The Stacks project

Lemma 85.14.2. In Situation 85.3.3 let $\mathcal{O}$ be a sheaf of rings on $\mathcal{C}_{total}$. If $K \in D(\mathcal{O})$ is an object, then $(K_ n, K(\varphi ))$ is a simplicial system of the derived category of modules. If $K$ is cartesian, so is the system.

Proof. This is immediate from the definitions. $\square$

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