Re: Minimal abelian subcategory

Now let R be a ring and M an R-module. Is there a minimal abelian subcategory of Mod-R containing M? If so, is there a canonical way to describe it?

This question, as posed, is too easy: Just take M and its identity arrow. It will be a zero-object in that subcategory. There may be a better question here guiding Walter Mazorchuk's intuition, but it will have to require something more than just containing the one object. Colin