"On Coalgebras over Algebras" by Adriana Balan and Alexander Kurz
 

On Coalgebras over Algebras

Document Type

Article

Publication Date

2011

Abstract

We extend Barr’s well-known characterization of the final coalgebra of a Set-endofunctor H as the completion of its initial algebra to the Eilenberg–Moore category Alg(M) of algebras associated to a Set-monad M, if H can be lifted to Alg(M). As further analysis, we introduce the notion of a commuting pair of endofunctors (T,H) with respect to a monad M and show that under reasonable assumptions, the final H-coalgebra can be obtained as the completion of the free M-algebra on the initial T-algebra.

Comments

This article was originally published in Theoretical Computer Science, volume 412, issue 38, in 2011. DOI: 10.1016/j.tcs.2011.03.021

Copyright

Elsevier

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