### 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 | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Publisher | Springer Verlag |

Pages | 336-347 |

Number of pages | 12 |

Volume | 1113 |

ISBN (Print) | 3540615504, 9783540615507 |

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) | 03029743 |

ISSN (Electronic) | 16113349 |

### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 1113, pp. 336-347). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1113). Springer Verlag.

**Equational properties of iteration in algebraically complete categories.** / Ésik, Z.; Labella, Anna.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 1113, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1113, Springer Verlag, pp. 336-347, 21st International Symposium on Mathematical Foundations of Computer Science, MFCS 1996, Cracow, Poland, 9/2/96.

}

TY - GEN

T1 - Equational properties of iteration in algebraically complete categories

AU - Ésik, Z.

AU - Labella, Anna

PY - 1996

Y1 - 1996

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84947945247&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84947945247&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84947945247

SN - 3540615504

SN - 9783540615507

VL - 1113

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 336

EP - 347

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

PB - Springer Verlag

ER -