Kerodon

Remark 9.2.2.2. Let $\operatorname{\mathcal{C}}$ be an ordinary category and let $W$ be a collection of morphisms of $\operatorname{\mathcal{C}}$. Then a morphism $f$ of $\operatorname{\mathcal{C}}$ is a transfinite composition of morphisms belonging to $W$ (in the sense of Definition 1.5.4.10) if and only if the corresponding morphism of the $\infty $-category $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ is a transfinite composition of morphisms belonging to $W$ (in the sense of Definition 9.2.2.1).