Could someone provide me a link to the proof of the adjointness of Hom and Tensor. I did an extensive google search but could not find anything self contained that presented the proof in full generality (or at least the generality I know). Let $R\to S$ be a ring homomorphism, let $M,N$ be $S$-modules and $Q$ an $R$-module. Then, we have $$\textrm{Hom}_R(M\otimes_S N,Q) \cong \textrm{Hom}_S(M,\textrm{Hom}_R(N,Q)$$
Adjointness of Hom and Tensor
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abstract-algebra
commutative-algebra
category-theory
tensor-products
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1What definition of the tensor product are you working with? – 2011-04-09
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1Rotman, An introduction to Homological Algebra, 2nd edition, proves it, and calls it the "adjoint isomorphism theorem". – 2011-04-09