From mboxrd@z Thu Jan  1 00:00:00 1970
X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2368
Path: news.gmane.org!not-for-mail
From: wlawvere@buffalo.edu
Newsgroups: gmane.science.mathematics.categories
Subject: Re:first isomorphism theorem
Date: Mon, 23 Jun 2003 14:43:36 -0400
Message-ID: <1056393816.3ef74a583a9e7@mail2.buffalo.edu>
NNTP-Posting-Host: main.gmane.org
Mime-Version: 1.0
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: 8bit
X-Trace: ger.gmane.org 1241018608 3796 80.91.229.2 (29 Apr 2009 15:23:28 GMT)
X-Complaints-To: usenet@ger.gmane.org
NNTP-Posting-Date: Wed, 29 Apr 2009 15:23:28 +0000 (UTC)
To: categories@mta.ca
Original-X-From: rrosebru@mta.ca Mon Jun 23 15:56:04 2003 -0300
Return-path: <cat-dist@mta.ca>
Envelope-to: categories-list@mta.ca
Delivery-date: Mon, 23 Jun 2003 15:56:04 -0300
Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10)
	id 19UWOH-0005LU-00
	for categories-list@mta.ca; Mon, 23 Jun 2003 15:50:09 -0300
Original-Sender: cat-dist@mta.ca
Precedence: bulk
X-Keywords: 
X-UID: 59
Original-Lines: 14
Xref: news.gmane.org gmane.science.mathematics.categories:2368
Archived-At: <http://permalink.gmane.org/gmane.science.mathematics.categories/2368>


Toby Bartels pointed out
>>the essence of the isomorphism theorem is that the forgetful functor to
>>sets not only preserves limits but also preserves images and coimages
>>even though it does not preserve coequalizers and cokernel pairs.


In fact, as recent papers of Adamek,Lawvere,& Rosicky, and also of
Pedicchio & Wood, have exploited, such forgetful functors do preserve
all coequalizers of pairs which admit a reflexivity in the category; the
preservation of images is a consequence.