  We use minimal tilting complexes to construct an explicit bijection between
the set of thick tensor ideals with the two-out-of-three property in the
category of finite-dimensional modules over a quantum group at a root of unity
and the set of thick tensor ideals in the subcategory of tilting modules. We
also explain why the analogous construction for rational representations of a
reductive algebraic group over a field of positive characteristic does not give
rise to a bijection.
