  We show that the category of simplicial sets is a co-reflective subcategory
of the category of cubical sets with connections, with the inclusion given by a
version of the straightening functor. We show that using the co-reflector, one
can transfer any cofibrantly generated model structure in which cofibrations
are monomorphisms to cubical sets, thus obtaining cubical analogues of the
Quillen and Joyal model structures.
