Proposition 7.55.
The functor
\[[-]_D\colon C\longrightarrow\Gest_{/\Gest(A_D)}\]
preserves finite limits. Moreover, every map \([Y]_D\to[X]_D\) induced by a morphism \(Y\to X\) in \(C\) is \(1\)-étale and \(1\)-proper.
Proof
See [Scholze 2026, Proposition 9.5].
References
- Peter Scholze. Geometry and Higher Category Theory. 2026.