From: Danilov Nikita <NikitaDanilov@yahoo.com>
To: categories@mta.ca
Subject: Re: Which is the simplest example?
Date: Fri, 16 Feb 2001 21:18:44 +0300 [thread overview]
Message-ID: <14989.28420.518530.766264@beta.namesys.com> (raw)
In-Reply-To: <200102161343.f1GDhuo24693@saul.cis.upenn.edu>
Peter Freyd writes:
> I said that the simplest example of a category with pullbacks but not
> products is the discrete category with two objects. Come to think of
> it, any category with exactly two morphisms is an example.
Initial question was
If a category C has pullbacs no terminal object, then has C finite
product?
Now, think of empty category (one without objects and morphisms):
(*) it doesn't contain terminal object
(*) it does have pullbacks of all pairs of objects (because there are none)
(*) it doesn't contain all finite products (as it doesn't contain limit
of empty diagram---terminal object)
Now, simplify _this_ counter-example. :)
Actually, if terminal object is considered as product of zero multipliers
(as it's usually does), then initial question contains answer in itself.
Nikita.
prev parent reply other threads:[~2001-02-16 18:18 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2001-02-16 13:43 Peter Freyd
2001-02-16 18:18 ` Danilov Nikita [this message]
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