Completing categorical algebras: Extended abstract

Stephen L. Bloom, Zoltán Ésik

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Let ∑ be a ranked set. A categorical ∑-algebra, c∑a for short, is a small category C equipped with a functor σC: Cn → 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 σc 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 Cω, 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 Cω.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 languageEnglish
Title of host publicationFourth IFIP International Conference on Theoretical Computer Science- TCS 2006
Subtitle of host publicationIFIP 19th Worm Computer Congress, TC-1, Foundations of Computer Science, August 23-24, 2006, Santiago Chile
EditorsGonzalo Navarro, Leopolo Bertossi, Yoshiharu Kohayakawa
Pages231-249
Number of pages19
DOIs
Publication statusPublished - Dec 27 2006

Publication series

NameIFIP International Federation for Information Processing
Volume209
ISSN (Print)1571-5736

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ASJC Scopus subject areas

  • Information Systems and Management

Cite this

Bloom, S. L., & Ésik, Z. (2006). Completing categorical algebras: Extended abstract. In G. Navarro, L. Bertossi, & Y. Kohayakawa (Eds.), 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