From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3179 Path: news.gmane.org!not-for-mail From: David Yetter Newsgroups: gmane.science.mathematics.categories Subject: Re: cracks and pots Date: Wed, 29 Mar 2006 09:02:27 -0500 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 (Apple Message framework v623) Content-Type: text/plain;charset=WINDOWS-1252;format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241019139 7585 80.91.229.2 (29 Apr 2009 15:32:19 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:32:19 +0000 (UTC) To: Categories Original-X-From: rrosebru@mta.ca Wed Mar 29 23:36:35 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 29 Mar 2006 23:36:35 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FOnwn-00005s-N9 for categories-list@mta.ca; Wed, 29 Mar 2006 23:35:45 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 125 Original-Lines: 31 Xref: news.gmane.org gmane.science.mathematics.categories:3179 Archived-At: I used the word 'faces' to describe the two aspects of category theory.=20= I see no actual separation in content, only a difference in emphasis=20= (esp. as regards applications) and public presentation. Even as Saunders, late in his life, gave lectures entitled 'All=20 Mathematics Belongs Together', so all category theory belongs together. D. Y. On 28 Mar 2006, at 03:01, dusko wrote: > i think david yetter's analysis of the dichotomy "categories as=20 > foundations" vs "categories as algebra" was spot on ---=A0 with = respect=20 > to people and the community. indeed, one could split most of our=20 > papers into one category or the other.=A0 > > but at the end of the day, i think, we'll all agree that the source of=20= > the unreasonable effectiveness of categorical algebra is its=20 > foundational content (although there is probably a lot of it that we=20= > dont understand yet); and the other way around.=A0eg,=A0if you look at=20= > grothendieck's work, he started working in algebra, and ended up=20 > developing foundational structures, because he needed them. and a lot=20= [lengthy further quotation omitted ...]