Varieties of Languages in a Category
Formal Languages and Automata Theory
2015-01-22 v1 Logic in Computer Science
Category Theory
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, Polak and Reutenauer, respectively, and yields new Eilenberg-type correspondences.
Keywords
Cite
@article{arxiv.1501.05180,
title = {Varieties of Languages in a Category},
author = {Jiri Adamek and Stefan Milius and Robert Myers and Henning Urbat},
journal= {arXiv preprint arXiv:1501.05180},
year = {2015}
}