This paper is a fundamental study of the Real 2-representation theory of 2-groups. It also contains many new results in the ordinary (non-Real) case. Our framework relies on a 2-equivariant Morita bicategory, where a novel construction of induction is introduced. We identify the Grothendieck ring of Real 2-representations as a Real variant of the Burnside ring of the fundamental group of the 2-group and study the Real categorical character theory. This paper unifies two previous lines of inquiry, the approach to 2-representation theory via Morita theory and Burnside rings, initiated by the first author and Wendland, and the Real 2-representation theory of 2-groups, as studied by the second author.

中文翻译：

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实 2 表示理论的 Burnside 环：线性理论

本文是对真实的基础研究2-表征理论2-团体。它还包含在普通（非真实）情况下的许多新结果。我们的框架依赖于2- 等变 Morita 双范畴，其中引入了一种新颖的归纳构造。我们识别 Real 的 Grothendieck 环2- 表示作为基本群的 Burnside 环的 Real 变体2- 分组和研究实分类字符理论。本文统一了之前的两条探究路线，2-通过森田理论和伯恩赛德环的表示理论，由第一作者和温德兰发起，真实2-表征理论2-组，由第二作者研究。