A Generalization of Watts's Theorem: Right Exact Functors on Module Categories. Issue 7 (2nd July 2016) - Nyman, A.; Smith, S. P.
Abstract : Watts's Theorem says that a right exact functor that commutes with direct sums is isomorphic to − ⊗ R B, where B is the R - S -bimodule FR . The main result in this article is the following one: If is a cocomplete category and is a right exact functor commuting with direct sums, then F is isomorphic to − ⊗ R ℱ, where ℱ is a suitable R -module in, i.e., a pair (ℱ, ρ) consisting of an object and a ring homomorphism . Part of the point is to give meaning to the notation − ⊗ R ℱ. That is done in the article by Artin and Zhang [1 ] on Abstract Hilbert Schemes. The present article is a natural extension of some of the ideas in the first part of their article.