7 Jun
2001
7 Jun
'01
5:10 p.m.
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" [...] 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?
by reversing the arrows, and replacing coproducts by products, we get that, for the function g:AxB->A holds B--<g',id>-->AxB--g-->A = B--g'-->A, ie g(g'(y),y) = g'(y) in words, the "coiterator" g' is just a fixpoint of g. -- dusko