Model categories 8 — My general theory is that the category of model categories is not itself a model category, but a 2-mod…

My general theory is that the category of model categories is not itself a model category, but a 2-model category. Weak equivalences of model categories are Quillen equivalences, and weak equivalences of Quillen functors are natural weak equivalences. Define a 2-model category and show the 2-category of model categories is one. Note that the homotopy 2-category at least makes sense (in a higher universe): we can just invert the Quillen equivalences and the natural weak equivalences. This localization process for an n-category has been studied by Andre Hirschowitz and Carlos Simpson in descent pour les n-champs, on xxx.