Definition 1.5.4.12. Let $\operatorname{\mathcal{C}}$ be a category which admits small colimits and let $S$ be a collection of morphisms of $\operatorname{\mathcal{C}}$. We will say that $S$ is *weakly saturated* if it is closed under pushouts (Definition 1.5.4.4), retracts (Variant 1.5.4.7), and transfinite composition (Definition 1.5.4.10).

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