## Iterative and Completely Iterative Monads

February 3rd, 2006 by Mauro JaskelioffNeil 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

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.

Ghani, N and Lüth, C and de Marchi, Solving Algebraic Equations using Coalgebra, Journal of Theoretical Informatics and Applications, 2003.

Neil Ghani and Tarmo Uustalu, Coproducts of Ideal Monads, Journal of Theoretical Informatics and Applications, 2004.