TY - JOUR
T1 - Algebraic classification of equivariant homotopy 2-types, I
AU - Moerdijk, Ieke
AU - Svensson, Jan Alve
N1 - Funding Information:
the Universities of Sydney and Louvain-la-Neuve. We are grateful to these institutions for their hospitality and support, and to Peter May for his general advice on equivariant topology. We would also like to thank Albrecht Dold, Saunders Mac Lane and Ross Street for helpful conversations, and Ronnie Brown for his comments on an earlier version of part of this paper. Finally, we acknowledge support from the Dutch Science Organization (NWO) and the Swedish Natural Science Research Council.
PY - 1993/10/8
Y1 - 1993/10/8
N2 - We show that the category of diagrams of 2-groupoids indexed by the orbit category O(G) of a group G admits a closed Quillen model structure. The associated homotopy category is then proved to be equivalent to the homotopy category of all G-spaces with the property that the nth homotopy group of each fixpoint set vanishes for n≥3. This result is the equivariant analogue of the classical Mac Lane-Whitehead correspondence between crossed modules and pointed connected CW-complexes (X, x0) for which πi(X, x0)=0 for i≥3.
AB - We show that the category of diagrams of 2-groupoids indexed by the orbit category O(G) of a group G admits a closed Quillen model structure. The associated homotopy category is then proved to be equivalent to the homotopy category of all G-spaces with the property that the nth homotopy group of each fixpoint set vanishes for n≥3. This result is the equivariant analogue of the classical Mac Lane-Whitehead correspondence between crossed modules and pointed connected CW-complexes (X, x0) for which πi(X, x0)=0 for i≥3.
UR - http://www.scopus.com/inward/record.url?scp=0000626516&partnerID=8YFLogxK
U2 - 10.1016/0022-4049(93)90094-A
DO - 10.1016/0022-4049(93)90094-A
M3 - Article
AN - SCOPUS:0000626516
SN - 0022-4049
VL - 89
SP - 187
EP - 216
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 1-2
ER -