Another approach to the Kan-Quillen model structure
Category Theory
2020-02-14 v2 Algebraic Topology
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.
Cite
@article{arxiv.1506.04887,
title = {Another approach to the Kan-Quillen model structure},
author = {Sean Moss},
journal= {arXiv preprint arXiv:1506.04887},
year = {2020}
}
Comments
24 pages; rewritten following journal feedback, results unchanged