Breen on Gerbes and 2Gerbes
Posted by John Baez
Back in the summer of 2004, at the Institute for Mathematics and its Applications, there was a workshop on $n$categories. It was an intense, exhausting affair. Amid endless talks on various definitions of weak $n$category, Larry Breen gave two talks introducing us to gerbes and 2gerbes. As the conference proceedings slouch slowly towards completion, you can now read his presentation, which has been polished into an excellent paper:

Lawrence Breen, Notes on 1 and 2gerbes, to appear in $n$Categories: Foundations and Applications, eds. J. Baez and P. May.
Abstract: These notes discuss in an informal manner the construction and some properties of 1 and 2gerbes. They are mainly based on the author’s previous work in this area, which is reviewed here, and to some extent improved upon. The main emphasis is on the description of the explicit manner in which one associates an appropriately defined nonabelian cocycle to a given 1 or 2gerbe with chosen local trivializations.
Re: Breen on Gerbes and 2Gerbes
Breen also mentions crossed modules as something
similar but I don’t see the direct comparison. What am I missing?
Since a gerbe is `on a space X’
I assumed the cross module should be over
C^\infty(X)??