The categorical kinematics is a groupoid-\textit{category} of the massive observers, with binary relative velocities as the invertible morphisms, instead of the isometric Lorentz transformations. In categorical kinematics the \textit{inverse} relative velocity, v^-1, must be interior-observer-dependent, and no more necessarily absolute as in the Einstein's isometric formulation, where v^-1≡-v. Within the categorical kinematics the transformation of the electric and magnetic fields relative to the moving observer, is slightly different, when compared with the transformations deduced by Heaviside in 1888-1889, derived by Lorentz in 1904, and by Einstein in 1905.

The adopted differential co-frame of not necessarily inertial observer, is not unique. The general transformations among adopted co-frames of observers are derived in terms of the binary relative velocity. These frame-transformations generalize the Robertson's test-theory of special relativity, for the categorical kinematics.

The main conclusion: observer-independence/dependence and the Lorentz-invariance/covariance are different concepts. The same statement holds in Newtonian physics: observer-independence is not be the same as the Galilean-group-invariance.