A Fibrational Approach to Automata Theory
نویسندگان
چکیده
For predual categories C andD 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. 1998 ACM Subject Classification F.4.3 Formal Languages
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