A Generalization of Watts's Theorem: Right Exact Functors on Module Categories. Issue 7 (2nd July 2016)

• Record Type: Journal Article
• Authors: Nyman, A.; Smith, S. P.
• Is Part Of: Communications in algebra. Volume 44:Issue 7(2016)
• Page Start: 3160
• Page End: 3170
• Publication Date: 2016-07-02
• Subjects: Watts's Theorem; Primary: 18F99 -- Secondary: 14A22 -- 16D90 -- 18A25; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2015.1065873
• Languages: English
• ISSNs: 0092-7872

Abstract

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.