From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7419 Path: news.gmane.org!not-for-mail From: claudio pisani Newsgroups: gmane.science.mathematics.categories Subject: Re: question on terminology Date: Sat, 25 Aug 2012 14:58:04 +0100 (BST) Message-ID: References: <977qHyDIk8016S03.1345865710@web03.cms.usa.net> Reply-To: claudio pisani NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1345941359 30512 80.91.229.3 (26 Aug 2012 00:35:59 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 26 Aug 2012 00:35:59 +0000 (UTC) To: "Fred E.J. Linton" , categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Sun Aug 26 02:35:59 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 1T5Qpb-0006Yu-Is for gsmc-categories@m.gmane.org; Sun, 26 Aug 2012 02:35:59 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:57475) by smtpy.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1T5QoL-0005GF-9V; Sat, 25 Aug 2012 21:34:41 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1T5QoX-0004AC-OH for categories-list@mlist.mta.ca; Sat, 25 Aug 2012 21:34:53 -0300 In-Reply-To: <977qHyDIk8016S03.1345865710@web03.cms.usa.net> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7419 Archived-At: =0A=0A--- Sab 25/8/12, Fred E.J. Linton ha scritto:=0A= =0A> Da: Fred E.J. Linton =0A> Oggetto: Re: categories: = question on terminology=0A> A: "claudio pisani" , categor= ies@mta.ca=0A> Data: Sabato 25 agosto 2012, 05:35=0A> Claudio Pisani asked,= =0A> =0A> > Is there a standard name for those presheaves X on a =0A> > cat= egory C such that Xf is a bijection for any f in C?=0A> =0A> Well, those pr= esheaves are exactly the "restrictions to C"=0A> of the =0A> presheaves on = the grouppoid reflection (the grouppoidal=0A> 'quotient') of C=0A> (by whic= h I mean the category got by declaring invertible=0A> every C-morphism).=0A= > =0A> Does that suggest "grouppoidal action of C" might work? I=0A> think = I'd tend =0A> to lobby against the use of the prefix "bi-" unless there=0A>= were *really* =0A> compelling reasons in favor of it.=0A> =0A> Cheers, -- = Fred=0A> =0A=0ADear Fred,=0Athanks for the suggestion.=0AIt seems to me tha= t its disadvantage is that "groupoidal action of C" may suggest that C itse= lf is a groupoid, but probably the ambiguity disappears in the right contex= t.=0ABy the way, I am actually interested in the (full and faithful, indexe= d) 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).=0AIn fact it seems to provide a useful link between left an= d right actions.=0A=0AClaudio=0A=0A=0A=0A=0A=0A=0A [For admin and other information see: http://www.mta.ca/~cat-dist/ ]