Notes on Lax Ends
Notes on Lax Ends
复制标题
关于宽松结束的注意事项
DOI：
--
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Kengo Hirata
中科院分区：
文献类型：
--
作者：
Kengo Hirata
在丰富的范畴理论中，自然外变换的概念比普通自然变换的概念更基本，而目的--普遍的自然变换--起着至关重要的作用。另一方面，2-范畴理论利用了其他几种自然变换，例如松弛变换和伪变换。对于这些弱变换，我们知道我们可以fiNe相应的自然外变换或结束。然而，很少有文献详细描述这样的结果。我们提供了一个关于Lax末端的详细计算，包括它与Lax极限的关系。我们证明了双范畴Coyoneda引理是双范畴Yoneda引理的对偶，还证明了任意松散端的权是饼权，但它可能不是松弛极限的权。
In enriched category theory, the notion of extranatural transformations is more fundamental than that of ordinary natural transformations, and the ends, the universal extranatural transformations, play a critical role. On the other hand, 2-category theory makes use of several other natural transformations, such as lax and pseudo transformations. For these weak transformations, it is known that we can define the corresponding extranatural transformations or ends. However, there is little literature describing such results in detail. We provide a detailed calculation of the lax end, including its relation to the lax limits. We prove the bicategorical coYoneda lemma as the dual of the bicategorical Yoneda lemma, and also show that the weight of any lax end is a PIE weight, but it might not be a weight for a lax limit.