From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9340 Path: news.gmane.org!.POSTED!not-for-mail From: =?Windows-1252?Q?Joyal=2C_Andr=E9?= Newsgroups: gmane.science.mathematics.categories Subject: Re: Fred Date: Mon, 11 Sep 2017 16:19:13 +0000 Message-ID: References: Reply-To: =?Windows-1252?Q?Joyal=2C_Andr=E9?= NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable X-Trace: blaine.gmane.org 1505225351 12518 195.159.176.226 (12 Sep 2017 14:09:11 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Tue, 12 Sep 2017 14:09:11 +0000 (UTC) To: John Baez , categories Original-X-From: majordomo@mlist.mta.ca Tue Sep 12 16:09:01 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 1drlrf-0001rl-30 for gsmc-categories@m.gmane.org; Tue, 12 Sep 2017 16:08:35 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:38804) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1drlsv-0005iI-BD; Tue, 12 Sep 2017 11:09:53 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1drlrF-0001jU-Ru for categories-list@mlist.mta.ca; Tue, 12 Sep 2017 11:08:09 -0300 Thread-Topic: categories: Re: Fred Thread-Index: AQHTJ+jIgpSvR85jc063DXLqDa7BLaKp6amAgAIbxYCAA78w+A== In-Reply-To: Accept-Language: en-US, en-CA Content-Language: en-US Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9340 Archived-At: Dear John, and category theorists,=0A= =0A= The fact that every category has an opposite introduces =0A= a symmetry in mathematics that would not be there otherwise. =0A= The category of sets is not self dual, but a disjoint union of sets =0A= is a coproduct, dual to a product. =0A= =0A= Thurston does not show esteem for logic.=0A= Most mathematicians are taking logic for granted; they just use it =0A= as a part of their natural language. =0A= It is obvious that human understanding depends on the =0A= the laws of thought, on logic. =0A= In a sense, category theory is a branch of mathematical logic,=0A= since it greatly improves mathematical thinking in general.=0A= A category theorist might say (not too loudly) that mathematical logic=0A= is a branch of category theory.=0A= =0A= Best,=0A= andr=E9=0A= =0A= ________________________________________=0A= From: John Baez [baez@math.ucr.edu]=0A= Sent: Friday, September 08, 2017 9:15 PM=0A= To: categories=0A= Subject: categories: Re: Fred=0A= =0A= Dear Categorists -=0A= =0A= Vaughan wrote:=0A= =0A= >> There is one other anecdote about UACT, nothing to do with Fred, that I= =0A= >> have always loved. In the course of MSRI director Bill Thurston'=0A= >> opening remarks, he said words to the effect that the notion of the=0A= >> opposite of a category made him nauseous. This was the only meeting I=0A= >> have ever attended where fully half the attendees drew in enough breath= =0A= >> to drop the air pressure by an audible amount.=0A= =0A= Since "nauseous" means "causing nausea", perhaps Thurston's remark=0A= had just sickened the audience.=0A= =0A= Emily wrote:=0A= =0A= > I=92ll confess that the idea of an opposite category appearing as the=0A= > codomain of a functor also makes me somewhat nauseated (the=0A= > domain of course is no problem).=0A= =0A= Now here is someone well-attuned to these subtleties of English!=0A= =0A= I've always been delighted by opposite categories. Sometimes I think=0A= we live in one. For example: if you flip forward in a book you=0A= eventually reach the back, but if you go back far enough you reach=0A= the foreword... and in the ancient past everything was younger.=0A= =0A= I always tell my students that since category theory reduces all of=0A= mathematics=0A= to the study of arrows, and the only mistake you can make with an arrow is= =0A= to get confused about which way it's pointing, they should expect to spend= =0A= many hours confused about exactly this.=0A= =0A= Best,=0A= jb=0A= =0A= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]