dc.contributor |
Centre de Recerca Matemàtica |
dc.contributor.author |
Fiore, Thomas M. |
dc.contributor.author |
Paoli, Simona |
dc.date.accessioned |
2009-04-02T07:38:44Z |
dc.date.available |
2009-04-02T07:38:44Z |
dc.date.created |
2008-08 |
dc.date.issued |
2008-08 |
dc.identifier.uri |
http://hdl.handle.net/2072/15187 |
dc.format.extent |
54 |
dc.format.extent |
438784 bytes |
dc.format.mimetype |
application/pdf |
dc.language.iso |
eng |
dc.publisher |
Centre de Recerca Matemàtica |
dc.relation.ispartofseries |
Prepublicacions del Centre de Recerca Matemàtica;827 |
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 (http://creativecommons.org/licenses/by-nc-nd/2.5/es/) |
dc.subject.other |
Categories (Matemàtica) |
dc.title |
A Thomason model structure on the category of small n-fold categories |
dc.type |
info:eu-repo/semantics/preprint |
dc.subject.udc |
512 - Àlgebra |
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. |