The large-structure tools of cohomology including toposes and derived categories stay close to arithmetic in practice, yet published foundations for them go beyond ZFC in logical strength. We reduce the gap by founding all the theorems of Grothendieck’s SGA, plus derived categories, at the level of Finite-Order Arithmetic, far below ZFC. This is the weakest possible foundation for the large-structure tools because one elementary topos of sets with infinity is already this strong.

中文翻译：

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基于有限阶算术的格罗腾迪克大结构

包括拓扑和派生类别在内的大型上同调结构工具在实践中与算术保持接近，但已发表的它们的基础在逻辑强度上超越了 ZFC。我们通过在远低于 ZFC 的有限阶算术级别上建立格洛腾迪克 SGA 的所有定理以及派生类别来缩小差距。这是大型结构工具可能最薄弱的基础，因为具有无穷大的集合的一个基本拓扑已经如此强大。