2015/10/24 by Junfu Wang, Wang, Junfu, Zhaoyong Huang +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1510.07098
openalex publication_date 2015/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In an abelian category \mathscrA with small \rm Ext groups, we show that there exists a one-to-one correspondence between any two of the following: balanced pairs, subfunctors F of \rm Ext1_\mathscrA(-,-) such that \mathscrA 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.