Electric and magnetic elds are relative. They depend not only on a choice of electromagnetic sources via Maxwell equations, but also on a choice of observer, a choice of material reference-system. In 1908 Minkowski defi ned electric and magnetic fields on a four-dimensional spacetime, as tensorial concomitants of observer. Minkowski de ned Lorentzgroup-covariance of concomitant tensor eld as group-action that commute with contractions. Present-day textbooks interpret Lorentz-group-covariance of concomitant tensor di erently than Minkowski in 1908. In 2003-2005 Tomislav Ivezic re-invented Minkowski's group-covariance. Diff erent interpretations of group-covariance, lead to di fferent relativity transformations of electric and magnetic fields.
An objective of present article is to explore third possibility, implicit in [Minkowski 1908, x11.6], where a set of all relativity transformations of all material observers forms a groupoid category, which is not a group.
