论文标题
高层理论中的平坦函子
Flat functors in higher topos theory
论文作者
论文摘要
对于一个小$ n $ -category $ \ mathscr {c} $和$ n $ -topos $ \ Mathscr {x} $，我们研究了函数$ f \ colon \ colon \ colon \ colon \ colon \ colon \ mathscr {c} \ to \ nathscr {x} $的必要条件，从$ \ MATHCAL {P}（\ MATHSCR {C}）_ n $ of PRESHEAVES在$ \ Mathscr {C} $上，对于任何$ n \ geq 1 $。这些结果将lurie的结果推广并统一$ n = \ infty $的结果，以及以$ n = 1 $的flat fuctors（dioconescu的定理）的经典特征。有趣的是，对于$ n = \ infty $，我们对Dioconescu定理的类似物需要过度重复。作为一个应用程序，我们表明，与$ n $ loce相关的$ \ infty $ -TOPO作为$ n $ -localic $ \ infty $ -topos相对于超级complete $ \ infty $ -topoi。
For a small $n$-category $\mathscr{C}$ and an $n$-topos $\mathscr{X}$, we study necessary and sufficient conditions for a functor $f \colon \mathscr{C} \to \mathscr{X}$ to determine a geometric morphism from $\mathscr{X}$ to the $n$-topos $\mathcal{P}(\mathscr{C})_n$ of presheaves on $\mathscr{C}$ for any $n \geq 1$. These results generalize and unify results of Lurie for $n=\infty$ and classical characterizations of flat functors (Diaconescu's theorem) for $n=1$. Interestingly, for $n=\infty$, our analogue of Diaconescu's theorem requires hypercompleteness. As an application, we show that the $\infty$-topos associated to an $n$-site behaves as an $n$-localic $\infty$-topos with respect to hypercomplete $\infty$-topoi.
