What are iteration theories?

Authors:
Jiří Adámek;Stefan Milius;Jiří Velebil
Affiliations:
Institute of Theoretical Computer Science, TU Braunschweig, Germany;Institute of Theoretical Computer Science, TU Braunschweig, Germany;Department of Mathematics, CVUT Prague, Czech Republic
Venue:
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Year:
2007

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Abstract

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