From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2009 Path: news.gmane.org!not-for-mail From: Steve Lack Newsgroups: gmane.science.mathematics.categories Subject: omega-completions Date: Tue, 12 Jun 2001 11:42:30 +1000 Message-ID: <15141.29574.371771.649453@milan.maths.usyd.edu.au> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241018279 1705 80.91.229.2 (29 Apr 2009 15:17:59 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:17:59 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Jun 12 01:00:07 2001 -0300 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f5C3Nh606393 for categories-list; Tue, 12 Jun 2001 00:23:43 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Mailer: VM 6.90 under 21.1 (patch 7) "Biscayne" XEmacs Lucid Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 19 Original-Lines: 14 Xref: news.gmane.org gmane.science.mathematics.categories:2009 Archived-At: I recently noticed the following fact, and wondered if this was known, and if so, whether there was a reference. Write w for the first infinite ordinal (pronounced omega, and thought of as a category). The free completion under w-colimits of a category K can be described as the category of fractions [w,K][S^-1], where [w,K] is the functor category, and S consists of all natural transformations of the form A(phi):A-->Af, where A:w-->K and f:w-->w are functors, and phi:1_w-->f a natural transformation. Steve Lack.