  We provide a new proof of the super duality equivalence between infinite-rank
parabolic BGG categories of general linear Lie (super) algebras conjectured by
Cheng and Wang and first proved by Cheng and Lam. We do this by establishing a
new uniqueness theorem for tensor product categorifications motivated by work
of Brundan, Losev, and Webster. Moreover we show that these BGG categories have
Koszul graded lifts and super duality can be lifted to a graded equivalence.
