arXiv 0809.33872008-09-25math.RAmath.RT

On extensions of covariantly finite subcategories

Xiao-Wu Chen

备注：: Comments are welcome!
发表信息：: Arch. Math. 93(2009), 29-35.

英文摘要：

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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