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Is the mixed model structure on TOP (Weak homotopy equivalences + Hurewicz fibrations) cofibrantly generated?

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    $\begingroup$ See the argument of "Homotopy of posets" by G. Raptis, Homology Homotopy Appl. 12 (2010), no. 2, 211–230, Remark 4.7. It would suffice to prove that for any cardinal $\mu$, there exists a cardinal $\nu > \mu$ such that the topological space $\mathcal{T}(P_\nu)$ is homotopy equivalent to a CW-complex. $\endgroup$
    – Philippe Gaucher
    Commented Mar 27, 2017 at 13:25
  • $\begingroup$ Great, thank you! $\endgroup$
    – Izael do Nascimento
    Commented Mar 27, 2017 at 13:28

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