Universal homotopy theories

Details Universal homotopy theories Universal homotopy theories

2000-07-11

arxiv.org/abs/math/0007070v1

Mathematics

Algebraic Topology

Scientific paper

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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