From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6932 Path: news.gmane.org!not-for-mail From: Peter May Newsgroups: gmane.science.mathematics.categories Subject: Re: Reference requested Date: Fri, 30 Sep 2011 08:56:07 -0500 Message-ID: References: <11E807BD-8A2D-423D-8D1B-117BC99B7CF8@mq.edu.au> Reply-To: Peter May NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1317409168 26164 80.91.229.12 (30 Sep 2011 18:59:28 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 30 Sep 2011 18:59:28 +0000 (UTC) Cc: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Fri Sep 30 20:59:23 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.30]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1R9iIr-00081F-A5 for gsmc-categories@m.gmane.org; Fri, 30 Sep 2011 20:59:21 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:37519) by smtpx.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1R9iGx-0005Ia-Jw; Fri, 30 Sep 2011 15:57:23 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1R9iGv-0002Cw-Sm for categories-list@mlist.mta.ca; Fri, 30 Sep 2011 15:57:21 -0300 In-Reply-To: <11E807BD-8A2D-423D-8D1B-117BC99B7CF8@mq.edu.au> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6932 Archived-At: Thanks everybody for comments, although I guess the use goes so far back into antiquity that the request for an original reference is unanswerable. For context, with two young collaborators (Bertrand Guillou and Mona Merling), I have a draft in progress tentatively entitled ``Chaotic categories and equivariant classifying spaces''. I prefer `chaotic' to `indiscrete' not just because of the `coarse' implications of the latter, but because indiscrete spaces are boring, `null or banal', whereas chaotic categories have genuinely significant applications. They are quite surprisingly central to the theory of universal bundles, equivariant or not. Via the (product-preserving) classifying space construction from categories (especially categories internal to spaces) to spaces, they provide a rich source of contractible spaces that can very easily be given interesting additional structure. That is just what one wants when constructing universal bundles. More fun, it is just what one wants to construct an E infinity operad of G-categories that defines `genuine' symmetric monoidal G-categories (which are not merely symmetric monoidal categories on which a group G acts in the obvious `naive' way). These which give rise to `genuine' G-spectra. Genuine G-spectra that define equivariant algebraic K-theory arise in precisely this way. All starting from chaotic trivialities. Cheers, Peter [For admin and other information see: http://www.mta.ca/~cat-dist/ ]