This paper develops a framework based on category theory which unifies the simultaneous consideration of timepoints, metrical relations, and meter inclusion founded on the category $\mathbf{R}\mathbf{e}\mathbf{l}$ of sets and binary relations. Metrical relations are defined as binary relations on the set of timepoints, and the subsequent use of the monoid they generate and of the corresponding functor to $\mathbf{R}\mathbf{e}\mathbf{l}$ allows us to define meter networks, i.e. networks of timepoints (or sets of timepoints) related by metrical relations. We compare this to existing theories of metrical conflict, such as those of Harald Krebs and Richard Cohn, and illustrate that these tools help to more effectively combine displacement and grouping dissonance and reflect analytical claims concerning nineteenth-century examples of complex hemiola and twentieth-century polymeter. We show that meter networks can be transformed into each other through meter network morphisms, which allows us to describe both meter displacements and meter inclusions. These networks are applied to various examples from the nineteenth and twentieth century.

本文开发了一个基于范畴论的框架，该框架统一了基于范畴的时间点、度量关系和计量包含的同时考虑$\mathbf{R}\mathbf{e}\mathbf{l}$集合和二元关系。度量关系被定义为时间点集上的二元关系，随后使用它们生成的幺半群和相应的仿函数来$\mathbf{R}\mathbf{e}\mathbf{l}$允许我们定义计量网络，即由度量关系相关的时间点（或时间点集）网络。我们将其与现有的度量冲突理论进行比较，例如 Harald Krebs 和 Richard Cohn 的理论，并说明这些工具有助于更有效地将位移和分组不和谐结合起来，并反映有关 19 世纪复杂 hemiola 和 20 世纪例子的分析主张万用表。我们表明，仪表网络可以通过仪表网络态射相互转换，这使我们能够描述仪表位移和仪表包含。这些网络适用于 19 世纪和 20 世纪的各种示例。