论文标题
二维双函数定理和分布定律
2-dimensional bifunctor theorems and distributive laws
论文作者
论文摘要
在本文中，我们考虑了两个具有共同代码的伪造者家族需要满足的条件，以使它们整理成双肢。在提供统一的框架之前，我们可以观察到这些条件与单调的分布定律之间的相似性，从而可以推断出这两个结果。我们通过证明LAX函子的双肢定理的版本来做到这一点。然后，我们表明这些广义分布定律可以安排到2类区域（b，c，d）中，这等同于lax（b，lax（c，d））。分配法对其相关的双交径的整理延伸至2个函数到LAX（$ b \ times c $，d），这对应于通过上述等效性进行的统一。我们还描述了整理本身限制等效的子类别。最后，我们展示了许多自然的分类结构，作为我们结果的特殊情况。
In this paper we consider the conditions that need to be satisfied by two families of pseudofunctors with a common codomain for them to be collated into a bifunctor. We observe similarities between these conditions and distributive laws of monads before providing a unified framework from which both of these results may be inferred. We do this by proving a version of the bifunctor theorem for lax functors. We then show that these generalised distributive laws may be arranged into a 2-category Dist(B,C,D), which is equivalent to Lax(B,Lax(C,D)). The collation of a distributive law into its associated bifunctor extends to a 2-functor into Lax($B \times C$, D), which corresponds to uncurrying via the aforementioned equivalence. We also describe subcategories on which collation itself restricts to an equivalence. Finally, we exhibit a number of natural categorical constructions as special cases of our result.
