  The Wiedemann-Franz law and Mott relation are textbook paradigms on the
ratios of the thermal and thermoelectric conductivities to electrical
conductivity, respectively. Deviations from them usually reveal insights for
intriguing phases of matter. The recent topological kagome magnets
TbMn$_6$Sn$_6$ and Mn$_3$Ge show confusingly opposite derivations in the Hall
measurement. We calculate the topological and disorder corrections to the
Wiedemann-Franz law and Mott relation for the Hall responses in topological
kagome magnets. The calculation indicates the dominance of the topological
correction in the experiments. More importantly, we derive analytic correction
formulas, which can universally capture the two opposite experiments with the
chemical potential as the only parameter and will be a powerful guidance for
future explorations on the magnetic topological matter.
