A categorical framework for the quantum harmonic oscillator

I will describe a categorical approach to the construction of symmetric Fock space, the state space of the quantum harmonic oscillator. Many of the conventional mathematical tools used to study this system -- such as raising and lowering operators, and coherent states -- emerge naturally from the category theory, and satisfy the usual equations. However, the formalism is more general than the conventional approach, and I will describe how to construct an infinite variety of 'exotic' Fock spaces. I will finish with the question: "Where has the 'quantumness' come from?".