Relational Constructions in Goguen Categories

Authors:
Michael Winter
Affiliations:
-
Venue:
ReIMICS '01 Revised Papers from the 6th International Conference and 1st Workshop of COST Action 274 TARSKI on Relational Methods in Computer Science
Year:
2001

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Abstract

Goguen categories were introduced as a suitable calculus for L-fuzzy relations, i.e., for relations taking values from an arbitrary complete Brouwerian lattice L instead of the unit interval [0, 1] of the real numbers. Such a category may provide some relational constructions as products, sums or subobjects. The aim of this paper is to show that under an assumption on the lattice L one may require without loss of generality that the related relations are crisp, i.e., all entries are either the least element 0 or the greatest element 1 of L.