Remark 7.6.5.6 (Duality). The simplicial set $( \bullet \rightrightarrows \bullet )$ is canonically isomorphic to its opposite $( \bullet \rightrightarrows \bullet )^{\operatorname{op}}$. Consequently, if $f_0, f_1: Y \rightarrow X$ are morphisms in an $\infty $-category $\operatorname{\mathcal{C}}$ which admit an equalizer $Z = \operatorname{Eq}(f_0, f_1)$, then $Z$ can be regarded as a coequalizer of $f_0$ and $f_1$ in the opposite $\infty $-category $\operatorname{\mathcal{C}}^{\operatorname{op}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$