On Algebras with Effectful Iteration

  • Stefan MiliusEmail author
  • Jiří Adámek
  • Henning Urbat
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11202)


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 \(\varphi F\), 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.


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© IFIP International Federation for Information Processing 2018

Authors and Affiliations

  1. 1.Czech Technical University in PraguePragueCzech Republic
  2. 2.Friedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

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