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arXiv · 1507.01065

Reedy categories and their generalizations

Michael Shulman
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Abstract

We observe that the Reedy model structure on a diagram category can be constructed by iterating an operation of "bigluing" model structures along a pair of functors and a natural transformation. This yields a new explanation of the definition of Reedy categories: they are almost exactly those small categories for which the category of diagrams and its model structure can be constructed by iterated bigluing. It also gives a consistent way to produce generalizations of Reedy categories, including the generalized Reedy categories of Cisinski and Berger-Moerdijk and the enriched Reedy categories of Angeltveit, but also new versions such as a combined notion of "enriched generalized Reedy category".

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Michael Shulman. 2015-07-04. Reedy categories and their generalizations. https://arxiv.org/abs/1507.01065

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