this in [KLP01], where a general construction of coalgebra enriched categories is given, motivated mostly by applications in the semantics of processes. (Categories of resumptions and hyperfunctions are the simplest examples of the construction.) While the semantic relevance and programming potential of hyperfunctions are still unclear, their conceptual simplicity and mathematical attraction call for a further investigation. In what follows we summarize what we have discovered so far. The rst thing to look at is the relationship between [A; B] ) A and [B; A]. One would expect an isomorphism, but it does not follow automatically. Instead, there is only a map in one direction AB : ([B; A] ) B) ! [A; B] |the anamorphism corresponding to a simple H A;B -coalgebra structure on [B; A] )<F9.93