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.