The usual duality for finite
dimensional vector spaces induces a duality F on the category of torsion free quotient
divisible abelian groups of finite rank with quasi-homomorphisms as morphisms. This
duality preserves rank, is exact, hence preserves quasi-direct sums, sends free groups
to divisible groups and conversely, and has the property that for all primes p, p-rank
FA = rank A − p-rank A.