Fuzzy Galois connections categorically

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...

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Bibliographic Details
Published in:Mathematical logic quarterly 2010-03, Vol.56 (2), p.131-147
Main Authors: Gutiérrez García, Javier, Mardones-Pérez, Iraide, de Prada Vicente, María Angeles, Zhang, Dexue
Format: Article
Language:English
Subjects:
category enriched over a unital quantale
contravariant fuzzy Galois connection
covariant fuzzy Galois connection
Girard quantale
Unital quantale
Ω-adjunction
Ω-relation
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Summary: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)
ISSN:0942-5616
1521-3870
DOI:10.1002/malq.200810044