Semi-abelian exact completions. (English) Zbl 1386.18037
Summary: 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.
MSC:
18E10 | Abelian categories, Grothendieck categories |
18A35 | Categories admitting limits (complete categories), functors preserving limits, completions |
18B15 | Embedding theorems, universal categories |