In abstract mathematical music theory, the data format of denotators is associated with set-valued presheaves over module categories. In this paper, we present an implementation of this concept framework in the Rubato Composer system, a Java application comprising a GUI for manipulation and combination of rubettes. These are plug-ins that can be added and connected for communication of denotator data. Rubato Composer is a GPL software and is accessible to the computer music community for download and collaboration. In this paper, the functionality, architecture, concept framework, and the implemented mathematical operators are presented and illustrated with a "functorial composition" as well as with two rubettes for the construction of embellishments (macro objects) and wallpaper ornaments (grids of transformations acting on motifs). In a musically more significant example, we sketch the functorial reconstruction of Pierre Boulez's classical composition structures pour deux pianos, Ia.