Reedy categories and the \(\varTheta\)-construction
type: Item
instance of: scholarly article
title: Reedy categories and the \(\varTheta\)-construction
zbMATH Open document ID: 1270.55014
author: Julie Bergner
author: Charles Rezk
published in: Mathematische Zeitschrift
publication date: 2013-06-18T00:00:00Z
full work available at URL: https://arxiv.org/abs/1110.1066
review text: The authors use the notion of multi-Reedy category to prove that if \(\mathcal{C}\) is a Reedy category, then \(\Theta\mathcal{C}\) is a Reedy category as well. This result gives a new proof that the categories \(\Theta_n\) are Reedy categories. Then the authors introduce the notion of elegant Reedy category, for which it is proved that the Reedy and injective model structures coincide. The authors conclude the paper with the notion of \(EZ\)-Reedy category (for Eilenberg Zilberg). It is proved that any \(EZ\)-Reedy category is elegant, and therefore Reedy and injective model structures coincide. And that the categories \(\Theta_k\) are \(EZ\)-Reedy for all \(k\geq 0\).
reviewed by: Philippe Gaucher
Mathematics Subject Classification ID: 55U35
Mathematics Subject Classification ID: 55U10
Mathematics Subject Classification ID: 18G55
zbMATH DE Number: 6176516
zbMATH Keywords: Reedy category
zbMATH Keywords: \(\varTheta\)-construction
zbMATH Keywords: injective model structure
zbMATH Keywords: simplicial set
MaRDI profile type: Publication
OpenAlex ID: W2033824108
arXiv ID: 1110.1066
cites work: Enriched Reedy categories
cites work: Geometry of loop spaces and the cobar construction
cites work: A cellular nerve for higher categories
cites work: On an extension of the notion of Reedy category
cites work: Q5580926
cites work: Q4790109
cites work: Symmetric cubical sets
DOI: 10.1007/S00209-012-1082-0
description: scientific article