The aim of this paper is to prove that the category of cubes with connections, introduced by R. Brown and Ph.J. Higgins,
is a strict test category in Grothendieck's sense. In particular this implies that cubical sets with connections are
models for homotopy types in a very precise sense, in a way that is compatible with the cartesian product.
@article{1296138523,
author = {Maltsiniotis, Georges},
title = {La cat\'egorie cubique avec connexions est une cat\'egorie test stricte},
journal = {Homology Homotopy Appl.},
volume = {11},
number = {1},
year = {2009},
pages = { 309-326},
language = {fr},
url = {http://dml.mathdoc.fr/item/1296138523}
}
Maltsiniotis, Georges. La catégorie cubique avec connexions est une catégorie test stricte. Homology Homotopy Appl., Tome 11 (2009) no. 1, pp. 309-326. http://gdmltest.u-ga.fr/item/1296138523/