Mansfield's imprimitivity theorem for full crossed products

For any maximal coaction $(A,G,\delta)$ and any closed normal subgroup $N$ of $G$, there exists an imprimitivity bimodule $Y_{G/N}^G(A)$ between the full crossed product $A\times_\delta G\times_{\widehat\delta\vert}N$ and $A\times_{\delta\vert}G/N$, together with $\operatorname{Inf}\widehat{\widehat\delta\vert}-\delta^{\text{dec}}$ compatible coaction $\delta_Y$ of $G$. The assignment $(A,\delta)\mapsto (Y_{G/N}^G(A),\delta_Y)$implements a natural equivalence between the crossed-product functors `` ${}\times G\times N$'' and `` ${}\times G/N$'', in the category whose objects are maximal coactions of $G$ and whose morphisms are isomorphism classes of right-Hilbert bimodule coactions of $G$.