# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Definition 1.4.4.15. Let $\operatorname{\mathcal{C}}$ be a category which admits small colimits and let $T$ be a collection of morphisms of $\operatorname{\mathcal{C}}$. We will say that $T$ is weakly saturated if it is closed under pushouts (Definition 1.4.4.4), retracts (Variant 1.4.4.7), and transfinite composition (Definition 1.4.4.10).