Re: Logical consequences of descent theory

[Bas Spitters <spitters@cs.ru.nl>]

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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