Example 8.2.0.2 (The Twisted Arrow Coupling). Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then the map $\lambda : \operatorname{Tw}(\operatorname{\mathcal{C}}) \rightarrow \operatorname{\mathcal{C}}^{\operatorname{op}} \times \operatorname{\mathcal{C}}$ of Notation 8.1.1.6 is a coupling of $\operatorname{\mathcal{C}}$ with itself (Proposition 8.1.1.11). We will refer to $\lambda $ as the twisted arrow coupling of the $\infty $-category $\operatorname{\mathcal{C}}$.
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