Reedy categories and the $Θ$-construction

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

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