A Fibrational Approach to Automata Theory
Formal Languages and Automata Theory
2015-11-06 v1 Category Theory
Abstract
For predual categories C and D 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, we obtain a new proof of Eilenberg's variety theorem along with several related results, covering varieties of languages and their coalgebraic modifications, Straubing's C-varieties, fully invariant local varieties, etc., within a single framework.
Keywords
Cite
@article{arxiv.1504.02692,
title = {A Fibrational Approach to Automata Theory},
author = {Liang-Ting Chen and Henning Urbat},
journal= {arXiv preprint arXiv:1504.02692},
year = {2015}
}