Generalised contact geometry as reduced generalised complex geometry

Generalised contact structures are studied from the point of view of reduced generalised complex structures, naturally incorporating non-coorientable structures as non-trivial fibering. The infinitesimal symmetries are described in detail, with a geometric description given in terms of gerbes. As an application of the reduction procedure, generalised coK\"ahler structures are defined in a way which extends the K\"ahler/coK\"ahler correspondence.