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.2017.3
URN: urn:nbn:de:0030-drops-80298
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8029/
Adámek, Jiri ;
Milius, Stefan
On Corecursive Algebras for Functors Preserving Coproducts
Abstract
For an endofunctor H on a hyper-extensive category preserving countable coproducts we describe the free corecursive algebra on Y as the coproduct of the terminal coalgebra for H and the free H-algebra on Y. As a consequence, we derive that H is a cia functor, i.e., its corecursive algebras are precisely the cias (completely iterative algebras). Also all functors H(-) + Y are then cia functors. For finitary set functors we prove that, conversely, if H is a cia functor, then it has the form H = W \times (-) + Y for some sets W and Y.
BibTeX - Entry
@InProceedings{admek_et_al:LIPIcs:2017:8029,
author = {Jiri Ad{\'a}mek and Stefan Milius},
title = {{On Corecursive Algebras for Functors Preserving Coproducts}},
booktitle = {7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)},
pages = {3:1--3:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-033-0},
ISSN = {1868-8969},
year = {2017},
volume = {72},
editor = {Filippo Bonchi and Barbara K{\"o}nig},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/8029},
URN = {urn:nbn:de:0030-drops-80298},
doi = {10.4230/LIPIcs.CALCO.2017.3},
annote = {Keywords: terminal coalgebra, free algebra, corecursive algebra, hyper-extensive category}
}
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Keywords: |
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terminal coalgebra, free algebra, corecursive algebra, hyper-extensive category |
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Collection: |
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7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017) |
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Issue Date: |
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2017 |
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Date of publication: |
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17.11.2017 |
