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Oct 20, 2010 at 14:23 comment added D.-C. Cisinski For the fact that any Frobenius category defines a model category, you may find a proof with Proposition 4.19 and Example 5.3 in a paper of mine: "Catégories dérivables", Bull. Soc. Math. France 138 (2010), 317-393 (but this is an old folklore result; I think the first instance of this appeared in the paper of A. Heller: "The loop-space functor in homological algebra", Trans. Amer. Math. Soc. 96 (1960), 382–394). The fact that C(A) is a Frobenius category for any additive category A is a nice exercise.
Oct 20, 2010 at 0:33 vote accept Agustí Roig
Oct 19, 2010 at 12:05 comment added Agustí Roig Thank you, Denis-Charles Cisinski: any reference for this result?
Oct 19, 2010 at 10:14 history answered D.-C. Cisinski CC BY-SA 2.5