  The Lohe hierarchy is a hierarchy of finite-dimensional aggregation models
consisting of the Kuramoto model, the complex Lohe sphere model, the Lohe
matrix model and the Lohe tensor model. In contrast, the Schr\"odinger-Lohe
model is the only known infinite-dimensional Lohe aggregation model in
literature. In this paper, we provide an explicit connection between the
Schr\"odinger-Lohe model and the complex Lohe sphere model, and then by
exploiting this explicit relation, we construct infinite-dimensional liftings
of the Lohe matrix and the Lohe tensor models. In this way, we establish the
Schr\"odinger-Lohe hierarchy which corresponds to the infinite-dimensional
extensions of the Lohe hierarchy. For the proposed hierarchy, we provide
sufficient frameworks leading to the complete aggregation in terms of coupling
strengths and initial configurations.
