From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7417 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Re: question on terminology Date: Fri, 24 Aug 2012 23:35:10 -0400 Message-ID: Reply-To: "Fred E.J. Linton" NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1345898535 24567 80.91.229.3 (25 Aug 2012 12:42:15 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 25 Aug 2012 12:42:15 +0000 (UTC) To: claudio pisani , Original-X-From: majordomo@mlist.mta.ca Sat Aug 25 14:42:14 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 1T5Fgo-00013o-BP for gsmc-categories@m.gmane.org; Sat, 25 Aug 2012 14:42:10 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:56394) by smtpy.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1T5Ffx-0008Kh-6O; Sat, 25 Aug 2012 09:41:17 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1T5Fg8-0007CN-3z for categories-list@mlist.mta.ca; Sat, 25 Aug 2012 09:41:28 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7417 Archived-At: 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-morphis= m). 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 --- > I have sometimes called them "biactions" since any such X (considered a= s, say, a left action of C) is paired with the obvious presheaf X' on C^op = (a right action of C): X'f =3D (Xf)^-1. = > Of course, they correspond, as categories over C, to discrete bifibrati= ons. > I also know that the separable or decidable presheaves are those for wh= ich every Xf is injective. > = > Claudio > = [For admin and other information see: http://www.mta.ca/~cat-dist/ ]