From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5557 Path: news.gmane.org!not-for-mail From: Bas Spitters Newsgroups: gmane.science.mathematics.categories Subject: Re: Logical consequences of descent theory Date: Fri, 5 Feb 2010 09:34:07 +0100 Message-ID: References: Reply-To: Bas Spitters NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1265416771 6485 80.91.229.12 (6 Feb 2010 00:39:31 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 6 Feb 2010 00:39:31 +0000 (UTC) To: Dusko Pavlovic Original-X-From: categories@mta.ca Sat Feb 06 01:39:28 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1NdYho-0007oa-JX for gsmc-categories@m.gmane.org; Sat, 06 Feb 2010 01:39:24 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NdY9e-0005ZD-Kx for categories-list@mta.ca; Fri, 05 Feb 2010 20:04:06 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5557 Archived-At: 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 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, > =A0author =3D =A0 =A0 =A0 "Dusko Pavlovic", > =A0title =3D =A0 =A0 =A0 =A0"Categorical interpolation: descent and the > =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0Beck-Chevalley condition without direc= t images", > =A0booktitle =3D =A0 =A0"Category Theory, Proceedings, Como 1990", > =A0editor =3D =A0 =A0 =A0 "A.~Carboni et al.", > =A0publisher =3D =A0 =A0"Springer Verlag", > =A0series =3D =A0 =A0LNM, > =A0volume =3D =A0 =A0"1488", > =A0pages =3D =A0 =A0 =A0 =A0"306--326", > =A0year =3D =A0 =A0 =A0 =A0 "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 > > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]