Notation 10.2.2.2. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $f$ be a morphism of $\operatorname{\mathcal{C}}$ having source $X$ and target $Y$. If $f$ is a quotient morphism, we will often visually emphasize this by denoting $f$ with a double-headed arrow (that is, we will write $f: X \twoheadrightarrow Y$ in place of $f: X \rightarrow Y$). Beware that this notation does *not* indicate that $f$ is an epimorphism (see Warning 10.2.2.10).

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