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math.AT2000
Universal homotopy theories
Daniel Dugger
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 localiza…
math.AT2000
Combinatorial model categories have presentations
Daniel Dugger
We show that every combinatorial model category can be obtained, up to Quillen equivalence, by localizing a model category of diagrams of simplicial sets. This says that any combin…