Universal Homotopy Theories
Copyright policy )Universal Homotopy Theories
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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Categorical embedding theorems, Mathematics(all), FOS: Mathematics, Abstract and axiomatic homotopy theory in algebraic topology, Algebraic Topology (math.AT), Mathematics - Category Theory, Category Theory (math.CT), Nonabelian homotopical algebra, Categories and theories, Mathematics - Algebraic Topology
Categorical embedding theorems, Mathematics(all), FOS: Mathematics, Abstract and axiomatic homotopy theory in algebraic topology, Algebraic Topology (math.AT), Mathematics - Category Theory, Category Theory (math.CT), Nonabelian homotopical algebra, Categories and theories, Mathematics - Algebraic Topology
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