The n-Category Café

As $n$-Café-regulars know, this is based on our series of joint articles

U. S., K. W.
Parallel transport and functors
(blog, arXiv)
Smooth 2-functors and differential forms
(blog, arXiv)
Connections on nonabelian gerbes and their holonomy
(blog, arXiv)

which in turn goes back to my joint work with John Baez

J. B. , U.S.
Higher gauge theory
(blog, arXiv)

and my thesis (blog, arXiv), where the diagrams for 2-holonomy first appeared, which we now identified as cells in the codescent 2-groupoid (the 2-groupoid of “2-paths in the Čech 2-groupoid”) and describe in precise detail. I had already talked about the basic idea in Vietri 05, where I also met Roger Picken whose work

M. Mackaay, R. Picken
Holonomy and parallel transport for abelian gerbes
(arXiv)

was very influential for the development of Higher gauge theory (John Baez’s review page) aka nonabelian differential cohomology (lecture notes).

Just recently Roger Picken with João Martins followed up on this in the non-abelian context

J. Martins, R. Picken
On two-dimensional holonomy
(arXiv)
Cubical 2-bundles with connection and Wilson spheres
(arXiv)

They use the cubical model for 2-groupoids where we use the globular one, but our two discussions of nonabelian differential cocycles are otherwise pretty close.