= Exponential of right monoid actions
{title2=$Y^X=\operatorname{Hom}_M(M\times X,Y)$}
Give $M\times X$ the diagonal <right monoid action>. On its <equivariant maps> into $Y$, define $(ek)(g,x)=e(kg,x)$. The <evaluation map of an exponential object> is $e(1,x)$ and <currying> of $h:Z\times X\to Y$ is $\widehat h(z)(g,x)=h(zg,x)$. Both maps are equivariant, and they are inverse under evaluation. The left multiplication $kg$ in this right action is essential in a noncommutative <monoid>.
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