论文标题
松弛的单体辅助，两变量纤维和伴侣的演算
Lax monoidal adjunctions, two-variable fibrations and the calculus of mates
论文作者
论文摘要
我们为$ \ infty $ - 类别的$ \ infty $ - 类别提供了伴侣的计算，并扩展了Lurie的含量不高的等价，以表明（op）LAX LAX自然变换对应于（CO）笛卡尔式纤维的地图，不一定保留（CO）卡车仪式。作为样品应用，我们在右伴函数上的LAX对称单体结构与左伴随函数上的Oplax对称单相结构之间的等效性之间的等效性之间的对称性单体$ \ indoidal $ \ infty $ - 与此类结构的水平和垂直组成兼容。 作为论文的技术核心，我们研究了两种$ \ infty $类别的产品的各种新型纤维。特别是，我们展示了如何将它们与两个因素之一划分，以及它们如何从$（\ infty，2）$类别的灰色张量产品中编码函子。
We provide a calculus of mates for functors to the $\infty$-category of $\infty$-categories and extend Lurie's unstraightening equivalences to show that (op)lax natural transformations correspond to maps of (co)cartesian fibrations that do not necessarily preserve (co)cartesian edges. As a sample application we obtain an equivalence between lax symmetric monoidal structures on right adjoint functors and oplax symmetric monoidal structures on the left adjoint functors between symmetric monoidal $\infty$-categories that is compatible with both horizontal and vertical composition of such structures. As the technical heart of the paper we study various new types of fibrations over a product of two $\infty$-categories. In particular, we show how they can be dualised over one of the two factors and how they encode functors out of the Gray tensor product of $(\infty, 2)$-categories.
