函子范畴中的一类广义内射对象

A Class of Generalized Injective Objects in Functor Categories

摘要

设F是从有限表现右R-模范畴到Abel群范畴的函子.若存在强FP-内射左R-模M,使得$F \cong-\otimes_{R} M$,则称F是强SFP-内射函子.利用同调代数中的方法,讨论并刻画强SFP-内射函子的同调性质,证明:强SFP-内射函子构成的类关于扩张、直积封闭,强SFP-内射函子构成的类是内射可解类.

Abstract

Let F be a functor from the category of finitely presented right R-modules to the category of Abelian groups. If there exists a strongly FP-injective left R-module M such that $F \cong-\otimes_{R} M$, then F is called a strongly SFP-injective functor. This paper adopts methods from homological algebra to study and characterize the homological properties of strongly SFP-injective functors. We prove that the class of strongly SFP-injective functors is closed under extensions and direct products, and the class consisting of strongly SFP-injective functors is an injective resolving class.

关键词

FP-内射模 / 强FP-内射模 / 强FP-内射函子 / 强SFP-内射函子

Key words

FP-injective module / strongly FP-injective module / strongly FP-injective functor / strongly SFP-injective functor

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基金资助

国家自然科学基金(12161049)