New interface

# On Algebras with Effectful Iteration

Abstract : For every finitary monad T on sets and every endofunctor F on the category of T-algebras we introduce the concept of an ffg-Elgot algebra for F, that is, an algebra admitting coherent solutions for finite systems of recursive equations with effects represented by the monad T. The goal of this paper is to study the existence and construction of free ffg-Elgot algebras. To this end, we investigate the locally ffg fixed point $\varphi F$φF, the colimit of all F-coalgebras with free finitely generated carrier, which is shown to be the initial ffg-Elgot algebra. This is the technical foundation for our main result: the category of ffg-Elgot algebras is monadic over the category of T-algebras.
Document type :
Conference papers
Domain :

Cited literature [12 references]

https://hal.inria.fr/hal-02044647
Contributor : Hal Ifip Connect in order to contact the contributor
Submitted on : Thursday, February 21, 2019 - 3:41:18 PM
Last modification on : Tuesday, January 19, 2021 - 10:16:03 AM
Long-term archiving on: : Wednesday, May 22, 2019 - 8:29:50 PM

### File

473364_1_En_9_Chapter.pdf
Files produced by the author(s)

### Citation

Stefan Milius, Jiří Adámek, Henning Urbat. On Algebras with Effectful Iteration. 14th International Workshop on Coalgebraic Methods in Computer Science (CMCS), Apr 2018, Thessaloniki, Greece. pp.144-166, ⟨10.1007/978-3-030-00389-0_9⟩. ⟨hal-02044647⟩

Record views