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Varieties of finite categories. (English) Zbl 0608.18002
The paper develops a theory of finitely generated categories with finitely many objects. The theory generalizes a notion of pseudovarieties given by P. M. Schützenberger and S. Eilenberg. The motivation is to provide stronger tools for investigations of finite-state machines and combinatorial properties of languages. Several interesting results are presented, for instance, the decidability problem - asking whether for given monoids S,T and a pseudovariety W of monoids, there exists a monoid \(X\in W\) such that S is divided by the wreath product of X and T - is reduced to the decidability of the membership problem for W.
Reviewer: V.Koubek

18B20 Categories of machines, automata
68Q70 Algebraic theory of languages and automata
20M35 Semigroups in automata theory, linguistics, etc.
20M07 Varieties and pseudovarieties of semigroups
08C15 Quasivarieties
Full Text: DOI EuDML
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