Spectral enrichments of model categories
Algebraic Topology
2007-05-23 v1 Category Theory
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.
Cite
@article{arxiv.math/0502006,
title = {Spectral enrichments of model categories},
author = {Daniel Dugger},
journal= {arXiv preprint arXiv:math/0502006},
year = {2007}
}