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28 March 2024
 
  » arxiv » math.AT/0007070

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Universal homotopy theories
Daniel Dugger ;
Date 11 Jul 2000
Subject Algebraic Topology; Category Theory | math.AT math.CT
AffiliationPurdue University
AbstractGiven 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.
Source arXiv, math.AT/0007070
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