  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.
