论文标题
数量的开放式封面和拓扑堆栈的可表示
Numerable open covers and representability of topological stacks
论文作者
论文摘要
我们证明，拓扑空间的数字开放式封面类是最小的类，其中包含覆盖层，上面有成对的分离元件和具有两个元素的数字覆盖物，其中有两个元素，在覆盖层的组成和粗化下封闭。我们将此结果应用于建立棕色的类似物的类似物，以实现拓扑空间的数字开放盖：拓扑空间位置上的简单预封面，可满足所有可达的式开放式盖的同型下降属性，并且仅当它满足其可用于具有两个元素的封面和带有配对的分离元素的封面时。我们还证明了这些结果的加强，以确保可以使用两个要素的覆盖物具有特定的简单形式。我们将这些结果应用于类似于Arxiv的拓扑空间上的堆栈的可表示标准：1912.10544。我们还使用这些结果来建立新的简单标准，以实现Abelian群体的链条复合物，以满足同型下降特性。
We prove that the class of numerable open covers of topological spaces is the smallest class that contains covers with pairwise disjoint elements and numerable covers with two elements, closed under composition and coarsening of covers. We apply this result to establish an analogue of the Brown--Gersten property for numerable open covers of topological spaces: a simplicial presheaf on the site of topological spaces satisfies the homotopy descent property for all numerable open covers if and only if it satisfies it for numerable covers with two elements and covers with pairwise disjoint elements. We also prove a strengthening of these results for manifolds, ensuring that covers with two elements can be taken to have a specific simple form. We apply these results to deduce a representability criterion for stacks on topological spaces similar to arXiv:1912.10544. We also use these results to establish new simple criteria for chain complexes of sheaves of abelian groups to satisfy the homotopy descent property.
