标题： 相对性原理的范畴观点 显示英文标题

标题： A Categorical View on the Principle of Relativity

摘要： 范畴论在数学中扮演着特殊角色——它将不同的分支统一在同一形式化体系下。 尽管在数学中具有这种整合能力，它似乎也为实验物理学家提供了适当的理论基础。 在本工作中，我们提出了范畴论在物理学中的另一个应用，与相对性原理相关。 参考系（惯性）的操作性构造表明，仅有一个参考系相对于另一个参考系的运动就足以区分两者。 当仅使用群论来连接参考系时，这一事实被隐藏了。 事实上，旋转和移动仅改变坐标，保持参考系惯性不变。 在经典和相对论领域，伽利略和洛伦兹（庞加莱）群的参考系变换只能通过加速实现。 除了提供范畴论在物理学中非平凡应用的例子外，我们还填补了当直接使用群论连接参考系时存在的空白。 显示英文摘要

摘要： Category theory plays a special character 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 (Poincar\'e) groups. Besides providing a non-trivial example of application of category theory in physics, we also fulfill the presented gap when one directly applies group theory for connecting frames.