Explore advanced mathematical concepts in this 47-minute lecture from the ESI's Thematic Programme on "Infinite-dimensional Geometry: Theory and Applications." Delve into the construction of principal PU(H)-bundles and Lie groupoids for manifolds with integral closed 3-forms. Learn how non-degenerate forms enable natural Lie 2-algebra quasi-isomorphisms connecting Baez-Rogers observables to weak symmetries of geometric structures, extending the classical Kostant-Souriau prequantisation map. Examine these complex mathematical structures through the lens of geometric prequantisation theory as applied to two-pectic manifolds.