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.CALCO.2015.221
URN: urn:nbn:de:0030-drops-55365
URL: https://drops.dagstuhl.de/opus/volltexte/2015/5536/
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Levy, Paul Blain

Final Coalgebras from Corecursive Algebras

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Abstract

We give a technique to construct a final coalgebra in which each element is a set of formulas of modal logic. The technique works for both the finite and the countable powerset functors. Starting with an injectively structured, corecursive algebra, we coinductively obtain a suitable subalgebra called the "co-founded part". We see—first with an example, and then in the general setting of modal logic on a dual adjunction—that modal theories form an injectively structured, corecursive algebra, so that this construction may be applied. We also obtain an initial algebra in a similar way. We generalize the framework beyond Set to categories equipped with a suitable factorization system, and look at the examples of Poset and Set-op .

BibTeX - Entry

@InProceedings{levy:LIPIcs:2015:5536,
  author =	{Paul Blain Levy},
  title =	{{Final Coalgebras from Corecursive Algebras}},
  booktitle =	{6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)},
  pages =	{221--237},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-84-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{35},
  editor =	{Lawrence S. Moss and Pawel Sobocinski},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5536},
  URN =		{urn:nbn:de:0030-drops-55365},
  doi =		{10.4230/LIPIcs.CALCO.2015.221},
  annote =	{Keywords: coalgebra, modal logic, bisimulation, category theory, factorization system}
}

Keywords: coalgebra, modal logic, bisimulation, category theory, factorization system
Collection: 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)
Issue Date: 2015
Date of publication: 28.10.2015


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