A note on the exact completion of a regular category, and its infinitary generalizations

Stephen Lack

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.

Keywords: regular category, exact category, exact completion, category of sheaves.

1991 MSC: 18A35, 18A40, 18E10, 18F20.

Theory and Applications of Categories, Vol. 5, 1999, No. 3, pp 70-80.

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