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Enriched model categories and an application to additive endomorphism spectra
Theory and applications of categories, Tome 18 (2007), pp. 400-439 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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We define the notion of an additive model category and prove that any stable, additive, combinatorial model category $\cal M$ has a model enrichment over $Sp^\Sigma(sAb)$ (symmetric spectra based on simplicial abelian groups). So to any object $X$ in $\cal M$ one can attach an endomorphism ring object, denoted $hEnd_ad(X)$, in the category $Sp^\Sigma(sAb)$. We establish some useful properties of these endomorphism rings.

We also develop a new notion in enriched category theory which we call `adjoint modules'. This is used to compare enrichments over one symmetric monoidal model category with enrichments over a Quillen equivalent one. In particular, it is used here to compare enrichments over $\Sp^\Sigma(s\Ab)$ and chain complexes.

Classification : 18D20, 55U35, 55P42, 18E05
Keywords: model categories, symmetric spectra, endomorphism ring 
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     author = {Daniel Dugger and Brooke Shipley},
     title = {Enriched model categories and an application to additive endomorphism spectra},
     journal = {Theory and applications of categories},
     pages = {400--439},
     year = {2007},
     volume = {18},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2007_18_a14/}
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Daniel Dugger; Brooke Shipley. Enriched model categories and an application to additive endomorphism spectra. Theory and applications of categories, Tome 18 (2007), pp. 400-439. http://geodesic.mathdoc.fr/item/TAC_2007_18_a14/