Recognisable Languages over Monads

This paper proposes monads as a framework for algebraic language theory. Examples of monads include words and trees, finite and infinite. Each monad comes with a standard notion of an algebra, called an Eilenberg-Moore algebra, which generalises algebras studied in language theory like semigroups or \(\omega \)-semigroups. On the abstract level of monads one can prove theorems like the Myhill-Nerode theorem, the Eilenberg theorem; one can also define profinite objects.

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