On extensions of covariantly finite subcategories

Details On extensions of covariantly finite subcategories On extensions of covariantly finite subcategories

2008-09-19

arxiv.org/abs/0809.3387v2

Arch. Math. 93(2009), 29-35.

Mathematics

Rings and Algebras

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Scientific paper

In \cite{GT}, Gentle and Todorov proved that in an abelian category with enough projective objects, the extension subcategory of two covariantly finite subcategories is still covariantly finite. We give an counterexample to show that Gentle-Todorov's theorem may fail in arbitrary abelian categories; we also prove that a triangulated version of Gentle-Todorov's theorem holds; we make applications of Gentle-Todorov's theorem to obtain short proofs to a classical result by Ringel and a recent result by Krause and Solberg.

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