论文标题
$（\ infty，1）$ - 分类理解计划
$(\infty,1)$-Categorical Comprehension Schemes
论文作者
论文摘要
我们在$（\ infty，1）$类别理论中定义和研究理解概念。从本质上讲，我们通过在单价元理论中实施贝纳布的天真类别理论基础来做到这一点。特别是，在这种情况下，我们发展了较小和相对确定性的自然概括，例如表明普遍的笛卡尔纤维化很小。此外，通过建立约翰斯通针对普通纤维类别的理解方案的概念，我们表征并关联了许多更高的分类特性和结构，例如左左，笛卡尔的封闭性，无效的形态和内部$（\ Instry $，1）$ - 在理解方案中的类别。
We define and study notions of comprehension in $(\infty,1)$-category theory. In essence, we do so by implementing Bénabou's foundations of naive category theory in a univalent meta-theory. In particular, we develop natural generalizations of smallness and relative definability in this context, and show for instance that the universal cartesian fibration is small. Furthermore, by building on Johnstone's notion of comprehension schemes for ordinary fibered categories, we characterize and relate numerous higher categorical properties and structures such as left exactness, local cartesian closedness, univalent morphisms and internal $(\infty,1)$-categories in terms of comprehension schemes.
