  We use the notion of multi-Reedy category to prove that, if $\mathcal C$ is a
Reedy category, then $\Theta \mathcal C$ is also a Reedy category. This result
gives a new proof that the categories $\Theta_n$ are Reedy categories. We then
define elegant Reedy categories, for which we prove that the Reedy and
injective model structures coincide.
