dc.contributor.author |
Fiore, Thomas M. |
dc.contributor.author |
Paoli, Simona |
dc.contributor.author |
Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica |
dc.date |
2008 |
dc.identifier |
https://ddd.uab.cat/record/44445 |
dc.identifier |
urn:oai:ddd.uab.cat:44445 |
dc.description.abstract |
We construct a cofibrantly generated Thomason model structure on the category of small n-fold categories and prove that it is Quillen equivalent to the standard model structure on the category of simplicial sets. An n-fold functor is a weak equivalence if and only if the diagonal of its n-fold nerve is a weak equivalence of simplicial sets. We introduce an n-fold Grothendieck construction for multisimplicial sets, and prove that it is a homotopy inverse to the n-fold nerve. As a consequence, the unit and counit of the adjunction between simplicial sets and n-fold categories are natural weak equivalences. |
dc.format |
application/pdf |
dc.language |
eng |
dc.publisher |
Centre de Recerca Matemàtica |
dc.relation |
Centre de Recerca Matemàtica. Prepublicacions ; |
dc.rights |
open access |
dc.rights |
Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús |
dc.rights |
https://creativecommons.org/licenses/by-nc-nd/2.5/ |
dc.subject |
Categories (Matemàtica) |
dc.title |
A Thomason model structure on the category of small n-fold categories |
dc.type |
Article |
dc.type |
Prepublicació |