### 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.

Language | English |
---|---|

Pages | 256-301 |

Number of pages | 46 |

Journal | Theory and Applications of Categories |

Volume | 29 |

Publication status | Published - 13 Jun 2014 |

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### Cite this

*Theory and Applications of Categories*,

*29*, 256-301.

}

*Theory and Applications of Categories*, vol. 29, pp. 256-301.

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

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - The theory and practice of reedy categories

AU - Riehl, Emily

AU - Verity, Dominic

PY - 2014/6/13

Y1 - 2014/6/13

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84902500170&partnerID=8YFLogxK

M3 - Article

VL - 29

SP - 256

EP - 301

JO - Theory and Applications of Categories

T2 - Theory and Applications of Categories

JF - Theory and Applications of Categories

SN - 1201-561X

ER -