Quote by john baez
It's hot up here in Waterloo, Canada!
...
In the Poincare 2group, the group of objects is the group of Lorentz
transformations, and the group of morphisms is the Poincare group.
That doesn't completely describe the Poincare 2group. You need to
know some other stuff, like:
If you have a morphism in here, which object does it start at, and
which object does it end at?
There's only one sensible answer to this question, I think, so I'll leave it as a puzzle.
You also need to decide how to compose morphisms. I'll leave that as a (harder) puzzle.

About the puzzleI think selfAdjoint has already figured it out but I did not follow all the discussion, so I will take a guess.
Someone, I think it was JB, suggested using letters T and S for "twist" and "shift", where T is an element of the Lorentz group and S is thought of as a translation (we are building the Poincaré group)
[SNIP]
[EDIT] GROAN. I just looked at the "Higher Yang Mills" paper that I lost a couple of days ago, while cleaning up the living room. the Poincaré 2group is explained as EXAMPLE 9. So the puzzle was already answered.
[/EDIT]
...I talked to Kea and she suggested one by Girelli and Pfeiffer, which I never got around to looking at it. Maybe I will now.
http://arxiv.org/abs/hepth/0309173
Higher gauge theory  differential versus integral formulation
Florian Girelli, Hendryk Pfeiffer
26 pages
DAMTP200386
J.Math.Phys. 45 (2004) 39493971
"The term higher gauge theory refers to the generalization of gauge theory to a theory of connections at two levels, essentially given by 1 and 2forms. So far, there have been two approaches to this subject. The differential picture uses nonAbelian 1 and 2forms in order to generalize the connection 1form of a conventional gauge theory to the next level. The integral picture makes use of curves and surfaces labeled with elements of nonAbelian groups and generalizes the formulation of gauge theory in terms of parallel transports..."
I hope Kea is better now and was wishing she would suddenly materialize amidst this thread.
Well, looking at Girelli/Pfeiffer, I see right away references
[15] J. C. Baez: Higher Yang–Mills theory (2002). Preprint hepth/0206130.
[19] J. C. Baez and A. Crans: Higher dimensional algebra VI: Lie 2algebras (2003). Preprint math.QA/0307263.
My posts are just not helpful in this thread at this point. I shall delete the next one.