论文标题
高层理论I：对应关系
Higher sheaf theory I: Correspondences
论文作者
论文摘要
我们证明了$（\ infty，n）$ - 信件类别的通用财产，从[GR17]中概括并提供新的证明$ n = 2 $。我们还提供了条件，在$ \ MATHCAL {C} $的较高类别的对应关系中，可以将函数扩展到$ \ Mathcal {C} $的免费共完成的更高类别的通信。这些结果将在本文的续集中用于构建$（\ ind，n）$ - 在派生的代数几何形状中的准植物和indosoherent Sheaves理论的分类版本。
We prove a universal property for the $(\infty, n)$-category of correspondences, generalizing and providing a new proof for the case $n = 2$ from [GR17]. We also provide conditions under which a functor out of a higher category of correspondences of $\mathcal{C}$ can be extended to a higher category of correspondences of the free cocompletion of $\mathcal{C}$. These results will be used in the sequels to this paper to construct $(\infty, n)$-categorical versions of the theories of quasicoherent and ind-coherent sheaves in derived algebraic geometry.
