Let G be discrete group and \(\mathcal F\) 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 \(\mathcal F\). This gives a model categorical criterion for maps that induce weak equivalences on H-orbits to be weak equivalences in the \(\mathcal F\)-model structure.

中文翻译：

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等距同构的通过轨道空间的模型结构

令G为离散组，\（\ mathcal F \）为G的子组的集合。我们表明，存在于权利的范畴左诱发模型结构摹-simplicial套，其中弱等价和上纤维化是诱导弱等价和上纤维化在地图上的^ h -orbits所有^ h在\（\ mathcal˚F\ ）。这给出了映射的模型分类准则，该映射将H轨道上的弱等价项诱导为\（\ mathcal F \）模型结构中的弱等价项。