Lemma 11.9.1.2. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then the morphism
\[ \lambda : \operatorname{Cospan}^{L,R}( \operatorname{Fun}(\Delta ^1, \operatorname{\mathcal{C}}) ) \rightarrow \operatorname{Fun}^{ \mathrm{iso}, \mathrm{all} }( \operatorname{\mathcal{C}}) \times \operatorname{Fun}^{ \mathrm{all}, \mathrm{iso} }( \operatorname{\mathcal{C}}) \]
is a left fibration of $\infty $-categories.