This talk was based on the now published article A note on the exact completion of a regular category, and its infinitary generalizations, Theory and Applications of Categories, 5(1999), 70–80. Abstract: A new description of the exact completion Ex(C) of a regular category C is given, using a certain topos Shv(C) of sheaves on C; the exact completion is then constructed as the closure of C in Shv(C) under finite limits and coequalizers of equivalence relations. An infinitary generalization is proved, and the classical description of the exact completion is derived.