Transactions of the American Mathematical Society

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ISSN 1088-6850(e) ISSN 0002-9947(p)

A model structure on the category of pro-simplicial sets

Author(s): Daniel C. Isaksen
Journal: Trans. Amer. Math. Soc. 353 (2001), 2805-2841.
MSC (2000): Primary 18E35, 55Pxx, 55U35; Secondary 14F35, 55P60
Posted: January 29, 2001
MathSciNet review: 1828474
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Abstract:

We study the category ${pro-}\mathcal{SS}$ of pro-simplicial sets, which arises in étale homotopy theory, shape theory, and pro-finite completion. We establish a model structure on ${pro-}\mathcal{SS}$ 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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