Remark 9.1.7.13. Let $\operatorname{\mathcal{C}}$ be a small category. Then the collection of projective cofibrations in $\operatorname{Fun}( \operatorname{\mathcal{C}}, \operatorname{Set_{\Delta }})$ is weakly saturated, in the sense of Definition 1.5.4.12. That is, it is closed under retracts, pushouts, and transfinite composition. See Proposition 1.5.4.13.
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