Action groupoid in protomodular categories

Dominique Bourn

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 $\mathbb C$.

Keywords: Protomodular categories; representation of actions; internal groupoids; abelian objects; central relations and center

2000 MSC: 25A05,18E05

Theory and Applications of Categories, Vol. 16, 2006, No. 2, pp 46-58.

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