Corollary 11.3.0.3. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then the construction $X \mapsto \operatorname{\mathcal{C}}_{X/}$ induces a bijection
\[ \xymatrix@R =50pt@C=50pt{ \{ \textnormal{Objects of $\operatorname{\mathcal{C}}$} \} / \textnormal{Isomorphism} \ar [d] \\ \{ \textnormal{Corepresentable left fibrations $\operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$} \} / \textnormal{Equivalence}.} \]