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.
Protolocalisations of exact Mal'cev categories / F. Borceux, M. Gran, S. Mantovani. - In: THEORY AND APPLICATIONS OF CATEGORIES. - ISSN 1201-561X. - 21:3(2008), pp. 37-60.
Protolocalisations of exact Mal'cev categories
S. MantovaniUltimo
2008
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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