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 ModuleThis entry contributed by Margherita Barile
Explore with Wolfram|Alpha
WolframAlpha
More things to try:
Cite this as:
Barile, Margherita. "Tensor Product Functor." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/TensorProductFunctor.html