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Notation 7.6.5.1. Let $( \bullet \rightrightarrows \bullet )$ denote the simplicial set given by the pushout $\Delta ^1 \coprod _{ \operatorname{\partial \Delta }^1 } \Delta ^1$. For any $\infty $-category $\operatorname{\mathcal{C}}$, we will identify morphisms from $( \bullet \rightrightarrows \bullet )$ to $\operatorname{\mathcal{C}}$ with pairs $(f_0, f_1)$, where $f_0: Y \rightarrow X$ and $f_1: Y \rightarrow X$ are morphisms of $\operatorname{\mathcal{C}}$ having the same source and target.