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Tensor Product Functor


For every module M over a unit ring R, the tensor product functor - tensor _RM is a covariant functor from the category of R-modules to itself. It maps every R-module N to N tensor _RM and every module homomorphism f:N-->P to the module homomorphism

 f tensor 1:N tensor _RM-->P tensor _RM

defined by

 f tensor 1(n tensor m)=f(n) tensor m.

The tensor product functor M tensor _R- is defined similarly.


See also

Exact Functor, Faithfully Flat Module, Flat Module

This entry contributed by Margherita Barile

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Cite this as:

Barile, Margherita. "Tensor Product Functor." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/TensorProductFunctor.html

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