Local Facts, Processes, and Gestures

In this chapter we describe the mathematical framework for the three fundamental layers of musical ontology: facts, processes, and gestures. The layer of facts is described by the theory of local and global compositions, a major topic in American Set Theory [765] and in the European school developed by the author and his collaborators [682]. The second layer is captured by the American Transformational Theory [605, 538] and, again in Europe, by the author’s theory of categorical limits (and colimits) as embedded in topos theory [714]. The third layer has been the author’s main concern in the last ten years [720, 723, 727], also paralleled by American research such as Robert S. Hatten’s work [446].