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- W1501768223 abstract "Eilenberg's variety theorem, a centerpiece of algebraic automata theory, establishes a bijective correspondence between varieties of languages and pseudovarieties of monoids. In the present paper this result is generalized to an abstract pair of algebraic categories: we introduce varieties of languages in a category C, and prove that they correspond to pseudovarieties of monoids in a closed monoidal category D, provided that C and D are dual on the level of finite objects. By suitable choices of these categories our result uniformly covers Eilenberg's theorem and three variants due to Pin, Polák and Reutenauer, respectively, and yields new Eilenberg-type correspondences." @default.
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- W1501768223 date "2015-07-01" @default.
- W1501768223 modified "2023-09-23" @default.
- W1501768223 title "Varieties of Languages in a Category" @default.
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- W1501768223 doi "https://doi.org/10.1109/lics.2015.46" @default.
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