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.