A model structure via orbit spaces for equivariant homotopy
Erdal, Mehmet Akif
Güçlükan İlhan, Aslı
Journal of Homotopy and Related Structures
1131 - 1141
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Let G be discrete group and FF be a collection of subgroups of G. We show that there exists a left induced model structure on the category of right G-simplicial sets, in which the weak equivalences and cofibrations are the maps that induce weak equivalences and cofibrations on H-orbits for all H in FF. This gives a model categorical criterion for maps that induce weak equivalences on H-orbits to be weak equivalences in the FF-model structure.