so given a small abelian ringoid x and an exact functor from x to _ab gp_, we can consider the composite x -> _ab gp_ -> _set_ ... which will still preserve limits... ??so will be a flat presheaf on (the underlying category of) x?? ...

so consider the grothendieck topology on x with coverings as follows... ??...

??topos of canonical sheaves on a finitely complete small category as classifying topos for "exact presheaves" on it?? or something??