From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5164 Path: news.gmane.org!not-for-mail From: Robin Adams Newsgroups: gmane.science.mathematics.categories Subject: Re: question Date: Tue, 22 Sep 2009 12:56:46 +0100 Message-ID: Reply-To: Robin Adams NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1253667942 9386 80.91.229.12 (23 Sep 2009 01:05:42 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 23 Sep 2009 01:05:42 +0000 (UTC) To: Categories list Original-X-From: categories@mta.ca Wed Sep 23 03:05:35 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1MqGIY-0000qp-TJ for gsmc-categories@m.gmane.org; Wed, 23 Sep 2009 03:05:35 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MqFlw-0007Q6-K0 for categories-list@mta.ca; Tue, 22 Sep 2009 21:31:52 -0300 Content-Disposition: inline Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5164 Archived-At: On Sunday 20 September 2009 14:21:13 jim stasheff wrote: > What do you call it when you have one (small) category being a (full) > subcategory of another , and every object in the big category is > isomorphic to one in the small category ? This is the case for the > category given by objects hom(S,A) ,and morphisms given by the equivalence > relation hom(T,A) ,as a subcategory of stack(A) . In Ad=E1mek, Herrlich and Strecker's book "The Joy of Cats", the small cate= gory=20 is said to be an "isomorphism-dense" subcategory of the big category. I do= n't=20 know how widespread this terminology is, though. > Is there an equivalence of categories ? Yes. Whenever A is a full, isomorphism-dense subcategory of B, then the=20 inclusion functor from A to B is an equivalence (Remark 4.10 in that book). =2D- Robin Adams Royal Holloway, University of London [For admin and other information see: http://www.mta.ca/~cat-dist/ ]