4 Jun
1994
4 Jun
'94
6:16 a.m.
I see that Casley has answered the query of Baez on the completeness and cocompleteness of V-Cat by giving the reference to the Betti, Carboni, Strret, Walters paper "Variation through enrichment" in JPAA 29 (1983), 109-127. That is a fine reference, and everyone should read that paper; but it was of course not my reason for believing the result at the time of writing my book, published in 1982 but available earlier as a preprint. The result that V-Cat is complete and cocomplete when V is so is much older, and is due to Harvey Wolff, J.Pure Appl. Algebra 4 (1974), 123-135. The paper of Betti et al. does indeed mention this reference - but some y younger colleagues may be unaware of the details of Wolff's contribution. Max Kelly.