So far in the chapter about model categories there isn't anything about the (many-adjunction variant of the) lifting principle, simply because I learned of its existence a couple of months after the first exposé. However, it is explained so some extent in the chapter about affine derived schemes.
I am moving it to model categories and use it to deduce the existence of the global projective model structure (the easy one, no Lurie cardinality argument is involved here), which is also necessary for the chapter on simplicial presheaves.
This will increase by 4 or 5 the number of pages of the chapter in model categories, but since I am simply moving stuff already written somewhere else in the notes (though deeply reshaping), I guess I am allowed to to that.
An important reason to discuss these ideas already in the first chapter is that I will use the global projective model structure in the discussion of homotopy colimits.
So far in the chapter about model categories there isn't anything about the (many-adjunction variant of the) lifting principle, simply because I learned of its existence a couple of months after the first exposé. However, it is explained so some extent in the chapter about affine derived schemes.
I am moving it to model categories and use it to deduce the existence of the global projective model structure (the easy one, no Lurie cardinality argument is involved here), which is also necessary for the chapter on simplicial presheaves.
This will increase by 4 or 5 the number of pages of the chapter in model categories, but since I am simply moving stuff already written somewhere else in the notes (though deeply reshaping), I guess I am allowed to to that.
An important reason to discuss these ideas already in the first chapter is that I will use the global projective model structure in the discussion of homotopy colimits.
Does anyone have any comment?