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.2015.50
URN: urn:nbn:de:0030-drops-55268
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5526/
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Chen, Liang-Ting ; Urbat, Henning

A Fibrational Approach to Automata Theory

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Abstract

For predual categories C and D we establish isomorphisms between opfibrations representing local varieties of languages in C, local pseudovarieties of D-monoids, and finitely generated profinite D-monoids. The global sections of these opfibrations are shown to correspond to varieties of languages in C, pseudovarieties of D-monoids, and profinite equational theories of D-monoids, respectively. As an application, a new proof of Eilenberg's variety theorem along with several related results is obtained, covering uniformly varieties of languages and their coalgebraic modifications, Straubing's C-varieties, and fully invariant local varieties.

BibTeX - Entry

@InProceedings{chen_et_al:LIPIcs:2015:5526,
  author =	{Liang-Ting Chen and Henning Urbat},
  title =	{{A Fibrational Approach to Automata Theory}},
  booktitle =	{6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)},
  pages =	{50--65},
  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/2015/5526},
  URN =		{urn:nbn:de:0030-drops-55268},
  doi =		{10.4230/LIPIcs.CALCO.2015.50},
  annote =	{Keywords: Eilenberg’s variety theorem, duality, coalgebra, Grothendieck fibration}
}

Keywords: Eilenberg’s variety theorem, duality, coalgebra, Grothendieck fibration
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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