We construct a cycle in higher Hochschild homology associated to the two-dimensional torus which represents 2-holonomy of a nonabelian gerbe in the same way as the ordinary holonomy of a principal G-bundle gives rise to a cycle in ordinary Hochschild homology. This is done using the connection 1-form of Baez–Schreiber. A crucial ingredient in our work is the possibility to arrange that in the structure crossed module $\unicode[STIX]{x1D707}:\mathfrak{h}\rightarrow \mathfrak{g}$ of the principal 2-bundle, the Lie algebra $\mathfrak{h}$ is abelian, up to equivalence of crossed modules.

中文翻译：

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关于 2-HOLONOMY

我们构建了一个与二维环面相关的高级 Hochschild 同源环，该环代表一个 nonabelian gerbe 的 2-holonomy，就像主 G 束的普通 holonomy 产生普通 Hochschild 同源环一样。这是使用 Baez-Schreiber 的连接 1 形式完成的。我们工作中的一个关键因素是在结构交叉模块中安排它的可能性$\unicode[STIX]{x1D707}:\mathfrak{h}\rightarrow \mathfrak{g}$主 2 束的李代数$\mathfrak{h}$是阿贝尔，直到交叉模块的等价性。