Reedy categories and the $\Theta$-construction

Abstract

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.

15 pages; final version to appear in Math. Z