The Stacks project

Lemma 92.22.4. Let $f : (\mathop{\mathit{Sh}}\nolimits (\mathcal{C}), \mathcal{O}) \to (\mathop{\mathit{Sh}}\nolimits (\mathcal{B}), \mathcal{O}_\mathcal {B})$ be a morphism of ringed topoi. There is a canonical map $L_ f \to \mathop{N\! L}\nolimits _ f$ which identifies the naive cotangent complex with the truncation $\tau _{\geq -1}L_ f$.

Proof. Special case of Lemma 92.18.10. $\square$

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