Geodesic
A note on the exact completion of a regular category, and its infinitary generalizations
Theory and applications of categories, Tome 5 (1999), pp. 70-80.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

A new description of the exact completion $\cal C_{ex/reg}$ of a regular category $\cal C$ is given, using a certain topos $Shv(\cal C)$ of sheaves on $\cal C$; the exact completion is then constructed as the closure of $\cal C$ in $Shv(\cal C)$ under finite limits and coequalizers of equivalence relations. An infinitary generalization is proved, and the classical description of the exact completion is derived.
Classification : 18A35, 18A40, 18E10, 18F20.
Keywords: regular category, exact category, exact completion, category of sheaves. 
@article{TAC_1999_5_a2,
     author = {Stephen Lack},
     title = {A note on the exact completion of a regular category, and its
infinitary generalizations},
     journal = {Theory and applications of categories},
     pages = {70--80},
     publisher = {mathdoc},
     volume = {5},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_1999_5_a2/}
}
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Stephen Lack. A note on the exact completion of a regular category, and its
infinitary generalizations. Theory and applications of categories, Tome 5 (1999), pp. 70-80. http://geodesic.mathdoc.fr/item/TAC_1999_5_a2/