A note on morphisms determined by objects. (English) Zbl 1321.18001
Summary: We prove that a Hom-finite additive category having determined morphisms on both sides is a dualizing variety. This complements a result by H. Krause [in: Algebras, quivers and representations. The Abel symposium 2011. Selected papers of the 8th Abel symposium, Balestrand, Norway, June 20–23, 2011. Berlin: Springer. 195–207 (2013; Zbl 1316.18014)]. 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.
MathOverflow Questions:
Word for two morphisms that are equivalent up to right-composition with isomorphismMSC:
| 18A25 | Functor categories, comma categories |
| 18E30 | Derived categories, triangulated categories (MSC2010) |
| 14A15 | Schemes and morphisms |
Citations:
Zbl 1316.18014References:
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