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The theory and practice of Reedy categories

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Emily Riehl and Dominic Verity

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 difficult to find in the literature. While the results
presented here are not new, our approach to their proofs is somewhat
novel. Specifically, we reduce 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.

Keywords:
reedy categories, homotopy limits and colimits, weighted limits and colimits

2010 MSC:
55U35, 18G30, 18D10

*Theory and Applications of Categories,*
Vol. 29, 2014,
No. 9, pp 256-301.

Published 2014-06-13.

http://www.tac.mta.ca/tac/volumes/29/9/29-09.pdf

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