On finite induced crossed modules and the homotopy 2-type of mapping cones,

Ronald Brown and Christopher D. Wensley

Results on the finiteness of induced crossed modules are proved both algebraically and topologically. Using the Van Kampen type theorem for the fundamental crossed module, applications are given to the 2-types of mapping cones of classifying spaces of groups. Calculations of the cohomology classes of some finite crossed modules are given, using crossed complex methods.

Keywords: crossed modules, homotopy 2­types, generalised van Kampen Theo­ rem, crossed resolution, Postnikov invariant.

AMS Classification (1991): 18G10, 20F38, 55P15, 55Q20.

Theory and Applications of Categories, Vol. 1, 1995, No. 3, pp 54-71.


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