On Products of Transition Systems

For an arbitrary set endofunctor F we give a sufficient and necessary criterium for the existence of products of F-coalgebras. In the case of transition systems, where F=P is the covariant powerset functor, we introduce impeding paths whose existence impedes the existence of the product. Moreover we show, that the product A⊗A of a finite transition system A exists if and only if the product A⊗B for each finite transition system B exists.