ScalingStacks

Definition 7.2. A pair $(\mathcal{C},f)$ satisfying these axioms (C.1–5) will be said to be a theory of $(\infty,n)$-categories. We define a subcategory $\thy_{(\infty,n)}$ of the $\infty$-category of $\infty$-categories: the objects are $\infty$-categories $\mathcal{C}$ that underlie a theory $(\mathcal{C},f)$ of $(\infty,n)$-categories, and the morphisms are equivalences of these $\infty$-categories.