2001/06/18 by Daniel C. Isaksen · 1 citation
Mathematics · #math.AT #msc:18E35 #msc:55Pxx #msc:55U35 #msc:14F35 #msc:55P60
published as Trans. Amer. Math. Soc. 353 (2001), 2805--2841
arxiv created 2001/06/18 · arxiv updated 2009/11/30
We study the category pro-SSet of pro-simplicial sets, which arises in etale homotopy theory, shape theory, and pro-finite completion. We establish a model structure on pro-SSet so that it is possible to do homotopy theory in this category. This model structure is closely related to the strict structure of Edwards and Hastings. In order to understand the notion of homotopy groups for pro-spaces we use local systems on pro-spaces. We also give several alternative descriptions of weak equivalences, including a cohomological characterization. We outline dual constructions for ind-spaces.