Geodesic
Enriched model categories and an application to additive endomorphism spectra
Theory and applications of categories, Tome 18 (2007), pp. 400-439

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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},
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     volume = {18},
     year = {2007},
     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/