From corecursive algebras to corecursive monads

Authors:
Jiří Adámek;Mahdieh Haddadi;Stefan Milius
Affiliations:
Institut für Theoretische Informatik, Technische Universität Braunschweig, Germany;Institut für Theoretische Informatik, Technische Universität Braunschweig, Germany;Institut für Theoretische Informatik, Technische Universität Braunschweig, Germany
Venue:
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
Year:
2011

Citing 7
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Abstract

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 a coproduct of the final coalgebra (considered as an algebra) and with 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 algebras.We also characterize the Eilenberg-Moore algebras for the free corecursive monad and call them Bloom algebras.