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I am just learning some basics of model categories, so pardon me if my question is trivial.

Suppose that $\mathfrak{C}$ is a category and there exists two model structures on $\mathfrak{C}$ (For example consider flat and injective model structures on R-Modules). Then which conditions are needed to verify that two model structures are equivalent?

In particular I want to know if the injective and flat model structure on $R$-Mod when the ring $R$ is a Noetherian ring, are equivalent.

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    $\begingroup$ Just follow the definition of Quillen equivalence...? $\endgroup$
    – Zhen Lin
    May 1, 2014 at 8:19
  • $\begingroup$ Do you have Hirschhorn or Hovey? $\endgroup$ May 1, 2014 at 14:35
  • $\begingroup$ Yes, I have Hovey's book, but I can't find any statement concerning the comparison of model structures. $\endgroup$
    – user38585
    May 1, 2014 at 18:23

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