Quantale Modules and their Operators, with Applications
arXiv:1002.0968 · doi:10.1093/logcom/exn088
Abstract
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.