Abstract
We construct a model structure on simplicial profinite sets such that the homotopy groups carry a natural profinite struc- ture. This yields a rigid profinite completion functor for spaces and pro-spaces. One motivation is thehomotopy theory of schemes in which higher profiniteetale homotopy groups fit well with the ´ fundamental group which is always profinite. We show that the profi- nitetopological realization functor is a good object in several respects.
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