When do completion processes give rise to extensive categories?

Steve Lack – 26 May 1999

This talk was based on the paper of the same name written with Enrico Vitale. Abstract: We consider various (free) completion processes: the exact completion and the regular completion of a category with weak finite limits, the pre-regular completion of a category with finite products and weak finite limits, the exact completion of a regular category, the regular reflection of a pre-regular category, and the filtered-colimit completion of a small category. In each case we give necessary and sufficient conditions for the completion to be extensive; or, in the case of the pre-regular completion, for the completion to satisfy a weakened notion of extensivity which we call pre-extensivity.