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.
Theory and Applications of Categories, Vol. 5, 1999, No. 3, pp 70-80 http://www.tac.mta.ca/tac/volumes/1999/n3/n3.dvi http://www.tac.mta.ca/tac/volumes/1999/n3/n3.ps ftp://ftp.tac.mta.ca/pub/tac/html/volumes/1999/n3/n3.dvi ftp://ftp.tac.mta.ca/pub/tac/html/volumes/1999/n3/n3.psTAC Home