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.
"Semi-abelian exact completions." Homology Homotopy Appl. 4 (1) 175 - 189, 2002.