Star-regularity and regular completions |
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Authors: | Marino Gran Zurab Janelidze |
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Institution: | 1. Institut de Recherche en Mathématique et Physique, Université catholique de Louvain, Chemin du Cyclotron 2, 1348 Louvain-la-Neuve, Belgium;2. Department of Mathematical Sciences, Stellenbosch University, Private Bag X1, Matieland, 7602, South Africa |
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Abstract: | In this paper we establish a new characterisation of star-regular categories, using a property of internal reflexive graphs, which is suggested by a recent result due to O. Ngaha Ngaha and the first author. We show that this property is, in a suitable sense, invariant under regular completion of a category in the sense of A. Carboni and E.M. Vitale. Restricting to pointed categories, where star-regularity becomes normality in the sense of the second author, this reveals an unusual behaviour of the exactness property of normality (i.e. the property that regular epimorphisms are normal epimorphisms) compared to other closely related exactness properties studied in categorical algebra. |
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Keywords: | 18A35 18C05 18D20 08B20 08B30 08B05 |
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