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Spectral enrichments of model categories

Daniel Dugger
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Abstract

We prove that every stable, combinatorial model category has a natural enrichment by symmetric spectra (or more precisely, a natural equivalence class of enrichments). This in some sense generalizes the simplicial enrichments of model categories provided by the Dwyer-Kan hammock localization. As one particular application, we are able to associate to every object of a stable, combinatorial model category a "homotopy endomorphism ring spectrum". The homotopy types of these ring spectra are preserved by Quillen equivalences, and so are an invariant for stable model categories.

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Daniel Dugger. 2005-02-01. Spectral enrichments of model categories. https://arxiv.org/abs/math/0502006

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