We provide the rigorous foundations for a categorical approach to the classification of ${\mathrm{C}}^{⁎}$-dynamics up to cocycle conjugacy. Given a locally compact group G, we consider a category of (twisted) G-${\mathrm{C}}^{⁎}$-algebras, where morphisms between two objects are allowed to be equivariant maps or exterior equivalences, which leads to the concept of so-called cocycle morphisms. An isomorphism in this category is precisely a cocycle conjugacy in the known sense. We show that this category allows sequential inductive limits, and that some known functors on the usual category of G-${\mathrm{C}}^{⁎}$-algebras extend. After observing that this setup allows a natural notion of (approximate) unitary equivalence, the main aim of the paper is to generalize the fundamental intertwining results commonly employed in the Elliott program for classifying ${\mathrm{C}}^{⁎}$-algebras. This reduces a given classification problem for ${\mathrm{C}}^{⁎}$-dynamics to the prevalence of certain uniqueness and existence theorems, and may provide a useful alternative to the Evans–Kishimoto intertwining argument in future research.

我们为分类方法的分类提供了严格的基础 ${\mathrm{C}}^{⁎}$-动力学直至循环共轭。给定一个局部紧群摹，我们考虑（扭曲）的一类摹-${\mathrm{C}}^{⁎}$-代数，其中两个对象之间的态射被允许为等变映射或外部等价，这导致了所谓的cocycle态射的概念。在已知的意义上，这一同构性恰好是cocycle共轭。我们证明了该类别允许连续的归纳极限，并且在G的通常类别上某些已知函子-${\mathrm{C}}^{⁎}$-代数扩展。在观察到这种设置允许（近似）unit等价的自然概念之后，本文的主要目的是概括在Elliott程序中通常用于分类的基本交织结果${\mathrm{C}}^{⁎}$-代数。这减少了给定的分类问题${\mathrm{C}}^{⁎}$-动力学解决了某些唯一性和存在性定理的普遍性，并可能为将来研究中的Evans-Kishimoto交织的争论提供有用的替代方法。