Remark 7.6.5.7 (Symmetry). The simplicial set $( \bullet \rightrightarrows \bullet )$ has a unique nontrivial automorphism, which exchanges its nondegenerate edges. It follows that, if $f_0, f_1: Y \rightarrow X$ are a pair of morphisms in an $\infty $-category $\operatorname{\mathcal{C}}$, then we can identify (co)equalizers of the pair $(f_0, f_1)$ with (co)equalizers of the pair $(f_1, f_0)$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$