  We prove that every dualizable Grothendieck category whose dual is again a
Grothendieck category satisfies Grothendieck's conditions Ab6 and Ab4*, by
taking a module-theoretic approach based on the Gabriel-Popescu embedding.
Combining this with a result by Stefanich, we conclude that the class of
dualizable linear cocomplete categories is precisely the class of linear
Grothendieck category satisfying Ab6 and Ab4*. This provides a complete answer
to a modified conjecture on the dualizability, originally posed by Brandenburg,
Chirvasitu, and Johnson-Freyd.
