### Abstract

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 language | English |
---|---|

Pages (from-to) | 61-69 |

Number of pages | 9 |

Journal | Theoretical Computer Science |

Volume | 195 |

Issue number | 1 |

Publication status | Published - Mar 20 1998 |

### Fingerprint

### Keywords

- Algebraically complete categories
- Fixed points
- Iteration theories

### ASJC Scopus subject areas

- Computational Theory and Mathematics

### Cite this

*Theoretical Computer Science*,

*195*(1), 61-69.

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

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 195, no. 1, pp. 61-69.

}

TY - JOUR

T1 - Equational properties of iteration in algebraically complete categories

AU - Ésik, Z.

AU - Labella, A.

PY - 1998/3/20

Y1 - 1998/3/20

N2 - 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.

AB - 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.

KW - Algebraically complete categories

KW - Fixed points

KW - Iteration theories

UR - http://www.scopus.com/inward/record.url?scp=0346703020&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346703020&partnerID=8YFLogxK

M3 - Article

VL - 195

SP - 61

EP - 69

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 1

ER -