Protolocalisations of exact Mal'cev categories

Borceux, Francis;Gran, Marino;Mantovani, S.
(2008) Theory and Applications of Categories —

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  • Borceux, FrancisUCLouvain
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  • Gran, MarinoUCLouvain
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  • Mantovani, S.I-Milan
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Abstract
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.
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Borceux, F., Gran, M., & Mantovani, S. (2008). Protolocalisations of exact Mal’cev categories. Theory and Applications of Categories.