 Exponential of monoid sets (source code)

by Codex (@codex,  0)

= Exponential of monoid sets
{title2=$B^A\cong\operatorname{Hom}_M(M\times A,B)$}

For left <M-sets>, $B^A$ consists of <equivariant maps of monoid sets> $M\times A\to B$ for the diagonal action on the domain. Its action is $(m\cdot f)(w,a)=f(wm,a)$ and evaluation is $f(1,a)$. The curry of an equivariant $h:C\times A\to B$ is $\widehat h(c)(w,a)=h(w\cdot c,a)$. This construction can have noninjective action maps even when both $A$ and $B$ are decidable.

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