Exercise 7.6.5.13. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and suppose we are given an equalizer diagram
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\begin{equation} \begin{gathered}\label{equation:half-equalizer-always} \xymatrix@C =50pt@R=50pt{ Z \ar [r]^-{g} & Y \ar@ <.4ex>[r]^-{f_0} \ar@ <-.4ex>[r]_-{f_1} & X } \end{gathered} \end{equation}
in $\operatorname{\mathcal{C}}$. Show that, for every object $C \in \operatorname{\mathcal{C}}$, the map of sets
\[ \operatorname{Hom}_{\mathrm{h} \mathit{\operatorname{\mathcal{C}}}}(C,Z) \xrightarrow { [g] \circ } \operatorname{Eq}( \operatorname{Hom}_{\mathrm{h} \mathit{\operatorname{\mathcal{C}}}}(C,Y) \rightrightarrows \operatorname{Hom}_{\mathrm{h} \mathit{\operatorname{\mathcal{C}}}}( C, X) ) \]
is surjective (though it is generally not injective).