modules finite congenerated are closed under extensions I have to prove some properties about modules finite cogenerated, I´ve already prove that mmodules finite cogenerated are closed under submodules, finite direct sums, but I can´t see how to prove that modules finite congenerated are closed under extensions. I´ve already tried a direct prove by definition, and using the other two properties, but I don´t get something useful.
Does anybody haver any idea?
Thanks for any comment!

It appears that the category of finitely cogenerated modules is not closed under extensions in general.
Researching this problem led me to this article by Wisbauer.
You need to see theorem 6.5 which I believe, when modified for this situation, says that the finitely cogenerated modules of $Mod-R$ are closed under extensions iff $R$ is right self-pseudoinjective. 
