The theory and practice of reedy categories

Emily Riehl, Dominic Verity

Research output: Contribution to journalArticleResearchpeer-review

Abstract

The goal of this paper is to demystify the role played by the Reedy category axioms in homotopy theory. With no assumed prerequisites beyond a healthy appetite for category theoretic arguments, we present streamlined proofs of a number of useful technical results, which are well known to folklore but di cult to nd in the literature. While the results presented here are not new, our approach to their proofs is somewhat novel. Speci cally, we reduce the much of the hard work involved to simpler computations involving weighted colimits and Leibniz (pushout-product) constructions. The general theory is developed in parallel with examples, which we use to prove that familiar formulae for homotopy limits and colimits indeed have the desired properties.

LanguageEnglish
Pages256-301
Number of pages46
JournalTheory and Applications of Categories
Volume29
Publication statusPublished - 13 Jun 2014

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Colimit
Homotopy Theory
Axioms
Homotopy

Cite this

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The theory and practice of reedy categories. / Riehl, Emily; Verity, Dominic.

In: Theory and Applications of Categories, Vol. 29, 13.06.2014, p. 256-301.

Research output: Contribution to journalArticleResearchpeer-review

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