Applied Categorical Structures

, Volume 3, Issue 3, pp 279-301

First online:

Quantaloids, enriched categories and automata theory

  • Kimmo I. RosenthalAffiliated withDepartment of Mathematics, Union College

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This article is intended to be an survey article outlining how the theory of quantaloids and categories enriched in them provides an effective means of analyzing both automata and tree automata. The emphasis is on the unification of concepts and how categorical methods provide insight into various calculations and theorems, both illuminating the original presentation as well as yielding conceptually simpler proofs. Proofs will be omitted and the emphasis is on providing the reader (even a relatively inexperienced one) with an understanding of the basic constructions and results.

Mathematics subject classifications (1991)

18B35 18D20 18B20 18F20

Key words

quantaloid nucleus Q-category Q-functor Q-bimodule relational presheaf automata tree automata