Proposition 8.1.1.11. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then the projection maps of Notation 8.1.1.6 determine a left fibration of simplicial sets
\[ (\lambda _{-}, \lambda _{+}): \operatorname{Tw}(\operatorname{\mathcal{C}}) \rightarrow \operatorname{\mathcal{C}}^{\operatorname{op}} \times \operatorname{\mathcal{C}}. \]