Noncommutative near-group fusion categories were completely classified in the previous work of the first author by using an operator algebraic method (and hence under the assumption of unitarity), and they were shown to be group theoretical though the corresponding pointed categories were not identified. In this note we give a purely algebraic construction of the noncommutative near-group fusion categories starting from pointed categories categorically Morita equivalent to them.

中文翻译：

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非对易近群融合范畴的代数实现

非对易近群融合类别在第一作者之前的工作中通过使用算子代数方法（因此在单一性假设下）被完全分类，尽管没有确定相应的指向类别，但它们被证明是群理论的。在这篇笔记中，我们给出了非交换近群融合类别的纯代数构造，从与它们在分类上等价的 Morita 尖类别开始。