For many (categorical) notions, there is a useful (often fantastic) dual notion. What about iteration? In a category with finite coproducts, we have a notion of iteration f:A-->A+B (written A -f-> A+B here) which in the case of sets and partial functions, for example, is completely specified by the Elgot equation A -f-> A+B -f"+1-> B = A -f"-> B recursive in f" (plus one more little, quite natural condition - see [Manes '92]) This awful looking mess, written using the infix morphism notation, actually looks quite neat when you draw the diagram. Now without meaning to start the "co"-wars again, - is there a useful notion of co-iteration? - what could it do for us, say in the category of partial functions? - is there a simple algebra/coalgebra context? Reference: [Manes '92] E.G.Manes, "Predicate Transformer Semantics", CUP 1992 Al Vilcius personal: al.r@vilcius.com business: avilcius@webpearls.com