ScalingStacks

Conjecture 15.13. The $\infty$-category underlying Verity’s $n$-trivial weak complicial sets [39, 40] is a homotopy theory of $(\infty,n)$-categories. The relative category consisting of Batanin’s $\omega$-categories [7] such that every $k$-cell is an equivalence for $k>n$, together with the class of morphisms which are essentially $k$-surjective for all $k$ is a theory of $(\infty,n)$-categories.