The cubical category with connections is a strict test category
The author shows that the cubical category with connections is a strict test category in the sense of Grothendieck, where connections are certain operations similar to degeneracies. This means that cubical sets with connections are models for homotopy theory in the same way as simplicial sets, with good behaviour on products. The category of cubes (without connections) is a test category, but the author shows that it is not a strict test category.
scientific article; zbMATH DE number 5664826