Large-scale control systems, such as intelligent vehicle highway systems and air traffic management systems are systems of very high complexity. In order to reduce complexity, the system architecture is usually designed to have a hierarchical structure. In such a structure, systems of higher functionality reside at higher levels (higher layers) of the hierarchy and are unaware of unnecessary lower-level details. In performing their tasks, higher levels use a coarser system model than lower levels. One of the main challenges in designing hierarchical models is the extraction of the hierarchy of models at various levels of abstraction that are compatible with the functionality and objectives of each layer. Technically, this process is done by grouping the system states into equivalence classes. Depending on the cardinality of the resulting quotient space, one obtains discrete or continuous abstractions. The paper under review considers continuous abstractions. To be more specific: consider a control system \(\dot{x}=f(x,u),\) \(x \in {\mathbb{R}}^n,\) \(u \in {\mathbb{R}}^m,\) and some map \(y=h(x),\) where \(y \colon {\mathbb{R}}^n \rightarrow {\mathbb{R}}^p,\) \(p \leq n.\) Using a generalized version of \(\Phi-\)related vector fields to control systems, the authors managed to define a control system \(\dot{y}=g(y,v),\) \(y \in {\mathbb{R}}^p,\) \(v \in {\mathbb{R}}^k,\) which can produce as trajectories all functions of the form \(y(t)=h(x(t)),\) where \(x(t)\) is a trajectory of the system \(\dot{x}=f(x,u).\) (In other words, \(h\) maps trajectories of the system \(\dot{x}=f(x,u)\) to trajectories of the system \(\dot{y}=g(y,v).\)) The system \(\dot{y}=g(y,v)\) is called the abstraction or the macromodel of the finer micromodel \(\dot{x}=f(x,u).\) The most important issue involved in the abstraction is to ensure that certain properties propagate from the macromodel to the micromodel. In this paper, controllability requests are addressed. In particular, the authors characterize linear quotient maps \(y=Cx,\) so that a linear system \(\dot{x}=Ax+Bu,\) \(x \in {\mathbb{R}}^n,\) \(u \in {\mathbb{R}}^m,\) is controllable if and only if the abstracted linear system \(\dot{y}=Fy+Gv,\) \(y \in {\mathbb{R}}^p,\) \(v \in {\mathbb{R}}^k,\) is controllable. As a byproduct, the authors obtain a hierarchical controllability criterion for linear systems from which one can recover the best of the known controllability algorithms from numerical linear algebra. Matlab implementation of the two algorithms is included in the appendix.