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Representation theory of Goguen categories

✍ Scribed by Michael Winter

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
392 KB
Volume
138
Category
Article
ISSN
0165-0114

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✦ Synopsis

Goguen categories constitute a suitable algebraic formalisation for L-fuzzy relations. It is well-known that an L-fuzzy relation may be represented by the set of all its -cuts. The aim of this paper is to show a similar result for Goguen categories. Furthermore, given an algebraic structure of relations, a Dedekind category R, and a complete Brouwerian lattice L, the idea above allows us to deΓΏne a Goguen category G such that the underlying structures are R and L. Using our pseudo-representation theorem we show that the representation theory of Goguen categories is equivalent to the representation theory of simple Dedekind categories. This result allows us to transfer known representation results for Dedekind categories to the theory of Goguen categories.

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