  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.
