From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5376 Path: news.gmane.org!not-for-mail From: Ross Street Newsgroups: gmane.science.mathematics.categories Subject: Re: A well kept secret? Date: Thu, 17 Dec 2009 16:08:30 +1100 Message-ID: References: Reply-To: Ross Street NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v936) Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1261101740 31598 80.91.229.12 (18 Dec 2009 02:02:20 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 18 Dec 2009 02:02:20 +0000 (UTC) To: Andrew Stacey , Original-X-From: categories@mta.ca Fri Dec 18 03:02:12 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1NLSAS-0007jw-Jr for gsmc-categories@m.gmane.org; Fri, 18 Dec 2009 03:02:08 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NLRkb-0000AV-F6 for categories-list@mta.ca; Thu, 17 Dec 2009 21:35:25 -0400 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5376 Archived-At: On 15/12/2009, at 5:41 AM, Andrew Stacey wrote: > In my department, the colloquium is called > "Mathematical Pearls" > I'm giving this talk in January. > > But for such a talk, I need a story. Dear Andrew Back in the early 90s Todd Trimble gave a beautiful colloquium talk to our Mathematics Department at Macquarie. It was based on a question in a book by Halmos which involved finding some group (topological I think) doing something or other. It was not a categorical problem as such. Todd spoke about groups in a category with finite products. The only categorical theorem he needed was that finite product preserving functors take groups to groups. I believe he took the definition of category as known but defined functor, product and internal group. My vague memory is that he found a group solving the analogous problem in some fairly combinatorial (presheaf?) category, then found a product preserving functor to topological spaces to obtain the desired group. I hope Todd is reading this and I have jogged his memory enough to write in more detail. It takes work and ingenuity to design such pearls. Best wishes, Ross [For admin and other information see: http://www.mta.ca/~cat-dist/ ]