Bridging Denotator Theory and Sheaf Neural Networks for Symbolic Music Generation

This framework provides a rigorous mathematical bridge between Guerino Mazzola's algebraic Denotator Theory and modern Sheaf Neural Networks (SNNs). By adapting hierarchical musical structures into cellular stalks and linear restriction matrices over incidence posets, we demonstrate how categorical limits and colimits govern local counterpoint restrictions and macroscopic temporal synthesis. We present a clear operational contrast between deterministic Baroque counterpoint constraints and continuous parallel transport operators in modern modal jazz, providing an explicit formulation to instantiate these properties within structural machine learning environments.