Geodesic
Internal crossed modules and Peiffer Condition
Theory and applications of categories, The Bourn Festschrift, Tome 23 (2010), pp. 113-135.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

In this paper we show that in a homological category in the sense of F. Borceux and D. Bourn, the notion of an internal precrossed module corresponding to a star-multiplicative graph, in the sense of G. Janelidze, can be obtained by directly internalizing the usual axioms of a crossed module, via equivariance. We then exhibit some sufficient conditions on a homological category under which this notion coincides with the notion of an internal crossed module due to G. Janelidze. We show that this is the case for any category of distributive $\Omega_2$-groups, in particular for the categories of groups with operations in the sense of G. Orzech.
Classification : 18D35, 18G50, 20L05, 20J15
Keywords: internal crossed module, reflexive graph, internal action, semiabelian category 
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     author = {Sandra Mantovani and Giuseppe Metere},
     title = {Internal crossed modules and  {Peiffer} {Condition}},
     journal = {Theory and applications of categories},
     pages = {113--135},
     publisher = {mathdoc},
     volume = {23},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2010_23_a5/}
}
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Sandra Mantovani; Giuseppe Metere. Internal crossed modules and  Peiffer Condition. Theory and applications of categories, The Bourn Festschrift, Tome 23 (2010), pp. 113-135. http://geodesic.mathdoc.fr/item/TAC_2010_23_a5/