  The attraction of using AFA is that it gives a set of tools for modeling circular phenomena of various sorts.  These tools are connected to important circular definitions, as we shall see.  We shall also be concerned with situating both the mathematics and the underlying intuitions in a broader picture, one derived from work in coalgebra. Incorporating concepts and results from category theory, coalgebra leads us to concepts such as corecursion and coinduction; these are in a sense duals to the more standard notions of recursion and induction. 