科研之友
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摘要
Watts's Theorem says that a right exact functor F : ModR -> ModS that commutes with direct sums is isomorphic to -circle times(R) B, where B is the R-S-bimodule FR. The main result in this article is the following one: If A is a cocomplete category and F : Mod(R) -> A is a right exact functor commuting with direct sums, then F is isomorphic to -circle times(R) F, where F is a suitable R-module in A, i.e., a pair(F, rho) consisting of an object F is an element of A and a ring homomorphism rho : R -> Hom(A)(F, F). Part of the point is to give meaning to the notation -circle times(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.
- 出版日期2016
