Kerodon

Notation 7.6.5.5. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $f_0, f_1: Y \rightarrow X$ be morphisms of $\operatorname{\mathcal{C}}$ having the same source and target. If there exists an object $Z \in \operatorname{\mathcal{C}}$ which is an equalizer of $f_0$ and $f_1$, then $Z$ is uniquely determined up to isomorphism (Proposition 7.1.1.12). To emphasize this uniqueness, we denote the object $Z$ (if it exists) by $\operatorname{Eq}(f_0, f_1)$. Similarly, if there exists an object $W \in \operatorname{\mathcal{C}}$ which is a coequalizer of $f_0$ and $f_1$, then $W$ is uniquely determined up to isomorphism; to emphasize this, we denote $W$ by $\operatorname{Coeq}(f_0,f_1)$.