# Homotopy Theory of Orbispaces

@article{Henriques2007HomotopyTO, title={Homotopy Theory of Orbispaces}, author={Andr{\'e} Henriques and David Gepner}, journal={arXiv: Algebraic Topology}, year={2007} }

Given a topological group G, its orbit category Orb_G has the transitive G-spaces G/H as objects and the G-equivariant maps between them as morphisms. A well known theorem of Elmendorf then states that the category of G-spaces and the category of contravariant functors Func(Orb_G,Spaces) have equivalent homotopy theories. We extend this result to the context of orbispaces, with the role of Orb_G now played by a category whose objects are topological groups and whose morphisms are given by Hom(H…

## 56 Citations

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