Remark 1.4.2.7. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. We will refer to the $\infty $-category $\operatorname{\mathcal{C}}^{\operatorname{op}}$ of Proposition 1.4.2.6 as the opposite of the $\infty $-category $\operatorname{\mathcal{C}}$. Note that:
The objects of $\operatorname{\mathcal{C}}^{\operatorname{op}}$ are the objects of $\operatorname{\mathcal{C}}$.
Given a pair of objects $X,Y \in \operatorname{\mathcal{C}}$, the datum of a morphism from $X$ to $Y$ in $\operatorname{\mathcal{C}}^{\operatorname{op}}$ is equivalent to the datum of a morphism from $Y$ to $X$ in $\operatorname{\mathcal{C}}$.