From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5730 Path: news.gmane.org!not-for-mail From: Marta Bunge Newsgroups: gmane.science.mathematics.categories Subject: RE: Re: fundamental localic groupoid? Date: Sun, 2 May 2010 11:14:14 -0400 Message-ID: Reply-To: Marta Bunge NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1272888862 28639 80.91.229.12 (3 May 2010 12:14:22 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 3 May 2010 12:14:22 +0000 (UTC) To: Peter Johnstone , Original-X-From: categories@mta.ca Mon May 03 14:14:21 2010 connect(): No such file or directory 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 4.69) (envelope-from ) id 1O8uXS-0002FY-2w for gsmc-categories@m.gmane.org; Mon, 03 May 2010 14:14:18 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1O8tz4-0000py-Sg for categories-list@mta.ca; Mon, 03 May 2010 08:38:46 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5730 Archived-At: Dear Peter=2C Dear David=2C Dear All=2C I was going to reply=2C but was too busy with non-mathematical things at th= e moment (a big move). =A0 The following are the papers relevant to David's question=2C beginning with= the one that Peter mentions: M. C. Bunge=2C=A0Classifying toposes and fundamental localic groupoids=2Cin= : Category Theory 1991=2C CMS Conference Procedings 13=2C American Mathemat= ical Society (1992)=2C 75-96.=A0 M. C. Bunge=2C=A0Universal Covering Localic Toposes=2CComptes Rendues Socie= te Royale du Canada 24 (1992)=2C 245-250. M. C. Bunge and I.Moerdijk=2COn the construction of the Grothendieck fundam= ental group of a topos by paths=2CJ. Pure and Applied Algebra 116 (1997)=2C= 99-113.=A0 Comments will have to wait=2C I'm afraid.=A0 Cordial regards=2C Marta ************************************************ Marta Bunge Professor Emerita Dept of Mathematics and Statistics=20 McGill UniversityBurnside Hall=2C Office 1005 805 Sherbrooke St. West Montreal=2C QC=2C Canada H3A 2K6 Office: (514) 398-3810/3800 =A0 Home: (514) 935-3618 marta.bunge@mcgill.ca=20 http://www.math.mcgill.ca/~bunge/ ************************************************ > From: P.T.Johnstone@dpmms.cam.ac.uk > To: droberts@maths.adelaide.edu.au=3B categories@mta.ca > Subject: categories: Re: fundamental localic groupoid? > Date: Sun=2C 2 May 2010 10:49:59 +0100 >=20 > I'm surprised that no-one has yet replied to David's original question > by citing the work of Marta Bunge=3B she has a paper called (I think) > "Classifying toposes and fundamental localic groupoids" dating from the > early 1990s. (Being away from home at present=2C I don't have the exact > reference to hand=3B I was hoping Marta would provide it.) >=20 > Peter Johnstone >=20 > On Apr 28 2010=2C David Roberts wrote: >=20 >>Hi all=2C >> >> it is (or should be) well known that the fundamental groupoid of a >> locally connected=2C semilocally 1-connected space X can be given a >> topology such that it is a topological groupoid (composition continuous >> etc). Without these assumptions on X there are counterexamples to the >> continuity of composition (c.f. misguided attempts to build a topologica= l >> fundamental group). I was wondering=2C though=2C if there is a localic >> fundamental groupoid of an arbitrary space. One could presumably pass th= e >> the topos Sh(X) and then consider the fundamental groupoid of that=2C bu= t I >> was wondering if there was a way to pass directly from the description o= f >> the arrows of Pi_1(X) as a set of classes of paths to a locale of classe= s >> of paths=2C and thence to a localic groupoid. My only 'evidence' that th= is >> might be the case is that the product in Loc is different to the product >> in Top=2C and so this may provide a work around the non-continuity of >> composition. >> >>Thanks=2C >> >>David Roberts >> = [For admin and other information see: http://www.mta.ca/~cat-dist/ ]