Subject: categories: Which is the simplest example?

From: Peter Freyd <[email-masked]>
Date: Fri, 16 Feb 2001 08:43:56 -0500 (EST)

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.

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From: Danilov Nikita <[email-masked]>
Date: Fri, 16 Feb 2001 21:18:44 +0300

> 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.