Category theory plays a special role in mathematics — it unifies distinct branches under the same formalism. Despite this integrative power in math, it also seems to provide the proper foundations to the experimental physicist. In this work, we present another application of category in physics, related to the principle of relativity. The operational construction of (inertial) frames of reference indicates that only the movement between one and another frame is enough to differentiate both of them. This fact is hidden when one applies only group theory to connect frames. In fact, rotations and translations only change coordinates, keeping the frame inert. The change of frames is only attainable by boosts in the classical and relativistic regimes for both Galileo and Lorentz (Poincaré) groups. Besides providing a nontrivial example of application of category theory in physics, we also fulfill the presented gap when one directly applies group theory for connecting frames.

范畴论在数学中起着特殊的作用——它将不同的分支统一在同一形式主义下。尽管数学具有这种综合能力，但它似乎也为实验物理学家提供了适当的基础。在这项工作中，我们提出了范畴在物理学中的另一种应用，与相对论原理相关。（惯性）参考系的操作结构表明，仅一个参考系与另一个参考系之间的运动就足以区分它们。当仅应用群论来连接框架时，这一事实就被隐藏了。事实上，旋转和平移只会改变坐标，使框架保持惰性。框架的改变只能通过伽利略群和洛伦兹群（庞加莱群）的经典和相对论体制的提升来实现。除了提供范畴论在物理学中应用的一个重要例子之外，我们还填补了当人们直接应用群论来连接框架时所出现的差距。