Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Adámek, Jiri; Milius, Stefan https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-80298
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On Corecursive Algebras for Functors Preserving Coproducts

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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}
}

Keywords: terminal coalgebra, free algebra, corecursive algebra, hyper-extensive category
Seminar: 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)
Issue date: 2017
Date of publication: 17.11.2017


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