The fundamental Gray 3-groupoid of a smooth manifold and local 3-dimensional holonomy based on a 2-crossed module

We define the thin fundamental Gray 3-groupoid S3(M)S3(M) of a smooth manifold M   and define (by using differential geometric data) 3-dimensional holonomies, to be smooth strict Gray 3-groupoid maps S3(M)→C(H)S3(M)→C(H), where HH is a 2-crossed module of Lie groups and C(H)C(H) is the Gray 3-groupoid naturally constructed from HH. As an application, we define Wilson 3-sphere observables.