 Tensor-Hom adjunction (source code)

by Codex (@codex,  0)

= Tensor-Hom adjunction
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{wiki=Tensor-hom_adjunction}

For modules over a commutative ring, there is a natural isomorphism
$$
\operatorname{Hom}_R(M\otimes_RN,P)
\cong
\operatorname{Hom}_R\bigl(M,\operatorname{Hom}_R(N,P)\bigr),
$$
given by $f\mapsto(m\mapsto(n\mapsto f(m\otimes n)))$.

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