论文标题
弱球状双重类别和弱单元
Weakly globular double categories and weak units
论文作者
论文摘要
基于弱球形的概念，弱的球状双重类别是一个弱$ 2 $类别的模型，众所周知，它们与tamsamani $ 2 $ - 类别相当。公平的$ 2 $ - 类别，由J. Kock介绍，模型弱$ 2 $ - 具有严格关联组成和弱单位法律的类别。在本文中，我们建立了弱的球状双重类别与公平$ 2 $类别之间的直接比较，并证明它们在本地化后与$ 2 $ - 等价性相同。这种比较为弱球状双重类别提供了新的启示，因为它通过弱球状条件编码了严格的关联，尽管不是严格的，构图，以及弱单位的类别。
Weakly globular double categories are a model of weak $2$-categories based on the notion of weak globularity, and they are known to be suitably equivalent to Tamsamani $2$-categories. Fair $2$-categories, introduced by J. Kock, model weak $2$-categories with strictly associative compositions and weak unit laws. In this paper we establish a direct comparison between weakly globular double categories and fair $2$-categories and prove they are equivalent after localisation with respect to the $2$-equivalences. This comparison sheds new light on weakly globular double categories as encoding a strictly associative, though not strictly unital, composition, as well as the category of weak units via the weak globularity condition.
