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Keywords:

  • Unital quantale;
  • category enriched over a unital quantale;
  • Ω-adjunction;
  • Ω-relation;
  • covariant fuzzy Galois connection;
  • contravariant fuzzy Galois connection;
  • Girard quantale

Abstract

This paper presents a systematic investigation of fuzzy (non-commutative) Galois connections in the sense of R. Bělohlávek [1], from the point of view of enriched category theory. The results obtained show that the theory of enriched categories makes it possible to present the theory of fuzzy Galois connections in a succinct way; and more importantly, it provides a useful method to express and to study the link and the difference between the commutative and the non-commutative worlds (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)