Geodesic
Compatible actions in semi-abelian categories
Homology, homotopy, and applications, Tome 22 (2020) no. 2, pp. 221-250.

Voir la notice de l'article provenant de la source International Press of Boston

The concept of a pair of compatible actions was introduced in the case of groups by Brown and Loday [6] and in the case of Lie algebras by Ellis [14]. In this article we extend it to the context of semi-abelian categories (that satisfy the Smith is Huq condition). We give a new construction of the Peiffer product, which specialises to the definitions known for groups and Lie algebras. We use it to prove our main result, on the connection between pairs of compatible actions and pairs of crossed modules over a common base object. We also study the Peiffer product in its own right, in terms of its universal properties, and prove its equivalence with existing definitions in specific cases.
DOI : 10.4310/HHA.2020.v22.n2.a14
Classification : 18D35, 18E10, 20J15
Keywords: semi-abelian category, pair of compatible actions, internal action, crossed module, Peiffer product, non-abelian tensor product 
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     title = {Compatible actions in semi-abelian categories},
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Davide di Micco; Tim Van der Linden. Compatible actions in semi-abelian categories. Homology, homotopy, and applications, Tome 22 (2020) no. 2, pp. 221-250. doi : 10.4310/HHA.2020.v22.n2.a14. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2020.v22.n2.a14/

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