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Quantaloids, enriched categories and automata theory

Abstract

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.

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Rosenthal, K.I. Quantaloids, enriched categories and automata theory. Appl Categor Struct 3, 279–301 (1995). https://doi.org/10.1007/BF00878445

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Mathematics subject classifications (1991)

  • 18B35
  • 18D20
  • 18B20
  • 18F20

Key words

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