Composing Monads for a Musical Performance

Abstract

Music is a testing challenge for formal information systems. Here we apply the full power of category theory to the challenge, involving the topos for data structuring and the monad for process. The topos handles many aspects of the data for a performance including the score and variants, the orchestral players, the conductor and the supporting infrastructure such as funding bodies. The monad as process controls the adjointness between the functors representing articulation and intonation, based on perceived activity in the brain in professional musicians. We present a musical performance as a categorical composition over time signatures that proceed in successive adjoint steps with the monad looking back and its associated comonad looking forward. The physical complexity of each musical sound operates in its respective time-frame, represented by a limit, as a colimit. The formalism can be implemented in a functional programming language such as Haskell.