English

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.

Keywords

Cite

@article{arxiv.math/0502006,
  title  = {Spectral enrichments of model categories},
  author = {Daniel Dugger},
  journal= {arXiv preprint arXiv:math/0502006},
  year   = {2007}
}
R2 v1 2026-07-22T17:15:06.844Z