Notation 5.31.
Given a class of morphisms \(\Sigma \subseteq \Ar(T)\), we define the following closures:
\(\Sigma^s\): the saturation (closure under composition, identities, and colimits).
\(\Sigma^{ss}\): the strong saturation (closure under composition, colimits, and 2-out-of-3).
\(\Sigma^m\): the smallest acyclic class containing \(\Sigma\).
\(\Sigma^c\): the smallest strongly saturated class closed under base change containing \(\Sigma\).