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arXiv · 1311.1854

A note on morphisms determined by objects

Xiao-Wu Chen·Jue Le
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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.

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Xiao-Wu Chen, Jue Le. 2013-11-08. A note on morphisms determined by objects. https://arxiv.org/abs/1311.1854

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