5 citations · 5 across the 4 of their papers we have counts for
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Ternary semi-direct products in semi-abelian categories
Arnaud Duvieusart
We study the construction of ternary semi-direct products in semi-abelian categories, following a definition of higher semi-direct product previously introduced by Carrasco and Ceg…
A direction functor approach to the cohomology of small categories
Stefano Ambra, Arnaud Duvieusart, Andrea Montoli
We show how the direction functors can be used to develop a cohomology theory for Barr-exact and S-Maltsev categories, where S is a suitable class of split epimorphisms with a fixe…
Fundamental groupoids for simplicial objects in Mal'tsev categories
Arnaud Duvieusart
We show that the category of internal groupoids in an exact Mal'tsev category is reflective, and in fact a Birkhoff subcategory of the category of simplicial objects. We then chara…
Galois theory and the categorical Peiffer commutator
Alan S. Cigoli, Arnaud Duvieusart, Marino Gran +1
We show that the Peiffer commutator previously defined by Cigoli, Mantovani and Metere can be used to characterize central extensions of precrossed modules with respect to the subc…
Higher commutator conditions for extensions in Mal'tsev categories
Arnaud Duvieusart, Marino Gran
We define a Galois structure on the category of pairs of equivalence relations in an exact Mal'tsev category, and characterize central and double central extensions in terms of hig…