 Yang-Mills gauge transformation

For $D_{\mu }={\partial }_{\mu }-ig{A}_{\mu }$ and matter transforming as $\psi \mapsto U\psi$, a Yang-Mills connection transforms inhomogeneously while its curvature transforms by conjugation, $F_{\mu \nu }\mapsto U{F}_{\mu \nu }{U}^{-1}$.