### Abstract

Let ∑ be a ranked set. A categorical ∑-algebra, c∑a for short, is a small category C equipped with a functor σ_{C}: C^{n} → C, for each σ ∈ ∑_{n}, n ≥ 0. A continuous categorical ∑-algebra is a c∑a which has an initial object and all colimits ofω-chains, i.e., functors ℕ→ C; each functor σ_{c} preserves colimits of ω-chains. (ℕ is the linearly ordered set of the nonnegative integers considered as a category as usual.) We prove that for any c∑a C there is an ω-continuous c∑a C^{ω}, unique up to equivalence, which forms a "free continuous completion" of C. We generalize the notion of inequation (and equation) and show the inequations or equations that hold in C also hold in C^{ω}.We then find examples of this completion when - C is a c∑a of finite∑-trees - C is an ordered ∑ algebra - C is a c∑a of finite A-sychronization trees - C is a c∑a of finite words on A.

Original language | English |
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Title of host publication | Fourth IFIP International Conference on Theoretical Computer Science- TCS 2006 |

Subtitle of host publication | IFIP 19th Worm Computer Congress, TC-1, Foundations of Computer Science, August 23-24, 2006, Santiago Chile |

Editors | Gonzalo Navarro, Leopolo Bertossi, Yoshiharu Kohayakawa |

Pages | 231-249 |

Number of pages | 19 |

DOIs | |

Publication status | Published - Dec 27 2006 |

### Publication series

Name | IFIP International Federation for Information Processing |
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Volume | 209 |

ISSN (Print) | 1571-5736 |

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### ASJC Scopus subject areas

- Information Systems and Management

### Cite this

*Fourth IFIP International Conference on Theoretical Computer Science- TCS 2006: IFIP 19th Worm Computer Congress, TC-1, Foundations of Computer Science, August 23-24, 2006, Santiago Chile*(pp. 231-249). (IFIP International Federation for Information Processing; Vol. 209). https://doi.org/10.1007/978-0-387-34735-6_20