From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4374 Path: news.gmane.org!not-for-mail From: lamarche Newsgroups: gmane.science.mathematics.categories Subject: Finite categories and filtered colimits, Date: Mon, 21 Apr 2008 21:04:21 +0200 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 (Apple Message framework v753) Content-Type: text/plain; charset=ISO-8859-1; delsp=yes; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241019905 13004 80.91.229.2 (29 Apr 2009 15:45:05 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:45:05 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Apr 23 08:53:06 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 23 Apr 2008 08:53:06 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1JodHH-0001Yg-3D for categories-list@mta.ca; Wed, 23 Apr 2008 08:36:43 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 23 Original-Lines: 28 Xref: news.gmane.org gmane.science.mathematics.categories:4374 Archived-At: Fellow category theorists, I'm looking for a ref for the following result: Let C be a finite category. Then TFAE -- C has colimits for all small filtered (well, directed is probably =20 better) diagrams. -- Idempotents split in C. This doesn't seem to be in Makkai-Par=E9 or Adamek-Rosicky, but surely =20= somebody must have observed this. Actually the result is a bit more =20 general since idempotents split in *any* category that has filtered =20 colimits. Thanks in advance, Fran=E7ois Lamarche