How iterative reflections of monads are constructed

摘要

Every ideal monad M on the category of sets is known to have a reflection M in the category of all iterative monads of Elgot. Here we describe the iterative reflection M as the monad of free iterative Eilenberg-Moore algebras for M. This yields numerous concrete examples: if M is the free-semigroup monad, then M is obtained by adding a single absorbing element; if M is the monad of finite trees then M is the monad of rational trees, etc.