On the Prequantisation Map for 2-Plectic Manifolds

For a manifold $M$ with an integral closed 3-form $\omega$, we construct $PU(H)$-bundle and Lie groupoid over its total space, together curving in the sense of gerbes. If form is non-degenerate, furthermore give natural 2-algebra quasi-isomorphism from observables $(M,\omega)$ to weak symmetries above geometric structure, generalising prequantisation map Kostant Souriau.