by Mauro Jaskelioff on February 3, 2006. Tagged as: Lunches.

Neil said:

Today I spoke about iterative and completely iterative monads. These monads constitute terms which are the solutions of equations of the form

for some functor . The monad is the smallest monad which contains unique solutions for all such equations. The rational monad is the smallest monad which contains solutions of such equations where is finite.

An open question is to understand the monad of solutions to equations defining not just terms but operators such as

$$p(x) = A(x,p(Bx))$$

We call these algebraic terms. Getting freeness properties for such classes of terms is the key to using the coproduct of monads to combining such iterative theories

For references see the work of Milius and some of my own.

Stefan Milius, Completely iterative algebras and completely iterative monads, Information and Computation, v.196 n.1, p.1-41, January 10, 2005. An old preprint.