论文标题
$ \ infty $ -Topoi II的左置本地化：Grothendieck拓扑
Left-exact Localizations of $\infty$-Topoi II: Grothendieck Topologies
论文作者
论文摘要
我们使用新的无环类和一致性的工具来重新审视Toën-Vezzosi和Lurie在Grothendieck拓扑上的工作。我们介绍了关于任何$ \ infty $ -TOPOS的扩展Grothendieck拓扑的概念，并证明了扩展的Grothendieck拓扑的位置与拓扑结构，拓扑本地化，律师 - 蒂尔尼拓扑结构的拓扑结构相关，这是同构的（律师拓扑，以及对Premopopology ot the Promopopology的变种）。因此，这些poset很小，并且具有框架的结构。我们还通过引入共同形态的概念来重新审视拓扑结构分解。我们重新审视了与扩展的Grothendieck拓扑相关的过度重复，超沉淀，超覆盖和超轨的概念。我们还介绍了强迫的概念，该概念是用于计算$ \ infty $ -topoi的工具。
We revisit the work of Toën--Vezzosi and Lurie on Grothendieck topologies, using the new tools of acyclic classes and congruences. We introduce a notion of extended Grothendieck topology on any $\infty$-topos, and prove that the poset of extended Grothendieck topologies is isomorphic to that of topological localizations, hypercomplete localizations, Lawvere--Tierney topologies, and covering topologies (a variation on the notion of pretopology). It follows that these posets are small and have the structure of a frame. We revisit also the topological--cotopological factorization by introducing the notion of a cotopological morphism. And we revisit the notions of hypercompletion, hyperdescent, hypercoverings and hypersheaves associated to an extended Grothendieck topology. We also introduce the notion of forcing, which is a tool to compute with localizations of $\infty$-topoi.
