Corecursive Algebras, Corecursive Monads and Bloom Monads

摘要

An algebra is called corecursive if from every coalgebra a uniquecoalgebra-to-algebra homomorphism exists into it. We prove that freecorecursive algebras are obtained as coproducts of the terminal coalgebra(considered as an algebra) and free algebras. The monad of free corecursivealgebras is proved to be the free corecursive monad, where the concept ofcorecursive monad is a generalization of Elgot's iterative monads, analogous tocorecursive algebras generalizing completely iterative algebras. We alsocharacterize the Eilenberg-Moore algebras for the free corecursive monad andcall them Bloom algebras.