From: "Dr. P.T. Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>
To: barr@triples.math.mcgill.ca (Michael Barr)
Cc: categories@mta.ca
Subject: Re: Neil Ghani's question
Date: Sat, 4 Apr 1998 15:57:18 +0100 (BST) [thread overview]
Message-ID: <E0yLUNi-0003Q6-00@owl.dpmms.cam.ac.uk> (raw)
In-Reply-To: <Pine.LNX.3.95.980404090557.9640B-100000@triples.math.mcgill.ca> from "Michael Barr" at Apr 4, 98 09:07:35 am
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
next prev parent reply other threads:[~1998-04-04 14:57 UTC|newest]
Thread overview: 3+ messages / expand[flat|nested] mbox.gz Atom feed top
1998-04-04 14:07 Michael Barr
1998-04-04 14:57 ` Dr. P.T. Johnstone [this message]
1998-04-06 2:06 Max Kelly
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