From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6115 Path: news.gmane.org!not-for-mail From: David Leduc Newsgroups: gmane.science.mathematics.categories Subject: Re: Equality as an adjunction Date: Sun, 5 Sep 2010 02:26:38 +0000 Message-ID: References: Reply-To: David Leduc 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: dough.gmane.org 1283701488 32100 80.91.229.12 (5 Sep 2010 15:44:48 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 5 Sep 2010 15:44:48 +0000 (UTC) Cc: categories To: Robert Seely Original-X-From: majordomo@mlist.mta.ca Sun Sep 05 17:44:47 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.139]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OsHOd-00057T-T3 for gsmc-categories@m.gmane.org; Sun, 05 Sep 2010 17:44:44 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:41072) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OsHNO-0007pC-Ib; Sun, 05 Sep 2010 12:43:26 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OsHNA-0005RH-T4 for categories-list@mlist.mta.ca; Sun, 05 Sep 2010 12:43:13 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6115 Archived-At: Do you mean that I am *all* wrong when I spell out the adjunction? Anyway, I will definitely read Lawvere's papers on the topic and maybe your thesis although I am a bit scared by this fibrational setting. On Sat, Sep 4, 2010 at 3:09 PM, Robert Seely wrote: > I *really* suggest you look at Lawvere's papers (and I also suggest > you might find my elaboration of these ideas helpful). =A0What is going > on here is essentially adjunctions (for sum and product, or > equivalently existential and universal quantification) to > substitution. =A0This sort of setup occurs in a fibrational setting, and > the functors involved are between fibres; =A0the underlying common story > is more compelling than just one example can suggest, I think. > > =A0- all the best, Robert > > On Sat, 4 Sep 2010, David Leduc wrote: > >> Sorry, I guess my mistake is that I've got the adjunction in the wrong >> direction: it is a left Kan extension: >> >> =A0[CxC,2](Lan_Delta P, Q) =3D~ [C,2](P, Q o Delta) >> >> And equality is given by Lan_Delta T : CxC -> 2. >> Does it always exist? >> >> And what was the right Kan extension in my previous mail when it exists? >> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]