Which is the simplest example?

Which is the simplest example?

[Peter Freyd]

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.

Re: Which is the simplest example?

[Danilov Nikita]

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.