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arXiv · 1504.02692

A Fibrational Approach to Automata Theory

Liang-Ting Chen·Henning Urbat
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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, we obtain a new proof of Eilenberg's variety theorem along with several related results, covering varieties of languages and their coalgebraic modifications, Straubing's C-varieties, fully invariant local varieties, etc., within a single framework.

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Liang-Ting Chen, Henning Urbat. 2015-04-10. A Fibrational Approach to Automata Theory. https://doi.org/10.4230/lipics.calco.2015.50

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