LIPIcs.CALCO.2015.50.pdf
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A Fibrational Approach to Automata Theory
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6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Conference on Algebra and Coalgebra in Computer Science (CALCO) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2015-10-28
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Liang-Ting Chen and Henning Urbat. A Fibrational Approach to Automata Theory. In 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 35, pp. 50-65, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.CALCO.2015.50
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.
Subject Classification
Keywords
- Eilenberg’s variety theorem
- duality
- coalgebra
- Grothendieck fibration
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