A Description of Iterative Reflections of Monads (Extended Abstract)

  • Jiří Adámek
  • Stefan Milius
  • Jiří Velebil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5504)


For ideal monads in Set (e. g. the finite list monad, the finite bag monad etc.) we have recently proved that every set generates a free iterative algebra. This gives rise to a new monad. We prove now that this monad is iterative in the sense of Calvin Elgot, in fact, this is the iterative reflection of the given ideal monad. This shows how to freely add unique solutions of recursive equations to a given algebraic theory. Examples: the monad of free commutative binary algebras has the monad of binary rational unordered trees as iterative reflection, and the finite list monad has the iterative reflection given by adding an absorbing element.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jiří Adámek
    • 1
  • Stefan Milius
    • 1
  • Jiří Velebil
    • 2
  1. 1.Institute of Theoretical Computer ScienceTechnical UniversityBraunschweigGermany
  2. 2.Faculty of Electrical EngineeringCzech Technical University of PragueCzech Republic

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