From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9332 Path: news.gmane.org!.POSTED!not-for-mail From: Emily Riehl Newsgroups: gmane.science.mathematics.categories Subject: Re: Fred Date: Thu, 7 Sep 2017 13:03:23 -0400 Message-ID: References: Reply-To: Emily Riehl NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 (Mac OS X Mail 9.3 \(3124\)) Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable X-Trace: blaine.gmane.org 1504880527 3732 195.159.176.226 (8 Sep 2017 14:22:07 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Fri, 8 Sep 2017 14:22:07 +0000 (UTC) To: "categories@mta.ca" Original-X-From: majordomo@mlist.mta.ca Fri Sep 08 16:22:02 2017 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.40]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1dqKAC-0008Kd-KH for gsmc-categories@m.gmane.org; Fri, 08 Sep 2017 16:21:44 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:37775) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1dqKAb-0002mH-0y; Fri, 08 Sep 2017 11:22:09 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1dqK8u-0004y7-Kz for categories-list@mlist.mta.ca; Fri, 08 Sep 2017 11:20:24 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9332 Archived-At: > There is one other anecdote about UACT, nothing to do with Fred, that = I > have always loved. In the course of MSRI director Bill Thurston's > opening remarks, he said words to the effect that the notion of the > opposite of a category made him nauseous. This was the only meeting I > have ever attended where fully half the attendees drew in enough = breath > to drop the air pressure by an audible amount. I=E2=80=99ll confess that the idea of an opposite category appearing as = the codomain of a functor also makes me somewhat nauseated (the domain = of course is no problem).=20 But this said, in the interest of full disclosure, I should admit that = in a joint paper with Cheng and Gurski someone =E2=80=94 Eugenia, I = believe? =E2=80=94 convinced us that the easiest way to think of a = functor=20 C x D =E2=80=94> E=20 admitting right adjoints in both variables is as a functor=20 C x D =E2=80=94> (E^op)^op because in this way (writing E=E2=80=99 for E^op) the other two adjoints = also have the form D x E=E2=80=99 =E2=80=94> C^op and=20 E=E2=80=99 x C =E2=80=94> D^op. Such two-variable adjunctions form the vertical binary morphisms in a = =E2=80=9Ccyclic double multi category=E2=80=9D of multivariable = adjunctions and parametrized mates: https://arxiv.org/abs/1208.4520 Regards, Emily =E2=80=94 Assistant Professor, Dept. of Mathematics Johns Hopkins University www.math.jhu.edu/~eriehl [For admin and other information see: http://www.mta.ca/~cat-dist/ ]