ScalingStacks

Remark 3.3. Rezk observed [34, § 10] that the $1$-category $E$ may be exhibited in $\cat_{1}$ as a pushout of more elementary $n$-categories:

$$E\cong\Delta^{3}\cup^{(\Delta^{\{0,2\}}\sqcup\Delta^{\{1,3\}})}(\Delta^{0}\sqcup\Delta^{0}).$$

Consequently, a strict $n$-category $X$ is gaunt if and only if for each $k\geq 0$ the following natural map is a bijection:

$$\Fun(C_{k},X)\to\Fun(\sigma^{k}(\Delta^{3}),X)\times_{\Fun(\sigma^{k}(\Delta^{\{0,2\}}\sqcup\Delta^{\{1,3\}}),X)}\Fun(\sigma^{k}(\Delta^{0}\sqcup\Delta^{0}),X).$$