"A functor is a morphism between categories" is a meaningless definition as far as I can tell. It's true that there's a category whose objects whose categories (actually, small categories to keep things logically sound) and whose morphisms are functors, but that fact doesn't characterize functors...
I suggest this be merged with Category theory, but for now I'll just correct it.
--MarkGall 13:05, 1 October 2009 (EDT)