Perhaps some one took notes on paper and hasn't thrown them out? It would be great to ad them to Jon's small nachlass. jim On Nov 2, 2007, at 8:30 PM, Michael Barr wrote:
I certainly heard Jon lecture on this a number of times. PUblication? Lot's of luck. A quick glance at MathSciNet shows that there are an awful lot of J. Beck's, at least one J.M. Beck and at least one Jonathan Beck, but no paper by our Jon Beck on descent theory. As for precise statement, don't even think about it. But my recollection was only whether a triple could descend across a functor. There were cocyle conditions that were necessary and sufficient. I think the "Beck-Chevalley condition" was a simple example.
At one point, Jon told my wife with some regret that, thanks to my insistence, he was finally published. He seemed constitutionally incapable of putting his thoughts in public.
I think you can suppose that if PTJ couldn't find it, it isn't there except in the (increasingly feeble) memories of those who heard him.
On Fri, 2 Nov 2007, JeanBenabou wrote:
Dear colleagues,
I hope someone, and in particular Prof. Peter Johnstone, will help me with the following information. I thought I had, with Jacques Roubaud, proved in our joint note at the "Comptes Rendus" which I mentioned in my previous mail proved a theorem on Monads and Descent. I must have been mistaken, and also the many persons who quoted this note, because in El Proposition 1.5.5 is the same theorem, but attributed to J. Beck.
I immediately "rushed" to the monumental bibliography of El to find the reference, and there, big surprise, there was no J. Beck at all among the 1262 references.
Thus i'd greatly appreciate to have the date and paper of the paper where Beck proved this theorem, and the precise statement he made, in particular, did he prove his theorem in the general context of fibered or indexed categories, or only in some very special case.
Many thanks for your help