Definition 5.4.5.12. Let $\operatorname{\mathcal{C}}$ be an $(\infty ,2)$-category. We say that a morphism $f: X \rightarrow Y$ of $\operatorname{\mathcal{C}}$ is an isomorphism if it is an isomorphism when viewed as a morphism in the $\infty $-category $\operatorname{Pith}(\operatorname{\mathcal{C}})$. We say that objects $X,Y \in \operatorname{\mathcal{C}}$ are isomorphic if there is an isomorphism from $X$ to $Y$ (that is, if $X$ and $Y$ are isomorphic when viewed as objects of the $\infty $-category $\operatorname{Pith}(\operatorname{\mathcal{C}})$).
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