Eilenberg-type correspondences, relating varieties of languages (eg of finite words, infinite
words, or trees) to pseudovarieties of finite algebras, form the backbone of algebraic …

This paper contributes to the techniques of topo-algebraic recognition for languages beyond
the regular setting as they relate to logic on words. In particular, we provide a general …

Profinite equations are an indispensable tool for the algebraic classification of formal
languages. Reiterman's theorem states that they precisely specify pseudovarieties, ie …

Starting from Boolean algebras of languages closed under quotients and using duality
theoretic insights, we derive the notion of Boolean spaces with internal monoids as …

Recently, two apparently quite different duality-based approaches to automata minimisation
have appeared. One is based on ideas that originated from the controllability-observability …

The transition structure α: X→ XA of a deterministic automaton with state set X and with
inputs from an alphabet A can be viewed both as an algebra and as a coalgebra. We use …

We introduce context-free languages of morphisms in monoidal categories, extending recent
work on the categorification of context-free languages, and regular languages of string …

Recently, Eilenberg's variety theorem was reformulated in the light of Stone's duality
theorem. On one level, this reformulation led to a unification of several existing Eilenberg …

The purpose of the present paper is to show that: Eilenberg-type correspondences=
Birkhoff's theorem for (finite) algebras+ duality. We consider algebras for a monad T on a …

For finite automata as coalgebras in a category C, we study languages they accept and
varieties of such languages. This generalizes Eilenberg's concept of a variety of languages …