The geometry of the total space of a principal bundle with regard to the action of the bundle's structure group is elegantly described by the bundle's operation, a collection of derivations consisting of the de Rham differential and the contraction and Lie derivatives of all vertical vector fields and satisfying the six Cartan relations. Connections and gauge transformations are defined by the way they behave under the action of the operation's derivations. In the first paper of a series of two extending the ordinary theory, we constructed an operational total space theory of strict principal 2--bundles with reference to the action of the structure strict 2--group. Expressing this latter through a crossed module $(\mathsans{E},\mathsans{G})$, the operation is based on the derived Lie group $\mathfrak{e}[1]\rtimes\mathsans{G}$. In this paper, the second of the series, an original formulation of the theory of $2$--connections and $1$-- and $2$--gauge transformations of principal $2$--bundles based on the operational framework is provided.

中文翻译：

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主 2-bundles II 的操作全空间理论：2-connections 和 1-和 2-gauge 变换

主丛关于丛结构群的作用的总空间几何由丛的运算优雅地描述，一组导数由 de Rham 微分和所有垂直向量场的收缩和李导数组成，满足六嘉当关系。连接和规范转换由它们在操作派生的作用下的行为方式定义。在扩展普通理论的一系列两篇论文的第一篇中，我们参照结构严格2-群的作用构造了严格主2-束的可操作的全空间理论。通过交叉模 $(\mathsans{E},\mathsans{G})$ 表示后者，该运算基于导出的李群 $\mathfrak{e}[1]\rtimes\mathsans{G}$。