Corecursive Algebras, Corecursive Monads and Bloom Monads

Jiří Adámek, Mahdie Haddadi, Stefan Milius, Andrzej Tarlecki
2014 Logical Methods in Computer Science  
An algebra is called corecursive if from every coalgebra a unique coalgebra-to-algebra homomorphism exists into it. We prove that free corecursive algebras are obtained as coproducts of the terminal coalgebra (considered as an algebra) and free algebras. The monad of free corecursive algebras is proved to be the free corecursive monad, where the concept of corecursive monad is a generalization of Elgot's iterative monads, analogous to corecursive algebras generalizing completely iterative
more » ... as. We also characterize the Eilenberg-Moore algebras for the free corecursive monad and call them Bloom algebras.
doi:10.2168/lmcs-10(3:19)2014 fatcat:idq7yt4xaza5rmvrssemgn4abi