论文标题
$ \ textbf {灰色} $ - 分类粘贴定理
A $\textbf{Gray}$-categorical pasting theorem
论文作者
论文摘要
$ \ textbf {灰色} $ - 类别的概念，一种半图片$ 3 $ - 类别，其中中间四个交叉互换削弱了同构，在三维类别理论的研究中是核心。在这种情况下，通常使用$ 2 $维粘贴图来表达$ 2 $ cells的复合材料是普遍的做法，但是在文献中没有彻底的治疗方法可以证明此过程是合理的。我们通过在$ \ textbf {灰色} $类别中提供正式粘贴方法来填补这一空白，并通过证明此类复合材料的定义是唯一的，可以选择合同的选择。
The notion of $\textbf{Gray}$-category, a semi-strict $3$-category in which the middle four interchange is weakened to an isomorphism, is central in the study of three-dimensional category theory. In this context it is common practice to use $2$-dimensional pasting diagrams to express composites of $2$-cells, however there is no thorough treatment in the literature justifying this procedure. We fill this gap by providing a formal approach to pasting in $\textbf{Gray}$-categories and by proving that such composites are uniquely defined up to a contractible groupoid of choices.
