Extensions of covariantly finite subcategories |
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Authors: | Xiao-Wu Chen |
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Institution: | (1) Department of Mathematics, University of Science and Technology of China, 230026 Hefei, Anhui Province, People’s Republic of China |
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Abstract: | Gentle and Todorov proved that in an abelian category with enough projective objects, the extension subcategory of two covariantly
finite subcategories is covariantly finite. We give an example to show that Gentle–Todorov’s theorem may fail in an arbitrary
abelian category; however we prove a triangulated version of Gentle–Todorov’s theorem which holds for arbitrary triangulated
categories; we apply Gentle–Todorov’s theorem to obtain short proofs of a classical result by Ringel and a recent result by
Krause and Solberg.
This project is partially supported by China Postdoctoral Science Foundation (No.s 20070420125 and 200801230). The author
also gratefully acknowledges the support of K. C. Wong Education Foundation, Hong Kong. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 18E30 Secondary 16G10 |
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