Kerodon

Remark 9.4.2.14 (Composition). Let $\kappa \leq \lambda $ be regular cardinals, let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $\infty $-categories which are $(\kappa ,\lambda )$-compactly generated, and let $\operatorname{\mathcal{E}}$ be an $\infty $-category which is $(\kappa ,\lambda )$-cocomplete. If $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ and $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$ are $(\kappa ,\lambda )$-compact functors, then the composition $(G \circ F): \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{E}}$ is $(\kappa ,\lambda )$-compact.