The theory and practice of Reedy categories

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.

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