Another approach to the Kan-Quillen model structure
arXiv:1506.04887 · doi:10.1007/s40062-019-00247-y
Abstract
By careful analysis of the comparison map from a simplicial set to its image under Kan's ex-infinity functor we obtain a new and combinatorial proof that it is a weak homotopy equivalence. Moreover, we obtain a presentation of it as a strong anodyne extension. From this description we are able to quickly deduce some basic facts about ex-infinity and hence provide a new construction of the Kan-Quillen model structure on simplicial sets, which avoids the use of topological spaces or minimal fibrations.
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