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2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) (2015)
Kyoto, Japan
July 6, 2015 to July 10, 2015
ISSN: 1043-6871
ISBN: 978-1-4799-8875-4
pp: 414-425
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.
INDEX TERMS
Automata, Boolean algebra, Lattices, Tensile stress, Generators, Structural rings,algebra, Eilenberg's theorem, varieties of languages, monoids, duality, automata, coalgebra
CITATION
Jiri Adamek, Robert S.R. Myers, Henning Urbat, Stefan Milius, "Varieties of Languages in a Category", 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), vol. 00, no. , pp. 414-425, 2015, doi:10.1109/LICS.2015.46
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