From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7423 Path: news.gmane.org!not-for-mail From: David Roberts Newsgroups: gmane.science.mathematics.categories Subject: Re: question on terminology Date: Tue, 28 Aug 2012 07:33:17 +0930 Message-ID: References: <977qHyDIk8016S03.1345865710@web03.cms.usa.net> Reply-To: David Roberts NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: ger.gmane.org 1346116771 26662 80.91.229.3 (28 Aug 2012 01:19:31 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 28 Aug 2012 01:19:31 +0000 (UTC) Cc: categories@mta.ca To: claudio pisani Original-X-From: majordomo@mlist.mta.ca Tue Aug 28 03:19:32 2012 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.128]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1T6ASp-0001rv-U4 for gsmc-categories@m.gmane.org; Tue, 28 Aug 2012 03:19:32 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:60037) by smtpy.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1T6ARw-0002xV-CO; Mon, 27 Aug 2012 22:18:36 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1T6ASD-0002mR-R2 for categories-list@mlist.mta.ca; Mon, 27 Aug 2012 22:18:53 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7423 Archived-At: The 'groupoidal quotient' is also the fundamental groupoid of the category considered as a homotopy type via the nerve. I would be tempted to call what you have a covering 'space' of the category, as the category of all these functors is equivalent to the category of covering spaces of the geometric realisation of the nerve. David On 25 August 2012 23:28, claudio pisani wrote: > > > --- Sab 25/8/12, Fred E.J. Linton ha scritto: > >> Da: Fred E.J. Linton >> Oggetto: Re: categories: question on terminology >> A: "claudio pisani" , categories@mta.ca >> Data: Sabato 25 agosto 2012, 05:35 >> Claudio Pisani asked, >> >>> Is there a standard name for those presheaves X on a >>> category C such that Xf is a bijection for any f in C? >> >> Well, those presheaves are exactly the "restrictions to C" >> of the >> presheaves on the grouppoid reflection (the grouppoidal >> 'quotient') of C >> (by which I mean the category got by declaring invertible >> every C-morphism). >> >> Does that suggest "grouppoidal action of C" might work? I >> think I'd tend >> to lobby against the use of the prefix "bi-" unless there >> were *really* >> compelling reasons in favor of it. >> >> Cheers, -- Fred >> > > Dear Fred, > thanks for the suggestion. > It seems to me that its disadvantage is that "groupoidal action of C" may suggest that C itself is a groupoid, but probably the ambiguity disappears in the right context. > By the way, I am actually interested in the (full and faithful, indexed) inclusion of presheaves on C' (where C' is the groupoid reflection of C) in presheaves on C and C^op (that is of groupoidal actions in left and in right actions). > In fact it seems to provide a useful link between left and right actions. > > Claudio > > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]