Dear Dusko, Thanks. This is interesting, did the Hyland/Moerdijk manuscript you cite ever appear? However, maybe I should have phrased my question as: Barr's theorem has an interesting logical corollary. This corollary has been used (impressively) by people like Mulvey, Vermeulen and Wraith to obtain mathematical results. I understood that it was suggested that a similar use has been made of descent theory. Maybe I misunderstood. Best, Bas On Wed, Feb 3, 2010 at 9:02 PM, Dusko Pavlovic <dusko@kestrel.edu> wrote:
On Feb 3, 2010, at 6:57 AM, Bas Spitters wrote:
A number of people have suggested that descent theory has been/ can be used to obtain logical results.
[snip]
Any suggestions or pointers about the logical interpretation of descent theory would be appreciated.
long long time ago there was a paper about the logical meaning of descent with the beck-chevalley condition:
@inproceedings{PavlovicD:interpolation, author = "Dusko Pavlovic", title = "Categorical interpolation: descent and the Beck-Chevalley condition without direct images", booktitle = "Category Theory, Proceedings, Como 1990", editor = "A.~Carboni et al.", publisher = "Springer Verlag", series = LNM, volume = "1488", pages = "306--326", year = "1991" }
more interestingly, one can also go back, and work out the exact logical conditions for descent, which are weaker than the beck-chevalley.
-- dusko
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