文章基本信息

标题：A Fibrational Approach to Automata Theory
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作者：Liang-Ting Chen ; Henning Urbat
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2015
卷号：35
页码：50-65
DOI：10.4230/LIPIcs.CALCO.2015.50
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：Eilenberg's variety theorem; duality; coalgebra; Grothendieck fibration