Topological Class of Morphisms

Let $\mathcal{E}$ be a Presentable Infinity Category, and $\overline{S}$ a Strongly Saturated Class of morphisms. We stay that $\overline{S}$ is topological if the following equivalent conditions is satisfied:

• There exists a subset $S\subseteq\overline{S}$ consisting of Embeddings such that $S$ generates $\overline{S}$ as a strongly saturated class.

• Given a pullback diagram:

  in $\mathcal{E}$, if $f\in\overline{S}$, then $f^{\prime}\in\overline{S}$. More concisely, $\overline{S}$ is stable under arbitrary base change.

References

• Lurie, Jacob. “Higher Topos Theory,” July 31, 2008. https://doi.org/10.48550/arXiv.math/0608040. (6.2.15)