License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2020.7
URN: urn:nbn:de:0030-drops-116503
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/11650/
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Adámek, Jiří

On Free Completely Iterative Algebras

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LIPIcs-CSL-2020-7.pdf (0.5 MB)

Abstract

For every finitary set functor F we demonstrate that free algebras carry a canonical partial order. In case F is bicontinuous, we prove that the cpo obtained as the conservative completion of the free algebra is the free completely iterative algebra. Moreover, the algebra structure of the latter is the unique continuous extension of the algebra structure of the free algebra.
For general finitary functors the free algebra and the free completely iterative algebra are proved to be posets sharing the same conservative completion. And for every recursive equation in the free completely iterative algebra the solution is obtained as the join of an ω-chain of approximate solutions in the free algebra.

BibTeX - Entry

@InProceedings{admek:LIPIcs:2020:11650,
  author =	{Ji?{\'\i} Ad{\'a}mek},
  title =	{{On Free Completely Iterative Algebras}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{7:1--7:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Maribel Fern{\'a}ndez and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11650},
  URN =		{urn:nbn:de:0030-drops-116503},
  doi =		{10.4230/LIPIcs.CSL.2020.7},
  annote =	{Keywords: free algebra, completely iterative algebra, terminal coalgebra, initial algebra, finitary functor}
}

Keywords: free algebra, completely iterative algebra, terminal coalgebra, initial algebra, finitary functor
Collection: 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)
Issue Date: 2020
Date of publication: 06.01.2020

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