La catégorie cubique avec connexions est une catégorie test stricte

Abstract

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.