Homology, Homotopy and Applications

Volume 4 (2002)

Number 1

Semi-abelian exact completions

Pages: 175 – 189

DOI: http://dx.doi.org/10.4310/HHA.2002.v4.n1.a10


Marino Gran (Laboratoire de Mathématiques Pures et Appliquées, Université du Littoral, Calais, France)


We characterize the categories which are projective covers of regular protomodular categories. Our result gives in particular a characterization of the categories with weak finite limits with the property that their exact completions are semi-abelian categories. As an application, we obtain a categorical proof of the recent characterization of semi-abelian varieties.


exact completion, protomodular and semi-abelian categories, semi-abelian varieties

2010 Mathematics Subject Classification

08C05, 18A35, 18B15, 18E10, 18G05, 18G50

Full Text (PDF format)