Variant 7.7.4.8. Let $\operatorname{\mathcal{QC}}$ denote the $\infty $-category of (small) $\infty $-categories (Construction 5.5.4.1). The $\infty $-category $\operatorname{\mathcal{QC}}$ has disjoint coproducts: if $\operatorname{\mathcal{C}}_0$ and $\operatorname{\mathcal{C}}_1$ are small $\infty $-categories, then the disjoint union $\operatorname{\mathcal{C}}= \operatorname{\mathcal{C}}_0 \amalg \operatorname{\mathcal{C}}_1$ is a coproduct of $\operatorname{\mathcal{C}}_0$ with $\operatorname{\mathcal{C}}_1$ in the $\infty $-category $\operatorname{\mathcal{QC}}$ (Example 7.6.1.17). The inclusion functors $\iota _0: \operatorname{\mathcal{C}}_0 \hookrightarrow \operatorname{\mathcal{C}}$ and $\iota _1: \operatorname{\mathcal{C}}_1 \hookrightarrow \operatorname{\mathcal{C}}$ are fully faithful, and are therefore monomorphisms in the $\infty $-category $\operatorname{\mathcal{QC}}$ (Corollary 9.3.4.34). Moreover, the pullback diagram of simplicial sets
is also categorical pullback square (Corollary 4.5.2.27), and therefore determines a pullback diagram in the $\infty $-category $\operatorname{\mathcal{QC}}$ (Example 7.6.3.4).