2024/11/10 by Ebrahimi, Ramin
#Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2411.06432
Let X be a skeletally small additive category. Using the canonical equivalence between two different presentations of the free abelian category over X, we give a new and simple characterization of definable subcategories of \rm Mod-X, and in particular definable subcategories of modules over rings. In the end, we give a conceptual proof of Auslander-Gruson-Jensen duality, which makes the duality between definable subcategories of left and right module more transparent.