Definition 9.2.4.1. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $W$ be a collection of morphisms of $\operatorname{\mathcal{C}}$, and let $W'$ denote the collection of those morphisms $w': X' \rightarrow Y'$ for which there exists a pushout square
\[ \xymatrix@C =50pt@R=50pt{ X \ar [d]^{w} \ar [r] & X' \ar [d]^{w'} \\ Y \ar [r] & Y', } \]
where $w \in W$. We say that a morphism $f$ of $\operatorname{\mathcal{C}}$ is a transfinite pushout of morphisms of $W$ if it is a transfinite composition of morphisms of $W'$, in the sense of Definition 9.2.2.1.