TERMINAL COALGEBRAS IN WELL-FOUNDED SET-THEORY

This paper shows that, in order to obtain the theorem of Aczel and Mendler on the existence of terminal coalgebras for an endofunctor on the category of sets, it is entirely unnecessary to delve into such exotica as non-well-founded set theory. In addition, we discuss the canonical map from the initial algebra for an endofunctor on sets to the terminal coalgebra and show that in many cases it embeds the former as a dense subset of the latter in a certain natural topology. By way of example, we calculate the terminal coalgebra for various simple endofunctors.