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3

Have you looked at the book Simplicial homotopy theory by Goerss and Jardine? They have a 60-pages Chapter 1 on simplicial sets, at the end of which they define the model structure on $\mathsf{sSet}$. IMHO the book is quite good. I'm not sure what you mean by "doesn't take the top down model structure approach", but definitions don't fall from the sky and ...


5

Here's a sketch of the proof why realizations of simplicial sets are CW complexes. Roughly speaking, a CW complex is a space built by one-by-one gluing in new simplices along their boundaries. If $X_\bullet$ is a simplicial set, then $|X_\bullet|$ is built by gluing together the spaces $X_n\times\Delta^n$, where you give $X_n$ the discrete topology. But ...



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