Universal homotopy theories

Preprint

11 July 2000

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0007070

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.

Keywords

UNIVERSAL HOMOTOPY
FORMALLY ADJOINING
HOMOTOPY COLIMITS
HOMOTOPY THEORY
SMALL CATEGORY
FRAMINGS
THEORY

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