From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6934 Path: news.gmane.org!not-for-mail From: "jpradines" Newsgroups: gmane.science.mathematics.categories Subject: Re: Reference requested Date: Fri, 30 Sep 2011 09:34:41 +0200 Message-ID: References: Reply-To: "jpradines" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain;format=flowed;charset="iso-8859-1";reply-type=response Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1317409588 29801 80.91.229.12 (30 Sep 2011 19:06:28 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 30 Sep 2011 19:06:28 +0000 (UTC) Cc: To: "Ronnie Brown" , "Peter May" Original-X-From: majordomo@mlist.mta.ca Fri Sep 30 21:06:23 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 1R9iPb-0002Z1-Qy for gsmc-categories@m.gmane.org; Fri, 30 Sep 2011 21:06:20 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:33989) by smtpx.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1R9iOK-0005uZ-HR; Fri, 30 Sep 2011 16:05:00 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1R9iOI-0002MQ-GI for categories-list@mlist.mta.ca; Fri, 30 Sep 2011 16:04:58 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6934 Archived-At: The use of a lot of terminologies stemming from topology for describing=20 purely algebraic properties seems to be widespread and fashionable among= an=20 important part of the community of categorists. This may be a convenient source of intuition and analogies by giving a=20 topological or geometrical fragrance to such algebraic concepts. However the considerable drawback is that this habit is a source of=20 unsolvable clashes for people who are currently using topological or more= =20 specially Lie groupoids, more generally structured (in Ehresmann's sense)= ,=20 i. e. internal, groupoids, who are obliged to create alternative=20 terminologies. For the special case of the duet discrete/undiscrete (or indiscrete, or=20 sometimes coarse) I'm personally using presently null/banal (there are a = lot=20 of different terminologies used by various authors). (As to the term "chaotic", I prefer to avoid comments, being afraid to=20 perturb the beautifully non chaotic weather we are presently enjoying in = our=20 region). Jean Pradines ----- Message d'origine -----=20 De : "Ronnie Brown" =C0 : "Peter May" Cc : Envoy=E9 : jeudi 29 septembre 2011 15:41 Objet : categories: Re: Reference requested > Why not use the term `indiscrete groupoid' for the functor that gives a > right adjoint to the functor Ob: Groupoids \to Sets? The left adjoin= t > 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 ther= e > 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 `Topolog= y > and groupoids'. > > Ronnie > > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]