From: "Ronnie Brown" <ronnie.profbrown@btinternet.com>
To: <categories@mta.ca>
Subject: Re: relations on graphs
Date: Fri, 9 Mar 2007 17:49:27 -0000 [thread overview]
Message-ID: <E1HPjr9-00067C-8y@mailserv.mta.ca> (raw)
Jamie Vicary states `the category of graphs is not a topos'. The situation
is not so simple, and is discussed for the combinatorially minded reader in
06.04 BROWN, R., MORRIS, I., SHRIMPTON, J. & WENSLEY, C.D.
Graphs of morphisms of graphs
http://www.informatics.bangor.ac.uk/public/mathematics/research/preprints/06/cathom06.html#06.04
There are categories of undirected graphs which are not toposes. But ...
Ronnie Brown
----- Original Message -----
From: "Jamie Vicary" <jamie.vicary@imperial.ac.uk>
To: <categories@mta.ca>
Sent: Friday, March 09, 2007 10:01 AM
Subject: categories: Re: relations on graphs
>> Is there any literature which discusses different
>> possible notions for relations on graphs?
>
> In any regular category, and certainly any topos, there is a well
> defined notion of relation, where a relation between two objects is a
> subobject of their product. These admit a * operation and compose in a
> well-behaved way; look towards the end of McLarty's category theory
> textbook for info on this.
>
> The category of directed graphs is certainly such a category, being
> regular. The category of graphs is not a topos, I believe, but might
> still be regular.
>
> Jamie Vicary.
>
next reply other threads:[~2007-03-09 17:49 UTC|newest]
Thread overview: 7+ messages / expand[flat|nested] mbox.gz Atom feed top
2007-03-09 17:49 Ronnie Brown [this message]
-- strict thread matches above, loose matches on Subject: below --
2007-03-09 22:40 Richard Garner
2007-03-09 19:10 Thomas Streicher
2007-03-09 17:02 Vaughan Pratt
2007-03-09 15:33 Jamie Vicary
2007-03-09 10:01 Jamie Vicary
2007-03-08 15:15 John Stell
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