiv.org/abs/2205.04171
Autor:
Bourn, Dominique
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: given any category E, a certain property of the fibration of points:
Externí odkaz:
http://arxiv.org/abs/2110.14280
Autor:
Bourn, Dominique
In a regular category $\mathbb E$, the direct image along a regular epimorphism $f$ of a preorder is not a preorder in general. In $Set$, its best preorder approximation is then its cocartesian image above $f$. In a regular category, the existence of
Externí odkaz:
http://arxiv.org/abs/2109.11381
Autor:
Bourn, Dominique
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 Algebra, introduced in (Gumm, 1983). Starting from a characterization of t
Externí odkaz:
http://arxiv.org/abs/2103.12387
Publikováno v:
in : "Joachim Lambek: the interplay of Mathematics, Logic and Linguistics", Outstanding Contributions to Logic, Vol. 20, Eds. C. Casadio and P. Scott, Springer, 59-104, 2021
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 characterizations of different flavour. Depending on the context, one can define Mal'
Externí odkaz:
http://arxiv.org/abs/1904.06719
Autor:
Bourn, Dominique, Montoli, Andrea
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 partial pointed protomodular and partial Maltsev categories, relatively to
Externí odkaz:
http://arxiv.org/abs/1801.09104