To an inclusion H ⊂ G of topological groups, we associate a spectrum DH⊂G which
coincides with the dualizing spectrum DG of Klein [Math. Ann. 319 (2001) 421-456]
when H = G. We also introduce a fibered spectrum analogue.
The main application is to give a purely homotopy theoretic construction of
Poincaré embeddings in stable codimension.