Strongly Saturated Class

Let $\mathcal{C}$ be an Infinity Category that admist all small Colimits, and $S$ be a collection of morphisms in $\mathcal{C}$. We say that $S$ is strongly saturated when:

• Morphisms in $S$ are stable under Pushout.
• The full subcategory of the Arrow Category spanned by $S$ is stable under small Colimits
• $S$ satisfies the 2-Out-Of-3 Property.

References

• Lurie, Jacob. “Higher Topos Theory,” July 31, 2008. https://doi.org/10.48550/arXiv.math/0608040. (5.5.4.5)