Varieties of Languages in a Category
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 l...
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| Vydáno v: | 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science s. 414 - 425 |
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| Jazyk: | angličtina |
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01.07.2015
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| ISSN: | 1043-6871 |
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| 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. |
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| AbstractList | 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. |
| Author | Urbat, Henning Milius, Stefan Adamek, Jiri Myers, Robert S. R. |
| Author_xml | – sequence: 1 givenname: Jiri surname: Adamek fullname: Adamek, Jiri organization: Inst. fur Theor. Inf., Tech. Univ. Braunschweig, Braunschweig, Germany – sequence: 2 givenname: Robert S. R. surname: Myers fullname: Myers, Robert S. R. organization: Inst. fur Theor. Inf., Tech. Univ. Braunschweig, Braunschweig, Germany – sequence: 3 givenname: Henning surname: Urbat fullname: Urbat, Henning organization: Inst. fur Theor. Inf., Tech. Univ. Braunschweig, Braunschweig, Germany – sequence: 4 givenname: Stefan surname: Milius fullname: Milius, Stefan organization: Lehrstuhl fur Theor. Inf., Friedrich-Alexander Univ. Erlangen-Nurnberg, Erlangen-Nurnberg, Germany |
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| Snippet | Eilenberg's variety theorem, a centerpiece of algebraic automata theory, establishes a bijective correspondence between varieties of languages and... |
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| SubjectTerms | algebra Automata Boolean algebra coalgebra duality Eilenberg's theorem Generators Lattices monoids Structural rings Tensile stress varieties of languages |
| Title | Varieties of Languages in a Category |
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