On the prequantisation map for 2-plectic manifolds

For a manifold $M$ with an integral closed 3-form $\omega$, we construct a $PU(H)$-bundle and a Lie groupoid over its total space, together with a curving in the sense of gerbes. If the form is non-degenerate, we furthermore give a natural Lie 2-algebra quasi-isomorphism from the observables of $(M,\omega)$ to the weak symmetries of the above geometric structure, generalising the prequantisation map of Kostant and Souriau.
Comment: Typos are corrected. A reference and an acknowledgement is added. A revised version (upon submission and refereeing) is now published. These revisions are not included in this arXiv version