发表机构
University of Kentucky; Kettering University（肯塔基大学; 凯特林大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为2-表示构建了基于双范畴迹的直观特征标理论，与限制和归纳相容，并在有限情形下具有次级特征标。
AI 中文摘要
群表示非常自然地允许高范畴化推广。这包括2-表示的归纳与限制，它们非常直接地平行于经典定义。然而，2-表示的恰当特征标理论一直较为模糊。在本文中，我们汲取多种动机，为2-表示提供一种直观的特征标理论。该理论建立在为描述拓扑不动点理论而发展的双范畴迹之上。我们使用Ben-Zvi和Nadler的次级迹，它们在微分分次范畴和Fourier-Mukai变换的背景下与Riemann-Roch和Lefschetz型定理相关联。其他动机来源包括Lipman关于Grothendieck对偶的工作，以及关键的Bartlett和Ganter--Kapranov的特征标方法。（后者又受到Hopkins、Kuhn和Ravenel关于等变Morava $E$-理论工作的启发。）我们的特征标与限制和归纳相容，并且在足够有限的情形下，允许一个次级特征标。
英文摘要
Group representations very comfortably admit a higher categorical generalization. This includes induction and restriction for 2-representations that very directly parallel classical definitions. An appropriate character theory for 2-representations has been more opaque. In this paper we draw from a range of motivations to provide an intuitive character theory for 2-representations. It is built from the bicategorical trace developed to describe topological fixed point theory. We use the secondary traces of Ben-Zvi and Nadler which connect to Riemann-Roch and Lefschetz-type theorems in the context of differential graded categories and Fourier-Mukai transforms. Additional sources of motivation include Lipmans' work on Grothendieck duality and, crucially, the Bartlett and Ganter--Kapranov approaches to characters. (The second of these was in turn motivated by Hopkins, Kuhn and Ravenel's work on equivariant Morava $E$-theories.) Our characters are compatible with restriction and induction and, in cases that are sufficiently finite, admit a secondary character.
