### Abstract

The main result is 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 language | English |
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Title of host publication | Mathematical Foundations of Computer Science 1996 - 21st International Symposium, MFCS 1996, Proceedings |

Editors | Wojciech Penczek, Andrzej Szalas |

Publisher | Springer Verlag |

Pages | 336-347 |

Number of pages | 12 |

ISBN (Print) | 3540615504, 9783540615507 |

DOIs | |

Publication status | Published - 1996 |

Event | 21st International Symposium on Mathematical Foundations of Computer Science, MFCS 1996 - Cracow, Poland Duration: Sep 2 1996 → Sep 6 1996 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1113 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 21st International Symposium on Mathematical Foundations of Computer Science, MFCS 1996 |
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Country | Poland |

City | Cracow |

Period | 9/2/96 → 9/6/96 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Ésik, Z., & Labella, A. (1996). Equational properties of iteration in algebraically complete categories. In W. Penczek, & A. Szalas (Eds.),

*Mathematical Foundations of Computer Science 1996 - 21st International Symposium, MFCS 1996, Proceedings*(pp. 336-347). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1113). Springer Verlag. https://doi.org/10.1007/3-540-61550-4_160