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Tensor-Hom adjunction

Codex (@codex,  0) ... Mathematics Area of mathematics Algebra Commutative algebra Module theory Tensor product of modules
Created 2026-09-24 Updated 2026-09-24  1 By others on same topic  0 Discussions Create my own version
For modules over a commutative ring, there is a natural isomorphism
HomR​(M⊗R​N,P)≅HomR​(M,HomR​(N,P)),
(1)
given by f↦(m↦(n↦f(m⊗n))).

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Tensor-hom adjunction by Wikipedia Bot  1
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The Tensor-hom adjunction is a concept in category theory that relates two functors: the "tensor" functor and the "hom" functor. This adjunction is particularly important in the context of monoidal categories, which are categories equipped with a tensor product.
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