From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8318 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Re: Is the category of group actions LCCC? Date: Sat, 06 Sep 2014 03:47:34 -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 1410018459 11658 80.91.229.3 (6 Sep 2014 15:47:39 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 6 Sep 2014 15:47:39 +0000 (UTC) Cc: Timothy Revell To: "categories" Original-X-From: majordomo@mlist.mta.ca Sat Sep 06 17:47:37 2014 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.127]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1XQIDB-0006G5-De for gsmc-categories@m.gmane.org; Sat, 06 Sep 2014 17:47:37 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:43957) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1XQICn-0003LC-Pv; Sat, 06 Sep 2014 12:47:13 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1XQICm-0000yy-CL for categories-list@mlist.mta.ca; Sat, 06 Sep 2014 12:47:12 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8318 Archived-At: On Tue, 02 Sep 2014 08:28:21 PM EDT, Timothy Revell asked: = > I'm wondering whether the category of ALL group actions is locally > Cartesian closed. ... = Borrowing ideas from several earlier followups to this question, I might = suggest the following as a quick and easy argument for a negative answer:= 1) an initial object in that "category of ALL group actions" is given by the trivial group's action on the empty set, ({e}, 0); 2) the slice of that category over ({e}, 0) "is" just the category Grp of groups and group homomorphisms (well, really, it's the full subcategor= y of ALL group actions on the empty set :-) but that's essentially just Grp= ); 3) the category of group actions is no more a LCCC than Grp is a CCC. Or have I overlooked some obvious fly in my proposed ointment :-) ? Cheers, -- Fred Linton [For admin and other information see: http://www.mta.ca/~cat-dist/ ]