On the global 2-holonomy for a 2-connection on a 2-bundle

A crossed module constitutes a strict 2-groupoid G and a G-valued 2-cocycle on a manifold defines a 2-bundle. A 2-connection on this 2-bundle is given by a Lie algebra g valued 1-form A and a Lie algebra h valued 2-form B over each coordinate chart together with 2-gauge transformations between them, which satisfy the compatibility condition. Locally, the path-ordered integral of A gives us the local 1-holonomy, and the surface-ordered integral of (A,B) gives us the local 2-holonomy. The transformation of local 2-holonomies from one coordinate chart to another is provided by the transition 2-arrow, which is constructed from a 2-gauge transformation. We can use the transition 2-arrows and the 2-arrows provided by the G-valued 2-cocycle to glue such local 2-holonomies together to get a global one, which is well defined. Namely we give an explicit algorithm for calculating the global 2-holonomy.