Centrality and normality in protomodular categories

Dominique Bourn and Marino Gran

We analyse the classical property of centrality of equivalence relations in terms of normal monomorphisms. For this purpose, the internal structure of connector is introduced, allowing to clarify classical results in Maltsev categories and to prove new ones in protomodular categories. This approach allows to work in the general context of finitely complete categories, without requiring the usual Barr exactness assumption.

Keywords: Maltsev and protomodular categories, abstract normal subobject, centrality of equivalence relations.

2000 MSC: 18D35, 08B05, 08C05.

Theory and Applications of Categories, Vol. 9, 2001, No. 8, pp 151-165.


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