Equational properties of iteration in algebraically complete categories

Z. Ésik, A. Labella

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19 Citations (Scopus)


We prove the following completeness theorem: If the fixed point operation over a category is defined by initiality, then the equations satisfied by the fixed point operation are exactly those of iteration theories. Thus, in such categories, the equational axioms of iteration theories provide a sound and complete axiomatization of the equational properties of the fixed point operation.

Original languageEnglish
Pages (from-to)61-89
Number of pages29
JournalTheoretical Computer Science
Issue number1
Publication statusPublished - Mar 20 1998



  • Algebraically complete categories
  • Fixed points
  • Iteration theories

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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