论文标题
双变量Yoneda引理和$（\ infty，2）$ - 通信类别
A bivariant Yoneda lemma and $(\infty,2)$-categories of correspondences
论文作者
论文摘要
每个人都知道，如果您有一个满足基本变化公式的双变量同源理论，则可以代表一类通信。对于协方差和逆转转移图在相互关联的理论，这些数据实际上是等效的。换句话说，对应关系的2类是连接到给定1类的通用方法，一组可满足基本变更公式的正确伴随。 通过Yoneda范式的双变量版本，我给出了更高类别理论中的对应关系的定义，并证明了Bivariant函数的扩展定理。此外，基于二维Grothendieck结构的存在，我提供了上述普遍性的证明。从道德上讲，这些方法采用了高级理论的“内部逻辑”：它们不明确使用任何特定模型。
Everyone knows that if you have a bivariant homology theory satisfying a base change formula, you get an representation of a category of correspondences. For theories in which the covariant and contravariant transfer maps are in mutual adjunction, these data are actually equivalent. In other words, a 2-category of correspondences is the universal way to attach to a given 1-category a set of right adjoints that satisfy a base change formula. Through a bivariant version of the Yoneda paradigm, I give a definition of correspondences in higher category theory and prove an extension theorem for bivariant functors. Moreover, conditioned on the existence of a 2-dimensional Grothendieck construction, I provide a proof of the aforementioned universal property. The methods, morally speaking, employ the `internal logic' of higher category theory: they make no explicit use of any particular model.
