Example 7.7.4.7. Let $\operatorname{\mathcal{S}}$ be the $\infty $-category of spaces (Construction 5.5.1.1). The $\infty $-category $\operatorname{\mathcal{S}}$ has disjoint coproducts: if $X_0$ and $X_1$ are Kan complexes, then the disjoint union $X = X_0 \amalg X_1$ is a coproduct of $X_0$ and $X_1$ in the $\infty $-category $\operatorname{\mathcal{S}}$ (Example 7.6.1.16). Here the inclusion maps $\iota _0: X_0 \hookrightarrow X$ and $\iota _1: X_1 \hookrightarrow X$ are monomorphisms in the $\infty $-category $\operatorname{\mathcal{S}}$ (Example 9.3.4.10), and the pullback diagram of simplicial sets
is also homotopy pullback square (Example 3.4.1.3), and therefore determines a pullback diagram in the $\infty $-category $\operatorname{\mathcal{S}}$ (Example 7.6.3.2).