From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3172 Path: news.gmane.org!not-for-mail From: dusko Newsgroups: gmane.science.mathematics.categories Subject: Re: cracks and pots Date: Tue, 28 Mar 2006 00:01:38 -0800 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 (Apple Message framework v746.2) Content-Type: text/plain;charset=WINDOWS-1252; delsp=yes;format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241019135 7559 80.91.229.2 (29 Apr 2009 15:32:15 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:32:15 +0000 (UTC) To: Categories Original-X-From: rrosebru@mta.ca Wed Mar 29 07:35:26 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 29 Mar 2006 07:35:26 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FOYsA-00053A-WA for categories-list@mta.ca; Wed, 29 Mar 2006 07:29:59 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 118 Original-Lines: 34 Xref: news.gmane.org gmane.science.mathematics.categories:3172 Archived-At: i think david yetter's analysis of the dichotomy "categories as =20 foundations" vs "categories as algebra" was spot on --- with respect =20= to people and the community. indeed, one could split most of our =20 papers into one category or the other. but at the end of the day, i think, we'll all agree that the source =20 of 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. eg, if 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= on the "algebra" side now is built upon them. ok, then for a while it =20= was thought that he exaggerated with foundations, and that a more =20 direct approach "could have been in better taste" (to cite =20 eilenberg). but maby the fermat theorem would have a more useful =20 proof if it was developed in grothendieck style. and nowadays, there =20 is a lot of foundational content in tannaka duality etc, in TQFT in =20 general, but we only see hints of it at the moment (and i for one =20 just see the reflections of these hints in other people's eyes). i am of course saying things very clear and familiar to many people =20 on this list, but maby they are worth saying nevertheless. it might =20 be good if the links between "categories as algebras" and "categories =20= as foundations" would not boil down just to the greatest of the =20 category theorists, leaving the rest of us in two camps. -- dusko