  Watts's Theorem says that a right exact functor F:Mod R-->Mod S that commutes
with direct sums is isomorphic to -\otimes_R B where B is the R-S-bimodule FR.
The main result in this paper is the following: if A is a cocomplete abelian
category and F:Mod R --> A is a right exact functor commuting with direct sums,
then F is isomorphic to - \otimes_R B where B is a suitable R-module in A,
i.e., a pair (B,f) consisting of an object B in A and a ring homomorphism f:R
--> Hom_A(B,B). Part of the point is to give meaning to the notation -\otimes_R
B. That is done in the paper by Artin and Zhang on Abstract Hilbert Schemes.
The present paper is a natural extension of some of the ideas in the first part
of their paper.
