Abstract
This chapter explains basic properties of left modules on unital quantales with the perspective towards fuzzy set theory. Typical constructions such as the fuzzy power set, Zadeh’s forward operator or binary operations defined according to Zadeh’s extension principle are constructions in the symmetric monoidal closed category of complete lattices and join preserving maps. Moreover, involutive left modules play a significant role in the representation theory of \(C^*\)-algebras.
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