Abstract We further the techniques developed by Etingof, Nikshych, and Ostrik in [7] to classify the C -based equivalences between two G-graded extensions of C , in terms of cohomological data. As a warm up for the proof of our classification result we reprove the classification of graded extensions of a fusion category, making extensive use of graphical calculus. We end by providing several practical applications of our classification result. These practical applications include methods to determine when two distinct G-graded extensions are monoidally equivalent, and tools to help compute the group of gauge auto-equivalences of a G-graded category.

中文翻译：

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分级融合类别的等价物

摘要 我们进一步使用了 Etingof、Nikshych 和 Ostrik 在 [7] 中开发的技术，根据上同调数据对 C 的两个 G 分级扩展之间基于 C 的等价进行分类。作为对我们分类结果证明的热身，我们重新证明了融合类别的分级扩展的分类，广泛使用了图形演算。我们最后提供了分类结果的几个实际应用。这些实际应用包括确定两个不同的 G 分级扩展何时是幺半群等价的方法，以及帮助计算 G 分级类别的规范自动等价组的工具。