. Using results of Trnkov'a, we first show that subcoalgebras are always closed under finite intersections. Assuming that the type functor F is bounded, we obtain a concrete representation of the terminal F -coalgebra. Several equivalent characterizations of boundedness are provided. 1. Introduction Universal coalgebra as a theory of state based systems has seen a rapid development within recent years. For a long time the article [Rut96] by J. Rutten has been the definite reference. Several of the results there have needed special conditions on the type functor, most prominently, preservation of weak pullbacks. Recently, more and more results have been proved that freed the general theory from particular assumptions on the type functor. The existence of terminal coalgebras could be proven under the rather weak hypothesis that the type functor is bounded. It was only through some fruitful discussions with Jiri Ad'amek that led us to realize the connection to a class of functors w...