I already know that given a compact Lie group $G$ it's category of (continuous unitary) representations Rep$(G)$ is compact, i.e. allows duals. However I can't seem to find a good reference about the case of non-compact groups or infinite-dimensional representations.
For example on how to construct the unit morphism.
Are there good references for this topic?
PS: As a physicist I was especially looking for the case of the Poincaré group.