Geodesic
The theory and practice of Reedy categories
Theory and applications of categories, Tome 29 (2014), pp. 256-301

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Publié le :
Classification : 55U35, 18G30, 18D10
Keywords: reedy categories, homotopy limits and colimits, weighted limits and colimits 
@article{TAC_2014_29_a8,
     author = {Emily Riehl and Dominic Verity},
     title = {The theory and practice of {Reedy} categories},
     journal = {Theory and applications of categories},
     pages = {256--301},
     publisher = {mathdoc},
     volume = {29},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2014_29_a8/}
}
TY  - JOUR
AU  - Emily Riehl
AU  - Dominic Verity
TI  - The theory and practice of Reedy categories
JO  - Theory and applications of categories
PY  - 2014
SP  - 256
EP  - 301
VL  - 29
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2014_29_a8/
LA  - en
ID  - TAC_2014_29_a8
ER  - 
%0 Journal Article
%A Emily Riehl
%A Dominic Verity
%T The theory and practice of Reedy categories
%J Theory and applications of categories
%D 2014
%P 256-301
%V 29
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2014_29_a8/
%G en
%F TAC_2014_29_a8
Emily Riehl; Dominic Verity. The theory and practice of Reedy categories. Theory and applications of categories, Tome 29 (2014), pp. 256-301. http://geodesic.mathdoc.fr/item/TAC_2014_29_a8/