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Universal homotopy theories

Daniel Dugger
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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.

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Daniel Dugger. 2000-07-11. Universal homotopy theories. https://arxiv.org/abs/math/0007070

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