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Mathematics  2011 

Enriched model categories and presheaf categories

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Abstract:

We collect in one place a variety of known and folklore results in enriched model category theory and add a few new twists. The central theme is a general procedure for constructing a Quillen adjunction, often a Quillen equivalence, between a given V-model category and a category of diagrams in V, where V is any good enriching category. From this perspective, we rederive the result of Schwede and Shipley that reasonable stable model categories are Quillen equivalent to diagram categories of spectra (alias categories of module spectra). The technical improvements and modifications of general model categorical results given here are applied to equivariant contexts in the sequels. They are bound to have applications in various other contexts.

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