Homology, Homotopy and Applications

Volume 1 (1999)

Number 1

Groupoids and crossed objects in algebraic topology

Pages: 1 – 78

DOI: http://dx.doi.org/10.4310/HHA.1999.v1.n1.a1


Ronald Brown (School of Mathematics, University of Wales, Bangor, Wales, United Kingdom)


This is an introductory survey of the passage from groups to groupoids and their higher dimensional versions, with most emphasis on calculations with crossed modules and the construction and use of homotopy double groupoids.


homotopy theory, groupoids, multiple groupoids, crossed modules, homotopy 2-types, crossed complexes, higher dimensional algebra

2010 Mathematics Subject Classification

01A60, 18Dxx, 18G55, 20Lxx, 55-02, 55-03, 55Q05

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