From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8307 Path: news.gmane.org!not-for-mail From: Timothy Revell Newsgroups: gmane.science.mathematics.categories Subject: Is the category of group actions LCCC? Date: Mon, 01 Sep 2014 10:12:36 +0100 Message-ID: Reply-To: Timothy Revell NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1409703950 2209 80.91.229.3 (3 Sep 2014 00:25:50 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 3 Sep 2014 00:25:50 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Wed Sep 03 02:25:44 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 1XOyOK-0004GJ-O9 for gsmc-categories@m.gmane.org; Wed, 03 Sep 2014 02:25:40 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:39553) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1XOyNa-0007GL-8k; Tue, 02 Sep 2014 21:24:54 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1XOyNa-0002FN-DU for categories-list@mlist.mta.ca; Tue, 02 Sep 2014 21:24:54 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8307 Archived-At: Dear All, I'm wondering whether the category of ALL group actions is locally Cartesian closed. This is NOT the functor category [G,Set] for some category G with one object, since we allow G to vary. To be more specific the category is as follows. - The objects are pairs (G,X), where G is a group and X is a G-Set. - A morphism (G,X) -> (G', X') is given by a pair (h,f), where h:G->G' is a group homomorphism and f: X -> X' is a function (a morphism in Set) such that for all g in G, x in X h(g) * f(x) = f(g * x) where * on the left denotes the group action of G' on X' and * on the right denotes the group action of G on X. All the best, Tim -- Timothy Revell, Department of Computer and Information Sciences, University of Strathclyde. The University of Strathclyde is a charitable body, registered in Scotland, with registration number SC015263. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]