The Catalan numbers count all sorts of interesting objects. For example, the nth Catalan number enumerates both the set of An of rooted plane trees with n edges, and the set Bn of rooted binary trees with n internal vertices. In fact for each n, the sets An and Bn are in bijection in a natural way, and one way of describing this bijection involves the use a particular stack machine. In this talk I shall outline how this stack machine works in category theoretic terms so that the bijection can be generalised to other 'Catalan Objects'.