Spectral enrichments of model categories
Daniel Dugger
ddugger@math.uoregon.edu
Abstract:
We prove that every stable, combinatorial model category has a natural
enrichment by symmetric spectra (really a natural equivalence class of
enrichments). This in some sense generalizes the simplicial
enrichment of model categories provided by the Dwyer-Kan hammock
localization. As a particular application, we associate to every
object in a stable, combinatorial model category a certain "homotopy
endomorphism ring spectrum". The homotopy type of this ring spectrum
is preserved by Quillen equivalences, and so serves as an invariant of
model categories.