Kerodon

Remark 9.2.2.11. In the statement of Proposition 9.2.2.10, it is not necessary to assume that $W$ is closed under the formation of all colimits in the $\infty $-category $\operatorname{Fun}( \Delta ^1, \operatorname{\mathcal{C}})$. It suffices to consider colimits of diagrams indexed by $\operatorname{N}_{\bullet }( \mathrm{Ord}_{ < \beta } )$ where $\beta $ is a limit ordinal; moreover, we can further restrict our attention to colimits which are preserved by the evaluation functors $\operatorname{ev}_{0}, \operatorname{ev}_{1}: \operatorname{Fun}(\Delta ^1, \operatorname{\mathcal{C}}) \rightarrow \operatorname{\mathcal{C}}$.