ScalingStacks

Definition 3.1. A strict $n$-category $X$ is gaunt if for any $1\leq k\leq n$, the $n$-category $X$ is local with respect to the natural functor

$$\sigma^{k-1}E\to\sigma^{k-1}(C_{0})=C_{k-1};$$

that is, the induced map

$$\cat_{n}(C_{k-1},X)\to\cat_{n}(\sigma^{k-1}E,X)$$

is a bijection. Equivalently, a strict $n$-category $X$ in gaunt just in case, for any $1\leq k\leq n$, any invertible $k$-morphism is an identity.

We write $\gaunt_{n}\subset\cat_{n}$ for the full subcategory spanned by the gaunt $n$-categories.