We show that strongly protomodular categories (as the category of groups for instance) provide an appropriate framework in which the commutator of two equivalence relations do coincide with the commutator of their associated normal subobjects, whereas it is not the case in any semi-abelian category.
Keywords: Commutator, unital, Mal'cev, protomodular, semi-abelian and strongly protomodular categories, fibration of points
2000 MSC: 18C99, 08B05, 18A20, 18D30
Theory and Applications of Categories,
Vol. 13, 2004,
No. 2, pp 27-40.