Prismatic site : fix a base prism \((A, I)\) for \(X\) a \(p{\hbox{-}}\)adic formal scheme over \(A/I\). Define \begin{align*} (X/A)_\prism = \left\{{ (A, I) \to (B, J) \in \mathop{\mathrm{Mor}}(\mathsf{Prism}), \operatorname{Spf}(B/J) \to X \text{ over } A/I }\right\} ,\end{align*} topologized via the flat topology on \(B/J\).