  We prove that the marked triangulation functor from the category of marked
cubical sets equipped with a model structure for ($n$-trivial, saturated)
comical sets to the category of marked simplicial set equipped with a model
structure for ($n$-trivial, saturated) complicial sets is a Quillen
equivalence. Our proof is based on the theory of cones, previously developed by
the first two authors together with Lindsey and Sattler.
