Homology, Homotopy and Applications

Volume 9 (2007)

Number 1

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

Pages: 75 – 106

DOI: https://dx.doi.org/10.4310/HHA.2007.v9.n1.a3


Behrang Noohi (Mathematics Department, Florida State University, Tallahassee, Fl., U.S.A.)


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, 2-group, 2-groupoid, crossed module, 2-type, lax 2-functors, weak 2-functors

2010 Mathematics Subject Classification

18D05, 18G50, 55U40

Published 1 January 2007

An earlier version of this article was made available online on November 23, 2006.