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DOI: 10.4230/LIPIcs.CALCO.2015.221
URN: urn:nbn:de:0030-drops-55365
URL: https://drops.dagstuhl.de/opus/volltexte/2015/5536/
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 | |
| Seminar: | 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015) | |
| Issue date: | 2015 | |
| Date of publication: | 28.10.2015 |
