Theorem 7.15.
The functor
\[j_!\colon \Shv_{\tau^{\ad}}(C^{\ad})\longrightarrow \Shv_{\tau}(C)\]
exhibits \(\Shv_{\tau}(C)\) as a complete fractured topos.
Proof
See [Lurie 2018, Theorem 20.6.3.4]; completeness follows from the associated geometric admissibility structure, by [Lurie 2018, Theorem 20.3.4.4].
References
- Jacob Lurie. Spectral Algebraic Geometry. under construction (version dated February 2018), www.math.ias.edu/~lurie/papers/SAG-rootfile.pdf. 2018.