Protolocalisations of exact Mal'cev categories

Francis Borceux, Marino Gran, Sandra Mantovani

A protolocalisation of a regular category is a full reflective regular subcategory, whose reflection preserves pullbacks of regular epimorphisms along arbitrary morphisms. We devote special attention to the epireflective protolocalisations of an exact Mal'cev category; we characterise them in terms of a corresponding closure operator on equivalence relations. We give some examples in algebra and in topos theory.

Keywords: protolocalisation, radical theory, homological category, semi-abelian category

2000 MSC: 18E40, 16A21,54H13

Theory and Applications of Categories, Vol. 21, 2008, No. 3, pp 37-60.

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