JOURNAL OF HOMOTOPY AND RELATED STRUCTURES, cilt.14, sa.4, ss.1131-1141, 2019 (SCI-Expanded)
Let G be discrete group and F 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 F. This gives a model categorical criterion for maps that induce weak equivalences on H-orbits to be weak equivalences in the F-model structure.