In mathematics, specifically homological algebra, the Eilenberg–Watts theorem tells when a functor between the categories of modules is given by an application of a tensor product. Precisely, it says that a functor F : M o d R → M o d S {\displaystyle F:\mathbf {Mod} _{R}\to \mathbf {Mod} _{S}} is additive, is right-exact and preserves coproducts if and only if it is of the form F ≃ − ⊗ R F ( R ) {\displaystyle F\simeq -\otimes _{R}F(R)} .
In mathematics, specifically homological algebra, the Eilenberg–Watts theorem tells when a functor between the categories of modules is given by an application of a tensor product. Precisely, it says that a functor F : M o d R → M o d S {\displaystyle F:\mathbf {Mod} _{R}\to \mathbf {Mod} _{S}} is additive, is right-exact and preserves coproducts if and only if it is of the form F ≃ − ⊗ R F ( R ) {\displaystyle F\simeq -\otimes _{R}F(R)} .
Source: Wikipedia "Eilenberg–Watts theorem" · CC BY-SA 4.0
Share this article: X · Bluesky