*by C. Russo*

Journal of Logic and Computation (2010), 20(4): 917-946.

Advance access December 2008.

doi:10.1093/logcom/exn088

The central topic of this work is the categories of modules over unital quantales. The main categorical properties are established and a special class of operators, called *Q*-module transforms, is defined. Such operators – that turn out to be precisely the homomorphisms between free objects in those categories – find concrete applications in two different branches of image processing, namely fuzzy image compression and mathematical morphology.