From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3489 Path: news.gmane.org!not-for-mail From: Jiri Adamek Newsgroups: gmane.science.mathematics.categories Subject: reflexive coequalizers Date: Mon, 6 Nov 2006 14:39:47 +0100 (CET) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241019337 8982 80.91.229.2 (29 Apr 2009 15:35:37 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:35:37 +0000 (UTC) To: categories net Original-X-From: rrosebru@mta.ca Mon Nov 6 21:50:49 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 06 Nov 2006 21:50:49 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GhFyq-0000A7-78 for categories-list@mta.ca; Mon, 06 Nov 2006 21:42:24 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 1 Original-Lines: 16 Xref: news.gmane.org gmane.science.mathematics.categories:3489 Archived-At: The indiscrete-category functor I: Set -> Cat is not algebraically exact as I claimed in my posting of October 9. But I is a full codomain restriction of one: as in that posting, let F be the forgetful functor the Gabriel-Ulmer theory T of categories to the theory of sets. Then Alg F is an algebraically exact functor from Set to Alg T, and the Yoneda embedding Y: Cat -> Alg T is fully faithful (since the dual of T is dense in Cat). It is easy to see that Alg F is naturally isomorphic to Y.I , thus, I preserves sifted colimits. xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx alternative e-mail address (in case reply key does not work): J.Adamek@tu-bs.de xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx