What Are Iteration Theories?

  • Jiří Adámek
  • Stefan Milius
  • Jiří Velebil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4708)


We prove that iteration theories can be introduced as algebras for the monad  Open image in new window on the category of signatures assigning to every signature  Open image in new window the rational- Open image in new window -tree signature. This supports the result that iteration theories axiomatize precisely the equational properties of least fixed points in domain theory: Open image in new window  is the monad of free rational theories and every free rational theory has a continuous completion.


Continuous Theory Rational Theory Equational Property Left Adjoint Forgetful Functor 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jiří Adámek
    • 1
  • Stefan Milius
    • 1
  • Jiří Velebil
    • 2
  1. 1.Institute of Theoretical Computer Science, TU BraunschweigGermany
  2. 2.Department of Mathematics, ČVUT PragueCzech Republic

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