ScalingStacks

Definition 8.1. Let $T_{0}$ be the smallest set of morphisms of $\pre(\gaunt_{n}^{\omega})$ that

• •

  contains the morphisms of Notation 6.5 (i.e., the morphisms that represent the fundamental pushouts of Axiom (C.3)), and

• •

  $T_{0}$ is stable under the operation $H\times_{C_{i}}(-)$ for $H\in\gaunt_{n}^{\omega}$.

Let $T$ be the saturated class of morphisms generated by $T_{0}$.

Define the $\infty$-category of $(\infty,n)$-precategories as the localization

$$\precat_{(\infty,n)}\mathrel{\mathop{:}}=T^{-1}\pre(\gaunt_{n}^{\omega}).$$