Here you can find the current version of a book that I am writing about algebraic language theory, which is called “Languages recognised by finite semigroups and their generalisations to objects such as trees and graphs, with an emphasis on definability in monadic second-order logic”. The book begins with some classical theory of finite semigroups, such as Green’s relations, but it is mainly devoted to generalisations beyond finite words (trees, graphs, or infinite words), which uses the methodology of monads and their Eilenberg-Moore algebras.

 

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