A model structure on the category of pro-simplicial sets
A model structure on the category of pro-simplicial sets
复制标题
准单纯集范畴的模型结构
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
Daniel Isaksen
中科院分区：
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作者：
Daniel Isaksen
我们研究原单纯集的范畴原 SSet，它出现在 etale 同伦理论、形状理论和原有限完备性中。我们在pro-SSet上建立了一个模型结构，使得在这个范畴上进行同伦理论成为可能。这种模型结构与爱德华兹和黑斯廷斯的严格结构密切相关。为了理解原空间的同伦群概念，我们在原空间上使用局部系统。我们还给出了弱等价的几种替代描述，包括上同调表征。我们概述了工业空间的双重结构。
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.