Computing homotopy types using crossed n-cubes of groups
Abstract:
This paper is a slightly edited version in {\small \LaTeX\ } of the paper
of the same title which appeared in the {\em Adams Memorial Symposium on
Algebraic Topology}, Vol 1, edited N. Ray and G Walker, Cambridge University
Press, 1992, 187-210. It gives a survey of some computational uses in homotopy
theory of various structures related to multiple groupoids.
Published in:
Adams Memorial Symposium on Algebraic Topology,
Vol 1, ed. N. Ray & G Walker, Cambridge Univ. Press (1992) 187-210.
The category of cubical sets with connections of Brown and Higgins
is introduced as a possible alternative to simplicial complexes
for carrying out a programme of combinatorial homotopy theory.
This paper provides a result crucial to the development of this theory,
that group objects in the category of cubical sets with connections
have the property of being Kan.
