From: Francois Magnan <fmagnan@cogniscienceinc.com>
To: categories@mta.ca
Subject: Re: Category of directed multigraphs with loops
Date: Fri, 21 Feb 2003 09:35:39 -0500 [thread overview]
Message-ID: <BF3233D9-45A9-11D7-9519-000393667F44@cogniscienceinc.com> (raw)
In-Reply-To: <20030217210914.94383.qmail@web12205.mail.yahoo.com>
Hi,
The product in the category of directed irreflexive multigraphs is
simple to compute. In fact, if you learn further about topos theory you
will learn that all finite limits in a presheaf topos are computed
pointwise. The category that interests you is a presheaf category since
it is the category of all functors from the category
------------>
C^op = A V
------------>
to the category of sets.
In simpler words, it means that if you take two graphs: G_1 and G_2
with vertices sets V_1 and V_2 and arrows sets A_1 and A_2
respectively. The product graph P=G_1 x G_2 will have V_P=V_1xV_2
(normal catesian product in sets) as vertices and A_P=A_1xA_2 as
arrows. The incidence relation are the expected ones.
For the reflexive directed multigraphs as all presheafs the recipe is
the same. I would suggest you to read the book:
M.La Palme Reyes, G. Reyes, Generic Figures and their glueings: A
constructive approach to functor categories.
Which is still unpublished as of now but I can send you a PDF.
Hope this helps,
Francois Magnan
On Monday, Feb 17, 2003, at 16:09 America/Montreal, Galchin Vasili
wrote:
>
> Hello,
>
> Given two graphs, A and B, I am trying figure out how to
> construct
> the product AxB. I have been rereading "Conceptual Mathemtatics" by
> Lawvere. The category of irreflexive graphs is one of the running
> examples
> throughout the book. I have been concentrating on the chapters
> concerned
> with the product of objects, but I don't see any details of how to
> construct AxB. Have I skipped over something?
>
> Regards, Bill Halchin
>
>
>
>
- --------------------------------------------
Francois Magnan
Recherche & Développement
Cogniscience Editeurs Inc.
fmagnan@cogniscienceinc.com
prev parent reply other threads:[~2003-02-21 14:35 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2003-02-17 21:09 Galchin Vasili
2003-02-21 14:35 ` Francois Magnan [this message]
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