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Universal homotopy theories. (English) Zbl 1009.55011
Author’s summary: “Begin with a small category $${\mathcal C}$$. The goal of this short note is to point out that there is such a thing as a ‘universal model category built from $${\mathcal C}$$’. We describe applications of this to the study of homotopy colimits, the Dwyer-Kan theory of framings, sheaf theory, and the homotopy theory of schemes”.

##### MSC:
 55U35 Abstract and axiomatic homotopy theory in algebraic topology 18G55 Nonabelian homotopical algebra (MSC2010) 18E20 Categorical embedding theorems 18C99 Categories and theories
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##### References:
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