This is a comment to the recently discussed Pavlovic-Pratt paper: M. Barr has proved in "Terminal Coalgebras ..."( TCS 114) that for bicontinuous set functors initial algebras carry a natural metric, and a Cauchy completion of that space is a final coalgebra. This result can be generalized to endofunctors F of any locally finitely presentable category. Side conditions: F preserve monomorphisms and have a point in F(O). Of the two functors used by Dusko and Vaughan, only F_2 satisfies the latter, of course. Its initial algebra is the set of all rationals in [O,1), which illustrates the idea quite well. The statement of the generalization I have in mind is that the structure of a final coalgebra T (which in a locally finitely presentable category is determined by morphisms from all finitely presentable objects B into T) is determined by the structure of an initial algebra I in the following sense: each hom(B,I) carries a natural metric and a Cauchy completion is hom(B,T). Thus, for endofunctors of Pos not only the elements of T but also its order is obtained by completing I . Jiri Adamek