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.
Homology, Homotopy and Applications, Vol. 11 (2009), No. 2, pp.309-326.
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