Hypercovers and simplicial presheaves
Hypercovers and simplicial presheaves
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DOI：
10.1017/s0305004103007175
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发表时间：
2002-05
影响因子：
0.8
通讯作者：
Daniel Dugger;Sharon Hollander;Daniel Isaksen
中科院分区：
文献类型：
--
作者：
Daniel Dugger;Sharon Hollander;Daniel Isaksen
我们利用超覆盖来研究单纯预凸集的同伦理论。主要结果表明，含有局部弱等价的单纯形预沉的模型结构可以通过在超覆盖上的局部化来构造。一个结果是，Fibrant对象可以用超覆盖下降条件来显式描述，而纤颤可以用相对下降条件来描述。我们给出了单纯预垂性同伦理论的这种新刻画的几个应用。
We use hypercovers to study the homotopy theory of simplicial presheaves. The main result says that model structures for simplicial presheaves involving local weak equivalences can be constructed by localizing at the hypercovers. One consequence is that the fibrant objects can be explicitly described in terms of a hypercover descent condition, and the fibrations can be described by a relative descent condition. We give a few applications for this new description of the homotopy theory of simplicial presheaves.