From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3346 Path: news.gmane.org!not-for-mail From: "Galchin Vasili" Newsgroups: gmane.science.mathematics.categories Subject: ramifications of Goldblatt's notion of a skeleton of a category Date: Thu, 29 Jun 2006 00:29:09 -0500 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019242 8343 80.91.229.2 (29 Apr 2009 15:34:02 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:34:02 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Sat Jul 1 19:27:50 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 01 Jul 2006 19:27:50 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Fwnu8-0004Wm-8s for categories-list@mta.ca; Sat, 01 Jul 2006 19:25:32 -0300 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 3 Original-Lines: 33 Xref: news.gmane.org gmane.science.mathematics.categories:3346 Archived-At: Hello, Rob Goldblatt in section 9.2 of his book "Topoi: The Categorical Analysis of Logic" introduces the notion of a "skeleton of a category C" which he defines as a "full subcategory C-sub-zero of C that is skeletal, and such that each C-object is isomorphic to one and only one C-sub-zero object". This statement seems to imply that we can have an "operator": skel: CAT -> CAT where CAT is the categories of (small) categories such that 1) skel is idempotent on any member of C of CAT, i.e. ] skel (skel (C)) = skel (C) 2) skel (C) = a "maximal" skeleton of C. I am struggling with 1) what "maximal" means in this case? E.g. is there some kind of order on all the skeletons of category C? 2) would the "operator" skel be a functor? Kind regards, Bill Halchin