Eilenberg–Watts theorem

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 $F : \mathbf{Mod}_R \to \mathbf{Mod}_S$ is additive, is right-exact and preserves coproducts if and only if it is of the form $F \simeq - \otimes_R F(R)$ .{{Cite web|url=https://mathoverflow.net/questions/159735/in-what-generality-does-eilenberg-watts-hold|title=In what generality does Eilenberg-Watts hold?|website=MathOverflow}}

For a proof, see [https://specksofmath.wordpress.com/2015/04/26/the-theorems-of-eilenberg-watts-part-1/ The theorems of Eilenberg & Watts (Part 1)]

References

Charles E. Watts, Intrinsic characterizations of some additive functors, Proc. Amer. Math. Soc. 11, 1960, 5–8.
Samuel Eilenberg, Abstract description of some basic functors, J. Indian Math. Soc. (N.S.) 24, 1960, 231–234 (1961).

Eilenberg–Watts theorem

References

Further reading