The Borel equivariant cohomology of a space with an action of a group \(G\) inherits a canonical module structure over the cohomology ring of \(BG\). Motivated by results on the cohomology of homogeneous spaces, and in particular, a compact connected Lie group and its maximal torus case, we generalize these to pairs of groups \(K \subseteq G\) such that the free module property of the \(G\)-equivariant cohomology of a space is captured by the restricted action to the subgroup \(K\).