Jiří Adámek ; Mahdie Haddadi ; Stefan Milius - Corecursive Algebras, Corecursive Monads and Bloom Monads

lmcs:707 - Logical Methods in Computer Science, September 11, 2014, Volume 10, Issue 3 - https://doi.org/10.2168/LMCS-10(3:19)2014
Corecursive Algebras, Corecursive Monads and Bloom Monads

Authors: Jiří Adámek ; Mahdie Haddadi ; Stefan Milius

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 algebras. We also characterize the Eilenberg-Moore algebras for the free corecursive monad and call them Bloom algebras.


Volume: Volume 10, Issue 3
Published on: September 11, 2014
Accepted on: June 25, 2015
Submitted on: March 14, 2012
Keywords: Computer Science - Logic in Computer Science


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