Algebraic classification of equivariant homotopy 2-types, I

Journal article, 1993

We show that the category of diagrams of 2-groupoids indexed by the orbit category View the MathML source(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.