It sais here that the canonical model structure on $Cat$ is cofibrantly generated. I found out that a generating trivial cofibration is the functor $I:*\rightarrow E $, where $E$ is the category with 2 isomorphic objects (and $*$ is mapped into one of them), but i can't find any information about the set of generating cofibrations (and I don't know how to work it out on my own). Any suggestion?
More in general does anyone know a book/article in which this argument is treated extensively?
The generating cofibrations are the inclusions $\emptyset \hookrightarrow \{ \ast \}$ and $\{ 0, 1 \} \hookrightarrow \{ 0 \to 1 \}$ plus the projection $\{ 0 \rightrightarrows 1 \} \to \{ 0 \rightarrow 1 \}$. It is easy to see that a functor has the right lifting property with respect to these if and only if it is fully faithful and surjective on objects.