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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