From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1222 Path: news.gmane.org!not-for-mail From: Paul Taylor Newsgroups: gmane.science.mathematics.categories Subject: Re: Skeleton of a category Date: Mon, 20 Sep 1999 18:44:56 +0100 (BST) Message-ID: <199909201744.SAA04812@wax.dcs.qmw.ac.uk> NNTP-Posting-Host: main.gmane.org X-Trace: ger.gmane.org 1241017649 30027 80.91.229.2 (29 Apr 2009 15:07:29 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:07:29 +0000 (UTC) To: categories@mta.ca Original-X-From: cat-dist Mon Sep 20 19:19:01 1999 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id QAA14841 for categories-list; Mon, 20 Sep 1999 16:56:08 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 13 Xref: news.gmane.org gmane.science.mathematics.categories:1222 Archived-At: > Would you let me know when the category has an equivalent skeleton? "every small category has a skeleton" iff the axiom of choice holds. See Exercise 3.26 in my book, or http://www.dcs.qmw.ac.uk/~pt/book/html/s3e.html#e3.26 for a preorder example. Exercise 4.37 defines "skeletal" http://www.dcs.qmw.ac.uk/~pt/book/html/s4e.html#e4.37 Paul