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I would like to ask for a list of references that explain the simplicial approximation theorem, barycentric subdivisions and Kan $Ex^{\infty}$ functor in details, fully exploiting the language of simplicial sets where needed (which is not what most of the books on algebraic topology do).

Thanks in advance!

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    $\begingroup$ Curtis's notes Simplicial Homotopy Theory (Advances in Math, 1971) are the place where I first saw this sort of discussion. $\endgroup$
    – Dan Ramras
    Commented Sep 15, 2016 at 4:05
  • $\begingroup$ Goerss-Jardine Simplicial homotopy theory might be of assistance (I do not know if the explicitely treat simplicial approximation though) $\endgroup$
    – Denis Nardin
    Commented Sep 15, 2016 at 12:06

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