
TL;DR
This paper provides a new characterization of definable subcategories in module categories over additive categories and rings, and offers a conceptual proof of Auslander-Gruson-Jensen duality to clarify the duality between subcategories.
Contribution
It introduces a simple characterization of definable subcategories using canonical equivalences and offers a conceptual proof of a fundamental duality in module theory.
Findings
New characterization of definable subcategories
Simplified proof of Auslander-Gruson-Jensen duality
Enhanced understanding of duality between subcategories
Abstract
Let be a skeletally small additive category. Using the canonical equivalence between two different presentations of the free abelian category over , we give a new and simple characterization of definable subcategories of , 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.
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Taxonomy
TopicsAdvanced Algebra and Logic · Advanced Topology and Set Theory · Rings, Modules, and Algebras
