Lemma 84.14.7. In Situation 84.3.3 let $\mathcal{O}$ be a sheaf of rings on $\mathcal{C}_{total}$. Let $(K_ n, K_\varphi )$ be a simplicial system of the derived category of modules. Assume

$f_\varphi ^{-1}\mathcal{O}_ n \to \mathcal{O}_ m$ is flat for $\varphi : [m] \to [n]$,

$(K_ n, K_\varphi )$ is cartesian,

$\mathop{\mathrm{Hom}}\nolimits (K_ i[t], K_ i) = 0$ for $i \geq 0$ and $t > 0$.

Then there exists a cartesian object $K$ of $D(\mathcal{O})$ whose associated simplicial system is isomorphic to $(K_ n, K_\varphi )$.

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