Remark 8.5.6.9. Let $F: \operatorname{\mathcal{C}}' \rightarrow \operatorname{\mathcal{C}}$ be a Morita equivalence of simplicial sets. Then pullback along $F$ induces a bijection
\[ \xymatrix@R =50pt@C=50pt{ \{ \textnormal{Cocartesian Fibrations $\operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$} \} / \textnormal{Equivalence} \ar [d] \\ \{ \textnormal{Cocartesian Fibrations $\operatorname{\mathcal{E}}' \rightarrow \operatorname{\mathcal{C}}'$} \} / \textnormal{Equivalence}. } \]
Moreover, if $\kappa $ is an uncountable cardinal, then a cocartesian fibration $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ is essentially $\kappa $-small if and only if its pullback $\operatorname{\mathcal{C}}' \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}'$ is essentially $\kappa $-small. This follows from the classification of Theorem 5.6.0.2, since the $\infty $-category $\operatorname{\mathcal{QC}}_{< \kappa }$ is idempotent complete (Example 8.5.4.20).