Exponential of right group actions
= Exponential of right group actions
{title2=$(fg)(x)=f(xg^{-1})g$}
For a <group>, evaluation at the identity identifies the <monoid> exponential with all set functions $X\to Y$. Its inverse is $e_f(g,x)=f(xg^{-1})g$, and the resulting function action is the displayed formula. Fixed functions are precisely <equivariant maps>. The inverse on the input is necessary for equivariance of evaluation and for the right-action law.