From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6928 Path: news.gmane.org!not-for-mail From: Ronnie Brown Newsgroups: gmane.science.mathematics.categories Subject: Re: Reference requested Date: Thu, 29 Sep 2011 14:41:03 +0100 Message-ID: References: Reply-To: Ronnie Brown 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 1317347661 21140 80.91.229.12 (30 Sep 2011 01:54:21 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 30 Sep 2011 01:54:21 +0000 (UTC) Cc: categories@mta.ca To: Peter May Original-X-From: majordomo@mlist.mta.ca Fri Sep 30 03:54:16 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 1R9SIo-0001dv-Bj for gsmc-categories@m.gmane.org; Fri, 30 Sep 2011 03:54:14 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:52398) by smtpx.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1R9SGn-0003US-Pq; Thu, 29 Sep 2011 22:52:09 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1R9SGm-0007PJ-7e for categories-list@mlist.mta.ca; Thu, 29 Sep 2011 22:52:08 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6928 Archived-At: Why not use the term `indiscrete groupoid' for the functor that gives a right adjoint to the functor Ob: Groupoids \to Sets? The left adjoint is then of course the `discrete groupoid'. This agrees with the terminology for discrete and indiscrete topologies. I confess to have used different terminology in various places. Of course one use of these notions is to show that the functor Ob preserves limits and colimits, which is a start on constructing them. It is not surprising that this concept occurs widely. In groupoids there is a notion of covering morphism and the universal cover of a group G is of course an indiscrete groupoid G'; this groupoid is by no means `trivial' since it comes equipped with a covering morphism p: G' \to G. This approach to covering space theory is given in my book `Topology and groupoids'. Ronnie Ronnie On 29/09/2011 02:35, Peter May wrote: > I have a reference question. Who first coined the term > ``chaotic category'' for a groupoid with a unique morphism > between each pair of object, and in what context? It is a > ridiculously elementary concept, but one that is extremely > useful in work on equivariant bundle theory that is needed > for equivariant infinite loop space theory and equivariant > algebraic K-theory. > > Peter May > > > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]