Abstract
By careful analysis of the embedding of a simplicial set into its image under Kan’s mathop {mathop {mathsf {Ex}}^infty } 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 can quickly deduce some basic facts about mathop {mathop {mathsf {Ex}}^infty } and hence provide a new construction of the Kan–Quillen model structure on simplicial sets, one which avoids the use of topological spaces or minimal fibrations.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
