= Gauge equivalence of principal connections
{title2=$A\sim g^{-1}Ag+g^{-1}dg$}
A gauge transformation is an automorphism of a <principal bundle> covering the identity on the base and commuting with its right group action. Pullback relates gauge-equivalent <principal connections>. Locally it acts by the displayed formula; the <gauge curvature> transforms by conjugation. Gauge functions on overlapping charts satisfy the bundle's transition compatibility. Infinitesimally $g=e^\varepsilon$ gives $\delta A=D_A\varepsilon$.
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