Alessandro and Pal-Kristian asked for a reference. Jan Rutten's work is
a good starting place for studying coalgebras, coinduction and
corecursion, see http://homepages.cwi.nl/~janr/, for example the
following might be interesting for this forum:

B. Jacobs and J.J.M.M. Rutten: A Tutorial on (Co)Algebras and
(Co)Induction. Bulletin of EATCS Vol. 62, 1997, pp. 222--259.
Available at http://www.cs.kun.nl/~bart/PAPERS/JR.ps.Z

Andrej