Notation 10.2.3.12. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $f: X \rightarrow Y$ be a morphism in $\operatorname{\mathcal{C}}$ which admits an image $Y_0 \subseteq Y$. It follows from Proposition 10.2.3.11 that the isomorphism class $[Y_0]$ is uniquely determined by $f$ (as an object of the partially ordered set $\operatorname{Sub}(Y)$; see Notation 9.2.4.26). To emphasize this, we will denote the isomorphism class $[Y_0]$ by $\operatorname{im}(f)$ and refer to it as *the* image of $f$. We will sometimes abuse notation by identifying $\operatorname{im}(f)$ with the object $Y_0$, viewed either as an object of the slice $\infty $-category $\operatorname{\mathcal{C}}_{/Y}$ or as an object of the $\infty $-category $\operatorname{\mathcal{C}}$.

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