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I am bit short with time, so for the moment I'll just say: there is the entry principal 2-bundle and the links it contains, that is about the notion of torsors over a 2-group. Looking at the entry, I see that this is very stubby, though.
I have found Larry Breen's various notes on torsors etc. to be very helpful. There has also recently been some papers by Aldrovandi and Noohi (one already published in Advances) that gives a nice treatment. Finally the Menagerie notes by myself do have the background on this but not, I think, in the version that you can get from my n-Lab pages. Have a look at those and see if they help.
and someone please make sure that this is linked to from some nLab page...
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