Proposition 7.56.
If a family \((X_i\to X)_i\) satisfies universal \(!\)-descent, then the map
\[\bigsqcup_i[X_i]_D\longrightarrow[X]_D\]
is an effective epimorphism in the relevant countable topos of Gestalten.
Proof
This is [Scholze 2026, Proposition 9.7]. The converse is not asserted there.
References
- Peter Scholze. Geometry and Higher Category Theory. 2026.