I have read on several forums like this one, that given a connection form $\omega$ on a principal bundle and its curvature form $\Omega$, I can state that $\Omega=d_\omega\omega$ alike I do in the case of torsion, namely that torsion is the covariant differential of a differential form. To me that does not make sense, because $\Omega=d\omega+\frac{1}{2}[\omega,\omega]$ and there is no representation in which that $\frac{1}{2}$ can arise.
Any explanations?