Set partitions closed under certain operations form a tensor category. They give rise to certain subgroups of the free orthogonal quantum group [Formula: see text], the so-called easy quantum groups, introduced by Banica and Speicher in 2009. This correspondence was generalized to two-colored set partitions, which, in addition, assign a black or white color to each point of a set. Globally colorized categories of partitions are those categories that are invariant with respect to arbitrary permutations of colors. This paper presents a classification of globally colorized categories. In addition, we show that the corresponding unitary quantum groups can be constructed from the orthogonal ones using tensor complexification.

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分区的全局彩色类别分类

在某些操作下关闭的集合分区形成张量类别。它们产生了自由正交量子群 [公式：见正文] 的某些子群，即所谓的易量子群，由 Banica 和 Speicher 在 2009 年引入。这种对应关系被推广到双色集分区，此外，为集合的每个点分配黑色或白色。分区的全局彩色类别是那些相对于任意颜色排列不变的类别。本文介绍了全局彩色类别的分类。此外，我们证明了相应的单一量子群可以使用张量复化从正交的量子群构建。