A generalization of Watts's Theorem: Right exact functors on module categories
| dc.creator | Nyman, A. | |
| dc.creator | Smith, S. Paul | |
| dc.date | 2008-06-04 | |
| dc.date.accessioned | 2026-07-07T09:42:42Z | |
| dc.date.available | 2026-07-07T09:42:42Z | |
| dc.description | 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. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/0806.0832 | |
| dc.identifier | http://arxiv.org/abs/0806.0832 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162278 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 18F99; 14A22, 16D90, 18A25 | |
| dc.title | A generalization of Watts's Theorem: Right exact functors on module categories | |
| dc.type | text |