On Coalgebras over Algebras

Authors

Adriana Balan, University Politehnica of Bucharest
Alexander Kurz, Chapman UniversityFollow

Document Type

Article

Publication Date

2010

Abstract

We extend Barr’s well-known characterization of the final coalgebra of a Set-endofunctor as the completion of its initial algebra to the Eilenberg-Moore category of algebras for a Set-monad M for functors arising as liftings. As an application we introduce the notion of commuting pair of endofunctors with respect to the monad M and show that under reasonable assumptions, the final coalgebra of one of the endofunctors involved can be obtained as the free algebra generated by the initial algebra of the other endofunctor.

Comments

This article was originally published in Electronic Notes in Theoretical Computer Science, volume 264, issue 2, in 2010. DOI: 10.1016/j.entcs.2010.07.013

Recommended Citation

A. Balan and A. Kurz, “On Coalgebras over Algebras,” Electronic Notes in Theoretical Computer Science, vol. 264, no. 2, pp. 47–62, Aug. 2010. DOI: 10.1016/j.entcs.2010.07.013

Copyright

Elsevier

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.