Universal homotopy theories
Algebraic Topology
2007-05-23 v1 Category Theory
Abstract
Given a small category C, we show that there is a universal way of expanding C into a model category, essentially by formally adjoining homotopy colimits. The technique of localization becomes a method for imposing `relations' into these universal gadgets. The paper develops this formalism and discusses various applications, for instance to the study of homotopy colimits, the Dwyer-Kan theory of framings, and to the homotopy theory of schemes.
Cite
@article{arxiv.math/0007070,
title = {Universal homotopy theories},
author = {Daniel Dugger},
journal= {arXiv preprint arXiv:math/0007070},
year = {2007}
}