English

A note on morphisms determined by objects

Representation Theory 2015-02-10 v1 Rings and Algebras

Abstract

We prove that a Hom-finite additive category having determined morphisms on both sides is a dualizing variety. This complements a result by Krause. We prove that in a Hom-finite abelian category having Serre duality, a morphism is right determined by some object if and only if it is an epimorphism. We give a characterization to abelian categories having Serre duality via determined morphisms.

Keywords

Cite

@article{arxiv.1311.1854,
  title  = {A note on morphisms determined by objects},
  author = {Xiao-Wu Chen and Jue Le},
  journal= {arXiv preprint arXiv:1311.1854},
  year   = {2015}
}
R2 v1 2026-06-22T02:03:26.153Z