In the context of Mal'cev categories, a left exact root for the congruence distributive property is given and investigated, namely the property that there is no non trivial internal group inside the fibres of the fibration of pointed objects. Indeed, when moreover the basic category $\mathbb{C}$ is Barr exact, the two previous properties are shown to be equivalent.
Keywords: congruence distributivity, Mal’cev, arithmetical and protomodular categories.
2000 MSC: 18C99, 08B10, 18D30, 08B05.
Theory and Applications of Categories, Vol. 8, 2001, No. 14, pp 391-407.
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