This paper contains some basic results on 2-groupoids, with special emphasis on computing derived mapping 2-groupoids between 2-groupoids and proving their invariance under strictification. Some of the results proven here are presumably folklore (but do not appear in the literature to the author's knowledge) and some of the results seem to be new. The main technical tool used throughout the paper is the Quillen model structure on the category of 2-groupoids introduced by Moerdijk and Svensson.
Homology, Homotopy and Applications, Vol. 9 (2007), No. 1, pp.75-106.
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The version above is dated January 5, 2007 and contains minor corrections. It is the version that will appear in print. An earlier version was made available online on November 23, 2006 and is available here: dvi dvi.gz ps ps.gz pdf