Enrichments of Additive Model Categories

We prove that any stable, additive, combinatorial model category M has a canonical model enrichment over Sp(sAb) (symmetric spectra based on simplicial abelian groups). So to any object X ∈ M one can attach an endomorphism ring object in this category, denoted hEndad(X). Since the homotopy theory of ring objects in Sp(sAb) is equivalent to the homotopy theory of differential graded algebras, one also has a homotopy endomorphism dga hEnddga(X). We prove that the homotopy type of hEndad(X)—and thus also hEnddga(X)—is an invariant of Quillen equivalences between additive model categories.