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arXiv · 1506.04887

Another approach to the Kan-Quillen model structure

Sean Moss
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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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Sean Moss. 2015-06-16. Another approach to the Kan-Quillen model structure. https://doi.org/10.1007/s40062-019-00247-y

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