categories: Re: co-iteration?

[Dusko Pavlovic <dusko@kestrel.edu>]

> 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