From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3960 Path: news.gmane.org!not-for-mail From: "Ronnie Brown" Newsgroups: gmane.science.mathematics.categories Subject: Re: Help! Date: Sun, 7 Oct 2007 10:23:18 +0100 Message-ID: <010f01c808c3$b2dc8320$4601a8c0@RONNIENEW> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain;format=flowed;charset="iso-8859-1";reply-type=original Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019628 11094 80.91.229.2 (29 Apr 2009 15:40:28 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:40:28 +0000 (UTC) To: "Categories list" Original-X-From: rrosebru@mta.ca Sun Oct 7 10:53:15 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 07 Oct 2007 10:53:15 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IeWVw-0000lM-Jk for categories-list@mta.ca; Sun, 07 Oct 2007 10:49:48 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 17 Original-Lines: 70 Xref: news.gmane.org gmane.science.mathematics.categories:3960 Archived-At: The great thing about categories is that they allow analogies between different mathematical structures: see the paper R. Brown and T. Porter) `Category Theory: an abstract setting for analogy and comparison', In: What is Category Theory? Advanced Studies in Mathematics and Logic, Polimetrica Publisher, Italy, (2006) 257-274. An example of the analogy is between the category of sets and the category of directed graphs: ``Higher order symmetry of graphs'', {\em Bull. Irish Math. Soc.} 32 (1994) 46-59. Here one easily sees non Boolean logics, of course. The word `analogy' seems to be underused in teaching undergraduates, but that is what abstraction is about, is it not? A teacher told me after a lecture on knots that was the first time he had heard the word analogy used in relation to mathematics! ( I discussed prime knots.) The other possibility is to advertise categorical structures: I advertised higher dimensional algebra to an international conference of neuroscientists in Delhi in 2003, pointing out the unlikelihood of the brain working entirely serially, and also the concept of colimit with an email analogy. A senior Indian neuroscientist came up to me afterwards and said that was the first time he had heard a seminar by a mathematician which made any sense! This is written up in (R. Brown and T. Porter), `Category theory and higher dimensional algebra: potential descriptive tools in neuroscience', Proceedings of the International Conference on Theoretical Neurobiology, Delhi, February 2003, edited by Nandini Singh, National Brain Research Centre, Conference Proceedings 1 (2003) 80-92. These are all downloadable from http://www.bangor.ac.uk/r.brown/publicfull.htm or my home page. See also http://www.bangor.ac.uk/r.brown/outofline/out-home.html for a general talk. As said before, I see higher dimensional algebra as the study of mathematical structures with operations defined under geometrical conditions, thus allowing a combination of algebra and geometry, in a way which even Atiyah might like (see his paper on `20th century mathematics' Bull LMS 44 (2002) 1-15, in which the words `category' and `groupoid' do not appear). I have found giving general talks makes one think hard about the underlying ideas and motivation. Ronnie ----- Original Message ----- From: "Michael Barr" To: "Categories list" Sent: Friday, October 05, 2007 1:52 PM Subject: categories: Help! > What would you say to an undergraduate math club about categories? I have > been thinking about it, but I am not sure what to say. Talk about > cohomology, which is what motivated E-M? I don't think so. Talk about > dual spaces of finite-dimensional vector spaces? Maybe, but then what? > > Michael