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May 20, 2011 at 14:01 comment added domenico fiorenza yes, it is the category of fibrant objects in $DG_\mathbf{Z}Sp(k)$, as I'm saying in my self-answer above. Actually in that answer I'm leaving quite implicit the fact that "category of fibrant objects" rather than "model category" is the right answer to my original question: thanks for having stressed this.
May 20, 2011 at 12:10 history answered DamienC CC BY-SA 3.0