3 papers
math.CT2026
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…
math.CT2019
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…
math.CT2019
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…