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

Equivalence of cubical and simplicial approaches to $(\infty,n)$-categories