From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/695 Path: news.gmane.org!not-for-mail From: "Dr. P.T. Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: Neil Ghani's question Date: Sat, 4 Apr 1998 15:57:18 +0100 (BST) Message-ID: References: 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 1241017126 26954 80.91.229.2 (29 Apr 2009 14:58:46 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:58:46 +0000 (UTC) Cc: categories@mta.ca To: barr@triples.math.mcgill.ca (Michael Barr) Original-X-From: cat-dist Sun Apr 5 17:41:29 1998 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id QAA22088 for categories-list; Sun, 5 Apr 1998 16:36:13 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f In-Reply-To: from "Michael Barr" at Apr 4, 98 09:07:35 am X-Mailer: ELM [version 2.4 PL25] Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 16 Xref: news.gmane.org gmane.science.mathematics.categories:695 Archived-At: Mike Barr's answer to Neil Ghani's question is very pretty, but unfortunately wrong. There are many examples of cartesian natural transformations (e.g. between functors Set --> Set) which are neither epic nor monic: for example, the natural transformation (-) x A --> (-) x B induced by an arbitrary map A --> B. The mistake in Mike's proof occurs when he says > Let E be the equalizer of u and v > and let h^B ---> E be any arrow. The trouble is that E could be the zero functor, so that there may not be any arrows h^B --> E. Peter Johnstone