Example 11.5.0.23. Let $X$ be a Kan complex, which we regard as an object of the $\infty $-category $\operatorname{\mathcal{S}}$ of spaces (Construction 5.5.1.1). Then:
The Kan complex $X$ is an initial object of the $\infty $-category $\operatorname{\mathcal{S}}$ if and only if it is empty.
The Kan complex $X$ is a final object of the $\infty $-category $\operatorname{\mathcal{S}}$ if and only if it is contractible.