Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

The classifying space of a crossed complex

Ronald Browna1 and Philip J. Higginsa2

a1 School of Mathematics, University of Wales, Dean Street, Bangor, Gwynedd LL57 1UT

a2 Department of Mathematical Sciences, University of Durham, Science Laboratories, South Road, Durham DH1 3LE

The aim of this paper is to show one more facet of the role of crossed complexes as generalisations of both groups (or groupoids) and of chain complexes. We do this by defining and establishing the main properties of a classifying space functor B: S0305004100070158_inline001 from the category of crossed complexes to the category of spaces.

(Received August 20 1990)

(Revised December 05 1990)