When do completion processes give rise to extensive categories?
Stephen Lack and E.M.Vitale
This appeared in Journal of Pure and
Applied Algebra 159:203-230, 2001.
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.
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Steve Lack
Last modified: Fri Aug 30 09:12:30 EST 2002