Notes on 2-groupoids, 2-groups and crossed-modules

Details Notes on 2-groupoids, 2-groups and crossed-modules Notes on 2-groupoids, 2-groups and crossed-modules

2005-12-05

arxiv.org/abs/math/0512106v3

Homotopy, Homology, and Applications, 9, (2007), no. 1, 75--106

Mathematics

Category Theory

An error in Definition 8.4 corrected. 29 pages

Scientific paper

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.

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