# Derived Operations in Goguen Categories

## Michael Winter

Goguen categories were introduced in as a suitable categorical description of ${\mathcal L}$-fuzzy relations, i.e., of relations taking values from an arbitrary complete Brouwerian lattice ${\mathcal L}$ instead of the unit interval $[0,1]$ of the real numbers. In this paper we want to study operations on morphisms of a Goguen category which are derived from suitable binary functions on the underlying lattice of scalar elements, i.e., on the abstract counterpart of ${\mathcal L}$.

Keywords: Goguen category, Fuzzy Relation, Dedekind category.

2000 MSC: 18B10, 03G15.

Theory and Applications of Categories, Vol. 10, 2002, No. 11, pp 220-247.

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