A Thomason Model Structure on the Category of Small nfold Categories
Abstract
We construct a cofibrantly generated Quillen model structure on the category of small nfold categories and prove that it is Quillen equivalent to the standard model structure on the category of simplicial sets. An nfold functor is a weak equivalence if and only if the diagonal of its nfold nerve is a weak equivalence of simplicial sets. This is an nfold analogue to Thomason's Quillen model structure on Cat. We introduce an nfold Grothendieck construction for multisimplicial sets, and prove that it is a homotopy inverse to the nfold nerve. As a consequence, we completely prove that the unit and counit of the adjunction between simplicial sets and nfold categories are natural weak equivalences.
 Publication:

arXiv eprints
 Pub Date:
 August 2008
 DOI:
 10.48550/arXiv.0808.4108
 arXiv:
 arXiv:0808.4108
 Bibcode:
 2008arXiv0808.4108F
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Category Theory;
 18D05;
 18G55 (Primary);
 55U10;
 55P99 (Secondary)
 EPrint:
 More details added. 23 new pages for a total of 77 pages.