Comment on `Index-free Heat Kernel Coefficients'

The article by Anton E. M. van de Ven, Class. Quantum Grav. $\mathbf{\text{15}}$ (1998), is one of the fundamental references for higher-order heat kernel coefficients in curved backgrounds and with non-abelian gauge connections. In this manuscript, we point out two errors and ambiguities in the ${\mathsf{a}}_5$ coefficient, which may also affect the higher-order ones.