Abstract
We use the notion of multi-Reedy category to prove that, if \(\mathcal C \) is a Reedy category, then \(\varTheta \mathcal C \) is also a Reedy category. This result gives a new proof that the categories \(\varTheta _n\) 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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Acknowledgments
The authors would like to thank the anonymous referee for a careful reading and helpful comments. The first-named author would also like to thank Clemens Berger for pointing out the reference [2].
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The authors were partially supported by NSF grants DMS-0805951 and DMS-1006054.
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Bergner, J.E., Rezk, C. Reedy categories and the \(\varTheta \)-construction. Math. Z. 274, 499–514 (2013). https://doi.org/10.1007/s00209-012-1082-0
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DOI: https://doi.org/10.1007/s00209-012-1082-0