Geodesic
Action groupoid in protomodular categories
Theory and applications of categories, Tome 16 (2006), pp. 46-58.

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

We give here some examples of non pointed protomodular categories $\mathbb C$ satisfying a property similar to the property of representation of actions which holds for the pointed protomodular category $Gp$ of groups: any slice category of $Gp$, any category of groupoids with a fixed set of objects, any essentially affine category. This property gives rise to an internal construction of the center of any object $X$, and consequently to a specific characterization of the abelian objects in $\mathbb C$.
Classification : 25A05, 18E05
Keywords: Protomodular categories, representation of actions, internal groupoids, abelian objects, central relations and center 
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     author = {Dominique Bourn},
     title = {Action groupoid in protomodular categories},
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     pages = {46--58},
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     volume = {16},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2006_16_a1/}
}
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Dominique Bourn. Action groupoid in protomodular categories. Theory and applications of categories, Tome 16 (2006), pp. 46-58. http://geodesic.mathdoc.fr/item/TAC_2006_16_a1/