A model structure on the category of pro-simplicial sets

By Daniel Isaksen. 2001

84 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/a4e111a4f60e147d572fe6c6a415c854981133d2

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Citations in the corpus

Strict Model Structures for Pro-categories (2001, unknown): “A T ] 2 8 A ug”
Calculating limits and colimits in pro-categories (2001, background): “) In several recent projects involving pro-categories [4] [10] [11] [12], we have found it necessary to compute various limits and colimits.”
More Concise Algebraic Topology: Localization, Completion, and Model Categories (2012, background): “There are interesting model categories for which the factorizations cannot be chosen to be functorial (see for example [68]), but they can be so chosen in the examples that are most commonly used.”
Profinite homotopy theory (2008, methodology): “equip pro-S with the model structure of [ 16 ].”