What is actually a first reference for the fact that for every polynomial endofunctor of Set a final coalgebra consists of all properly labelled (finite and infinite) trees? I suspect the first authors to study this were Arbib and Manes in their "Parametrized data types do not need...", Information and control 52 (1982), 139-158. However, it is obvious from that paper that Arbib and Manes were definitely unaware of the general statement, which explains why they only mention some special cases in their book in 1986. Jiri Adamek xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx alternative e-mail address (in case reply key does not work): J.Adamek@tu-bs.de xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx