For a published reference see: MR2591923 (2010k:18022) Maltsiniotis, Georges(F-PARIS7-IMJ) La catégorie cubique avec connexions est une catégorie test stricte. (French. English summary) [The category of cubes with connections is a strict test category] Homology, Homotopy Appl. 11 (2009), no. 2, 309–326. Best, Fernando On Thu, 15 Sep 2011 21:06:32 +0200, Urs Schreiber wrote:
So my question is, is it known whether the category of cubical sets, with or without connections, admits an excellent model structure?
The only model structure on cubical sets that I am aware of is that given by Jardine:
http://ncatlab.org/nlab/show/model+structure+on+cubical+sets
Its cofibrations are the monos, but the other axioms of "excellent" (HTT A.3.2.16) seem problematic. But I haven't really thought about it.
-- Fernando Muro Universidad de Sevilla, Departamento de Álgebra http://personal.us.es/fmuro [For admin and other information see: http://www.mta.ca/~cat-dist/ ]