A model structure on the category of pro-simplicial sets

Details A model structure on the category of pro-simplicial sets A model structure on the category of pro-simplicial sets

2001-06-18

arxiv.org/abs/math/0106152v1

Trans. Amer. Math. Soc. 353 (2001), 2805--2841

Mathematics

Algebraic Topology

Scientific paper

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.

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