A Fibrational Approach to Automata Theory

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, a new proof of Eilenberg’s variety theorem along with several related results is obtained, covering uniformly varieties of languages and their coalgebraic modifications, Straubing’s C-varieties, and fully invariant local varieties. 1998 ACM Subject Classification F.4.3 Formal Languages Keywords and phrases Eilenberg’s variety theorem, duality, coalgebra, Grothendieck fibration Digital Object Identifier 10.4230/LIPIcs.CALCO.2015.50

• Type: Journal
• Year: 2015
• Where: CALCO
• Authors: Liang-Ting Chen, Henning Urbat
• Keywords: CALCO 2015, Mathematics