Variant 8.5.6.10. Let $F: \operatorname{\mathcal{C}}' \rightarrow \operatorname{\mathcal{C}}$ be a Morita equivalence of simplicial sets. Then pullback along $F$ induces a bijection
\[ \xymatrix@R =50pt@C=50pt{ \{ \textnormal{Left Fibrations $\operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$} \} / \textnormal{Equivalence} \ar [d] \\ \{ \textnormal{Left Fibrations $\operatorname{\mathcal{E}}' \rightarrow \operatorname{\mathcal{C}}'$} \} / \textnormal{Equivalence}. } \]