In an abelian category A with small Ext groups, we show that there exists a one-to-one correspondence between any two of the following: balanced pairs, subfunctors F of Ext 1 A (−, −) such that A has enough F-projectives and enough F-injectives and Quillen exact structures E with enough E -projectives and enough E -injectives. In this case, we get a strengthened version of the translation of the Wakamatsu lemma to the exact context, and also prove that subcategories which are E -resolving and epimorphic precovering with kernels in their right E -orthogonal class and subcategories which are E -coresolving and monomorphic preenveloping with cokernels in their left E -orthogonal class are determined by each other. Then we apply these results to construct some (pre)enveloping and (pre)covering classes and complete hereditary E -cotorsion pairs in the module category.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.